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This is PART 23: Centers X(44001) - X(46000)

PART 1: Introduction and Centers X(1) - X(1000) PART 2: Centers X(1001) - X(3000) PART 3: Centers X(3001) - X(5000)
PART 4: Centers X(5001) - X(7000) PART 5: Centers X(7001) - X(10000) PART 6: Centers X(10001) - X(12000)
PART 7: Centers X(12001) - X(14000) PART 8: Centers X(14001) - X(16000) PART 9: Centers X(16001) - X(18000)
PART 10: Centers X(18001) - X(20000) PART 11: Centers X(20001) - X(22000) PART 12: Centers X(22001) - X(24000)
PART 13: Centers X(24001) - X(26000) PART 14: Centers X(26001) - X(28000) PART 15: Centers X(28001) - X(30000)
PART 16: Centers X(30001) - X(32000) PART 17: Centers X(32001) - X(34000) PART 18: Centers X(34001) - X(36000)
PART 19: Centers X(36001) - X(38000) PART 20: Centers X(38001) - X(40000) PART 21: Centers X(40001) - X(42000)
PART 22: Centers X(42001) - X(44000) PART 23: Centers X(44001) - X(46000) PART 24: Centers X(46001) - X(48000)
PART 25: Centers X(48001) - X(50000) PART 26: Centers X(50001) - X(52000) PART 27: Centers X(52001) - X(54000)
PART 28: Centers X(54001) - X(56000) PART 29: Centers X(56001) - X(58000) PART 30: Centers X(58001) - X(60000)
PART 31: Centers X(60001) - X(62000) PART 32: Centers X(62001) - X(64000) PART 33: Centers X(64001) - X(66000)
PART 34: Centers X(66001) - X(68000) PART 35: Centers X(68001) - X(70000) PART 36: Centers X(70001) - X(72000)

X(44001) = VIJAY 11TH PARALLEL TRANSFORM OF X(100)

Barycentrics    (a - b)^2*(a - c)^2*(2*a^5 - 2*a^4*b - 3*a^3*b^2 + 3*a^2*b^3 + 2*a*b^4 - 2*b^5 - 2*a^4*c + 8*a^3*b*c - 3*a^2*b^2*c - 9*a*b^3*c + 6*b^4*c - 3*a^3*c^2 - 3*a^2*b*c^2 + 14*a*b^2*c^2 - 4*b^3*c^2 + 3*a^2*c^3 - 9*a*b*c^3 - 4*b^2*c^3 + 2*a*c^4 + 6*b*c^4 - 2*c^5) : :

X(44001) lies on these lines: {100, 693}, {1252, 31272}

X(44002) = VIJAY 11TH PARALLEL TRANSFORM OF X(101)

Barycentrics    (a - b)^2*(a - c)^2*(2*a^8 - 2*a^7*b - 3*a^5*b^3 + 3*a^4*b^4 + 2*a^2*b^6 - 2*a*b^7 - 2*a^7*c + 2*a^6*b*c + 3*a^5*b^2*c - 3*a^4*b^3*c - 4*a^2*b^5*c + 6*a*b^6*c - 2*b^7*c + 3*a^5*b*c^2 - 3*a^2*b^4*c^2 - 6*a*b^5*c^2 + 6*b^6*c^2 - 3*a^5*c^3 - 3*a^4*b*c^3 + 10*a^2*b^3*c^3 + 2*a*b^4*c^3 - 6*b^5*c^3 + 3*a^4*c^4 - 3*a^2*b^2*c^4 + 2*a*b^3*c^4 + 4*b^4*c^4 - 4*a^2*b*c^5 - 6*a*b^2*c^5 - 6*b^3*c^5 + 2*a^2*c^6 + 6*a*b*c^6 + 6*b^2*c^6 - 2*a*c^7 - 2*b*c^7) : :

X(44002) lies on these lines: {101, 3261}, {23990, 31273}

X(44003) = VIJAY 12TH PARALLEL TRANSFORM OF X(3)

Barycentrics    a^10*b^2 - 6*a^6*b^6 + 8*a^4*b^8 - 3*a^2*b^10 + a^10*c^2 - 4*a^8*b^2*c^2 + 7*a^6*b^4*c^2 - 5*a^4*b^6*c^2 + b^10*c^2 + 7*a^6*b^2*c^4 - 6*a^4*b^4*c^4 + 3*a^2*b^6*c^4 - 4*b^8*c^4 - 6*a^6*c^6 - 5*a^4*b^2*c^6 + 3*a^2*b^4*c^6 + 6*b^6*c^6 + 8*a^4*c^8 - 4*b^4*c^8 - 3*a^2*c^10 + b^2*c^10 : :
X(44003) = 3 X[2] - 4 X[2972], 5 X[3091] - 4 X[34334], 5 X[3522] - 4 X[40948]

X(44003) lies on these lines: {2, 1972}, {3, 35311}, {4, 6662}, {20, 5663}, {107, 14919}, {253, 18019}, {1294, 15054}, {2979, 42329}, {3091, 34334}, {3164, 11794}, {3448, 9033}, {3522, 40948}, {5889, 15318}, {6563, 25053}, {7500, 20213}, {14570, 41673}, {23061, 43768}

X(44003) = reflection of X(35360) in X(2972)
X(44003) = anticomplement of X(35360)
X(44003) = anticomplement of the isogonal conjugate of X(23286)
X(44003) = X(44715)-of-anti-Euler-triangle
X(44003) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {54, 7253}, {95, 21300}, {97, 7192}, {656, 2888}, {810, 17035}, {2148, 525}, {2167, 850}, {2168, 14618}, {2169, 523}, {2190, 520}, {2616, 4}, {2623, 5905}, {14533, 4560}, {15412, 21270}, {15958, 6758}, {23286, 8}, {34386, 17217}, {36134, 110}
X(44003) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2972, 35360, 2}, {3448, 39352, 44004}, {34186, 39352, 3448}

X(44004) = VIJAY 12TH PARALLEL TRANSFORM OF X(5)

Barycentrics    2*a^12 - 5*a^10*b^2 + 2*a^8*b^4 + 6*a^6*b^6 - 10*a^4*b^8 + 7*a^2*b^10 - 2*b^12 - 5*a^10*c^2 + 10*a^8*b^2*c^2 - 9*a^6*b^4*c^2 + 11*a^4*b^6*c^2 - 10*a^2*b^8*c^2 + 3*b^10*c^2 + 2*a^8*c^4 - 9*a^6*b^2*c^4 - 2*a^4*b^4*c^4 + 3*a^2*b^6*c^4 + 6*b^8*c^4 + 6*a^6*c^6 + 11*a^4*b^2*c^6 + 3*a^2*b^4*c^6 - 14*b^6*c^6 - 10*a^4*c^8 - 10*a^2*b^2*c^8 + 6*b^4*c^8 + 7*a^2*c^10 + 3*b^2*c^10 - 2*c^12 : :
X(44004) = 3 X[2] - 4 X[35442]

X(44004) lies on these lines: {2, 35311}, {20, 10620}, {3448, 9033}, {5965, 43768}, {15319, 15801}

X(44004) = reflection of X(35311) in X(35442)
X(44004) = anticomplement of X(35311)
X(44004) = anticomplement of the isogonal conjugate of X(39180)
X(44004) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {656, 2889}, {1173, 7253}, {31626, 7192}, {39180, 8}, {39181, 21271}, {39183, 21270}, {40410, 21300}
X(44004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3448, 39352, 44003}, {35311, 35442, 2}

X(44005) = VIJAY 12TH PARALLEL TRANSFORM OF X(9)

Barycentrics    a^5*b - 6*a^3*b^3 + 8*a^2*b^4 - 3*a*b^5 + a^5*c - 4*a^4*b*c + 7*a^3*b^2*c - 5*a^2*b^3*c + b^5*c + 7*a^3*b*c^2 - 6*a^2*b^2*c^2 + 3*a*b^3*c^2 - 4*b^4*c^2 - 6*a^3*c^3 - 5*a^2*b*c^3 + 3*a*b^2*c^3 + 6*b^3*c^3 + 8*a^2*c^4 - 4*b^2*c^4 - 3*a*c^5 + b*c^5 : :
X(44005) = 3 X[2] - 4 X[3119]

X(44005) lies on these lines: {2, 3119}, {144, 20095}, {149, 6366}, {658, 41798}, {3448, 14732}, {10405, 18359}

X(44005) = reflection of X(35312) in X(3119)
X(44005) = anticomplement of X(35312)
X(44005) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {650, 2890}, {1174, 693}, {2346, 21302}, {6605, 20295}, {10482, 513}
X(44005) = {X(3119),X(35312)}-harmonic conjugate of X(2)

X(44006) = VIJAY 12TH PARALLEL TRANSFORM OF X(10)

Barycentrics    2*a^3 - a^2*b - a*b^2 - 2*b^3 - a^2*c + 3*b^2*c - a*c^2 + 3*b*c^2 - 2*c^3 : :
X(44006) = 3 X[2] - 4 X[3120], 5 X[4442] - 2 X[4831], 4 X[4442] - X[31301], 4 X[4831] - 5 X[16704], 8 X[4831] - 5 X[31301], 2 X[4938] - 5 X[17491]

X(44006) lies on these lines: {2, 846}, {100, 4080}, {145, 9802}, {148, 690}, {149, 900}, {244, 24429}, {516, 20045}, {726, 21282}, {740, 4938}, {896, 28546}, {902, 28550}, {903, 3315}, {962, 20041}, {1836, 17147}, {3006, 28526}, {3434, 20068}, {3663, 29823}, {3729, 31079}, {3936, 28530}, {3952, 24715}, {3995, 20292}, {4365, 20290}, {4442, 4831}, {4651, 33099}, {4683, 17163}, {4781, 17719}, {4854, 8025}, {5057, 17495}, {5695, 31017}, {5880, 31035}, {5905, 20011}, {9263, 29340}, {17135, 33098}, {17140, 33095}, {17162, 17770}, {17164, 24851}, {17165, 33094}, {17355, 31098}, {17484, 19998}, {17690, 25253}, {17764, 32856}, {17767, 33136}, {17780, 21093}, {20064, 30699}, {20077, 20084}, {20098, 38514}, {24311, 27704}, {24697, 27812}, {24723, 31025}, {26073, 30578}, {27804, 33097}, {28542, 32848}, {29824, 32857}, {31011, 32846}

X(44006) = reflection of X(i) in X(j) for these {i,j}: {4427, 3120}, {16704, 4442}, {31301, 16704}
X(44006) = anticomplement of X(4427)
X(44006) = anticomplement of the isotomic conjugate of X(4608)
X(44006) = X(4608)-Ceva conjugate of X(2)
X(44006) = crossdifference of every pair of points on line {5029, 20976}
X(44006) = barycentric product X(86)*X(24070)
X(44006) = barycentric quotient X(24070)/X(10)
X(44006) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {31, 14779}, {513, 2891}, {649, 41821}, {692, 24074}, {1126, 513}, {1171, 7192}, {1255, 20295}, {1268, 21301}, {3248, 39348}, {4608, 6327}, {6578, 21295}, {8701, 3952}, {28615, 514}, {31010, 21287}, {32014, 17217}, {32018, 21304}, {33635, 4462}, {37212, 668}, {40438, 512}
X(44006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {149, 4440, 17154}, {149, 17154, 20042}, {3120, 4427, 2}, {4683, 17163, 43990}

X(44007) = VIJAY 12TH PARALLEL TRANSFORM OF X(512)

Barycentrics    a^2*(b - c)*(b + c)*(4*a^4*b^4 - a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 4*a^4*c^4 - 7*a^2*b^2*c^4 + 7*b^4*c^4) : :
X(44007) = 7 X[2] - 4 X[23610], 11 X[2] - 8 X[38237], 11 X[23610] - 14 X[38237]

X(44007) lies on these lines: {2, 512}, {69, 9009}, {669, 8617}, {888, 39361}, {1272, 2872}, {9463, 38366}, {9998, 14606}

X(44007) = anticomplement of the isogonal conjugate of X(23342)
X(44007) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {538, 21221}, {662, 538}, {2234, 148}, {3231, 21220}, {5118, 192}, {23342, 8}, {24037, 888}, {24041, 9147}, {30736, 21294}, {30938, 150}, {36133, 3228}

X(44008) = VIJAY 12TH PARALLEL TRANSFORM OF X(513)

Barycentrics    a*(b - c)*(4*a^2*b^2 - a^2*b*c - 7*a*b^2*c + 4*a^2*c^2 - 7*a*b*c^2 + 7*b^2*c^2) : :
X(44008) = 7 X[2] - 4 X[8027], 3 X[2] - 4 X[14434], 5 X[2] - 4 X[14474], 11 X[2] - 8 X[38238], 3 X[8027] - 7 X[14434], 5 X[8027] - 7 X[14474], 11 X[8027] - 14 X[38238], 6 X[8027] - 7 X[43928], 5 X[14434] - 3 X[14474], 11 X[14434] - 6 X[38238], 11 X[14474] - 10 X[38238], 6 X[14474] - 5 X[43928], 12 X[38238] - 11 X[43928]

X(44008) lies on these lines: {2, 513}, {8, 20295}, {891, 39360}, {1655, 31290}, {3240, 38349}, {17794, 21297}, {21219, 26824}

X(44008) = reflection of X(43928) in X(14434)
X(44008) = anticomplement of X(43928)
X(44008) = anticomplement of the isogonal conjugate of X(23343)
X(44008) = anticomplement of the isotomic conjugate of X(41314)
X(44008) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {100, 29824}, {101, 536}, {536, 150}, {765, 891}, {899, 149}, {1293, 3999}, {3230, 4440}, {3994, 3448}, {4009, 33650}, {6381, 21293}, {6632, 41314}, {7045, 30704}, {23343, 8}, {23891, 69}, {34075, 3227}, {41314, 6327}
X(44008) = X(41314)-Ceva conjugate of X(2)
{X(14434),X(43928)}-harmonic conjugate of X(2)

X(44009) = VIJAY 12TH PARALLEL TRANSFORM OF X(514)

Barycentrics    (b - c)*(7*a^2 - 7*a*b + 4*b^2 - 7*a*c - b*c + 4*c^2) : :
X(44009) = 3 X[2] - 4 X[6544], 7 X[2] - 4 X[6545], X[2] - 4 X[6546], 5 X[2] - 8 X[10196], 5 X[2] - 4 X[14475], 11 X[2] - 8 X[21204], X[3621] + 8 X[5592], 8 X[4468] + X[26853], 7 X[4678] - 16 X[32212], 7 X[6544] - 3 X[6545], X[6544] - 3 X[6546], 5 X[6544] - 6 X[10196], 5 X[6544] - 3 X[14475], 11 X[6544] - 6 X[21204], 2 X[6544] - 3 X[31992], X[6545] - 7 X[6546], 6 X[6545] - 7 X[6548], 5 X[6545] - 14 X[10196], 5 X[6545] - 7 X[14475], 11 X[6545] - 14 X[21204], 2 X[6545] - 7 X[31992], 6 X[6546] - X[6548], 5 X[6546] - 2 X[10196], 5 X[6546] - X[14475], 11 X[6546] - 2 X[21204], 5 X[6548] - 12 X[10196], 5 X[6548] - 6 X[14475], 11 X[6548] - 12 X[21204], X[6548] - 3 X[31992], 11 X[10196] - 5 X[21204], 4 X[10196] - 5 X[31992], 11 X[14475] - 10 X[21204], 2 X[14475] - 5 X[31992], 4 X[21204] - 11 X[31992]

X(44009) lies on these lines: {2, 514}, {144, 4468}, {192, 4777}, {513, 17488}, {900, 17487}, {1654, 28209}, {3621, 5592}, {4448, 28151}, {4678, 32212}, {4776, 31056}, {6009, 20533}, {14779, 28179}, {20042, 33920}, {24616, 27484}, {30579, 33888}

X(44009) = reflection of X(i) in X(j) for these {i,j}: {2, 31992}, {6548, 6544}, {14475, 10196}, {31992, 6546}
X(44009) = anticomplement of X(6548)
X(44009) = anticomplement of the isogonal conjugate of X(23344)
X(44009) = anticomplement of the isotomic conjugate of X(17780)
X(44009) = X(17780)-Ceva conjugate of X(2)
X(44009) = crosssum of X(649) and X(1017)
X(44009) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {31, 20042}, {44, 150}, {100, 21282}, {101, 320}, {110, 17145}, {163, 17160}, {519, 21293}, {692, 519}, {902, 149}, {906, 3007}, {1023, 69}, {1110, 900}, {1252, 21297}, {1415, 1266}, {2149, 4453}, {2251, 4440}, {2429, 21296}, {3257, 32032}, {3689, 33650}, {3939, 5176}, {3943, 21294}, {4169, 21287}, {9459, 9263}, {17780, 6327}, {21805, 3448}, {23344, 8}, {23703, 3434}, {23990, 21222}, {24004, 315}, {30731, 21286}, {32665, 903}, {32666, 24841}, {32739, 17495}, {34067, 24715}, {34080, 4887}
X(44009) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6544, 6548, 2}, {6548, 31992, 6544}

X(44010) = VIJAY 12TH PARALLEL TRANSFORM OF X(523)

Barycentrics    (b - c)*(b + c)*(7*a^4 - 7*a^2*b^2 + 4*b^4 - 7*a^2*c^2 - b^2*c^2 + 4*c^4) : :
X(44010) = 3 X[2] - 4 X[1649], 7 X[2] - 4 X[8029], 5 X[2] - 4 X[8371], 19 X[2] - 16 X[10189], 5 X[2] - 8 X[10190], 11 X[2] - 8 X[10278], X[2] - 4 X[11123], 7 X[2] + 8 X[34752], X[20] + 8 X[8151], X[148] + 8 X[36955], 7 X[1649] - 3 X[8029], 5 X[1649] - 3 X[8371], 2 X[1649] - 3 X[9168], 19 X[1649] - 12 X[10189], 5 X[1649] - 6 X[10190], 11 X[1649] - 6 X[10278], X[1649] - 3 X[11123], 7 X[1649] + 6 X[34752], 7 X[3523] - 4 X[16220], 7 X[3523] - 16 X[32204], 7 X[5466] - 6 X[8029], 5 X[5466] - 6 X[8371], X[5466] - 3 X[9168], 19 X[5466] - 24 X[10189], 5 X[5466] - 12 X[10190], 11 X[5466] - 12 X[10278], X[5466] - 6 X[11123], 7 X[5466] + 12 X[34752], 8 X[6563] + X[31299], 5 X[8029] - 7 X[8371], 2 X[8029] - 7 X[9168], 19 X[8029] - 28 X[10189], 5 X[8029] - 14 X[10190], 11 X[8029] - 14 X[10278], X[8029] - 7 X[11123], X[8029] + 2 X[34752], 2 X[8371] - 5 X[9168], 19 X[8371] - 20 X[10189], 11 X[8371] - 10 X[10278], X[8371] - 5 X[11123], 7 X[8371] + 10 X[34752], X[8596] - 4 X[14443], 19 X[9168] - 8 X[10189], 5 X[9168] - 4 X[10190], 11 X[9168] - 4 X[10278], 7 X[9168] + 4 X[34752], X[9180] + 4 X[36955], 10 X[10189] - 19 X[10190], 22 X[10189] - 19 X[10278], 4 X[10189] - 19 X[11123], 14 X[10189] + 19 X[34752], 11 X[10190] - 5 X[10278], 2 X[10190] - 5 X[11123], 7 X[10190] + 5 X[34752], 2 X[10278] - 11 X[11123], 7 X[10278] + 11 X[34752], 7 X[11123] + 2 X[34752], X[14683] + 8 X[36739], X[16220] - 4 X[32204]

X(44010) lies on the Steiner-Wallace right hyperbola, the Kiepert circumhyperbola of the anticomplementary triangle, and these lines: {1, 17161}, {2, 523}, {20, 1499}, {147, 2793}, {148, 9180}, {194, 3906}, {512, 33884}, {525, 11148}, {616, 27551}, {617, 27550}, {690, 8591}, {2799, 9123}, {2896, 12073}, {3413, 30508}, {3414, 30509}, {3523, 16220}, {4226, 14611}, {6031, 6194}, {7616, 41298}, {7665, 9185}, {8596, 14443}, {8723, 11003}, {8782, 9147}, {9125, 9979}, {9742, 30474}, {14683, 36739}, {33921, 39356}

X(44010) = anticomplement of X(5466)
X(44010) = reflection of X(i) in X(j) for these {i,j}: {2, 9168}, {148, 9180}, {2408, 18311}, {5466, 1649}, {8371, 10190}, {9168, 11123}, {9485, 9131}, {9979, 9125}
X(44010) = anticomplement of the isogonal conjugate of X(5467)
X(44010) = anticomplement of the isotomic conjugate of X(5468)
X(44010) = X(5468)-Ceva conjugate of X(2)
X(44010) = crosssum of X(512) and X(39689)
X(44010) = crossdifference of every pair of points on line {187, 20977}
X(44010) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {99, 21298}, {110, 17491}, {162, 41724}, {163, 524}, {187, 21221}, {524, 21294}, {662, 316}, {896, 3448}, {922, 148}, {1101, 690}, {1576, 17497}, {4235, 21270}, {4570, 30709}, {4575, 858}, {5467, 8}, {5468, 6327}, {6629, 21293}, {14567, 21220}, {16702, 150}, {23889, 69}, {24039, 315}, {36034, 9140}, {36134, 23061}, {36142, 671}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1649, 5466, 2}, {5466, 9168, 1649}

X(44011) = X(4)X(69)∩X(115)X(512)

Barycentrics    a^2*(b - c)^2*(b + c)^2*(a^8 - a^6*b^2 + a^4*b^4 - a^2*b^6 - a^6*c^2 + 3*a^4*b^2*c^2 - 3*a^2*b^4*c^2 + 3*b^6*c^2 + a^4*c^4 - 3*a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + 3*b^2*c^6) : :
X(44011) = 3 X[6787] - X[12833], 3 X[6787] + X[31513], X[13137] - 3 X[14639]

See Antreas Hatzipolakis and Peter Moses, euclid 1836.

X(44011) lies on these lines: {4, 69}, {115, 512}, {3111, 7844}, {5139, 36471}, {13137, 14639}

X(44011) = midpoint of X(12833) and X(31513)
X(44011) = reflection of X(15630) in X(115)
X(44011) = polar circle inverse of X(877)
X(44011) = crosssum of X(99) and X(34473)
X(44011) = crossdifference of every pair of points on line {2421, 3049}
X(44011) = {X(6787),X(31513)}-harmonic conjugate of X(12833)

X(44012) = X(4)X(9)∩X(116)X(514)

Barycentrics    (a - b - c)*(b - c)^2*(a^5 - 4*a^4*b + 4*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4 - 2*b^5 - 4*a^4*c + 5*a^3*b*c - a^2*b^2*c - a*b^3*c + b^4*c + 4*a^3*c^2 - a^2*b*c^2 - 4*a*b^2*c^2 + b^3*c^2 - 2*a^2*c^3 - a*b*c^3 + b^2*c^3 + 3*a*c^4 + b*c^4 - 2*c^5) : :
X(44012) = X[927] - 5 X[31640]

See Antreas Hatzipolakis and Peter Moses, euclid 1836.

X(44012) lies on these lines: {4, 9}, {11, 14330}, {116, 514}, {523, 31648}, {927, 31640}, {40483, 40554}

X(44012) = midpoint of X(1146) and X(1566)
X(44012) = reflection of X(i) in X(j) for these {i,j}: {15634, 116}, {40554, 40483}
X(44012) = polar circle inverse of X(41321)
X(44012) = crosssum of X(101) and X(38692)
X(44012) = crossdifference of every pair of points on line {1459, 2426}

X(44013) = X(4)X(8)∩X(11)X(513)

Barycentrics    a*(b - c)^2*(a^6 - a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - a*b^5 - a^5*c + a^4*b*c + 6*a^3*b^2*c - 4*a^2*b^3*c - 5*a*b^4*c + 3*b^5*c - 2*a^4*c^2 + 6*a^3*b*c^2 - 14*a^2*b^2*c^2 + 10*a*b^3*c^2 + 2*a^3*c^3 - 4*a^2*b*c^3 + 10*a*b^2*c^3 - 6*b^3*c^3 + a^2*c^4 - 5*a*b*c^4 - a*c^5 + 3*b*c^5) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1836.

X(44013) lies on these lines: {4, 8}, {11, 513}, {2969, 3326}, {10893, 31849}, {13273, 17101}, {15313, 38385}

X(44013) = midpoint of X(i) and X(j) for these {i,j}: {3259, 38389}, {31512, 34151}
X(44013) = reflection of X(i) in X(j) for these {i,j}: {3937, 33646}, {15635, 11}
X(44013) = crosssum of X(100) and X(38693)
X(44013) = crossdifference of every pair of points on line {2427, 22383}

X(44014) = X(1)X(4)∩X(124)X(522)

Barycentrics    (a - b - c)*(b - c)^2*(a^9 + 2*a^8*b - 4*a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^3*b^6 + 4*a^2*b^7 + a*b^8 - 2*b^9 + 2*a^8*c - 7*a^7*b*c + 7*a^6*b^2*c + 5*a^5*b^3*c - 17*a^4*b^4*c + 11*a^3*b^5*c + 5*a^2*b^6*c - 9*a*b^7*c + 3*b^8*c - 4*a^7*c^2 + 7*a^6*b*c^2 - 10*a^5*b^2*c^2 + 13*a^4*b^3*c^2 + 8*a^3*b^4*c^2 - 23*a^2*b^5*c^2 + 6*a*b^6*c^2 + 3*b^7*c^2 - 4*a^6*c^3 + 5*a^5*b*c^3 + 13*a^4*b^2*c^3 - 30*a^3*b^3*c^3 + 14*a^2*b^4*c^3 + 9*a*b^5*c^3 - 7*b^6*c^3 + 6*a^5*c^4 - 17*a^4*b*c^4 + 8*a^3*b^2*c^4 + 14*a^2*b^3*c^4 - 14*a*b^4*c^4 + 3*b^5*c^4 + 11*a^3*b*c^5 - 23*a^2*b^2*c^5 + 9*a*b^3*c^5 + 3*b^4*c^5 - 4*a^3*c^6 + 5*a^2*b*c^6 + 6*a*b^2*c^6 - 7*b^3*c^6 + 4*a^2*c^7 - 9*a*b*c^7 + 3*b^2*c^7 + a*c^8 + 3*b*c^8 - 2*c^9) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1836.

X(44014) lies on these lines: {1, 4}, {11, 21172}, {124, 522}, {2829, 39762}, {3318, 3326}, {7004, 21189}

X(44014) = midpoint of X(10017) and X(38357)
X(44014) = reflection of X(15633) in X(124)
X(44014) = polar circle inverse of X(23987)
X(44014) = crosssum of X(109) and X(38691)
X(44014) = crossdifference of every pair of points on line {652, 2425}

X(44015) = GIBERT (5,6,1) POINT

Barycentrics    5*a^2*S/Sqrt[3] + a^2*SA + 12*SB*SC : :

X(44015) lies on the cubic K1236 and these lines: {2, 43240}, {3, 42629}, {4, 42779}, {5, 16}, {6, 17505}, {13, 3830}, {14, 3839}, {15, 3146}, {17, 1657}, {20, 42546}, {61, 12102}, {62, 42106}, {376, 16241}, {381, 16961}, {382, 16960}, {396, 35404}, {397, 42692}, {546, 42782}, {550, 42683}, {631, 43467}, {3090, 42954}, {3091, 34755}, {3412, 42085}, {3523, 5366}, {3525, 10646}, {3526, 42891}, {3534, 43199}, {3545, 43777}, {3627, 34754}, {3628, 43106}, {3845, 43418}, {3854, 5344}, {3855, 42935}, {3858, 43775}, {3860, 11543}, {3861, 42695}, {5054, 16966}, {5056, 43485}, {5070, 42689}, {5073, 42691}, {5076, 42630}, {5237, 42114}, {5238, 42109}, {5321, 14893}, {5339, 43030}, {5340, 16809}, {5350, 11542}, {5352, 42113}, {9862, 36962}, {10124, 42123}, {10645, 12103}, {10653, 41106}, {11001, 42795}, {11481, 42962}, {11488, 42434}, {11489, 41974}, {12100, 37832}, {12101, 42520}, {12108, 42146}, {12811, 43241}, {12820, 38335}, {12821, 42969}, {15022, 43300}, {15682, 33607}, {15686, 43483}, {15687, 42781}, {15688, 43544}, {15697, 42952}, {15699, 42686}, {15703, 33416}, {15718, 42528}, {15722, 42625}, {16239, 42685}, {16242, 43249}, {16267, 42119}, {16644, 42429}, {16943, 22901}, {16962, 42130}, {16963, 42095}, {16964, 42815}, {19709, 43545}, {19710, 41121}, {21734, 42092}, {22236, 43010}, {23302, 33923}, {31074, 37776}, {33699, 42777}, {35409, 43542}, {35731, 42177}, {36967, 42817}, {40693, 43466}, {41100, 42129}, {41108, 43368}, {41113, 42480}, {41120, 43006}, {41943, 43401}, {41973, 42970}, {41987, 43111}, {41990, 42953}, {42087, 42916}, {42090, 43403}, {42091, 42488}, {42093, 42991}, {42098, 42158}, {42099, 42156}, {42101, 42923}, {42117, 42992}, {42120, 42915}, {42125, 42897}, {42133, 43292}, {42145, 42598}, {42150, 42806}, {42152, 42909}, {42160, 42982}, {42163, 42922}, {42180, 42243}, {42182, 42242}, {42433, 43029}, {42436, 42818}, {42474, 42996}, {42495, 42994}, {42613, 43782}, {42684, 42960}, {42775, 42937}, {42799, 43475}, {42814, 43031}, {42888, 43311}, {42896, 43033}, {42913, 43644}, {42928, 43193}, {42946, 43499}, {42957, 42979}, {42998, 43424}, {43032, 43235}, {43398, 43556}

X(44015) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 42094, 19107}, {13, 42154, 42506}, {16, 42138, 16808}, {16, 42813, 42138}, {396, 35404, 43645}, {5318, 16808, 16965}, {5318, 42138, 16}, {5318, 42693, 5}, {5318, 42813, 16808}, {5335, 43364, 42103}, {10645, 43637, 12103}, {10646, 42142, 42581}, {12816, 19107, 42094}, {16808, 16965, 16967}, {16808, 42905, 42813}, {16964, 42815, 43014}, {16966, 42127, 36968}, {18582, 36969, 42100}, {18582, 42100, 16241}, {19106, 42128, 17}, {34754, 43195, 3627}, {41121, 42941, 42529}, {42105, 42903, 43004}, {42114, 43465, 5237}, {42120, 42921, 42915}, {42125, 42990, 42897}, {42134, 42162, 15}, {42137, 42166, 10645}, {42142, 42161, 10646}, {43328, 43630, 396}

X(44016) = GIBERT (-5,6,1) POINT

Barycentrics    5*a^2*S/Sqrt[3] - a^2*SA - 12*SB*SC : :

X(44016) lies on the cubic K1236 and these lines: {2, 43241}, {3, 42630}, {4, 42780}, {5, 15}, {6, 17505}, {13, 3839}, {14, 3830}, {16, 3146}, {18, 1657}, {20, 42545}, {61, 42103}, {62, 12102}, {376, 16242}, {381, 16960}, {382, 16961}, {395, 35404}, {398, 42693}, {546, 42781}, {550, 42682}, {631, 43468}, {3090, 42955}, {3091, 34754}, {3411, 42086}, {3523, 5365}, {3525, 10645}, {3526, 42890}, {3534, 43200}, {3545, 43778}, {3627, 34755}, {3628, 43105}, {3845, 43419}, {3854, 5343}, {3855, 42934}, {3858, 43776}, {3860, 11542}, {3861, 42694}, {5054, 16967}, {5056, 43486}, {5070, 42688}, {5073, 42690}, {5076, 42629}, {5237, 42108}, {5238, 42111}, {5318, 14893}, {5339, 16808}, {5340, 43031}, {5349, 11543}, {5351, 42112}, {9862, 36961}, {10124, 42122}, {10646, 12103}, {10654, 41106}, {11001, 42796}, {11480, 42963}, {11488, 41973}, {11489, 42433}, {12100, 37835}, {12101, 42521}, {12108, 42143}, {12811, 43240}, {12820, 42968}, {12821, 38335}, {15022, 43301}, {15682, 33606}, {15686, 43484}, {15687, 42782}, {15688, 43545}, {15697, 42953}, {15699, 42687}, {15703, 33417}, {15718, 42529}, {15722, 42626}, {16239, 42684}, {16241, 43248}, {16268, 42120}, {16645, 42430}, {16942, 22855}, {16962, 42098}, {16963, 42131}, {16965, 42816}, {19709, 43544}, {19710, 41122}, {21734, 42089}, {22238, 43011}, {23303, 33923}, {31074, 37775}, {33699, 42778}, {35409, 43543}, {36968, 42818}, {40694, 43465}, {41101, 42132}, {41107, 43369}, {41112, 42481}, {41119, 43007}, {41944, 43402}, {41974, 42971}, {41987, 43110}, {41990, 42952}, {42088, 42917}, {42090, 42489}, {42091, 43404}, {42094, 42990}, {42095, 42157}, {42100, 42153}, {42102, 42922}, {42118, 42993}, {42119, 42914}, {42128, 42896}, {42134, 43293}, {42144, 42599}, {42149, 42908}, {42151, 42805}, {42161, 42983}, {42166, 42923}, {42179, 42245}, {42181, 42244}, {42434, 43028}, {42435, 42817}, {42475, 42997}, {42494, 42995}, {42612, 43781}, {42685, 42961}, {42776, 42936}, {42800, 43476}, {42813, 43030}, {42889, 43310}, {42897, 43032}, {42912, 43649}, {42929, 43194}, {42947, 43500}, {42956, 42978}, {42999, 43425}, {43033, 43234}, {43397, 43557}

X(44016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 42093, 19106}, {14, 42155, 42507}, {15, 42135, 16809}, {15, 42814, 42135}, {395, 35404, 43646}, {5321, 16809, 16964}, {5321, 42135, 15}, {5321, 42692, 5}, {5321, 42814, 16809}, {5334, 43365, 42106}, {10645, 42139, 42580}, {10646, 43636, 12103}, {12817, 19106, 42093}, {16809, 16964, 16966}, {16809, 42904, 42814}, {16965, 42816, 43015}, {16967, 42126, 36967}, {18581, 36970, 42099}, {18581, 42099, 16242}, {19107, 42125, 18}, {34755, 43196, 3627}, {41122, 42940, 42528}, {42104, 42902, 43005}, {42111, 43466, 5238}, {42119, 42920, 42914}, {42128, 42991, 42896}, {42133, 42159, 16}, {42136, 42163, 10646}, {42139, 42160, 10645}, {43329, 43631, 395}

X(44017) = GIBERT (51,8,-5) POINT

Barycentrics    17*Sqrt[3]*a^2*S - 5*a^2*SA + 16*SB*SC : :

X(44017) lies on the cubic K1236 and these lines: {6, 15684}, {13, 11737}, {14, 3839}, {15, 8703}, {16, 15707}, {17, 42805}, {61, 43646}, {62, 1656}, {396, 12108}, {397, 3857}, {398, 3853}, {3412, 5237}, {3529, 10653}, {5340, 43784}, {5352, 43018}, {11481, 42892}, {11488, 15702}, {11542, 42952}, {12820, 43417}, {16242, 41977}, {16267, 33416}, {16960, 42501}, {16963, 43542}, {16966, 42636}, {18582, 43250}, {36967, 42935}, {37641, 42921}, {37835, 41119}, {40693, 42592}, {40694, 42961}, {41107, 42093}, {41108, 42104}, {41992, 42488}, {42087, 43230}, {42091, 42520}, {42094, 42968}, {42118, 43245}, {42131, 43305}, {42147, 42966}, {42153, 42612}, {42154, 42967}, {42155, 43007}, {42163, 43033}, {42499, 43554}, {42502, 42917}, {42506, 42512}, {42510, 43014}, {42516, 42529}, {42543, 42585}, {42581, 43025}, {42628, 43104}, {42634, 42915}, {42778, 42918}, {42796, 42912}, {42893, 42984}, {42923, 42940}, {42993, 43416}

X(44017) = {X(15),X(42800)}-harmonic conjugate of X(41972)

X(44018) = GIBERT (51,-8,5) POINT

Barycentrics    17*Sqrt[3]*a^2*S + 5*a^2*SA - 16*SB*SC : :

X(44018) lies on the cubic K1236 and these lines: {6, 15684}, {13, 3839}, {14, 11737}, {15, 15707}, {16, 8703}, {18, 42806}, {61, 1656}, {62, 43645}, {395, 12108}, {397, 3853}, {398, 3857}, {3411, 5238}, {3529, 10654}, {5339, 43783}, {5351, 43019}, {11480, 42893}, {11489, 15702}, {11543, 42953}, {12821, 43416}, {16241, 41978}, {16268, 33417}, {16961, 42500}, {16962, 43543}, {16967, 42635}, {18581, 43251}, {36968, 42934}, {37640, 42920}, {37832, 41120}, {40693, 42960}, {40694, 42593}, {41107, 42105}, {41108, 42094}, {41992, 42489}, {42088, 43231}, {42090, 42521}, {42093, 42969}, {42117, 43244}, {42130, 43304}, {42148, 42967}, {42154, 43006}, {42155, 42966}, {42156, 42613}, {42166, 43032}, {42498, 43555}, {42503, 42916}, {42507, 42513}, {42511, 43015}, {42517, 42528}, {42544, 42584}, {42580, 43024}, {42627, 43101}, {42633, 42914}, {42777, 42919}, {42795, 42913}, {42892, 42985}, {42922, 42941}, {42992, 43417}

X(44018) = {X(16),X(42799)}-harmonic conjugate of X(41971)

X(44019) = GIBERT (59,30,39) POINT

Barycentrics    59*a^2*S/Sqrt[3] + 39*a^2*SA + 60*SB*SC : :

X(44019) lies on the cubic K1236 and these lines: {14, 11737}, {15, 3146}, {17, 42121}, {3412, 43013}, {5339, 16960}, {5351, 42922}, {10646, 42926}, {11489, 16267}, {11542, 43635}, {15701, 16644}, {16241, 43242}, {16808, 43293}, {33607, 42632}, {35401, 43245}, {41101, 43478}, {42100, 43491}, {42111, 42993}, {42156, 42630}, {42158, 42817}, {42511, 43366}, {42530, 43008}, {42581, 43241}, {42900, 42916}, {42920, 43426}, {42998, 43371}, {43226, 43301}

X(44020) = GIBERT (-59,30,39) POINT

Barycentrics    59*a^2*S/Sqrt[3] - 39*a^2*SA - 60*SB*SC : :

X(44020) lies on the cubic K1236 and these lines: {13, 11737}, {16, 3146}, {18, 42124}, {3411, 43012}, {5340, 16961}, {5352, 42923}, {10645, 42927}, {11488, 16268}, {11543, 43634}, {15701, 16645}, {16242, 43243}, {16809, 43292}, {33606, 42631}, {35401, 43244}, {41100, 43477}, {42099, 43492}, {42114, 42992}, {42153, 42629}, {42157, 42818}, {42510, 43367}, {42531, 43009}, {42580, 43240}, {42901, 42917}, {42921, 43427}, {42999, 43370}, {43227, 43300}

leftri

Points associated with Vijay-Hutson triangles: X(44021)-X(44025)

rightri

This preamble is contributed by Clark Kimberling (July 21, 2021), based on notes from Dasari Naga Vijay Krishna, July 21, 2021 and later from Peter Moses and César Lozada.

In the plane of a triangle ABC, let
Pa = parabola with A as its focus and BC as its directrix, define Pb and Pc cyclically;
A' = apex of equilateral triangle erected externally on the side BC, define B' and C' cyclically;
A'' = apex of equilateral triangle erected internally on the side BC, define B'' and C'' cyclically;
Ab = (triangle BCA')∩Pb, and define Bc and Ca cyclically; see Vijay 3 parabolas and 6 points.png Ac = (triangle BCA') ∩Pc, and define Ba and Cb cyclically;
A'b = (triangle BCA")∩Pb, and define B'c and C'a cyclically;
A'c = (triangle BCA")∩Pc, and define B'a and C'b cyclically;
A1 = CaCb∩BcBa, B1 = CaCb∩AbAc, C1 = AbAc∩BcBa;
A2 = AbCb∩BcAc, B2 = CaBa∩BcAc, C2 = CaBa∩AbCb;
A3 = C'aC'b∩B'cB'a, B3 = C'aC'b∩A'bA'c, C3 = A'bA'c∩B'cB'a;
A4 = A'bC'b∩B'cA'c, B4 = C'aB'a∩B'cA'c, C4 = C'aB'a∩A'bC'b;

Barycentrics for points defined above:

A' = -a^2*sqrt(3) : S+SC*sqrt(3) : S+SB*sqrt(3)
Ab = -c*a^2*sqrt(3) : 4*R*S : c*(S + SB*sqrt(3))
Ac = -b*a^2*sqrt(3) : b*(S + SC*sqrt(3)) : 4*R*S
A1 = - (4096*R^4*S^4 - 256*a*c*R^2*S^4 - 256*a*b*R^2*S^4 + 16*a^2*b*c*S^4 - 256*sqrt(3)*a*b*c^2*R^2*S^3 - 256*sqrt(3)*a*b^2*c*R^2*S^3 + 16*sqrt(3)*a^2*b*c^3*S^3 + 16*sqrt(3)*a^2*b^3*c*S^3 + 192*a*c^5*R^2*S^2 - 192*a*b*c^4*R^2*S^2 - 384*a^3*c^3*R^2*S^2 - 768*a^2*b^2*c^2*R^2*S^2 - 192*a*b^4*c*R^2*S^2 + 192*a^5*c*R^2*S^2 + 192*a*b^5*R^2*S^2 - 384*a^3*b^3*R^2*S^2 + 192*a^5*b*R^2*S^2 + 192*a^2*b^2*c^3*R*S^2 + 192*a^2*b^3*c^2*R*S^2 + 24*a^4*b*c^3*S^2 + 24*a^4*b^3*c*S^2 - 24*a^6*b*c*S^2 - 32*3^(3/2)*a^2*b^2*c^5*R*S + 32*3^(3/2)*a^2*b^3*c^4*R*S + 32*3^(3/2)*a^2*b^4*c^3*R*S + 32*3^(3/2)*a^4*b^2*c^3*R*S - 32*3^(3/2)*a^2*b^5*c^2*R*S + 32*3^(3/2)*a^4*b^3*c^2*R*S - 4*3^(3/2)*a^2*b*c^7*S + 4*3^(3/2)*a^2*b^3*c^5*S + 8*3^(3/2)*a^4*b*c^5*S + 4*3^(3/2)*a^2*b^5*c^3*S - 16*3^(3/2)*a^4*b^3*c^3*S - 4*3^(3/2)*a^6*b*c^3*S - 4*3^(3/2)*a^2*b^7*c*S + 8*3^(3/2)*a^4*b^5*c*S - 4*3^(3/2)*a^6*b^3*c*S - 9*a^2*b*c^9 + 36*a^2*b^3*c^7 + 18*a^4*b*c^7 - 54*a^2*b^5*c^5 - 18*a^4*b^3*c^5 + 36*a^2*b^7*c^3 - 18*a^4*b^5*c^3 - 18*a^8*b*c^3 - 9*a^2*b^9*c + 18*a^4*b^7*c - 18*a^8*b^3*c + 9*a^10*b*c) : 2*b^2*c*(64*R^2*S^2 - 4*a*b*S^2 - 16*sqrt(3)*a*b*c*R*S - 9*a*b*c^4 + 6*a*b^3*c^2 + 6*a^3*b*c^2 + 3*a*b^5 - 6*a^3*b^3 + 3*a^5*b) *(8*sqrt(3)*R*S - 2*sqrt(3)*a*S - 3*a*b^2 - 3*a*c^2 + 3*a^3) : 2*b*c^2*(64*R^2*S^2 - 4*a*c*S^2 - 16*sqrt(3)*a*b*c*R*S + 3*a*c^5 + 6*a*b^2*c^3 - 6*a^3*c^3 - 9*a*b^4*c + 6*a^3*b^2*c + 3*a^5*c)*(8*sqrt(3)*R*S - 2*sqrt(3)*a*S - 3*a*b^2 - 3*a*c^2 + 3*a^3)

A2 = a*(9*b*c^9 - 36*b^3*c^7 - 36*a^2*b*c^7 + 54*b^5*c^5 + 36*a^2*b^3*c^5 + 54*a^4*b*c^5 + 8*3^(3/2)*S*a^2*b*c^5 - 24*S^2*b*c^5 + 192*R^2*S^2*c^4 - 36*b^7*c^3 + 36*a^2*b^5*c^3 + 36*a^4*b^3*c^3 - 16*3^(3/2)*S*a^2*b^3*c^3 + 48*S^2*b^3*c^3 - 36*a^6*b*c^3 - 16*3^(3/2)*S*a^4*b*c^3 - 48*S^2*a^2*b*c^3 + 384*R^2*S^2*a*c^3 - 384*R^2*S^2*b^2*c^2 - 384*R^2*S^2*a*b*c^2 + 9*b^9*c - 36*a^2*b^7*c + 54*a^4*b^5*c + 8*3^(3/2)*S*a^2*b^5*c - 24*S^2*b^5*c - 36*a^6*b^3*c - 16*3^(3/2)*S*a^4*b^3*c - 48*S^2*a^2*b^3*c - 384*R^2*S^2*a*b^2*c + 9*a^8*b*c + 8*3^(3/2)*S*a^6*b*c + 72*S^2*a^4*b*c + 32*sqrt(3)*S^3*a^2*b*c - 768*R^2*S^2*a^2*b*c + 16*S^4*b*c - 384*R^2*S^2*a^3*c - 256*sqrt(3)*R^2*S^3*a*c + 192*R^2*S^2*b^4 + 384*R^2*S^2*a*b^3 - 384*R^2*S^2*a^3*b - 256*sqrt(3)*R^2*S^3*a*b - 192*R^2*S^2*a^4 - 256*sqrt(3)*R^2*S^3*a^2 - 256*R^2*S^4) : 8*R*S*b*(3^(3/2)*c^7 + 2*3^(3/2)*a*c^6 - 3^(5/2)*b^2*c^5 - 3^(3/2)*a^2*c^5 - 6*S*c^5 - 4*3^(3/2)*a*b^2*c^4 - 4*3^(3/2)*a^3*c^4 - 24*S*a*c^4 - 24*R*S*c^4 + 3^(5/2)*b^4*c^3 - 2*3^(3/2)*a^2*b^2*c^3 + 12*S*b^2*c^3 - 3^(3/2)*a^4*c^3 - 12*S*a^2*c^3 - 48*R*S*a*c^3 - 4*sqrt(3)*S^2*c^3 + 2*3^(3/2)*a*b^4*c^2 - 4*3^(3/2)*a^3*b^2*c^2 + 24*S*a*b^2*c^2 + 48*R*S*b^2*c^2 + 48*R*S*a*b*c^2 + 2*3^(3/2)*a^5*c^2 + 24*S*a^3*c^2 + 8*sqrt(3)*S^2*a*c^2 - 3^(3/2)*b^6*c + 3^(5/2)*a^2*b^4*c - 6*S*b^4*c - 3^(5/2)*a^4*b^2*c - 12*S*a^2*b^2*c + 48*R*S*a*b^2*c + 4*sqrt(3)*S^2*b^2*c + 96*R*S*a^2*b*c + 3^(3/2)*a^6*c + 18*S*a^4*c + 48*R*S*a^3*c + 4*3^(3/2)*S^2*a^2*c + 32*sqrt(3)*R*S^2*a*c + 8*S^3*c - 24*R*S*b^4 - 48*R*S*a*b^3 + 48*R*S*a^3*b + 32*sqrt(3)*R*S^2*a*b + 24*R*S*a^4 + 32*sqrt(3)*R*S^2*a^2 + 32*R*S^3) : -8*R*S*c*(3^(3/2)*b*c^6 - 3^(5/2)*b^3*c^4 - 2*3^(3/2)*a*b^2*c^4 - 3^(5/2)*a^2*b*c^4 + 6*S*b*c^4 + 24*R*S*c^4 + 48*R*S*a*c^3 + 3^(5/2)*b^5*c^2 + 4*3^(3/2)*a*b^4*c^2 + 2*3^(3/2)*a^2*b^3*c^2 - 12*S*b^3*c^2 + 4*3^(3/2)*a^3*b^2*c^2 - 24*S*a*b^2*c^2 - 48*R*S*b^2*c^2 + 3^(5/2)*a^4*b*c^2 + 12*S*a^2*b*c^2 - 48*R*S*a*b*c^2 - 4*sqrt(3)*S^2*b*c^2 - 48*R*S*a*b^2*c - 96*R*S*a^2*b*c - 48*R*S*a^3*c - 32*sqrt(3)*R*S^2*a*c - 3^(3/2)*b^7 - 2*3^(3/2)*a*b^6 + 3^(3/2)*a^2*b^5 + 6*S*b^5 + 4*3^(3/2)*a^3*b^4 + 24*S*a*b^4 + 24*R*S*b^4 + 3^(3/2)*a^4*b^3 + 12*S*a^2*b^3 + 48*R*S*a*b^3 + 4*sqrt(3)*S^2*b^3 - 2*3^(3/2)*a^5*b^2 - 24*S*a^3*b^2 - 8*sqrt(3)*S^2*a*b^2 - 3^(3/2)*a^6*b - 18*S*a^4*b - 48*R*S*a^3*b - 4*3^(3/2)*S^2*a^2*b - 32*sqrt(3)*R*S^2*a*b - 8*S^3*b - 24*R*S*a^4 - 32*sqrt(3)*R*S^2*a^2 - 32*R*S^3)

Barycentrics for A″, A'b, A'c, A3, A4 are obtained by replacing sqrt(3) by -sqrt(3) in the barycentrics for A', Ab, Ac, A1, A2, respectively. In this manner, X(44023) is obtained from X(44021) and X(4402) from X(44022).

Related triangles are here named as follows:

A1B1C1 = 1st Vijay-Hutson triangle;
A2B2C2 = 2nd Vijay-Hutson triangle;
A3B3C3 = 3rd Vijay-Hutson triangle;
A4B4C4 = 4th Vijay-Hutson triangle.

Perspectors:

X(44021) = AA1∩BB1∩CC1;
X(44022) = AA2∩BB2∩CC2;
X(44023) = AA3∩BB3∩CC3;
X(44024) = AA4∩BB4∩CC4;
X(44025) = A2A4∩B2B∩C2C4.

X(44021) = PERSPECTOR OF THESE TRIANGLES: ABC AND 1ST VIJAY-HUTSON TRIANGLE

Barycentrics    a^2*(a^4+(b^2-2*c^2)*a^2+2*(2-sqrt(3))*b^2*c*a-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+2*(2-sqrt(3))*b*c^2*a+(b^2-c^2)*(b^2+2*c^2)) : :

Construction: X(44021)

X(44021) lies on these lines: {}

X(44022) = PERSPECTOR OF THESE TRIANGLES: ABC AND 2ND VIJAY-HUTSON TRIANGLE

Barycentrics    (-(-a+b+c)*(a+b-c)*sqrt(3)+4*a*c+2*S)*(-(-a+b+c)*(a-b+c)*sqrt(3)+4*a*b+2*S) : :

Constructions: X(44022) and, if you have GeoGebra, X(44022)A

X(44022) lies on these lines: {44024, 44025}

X(44023) = PERSPECTOR OF THESE TRIANGLES: ABC AND 3RD VIJAY-HUTSON TRIANGLE

Barycentrics    a^2*(a^4+(b^2-2*c^2)*a^2+2*(2+sqrt(3))*b^2*c*a-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+2*(2+sqrt(3))*b*c^2*a+(b^2-c^2)*(b^2+2*c^2)) : :

Construction: X(44023)

X(44023) lies on these lines: {}

X(44024) = PERSPECTOR OF THESE TRIANGLES: ABC AND 4TH VIJAY-HUTSON TRIANGLE

Barycentrics    ((-a+b+c)*(a+b-c)*sqrt(3)+4*a*c+2*S)*((-a+b+c)*(a-b+c)*sqrt(3)+4*a*b+2*S) : :

Construction: X(44024)

X(44024) lies on these lines: {44022, 44025}

X(44025) = PERSPECTOR OF THESE TRIANGLES: 2ND AND 4TH VIJAY-HUTSON TRIANGLE

Barycentrics    -4*a*((b^2+c^2)*a^5-(b+c)*(b^2-3*b*c+c^2)*a^4-(2*b^4+2*c^4-b*c*(3*b^2+2*b*c+3*c^2))*a^3+(b+c)*(2*b^4+2*c^4-b*c*(5*b^2+2*b*c+5*c^2))*a^2+(b^2-3*b*c+c^2)*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c))*S+a^10-3*(b+c)*a^9+(b^2+15*b*c+c^2)*a^8+6*(b+c)*(b^2-3*b*c+c^2)*a^7-(8*b^4+8*c^4+b*c*(21*b^2+10*b*c+21*c^2))*a^6+4*(b+c)*(7*b^2-6*b*c+7*c^2)*b*c*a^5+(8*b^6+8*c^6-b*c*(b^2-6*b*c+c^2)*(b+c)^2)*a^4-2*(b^2-c^2)*(b-c)*(3*b^4+3*c^4+b*c*(7*b^2+4*b*c+7*c^2))*a^3-(b^4+c^4-5*(b^2+c^2)*b*c)*(b^2-c^2)^2*a^2+(b^2-c^2)^3*(b-c)*(3*b^2-2*b*c+3*c^2)*a-(b^2-c^2)^4*(b-c)^2 : :

Construction: X(44025)

X(44025) lies on these lines: {44022, 44024}

X(44026) = X(51)X(31392)∩X(140)X(389)

Barycentrics    a^2*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 4*a^6*c^2 + 5*a^4*b^2*c^2 + a^2*b^4*c^2 - 2*b^6*c^2 + 6*a^4*c^4 + a^2*b^2*c^4 + 2*b^4*c^4 - 4*a^2*c^6 - 2*b^2*c^6 + c^8)*(a^10*b^2 - 5*a^8*b^4 + 10*a^6*b^6 - 10*a^4*b^8 + 5*a^2*b^10 - b^12 + a^10*c^2 - 4*a^8*b^2*c^2 + a^6*b^4*c^2 + 12*a^4*b^6*c^2 - 16*a^2*b^8*c^2 + 6*b^10*c^2 - 5*a^8*c^4 + a^6*b^2*c^4 + 2*a^4*b^4*c^4 + 11*a^2*b^6*c^4 - 15*b^8*c^4 + 10*a^6*c^6 + 12*a^4*b^2*c^6 + 11*a^2*b^4*c^6 + 20*b^6*c^6 - 10*a^4*c^8 - 16*a^2*b^2*c^8 - 15*b^4*c^8 + 5*a^2*c^10 + 6*b^2*c^10 - c^12) : :
X(44026) = 3 X[51] - X[31392]

See Antreas Hatzipolakis and Peter Moses, euclid 1862.

X(44026) lies on these lines: {51, 31392}, {140, 389}, {143, 32638}, {195, 14367}, {10095, 14051}, {11557, 43966}

X(44026) = reflection of X(14051) in X(10095)

X(44027) = X(30)X(511)∩X(6153)X(34804)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 3*a^4*c^2 + 3*a^2*b^2*c^2 + b^4*c^2 + 3*a^2*c^4 + b^2*c^4 - c^6)*(a^16 - 6*a^14*b^2 + 14*a^12*b^4 - 14*a^10*b^6 + 14*a^6*b^10 - 14*a^4*b^12 + 6*a^2*b^14 - b^16 - 6*a^14*c^2 + 25*a^12*b^2*c^2 - 38*a^10*b^4*c^2 + 27*a^8*b^6*c^2 - 18*a^6*b^8*c^2 + 23*a^4*b^10*c^2 - 18*a^2*b^12*c^2 + 5*b^14*c^2 + 14*a^12*c^4 - 38*a^10*b^2*c^4 + 29*a^8*b^4*c^4 - 2*a^6*b^6*c^4 - 15*a^4*b^8*c^4 + 26*a^2*b^10*c^4 - 14*b^12*c^4 - 14*a^10*c^6 + 27*a^8*b^2*c^6 - 2*a^6*b^4*c^6 + 3*a^4*b^6*c^6 - 14*a^2*b^8*c^6 + 27*b^10*c^6 - 18*a^6*b^2*c^8 - 15*a^4*b^4*c^8 - 14*a^2*b^6*c^8 - 34*b^8*c^8 + 14*a^6*c^10 + 23*a^4*b^2*c^10 + 26*a^2*b^4*c^10 + 27*b^6*c^10 - 14*a^4*c^12 - 18*a^2*b^2*c^12 - 14*b^4*c^12 + 6*a^2*c^14 + 5*b^2*c^14 - c^16) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1867.

X(44027) lies on these lines: {30, 511}, {6153, 34804}, {13418, 25043}

X(44028) = X(2)X(3459)∩X(30)X(511)

Barycentrics    (a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^12 - 5*a^10*b^2 + 10*a^8*b^4 - 10*a^6*b^6 + 5*a^4*b^8 - a^2*b^10 - 5*a^10*c^2 + 16*a^8*b^2*c^2 - 17*a^6*b^4*c^2 + 8*a^4*b^6*c^2 - 4*a^2*b^8*c^2 + 2*b^10*c^2 + 10*a^8*c^4 - 17*a^6*b^2*c^4 + a^4*b^4*c^4 + 5*a^2*b^6*c^4 - 8*b^8*c^4 - 10*a^6*c^6 + 8*a^4*b^2*c^6 + 5*a^2*b^4*c^6 + 12*b^6*c^6 + 5*a^4*c^8 - 4*a^2*b^2*c^8 - 8*b^4*c^8 - a^2*c^10 + 2*b^2*c^10) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1869.

X(44028) lies on these lines: {2, 3459}, {30, 511}, {547, 13856}, {549, 18016}, {930, 6150}, {1157, 13512}, {1263, 16336}, {6592, 10615}, {10109, 34768}, {11671, 19552}, {14051, 34804}, {14072, 16337}, {16766, 21230}, {25148, 38899}, {30482, 30483}, {38615, 40631}

X(44028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {930, 19553, 6150}, {6592, 24385, 10615}, {15345, 25043, 32551}

X(44029) = X(17)X(619)∩X(61)X(618)

Barycentrics    (a^2 - 3*b^2 - 3*c^2 - 2*Sqrt[3]*S)*(7*a^2 - b^2 - c^2 + 2*Sqrt[3]*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1884.

X(44029) lies on the Kiepert circumhyperbola of the medial triangle and these lines: {2, 5487}, {3, 22113}, {15, 22916}, {17, 619}, {61, 618}, {114, 16002}, {148, 33413}, {630, 42672}, {3618, 44031}, {6292, 11132}, {8259, 30472}, {11298, 33620}, {11300, 33618}, {11301, 33621}, {11307, 42989}

X(44029) = complement of X(5487)
X(44029) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 34540}, {163, 30215}, {30215, 21253}
X(44029) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 34540}, {99, 30215}
X(44029) = Dao image of X(17)
X(44029) = barycentric quotient X(34540)/X(5487)
X(44029) = {X(35689),X(36782)}-harmonic conjugate of X(627)

X(44030) = X(5)X(302)∩X(17)X(299)

Barycentrics    3*a^4 - 7*a^2*b^2 + 4*b^4 - 7*a^2*c^2 - 14*b^2*c^2 + 4*c^4 - 2*Sqrt[3]*(a^2 + 2*b^2 + 2*c^2)*S : :
X(44030) = 3 X[2] + X[5487]

See Antreas Hatzipolakis and Peter Moses, euclid 1884.

X(44030) lies on these lines: {2, 5487}, {5, 302}, {17, 299}, {99, 33387}, {140, 14144}, {298, 22113}, {383, 16626}, {532, 41121}, {629, 6670}, {3763, 44032}, {5981, 5982}, {6673, 11132}, {7796, 40334}, {7891, 43028}, {7901, 22893}, {11303, 22911}, {11308, 42672}, {11309, 30471}, {16645, 33020}, {33959, 42813}

X(44030) = {X(629),X(22891)}-harmonic conjugate of X(11290)

X(44031) = X(18)X(618)∩X(62)X(619)

Barycentrics    (7*a^2 - b^2 - c^2 - 2*Sqrt[3]*S)*(a^2 - 3*b^2 - 3*c^2 + 2*Sqrt[3]*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1884.

X(44031) lies on the Kiepert circumhyperbola of the medial triangle and these lines: {2, 5488}, {3, 22114}, {16, 22871}, {18, 618}, {62, 619}, {114, 16001}, {148, 33412}, {629, 42673}, {3411, 36781}, {3618, 44029}, {6292, 11133}, {8260, 30471}, {11297, 33621}, {11299, 33619}, {11302, 33620}, {11308, 42988}

X(44031) = complement of X(5488)
X(44031) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 34541}, {163, 30216}, {30216, 21253}
X(44031) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 34541}, {99, 30216}
X(44031) = Dao image of X(18)
X(44031) = barycentric quotient X(34541)/X(5488)

X(44032) = X(5)X(303)∩X(18)X(298)

Barycentrics    3*a^4 - 7*a^2*b^2 + 4*b^4 - 7*a^2*c^2 - 14*b^2*c^2 + 4*c^4 + 2*Sqrt[3]*(a^2 + 2*b^2 + 2*c^2)*S : :
X(44032) = 3 X[2] + X[5488]

See Antreas Hatzipolakis and Peter Moses, euclid 1884.

X(44032) lies on these lines: {2, 5488}, {5, 303}, {18, 298}, {99, 33386}, {140, 14145}, {299, 22114}, {533, 41122}, {630, 6669}, {1080, 16627}, {3763, 44030}, {5980, 5983}, {6674, 11133}, {7796, 40335}, {7891, 43029}, {7901, 22847}, {11304, 22866}, {11307, 42673}, {11310, 30472}, {16644, 33020}, {33960, 42814}

X(44032) = {X(630),X(22846)}-harmonic conjugate of X(11289)

X(44033) = X(17)X(623)∩X(61)X(33526)

Barycentrics    a^2*(a^2 - 3*b^2 - 3*c^2 - 2*Sqrt[3]*S)*(a^2 - b^2 - c^2 - 2*Sqrt[3]*S)*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + 6*b^2*c^2 - 2*c^4 + 2*Sqrt[3]*a^2*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1884.

X(44033) lies on these lines: {17, 623}, {61, 33526}

X(44033) = barycentric quotient X(2004)/X(18813)

X(44034) = (name pending)

Barycentrics    (a^2 - b^2 - c^2 - 2*Sqrt[3]*S)*(3*a^6*b^2 - 5*a^4*b^4 + a^2*b^6 + b^8 + 3*a^6*c^2 - 18*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 2*b^6*c^2 - 5*a^4*c^4 - 7*a^2*b^2*c^4 - 6*b^4*c^4 + a^2*c^6 + 2*b^2*c^6 + c^8 - 2*Sqrt[3]*(b^2 + c^2)*(a^4 + 2*a^2*b^2 - b^4 + 2*a^2*c^2 + 2*b^2*c^2 - c^4)*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1884.

X(44034) lies on this line: {61, 302}

X(44035) = X(18)X(624)∩X(62)X(33527)

Barycentrics    a^2*(a^2 - 3*b^2 - 3*c^2 + 2*Sqrt[3]*S)*(a^2 - b^2 - c^2 + 2*Sqrt[3]*S)*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + 6*b^2*c^2 - 2*c^4 - 2*Sqrt[3]*a^2*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1884.

X(44035) lies on these lines: {18, 624}, {62, 33527}

X(44035) = barycentric quotient X(2005)/X(18814)

X(44036) = (name pending)

Barycentrics    (a^2 - b^2 - c^2 + 2*Sqrt[3]*S)*(3*a^6*b^2 - 5*a^4*b^4 + a^2*b^6 + b^8 + 3*a^6*c^2 - 18*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 2*b^6*c^2 - 5*a^4*c^4 - 7*a^2*b^2*c^4 - 6*b^4*c^4 + a^2*c^6 + 2*b^2*c^6 + c^8 + 2*Sqrt[3]*(b^2 + c^2)*(a^4 + 2*a^2*b^2 - b^4 + 2*a^2*c^2 + 2*b^2*c^2 - c^4)*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1884.

X(44036) lies on this line: {62,303}

X(44037) = X(3)X(6)∩X(2911)X(5405)

Barycentrics    a^2*(a^4*b - 2*a^2*b^3 + b^5 + a^4*c - 3*a^3*b*c - a^2*b^2*c + 3*a*b^3*c - a^2*b*c^2 - 2*a*b^2*c^2 - b^3*c^2 - 2*a^2*c^3 + 3*a*b*c^3 - b^2*c^3 + c^5 + 2*(a^2*b - b^3 + a^2*c + a*b*c - c^3)*S) : :

See Stanley Rabinowitz, Antreas Hatzipolakis and Peter Moses, euclid 1887.

X(44037) lies on these lines: {3,6}, {3911,5405}, {8953,17102}

X(44038) = X(1)X(485)∩X(4)X(9)

Barycentrics    a^4 - a^3*b + a^2*b^2 + a*b^3 - 2*b^4 - a^3*c + 2*a^2*b*c - a*b^2*c + a^2*c^2 - a*b*c^2 + 4*b^2*c^2 + a*c^3 - 2*c^4 + 2*a*(a - b - c)*S : :

See Stanley Rabinowitz, Antreas Hatzipolakis and Peter Moses, euclid 1887.

X(44038) lies on these lines: {1, 485}, {4, 9}, {5, 30556}, {80, 30432}, {355, 30557}, {388, 8957}, {908, 13386}, {1336, 5727}, {1378, 5778}, {1478, 6204}, {1698, 32555}, {1737, 6203}, {1867, 12938}, {3300, 7951}, {3577, 13426}, {5219, 5393}, {5292, 18992}, {5691, 32556}, {5747, 13883}, {5822, 13936}, {8953, 35800}, {10590, 30324}, {18391, 30325}

X(44038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 14121, 6212}, {10, 31561, 6213}, {19925, 31594, 31562}

leftri

Points associated with Vijay incentral circles and excentral circles: X(44039)-X(44041)

rightri

This preamble is contributed by Clark Kimberling (July 26, 2021), based on notes from Dasari Naga Vijay Krishna, July 25, 2021.

In the plane of a triangle ABC, let
A'B'C' = excentral triangle
Oa = circle with diameter BC, and define Ob and Oc cyclically;
Ab = BB'∩Oa, and define Bc and Ca cyclically;
Ac = CC'∩Oa, and define Ba and Cb cyclically;
A'b = A'C'∩Oa, and define B'c and C'a cyclically;
A'c = A'B'∩Oa, and define B'a and C'b cyclically;
Oe = circle {{A'b, A'c, B'c, B'a, C'a, C'b}}, here named the Vijay excentral circle;
OIa = circle {{C'a, B'a, Ab, Ac, Bc, Cb}}, here named the Vijay a-incentral circle;
OIb = circle {{A'b, C'b, Ba, Bc, Ca, Ac}}, here named the Vijay b-incentral circle;
OIc = circle {{B'c, A'c, Ca, Cb, Ab, Ba}}, here named the Vijay c-incentral circle;
Pa = polar of A wrt Oe, and define Pb and Pc cyclically;
L'a = polar of A wrt OIa, and define L'b and L'c cyclically.

Barycentric equations for Vijay incentral and excentral circles and their centers:

Vijay excentral circle:
(s - b)(s - c)x^2 + (s -c)(s - a)y^2 + (s - a)(s - b)z^2 + s(ayz + bzx + cxy) = 0, with center X(10) = b + c : c + a : a + b

Vijay a-incentral circle:
(s - b)(s - c)x^2 - (s)(s - b)y^2 - (s)(s - c)z^2 + (s - a)(- ayz + bzx + cxy) = 0, with center b + c : c - a : b - a

Vijay b-incentral circle:
-s(s - a)x^2 +(s - a)(s - c)y^2 - (s)(s - c)z^2 + (s - b)(ayz - bzx + cxy) = 0, with center c - b : c + a : a - b

Vijay c-incentral circle:
-s(s - a)x^2 - (s)(s - b)y^2 + (s - a)(s - b)z^2 + (s - c)(ayz + bzx - cxy) = 0, with center b - c : a - c : a + b

Define 6 points by the following intersections :

A1 = B'cB'a∩C'aC'b, B1 = C'aC'b∩ A'bA'c, C1 = A'bA'c∩B'cB'a;
A2 = BcBa∩CaCb, B2 = CaCb∩ AbAc, C2 = AbAc∩BcBa;
A3 = C'aA'c∩ B'aA'b∩CaAc∩BaAb∩BC = midpoint of BC,
B3 = B'aA'b∩B'cC'b∩ BaAb∩ BcCb∩CA = midpoint of CA,
C3 = B'cC'b∩ C'aA'c∩ BcCb∩ CaAc∩AB = midpoint of AB;
A4 = center of Vijay a-incentral circle, and define B4 and C4 cyclically;
A5 = Pb∩Pc, and define B5 and C5 cyclically;
A6 = L'b∩L'c, and define B6 and C6 cyclically

Barycentrics for points defined above:

Ab = a : c - a : c, Ac = a : b : b - a
A'b = -a : a + c : c, A'c = -a : b : a + b
A1 = -a(b + c) : SC : SB
A2 = 0 : s - c : s - b
A3 = 0 : 1 : 1;
A4 = b + c : c - a : b - a
A5 = 4*(s - a)^2*(s - b)*(s - c) - s^2*a^2 : s^2*a*b - 2*s*c*(s - a)*(s - b) : s^2*a*c - 2*s*b*(s - c)*(s - a)
A6 = ((b + c)*(b + c - 2*a)*(s - b)*(s - c)) : ((s - b)*(a*b*(s - c) + 2*c*(s - a)*(s - b))) : ((s - c)*(a*c*(s - b) + 2*b*(s - a)*(s - c)))

Related triangles are here named:

A1B1C1 = Vijay excentral triangle;
A2B2C2 = intouch triangle;
A3B3C3 = medial triangle ;
A4B4C4 = Vijay abc-incentral triangle; Also, A4B4C4 = Wasat triangle
A5B5C5 = Vijay polar excentral triangle;
A6B6C6 = Vijay polar incentral triangle.

Collinearities:

A1, A2, A4 are collinear;
A1, A3, A' are collinear.

Perspectors :

AA'∩BB'∩CC' = X(1) = incenter = a : b : c
AA3∩BB3∩CC3 = A4A'∩B4B'∩C4C' = X(2) = centroid = 1 : 1 : 1,
AA1∩BB1∩CC1 = X(4) = orthocenter= SB SC : SC SA : SA SB
AA2∩BB2∩CC2 = X(7) = Gergonne point = 1/(s-a) : 1/(s-b) : 1/(s-c)
A1A3A'∩B1B3B'∩C1C3C' = X(9) = mittenpunkt = a(s -a) : b(s-b) : c(s-c)
A3A4∩B3B4∩C3C4 = X(10) = Spieker center = center of Vijay excentral eircle = b + c : c + a : a + b
A2A'∩B2B'∩C2C'= X(57) = a(s-b)(s-c) : b(s-a)(s-c) : c(s-a)(s-b)
A1A2A4∩B1B2B4∩C1C2C4 = X(226) = (b+c)(s-b)(s-c) : (c+a)(s-a)(s-c) : (a+b)(s-a)(s-b)
AA4∩BB4∩CC4 = X(514) = b-c : c-a : a-b
AA5∩BB5∩CC5 = X(2051) = 1/(a^3 - a (b^2 - b c + c^2) - b c(b + c)) : :
A5A'∩B5B'∩C5C' = X(44039)
AA6∩BB6∩CC6 = X(44040)
A5A6∩B5B6∩C5C6; = X(44041)

Constructions:

X(44039)
Vijay a-incentral circle.pdf
Vijay b-incentral circle.pdf
Vijay c-incentral circle.pdf
Vijay exncentral circle.pdf

The Vijay excentral circle is the Spieker radical circle. The Vijay incentral circles are the extraversions of the Spieker radical circle. That is, the Vijay a-incentral circle is the radical circle of the incircle and the B- and C-excircles, and cyclically for the Vijay b- and c-incentral circles. (Randy Hutson, September 30, 2021)

The Vijay excentral circle and the three Vijay incentral circles are Taylor circles of the excentral triangle. (Dao Thanh Oai, October 26, 2021)

A1B1C1 = Vijay excentral triangle is the 2nd extouch triangle of ABC (César Lozada, December 6, 2022)

X(44039) = PERSPECTOR OF EXCENTRAL TRIANGLE AND VIJAY POLAR EXCENTRAL TRIANGLE

Barycentrics    2*a^6*b + a^5*b^2 - 2*a^4*b^3 - a*b^6 + 2*a^6*c + 2*a^4*b^2*c - a^3*b^3*c - 3*a^2*b^4*c + a*b^5*c - b^6*c + a^5*c^2 + 2*a^4*b*c^2 - 6*a^3*b^2*c^2 + 3*a^2*b^3*c^2 + a*b^4*c^2 - b^5*c^2 - 2*a^4*c^3 - a^3*b*c^3 + 3*a^2*b^2*c^3 - 2*a*b^3*c^3 + 2*b^4*c^3 - 3*a^2*b*c^4 + a*b^2*c^4 + 2*b^3*c^4 + a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :

X(44039) lies on these lines: {1, 2051}, {3, 10}, {4, 30116}, {8, 573}, {65, 29069}, {145, 9535}, {181, 10950}, {386, 944}, {516, 31785}, {517, 2901}, {572, 1220}, {950, 5710}, {952, 970}, {1503, 31799}, {1682, 10944}, {1695, 3632}, {1742, 5691}, {1746, 5260}, {1764, 17751}, {2098, 9554}, {2099, 9553}, {3436, 22020}, {3667, 9961}, {3869, 22022}, {4276, 11491}, {5264, 10572}, {5587, 19858}, {5690, 35203}, {5853, 10443}, {5881, 9548}, {5882, 37698}, {6999, 41232}, {9566, 12645}, {9567, 18526}, {9569, 37727}, {10406, 37734}, {10407, 15950}, {10440, 28236}, {10470, 26115}, {11322, 24996}, {29825, 30389}

X(44039) = midpoint of X(8) and X(10454)
X(44039) = X(23512)-Ceva conjugate of X(1766)
X(44039) = barycentric product X(321)*X(40456)
X(44039) = barycentric quotient X(40456)/X(81)
X(44039) = {X(2536),X(2537)}-harmonic conjugate of X(23361)

X(44040) = PERSPECTOR OF ABC AND VIJAY POLAR INCENTRAL TRIANGLE

Barycentrics    (s-a)/(b*c*(s - a) + 2*a*(s - b)(s - c)) : :
Barycentrics    (a - b - c)*(a^2*b - b^3 - a^2*c - a*b*c - a*c^2 + b*c^2)*(a^2*b + a*b^2 - a^2*c + a*b*c - b^2*c + c^3) : :

X(44040) lies on these lines: on lines {1, 28997}, {10, 7069}, {11, 596}, {55, 4075}, {72, 519}, {78, 30568}, {307, 1210}, {497, 24068}, {522, 1329}, {1089, 2310}, {2325, 3694}, {2757, 6789}, {3710, 4723}, {3971, 4314}, {6534, 11238}, {6700, 7515}, {30144, 34587}

X(44040) = X(i)-cross conjugate of X(j) for these (i,j): {3270, 3239}, {21031, 8}
X(44040) = cevapoint of X(2310) and X(3700)
X(44040) = trilinear pole of line {1639, 8611}
X(44040) = X(i)-isoconjugate of X(j) for these (i,j): {56, 404}, {604, 32939}, {7128, 39006}
X(44040) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 32939}, {9, 404}, {3239, 20293}, {3270, 39006}, {3710, 42705}

X(44041) = PERSPECTOR OF VIJAY POLAR INCENTRAL TRIANGLE AND VIJAY POLAR EXCENTRAL TRIANGLE

Barycentrics    (-3*b^2*c^11-2*a*b*c^11+a^2*c^11-3*b^3*c^10+6*a*b^2*c^10+3*a^2*b*c^10-2*a^3*c^10+12*b^4*c^9+6*a*b^3*c^9-6*a^2*b^2*c^9+6*a^3*b*c^9-6*a^4*c^9+12*b^5*c^8-24*a*b^4*c^8+6*a^2*b^3*c^8-2*a^3*b^2*c^8-10*a^4*b*c^8+6*a^5*c^8-18*b^6*c^7-4*a*b^5*c^7+21*a^2*b^4*c^7-32*a^3*b^3*c^7+11*a^4*b^2*c^7-6*a^5*b*c^7+12*a^6*c^7-18*b^7*c^6+36*a*b^6*c^6-25*a^2*b^5*c^6+4*a^3*b^4*c^6-a^4*b^3*c^6-18*a^5*b^2*c^6+12*a^6*b*c^6-6*a^7*c^6+12*b^8*c^5-4*a*b^7*c^5-25*a^2*b^6*c^5+52*a^3*b^5*c^5-26*a^4*b^4*c^5-2*a^5*b^3*c^5+a^6*b^2*c^5+2*a^7*b*c^5-10*a^8*c^5+12*b^9*c^4-24*a*b^8*c^4+21*a^2*b^7*c^4+4*a^3*b^6*c^4-26*a^4*b^5*c^4+8*a^5*b^4*c^4-a^6*b^3*c^4+10*a^7*b^2*c^4-6*a^8*b*c^4+2*a^9*c^4-3*b^10*c^3+6*a*b^9*c^3+6*a^2*b^8*c^3-32*a^3*b^7*c^3-a^4*b^6*c^3-2*a^5*b^5*c^3-a^6*b^4*c^3+28*a^7*b^3*c^3-4*a^8*b^2*c^3+3*a^10*c^3-3*b^11*c^2+6*a*b^10*c^2-6*a^2*b^9*c^2-2*a^3*b^8*c^2+11*a^4*b^7*c^2-18*a^5*b^6*c^2+a^6*b^5*c^2+10*a^7*b^4*c^2-4*a^8*b^3*c^2+4*a^9*b^2*c^2+a^10*b*c^2-2*a*b^11*c+3*a^2*b^10*c+6*a^3*b^9*c-10*a^4*b^8*c-6*a^5*b^7*c+12*a^6*b^6*c+2*a^7*b^5*c-6*a^8*b^4*c+a^10*b^2*c+a^2*b^11-2*a^3*b^10-6*a^4*b^9+6*a^5*b^8+12*a^6*b^7-6*a^7*b^6-10*a^8*b^5+2*a^9*b^4+3*a^10*b^3) : :

X(44041) lies on this line: {2051,44040}

X(44042) = X(11)X(2679)∩X(55)X(805)

Barycentrics    a^2*(a - b - c)*(b - c)^2*(a^4*b^2 - a^2*b^4 + a^4*b*c + a^4*c^2 - b^3*c^3 - a^2*c^4)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44042) lies on the incircle and these lines: {11, 2679}, {12, 33330}, {55, 805}, {56, 2698}, {511, 3027}, {512, 3023}, {5148, 6022}, {5217, 38703}, {5432, 22103}, {13183, 31513}, {20403, 33965}

X(44043) = X(11)X(650)∩X(55)X(927)

Barycentrics    (a - b - c)*(b - c)^2*(a^4 - 2*a^3*b + a^2*b^2 - 2*a^3*c + a^2*b*c + b^3*c + a^2*c^2 - 2*b^2*c^2 + b*c^3)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44043) lies on the incircle and these lines: {11, 650}, {12, 33331}, {55, 927}, {56, 2724}, {497, 14732}, {514, 3022}, {516, 1362}, {3322, 30331}, {5432, 40554}, {31891, 40629}

X(44043) = reflection of X(3022) in the Soddy line

X(44044) = X(11)X(6129)∩X(55)X(1309)

Barycentrics    (a - b - c)*(b - c)^2*(a^6 - 2*a^4*b^2 + a^2*b^4 - a^4*b*c + 2*a^3*b^2*c - 2*a*b^4*c + b^5*c - 2*a^4*c^2 + 2*a^3*b*c^2 - 2*a^2*b^2*c^2 + 2*a*b^3*c^2 + 2*a*b^2*c^3 - 2*b^3*c^3 + a^2*c^4 - 2*a*b*c^4 + b*c^5)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44044) lies on the incircle and these lines: {11, 6129}, {12, 39535}, {55, 1309}, {56, 2734}, {515, 1361}, {522, 1364}, {1464, 3324}, {3025, 35013}, {3319, 5882}, {5432, 40558}, {6284, 13756}

X(44045) = X(11)X(5519)∩X(55)X(6078)

Barycentrics    a^2*(a - b - c)*(b - c)^2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3 - 3*a^2*c + a*b*c + 3*a*c^2 - c^3)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44045) lies on the incircle and these lines: {11, 5519}, {55, 6078}, {56, 28914}, {518, 3021}, {1358, 3309}, {3689, 5580}

X(44046) = X(11)X(5516)∩X(55)X(6079)

Barycentrics    (a - b - c)*(b - c)^2*(a^3 + a^2*b + a^2*c - 5*a*b*c + b^2*c + b*c^2)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44046) lies on the incircle and these lines: {11, 5516}, {55, 6079}, {350, 5579}, {519, 6018}, {1357, 3667}, {1358, 4106}, {3021, 4009}, {5577, 24840}, {34194, 34587}

X(44046) = reflection of X(3022) in the Nagel line

X(44047) = X(11)X(35580)∩X(55)X(6081)

Barycentrics    a^2*(a - b - c)*(b - c)^2*(a^8 - 2*a^7*b - 2*a^6*b^2 + 6*a^5*b^3 - 6*a^3*b^5 + 2*a^2*b^6 + 2*a*b^7 - b^8 - 2*a^7*c + 3*a^6*b*c - 7*a^4*b^3*c + 6*a^3*b^4*c + 5*a^2*b^5*c - 4*a*b^6*c - b^7*c - 2*a^6*c^2 + 6*a^4*b^2*c^2 - 6*a^2*b^4*c^2 + 2*b^6*c^2 + 6*a^5*c^3 - 7*a^4*b*c^3 - 2*a^2*b^3*c^3 + 2*a*b^4*c^3 + b^5*c^3 + 6*a^3*b*c^4 - 6*a^2*b^2*c^4 + 2*a*b^3*c^4 - 2*b^4*c^4 - 6*a^3*c^5 + 5*a^2*b*c^5 + b^3*c^5 + 2*a^2*c^6 - 4*a*b*c^6 + 2*b^2*c^6 + 2*a*c^7 - b*c^7 - c^8)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44047) lies on the incircle these lines: {11, 35580}, {55, 6081}, {521, 3318}, {1359, 6001}, {3319, 12680}

X(44048) = X(11)X(31654)∩X(55)X(6082)

Barycentrics    (a - b - c)*(b - c)^2*(a^6 + 2*a^4*b^2 + a^2*b^4 + 10*a^4*b*c - 7*a^2*b^3*c + b^5*c + 2*a^4*c^2 - 7*a^2*b^2*c^2 - 7*a^2*b*c^3 + 2*b^3*c^3 + a^2*c^4 + b*c^5)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44048) lies on the incircle and these lines: {11, 31654}, {12, 6092}, {55, 6082}, {56, 6093}, {524, 6019}, {1499, 3325}

X(44049) = X(11)X(33504)∩X(55)X(2867)

Barycentrics    (a - b - c)*(b - c)^2*(a^10 - 2*a^6*b^4 + a^2*b^8 + 2*a^8*b*c - 3*a^6*b^3*c + a^4*b^5*c - a^2*b^7*c + b^9*c - a^6*b^2*c^2 + 2*a^4*b^4*c^2 - a^2*b^6*c^2 - 3*a^6*b*c^3 + 2*a^4*b^3*c^3 + a^2*b^5*c^3 - 2*a^6*c^4 + 2*a^4*b^2*c^4 + a^4*b*c^5 + a^2*b^3*c^5 - 2*b^5*c^5 - a^2*b^2*c^6 - a^2*b*c^7 + a^2*c^8 + b*c^9)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44049) lies on the incircle these lines: {11, 33504}, {55, 2867}, {525, 6020}, {1503, 3320}

X(44050) = X(11)X(35581)∩X(55)X(16170)

Barycentrics    a^2*(a - b - c)*(b - c)^2*(a^12*b^2 - 5*a^10*b^4 + 10*a^8*b^6 - 10*a^6*b^8 + 5*a^4*b^10 - a^2*b^12 + a^12*b*c - 4*a^10*b^3*c + 6*a^8*b^5*c - 4*a^6*b^7*c + a^4*b^9*c + a^12*c^2 - 2*a^10*b^2*c^2 + 2*a^8*b^4*c^2 - 4*a^6*b^6*c^2 + 5*a^4*b^8*c^2 - 2*a^2*b^10*c^2 - 4*a^10*b*c^3 + 6*a^8*b^3*c^3 - 4*a^6*b^5*c^3 + 5*a^4*b^7*c^3 - 2*a^2*b^9*c^3 - b^11*c^3 - 5*a^10*c^4 + 2*a^8*b^2*c^4 + 8*a^6*b^4*c^4 - 7*a^4*b^6*c^4 + 2*a^2*b^8*c^4 + 6*a^8*b*c^5 - 4*a^6*b^3*c^5 - 7*a^4*b^5*c^5 + 2*a^2*b^7*c^5 + 4*b^9*c^5 + 10*a^8*c^6 - 4*a^6*b^2*c^6 - 7*a^4*b^4*c^6 + 2*a^2*b^6*c^6 - 4*a^6*b*c^7 + 5*a^4*b^3*c^7 + 2*a^2*b^5*c^7 - 6*b^7*c^7 - 10*a^6*c^8 + 5*a^4*b^2*c^8 + 2*a^2*b^4*c^8 + a^4*b*c^9 - 2*a^2*b^3*c^9 + 4*b^5*c^9 + 5*a^4*c^10 - 2*a^2*b^2*c^10 - b^3*c^11 - a^2*c^12)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44050) lies on the incircle and these lines: {11, 35581}, {55, 16170}, {56, 16169}, {526, 33965}, {5663, 33964}

X(44051) = X(11)X(35582)∩X(55)X(20404)

Barycentrics    (a - b - c)*(b - c)^2*(a^10 - 2*a^6*b^4 + a^2*b^8 + 4*a^8*b*c - 6*a^6*b^3*c + 4*a^4*b^5*c - 3*a^2*b^7*c + b^9*c - 2*a^6*b^2*c^2 + 4*a^4*b^4*c^2 - 3*a^2*b^6*c^2 - 6*a^6*b*c^3 + 4*a^4*b^3*c^3 + a^2*b^5*c^3 - 2*a^6*c^4 + 4*a^4*b^2*c^4 + a^2*b^4*c^4 + 4*a^4*b*c^5 + a^2*b^3*c^5 - 2*b^5*c^5 - 3*a^2*b^2*c^6 - 3*a^2*b*c^7 + a^2*c^8 + b*c^9)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44051) lies on the incircle and these lines: {11, 35582}, {55, 20404}, {542, 6023}, {690, 6027}, {804, 33965}, {2782, 33964}

X(44052) = X(11)X(35587)∩X(900)X(3025)

Barycentrics    (a - b - c)*(b - c)^2*(a^6 - 2*a^4*b^2 + a^2*b^4 - 2*a^4*b*c + 4*a^3*b^2*c + a^2*b^3*c - 4*a*b^4*c + b^5*c - 2*a^4*c^2 + 4*a^3*b*c^2 - 7*a^2*b^2*c^2 + 4*a*b^3*c^2 + a^2*b*c^3 + 4*a*b^2*c^3 - 2*b^3*c^3 + a^2*c^4 - 4*a*b*c^4 + b*c^5)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44052) lies on the incircle and these lines: {11, 35587}, {900, 3025}, {952, 13756}, {6018, 12743}

X(44052) = reflection of X(3025) in the X(1)X(5) line

X(44053) = X(11)X(35591)∩X(12)X(33333)

Barycentrics    a^2*(a - b - c)*(b - c)^2*(a^12*b^2 - 5*a^10*b^4 + 10*a^8*b^6 - 10*a^6*b^8 + 5*a^4*b^10 - a^2*b^12 + a^12*b*c - 4*a^10*b^3*c + 6*a^8*b^5*c - 4*a^6*b^7*c + a^4*b^9*c + a^12*c^2 - 6*a^10*b^2*c^2 + 10*a^8*b^4*c^2 - 4*a^6*b^6*c^2 - 3*a^4*b^8*c^2 + 2*a^2*b^10*c^2 - 4*a^10*b*c^3 + 6*a^8*b^3*c^3 - 3*a^4*b^7*c^3 + 2*a^2*b^9*c^3 - b^11*c^3 - 5*a^10*c^4 + 10*a^8*b^2*c^4 - 4*a^6*b^4*c^4 + a^4*b^6*c^4 - 2*a^2*b^8*c^4 + 6*a^8*b*c^5 + a^4*b^5*c^5 - 2*a^2*b^7*c^5 + 4*b^9*c^5 + 10*a^8*c^6 - 4*a^6*b^2*c^6 + a^4*b^4*c^6 + 2*a^2*b^6*c^6 - 4*a^6*b*c^7 - 3*a^4*b^3*c^7 - 2*a^2*b^5*c^7 - 6*b^7*c^7 - 10*a^6*c^8 - 3*a^4*b^2*c^8 - 2*a^2*b^4*c^8 + a^4*b*c^9 + 2*a^2*b^3*c^9 + 4*b^5*c^9 + 5*a^4*c^10 + 2*a^2*b^2*c^10 - b^3*c^11 - a^2*c^12)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44053) lies on the incircle and these lines: {11, 35591}, {12, 33333}, {56, 15907}, {1154, 7159}, {1510, 3327}

X(44054) = X(526)X(3025)∩X(900)X(33965)

Barycentrics    a^2*(a - b - c)*(b - c)^2*(a^2 - b^2 + b*c - c^2)^2*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^5*c + 2*a^3*b^2*c - 2*a^2*b^3*c + 2*b^5*c - a^4*c^2 + 2*a^3*b*c^2 - a^2*b^2*c^2 + 2*a*b^3*c^2 - b^4*c^2 + 4*a^3*c^3 - 2*a^2*b*c^3 + 2*a*b^2*c^3 - 4*b^3*c^3 - a^2*c^4 - b^2*c^4 - 2*a*c^5 + 2*b*c^5 + c^6)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44054) lies on the incircle and these lines: {526, 3025}, {900, 33965}, {952, 33964}, {2771, 31524}, {5663, 13756}, {8674, 31522}

X(44054) = reflection of X(33965) in the X(1)X(5) line

X(44055) = X(55)X(35011)∩X(1361)X(25485)

Barycentrics    a^2*(a - b - c)*(b - c)^2*(a^8 - 2*a^7*b - 2*a^6*b^2 + 6*a^5*b^3 - 6*a^3*b^5 + 2*a^2*b^6 + 2*a*b^7 - b^8 - 2*a^7*c + 6*a^6*b*c - 2*a^5*b^2*c - 11*a^4*b^3*c + 10*a^3*b^4*c + 4*a^2*b^5*c - 6*a*b^6*c + b^7*c - 2*a^6*c^2 - 2*a^5*b*c^2 + 11*a^4*b^2*c^2 - 2*a^3*b^3*c^2 - 10*a^2*b^4*c^2 + 4*a*b^5*c^2 + b^6*c^2 + 6*a^5*c^3 - 11*a^4*b*c^3 - 2*a^3*b^2*c^3 + 8*a^2*b^3*c^3 - b^5*c^3 + 10*a^3*b*c^4 - 10*a^2*b^2*c^4 - 6*a^3*c^5 + 4*a^2*b*c^5 + 4*a*b^2*c^5 - b^3*c^5 + 2*a^2*c^6 - 6*a*b*c^6 + b^2*c^6 + 2*a*c^7 + b*c^7 - c^8)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1907.

X(44055) lies on the incircle and these lines: {55, 35011}, {1361, 25485}, {2800, 3319}, {2818, 13756}, {3025, 8677}, {3326, 3738}

X(44056) = X(5)X(51)∩X(23)X(1493)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 7*a^4*b^4*c^2 - 2*a^2*b^6*c^2 - 2*b^8*c^2 + 2*a^6*c^4 + 7*a^4*b^2*c^4 + a^2*b^4*c^4 + b^6*c^4 + 2*a^4*c^6 - 2*a^2*b^2*c^6 + b^4*c^6 - 3*a^2*c^8 - 2*b^2*c^8 + c^10) : :
X(44056) = 3 X[51] - 2 X[13365], 3 X[51] - X[21230], 3 X[52] + X[43581], 3 X[143] - 2 X[973], X[195] + 3 X[3060], 3 X[195] + X[13423], X[1493] + 2 X[16982], 9 X[3060] - X[13423], 3 X[3060] - X[32196], 5 X[3567] - X[12307], 3 X[5946] - X[7691], X[6153] - 3 X[21849], 3 X[7730] + X[12316], 9 X[11002] - X[12325], 2 X[12242] + X[13421], 3 X[13363] - 2 X[32348], 3 X[13364] - 2 X[13565], X[13423] - 3 X[32196], 3 X[20424] - X[43581]

See Antreas Hatzipolakis and Peter Moses, euclid 1909.

X(44056) lies on these lines: {5, 51}, {23, 1493}, {30, 10115}, {54, 2937}, {156, 195}, {511, 8254}, {568, 43816}, {1112, 2914}, {3519, 7533}, {3567, 12307}, {3581, 12006}, {5446, 32423}, {5946, 7691}, {6102, 15800}, {6153, 21849}, {6288, 18427}, {6689, 10627}, {6746, 12300}, {7512, 10610}, {7545, 13368}, {7730, 12316}, {10628, 11262}, {11002, 12325}, {11802, 16881}, {11803, 25338}, {12242, 13421}, {12291, 26864}, {13363, 32348}, {14449, 22051}, {36853, 38898}

X(44056) = midpoint of X(i) and X(j) for these {i,j}: {52, 20424}, {54, 10263}, {195, 32196}, {6102, 15800}, {13368, 15801}, {14449, 22051}, {36853, 38898}
X(44056) = reflection of X(i) in X(j) for these {i,j}: {1209, 10095}, {10627, 6689}, {11802, 16881}, {21230, 13365}
X(44056) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {51, 21230, 13365}, {195, 3060, 32196}

X(44057) = X(4)X(54)∩X(30)X(18402)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^12*b^2 - 4*a^10*b^4 + 5*a^8*b^6 - 5*a^4*b^10 + 4*a^2*b^12 - b^14 + a^12*c^2 - 6*a^10*b^2*c^2 + 10*a^8*b^4*c^2 - 7*a^6*b^6*c^2 + 6*a^4*b^8*c^2 - 7*a^2*b^10*c^2 + 3*b^12*c^2 - 4*a^10*c^4 + 10*a^8*b^2*c^4 - 4*a^6*b^4*c^4 - a^4*b^6*c^4 + 2*a^2*b^8*c^4 - 3*b^10*c^4 + 5*a^8*c^6 - 7*a^6*b^2*c^6 - a^4*b^4*c^6 + 2*a^2*b^6*c^6 + b^8*c^6 + 6*a^4*b^2*c^8 + 2*a^2*b^4*c^8 + b^6*c^8 - 5*a^4*c^10 - 7*a^2*b^2*c^10 - 3*b^4*c^10 + 4*a^2*c^12 + 3*b^2*c^12 - c^14) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1909.

X(44057) lies on the cubic K464 and these lines: {4, 54}, {30, 18402}, {133, 35592}, {137, 403}, {143, 6798}, {186, 16337}, {1263, 32215}, {1986, 14106}, {6368, 18314}, {6801, 37766}, {21268, 32410}, {33643, 37943}

X(44057) = polar circle inverse of X(54)
X(44057) = orthic isogonal conjugate of X(10214)
X(44057) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 10214}, {37766, 11062}
X(44057) = X(2169)-isoconjugate of X(39431)
X(44057) = crossdifference of every pair of points on line {14533, 17434}
X(44057) = barycentric quotient X(53)/X(39431)

X(44058) = X(30)X(5171)∩X(32)X(1316)

Barycentrics   a^12 - 2*a^10*b^2 + a^4*b^8 - 2*a^10*c^2 + 3*a^8*b^2*c^2 + a^6*b^4*c^2 - 2*a^2*b^8*c^2 + a^6*b^2*c^4 - 4*a^4*b^4*c^4 + 2*a^2*b^6*c^4 - 2*b^8*c^4 + 2*a^2*b^4*c^6 + 4*b^6*c^6 + a^4*c^8 - 2*a^2*b^2*c^8 - 2*b^4*c^8 : :

See Antreas Hatzipolakis and Peter Moses, euclid 1913.

X(44058) lies on these lines: {30, 5171}, {32, 1316}, {182, 523}, {1078, 36163}, {1691, 2453}, {2452, 5034}, {7793, 36181}, {7815, 11007}, {10796, 15539}, {13356, 36157}, {32761, 36822}

X(44059) = ISOGONAL CONJUGATE OF X(8760)

Barycentrics    a*(a - b)*(a - c)*(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5 - a^4*c - 2*a^3*b*c + 2*a^2*b^2*c - 2*a*b^3*c - b^4*c + 2*a*b*c^3 - a*c^4 - b*c^4 + c^5)*(a^5 - a^4*b - a*b^4 + b^5 + a^4*c - 2*a^3*b*c + 2*a*b^3*c - b^4*c - 2*a^3*c^2 + 2*a^2*b*c^2 - 2*a^2*c^3 - 2*a*b*c^3 + a*c^4 - b*c^4 + c^5) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1915.

X(44059) lies on the circumcircle and these lines: {3, 43363}, {4, 20623}, {103, 18446}, {104, 5848}, {105, 5603}, {929, 1633}, {1295, 5759}, {11456, 32726}

X(44059) = reflection of X(i) in X(j) for these {i,j}: {4, 20623}, {43363, 3}
X(44059) = isogonal conjugate of X(8760)
X(44059) = Thomson-isogonal conjugate of X(44670)
X(44059) = Collings transform of X(20623)
X(44059) = Λ(PU(125))
X(44059) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8760}, {513, 2000}, {650, 2002}
X(44059) = trilinear pole of line X6)X(8758)
X(44059) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 8760}, {101, 2000}, {109, 2002}

X(44060) = X(3)X(5896)∩X(74)X(1498)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(3*a^4 - 6*a^2*b^2 + 3*b^4 + 2*a^2*c^2 + 2*b^2*c^2 - 5*c^4)*(3*a^4 + 2*a^2*b^2 - 5*b^4 - 6*a^2*c^2 + 2*b^2*c^2 + 3*c^4) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1915.

X(44060) lies on the circumcircle and these lines: {3, 5896}, {74, 1498}, {98, 38253}, {110, 13302}, {1294, 3529}, {1297, 9909}, {1301, 5502}, {1302, 35311}, {2373, 35510}, {2693, 12096}, {2697, 5159}, {7396, 34168}

X(44060) = reflection of X(5896) in X(3)
X(44060) = X(15750)-cross conjugate of X(250)
X(44060) = cevapoint of X(154) and X(647)
X(44060) = Λ(radical axis of circumcircle and midheight circle)
X(44060) = trilinear pole of line X(6)X(1204)
X(44060) = X(i)-isoconjugate of X(j) for these (i,j): {162, 13611}, {525, 18594}, {656, 3146}, {1577, 38292}, {8611, 18624}, {24018, 33630}
X(44060) = barycentric product X(i)*X(j) for these {i,j}: {107, 36609}, {110, 38253}, {112, 35510}, {648, 3532}, {1301, 40170}
X(44060) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 3146}, {647, 13611}, {1301, 14572}, {1576, 38292}, {3532, 525}, {15400, 14638}, {32676, 18594}, {32713, 33630}, {35510, 3267}, {36609, 3265}, {38253, 850}

X(44061) = X(3)X(9076)∩X(5)X(111)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 2*a^4*c^2 - a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6)*(a^6 - 2*a^4*b^2 - 2*a^2*b^4 + b^6 - a^4*c^2 - a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1915.

X(44061) lies on the circumcircle and these lines: {3, 9076}, {5, 111}, {74, 32233}, {98, 35921}, {110, 32312}, {376, 29011}, {691, 14570}, {733, 10796}, {755, 1352}, {930, 11634}, {933, 4235}, {935, 1634}, {1141, 43084}, {1291, 7472}, {2070, 2770}, {2373, 7488}, {2374, 3518}, {3563, 7576}, {9084, 13595}, {10102, 37760}, {12107, 43663}, {12122, 14388}, {12584, 36833}, {37943, 40119}

X(44061) = reflection of X(9076) in X(3)
X(44061) = Thomson isogonal conjugate of X(9019)
X(44061) = Collings transform of X(37454)
X(44061) = X(798)-isoconjugate of X(11056)
X(44061) = cevapoint of X(i) and X(j) for these (i,j): {523, 37454}, {599, 2525}
X(44061) = trilinear pole of line X(6)X(16511)
X(44061) = barycentric quotient X(99)/X(11056)

X(44062) = X(2)X(15240)∩X(74)X(12118)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 6*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 6*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 6*a^4*b^2*c^4 - 6*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 6*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 6*a^6*b^2*c^2 - 6*a^4*b^4*c^2 + 6*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 2*a^4*b^2*c^4 - 6*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 6*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10) : :
X(44062) = 3 X[2] - 4 X[15240]

See Antreas Hatzipolakis and Peter Moses, euclid 1915.

X(44062) lies on the circumcircle and these lines: {2, 15240}, {74, 12118}, {110, 13223}, {1299, 35471}, {1300, 12084}, {2374, 26284}, {3563, 7391}, {21213, 40120}, {37978, 40118}

X(44062) = anticomplement of X(15241)
X(44062) = reflection of X(15241) in X(15240)
X(44062) = Collings transform of X(6640)
X(44062) = cevapoint of X(523) and X(6640)
X(44062) = circumnormal-isogonal conjugate of X(45780)
X(44062) = circumcircle antipode of X(45780)
X(44062) = {X(15240),X(15241)}-harmonic conjugate of X(2)

X(44063) = X(74)X(1071)∩X(105)X(7965)

Barycentrics    a*(a - b)*(a - c)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*b*c + a^3*b^2*c + a^2*b^3*c - a*b^4*c - a^4*c^2 - 3*a^3*b*c^2 + 4*a^2*b^2*c^2 + a*b^3*c^2 - b^4*c^2 - 3*a^2*b*c^3 + a*b^2*c^3 - a^2*c^4 - a*b*c^4 - b^2*c^4 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*b*c - 3*a^3*b^2*c - 3*a^2*b^3*c - a*b^4*c - a^4*c^2 + a^3*b*c^2 + 4*a^2*b^2*c^2 + a*b^3*c^2 - b^4*c^2 + a^2*b*c^3 + a*b^2*c^3 - a^2*c^4 - a*b*c^4 - b^2*c^4 + c^6) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1915.

X(44063) lies on the circumcircle and these lines: {3, 43659}, {74, 1071}, {102, 16132}, {105, 7965}, {1295, 30264}, {1297, 30271}, {2752, 14083}, {5951, 11491}

X(44063) = reflection of X(43659) in X(3)
X(44063) = Collings transform of X(33178)
X(44063) = cevapoint of X(513) and X(33178)

X(44064) = X(3)X(39437)∩X(20)X(1299)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 8*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 8*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 10*a^4*b^2*c^4 - 10*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 8*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 8*a^6*b^2*c^2 - 10*a^4*b^4*c^2 + 8*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 2*a^4*b^2*c^4 - 10*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 8*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1915.

X(44064) lies on the circumcircle and these lines: {3, 39437}, {20, 1299}, {22, 40120}, {74, 11411}, {1300, 11413}, {1301, 30512}, {1370, 3563}, {2374, 26283}, {2383, 12225}, {4226, 39417}, {11634, 30251}, {15329, 30249}, {16386, 32710}, {16387, 40119}, {22239, 40049}, {37929, 40118}

X(44064) = reflection of X(39437) in X(3)
X(44064) = Collings transform of X(3548)
X(44064) = cevapoint of X(523) and X(3548)
X(44064) = trilinear pole of line X(6)X(9820)

X(44065) = X(20)X(759)∩X(915)X(3561)

Barycentrics    a*(a - b)*(a - c)*(a^6 - a^5*b - a^4*b^2 + 2*a^3*b^3 - a^2*b^4 - a*b^5 + b^6 - 2*a^4*b*c + a^3*b^2*c + 3*a^2*b^3*c - a*b^4*c - b^5*c - a^4*c^2 - a^3*b*c^2 + 4*a^2*b^2*c^2 + 3*a*b^3*c^2 - b^4*c^2 - a^2*b*c^3 + a*b^2*c^3 + 2*b^3*c^3 - a^2*c^4 - 2*a*b*c^4 - b^2*c^4 - b*c^5 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^5*c - 2*a^4*b*c - a^3*b^2*c - a^2*b^3*c - 2*a*b^4*c - b^5*c - a^4*c^2 + a^3*b*c^2 + 4*a^2*b^2*c^2 + a*b^3*c^2 - b^4*c^2 + 2*a^3*c^3 + 3*a^2*b*c^3 + 3*a*b^2*c^3 + 2*b^3*c^3 - a^2*c^4 - a*b*c^4 - b^2*c^4 - a*c^5 - b*c^5 + c^6) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1915.

X(44065) lies on the circumcircle and these lines: {3, 39439}, {20, 759}, {104, 30267}, {107, 13589}, {915, 3651}, {1301, 4242}, {1304, 36167}, {2071, 12030}, {4220, 15344}, {9061, 26253}, {11413, 39435}, {14987, 30268}, {22239, 37964}

X(44065) = reflection of X(39439) in X(3)
X(44065) = cevapoint of X(3) and X(6003)

X(44066) = X(3)X(43657)∩X(548)X(1141)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 7*a^4*c^2 + 5*a^2*b^2*c^2 - 7*b^4*c^2 + 11*a^2*c^4 + 11*b^2*c^4 - 5*c^6)*(a^6 - 7*a^4*b^2 + 11*a^2*b^4 - 5*b^6 - a^4*c^2 + 5*a^2*b^2*c^2 + 11*b^4*c^2 - a^2*c^4 - 7*b^2*c^4 + c^6) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1915.

X(44066) lies on the circumcircle and these lines: {3, 43657}, {548, 1141}, {550, 13597}, {2383, 14865}, {5966, 14706}, {14979, 35452}, {23096, 37920}, {33643, 34864}

X(44066) = reflection of X(43657) in X(3)

X(44067) = X(54)X(2575)∩X(110)X(1113)

Barycentrics    a^2*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(-((a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)) + a^2*(-a^2 + b^2 + c^2)*(1 - J)) : :

See Tran Viet Hung and Peter Moses, euclid 1936.

X(44067) lies on these lines: {54, 2575}, {110, 1113}, {184, 31954}, {186, 323}, {576, 24650}, {1092, 25407}, {1114, 15463}, {1312, 32423}, {1347, 13415}, {3357, 32616}, {8116, 15462}, {13414, 34507}, {14500, 18400}

X(44067) = reflection of X(44068) in X(11597)
X(44067) = {X(186),X(3043)}-harmonic conjugate of X(44068)
X(44067) = {X(1151),X(22115)}-harmonic conjugate of X(44068)
X(44067) = X(i)-isoconjugate of X(j) for these (i,j): {94, 2578}, {265, 2588}, {1823, 10412}, {1989, 2582}, {2166, 2574}, {2577, 14592}, {2581, 14582}, {2584, 6344}, {2587, 43083}, {36061, 39240}
X(44067) = barycentric product X(i)*X(j) for these {i,j}: {50, 15164}, {186, 8115}, {323, 1113}, {526, 39298}, {2575, 14590}, {2580, 6149}, {8106, 10411}, {14591, 22340}
X(44067) = barycentric quotient X(i)/X(j) for these {i,j}: {50, 2574}, {186, 2592}, {323, 22339}, {1113, 94}, {2575, 14592}, {2576, 2166}, {6149, 2582}, {8106, 10412}, {8115, 328}, {14590, 15165}, {14591, 1114}, {15164, 20573}, {19627, 42668}, {34397, 8105}, {39298, 35139}, {42667, 14582}
X(44067) = {X(110),X(15461)}-harmonic conjugate of X(1113)

X(44068) = X(54)X(2574)∩X(110)X(1114)

Barycentrics    a^2*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(-((a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)) + a^2*(-a^2 + b^2 + c^2)*(1 + J)) : :

See Tran Viet Hung and Peter Moses, euclid 1936.

X(44068) lies on these lines: {54, 2574}, {110, 1114}, {184, 31955}, {186, 323}, {576, 24651}, {1092, 25408}, {1113, 15463}, {1313, 32423}, {1346, 13414}, {3357, 32617}, {8115, 15462}, {13415, 34507}, {14499, 18400}

X(44068) = reflection of X(44067) in X(11597)
X(44068) = X(i)-isoconjugate of X(j) for these (i,j): {94, 2579}, {265, 2589}, {1822, 10412}, {1989, 2583}, {2166, 2575}, {2576, 14592}, {2580, 14582}, {2585, 6344}, {2586, 43083}, {36061, 39241}
X(44068) = barycentric product X(i)*X(j) for these {i,j}: {50, 15165}, {186, 8116}, {323, 1114}, {526, 39299}, {2574, 14590}, {2581, 6149}, {8105, 10411}, {14591, 22339}
X(44068) = barycentric quotient X(i)/X(j) for these {i,j}: {50, 2575}, {186, 2593}, {323, 22340}, {1114, 94}, {2574, 14592}, {2577, 2166}, {6149, 2583}, {8105, 10412}, {8116, 328}, {14590, 15164}, {14591, 1113}, {15165, 20573}, {19627, 42667}, {34397, 8106}, {39299, 35139}, {42668, 14582}
X(44068) = {X(110),X(15460)}-harmonic conjugate of X(1114)
X(44068) = {X(186),X(3043)}-harmonic conjugate of X(44067)
X(44068) = {X(1151),X(22115)}-harmonic conjugate of X(44067)

X(44069) = ANTIGONAL IMAGE OF X(1276)

Barycentrics    (a^2 + a*b + b^2 - c^2)*(a^2 - b^2 + a*c + c^2)*(-(Sqrt[3]*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*b*c - a^3*b^2*c + a^2*b^3*c + a*b^4*c - a^4*c^2 - a^3*b*c^2 + 4*a^2*b^2*c^2 - a*b^3*c^2 - b^4*c^2 + a^2*b*c^3 - a*b^2*c^3 - a^2*c^4 + a*b*c^4 - b^2*c^4 + c^6)) - 2*(a - b - c)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - a*b*c + b^2*c - a*c^2 + b*c^2 - c^3)*S) : :

X(44069) lies on the cubic K060 and these lines: {5, 6192}, {13, 79}, {14, 39151}, {30, 5673}, {80, 11582}, {265, 36933}, {517, 36932}, {621, 14206}, {5627, 36910}, {7026, 12699}, {11600, 14452}, {34299, 38944}

X(44069) = antigonal image of X(1276)
X(44069) = symgonal image of X(33397)
X(44069) = X(5357)-isoconjugate of X(7060)
X(44069) = cevapoint of X(5673) and X(6192)
X(44069) = barycentric quotient X(i)/X(j) for these {i,j}: {11073, 7060}, {19304, 5357}

X(44070) = ANTIGONAL IMAGE OF X(1277)

Barycentrics    (a^2 + a*b + b^2 - c^2)*(a^2 - b^2 + a*c + c^2)*(-(Sqrt[3]*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*b*c - a^3*b^2*c + a^2*b^3*c + a*b^4*c - a^4*c^2 - a^3*b*c^2 + 4*a^2*b^2*c^2 - a*b^3*c^2 - b^4*c^2 + a^2*b*c^3 - a*b^2*c^3 - a^2*c^4 + a*b*c^4 - b^2*c^4 + c^6)) + 2*(a - b - c)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - a*b*c + b^2*c - a*c^2 + b*c^2 - c^3)*S) : :

X(44070 lies on the cubic K060 and these lines: {5, 6191}, {13, 39150}, {14, 79}, {30, 5672}, {80, 11581}, {265, 36932}, {517, 36933}, {622, 14206}, {5627, 36910}, {7043, 12699}, {11601, 14452}, {34299, 38943}

X(44070) = antigonal image of X(1277)
X(44070) = symgonal image of X(33396)
X(44070) = X(5353)-isoconjugate of X(7059)
X(44070) = cevapoint of X(5672) and X(6191)
X(44070) = barycentric quotient X(i)/X(j) for these {i,j}: {11072, 7059}, {19305, 5353}

X(44071) = ANTIGONAL IMAGE OF X(8444)

Barycentrics    (a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(3*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^4*b*c + a^3*b^2*c - a^2*b^3*c - a*b^4*c - a^4*c^2 + a^3*b*c^2 + a*b^3*c^2 - b^4*c^2 - a^2*b*c^3 + a*b^2*c^3 - a^2*c^4 - a*b*c^4 - b^2*c^4 + c^6) + 2*Sqrt[3]*(a - b - c)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c + a*b*c + b^2*c - a*c^2 + b*c^2 - c^3)*S) : :

X(44071) lies on the cubic K060 and these lines: {13, 80}, {30, 1276}, {79, 11600}, {101, 1141}, {203, 37710}, {265, 17405}, {355, 11752}, {621, 14213}, {1834, 11072}, {11099, 36941}, {11582, 19658}, {34303, 38944}

X(44071) = antigonal image of X(8444)
X(44071) = X(i)-isoconjugate of X(j) for these (i,j): {5353, 7344}, {6149, 17405}
X(44071) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 17405}, {11072, 7344}

X(44072) = ANTIGONAL IMAGE OF X(8454)

Barycentrics    (a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(3*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^4*b*c + a^3*b^2*c - a^2*b^3*c - a*b^4*c - a^4*c^2 + a^3*b*c^2 + a*b^3*c^2 - b^4*c^2 - a^2*b*c^3 + a*b^2*c^3 - a^2*c^4 - a*b*c^4 - b^2*c^4 + c^6) - 2*Sqrt[3]*(a - b - c)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c + a*b*c + b^2*c - a*c^2 + b*c^2 - c^3)*S) : :

X(44072) lies on the cubic K060 and these lines: {14, 80}, {30, 1277}, {79, 11601}, {101, 1141}, {202, 37710}, {265, 17406}, {355, 11789}, {622, 14213}, {1834, 11073}, {11100, 36940}, {11581, 19658}, {34303, 38943}

X(44072) = antigonal image of X(8454)
X(44072) = X(i)-isoconjugate of X(j) for these (i,j): {5357, 7345}, {6149, 17406}
X(44072) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 17406}, {11073, 7345}

X(44073) = CROSSSUM OF X(64) AND X(5923)

Barycentrics    a^2*(3*a^4 - 2*a^2*b^2 - b^4 - 2*a^2*c^2 + 2*b^2*c^2 - c^4)*(a^10*b^2 - 3*a^8*b^4 + 2*a^6*b^6 + 2*a^4*b^8 - 3*a^2*b^10 + b^12 + a^10*c^2 - a^8*b^2*c^2 + 2*a^6*b^4*c^2 - 2*a^4*b^6*c^2 - 3*a^2*b^8*c^2 + 3*b^10*c^2 - 3*a^8*c^4 + 2*a^6*b^2*c^4 + 6*a^2*b^6*c^4 - 5*b^8*c^4 + 2*a^6*c^6 - 2*a^4*b^2*c^6 + 6*a^2*b^4*c^6 + 2*b^6*c^6 + 2*a^4*c^8 - 3*a^2*b^2*c^8 - 5*b^4*c^8 - 3*a^2*c^10 + 3*b^2*c^10 + c^12)::

X(44073) = Q(X(20)), where Q is defined at X(34815).

X(44073) lies on these lines: {3, 41489}, {20, 14615}, {22, 110}, {3164, 3522}, {3515, 34815}, {10607, 11413}, {31388, 37198}

X(44073) = crosssum of X(64) and X(5922)

X(44074) = CROSSSUM OF X(84) AND X(5923)

Barycentrics    a^2*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c + b^2*c - a*c^2 + b*c^2 - c^3)*(a^7*b - a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 - 3*a^2*b^6 - a*b^7 + b^8 + a^7*c - a^6*b*c + a^5*b^2*c + 3*a^4*b^3*c - 5*a^3*b^4*c - 3*a^2*b^5*c + 3*a*b^6*c + b^7*c - a^6*c^2 + a^5*b*c^2 - 4*a^4*b^2*c^2 + 2*a^3*b^3*c^2 + 7*a^2*b^4*c^2 - 3*a*b^5*c^2 - 2*b^6*c^2 - 3*a^5*c^3 + 3*a^4*b*c^3 + 2*a^3*b^2*c^3 - 2*a^2*b^3*c^3 + a*b^4*c^3 - b^5*c^3 + 3*a^4*c^4 - 5*a^3*b*c^4 + 7*a^2*b^2*c^4 + a*b^3*c^4 + 2*b^4*c^4 + 3*a^3*c^5 - 3*a^2*b*c^5 - 3*a*b^2*c^5 - b^3*c^5 - 3*a^2*c^6 + 3*a*b*c^6 - 2*b^2*c^6 - a*c^7 + b*c^7 + c^8) : :

X(44074) = Q(X(40)), where Q is defined at X(34815).

X(44074) lies on these lines: {3, 1167}, {36, 7114}, {40, 329}, {101, 102}, {165, 1745}, {1617, 9786}, {1785, 5119}

X(44074) = crosssum of X(84) and X(5923)

X(44075) = CROSSSUM OF X(40) AND X(5881)

Barycentrics    a^2*(a^7*b + a^6*b^2 - 3*a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 + 3*a^2*b^6 - a*b^7 - b^8 + a^7*c - 5*a^6*b*c + 3*a^5*b^2*c + 9*a^4*b^3*c - 9*a^3*b^4*c - 3*a^2*b^5*c + 5*a*b^6*c - b^7*c + a^6*c^2 + 3*a^5*b*c^2 - 12*a^4*b^2*c^2 + 6*a^3*b^3*c^2 + 9*a^2*b^4*c^2 - 9*a*b^5*c^2 + 2*b^6*c^2 - 3*a^5*c^3 + 9*a^4*b*c^3 + 6*a^3*b^2*c^3 - 18*a^2*b^3*c^3 + 5*a*b^4*c^3 + b^5*c^3 - 3*a^4*c^4 - 9*a^3*b*c^4 + 9*a^2*b^2*c^4 + 5*a*b^3*c^4 - 2*b^4*c^4 + 3*a^3*c^5 - 3*a^2*b*c^5 - 9*a*b^2*c^5 + b^3*c^5 + 3*a^2*c^6 + 5*a*b*c^6 + 2*b^2*c^6 - a*c^7 - b*c^7 - c^8) : :

X(44075) = Q(X(84)), where Q is defined at X(34815).

X(44075) lies on these lines: {3, 947}, {4, 34589}, {36, 7114}, {40, 145}, {56, 102}, {945, 38667}, {946, 21228}, {1753, 10085}, {12704, 36986}, {34040, 38674}

X(44075) = crosssum of X(40) and X(5881)
X(44075) = {X(3),X(34046)}-harmonic conjugate of X(947)

X(44076) = X(3)X(68)∩X(5)X(49)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^8 - 3*a^6*b^2 + a^4*b^4 - a^2*b^6 + b^8 - 3*a^6*c^2 + a^2*b^4*c^2 - 4*b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 + 6*b^4*c^4 - a^2*c^6 - 4*b^2*c^6 + c^8) : :
X(44076) = 2 X[5] - 3 X[12022], 3 X[5] - 4 X[43575], 4 X[143] - 3 X[7576], 3 X[185] - 2 X[43577], 3 X[381] - 2 X[12134], 3 X[381] - 4 X[12241], 4 X[389] - 3 X[38321], 3 X[568] - 2 X[3575], 3 X[568] - 4 X[13292], 3 X[3060] - 2 X[11819], 7 X[3526] - 12 X[12024], 5 X[3567] - 4 X[31830], 3 X[3830] - 2 X[16655], 5 X[3843] - 6 X[16657], 4 X[3853] - 3 X[16658], 5 X[5076] - 4 X[16621], 4 X[5446] - 3 X[7540], 3 X[5890] - X[12278], 3 X[5890] - 4 X[43588], X[6240] - 4 X[11264], 7 X[9781] - 6 X[13490], 3 X[10116] - X[43577], 3 X[11245] - 2 X[31833], 6 X[11245] - 5 X[37481], 8 X[11745] - 9 X[13321], 3 X[12022] - X[14516], 9 X[12022] - 8 X[43575], X[12278] - 4 X[43588], X[12289] + 2 X[32358], 4 X[12362] - 3 X[23039], 2 X[12370] + X[34799], 4 X[13630] - 3 X[38323], 3 X[14516] - 8 X[43575], 8 X[16656] - 9 X[38335], 4 X[16881] - 3 X[38322], 4 X[17712] - 3 X[36987], 2 X[31831] - 3 X[34664], 4 X[31833] - 5 X[37481]-

See Antreas Hatzipolakis and Peter Moses, euclid 1943.

X(44076) lies on these lines: {3, 68}, {4, 1994}, {5, 49}, {20, 18917}, {30, 5889}, {52, 10112}, {125, 12038}, {140, 26913}, {143, 7576}, {155, 18396}, {156, 403}, {184, 9927}, {185, 10111}, {195, 31724}, {235, 10540}, {378, 32140}, {381, 11426}, {382, 1351}, {389, 38321}, {427, 37472}, {511, 11750}, {539, 5562}, {542, 12162}, {546, 11422}, {550, 41724}, {568, 3575}, {569, 37347}, {578, 5576}, {895, 3521}, {1092, 37452}, {1147, 2072}, {1154, 12225}, {1181, 12293}, {1353, 8537}, {1498, 31725}, {1568, 41597}, {1614, 15761}, {1658, 3580}, {1885, 18439}, {1993, 18569}, {2055, 36245}, {2070, 9920}, {2883, 31726}, {2888, 35921}, {2931, 33563}, {3060, 11819}, {3410, 35500}, {3448, 3520}, {3526, 12024}, {3530, 38397}, {3549, 18925}, {3564, 12605}, {3567, 31830}, {3627, 16659}, {3830, 16655}, {3843, 16657}, {3853, 16658}, {5076, 16621}, {5254, 22146}, {5446, 7540}, {5448, 13851}, {5449, 13367}, {5609, 43865}, {5663, 18560}, {5890, 12278}, {5894, 10620}, {6101, 13470}, {6102, 6240}, {6193, 18531}, {6242, 12899}, {6639, 14852}, {6644, 18912}, {6759, 11799}, {6776, 8548}, {7399, 13353}, {7488, 12254}, {7506, 39571}, {7517, 9833}, {7526, 11442}, {7527, 43818}, {7545, 15873}, {7553, 13142}, {7577, 9545}, {8550, 39562}, {9140, 43608}, {9544, 16868}, {9703, 9820}, {9704, 10254}, {9707, 10201}, {9781, 13490}, {10018, 32171}, {10020, 11464}, {10114, 11562}, {10224, 16000}, {10226, 10264}, {10539, 18390}, {10619, 18475}, {10627, 11565}, {10897, 35836}, {10898, 35837}, {10938, 12421}, {11245, 31833}, {11381, 12897}, {11432, 14542}, {11449, 26917}, {11457, 12084}, {11564, 16665}, {11585, 22115}, {11745, 13321}, {12121, 43616}, {12233, 15087}, {12362, 23039}, {12383, 22467}, {12428, 18455}, {12902, 19362}, {13160, 32046}, {13352, 18381}, {13371, 25739}, {13488, 15531}, {13561, 37118}, {13630, 38323}, {13754, 18563}, {15032, 34007}, {15034, 43866}, {15062, 43895}, {15559, 34514}, {15760, 31804}, {15800, 31802}, {16163, 43604}, {16266, 37444}, {16656, 38335}, {16881, 38322}, {17712, 36987}, {17845, 37489}, {17928, 18952}, {18356, 18570}, {18383, 34986}, {18403, 22660}, {18420, 36753}, {18430, 23047}, {18447, 18970}, {18494, 37493}, {18533, 18951}, {18914, 22663}, {20126, 43903}, {20417, 43907}, {23294, 23336}, {23328, 35498}, {23335, 37495}, {26879, 37814}, {30714, 43817}, {31723, 36747}, {31831, 34664}, {32138, 35491}, {34153, 43615}, {36253, 43839}

X(44076) = midpoint of X(i) and X(j) for these {i,j}: {4, 34799}, {5889, 12289}
X(44076) = reflection of X(i) in X(j) for these {i,j}: {3, 6146}, {4, 12370}, {52, 10112}, {185, 10116}, {3575, 13292}, {5889, 32358}, {6101, 13470}, {6102, 11264}, {6240, 6102}, {6242, 12899}, {7553, 13142}, {10627, 11565}, {11381, 12897}, {11562, 10114}, {12134, 12241}, {12162, 13403}, {14516, 5}, {16659, 3627}, {18436, 12605}, {18439, 1885}, {18563, 21659}, {31656, 32410}
X(44076) = crossdifference of every pair of points on line {2081, 6753}
X(44076) = X(34799)-of-Euler-triangle
X(44076) = X(14516)-of-Johnson-triangle
X(44076) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {49, 265, 5}, {68, 12118, 9932}, {68, 19467, 3}, {155, 18396, 18404}, {184, 9927, 10024}, {427, 43595, 37472}, {567, 6288, 5}, {578, 18474, 5576}, {1899, 12118, 3}, {3575, 13292, 568}, {6193, 18945, 18531}, {9703, 10255, 9820}, {10226, 10264, 43607}, {11245, 31833, 37481}, {12022, 14516, 5}, {12134, 12241, 381}, {12383, 43808, 22467}, {13434, 41171, 5}, {13561, 43394, 37118}, {13851, 43844, 5448}, {14852, 19357, 6639}, {15317, 18445, 12161}, {18350, 43821, 5}, {18533, 18951, 37490}, {23236, 43821, 18350}, {25739, 34148, 13371}, {34782, 41587, 2070}

leftri

Points of the form tgX or gtX, where X is on the Euler line: X(44077)-X(44155)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, August 8-11, 2021.

For any triangle center P, let gP and tP denote the isogonal conjugate of P and the isotomic conjugate of P, respectively. Centers X(44077)-X(44127) are points of the form tg(X), and X(44128)-X(44155) of the form gt(X), where X lies on the Euler line. The appearance of (h,i,j,k,m) in the following list means that X(j) is on the Euler line, and (X(h), X(i), X(j), X(k), X(m)) = (gtX, tX, X, gX, tgX):

(6,2,2,6,76)
(184,264,3,4,69)
(25,69,4,3,264)
(51,95,5,54,311)
(154,253,20,64,14615)
(2194,1441,21,65,314)
(206,18018,22,66,315)
(18374,18019,23,67,316)
(44077,20563,24,68,317)
(1974,305,25,69,4)
(44078,20564,26,70,44128)
(1474,306,27,71,44129)
(2203,20336,28,72,286)
(2299,307,29,73,44130)
(1495,1494,30,74,3260)
(13366,40410,140,1173,1232)
(34397,328,186,265,340)
(9418,18024,237,290,511)
(232,287,297,248,44132)
(26864,36889,376,3426,44133)
(1915,9229,384,695,9230)
(1971,1972,401,1987,44137)
(44089,40708,419,36214,17984)
(1843,1799,427,1176,1235)
(40952,40412,442,1175,1234)
(10311,42313,458,43718,44144)
(44102,30786,468,895,44146)
(11402,8797,631,3527,44149)
(2393,2373,858,1177,1236)
(44123,22339,1113,2574,15164)
(44124,22340,1114,2575,15165)

Recall that if L is a line, then gL and tL are conics, and tgL and gtL are lines. Each X on the Euler lines is given by a combo X(2) + k*(X(3), and the locus of gtX is the line

4*(a^2 + b^2 + c^2)*(2 + 3*k)*S^2 X[6] - 3*a^2*b^2*c^2*(3 + J^2)*k*X[25], which, for each k, is a point on the line X(6)X(25).

The locus of tgX is the line

16*S^4*X[6] - a^2*b^2*c^2*(a^2 + b^2 + c^2)*(J^2 - 9 - 12*k)*X[69], which, for each k, is a point on the line X(6)X(69).

X(44077) = ISOGONAL CONJUGATE OF X(20563)

Barycentrics    a^4*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4) : :

X(44077) lies on these lines: {2, 19128}, {3, 12058}, {4, 569}, {6, 25}, {22, 9967}, {23, 8538}, {24, 52}, {49, 3517}, {54, 7487}, {68, 3542}, {97, 37114}, {110, 6353}, {136, 11547}, {156, 13292}, {182, 427}, {186, 2979}, {235, 6146}, {237, 10316}, {297, 10349}, {343, 468}, {378, 14855}, {393, 14593}, {394, 37488}, {403, 18474}, {419, 2001}, {421, 2052}, {428, 5476}, {460, 2909}, {511, 21213}, {567, 18494}, {577, 3135}, {578, 3575}, {973, 10274}, {1092, 3515}, {1112, 16165}, {1204, 6293}, {1209, 7505}, {1501, 2211}, {1593, 10984}, {1614, 3089}, {1899, 41603}, {1976, 13854}, {1994, 6403}, {2175, 14975}, {2207, 39109}, {2351, 3003}, {2917, 21660}, {3131, 10634}, {3132, 10635}, {3133, 39110}, {3155, 10897}, {3156, 10898}, {3162, 40825}, {3518, 11422}, {3541, 13336}, {4232, 9544}, {5063, 23195}, {5064, 19124}, {5094, 43650}, {5200, 13440}, {5622, 32064}, {5651, 37453}, {6524, 32713}, {6620, 40366}, {6623, 14157}, {6676, 19154}, {6756, 32046}, {6995, 11003}, {7494, 19121}, {7499, 19126}, {8717, 35481}, {8780, 41615}, {9677, 35765}, {10151, 18376}, {11383, 20986}, {11424, 12173}, {11470, 21284}, {11550, 37981}, {11819, 34114}, {12140, 38534}, {12228, 15473}, {12294, 22352}, {13198, 31383}, {13352, 18533}, {13567, 41729}, {13851, 15125}, {14580, 42295}, {15139, 26958}, {15750, 43652}, {18381, 20303}, {19137, 37439}, {27369, 34396}, {32078, 37457}, {32379, 39571}, {32734, 39111}, {33581, 40352}, {34945, 39575}, {37460, 43574}, {37480, 37931}, {41609, 42463}

X(44077) = isogonal conjugate of X(20563)
X(44077) = isogonal conjugate of anticomplement of X(40939)
X(44077) = isogonal conjugate of isotomic conjugate of X(24)
X(44077) = isogonal conjugate of polar conjugate of X(8745)
X(44077) = polar conjugate of isotomic conjugate of X(571)
X(44077) = anticomplement of complementary conjugate of X(40939)
X(44077) = trilinear product X(i)*X(j) for these {i,j}: {19, 571}, {24, 31}, {25, 47}, {32, 1748}, {48, 8745}, {163, 6753}, {317, 560}, {393, 563}, {1096, 1147}, {1973, 1993}, {2148, 14576}, {2180, 8882}, {2333, 18605}, {9247, 11547}
X(44077) = X(i)-Ceva conjugate of X(j) for these (i,j): {24, 571}, {393, 32}
X(44077) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20563}, {3, 20571}, {63, 5392}, {68, 75}, {69, 91}, {76, 1820}, {96, 18695}, {304, 2165}, {326, 847}, {561, 2351}, {925, 14208}, {2168, 28706}, {3267, 36145}, {24018, 30450}, {32132, 33808}
X(44077) = crosspoint of X(i) and X(j) for these (i,j): {6, 34438}, {24, 8745}
X(44077) = crosssum of X(i) and X(j) for these (i,j): {2, 37444}, {339, 3265}, {394, 16391}
X(44077) = barycentric product X(i)*X(j) for these {i,j}: {3, 8745}, {4, 571}, {6, 24}, {19, 47}, {25, 1993}, {31, 1748}, {32, 317}, {52, 8882}, {54, 14576}, {68, 36416}, {107, 30451}, {110, 6753}, {112, 924}, {136, 23357}, {158, 563}, {184, 11547}, {371, 5412}, {372, 5413}, {393, 1147}, {512, 41679}, {648, 34952}, {1304, 14397}, {1609, 34756}, {1783, 34948}, {1824, 18605}, {1974, 7763}, {2180, 2190}, {2203, 42700}, {2207, 9723}, {2211, 31635}, {2965, 14111}, {14591, 43088}, {15423, 32734}, {18883, 34397}
X(44077) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 20563}, {19, 20571}, {24, 76}, {25, 5392}, {32, 68}, {47, 304}, {52, 28706}, {136, 23962}, {317, 1502}, {560, 1820}, {563, 326}, {571, 69}, {924, 3267}, {1147, 3926}, {1501, 2351}, {1748, 561}, {1973, 91}, {1974, 2165}, {1993, 305}, {2180, 18695}, {2207, 847}, {5412, 34391}, {5413, 34392}, {6753, 850}, {7763, 40050}, {8745, 264}, {8882, 34385}, {11547, 18022}, {14576, 311}, {14585, 16391}, {30451, 3265}, {32713, 30450}, {34397, 37802}, {34948, 15413}, {34952, 525}, {36416, 317}, {36417, 14593}, {41679, 670}
X(44077) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {24, 35603, 52}, {25, 34397, 184}, {52, 34116, 1147}, {184, 1495, 1660}, {184, 1974, 25}, {1501, 2211, 17409}, {5412, 5413, 14576}

X(44078) = ISOGONAL CONJUGATE OF X(20564)

Barycentrics    a^4*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 2*b^6*c^2 - 2*b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8) : :

X(44078) lies on these lines: {2, 43811}, {6, 25}, {26, 34116}, {70, 7505}, {110, 41674}, {156, 32358}, {182, 5133}, {237, 20968}, {343, 19154}, {381, 11572}, {403, 6759}, {418, 9407}, {569, 11818}, {578, 7576}, {1092, 14070}, {1147, 2070}, {1204, 37954}, {1370, 15462}, {1576, 3135}, {1614, 39571}, {1899, 19128}, {1976, 40366}, {2211, 22075}, {3542, 32377}, {5012, 7394}, {6152, 10274}, {7426, 41628}, {7499, 19127}, {7528, 40441}, {9306, 37636}, {9818, 10984}, {10201, 10539}, {10540, 14852}, {11206, 13198}, {11424, 18494}, {13490, 32046}, {15139, 37453}, {19121, 43653}, {21213, 34117}, {22151, 27084}

X(44078) = isogonal conjugate of X(20564)
X(44078) = isogonal conjugate of isotomic conjugate of X(26)
X(44078) = isogonal conjugate of polar conjugate of X(8746)
X(44078) = X(2165)-Ceva conjugate of X(32)
X(44078) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20564}, {70, 75}, {76, 2158}, {1288, 14208}
X(44078) = crosspoint of X(i) and X(j) for these (i,j): {6, 34439}, {26, 8746}
X(44078) = crosssum of X(i) and X(j) for these (i,j): {2, 14790}, {339, 6563}
X(44078) = trilinear product X(i)*X(j) for these {i,j}: {26, 31}, {48, 8746}
X(44078) = barycentric product X(i)*X(j) for these {i,j}: {3, 8746}, {6, 26}, {70, 36418}, {2165, 34116}
X(44078) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 20564}, {26, 76}, {32, 70}, {560, 2158}, {8746, 264}, {34116, 7763}
X(44078) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {154, 34397, 184}, {184, 1974, 51}, {18374, 19153, 1974}

X(44079) = POLAR CONJUGATE OF X(40830)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 4*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

Let A'B'C' be the midheight triangle. Let AB, AC be the orthogonal projections of A' on CA, AB, resp. Define BC, BA, CA, CB cyclically. Let A" = BCBA∩CACB, and define B", C" cyclically. Triangle A"B"C" is homothetic to the orthic triangle at X(44079). (Randy Hutson, August 24, 2021)

X(44079) lies on these lines: {2, 12058}, {4, 5943}, {6, 25}, {24, 13346}, {52, 21841}, {181, 2212}, {185, 235}, {186, 36987}, {237, 22401}, {373, 427}, {389, 3089}, {394, 11470}, {403, 15030}, {460, 15575}, {468, 3917}, {511, 6353}, {1112, 5642}, {1196, 2211}, {1395, 3271}, {1585, 12298}, {1586, 12299}, {1593, 17825}, {1596, 9730}, {1597, 5892}, {1598, 5462}, {1853, 11381}, {1899, 41735}, {2356, 23638}, {3060, 4232}, {3088, 11695}, {3167, 21313}, {3168, 43976}, {3517, 5446}, {3542, 5562}, {3819, 38282}, {5200, 6291}, {5640, 6995}, {5650, 37453}, {5889, 16879}, {5891, 37942}, {5907, 6622}, {6000, 6623}, {6403, 21849}, {6524, 41762}, {6525, 6620}, {6677, 37511}, {6688, 8889}, {6754, 16240}, {6756, 11750}, {7378, 11451}, {7398, 9822}, {7487, 10110}, {7507, 27355}, {7714, 11179}, {7715, 10095}, {7718, 23841}, {8754, 14569}, {8780, 34382}, {9967, 10154}, {10151, 32062}, {10539, 21651}, {10565, 11574}, {10601, 19124}, {11363, 16980}, {12133, 17853}, {13598, 27082}, {15462, 41671}, {16194, 37984}, {21746, 40976}, {21971, 31670}, {26958, 34146}, {30443, 34944}, {32263, 41588}, {35603, 43844}, {36417, 42295}, {37643, 41715}, {37894, 40413}

X(44079) = polar conjugate of X(40830)
X(44079) = isogonal conjugate of isotomic conjugate of X(235)
X(44079) = polar conjugate of isotomic conjugate of X(800)
X(44079) = X(i)-Ceva conjugate of X(j) for these (i,j): {235, 800}, {6529, 2489}, {30249, 647}
X(44079) = X(i)-isoconjugate of X(j) for these (i,j): {48, 40830}, {63, 801}, {69, 775}, {304, 41890}, {326, 1105}, {821, 3964}
X(44079) = crosspoint of X(i) and X(j) for these (i,j): {4, 41489}, {6, 43695}, {25, 6524}
X(44079) = crosssum of X(i) and X(j) for these (i,j): {2, 11413}, {3, 37669}, {69, 3964}
X(44079) = barycentric product X(i)*X(j) for these {i,j}: {4, 800}, {6, 235}, {19, 774}, {25, 13567}, {53, 16035}, {185, 393}, {512, 41678}, {820, 6520}, {1096, 6508}, {1624, 2501}, {1824, 18603}, {1973, 17858}, {2207, 41005}, {2883, 41489}, {3199, 19166}, {6509, 6524}, {13854, 41580}, {14091, 43695}, {14569, 19180}, {40144, 41602}
X(44079) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 40830}, {25, 801}, {185, 3926}, {235, 76}, {774, 304}, {800, 69}, {820, 1102}, {1624, 4563}, {1973, 775}, {1974, 41890}, {2207, 1105}, {6509, 4176}, {13567, 305}, {16035, 34386}, {17858, 40364}, {41580, 34254}, {41678, 670}
X(44079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 51, 1843}, {25, 19118, 154}, {235, 2883, 22970}, {1843, 15010, 51}, {5943, 9729, 18928}, {6620, 34854, 40325}, {13567, 41580, 185}

X(44080) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(378)

Barycentrics    a^4*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 4*b^2*c^2 + c^4) : :

Let A'B'C' be the triangle described in ADGEOM #2697 (8/26/2015, Tran Quang Hung). A'B'C' is homothetic to the anti-Ara triangle at X(44080). (Randy Hutson, August 24, 2021)

X(44080) lies on these lines: {4, 110}, {6, 25}, {22, 37511}, {23, 6403}, {24, 6800}, {32, 40351}, {49, 1598}, {54, 3089}, {112, 9463}, {156, 6756}, {182, 468}, {186, 15080}, {235, 578}, {378, 4550}, {403, 14389}, {421, 43976}, {427, 3818}, {568, 19456}, {569, 3542}, {576, 1112}, {692, 11383}, {974, 11438}, {1092, 1593}, {1204, 7729}, {1351, 41615}, {1397, 14975}, {1597, 22115}, {1614, 7487}, {1885, 13346}, {1968, 35325}, {1993, 40914}, {1995, 39588}, {2935, 15106}, {3047, 8537}, {3051, 17409}, {3091, 22750}, {3135, 26880}, {3147, 13336}, {3148, 14961}, {3292, 12294}, {3515, 10984}, {3516, 43652}, {3520, 7998}, {3575, 6759}, {4232, 11003}, {4846, 18533}, {5012, 6353}, {5094, 5651}, {5622, 37643}, {5640, 37777}, {6622, 13434}, {6623, 15033}, {6995, 9544}, {7493, 19131}, {8717, 10295}, {9465, 41363}, {9703, 18535}, {9826, 12106}, {10117, 37473}, {10250, 12099}, {10274, 11576}, {10540, 18494}, {11250, 13416}, {11382, 19119}, {11424, 37197}, {11425, 38396}, {11470, 19504}, {11472, 15136}, {11550, 32125}, {12165, 17838}, {12173, 26883}, {12192, 16080}, {12324, 43617}, {12828, 37644}, {14826, 28419}, {15018, 37962}, {15056, 30100}, {15139, 36990}, {15920, 43462}, {18385, 18390}, {19126, 41584}, {19127, 41585}, {19154, 37897}, {21284, 35268}, {21766, 35477}, {21841, 32046}, {32235, 32250}, {35473, 41462}, {37453, 43650}, {37933, 40280}

X(44080) = isogonal conjugate of isotomic conjugate of X(378)
X(44080) = polar conjugate of isotomic conjugate of X(5063)
X(44080) = X(i)-Ceva conjugate of X(j) for these (i,j): {378, 5063}, {18850, 577}
X(44080) = X(i)-isoconjugate of X(j) for these (i,j): {63, 34289}, {75, 4846}, {304, 34288}, {1302, 14208}, {3267, 36149}
X(44080) = crossdifference of every pair of points on line {525, 686}
X(44080) = barycentric product X(i)*X(j) for these {i,j}: {4, 5063}, {6, 378}, {25, 15066}, {112, 8675}, {232, 11653}, {648, 42660}, {1974, 32833}, {2203, 42704}, {4846, 36429}, {5891, 8882}, {8749, 10564}
X(44080) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 34289}, {32, 4846}, {378, 76}, {1974, 34288}, {5063, 69}, {5891, 28706}, {8675, 3267}, {15066, 305}, {32833, 40050}, {42660, 525}
X(44080) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 34397, 1974}, {154, 20987, 1495}, {184, 1495, 206}, {184, 1974, 34397}, {1495, 1843, 25}, {4232, 11003, 19128}, {5651, 19124, 5094}, {10539, 13352, 5654}

X(44081) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(379)

Barycentrics    a^2*(a^5 - a*b^4 + a^2*b^2*c - b^4*c + a^2*b*c^2 + 2*a*b^2*c^2 + b^3*c^2 + b^2*c^3 - a*c^4 - b*c^4) : :

X(44081) lies on these lines: {4, 24019}, {6, 25}, {32, 56}, {48, 354}, {65, 1973}, {163, 5398}, {284, 940}, {572, 7580}, {579, 5347}, {604, 1427}, {662, 30962}, {851, 2278}, {942, 2172}, {1400, 9447}, {1449, 1763}, {1836, 2201}, {1837, 7119}, {1914, 2352}, {2185, 37419}, {2187, 2266}, {2260, 4275}, {2360, 4251}, {3002, 11334}, {3198, 3745}, {5546, 19245}, {5802, 37388}, {9247, 40955}, {11365, 22131}

X(44081) = isogonal conjugate of isotomic conjugate of X(379)
X(44081) = crosssum of X(2) and X(31015)
X(44081) = crossdifference of every pair of points on line {525, 1734}
X(44081) = barycentric product X(6)*X(379)
X(44081) = barycentric quotient X(379)/X(76)
X(44081) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 25, 39690}, {910, 1100, 17441}

X(44082) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(382)

Barycentrics    a^2*(3*a^4 - a^2*b^2 - 2*b^4 - a^2*c^2 + 4*b^2*c^2 - 2*c^4) : :
X(44082) = 2 X[6] - 5 X[1974], X[6] + 5 X[20987], 4 X[24] - X[1204], 2 X[24] + X[26883], X[1092] + 2 X[7517], X[1204] + 2 X[26883], X[1974] + 2 X[20987], X[10539] + 2 X[37440]

X(44082) lies on these lines: {2, 6030}, {3, 32062}, {4, 11202}, {6, 25}, {22, 3819}, {23, 2979}, {24, 1204}, {26, 5891}, {125, 6353}, {182, 11451}, {185, 3517}, {186, 11204}, {237, 5206}, {343, 37897}, {373, 3796}, {382, 33556}, {394, 20850}, {403, 18376}, {427, 15448}, {428, 10192}, {462, 5349}, {463, 5350}, {468, 11550}, {511, 35264}, {549, 16654}, {569, 13364}, {576, 9544}, {578, 26882}, {1092, 7517}, {1147, 18378}, {1154, 10539}, {1501, 34481}, {1598, 13367}, {1899, 4232}, {1995, 6688}, {2070, 18435}, {3060, 35265}, {3066, 5644}, {3089, 21659}, {3091, 32340}, {3098, 37913}, {3129, 5238}, {3130, 5237}, {3148, 37512}, {3167, 21969}, {3292, 8780}, {3357, 11270}, {3515, 10606}, {3518, 5890}, {3549, 32332}, {3574, 37122}, {3845, 39242}, {3917, 9909}, {5012, 14002}, {5020, 22112}, {5066, 34513}, {5157, 40670}, {5198, 17821}, {5200, 23253}, {5562, 9714}, {5892, 7506}, {5943, 6800}, {5972, 7391}, {6515, 24981}, {6524, 16240}, {6636, 10546}, {6644, 14855}, {7387, 36987}, {7487, 43831}, {7505, 13419}, {7714, 35260}, {9157, 9998}, {9707, 10110}, {9934, 17853}, {10096, 34514}, {10250, 19128}, {10282, 10594}, {10301, 23292}, {11206, 18950}, {11438, 14157}, {11442, 32223}, {11459, 37939}, {12083, 43586}, {12099, 15647}, {12292, 16219}, {12310, 41619}, {13474, 32534}, {13861, 14845}, {14070, 15030}, {15035, 15682}, {15246, 16187}, {15305, 37940}, {15750, 15811}, {16194, 18324}, {16658, 23329}, {19219, 23275}, {20897, 35007}, {21356, 43653}, {21663, 35450}, {22165, 37904}, {23039, 37956}, {23293, 37760}, {23325, 37943}, {26880, 32078}, {27355, 37476}, {33849, 37687}, {36990, 37453}, {37070, 42400}, {37478, 37936}, {37480, 37925}, {38435, 43614}, {40350, 42295}

X(44082) = isogonal conjugate of isotomic conjugate of X(382)
X(44082) = X(16835)-Ceva conjugate of X(6)
X(44082) = X(i)-isoconjugate of X(j) for these (i,j): {75, 11270}, {14208, 33640}
X(44082) = crosspoint of X(6) and X(43719)
X(44082) = crosssum of X(2) and X(3529)
X(44082) = barycentric product X(i)*X(j) for these {i,j}: {6, 382}, {31, 14212}, {11270, 36431}
X(44082) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 11270}, {382, 76}, {14212, 561}
X(44082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6030, 17508}, {24, 26883, 1204}, {25, 154, 51}, {25, 184, 34417}, {25, 1495, 184}, {25, 9777, 31860}, {25, 26864, 17810}, {51, 154, 184}, {51, 1495, 154}, {184, 34417, 15004}, {186, 11455, 11204}, {5020, 22352, 22112}, {6353, 31383, 125}, {8780, 33586, 3292}, {9909, 35259, 3917}, {10282, 10594, 11424}, {11270, 16835, 3357}, {13366, 26864, 184}, {13595, 26881, 182}, {17810, 26864, 13366}, {26882, 34484, 578}

X(44083) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(383)

Barycentrics    a^2*(Sqrt[3]*(a^8 - a^6*b^2 + 3*a^4*b^4 - 3*a^2*b^6 - a^6*c^2 + 4*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 2*b^6*c^2 + 3*a^4*c^4 + 3*a^2*b^2*c^4 + 4*b^4*c^4 - 3*a^2*c^6 - 2*b^2*c^6) - 2*(a^2 + b^2 + c^2)*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + 4*b^2*c^2 - 2*c^4)*S) : :

X(44083) lies on these lines: {6, 25}, {15, 3148}, {16, 237}, {62, 20897}, {182, 3129}, {263, 3457}, {418, 11516}, {460, 5321}, {462, 1503}, {463, 5480}, {511, 3130}, {1352, 33529}, {1976, 3458}, {2871, 11081}, {3098, 3132}, {3131, 5092}, {5191, 41407}, {5334, 6620}, {6641, 11515}, {10645, 37457}, {10646, 41275}, {11486, 41266}, {34098, 37776}

X(44083) = isogonal conjugate of isotomic conjugate of X(383)
X(44083) = barycentric product X(6)*X(383)
X(44083) = barycentric quotient X(383)/X(76)

X(44084) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(403)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :
X(44084) = 3 X[51] + X[1495], 3 X[403] + X[1986], X[974] - 3 X[16227], X[1514] + 3 X[16227], 3 X[3060] - 4 X[21847], X[3580] + 3 X[12824], 3 X[10151] - X[12133], X[11064] - 3 X[41670], X[11799] + 3 X[16222]

X(44084) lies on these lines: {2, 37511}, {4, 4846}, {6, 25}, {23, 19128}, {24, 5446}, {30, 9826}, {52, 3542}, {107, 421}, {110, 34382}, {113, 403}, {125, 15126}, {136, 6530}, {143, 21841}, {181, 14975}, {185, 26869}, {186, 10564}, {235, 389}, {237, 14961}, {323, 37962}, {373, 5094}, {378, 5892}, {419, 41253}, {420, 33873}, {427, 5943}, {428, 11645}, {460, 512}, {462, 6111}, {463, 6110}, {468, 511}, {685, 13137}, {974, 1514}, {1113, 24651}, {1114, 24650}, {1154, 37942}, {1216, 7505}, {1503, 11746}, {1560, 2679}, {1593, 37475}, {1595, 15026}, {1596, 5946}, {1885, 9729}, {1899, 41580}, {2211, 3124}, {2356, 20962}, {2854, 15471}, {2904, 41597}, {2935, 21663}, {2979, 38282}, {3060, 6353}, {3088, 15024}, {3089, 3567}, {3147, 10625}, {3291, 35325}, {3292, 19504}, {3515, 37497}, {3575, 10110}, {3917, 37453}, {4232, 6403}, {5093, 21313}, {5095, 9027}, {5447, 10018}, {5504, 37951}, {5643, 14865}, {5651, 11470}, {5663, 37984}, {5889, 6622}, {5890, 6623}, {6524, 14593}, {6620, 41370}, {6756, 10095}, {6785, 14165}, {7487, 9781}, {7493, 9967}, {7729, 11381}, {8889, 11451}, {9827, 23411}, {10539, 12235}, {10540, 19456}, {11060, 14581}, {11799, 16222}, {11807, 25564}, {12006, 13488}, {12058, 30771}, {12135, 23841}, {13391, 37935}, {13416, 37911}, {13417, 15131}, {14595, 18384}, {14641, 35490}, {15073, 35260}, {15151, 15311}, {15360, 37943}, {15887, 43831}, {17409, 42295}, {18947, 41724}, {20961, 40976}, {23291, 41715}, {27365, 35264}, {32715, 40388}, {34114, 37440}, {37477, 37933}, {39024, 41363}, {40135, 40352}

X(44084) = midpoint of X(i) and X(j) for these {i,j}: {468, 1112}, {974, 1514}
X(44084) = reflection of X(13416) in X(37911)
X(44084) = polar conjugate of X(40832)
X(44084) = isogonal conjugate of isotomic conjugate of X(403)
X(44084) = polar conjugate of isotomic conjugate of X(3003)
X(44084) = pole wrt polar circle of trilinear polar of X(40832) (line X(69)X(850))
X(44084) = X(i)-Ceva conjugate of X(j) for these (i,j): {403, 3003}, {22239, 647}, {32715, 512}
X(44084) = X(i)-isoconjugate of X(j) for these (i,j): {48, 40832}, {63, 2986}, {69, 36053}, {75, 5504}, {304, 14910}, {326, 1300}, {656, 18878}, {662, 15421}, {687, 24018}, {1577, 43755}, {3265, 36114}, {4592, 15328}, {10420, 14208}, {18879, 20902}, {36062, 39988}
X(44084) = crosspoint of X(i) and X(j) for these (i,j): {4, 8749}, {6, 11744}, {25, 18384}, {250, 32695}
X(44084) = crosssum of X(i) and X(j) for these (i,j): {2, 2071}, {3, 11064}, {125, 41077}
X(44084) = crossdifference of every pair of points on line {394, 525}
X(44084) = barycentric product X(i)*X(j) for these {i,j}: {4, 3003}, {6, 403}, {19, 1725}, {25, 3580}, {107, 686}, {111, 12828}, {113, 8749}, {158, 2315}, {393, 13754}, {512, 16237}, {648, 21731}, {1609, 16172}, {1824, 18609}, {1986, 1989}, {1990, 14264}, {2501, 15329}, {6334, 32713}, {8791, 12824}, {18384, 34834}, {34104, 40388}
X(44084) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 40832}, {25, 2986}, {32, 5504}, {112, 18878}, {403, 76}, {512, 15421}, {686, 3265}, {1576, 43755}, {1725, 304}, {1973, 36053}, {1974, 14910}, {1986, 7799}, {2207, 1300}, {2315, 326}, {2489, 15328}, {3003, 69}, {3580, 305}, {8749, 40423}, {11060, 12028}, {12824, 37804}, {12828, 3266}, {13754, 3926}, {14581, 15454}, {15329, 4563}, {16237, 670}, {18384, 40427}, {21731, 525}, {32713, 687}, {40354, 10419}
X(44084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 34397, 1495}, {51, 34417, 9969}, {186, 15472, 10564}, {373, 12294, 5094}, {1514, 16227, 974}, {1974, 34417, 25}, {2211, 3124, 14580}, {3575, 43823, 10110}, {4232, 11002, 6403}, {9777, 40114, 21639}

X(44085) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(404)

Barycentrics    a^3*(a^3 - a*b^2 + a*b*c + b^2*c - a*c^2 + b*c^2) : :

X(44085) lies on these lines: {2, 5820}, {3, 1408}, {6, 25}, {11, 1746}, {22, 37516}, {31, 692}, {37, 26890}, {42, 2317}, {44, 26885}, {49, 37509}, {54, 65}, {55, 572}, {56, 580}, {57, 36059}, {58, 7428}, {81, 5012}, {110, 6043}, {181, 215}, {182, 940}, {199, 4271}, {209, 2323}, {212, 604}, {226, 5137}, {228, 7113}, {354, 1428}, {386, 1437}, {394, 36741}, {511, 5347}, {569, 5707}, {578, 5706}, {643, 4203}, {1006, 1319}, {1011, 4268}, {1092, 36745}, {1147, 36754}, {1402, 2361}, {1404, 14547}, {1412, 13329}, {1466, 7335}, {1790, 5132}, {1864, 10535}, {1993, 4259}, {2056, 21779}, {2174, 23201}, {2206, 2220}, {2213, 14528}, {2261, 10537}, {2264, 10536}, {2328, 5053}, {2330, 3745}, {2979, 33844}, {3057, 37399}, {3271, 20988}, {3666, 3955}, {3752, 26884}, {3796, 36740}, {3917, 5096}, {4224, 18191}, {4260, 34986}, {4265, 22352}, {4383, 9306}, {4387, 24265}, {4579, 32926}, {4641, 7193}, {4697, 24253}, {5061, 5432}, {5091, 11246}, {5124, 22080}, {5322, 8679}, {5323, 34148}, {5371, 14567}, {5651, 37679}, {5718, 37527}, {5800, 11427}, {10984, 36746}, {11003, 37685}, {13323, 19765}, {13346, 37537}, {14599, 21757}, {18178, 37231}, {19554, 40972}, {20989, 23638}, {22112, 37682}, {23202, 40956}, {23292, 26020}, {34880, 37115}, {37275, 37566}, {37674, 43650}

X(44085) = isogonal conjugate of isotomic conjugate of X(404)
X(44085) = X(i)-Ceva conjugate of X(j) for these (i,j): {3453, 1333}, {7012, 1415}
X(44085) = X(7)-isoconjugate of X(44040)
X(44085) = crosspoint of X(59) and X(163)
X(44085) = crosssum of X(i) and X(j) for these (i,j): {2, 5046}, {11, 1577}
X(44085) = crossdifference of every pair of points on line {525, 3762}
X(44085) = barycentric product X(i)*X(j) for these {i,j}: {6, 404}, {31, 32939}, {1415, 20293}, {2203, 42705}, {7012, 39006}
X(44085) = barycentric quotient X(i)/X(j) for these {i,j}: {41, 44040}, {404, 76}, {32939, 561}, {39006, 17880}
X(44085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 184, 2194}, {81, 5012, 5135}, {212, 604, 2352}, {13366, 40952, 6}

X(44086) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(406)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c - b^2*c - a*c^2 - b*c^2 - c^3) : :

X(44086) lies on these lines: {1, 41609}, {4, 32911}, {6, 25}, {24, 60}, {31, 1195}, {33, 2911}, {42, 2212}, {55, 14975}, {81, 6353}, {213, 607}, {235, 5706}, {406, 5739}, {427, 4383}, {429, 16471}, {451, 32782}, {468, 940}, {608, 2355}, {1061, 41740}, {1172, 4207}, {1185, 2211}, {1191, 11396}, {1193, 22479}, {1203, 7713}, {1386, 41611}, {1395, 2308}, {1593, 36745}, {1598, 37509}, {1783, 7102}, {1829, 16466}, {1885, 37537}, {1892, 34048}, {1993, 35973}, {2204, 2271}, {3194, 37384}, {3515, 36746}, {3517, 36750}, {3542, 5707}, {3681, 6198}, {3690, 7071}, {4232, 37685}, {5089, 16972}, {5094, 37679}, {7378, 14997}, {8889, 37680}, {15750, 37501}, {22131, 26893}, {22132, 26885}, {23122, 26892}, {37453, 37674}, {37633, 38282}

X(44086) = isogonal conjugate of isotomic conjugate of X(406)
X(44086) = polar conjugate of isotomic conjugate of X(36744)
X(44086) = X(406)-Ceva conjugate of X(36744)
X(44086) = crosssum of X(905) and X(26933)
X(44086) = crossdifference of every pair of points on line {525, 4131}
X(44086) = barycentric product X(i)*X(j) for these {i,j}: {4, 36744}, {6, 406}, {9, 1452}, {19, 12514}, {25, 5739}, {1824, 27174}, {2203, 42707}
X(44086) = barycentric quotient X(i)/X(j) for these {i,j}: {406, 76}, {1452, 85}, {5739, 305}, {12514, 304}, {36744, 69}
X(44086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 19118, 2203}, {31, 40976, 11383}, {607, 3195, 1824}, {2299, 3192, 25}

X(44087) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(411)

Barycentrics    a^3*(a^6 - a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - a*b^5 - a^5*c - a^4*b*c + a*b^4*c + b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a^3*c^3 - 2*b^3*c^3 + a^2*c^4 + a*b*c^4 - a*c^5 + b*c^5) : :

X(44087) lies on these lines: {6, 25}, {33, 10537}, {34, 14529}, {54, 36009}, {110, 35996}, {182, 25514}, {198, 6056}, {212, 692}, {223, 36059}, {572, 8021}, {578, 7497}, {580, 859}, {581, 1437}, {1035, 7335}, {1212, 26890}, {1427, 26884}, {1503, 25985}, {1859, 2182}, {1875, 26888}, {1905, 40660}, {2175, 20991}, {2262, 11428}, {2360, 7420}, {3220, 20122}, {3556, 19349}, {4224, 5135}, {4228, 5012}, {5752, 41608}, {7113, 23204}, {9306, 19544}, {14547, 20986}, {18621, 19354}, {19649, 33883}, {23292, 37362}

X(44087) = isogonal conjugate of isotomic conjugate of X(411)
X(44087) = X(24033)-Ceva conjugate of X(1415)
X(44087) = crosssum of X(i) and X(j) for these (i,j): {2, 6895}, {1577, 2968}
X(44087) = barycentric product X(i)*X(j) for these {i,j}: {1, 1630}, {6, 411}, {19, 3561}, {55, 34035}
X(44087) = barycentric quotient X(i)/X(j) for these {i,j}: {411, 76}, {1630, 75}, {3561, 304}, {34035, 6063}
X(44087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 184, 2194}, {10536, 11429, 2182}

X(44088) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(418)

Barycentrics    a^6*(a^2 - b^2 - c^2)^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4) : :

X(44088) lies on these lines: {6, 25}, {182, 20792}, {216, 6751}, {217, 27374}, {237, 6752}, {418, 31353}, {436, 8795}, {1147, 23163}, {1176, 17974}, {1576, 14533}, {1614, 13450}, {3518, 9792}, {6759, 8887}, {10282, 19189}, {14575, 14585}, {20775, 34980}

X(44088) = isogonal conjugate of isotomic conjugate of X(418)
X(44088) = isogonal conjugate of polar conjugate of X(217)
X(44088) = X(184)-Ceva conjugate of X(217)
X(44088) = X(i)-isoconjugate of X(j) for these (i,j): {75, 8795}, {92, 276}, {158, 34384}, {264, 40440}, {275, 1969}, {304, 8794}, {561, 8884}, {822, 42369}, {1577, 42405}, {2167, 18027}, {2190, 18022}, {4602, 15422}, {6521, 34386}, {16813, 20948}, {18833, 19174}, {24018, 42401}
X(44088) = crosspoint of X(i) and X(j) for these (i,j): {184, 14585}, {217, 418}
X(44088) = crosssum of X(i) and X(j) for these (i,j): {264, 18027}, {276, 8795}, {525, 41219}
X(44088) = barycentric product X(i)*X(j) for these {i,j}: {3, 217}, {5, 14585}, {6, 418}, {32, 5562}, {51, 577}, {53, 23606}, {110, 42293}, {184, 216}, {255, 2179}, {343, 14575}, {394, 40981}, {1092, 3199}, {1576, 17434}, {1625, 39201}, {2181, 4100}, {3049, 23181}, {6798, 8565}, {10316, 27372}, {13450, 36433}, {14586, 34983}, {15451, 32661}, {22075, 41168}, {23963, 35442}, {23964, 41219}, {27374, 28724}, {28706, 40373}, {40823, 42353}
X(44088) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 8795}, {51, 18027}, {107, 42369}, {184, 276}, {216, 18022}, {217, 264}, {418, 76}, {577, 34384}, {1501, 8884}, {1576, 42405}, {1974, 8794}, {5562, 1502}, {9247, 40440}, {9426, 15422}, {14574, 16813}, {14575, 275}, {14585, 95}, {23606, 34386}, {32713, 42401}, {34983, 15415}, {40373, 8882}, {40981, 2052}, {41219, 36793}, {41331, 19174}, {42293, 850}

X(44089) = ISOGONAL CONJUGATE OF X(40708)

Barycentrics    a^2*(a^2 - b*c)*(a^2 + b*c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) : :

X(44089) lies on the cubic K1033 and these lines: {2, 37893}, {4, 3398}, {6, 25}, {24, 3095}, {32, 11325}, {112, 5970}, {186, 35002}, {230, 1576}, {237, 10313}, {250, 325}, {378, 26316}, {385, 419}, {403, 6033}, {427, 7792}, {428, 32085}, {460, 6531}, {577, 20885}, {827, 14568}, {1316, 30737}, {1691, 2679}, {2086, 18902}, {2211, 8789}, {2456, 19128}, {2489, 3804}, {2971, 8744}, {3001, 21284}, {3186, 7766}, {3767, 20968}, {4027, 39927}, {5117, 7875}, {5140, 14581}, {5186, 15014}, {5254, 15257}, {5304, 6620}, {5305, 10547}, {6353, 7774}, {7467, 19121}, {7735, 14575}, {7778, 37453}, {10312, 27369}, {10317, 21177}, {12052, 37980}, {12054, 35476}, {12131, 41204}, {16315, 38861}, {16950, 37891}

X(44089) = isogonal conjugate of X(40708)
X(44089) = polar conjugate of X(18896)
X(44089) = isogonal conjugate of isotomic conjugate of X(419)
X(44089) = polar conjugate of isotomic conjugate of X(1691)
X(44089) = polar conjugate of isogonal conjugate of X(14602)
X(44089) = X(419)-Ceva conjugate of X(1691)
X(44089) = X(14602)-cross conjugate of X(1691)
X(44089) = crosspoint of X(i) and X(j) for these (i,j): {6, 43721}, {250, 32696}, {6531, 32085}
X(44089) = crosssum of X(i) and X(j) for these (i,j): {125, 6333}, {3917, 36212}
X(44089) = crossdifference of every pair of points on line {525, 3933}
X(44089) = pole wrt polar circle of trilinear polar of X(18896) (line X(850)X(2528))
X(44089) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40708}, {3, 1934}, {48, 18896}, {63, 1916}, {69, 1581}, {75, 36214}, {256, 337}, {291, 7019}, {295, 7018}, {304, 694}, {305, 1967}, {334, 7015}, {336, 40810}, {525, 37134}, {561, 17970}, {656, 18829}, {805, 14208}, {1927, 40050}, {3708, 39292}, {3933, 43763}, {7116, 18895}, {9468, 40364}
X(44089) = trilinear product X(i)*X(j) for these {i,j}: {4, 1933}, {19, 1691}, {25, 1580}, {31, 419}, {92, 14602}, {162, 5027}, {172, 2201}, {242, 7122}, {385, 1973}, {560, 17984}, {804, 32676}, {1914, 7119}, {1966, 1974}, {1969, 18902}, {2203, 4039}, {2210, 7009}, {4164, 8750}
X(44089) = barycentric product X(i)*X(j) for these {i,j}: {4, 1691}, {6, 419}, {19, 1580}, {25, 385}, {32, 17984}, {92, 1933}, {112, 804}, {171, 2201}, {172, 242}, {232, 40820}, {238, 7119}, {264, 14602}, {648, 5027}, {1474, 4039}, {1783, 4164}, {1840, 5009}, {1914, 7009}, {1966, 1973}, {1974, 3978}, {1976, 39931}, {2086, 18020}, {2207, 12215}, {2211, 14382}, {2489, 17941}, {3563, 12829}, {4027, 17980}, {4107, 8750}, {5026, 8753}, {6531, 36213}, {8623, 32085}, {8744, 36820}, {11325, 39927}, {18022, 18902}, {20964, 31905}, {22061, 34856}, {24284, 32713}, {32542, 41204}
X(44089) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 18896}, {6, 40708}, {19, 1934}, {25, 1916}, {32, 36214}, {112, 18829}, {172, 337}, {250, 39292}, {385, 305}, {419, 76}, {804, 3267}, {1501, 17970}, {1580, 304}, {1691, 69}, {1914, 7019}, {1933, 63}, {1966, 40364}, {1973, 1581}, {1974, 694}, {2086, 125}, {2201, 7018}, {2211, 40810}, {3978, 40050}, {4039, 40071}, {4164, 15413}, {5027, 525}, {7009, 18895}, {7119, 334}, {8623, 3933}, {10311, 8842}, {14599, 7015}, {14601, 15391}, {14602, 3}, {14603, 40360}, {17984, 1502}, {18892, 7116}, {18902, 184}, {32676, 37134}, {32696, 39291}, {36213, 6393}, {36417, 17980}
X(44089) = {X(1974),X(10311)}-harmonic conjugate of X(25)

X(44090) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(420)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 + a^2*b^2 - b^4 + a^2*c^2 - b^2*c^2 - c^4) : :

X(44090) lies on these lines: {2, 37895}, {6, 25}, {39, 11380}, {83, 12143}, {183, 37453}, {186, 9301}, {250, 21284}, {297, 39101}, {385, 468}, {403, 12188}, {419, 39089}, {420, 7779}, {427, 1031}, {685, 36897}, {2207, 33874}, {2211, 32748}, {2967, 19128}, {5064, 37765}, {5094, 11174}, {5201, 37920}, {6240, 13111}, {6353, 7766}, {8743, 11325}, {16318, 39095}, {19556, 41533}, {37197, 39646}, {37912, 41676}

X(44090) = isogonal conjugate of isotomic conjugate of X(420)
X(44090) = polar conjugate of isotomic conjugate of X(2076)
X(44090) = X(i)-Ceva conjugate of X(j) for these (i,j): {420, 2076}, {17980, 25}
X(44090) = X(i)-isoconjugate of X(j) for these (i,j): {63, 11606}, {1799, 17957}, {17949, 34055}
X(44090) = crosssum of X(125) and X(24284)
X(44090) = crossdifference of every pair of points on line {525, 7767}
X(44090) = barycentric product X(i)*X(j) for these {i,j}: {4, 2076}, {6, 420}, {19, 17799}, {25, 7779}, {112, 9479}, {648, 5113}, {1843, 40850}, {3563, 12830}, {8290, 17980}, {17442, 34054}, {17997, 41676}, {18010, 35325}
X(44090) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 11606}, {420, 76}, {1843, 17949}, {2076, 69}, {5113, 525}, {7779, 305}, {9479, 3267}, {17799, 304}, {17980, 9477}, {17997, 4580}

X(44091) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(428)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^2 + b^2 + c^2) : :

X(44091) lies on these lines: {4, 5092}, {6, 25}, {22, 19137}, {23, 11574}, {24, 3098}, {182, 10594}, {187, 27369}, {235, 20300}, {237, 22052}, {373, 5157}, {419, 32085}, {428, 3589}, {468, 34573}, {511, 3518}, {577, 20897}, {800, 34416}, {1176, 5943}, {1209, 18358}, {1511, 11566}, {1598, 12017}, {1976, 33631}, {1995, 19126}, {3089, 18381}, {3129, 11515}, {3130, 11516}, {3148, 10979}, {3517, 33878}, {3618, 7714}, {3619, 6353}, {3620, 4232}, {3630, 41584}, {3819, 41435}, {3867, 10301}, {5085, 5198}, {5140, 38010}, {5480, 13367}, {5651, 37485}, {5888, 37977}, {6756, 37513}, {6995, 15080}, {7487, 11430}, {7505, 42786}, {7545, 19129}, {7576, 19130}, {7713, 16491}, {9822, 13595}, {9967, 37440}, {10282, 14853}, {10564, 37458}, {10986, 41413}, {11387, 37505}, {11424, 23041}, {12106, 37511}, {12272, 32127}, {13417, 38851}, {13562, 32269}, {13861, 19131}, {14561, 37122}, {17508, 35502}, {18533, 43621}, {18912, 39874}, {19128, 34484}, {20190, 26863}, {20772, 32114}, {20832, 33844}, {28666, 39784}, {28708, 31670}, {32217, 41579}, {33578, 40947}, {35259, 37491}, {40325, 41412}, {40981, 42671}

X(44091) = isogonal conjugate of isotomic conjugate of X(428)
X(44091) = polar conjugate of isotomic conjugate of X(5007)
X(44091) = X(428)-Ceva conjugate of X(5007)
X(44091) = X(i)-isoconjugate of X(j) for these (i,j): {63, 10159}, {75, 41435}, {304, 3108}, {656, 35137}, {4592, 31065}, {7953, 14208}
X(44091) = crosssum of X(69) and X(3933)
X(44091) = barycentric product X(i)*X(j) for these {i,j}: {4, 5007}, {6, 428}, {19, 17469}, {25, 3589}, {28, 21802}, {112, 7927}, {393, 22352}, {607, 7198}, {608, 4030}, {648, 8664}, {1974, 39998}, {2207, 7767}, {2333, 17200}, {2489, 10330}, {11205, 32085}
X(44091) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 10159}, {32, 41435}, {112, 35137}, {428, 76}, {1974, 3108}, {2489, 31065}, {3589, 305}, {5007, 69}, {7927, 3267}, {8664, 525}, {11205, 3933}, {17469, 304}, {21802, 20336}, {22352, 3926}, {39998, 40050}
X(44091) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 1974, 1843}, {25, 19118, 7716}, {1974, 8541, 19118}, {7716, 8541, 1843}, {7716, 19118, 8541}, {9969, 18374, 21637}, {10641, 10642, 232}, {13595, 19121, 9822}, {19136, 20987, 6467}

X(44092) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(429)

Barycentrics    a^2*(b + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a*b + b^2 + a*c + c^2) : :

X(44092) lies on these lines: {4, 970}, {6, 25}, {19, 2238}, {24, 13323}, {33, 862}, {81, 7438}, {181, 213}, {209, 21874}, {210, 430}, {235, 5799}, {242, 41234}, {407, 1828}, {427, 5743}, {429, 960}, {468, 6703}, {511, 1812}, {1973, 20970}, {2092, 2354}, {2212, 40984}, {2273, 23638}, {2339, 4199}, {2355, 42067}, {2356, 2653}, {3966, 5130}, {4104, 39579}, {4185, 4383}, {5139, 20623}, {7713, 10974}, {8754, 42072}, {11383, 22080}, {16589, 17442}, {16980, 26377}, {18591, 28266}, {21810, 40966}, {42068, 42071}

X(44092) = polar conjugate of X(40827)
X(44092) = isogonal conjugate of isotomic conjugate of X(429)
X(44092) = polar conjugate of isotomic conjugate of X(2092)
X(44092) = pole wrt polar circle of trilinear polar of X(40827) (line X(850)X(4374))
X(44092) = X(i)-Ceva conjugate of X(j) for these (i,j): {429, 2092}, {1783, 2489}, {40097, 647}, {40976, 3725}
X(44092) = X(i)-isoconjugate of X(j) for these (i,j): {48, 40827}, {63, 14534}, {69, 2363}, {75, 1798}, {86, 1791}, {274, 2359}, {283, 31643}, {304, 1169}, {332, 961}, {662, 15420}, {1220, 1444}, {1240, 1437}, {1790, 30710}, {2298, 17206}, {4581, 4592}, {15419, 36147}
X(44092) = crosspoint of X(i) and X(j) for these (i,j): {4, 1880}, {6, 43703}, {25, 1824}, {1829, 2354}
X(44092) = crosssum of X(i) and X(j) for these (i,j): {2, 16049}, {3, 1812}, {69, 1444}
X(44092) = crossdifference of every pair of points on line {525, 7254}
X(44092) = barycentric product X(i)*X(j) for these {i,j}: {4, 2092}, {6, 429}, {10, 2354}, {19, 2292}, {25, 1211}, {28, 21810}, {34, 21033}, {37, 1829}, {42, 1848}, {92, 3725}, {225, 2269}, {226, 40976}, {278, 40966}, {393, 22076}, {607, 41003}, {608, 3704}, {648, 42661}, {960, 1880}, {1193, 1826}, {1228, 1974}, {1426, 3965}, {1474, 20653}, {1824, 3666}, {1843, 27067}, {1973, 18697}, {2300, 41013}, {2333, 4357}, {4267, 8736}, {7140, 40153}, {8750, 21124}, {20967, 40149}
X(44092) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 40827}, {25, 14534}, {32, 1798}, {213, 1791}, {429, 76}, {444, 8033}, {512, 15420}, {1193, 17206}, {1211, 305}, {1228, 40050}, {1824, 30710}, {1826, 1240}, {1829, 274}, {1848, 310}, {1880, 31643}, {1918, 2359}, {1973, 2363}, {1974, 1169}, {2092, 69}, {2269, 332}, {2292, 304}, {2300, 1444}, {2333, 1220}, {2354, 86}, {2489, 4581}, {3725, 63}, {6371, 15419}, {18697, 40364}, {20653, 40071}, {20967, 1812}, {21033, 3718}, {21810, 20336}, {22076, 3926}, {40966, 345}, {40976, 333}, {42661, 525}

X(44093) = ISOGONAL CONJUGATE OF X(40414)

Barycentrics    a^2*(b + c)*(a^2 - b^2 - c^2)*(2*a^3 + a^2*b + b^3 + a^2*c - b^2*c - b*c^2 + c^3) : :
Trilinears    a ((tan B)/(c + a) + (tan C)/(a + b)) : :

X(44093) lies on these lines: {3, 2327}, {6, 25}, {9, 37225}, {41, 2092}, {48, 18591}, {71, 228}, {101, 2983}, {125, 1213}, {185, 573}, {198, 2245}, {213, 1042}, {219, 22076}, {284, 3145}, {391, 6776}, {407, 1901}, {408, 22344}, {440, 18650}, {572, 13367}, {579, 13738}, {610, 851}, {855, 40979}, {966, 1899}, {1017, 3269}, {1204, 37499}, {1426, 30456}, {1473, 22440}, {1713, 13724}, {1765, 13734}, {1834, 1842}, {2197, 2200}, {2261, 3330}, {2269, 3270}, {2287, 4220}, {3142, 40942}, {3292, 22133}, {3937, 14597}, {5279, 10381}, {5746, 37384}, {5755, 7420}, {5776, 37194}, {5802, 28076}, {5929, 7291}, {9119, 41609}, {11064, 18648}, {13851, 32431}, {18210, 18675}, {18592, 26934}, {21663, 37508}, {21810, 21811}, {22073, 22356}, {22088, 23222}, {23526, 40733}

X(44093) = isogonal conjugate of X(40414)
X(44093) = isogonal conjugate of isotomic conjugate of X(440)
X(44093) = isotomic conjugate of polar conjugate of X(40984)
X(44093) = isogonal conjugate of polar conjugate of X(1834)
X(44093) = X(i)-Ceva conjugate of X(j) for these (i,j): {101, 647}, {1834, 40984}, {2264, 40977}
X(44093) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40414}, {2, 40431}, {27, 1257}, {81, 40445}, {286, 2983}, {951, 31623}
X(44093) = crosspoint of X(i) and X(j) for these (i,j): {6, 71}, {440, 1834}
X(44093) = crosssum of X(i) and X(j) for these (i,j): {2, 27}, {4, 2322}, {333, 18134}
X(44093) = crossdifference of every pair of points on line {447, 525}
X(44093) = trilinear product X(i)*X(j) for these {i,j}: {6, 18673}, {31, 440}, {48, 1834}, {71, 1104}, {73, 2264}, {213, 18650}, {810, 14543}, {950, 1409}, {1333, 21671}, {1842, 3990}, {2200, 17863}
X(44093) = barycentric product X(i)*X(j) for these {i,j}: {1, 18673}, {3, 1834}, {6, 440}, {42, 18650}, {58, 21671}, {63, 40977}, {69, 40984}, {71, 40940}, {72, 1104}, {73, 950}, {228, 17863}, {647, 14543}, {1214, 2264}, {1842, 3682}, {4574, 29162}
X(44093) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40414}, {31, 40431}, {42, 40445}, {228, 1257}, {440, 76}, {1104, 286}, {1834, 264}, {2200, 2983}, {2264, 31623}, {14543, 6331}, {18650, 310}, {18673, 75}, {21671, 313}, {40977, 92}, {40984, 4}
X(44093) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1400, 1409, 1425}

X(44094) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(443)

Barycentrics    a^2*(a^4 - b^4 + 4*a^2*b*c + 4*a*b^2*c + 4*a*b*c^2 + 2*b^2*c^2 - c^4) : :

X(44094) lies on these lines: {1, 7085}, {3, 81}, {6, 25}, {21, 19783}, {22, 37492}, {31, 1475}, {37, 26867}, {42, 604}, {55, 1100}, {56, 228}, {57, 17441}, {65, 1398}, {86, 16353}, {199, 4254}, {212, 2260}, {218, 26885}, {333, 16352}, {386, 37257}, {387, 4185}, {394, 4260}, {427, 5800}, {474, 41014}, {940, 7484}, {967, 5156}, {999, 1260}, {1002, 1617}, {1011, 5120}, {1014, 37262}, {1203, 11365}, {1249, 37386}, {1410, 1466}, {1449, 5285}, {1593, 5706}, {1824, 2285}, {1834, 4214}, {2082, 2355}, {2187, 10460}, {2192, 42447}, {2256, 3690}, {2308, 7083}, {2328, 4253}, {3745, 12329}, {3796, 5138}, {3945, 37261}, {4224, 37666}, {4231, 14912}, {4383, 11284}, {4649, 5329}, {5020, 32911}, {5042, 40984}, {5208, 37248}, {5256, 37581}, {5278, 19309}, {5347, 36740}, {5707, 7395}, {5746, 11323}, {5802, 37385}, {6642, 37509}, {7387, 36750}, {7485, 14996}, {9709, 33078}, {10037, 16473}, {10046, 16472}, {11350, 37502}, {11414, 36742}, {11435, 19354}, {16408, 33172}, {16419, 37633}, {17379, 37090}, {17778, 37099}, {19310, 37652}, {20009, 39696}, {20018, 37091}, {20835, 37507}, {22080, 37500}, {24597, 25514}, {36746, 37198}

X(44094) = isogonal conjugate of isotomic conjugate of X(443)
X(44094) = crosspoint of X(6) and X(2213)
X(44094) = crosssum of X(2) and X(452)
X(44094) = crossdifference of every pair of points on line {449, 525}
X(44094) = barycentric product X(6)*X(443)
X(44094) = barycentric quotient X(443)/X(76)
X(44094) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 154, 5320}, {6, 37538, 25}, {22, 37685, 37492}, {940, 36741, 7484}

X(44095) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(445)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + c^2)*(a^2*b - b^3 + a^2*c + 2*a*b*c + b^2*c + b*c^2 - c^3) : :

X(44095) lies on these lines: {4, 583}, {6, 25}, {19, 1990}, {24, 584}, {186, 17454}, {216, 16453}, {230, 30677}, {393, 14018}, {403, 8818}, {468, 17718}, {607, 2178}, {1030, 2332}, {1172, 2245}, {1841, 2260}, {1865, 15762}, {2174, 2594}, {2911, 11399}, {3284, 20840}, {4275, 8743}, {5153, 39575}, {16777, 41320}

X(44095) = isogonal conjugate of isotomic conjugate of X(445)
X(44095) = polar conjugate of isotomic conjugate of X(500)
X(44095) = X(i)-Ceva conjugate of X(j) for these (i,j): {19, 1841}, {445, 500}
X(44095) = X(i)-isoconjugate of X(j) for these (i,j): {1794, 30690}, {7100, 40435}
X(44095) = barycentric product X(i)*X(j) for these {i,j}: {1, 1844}, {4, 500}, {6, 445}, {19, 16585}, {34, 31938}, {35, 1838}, {942, 6198}, {1442, 1859}, {1841, 3219}, {1865, 40214}, {7282, 14547}
X(44095) = barycentric quotient X(i)/X(j) for these {i,j}: {445, 76}, {500, 69}, {1838, 20565}, {1841, 30690}, {1844, 75}, {6198, 40422}, {14975, 943}, {16585, 304}, {31938, 3718}, {40956, 7100}
X(44095) = {X(186),X(41502)}-harmonic conjugate of X(17454)

X(44096) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(450)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - a^2*b^2 + a^2*b*c - b^3*c - a^2*c^2 + 2*b^2*c^2 - b*c^3)*(a^4 - a^2*b^2 - a^2*b*c + b^3*c - a^2*c^2 + 2*b^2*c^2 + b*c^3) : :

X(44096) lies on these lines: {6, 25}, {30, 250}, {112, 23200}, {237, 32713}, {450, 40888}, {1093, 14152}, {1249, 14575}, {1316, 37778}, {1576, 1990}, {2489, 42658}, {2790, 41204}, {2967, 22151}, {3284, 34854}, {4558, 15143}, {6524, 23606}, {6644, 30258}, {10788, 18533}, {15262, 20975}, {15274, 37196}, {17907, 37893}, {34396, 40138}, {37458, 42873}

X(44096) = isogonal conjugate of isotomic conjugate of X(450)
X(44096) = isogonal conjugate of polar conjugate of X(41368)
X(44096) = X(i)-isoconjugate of X(j) for these (i,j): {75, 1942}, {2713, 14208}, {7108, 40843}
X(44096) = crosspoint of X(450) and X(41368)
X(44096) = crossdifference of every pair of points on line {525, 41005}
X(44096) = barycentric product X(i)*X(j) for these {i,j}: {3, 41368}, {6, 450}, {25, 40888}, {48, 41497}, {112, 2797}, {243, 1950}, {1935, 2202}, {1936, 7120}, {1940, 1951}, {1981, 21761}, {23582, 35236}
X(44096) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 1942}, {450, 76}, {2797, 3267}, {35236, 15526}, {40888, 305}, {41368, 264}, {41497, 1969}

X(44097) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(451)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - a*b*c - b^2*c - a*c^2 - b*c^2 - c^3) : :

X(44097) lies on these lines: {4, 37509}, {6, 25}, {24, 36750}, {42, 14975}, {81, 468}, {407, 3194}, {427, 32911}, {430, 1172}, {451, 2895}, {940, 37453}, {1203, 1829}, {1593, 36754}, {1783, 7140}, {1824, 21353}, {1994, 35973}, {2204, 20970}, {2211, 21753}, {2308, 40976}, {3515, 36742}, {3516, 36745}, {4383, 5094}, {5706, 37197}, {6353, 37685}, {8889, 14997}, {11396, 16466}, {11398, 16472}, {11399, 16473}, {14996, 38282}, {15750, 36746}, {21779, 35325}, {22122, 26893}, {22123, 26885}

X(44097) = isogonal conjugate of isotomic conjugate of X(451)
X(44097) = polar conjugate of isotomic conjugate of X(1030)
X(44097) = X(i)-Ceva conjugate of X(j) for these (i,j): {451, 1030}, {1824, 25}
X(44097) = X(i)-isoconjugate of X(j) for these (i,j): {63, 1029}, {69, 267}, {304, 3444}, {306, 40143}, {502, 1444}, {17206, 21353}
X(44097) = crosspoint of X(250) and X(1783)
X(44097) = crosssum of X(125) and X(905)
X(44097) = barycentric product X(i)*X(j) for these {i,j}: {4, 1030}, {6, 451}, {19, 191}, {25, 2895}, {28, 21873}, {37, 2906}, {281, 8614}, {393, 22136}, {501, 1826}, {607, 41808}, {648, 42653}, {1474, 21081}, {1783, 31947}, {1824, 40592}, {1973, 20932}, {2203, 42710}, {8750, 21192}
X(44097) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 1029}, {191, 304}, {451, 76}, {501, 17206}, {1030, 69}, {1973, 267}, {1974, 3444}, {2203, 40143}, {2333, 502}, {2895, 305}, {2906, 274}, {8614, 348}, {20932, 40364}, {21081, 40071}, {21873, 20336}, {22136, 3926}, {31947, 15413}, {42653, 525}

X(44098) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(452)

Barycentrics    a^2*(a - b - c)*(3*a^3 + 3*a^2*b + a*b^2 + b^3 + 3*a^2*c + 2*a*b*c - b^2*c + a*c^2 - b*c^2 + c^3) : :

X(44098) lies on these lines: {1, 40970}, {6, 25}, {31, 198}, {33, 2264}, {41, 55}, {58, 13737}, {65, 5338}, {81, 35259}, {199, 37500}, {218, 5285}, {221, 1395}, {228, 3052}, {284, 13615}, {461, 5802}, {940, 4223}, {1011, 37504}, {1184, 5371}, {1724, 37320}, {1754, 37412}, {1834, 28076}, {2175, 7074}, {2256, 26885}, {2328, 4254}, {2352, 3207}, {3053, 21779}, {3145, 4255}, {3745, 40131}, {3796, 32911}, {4220, 4383}, {4252, 13738}, {4260, 9909}, {5020, 5138}, {5135, 17825}, {7412, 11425}, {9306, 37492}, {17811, 36740}, {19309, 19727}, {19732, 37149}, {19764, 37284}, {35264, 37685}, {35273, 37553}, {37367, 37646}, {37516, 37672}, {37519, 40956}

X(44098) = isogonal conjugate of isotomic conjugate of X(452)
X(44098) = X(i)-isoconjugate of X(j) for these (i,j): {75, 2213}, {85, 2336}
X(44098) = crosspoint of X(380) and X(1453)
X(44098) = crosssum of X(2) and X(37435)
X(44098) = crossdifference of every pair of points on line {525, 3676}
X(44098) = barycentric product X(i)*X(j) for these {i,j}: {1, 380}, {6, 452}, {9, 1453}
X(44098) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 2213}, {380, 75}, {452, 76}, {1453, 85}, {2175, 2336}
X(44098) = {X(25),X(5320)}-harmonic conjugate of X(6)

X(44099) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(460)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(44099) lies on these lines: {4, 3972}, {6, 25}, {24, 9737}, {32, 40325}, {112, 5140}, {230, 460}, {250, 37777}, {317, 1007}, {468, 14052}, {669, 2489}, {1196, 14575}, {2032, 15630}, {2971, 14581}, {3080, 40981}, {3148, 10314}, {3517, 10983}, {7714, 37765}, {7735, 41762}, {8754, 16318}, {9407, 40350}, {11470, 40801}, {12294, 35387}, {27369, 33874}, {32696, 34854}, {40121, 43291}

X(44099) = isogonal conjugate of isotomic conjugate of X(460)
X(44099) = polar conjugate of isotomic conjugate of X(1692)
X(44099) = X(i)-Ceva conjugate of X(j) for these (i,j): {460, 1692}, {32696, 2489}
X(44099) = X(i)-isoconjugate of X(j) for these (i,j): {63, 8781}, {69, 8773}, {75, 43705}, {304, 2987}, {305, 36051}, {326, 35142}, {561, 42065}, {3265, 36105}, {10425, 14208}, {32654, 40364}
X(44099) = crosspoint of X(i) and X(j) for these (i,j): {4, 39645}, {18020, 20031}
X(44099) = crosssum of X(69) and X(6393)
X(44099) = crossdifference of every pair of points on line {525, 3926}
X(44099) = barycentric product X(i)*X(j) for these {i,j}: {4, 1692}, {6, 460}, {19, 8772}, {25, 230}, {648, 42663}, {1733, 1973}, {2207, 3564}, {2211, 14265}, {2489, 4226}, {5477, 8753}, {12829, 17980}, {14581, 36875}, {39072, 39645}
X(44099) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 8781}, {32, 43705}, {230, 305}, {460, 76}, {1501, 42065}, {1692, 69}, {1733, 40364}, {1973, 8773}, {1974, 2987}, {2207, 35142}, {8772, 304}, {14581, 36891}, {36417, 3563}, {42663, 525}
X(44099) = {X(25),X(10311)}-harmonic conjugate of X(1843)

X(44100) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(461)

Barycentrics    a^2*(a - b - c)*(3*a + b + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) : :

X(44100) lies on these lines: {4, 37681}, {6, 25}, {33, 3715}, {235, 3332}, {391, 461}, {427, 37650}, {468, 4648}, {607, 1253}, {991, 3515}, {1172, 28044}, {1279, 11396}, {1398, 1471}, {1452, 1456}, {1593, 13329}, {1829, 7290}, {2293, 40976}, {3945, 6353}, {5094, 17337}, {5222, 7717}, {7713, 16469}, {11383, 21002}, {11406, 14975}, {14004, 17349}, {17245, 37453}

X(44100) = isogonal conjugate of isotomic conjugate of X(461)
X(44100) = polar conjugate of isotomic conjugate of X(4258)
X(44100) = X(461)-Ceva conjugate of X(4258)
X(44100) = X(i)-isoconjugate of X(j) for these (i,j): {77, 5936}, {222, 40023}, {348, 25430}, {905, 4624}, {2334, 7182}, {4614, 17094}, {4866, 7056}, {5545, 14208}
X(44100) = barycentric product X(i)*X(j) for these {i,j}: {4, 4258}, {6, 461}, {9, 5338}, {19, 4512}, {25, 391}, {33, 1449}, {41, 5342}, {108, 4827}, {112, 4843}, {607, 3616}, {648, 8653}, {1172, 37593}, {1334, 31903}, {1474, 4061}, {1973, 4673}, {2203, 42712}, {2212, 19804}, {2299, 5257}, {2332, 3671}, {3361, 7079}, {4765, 8750}, {4832, 36797}, {7071, 21454}, {14625, 37908}
X(44100) = barycentric quotient X(i)/X(j) for these {i,j}: {33, 40023}, {391, 305}, {461, 76}, {607, 5936}, {1449, 7182}, {2212, 25430}, {4061, 40071}, {4258, 69}, {4512, 304}, {4673, 40364}, {4827, 35518}, {4832, 17094}, {4843, 3267}, {5338, 85}, {5342, 20567}, {8653, 525}, {8750, 4624}, {37593, 1231}
X(44100) = {X(607),X(2212)}-harmonic conjugate of X(7071)

X(44101) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(464)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^4 + 4*a^3*b + 2*a^2*b^2 + b^4 + 4*a^3*c + 4*a^2*b*c + 2*a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(44101) lies on these lines: {3, 48}, {6, 25}, {19, 5706}, {56, 1409}, {185, 37499}, {281, 5767}, {572, 19357}, {573, 1181}, {579, 2360}, {608, 26888}, {610, 1754}, {965, 3740}, {966, 6776}, {1213, 1899}, {1400, 19349}, {1473, 14597}, {1826, 5786}, {2260, 16466}, {2261, 5776}, {2269, 19354}, {3167, 22133}, {3190, 38868}, {4269, 37250}, {5746, 37383}, {5816, 6146}, {10605, 37508}, {18396, 32431}, {18675, 26934}

X(44101) = isogonal conjugate of isotomic conjugate of X(464)
X(44101) = isogonal conjugate of polar conjugate of X(387)
X(44101) = crosspoint of X(387) and X(464)
X(44101) = crosssum of X(2) and X(6994)
X(44101) = crossdifference of every pair of points on line {525, 7649}
X(44101) = barycentric product X(i)*X(j) for these {i,j}: {3, 387}, {6, 464}
X(44101) = barycentric quotient X(i)/X(j) for these {i,j}: {387, 264}, {464, 76}
X(44101) = {X(6),X(154)}-harmonic conjugate of X(1474)

X(44102) = ISOGONAL CONJUGATE OF X(30786)

Barycentrics    a^2*(2*a^2 - b^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) : :
Trilinears    (tan A) (sin A - 3 cos A tan ω) : :
X(44102) = 2 X[6] + X[1495], 5 X[6] + X[12367], 3 X[6] + X[19596], 2 X[110] + X[32127], X[186] - 3 X[19128], 2 X[468] + X[5095], X[468] + 2 X[15471], X[858] - 4 X[32300], X[1205] - 4 X[35371], 5 X[1495] - 2 X[12367], 3 X[1495] - 2 X[19596], X[3292] - 4 X[6593], X[5095] - 4 X[15471], 2 X[5972] + X[32220], X[8262] + 2 X[41595], X[12167] + 5 X[34397], X[12367] - 5 X[18374], 3 X[12367] - 5 X[19596], 2 X[12367] + 5 X[21639], 2 X[15126] + X[32264], 2 X[15303] + X[32225], 3 X[18374] - X[19596], 2 X[18374] + X[21639], 2 X[19596] + 3 X[21639], X[32250] - 4 X[37984], X[32260] - 4 X[35370]

The trilinear polar of X(44102) passes through X(351).

Let A'B'C' be the medial triangle. Let OA be the circumcircle of AB'C'. Let A" be the perspector of OA. Let LA be the polar of A" wrt OA. Define LB, LC cyclically. Let A* = LB∩LC, B* = LC∩LA, C* = LA∩LB. The lines AA*, BB*, CC* concur in X(44102). (Randy Hutson, August 24, 2021)

X(44102) lies on these lines: {3, 11470}, {4, 575}, {6, 25}, {22, 11511}, {23, 11416}, {24, 576}, {26, 8538}, {39, 9515}, {49, 32284}, {69, 38282}, {110, 8681}, {112, 843}, {182, 378}, {185, 34117}, {186, 249}, {187, 23200}, {193, 19122}, {216, 37457}, {235, 8550}, {237, 3284}, {340, 420}, {403, 542}, {419, 648}, {427, 597}, {460, 1990}, {462, 23713}, {463, 23712}, {468, 524}, {512, 1692}, {538, 37912}, {577, 41275}, {599, 37453}, {800, 14575}, {858, 32300}, {895, 37777}, {1112, 9019}, {1177, 1205}, {1249, 41762}, {1353, 19155}, {1503, 10151}, {1576, 3003}, {1594, 25555}, {1597, 5050}, {1691, 9217}, {1899, 41719}, {1968, 10568}, {1976, 8749}, {1986, 25556}, {1992, 6353}, {1995, 9813}, {2070, 18449}, {2080, 23164}, {2207, 39238}, {2356, 20958}, {2450, 23583}, {2781, 21663}, {3098, 35472}, {3148, 5158}, {3199, 34154}, {3455, 39840}, {3515, 11477}, {3516, 10541}, {3517, 11482}, {3518, 8537}, {3520, 20190}, {3542, 43844}, {3564, 37942}, {3618, 8889}, {3629, 41584}, {4232, 5032}, {4235, 14608}, {4663, 11363}, {5007, 27369}, {5038, 11380}, {5085, 11410}, {5092, 35473}, {5097, 6403}, {5140, 8744}, {5182, 15014}, {5562, 35603}, {5621, 34146}, {5622, 6000}, {5967, 37778}, {5972, 32220}, {6620, 40138}, {6623, 6776}, {6636, 11574}, {7485, 19126}, {7487, 37505}, {7502, 9967}, {7505, 34507}, {7514, 19131}, {8548, 10539}, {8549, 26883}, {8584, 41585}, {8743, 40325}, {9306, 41614}, {9407, 20975}, {9544, 15531}, {9729, 43815}, {10018, 40107}, {10168, 37118}, {10282, 15073}, {10295, 19924}, {10317, 21419}, {10423, 41511}, {10510, 21284}, {10540, 39562}, {10594, 22234}, {11206, 18919}, {11255, 37440}, {11550, 23327}, {12007, 39871}, {12220, 37913}, {13198, 41744}, {14273, 33919}, {14580, 32740}, {14848, 18494}, {14912, 19123}, {15118, 32239}, {15126, 15128}, {15139, 32251}, {15387, 32729}, {16868, 18553}, {18386, 38072}, {18533, 20423}, {18800, 37855}, {18860, 22087}, {19127, 22352}, {20959, 40976}, {21213, 21969}, {23061, 37977}, {25406, 40196}, {32113, 32226}, {32250, 37984}, {32260, 35370}, {32713, 34854}, {34774, 41602}, {36696, 41363}, {39561, 39588}

X(44102) = midpoint of X(i) and X(j) for these {i,j}: {6, 18374}, {23, 11416}, {110, 37784}, {1495, 21639}, {2070, 18449}, {10540, 39562}
X(44102) = reflection of X(i) in X(j) for these {i,j}: {1495, 18374}, {21639, 6}, {32127, 37784}
X(44102) = isogonal conjugate of X(30786)
X(44102) = polar conjugate of X(18023)
X(44102) = isogonal conjugate of complement of X(7665)
X(44102) = isogonal conjugate of isotomic conjugate of X(468)
X(44102) = polar conjugate of isotomic conjugate of X(187)
X(44102) = polar conjugate of isogonal conjugate of X(14567)
X(44102) = X(i)-Ceva conjugate of X(j) for these (i,j): {468, 187}, {8744, 14580}, {8753, 25}, {10423, 647}, {32709, 8644}
X(44102) = X(i)-cross conjugate of X(j) for these (i,j): {14567, 187}, {21905, 110}, {21906, 14273}, {41911, 4}
X(44102) = crosspoint of X(i) and X(j) for these (i,j): {4, 8791}, {6, 1177}, {25, 8753}
X(44102) = crosssum of X(i) and X(j) for these (i,j): {2, 858}, {3, 22151}, {69, 6390}, {125, 14417}
X(44102) = crossdifference of every pair of points on line {69, 525}
X(44102) = pole wrt polar circle of trilinear polar of X(18023) (line X(76)X(850))
X(44102) = X(i)-isoconjugate of X(j) for these (i,j): {1, 30786}, {48, 18023}, {63, 671}, {69, 897}, {75, 895}, {76, 36060}, {111, 304}, {305, 923}, {326, 17983}, {336, 5968}, {525, 36085}, {561, 14908}, {656, 892}, {662, 14977}, {691, 14208}, {799, 10097}, {3267, 36142}, {3718, 7316}, {3926, 36128}, {4025, 5380}, {4563, 23894}, {4592, 5466}, {5547, 7182}, {14210, 15398}, {20884, 41511}, {31125, 34055}, {32740, 40364}
X(44102) = barycentric product X(i)*X(j) for these {i,j}: {4, 187}, {6, 468}, {19, 896}, {25, 524}, {28, 21839}, {92, 922}, {110, 14273}, {111, 5095}, {112, 690}, {162, 2642}, {184, 37778}, {232, 5967}, {250, 1648}, {264, 14567}, {351, 648}, {393, 3292}, {419, 18872}, {512, 4235}, {607, 7181}, {608, 3712}, {1177, 1560}, {1474, 4062}, {1783, 14419}, {1824, 16702}, {1973, 14210}, {1974, 3266}, {1990, 9717}, {2052, 23200}, {2203, 42713}, {2207, 6390}, {2333, 6629}, {2482, 8753}, {2489, 5468}, {2501, 5467}, {3053, 5203}, {3563, 5477}, {4750, 8750}, {5026, 17980}, {5140, 34161}, {5642, 8749}, {6531, 9155}, {6593, 8791}, {8744, 14357}, {8882, 41586}, {12828, 14910}, {14248, 32459}, {14417, 32713}, {14432, 32674}, {14581, 36890}, {14776, 42760}, {15471, 21448}, {17983, 39689}, {18020, 21906}, {22105, 35325}, {32740, 34336}, {34397, 43084}, {35282, 43717}, {36128, 42081}, {40347, 41616}
X(44102) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 18023}, {6, 30786}, {25, 671}, {32, 895}, {112, 892}, {187, 69}, {351, 525}, {468, 76}, {512, 14977}, {524, 305}, {560, 36060}, {669, 10097}, {690, 3267}, {896, 304}, {922, 63}, {1501, 14908}, {1560, 1236}, {1648, 339}, {1843, 31125}, {1973, 897}, {1974, 111}, {2207, 17983}, {2211, 5968}, {2489, 5466}, {2642, 14208}, {3266, 40050}, {3292, 3926}, {4062, 40071}, {4235, 670}, {5095, 3266}, {5467, 4563}, {6593, 37804}, {8541, 42008}, {9155, 6393}, {14210, 40364}, {14273, 850}, {14419, 15413}, {14567, 3}, {14581, 9214}, {15471, 11059}, {18872, 40708}, {21839, 20336}, {21906, 125}, {23200, 394}, {32676, 36085}, {32740, 15398}, {36417, 8753}, {37778, 18022}, {39689, 6390}, {40354, 9139}, {41586, 28706}, {41616, 37803}, {41911, 625}, {42671, 36894}
X(44102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 25, 8541}, {6, 154, 10602}, {6, 184, 40673}, {6, 206, 6467}, {6, 1974, 1843}, {6, 9973, 39125}, {6, 19118, 1974}, {6, 19132, 19459}, {6, 19136, 51}, {6, 19153, 184}, {6, 41593, 21637}, {25, 8541, 1843}, {460, 1990, 8754}, {468, 12828, 32225}, {468, 15471, 5095}, {1177, 34470, 1205}, {1974, 8541, 25}, {6593, 41612, 5642}, {6593, 41616, 5095}, {8739, 8740, 232}, {9407, 20975, 42671}, {12828, 15303, 5095}, {40135, 42671, 20975}

X(44103) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(469)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a*b + b^2 + a*c + b*c + c^2) : :

X(44103) lies on these lines: {2, 17171}, {4, 9}, {6, 25}, {24, 572}, {27, 17277}, {28, 579}, {32, 3437}, {33, 2269}, {34, 1400}, {37, 1829}, {48, 581}, {216, 28348}, {219, 5752}, {284, 14017}, {378, 37508}, {391, 6995}, {427, 1213}, {428, 17330}, {444, 992}, {468, 17398}, {469, 5224}, {577, 37259}, {583, 17523}, {607, 4277}, {608, 28615}, {672, 5338}, {941, 1039}, {1100, 11363}, {1108, 40964}, {1172, 4222}, {1409, 19366}, {1452, 2285}, {1453, 2260}, {1593, 37499}, {1696, 2336}, {1730, 37388}, {1765, 37395}, {1779, 2253}, {1828, 1841}, {1865, 1894}, {1875, 1880}, {1901, 37376}, {1973, 4270}, {2178, 22479}, {2189, 3453}, {2193, 11334}, {2204, 2220}, {2245, 4185}, {2278, 20832}, {2287, 7466}, {2332, 4254}, {4186, 4271}, {4214, 5036}, {4253, 17562}, {4288, 20846}, {5090, 17275}, {5227, 5739}, {5738, 7289}, {5742, 37362}, {5755, 7497}, {5839, 7718}, {6748, 37226}, {6985, 15945}, {7017, 29395}, {7490, 37650}, {7649, 20979}, {7714, 37654}, {9306, 22133}, {11396, 16777}, {12135, 17362}, {13738, 18591}, {14597, 26892}, {21767, 42448}, {26671, 37279}, {34265, 37390}, {37245, 37500}, {43739, 43742}

X(44103) = isogonal conjugate of isotomic conjugate of X(469)
X(44103) = polar conjugate of isotomic conjugate of X(386)
X(44103) = X(469)-Ceva conjugate of X(386)
X(44103) = X(i)-isoconjugate of X(j) for these (i,j): {63, 43531}, {69, 2214}, {835, 905}, {1332, 43927}, {1459, 37218}
X(44103) = crosssum of X(2) and X(7560)
X(44103) = crossdifference of every pair of points on line {525, 1459}
X(44103) = barycentric product X(i)*X(j) for these {i,j}: {4, 386}, {6, 469}, {19, 28606}, {25, 5224}, {34, 3876}, {112, 23879}, {607, 33949}, {648, 42664}, {834, 1897}, {1783, 14349}, {1973, 33935}, {2203, 42714}
X(44103) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 43531}, {386, 69}, {469, 76}, {834, 4025}, {1783, 37218}, {1973, 2214}, {3876, 3718}, {5224, 305}, {8637, 1459}, {8750, 835}, {14349, 15413}, {23879, 3267}, {28606, 304}, {33935, 40364}, {42664, 525}
X(44103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 25, 1474}, {9, 7713, 19}, {2333, 2354, 19}

X(44104) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(474)

Barycentrics    a^3*(a^3 - a*b^2 + 2*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :

X(44104) lies on these lines: {1, 26890}, {6, 25}, {31, 5042}, {41, 20230}, {42, 1397}, {54, 7501}, {55, 4268}, {81, 182}, {199, 4266}, {212, 40956}, {228, 604}, {569, 39271}, {578, 37305}, {940, 43650}, {1011, 5053}, {1092, 36754}, {1147, 37509}, {1408, 4255}, {1412, 4191}, {1743, 26885}, {1790, 37502}, {1993, 4260}, {2175, 2308}, {2206, 16946}, {2256, 26867}, {2260, 6056}, {2999, 26884}, {3796, 37492}, {3917, 36741}, {3920, 43146}, {3955, 5256}, {4383, 5651}, {5012, 5138}, {5347, 37516}, {5706, 11424}, {9306, 32911}, {10984, 36742}, {11429, 40971}, {13323, 19767}, {16187, 37687}, {19354, 42447}, {22080, 36743}, {22112, 37674}, {22352, 36740}, {24265, 32915}, {36745, 43652}

X(44104) = isogonal conjugate of isotomic conjugate of X(474)
X(44104) = crosssum of X(2) and X(2478)
X(44104) = crossdifference of every pair of points on line {525, 4462}
X(44104) = barycentric product X(6)*X(474)
X(44104) = barycentric quotient X(474)/X(76)
X(44104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 184, 5320}, {6, 37538, 51}, {5012, 37685, 5138}

X(44105) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(475)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c + 2*a*b*c - b^2*c - a*c^2 - b*c^2 - c^3) : :
Trilinears    sin A (sin A + sin B + sin C - tan A) : :
Trilinears    (tan A) (s cos A - R sin A) : :
Trilinears    a tan A - 2 s sin A : :

X(44105) lies on these lines: {4, 81}, {6, 25}, {24, 36754}, {31, 2356}, {42, 1395}, {56, 22348}, {222, 1876}, {394, 10477}, {427, 940}, {468, 4383}, {607, 2355}, {608, 1824}, {1396, 4196}, {1398, 34046}, {1468, 22479}, {1593, 36746}, {1598, 36750}, {1870, 3873}, {1892, 37543}, {2212, 2308}, {3157, 14054}, {3194, 28076}, {3195, 20231}, {3515, 36745}, {3516, 37501}, {3517, 37509}, {3575, 5706}, {4231, 39588}, {4663, 41611}, {5090, 5711}, {5094, 37674}, {5347, 21213}, {5422, 35973}, {5710, 12135}, {6353, 32911}, {6995, 37685}, {7378, 14996}, {8889, 37633}, {11363, 16466}, {22131, 26885}, {22132, 26893}, {23122, 26884}, {37453, 37679}, {37680, 38282}

X(44105) = isogonal conjugate of isotomic conjugate of X(475)
X(44105) = polar conjugate of isotomic conjugate of X(36743)
X(44105) = X(475)-Ceva conjugate of X(36743)
X(44105) = crosssum of X(2) and X(27505)
X(44105) = crossdifference of every pair of points on line {525, 20296}
X(44105) = barycentric product X(i)*X(j) for these {i,j}: {4, 36743}, {6, 475}, {2203, 42715}
X(44105) = barycentric quotient X(i)/X(j) for these {i,j}: {475, 76}, {36743, 69}
X(44105) = {X(42),X(1395)}-harmonic conjugate of X(11383)

X(44106) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(546)

Barycentrics    a^2*(2*a^4 + a^2*b^2 - 3*b^4 + a^2*c^2 + 6*b^2*c^2 - 3*c^4) : :

X(44106) lies on these lines: {2, 14488}, {3, 27355}, {4, 11270}, {6, 25}, {22, 373}, {23, 5643}, {107, 42400}, {110, 21849}, {125, 428}, {143, 43844}, {185, 10594}, {237, 37512}, {389, 14157}, {462, 5350}, {463, 5349}, {511, 13595}, {575, 26881}, {576, 35264}, {1204, 5198}, {1216, 18369}, {1598, 10605}, {1899, 7714}, {1995, 3917}, {3051, 40350}, {3060, 3292}, {3066, 9909}, {3129, 5237}, {3130, 5238}, {3148, 5206}, {3517, 11424}, {3518, 10110}, {3574, 21841}, {3819, 15107}, {3845, 32110}, {4224, 37687}, {5012, 32237}, {5020, 5650}, {5076, 43604}, {5092, 11451}, {5097, 9544}, {5133, 32223}, {5200, 23263}, {5446, 13621}, {5462, 18378}, {5562, 13861}, {5651, 33586}, {5892, 5899}, {6636, 6688}, {6756, 11572}, {6995, 11550}, {7398, 43653}, {7496, 10219}, {7502, 14845}, {7527, 13570}, {7545, 13754}, {7576, 13851}, {9306, 21969}, {9781, 10282}, {10117, 34468}, {10170, 21308}, {10193, 35484}, {10301, 13567}, {10601, 20850}, {11002, 34986}, {11160, 14826}, {11438, 32062}, {11695, 12088}, {11745, 43831}, {12002, 37495}, {12041, 12101}, {12087, 17704}, {13363, 37947}, {13364, 37513}, {13399, 16654}, {13474, 16835}, {15873, 21659}, {16240, 24862}, {16836, 37925}, {19219, 23269}, {21243, 32225}, {26276, 33798}, {26882, 37505}, {34481, 40130}, {37649, 37897}, {37945, 43584}

X(44106) = isogonal conjugate of isotomic conjugate of X(546)
X(44106) = crosspoint of X(6) and X(16835)
X(44106) = crosssum of X(2) and X(550)
X(44106) = barycentric product X(6)*X(546)
X(44106) = barycentric quotient X(546)/X(76)
X(44106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 5943, 22352}, {25, 51, 1495}, {25, 11402, 41424}, {25, 17810, 184}, {25, 34417, 51}, {51, 154, 34566}, {51, 184, 34565}, {51, 1495, 13366}, {184, 17810, 51}, {184, 34417, 17810}, {184, 34565, 13366}, {1495, 34565, 184}, {1843, 19136, 21639}, {3066, 9909, 43650}, {3518, 10110, 13367}, {6030, 20190, 22352}, {6636, 10545, 6688}, {10601, 20850, 35268}, {11451, 37913, 5092}, {13364, 37936, 37513}, {34484, 38848, 389}

X(44107) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(547)

Barycentrics    a^2*(2*a^4 - 7*a^2*b^2 + 5*b^4 - 7*a^2*c^2 - 10*b^2*c^2 + 5*c^4) : :
X(44107) = 3 X[7496] - 7 X[15018], X[7496] - 7 X[15019], 9 X[7496] - 7 X[41462], X[15018] - 3 X[15019], 3 X[15018] - X[41462], 9 X[15019] - X[41462]

X(44107) lies on these lines: {4, 14491}, {6, 25}, {23, 15516}, {52, 33533}, {74, 389}, {110, 22330}, {143, 37513}, {323, 5943}, {373, 576}, {511, 7496}, {575, 11002}, {578, 35479}, {1351, 5650}, {1570, 13410}, {1994, 10545}, {1995, 15520}, {3060, 5092}, {3066, 11482}, {3098, 5422}, {3292, 5097}, {3527, 3531}, {3567, 11430}, {3581, 15038}, {3630, 37439}, {3819, 12834}, {3917, 37517}, {4550, 14831}, {5007, 5191}, {5093, 5651}, {5446, 15037}, {5476, 37644}, {5643, 15082}, {5892, 37496}, {5946, 10564}, {6800, 22234}, {10095, 43844}, {10110, 15032}, {10546, 34986}, {11381, 11432}, {11438, 35477}, {11464, 37505}, {11477, 22112}, {12112, 14483}, {13202, 16657}, {13321, 14805}, {13367, 22233}, {13474, 43596}, {13857, 37648}, {14389, 32225}, {14810, 16981}, {14848, 37638}, {15107, 21849}, {16226, 37470}, {16655, 34564}, {18583, 41586}, {33878, 43650}

X(44107) = isogonal conjugate of isotomic conjugate of X(547)
X(44107) = crosspoint of X(i) and X(j) for these (i,j): {4, 30537}, {6, 14483}
X(44107) = crosssum of X(i) and X(j) for these (i,j): {2, 549}, {3, 15018}
X(44107) = barycentric product X(6)*X(547)
X(44107) = barycentric quotient X(547)/X(76)
X(44107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 51, 1495}, {6, 1495, 13366}, {6, 31860, 11402}, {51, 15004, 34565}, {51, 34565, 13366}, {184, 34417, 41424}, {184, 34566, 13366}, {1495, 34565, 6}, {5097, 5640, 3292}, {9777, 15004, 51}, {21849, 34545, 22352}

X(44108) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(548)

Barycentrics    a^2*(6*a^4 - 5*a^2*b^2 - b^4 - 5*a^2*c^2 + 2*b^2*c^2 - c^4) : :
X(44108) = 4 X[6] - 7 X[21637], 5 X[1614] + X[3520], 2 X[1614] + X[13367], 2 X[3520] - 5 X[13367]

X(44108) lies on these lines: {6, 25}, {54, 26863}, {110, 3819}, {156, 5891}, {185, 9707}, {186, 43596}, {373, 35264}, {1147, 36987}, {1154, 43844}, {1511, 17853}, {1614, 3520}, {1994, 32237}, {2979, 3292}, {3167, 35268}, {3796, 5650}, {3917, 6800}, {5012, 6688}, {5890, 10282}, {5943, 35265}, {6455, 10132}, {6456, 10133}, {6676, 24981}, {6759, 32062}, {7409, 31383}, {7426, 11225}, {8780, 43650}, {9306, 40916}, {9705, 15644}, {9706, 13598}, {10619, 16252}, {11003, 11451}, {11204, 11456}, {11381, 19357}, {11424, 14530}, {11430, 11455}, {11464, 21663}, {14845, 32046}, {15602, 37457}, {15647, 32226}, {18435, 18475}, {18555, 36966}, {18950, 35260}, {26881, 34986}, {31652, 42671}, {32078, 41212}

X(44108) = isogonal conjugate of isotomic conjugate of X(548)
X(44108) = crosssum of X(2) and X(3627)
X(44108) = barycentric product X(6)*X(548)
X(44108) = barycentric quotient X(548)/X(76)
X(44108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {51, 154, 1495}, {51, 11402, 34566}, {154, 184, 51}, {184, 1495, 13366}, {184, 34417, 17809}, {1495, 34565, 25}, {11402, 34566, 13366}

X(44109) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(549)

Barycentrics    a^2*(4*a^4 - 5*a^2*b^2 + b^4 - 5*a^2*c^2 - 2*b^2*c^2 + c^4) : :
Trilinears    a^2 (4 cos A + cos(B - C)) : :
Trilinears    a^2 (2 sec A + 5 sec B sec C) : :
X(44109) = X[7492] - 5 X[11003], 3 X[7492] + 5 X[11004], X[7492] + 5 X[11422], 3 X[7492] - 5 X[15080], 3 X[11003] + X[11004], 3 X[11003] - X[15080], X[11004] - 3 X[11422], 3 X[11422] + X[15080]

X(44109) lies on these lines: {2, 43150}, {5, 24981}, {6, 25}, {22, 37517}, {23, 5097}, {39, 5191}, {49, 15037}, {52, 32136}, {54, 74}, {110, 373}, {125, 8550}, {182, 3292}, {187, 34396}, {217, 9408}, {237, 5008}, {323, 3917}, {389, 11423}, {394, 12017}, {399, 567}, {468, 12007}, {511, 7492}, {542, 14389}, {569, 15068}, {576, 6800}, {578, 11381}, {1181, 13093}, {1199, 10282}, {1351, 35268}, {1353, 13394}, {1493, 10625}, {1511, 9730}, {1614, 26863}, {1692, 40130}, {1970, 9412}, {1976, 39389}, {1993, 3098}, {1994, 15107}, {1995, 39561}, {2030, 9463}, {2317, 23202}, {2930, 12039}, {3060, 7712}, {3131, 34754}, {3132, 34755}, {3167, 43650}, {3431, 5890}, {3531, 10982}, {3574, 31804}, {3581, 14831}, {3631, 7499}, {3796, 33878}, {4550, 18445}, {5050, 5651}, {5052, 14567}, {5462, 9704}, {5477, 30516}, {5562, 32046}, {5640, 15516}, {5642, 37648}, {5892, 9703}, {5943, 9544}, {5965, 7495}, {5972, 33749}, {6090, 22112}, {6221, 10133}, {6398, 10132}, {7394, 42785}, {7494, 11008}, {7592, 11438}, {7687, 12022}, {7998, 9716}, {9545, 9729}, {9706, 43584}, {9781, 13472}, {10111, 12900}, {10539, 27355}, {10545, 34545}, {10619, 12233}, {10984, 37483}, {11002, 11663}, {11126, 36755}, {11127, 36756}, {11179, 13857}, {11403, 14490}, {11424, 19347}, {11426, 26883}, {11427, 11550}, {11449, 15012}, {11935, 40280}, {12038, 43845}, {12112, 15033}, {12161, 14531}, {12242, 34224}, {13196, 30749}, {13353, 41597}, {13434, 15052}, {13630, 41673}, {13754, 14805}, {14683, 18553}, {14810, 23061}, {14912, 37643}, {15019, 35265}, {17847, 34468}, {18358, 37649}, {20080, 43653}, {20583, 37904}, {21849, 26881}, {22052, 23606}, {26316, 36212}, {32225, 37644}, {35497, 43612}, {36987, 37496}

X(44109) = midpoint of X(i) and X(j) for these {i,j}: {11003, 11422}, {11004, 15080}
X(44109) = isogonal conjugate of isotomic conjugate of X(549)
X(44109) = isogonal conjugate of polar conjugate of X(6749)
X(44109) = X(75)-isoconjugate of X(14483)
X(44109) = crosspoint of X(i) and X(j) for these (i,j): {6, 3431}, {549, 6749}
X(44109) = crosssum of X(i) and X(j) for these (i,j): {2, 381}, {3, 11004}
X(44109) = crossdifference of every pair of points on line {525, 14391}
X(44109) = barycentric product X(i)*X(j) for these {i,j}: {3, 6749}, {6, 549}
X(44109) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 14483}, {549, 76}, {6749, 264}
X(44109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 184, 1495}, {6, 1495, 51}, {6, 26864, 34417}, {6, 31860, 9777}, {25, 34565, 51}, {49, 15037, 43586}, {54, 15032, 11430}, {110, 575, 373}, {154, 34566, 51}, {182, 3292, 5650}, {184, 11402, 13366}, {184, 13366, 51}, {184, 15004, 154}, {184, 34417, 26864}, {323, 5012, 5092}, {323, 5092, 3917}, {1353, 13394, 41586}, {1495, 13366, 6}, {3520, 15032, 43596}, {5012, 34986, 3917}, {5092, 34986, 323}, {11003, 11004, 15080}, {11402, 17809, 184}, {11422, 15080, 11004}, {11430, 15032, 185}, {15087, 18475, 14831}, {22330, 32237, 11002}, {26864, 34417, 1495}

X(44110) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(550)

Barycentrics    a^2*(4*a^4 - 3*a^2*b^2 - b^4 - 3*a^2*c^2 + 2*b^2*c^2 - c^4) : :
X(44110) = 3 X[9544] + X[37913], 3 X[11464] - X[35473], 3 X[26881] - X[37913]

X(44110) lies on these lines: {2, 18553}, {3, 33556}, {4, 36809}, {5, 11565}, {6, 25}, {22, 3292}, {23, 21969}, {26, 14531}, {49, 5899}, {52, 37936}, {110, 3917}, {125, 10192}, {156, 5562}, {182, 35264}, {185, 186}, {235, 10619}, {237, 35007}, {343, 24981}, {373, 5012}, {378, 6759}, {389, 26882}, {394, 35268}, {511, 9544}, {549, 13399}, {569, 27355}, {575, 12834}, {1092, 35243}, {1147, 12083}, {1196, 14567}, {1204, 17821}, {1368, 5642}, {1370, 13857}, {1498, 11410}, {1501, 40130}, {1511, 14855}, {1597, 14530}, {1899, 35260}, {2070, 14831}, {2937, 41597}, {2979, 7712}, {3060, 32237}, {3131, 5238}, {3132, 5237}, {3155, 6453}, {3156, 6454}, {3431, 11455}, {3520, 16835}, {3787, 8627}, {3796, 5651}, {3819, 15080}, {5181, 22165}, {5206, 41275}, {5446, 9704}, {5650, 6800}, {5943, 11003}, {5944, 12162}, {6000, 11464}, {6143, 14864}, {6146, 37942}, {6241, 11270}, {6449, 10132}, {6450, 10133}, {6623, 19467}, {6677, 35266}, {6688, 10546}, {7378, 31383}, {7494, 21356}, {7499, 20582}, {7514, 10539}, {8024, 35356}, {8703, 10990}, {8877, 32729}, {8889, 11206}, {8908, 26886}, {9545, 13598}, {9705, 12088}, {9833, 11572}, {10151, 16252}, {10154, 41586}, {10540, 15030}, {10565, 11160}, {10575, 32171}, {11202, 11456}, {11245, 15448}, {11403, 14528}, {11422, 21849}, {11424, 18535}, {11430, 13596}, {11645, 31074}, {12038, 18859}, {12106, 16226}, {13417, 15647}, {13491, 37968}, {13620, 43605}, {14581, 14585}, {14862, 18560}, {15712, 23060}, {16003, 34477}, {20773, 21649}, {22115, 36987}, {31255, 43273}, {32379, 43581}, {32737, 40352}, {34148, 37945}, {34484, 37505}, {34782, 43831}, {35259, 43650}, {37457, 37512}, {37904, 41149}

X(44110) = midpoint of X(9544) and X(26881)
X(44110) = isogonal conjugate of isotomic conjugate of X(550)
X(44110) = X(33640)-Ceva conjugate of X(647)
X(44110) = X(75)-isoconjugate of X(16835)
X(44110) = crosspoint of X(6) and X(11270)
X(44110) = crosssum of X(2) and X(382)
X(44110) = crossdifference of every pair of points on line {525, 31072}
X(44110) = barycentric product X(6)*X(550)
X(44110) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 16835}, {550, 76}
X(44110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 34986, 21969}, {25, 184, 13366}, {25, 13366, 51}, {25, 17809, 15004}, {26, 43844, 14531}, {154, 184, 1495}, {154, 26864, 184}, {184, 1495, 51}, {184, 15004, 17809}, {184, 34417, 11402}, {184, 41424, 34566}, {1495, 13366, 25}, {1614, 10282, 185}, {3796, 8780, 5651}, {6759, 9707, 13367}, {6759, 13367, 11381}, {6800, 9306, 22352}, {9306, 22352, 5650}, {10540, 18475, 15030}, {11202, 11456, 21663}, {11402, 34417, 34565}, {11430, 14157, 32062}, {14530, 19357, 26883}, {15004, 17809, 13366}, {34417, 34565, 51}

X(44111) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(632)

Barycentrics    a^2*(4*a^4 - 7*a^2*b^2 + 3*b^4 - 7*a^2*c^2 - 6*b^2*c^2 + 3*c^4) : :

X(44111) lies on these lines: {2, 11668}, {6, 25}, {22, 15520}, {54, 34567}, {185, 1199}, {373, 34545}, {389, 21844}, {567, 14831}, {569, 14531}, {575, 1994}, {576, 22352}, {578, 21663}, {1993, 5650}, {3060, 22330}, {3284, 26907}, {3292, 5422}, {3567, 13472}, {3796, 11482}, {3819, 11004}, {5012, 5097}, {5041, 34396}, {5462, 9703}, {5943, 11422}, {6427, 10133}, {6428, 10132}, {7499, 32455}, {7592, 11381}, {10110, 11423}, {10605, 11426}, {10625, 36153}, {11003, 21849}, {11225, 14389}, {11550, 14912}, {13367, 35479}, {15030, 15087}, {15032, 32062}, {22112, 37672}, {27355, 43844}

X(44111) = isogonal conjugate of isotomic conjugate of X(632)
X(44111) = crosspoint of X(6) and X(13472)
X(44111) = crosssum of X(2) and X(1656)
X(44111) = barycentric product X(i)*X(j) for these {i,j}: {6, 632}, {233, 39667}
X(44111) = barycentric quotient X(i)/X(j) for these {i,j}: {632, 76}, {39667, 31617}
X(44111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 184, 34565}, {6, 11402, 15004}, {6, 13366, 51}, {184, 15004, 17810}, {184, 17810, 1495}, {184, 34565, 51}, {575, 1994, 3917}, {1199, 37505, 185}, {1495, 13366, 11402}, {1495, 15004, 51}, {5012, 5097, 21969}, {11402, 15004, 1495}, {11402, 17810, 184}, {13366, 34565, 184}, {13366, 34566, 6}, {34545, 34986, 373}

X(44112) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(851)

Barycentrics    a^3*(b + c)*(a^4 - a^2*b^2 + a^2*b*c - b^3*c - a^2*c^2 + 2*b^2*c^2 - b*c^3) : :

X(44112) lies on these lines: {6, 25}, {86, 7413}, {667, 788}, {692, 2245}, {851, 1936}, {862, 3330}, {1253, 22369}, {1397, 40984}, {1402, 1918}, {1834, 14529}, {3948, 4579}, {3955, 4199}, {4204, 26890}, {18610, 23440}, {18611, 23526}, {18619, 23420}

X(44112) = isogonal conjugate of isotomic conjugate of X(851)
X(44112) = X(26884)-Ceva conjugate of X(42669)
X(44112) = X(i)-isoconjugate of X(j) for these (i,j): {2, 35145}, {75, 37142}, {76, 2249}, {314, 1937}, {333, 1952}, {1945, 28660}, {4391, 41206}, {6332, 41207}, {31623, 40843}
X(44112) = crosssum of X(2) and X(14956)
X(44112) = crossdifference of every pair of points on line {75, 525}
X(44112) = barycentric product X(i)*X(j) for these {i,j}: {1, 42669}, {6, 851}, {31, 8680}, {37, 26884}, {65, 1951}, {71, 1430}, {73, 2202}, {112, 9391}, {213, 5088}, {243, 1409}, {647, 23353}, {669, 15418}, {810, 1981}, {1400, 1936}, {1402, 1944}
X(44112) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 35145}, {32, 37142}, {560, 2249}, {851, 76}, {1402, 1952}, {1936, 28660}, {1944, 40072}, {1951, 314}, {5088, 6385}, {8680, 561}, {9391, 3267}, {15418, 4609}, {23353, 6331}, {26884, 274}, {42669, 75}

X(44113) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(860)

Barycentrics    a^2*(b + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + b*c - c^2)*(a^2 - b^2 + c^2) : :

X(44113) lies on these lines: {1, 429}, {4, 5396}, {6, 25}, {19, 4272}, {24, 5398}, {33, 430}, {34, 407}, {42, 1824}, {58, 20832}, {73, 1426}, {81, 4231}, {199, 2193}, {225, 2594}, {228, 40590}, {235, 5721}, {386, 4185}, {427, 5718}, {431, 1834}, {442, 37697}, {468, 35466}, {500, 7414}, {580, 20837}, {581, 37194}, {607, 20970}, {608, 2092}, {661, 663}, {851, 1465}, {860, 1870}, {1068, 5399}, {1193, 40985}, {1395, 20966}, {1427, 22348}, {1464, 1835}, {1718, 37982}, {1897, 17987}, {2238, 5089}, {2245, 2361}, {2355, 40976}, {3002, 37908}, {3136, 37695}, {3195, 40984}, {4194, 19783}, {4204, 40937}, {5090, 5725}, {5724, 12135}, {6353, 24597}, {10974, 11398}, {22134, 26893}, {31187, 37453}, {37368, 37732}

X(44113) = isogonal conjugate of isotomic conjugate of X(860)
X(44113) = polar conjugate of isotomic conjugate of X(2245)
X(44113) = X(i)-Ceva conjugate of X(j) for these (i,j): {860, 2245}, {1299, 2178}, {8749, 607}, {14776, 512}, {36067, 647}
X(44113) = X(i)-isoconjugate of X(j) for these (i,j): {3, 14616}, {7, 1793}, {63, 24624}, {69, 759}, {77, 6740}, {80, 1444}, {86, 1807}, {283, 18815}, {304, 34079}, {328, 17104}, {332, 1411}, {339, 9274}, {348, 2341}, {525, 37140}, {1437, 20566}, {1790, 18359}, {1812, 2006}, {2161, 17206}, {3267, 32671}, {4467, 36061}, {7254, 36804}, {9273, 20902}, {14208, 36069}, {18160, 32662}, {23189, 35174}, {23226, 35139}
X(44113) = crossdifference of every pair of points on line {63, 525}
X(44113) = barycentric product X(i)*X(j) for these {i,j}: {4, 2245}, {6, 860}, {9, 1835}, {19, 758}, {25, 3936}, {28, 4053}, {33, 18593}, {36, 1826}, {37, 1870}, {42, 17923}, {92, 3724}, {112, 6370}, {162, 2610}, {186, 8818}, {225, 2323}, {281, 1464}, {320, 2333}, {607, 41804}, {648, 42666}, {661, 4242}, {1400, 5081}, {1824, 3218}, {1832, 7127}, {1845, 2250}, {1880, 4511}, {1897, 21828}, {1973, 35550}, {1983, 24006}, {2171, 17515}, {2361, 40149}, {4707, 8750}, {6739, 8749}, {7113, 41013}, {36125, 40988}
X(44113) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 14616}, {25, 24624}, {36, 17206}, {41, 1793}, {186, 34016}, {213, 1807}, {607, 6740}, {758, 304}, {860, 76}, {1464, 348}, {1824, 18359}, {1826, 20566}, {1835, 85}, {1870, 274}, {1880, 18815}, {1973, 759}, {1974, 34079}, {1983, 4592}, {2212, 2341}, {2245, 69}, {2323, 332}, {2333, 80}, {2361, 1812}, {2610, 14208}, {3724, 63}, {3936, 305}, {4053, 20336}, {4242, 799}, {5081, 28660}, {6370, 3267}, {7113, 1444}, {8818, 328}, {8882, 39277}, {17923, 310}, {18593, 7182}, {21828, 4025}, {32676, 37140}, {34397, 40214}, {35550, 40364}, {42666, 525}

X(44114) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(868)

Barycentrics    a^2*(b - c)^2*(b + c)^2*(a^2*b^2 - b^4 + a^2*c^2 - c^4) : :
Trilinears    a^2 (sin 2B sin(A - C) csc(A - B) - sin 2C sin(A - B) csc(A - C)) : :
X(44114) = X[2421] - 3 X[5968]

X(44114) lies on these lines: {4, 9513}, {6, 25}, {74, 8753}, {125, 136}, {182, 37930}, {235, 43278}, {287, 36898}, {325, 40810}, {351, 865}, {511, 2421}, {512, 2088}, {525, 3143}, {577, 42847}, {868, 35088}, {878, 15630}, {1562, 5139}, {1625, 39846}, {1648, 8029}, {2433, 9178}, {2493, 2871}, {2679, 38974}, {2971, 3269}, {3292, 33928}, {3455, 11060}, {3563, 17974}, {6786, 36790}, {7417, 34211}, {13210, 16175}, {14995, 32225}, {16186, 34291}, {21046, 22212}, {23350, 32112}, {34980, 38356}, {39374, 40083}, {39691, 41221}, {41670, 42742}

X(44114) = polar conjugate of X(41174)
X(44114) = isogonal conjugate of isotomic conjugate of X(868)
X(44114) = polar conjugate of isotomic conjugate of X(41172)
X(44114) = tripolar centroid of X(14998)
X(44114) = pole wrt polar circle of trilinear polar of X(41174) (line X(110)X(685))
X(44114) = X(i)-Ceva conjugate of X(j) for these (i,j): {232, 2491}, {511, 3569}, {868, 41172}, {882, 22260}, {1976, 512}, {3124, 2679}, {3563, 647}, {34854, 17994}, {39644, 669}, {40810, 41167}, {43717, 2489}
X(44114) = X(i)-isoconjugate of X(j) for these (i,j): {48, 41174}, {98, 24041}, {99, 36084}, {110, 36036}, {162, 17932}, {163, 43187}, {249, 1821}, {250, 336}, {290, 1101}, {293, 18020}, {662, 2966}, {685, 4592}, {799, 2715}, {811, 43754}, {1910, 4590}, {1976, 24037}, {4563, 36104}, {4575, 22456}, {6394, 24000}, {17974, 23999}, {18024, 23995}
X(44114) = crosspoint of X(i) and X(j) for these (i,j): {4, 2395}, {6, 35364}, {232, 16230}, {511, 3569}, {512, 1976}, {850, 1916}, {882, 40810}, {17994, 34854}
X(44114) = crosssum of X(i) and X(j) for these (i,j): {2, 4226}, {3, 2421}, {98, 2966}, {99, 325}, {287, 43754}, {1576, 1691}, {2715, 14601}, {6394, 17932}, {17941, 40820}
X(44114) = crossdifference of every pair of points on line {99, 249}
X(44114) = barycentric product X(i)*X(j) for these {i,j}: {4, 41172}, {6, 868}, {115, 511}, {125, 232}, {237, 338}, {240, 3708}, {297, 20975}, {325, 3124}, {339, 2211}, {512, 2799}, {523, 3569}, {525, 17994}, {647, 16230}, {684, 2501}, {690, 8430}, {850, 2491}, {1109, 1755}, {1637, 32112}, {1640, 23350}, {1648, 5968}, {1916, 2679}, {1959, 2643}, {1976, 35088}, {2028, 14501}, {2029, 14502}, {2088, 14356}, {2395, 41167}, {2396, 22260}, {2421, 8029}, {2489, 6333}, {2970, 3289}, {2971, 6393}, {3121, 42703}, {3269, 6530}, {3563, 41181}, {4092, 43034}, {5360, 16732}, {6041, 34765}, {6328, 34349}, {8754, 36212}, {9417, 23994}, {9418, 23962}, {14618, 39469}, {14966, 23105}, {15526, 34854}, {15630, 32458}, {17209, 21043}, {36471, 39644}
X(44114) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 41174}, {115, 290}, {232, 18020}, {237, 249}, {325, 34537}, {338, 18024}, {511, 4590}, {512, 2966}, {523, 43187}, {647, 17932}, {661, 36036}, {669, 2715}, {684, 4563}, {798, 36084}, {868, 76}, {882, 39291}, {1084, 1976}, {1755, 24041}, {1959, 24037}, {2086, 40820}, {2211, 250}, {2421, 31614}, {2422, 41173}, {2489, 685}, {2491, 110}, {2501, 22456}, {2643, 1821}, {2679, 385}, {2799, 670}, {2971, 6531}, {3049, 43754}, {3124, 98}, {3269, 6394}, {3569, 99}, {3708, 336}, {5360, 4567}, {6041, 34761}, {8029, 43665}, {8430, 892}, {8754, 16081}, {9417, 1101}, {9418, 23357}, {9427, 14601}, {15630, 41932}, {16230, 6331}, {17994, 648}, {20975, 287}, {21906, 5967}, {22260, 2395}, {23099, 2422}, {23216, 14600}, {23350, 6035}, {34854, 23582}, {39469, 4558}, {40810, 39292}, {41167, 2396}, {41172, 69}, {43034, 7340}
X(44114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3124, 20975, 6784}

X(44115) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(964)

Barycentrics    a^2*(a^4 + a^3*b + a^2*b^2 + a*b^3 + a^3*c + 2*a^2*b*c + 2*a*b^2*c + b^3*c + a^2*c^2 + 2*a*b*c^2 + 2*b^2*c^2 + a*c^3 + b*c^3) : :

X(44115) lies on these lines: {1, 37317}, {6, 25}, {31, 37}, {32, 55}, {42, 560}, {58, 405}, {65, 1395}, {81, 37325}, {171, 29674}, {172, 2352}, {199, 4261}, {209, 2273}, {354, 1104}, {386, 2915}, {580, 37320}, {757, 30962}, {1011, 1333}, {1098, 37314}, {1724, 4205}, {1834, 37398}, {2206, 2278}, {2288, 10537}, {2328, 4264}, {2363, 4195}, {3666, 13723}, {3695, 5264}, {4204, 5115}, {4239, 32911}, {4252, 37246}, {5156, 37327}, {5269, 17742}, {5280, 5285}, {5398, 37527}, {6043, 37652}, {9306, 40153}, {10457, 13733}, {16466, 27802}, {16974, 20985}, {17126, 17776}, {17526, 18141}, {17698, 37522}, {19309, 19728}, {35612, 36011}, {37315, 37646}

X(44115) = isogonal conjugate of isotomic conjugate of X(964)
X(44115) = crosssum of X(2) and X(17676)
X(44115) = crossdifference of every pair of points on line {525, 3004}
X(44115) = barycentric product X(6)*X(964)
X(44115) = barycentric quotient X(964)/X(76)

X(44116) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1003)

Barycentrics    a^2*(3*a^4 - a^2*b^2 - a^2*c^2 + 2*b^2*c^2) : :

X(44116) lies on these lines: {2, 5033}, {6, 25}, {23, 5028}, {32, 110}, {39, 6800}, {182, 14567}, {187, 15066}, {251, 9544}, {287, 10603}, {574, 15080}, {576, 20976}, {1184, 8780}, {1196, 35264}, {1383, 2987}, {1501, 3231}, {1691, 5651}, {1692, 1995}, {1799, 3620}, {2001, 10546}, {2030, 8585}, {2374, 40819}, {2502, 3506}, {3053, 6090}, {3094, 35268}, {3098, 8627}, {3291, 35259}, {3292, 5017}, {3552, 4563}, {5034, 11003}, {5206, 7998}, {5207, 30747}, {5475, 14389}, {5477, 37644}, {5640, 39764}, {7737, 37645}, {7781, 10330}, {7798, 35356}, {8588, 41462}, {9465, 35265}, {13410, 39561}, {14002, 39024}, {14609, 32729}, {15513, 21766}, {20080, 40405}, {22112, 39560}, {26881, 34945}

X(44116) = isogonal conjugate of isotomic conjugate of X(1003)
X(44116) = crosssum of X(2) and X(33017)
X(44116) = crossdifference of every pair of points on line {525, 9148}
X(44116) = barycentric product X(6)*X(1003)
X(44116) = barycentric quotient X(1003)/X(76)
X(44116) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1501, 3231, 41412}, {9306, 41412, 3231}, {35259, 40825, 3291}

X(44117) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1006)

Barycentrics    a^3*(a^6 - a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - a*b^5 - a^5*c - a^4*b*c + 2*a^2*b^3*c + a*b^4*c - b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a^3*c^3 + 2*a^2*b*c^3 + 2*b^3*c^3 + a^2*c^4 + a*b*c^4 - a*c^5 - b*c^5) : :

X(44117) lies on these lines: {6, 25}, {31, 21741}, {41, 9247}, {54, 7412}, {110, 4223}, {199, 5755}, {228, 2148}, {389, 20837}, {405, 41608}, {578, 37194}, {1243, 36009}, {1426, 19365}, {1437, 5398}, {1465, 26889}, {1824, 11428}, {1827, 10535}, {2193, 23606}, {2355, 10536}, {3145, 5396}, {4220, 5012}, {5135, 5718}, {6759, 37387}, {11003, 35988}, {11383, 19350}, {24597, 37367}, {26866, 34042}, {26885, 40937}, {33718, 34396}

X(44117) = isogonal conjugate of isotomic conjugate of X(1006)
X(44117) = X(75)-isoconjugate of X(1243)
X(44117) = crosssum of X(2) and X(6839)
X(44117) = crossdifference of every pair of points on line {525, 36038}
X(44117) = barycentric product X(i)*X(j) for these {i,j}: {1, 2302}, {6, 1006}
X(44117) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 1243}, {1006, 76}, {2302, 75}
X(44117) = {X(184),X(5320)}-harmonic conjugate of X(25)

X(44118) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1008)

Barycentrics    a^2*(a^5*b + a^4*b^2 + a^3*b^3 + a^2*b^4 + a^5*c + 2*a^4*b*c + 2*a^3*b^2*c + 2*a^2*b^3*c + a*b^4*c + a^4*c^2 + 2*a^3*b*c^2 + 3*a^2*b^2*c^2 + 3*a*b^3*c^2 + b^4*c^2 + a^3*c^3 + 2*a^2*b*c^3 + 3*a*b^2*c^3 + 2*b^3*c^3 + a^2*c^4 + a*b*c^4 + b^2*c^4) : :

X(44118) lies on these lines: {2, 31}, {6, 25}, {22, 3736}, {32, 16372}, {39, 33714}, {58, 19310}, {82, 18147}, {386, 37576}, {612, 1918}, {968, 2339}, {2274, 5322}, {2328, 4279}, {4261, 23868}, {5132, 37577}, {10457, 37254}, {16466, 36025}, {16478, 20985}, {26885, 40728}, {28660, 33737}

X(44118) = isogonal conjugate of isotomic conjugate of X(1008)
X(44118) = crossdifference of every pair of points on line {525, 3250}
X(44118) = barycentric product X(6)*X(1008)
X(44118) = barycentric quotient X(1008)/X(76)

X(44119) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1010)

Barycentrics    a^2*(a + b)*(a + c)*(a^2 + b^2 + 2*b*c + c^2) : :

X(44119) lies on these lines: {1, 21}, {6, 25}, {27, 3914}, {42, 284}, {55, 1333}, {86, 33124}, {110, 28476}, {112, 38883}, {171, 306}, {172, 228}, {199, 2092}, {213, 26885}, {314, 14012}, {333, 6043}, {386, 11337}, {387, 4198}, {593, 4184}, {612, 2303}, {941, 4264}, {1011, 5019}, {1043, 2363}, {1096, 41364}, {1193, 2360}, {1396, 2263}, {1397, 39780}, {1402, 4215}, {1408, 34046}, {1412, 1458}, {1430, 1848}, {1437, 23122}, {1460, 2286}, {1724, 37314}, {1754, 37419}, {1781, 40973}, {1790, 3736}, {1951, 20967}, {2177, 33628}, {2285, 4206}, {2305, 22080}, {2308, 16470}, {2332, 7169}, {2355, 41015}, {3751, 40571}, {4320, 5323}, {4418, 18697}, {4749, 20988}, {6051, 37322}, {7093, 13588}, {16488, 21747}, {17016, 17521}, {17587, 32929}, {17594, 27174}, {20986, 23381}, {22389, 40956}, {24632, 26034}, {24941, 30851}, {26266, 27041}, {30941, 33171}, {30965, 32783}

X(44119) = isogonal conjugate of isotomic conjugate of X(1010)
X(44119) = X(i)-Ceva conjugate of X(j) for these (i,j): {907, 3733}, {5331, 284}
X(44119) = X(1460)-cross conjugate of X(4206)
X(44119) = X(i)-isoconjugate of X(j) for these (i,j): {65, 30479}, {75, 1245}, {76, 2281}, {226, 2339}, {307, 1039}, {313, 1472}, {321, 2221}, {523, 1310}, {525, 36099}, {661, 37215}, {1036, 1441}, {14208, 32691}, {21750, 40831}, {31993, 34260}
X(44119) = crosspoint of X(2303) and X(5323)
X(44119) = crosssum of X(i) and X(j) for these (i,j): {2, 26117}, {10, 4656}, {1214, 12709}
X(44119) = crossdifference of every pair of points on line {525, 661}
X(44119) = barycentric product X(i)*X(j) for these {i,j}: {1, 2303}, {6, 1010}, {9, 5323}, {21, 2285}, {27, 7085}, {28, 5227}, {29, 2286}, {58, 2345}, {63, 4206}, {81, 612}, {99, 2484}, {110, 6590}, {112, 23874}, {162, 2522}, {163, 2517}, {284, 388}, {333, 1460}, {662, 8678}, {799, 8646}, {1038, 1172}, {1098, 8898}, {1333, 4385}, {1412, 3974}, {1790, 7102}, {2203, 19799}, {2287, 4320}, {2327, 7103}, {2328, 7365}, {5331, 34261}, {7252, 14594}, {19459, 40411}
X(44119) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 1245}, {110, 37215}, {163, 1310}, {284, 30479}, {388, 349}, {560, 2281}, {612, 321}, {1010, 76}, {1038, 1231}, {1184, 3914}, {1460, 226}, {2194, 2339}, {2204, 1039}, {2206, 2221}, {2285, 1441}, {2286, 307}, {2303, 75}, {2345, 313}, {2484, 523}, {2517, 20948}, {2522, 14208}, {3974, 30713}, {4206, 92}, {4320, 1446}, {4385, 27801}, {5227, 20336}, {5323, 85}, {6590, 850}, {7085, 306}, {8646, 661}, {8678, 1577}, {19459, 18589}, {23874, 3267}, {32676, 36099}
X(44119) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 2206, 284}, {58, 2328, 31}, {2194, 37538, 1474}

X(44120) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1011)

Barycentrics    a^4*(a^3*b - a*b^3 + a^3*c + a^2*b*c - a*b^2*c - b^3*c - a*b*c^2 - 2*b^2*c^2 - a*c^3 - b*c^3) : :

X(44120) lies on these lines: {6, 25}, {32, 560}, {48, 33718}, {86, 9306}, {110, 17379}, {182, 6998}, {584, 692}, {1092, 37474}, {1098, 13323}, {1185, 9455}, {1437, 37507}, {4269, 33714}, {5012, 17349}, {5145, 17104}, {5651, 15668}, {7193, 13723}, {9544, 37677}, {17259, 43650}, {20986, 20992}, {26885, 37316}, {33745, 41248}, {37317, 42463}

X(44120) = isogonal conjugate of isotomic conjugate of X(1011)
X(44120) = X(i)-isoconjugate of X(j) for these (i,j): {75, 1246}, {76, 2282}, {28624, 40495}
X(44120) = crossdifference of every pair of points on line {525, 3261}
X(44120) = barycentric product X(i)*X(j) for these {i,j}: {1, 2304}, {6, 1011}, {32, 10449}, {41, 37523}, {2175, 27339}, {28623, 32739}
X(44120) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 1246}, {560, 2282}, {1011, 76}, {2304, 75}, {10449, 1502}, {27339, 41283}, {37523, 20567}
X(44120) = {X(6),X(25)}-harmonic conjugate of X(40954)

X(44121) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1012)

Barycentrics    a^3*(a^6 - a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - a*b^5 - a^5*c + 4*a^4*b*c - 2*a^2*b^3*c + a*b^4*c - 2*b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a^3*c^3 - 2*a^2*b*c^3 + 4*b^3*c^3 + a^2*c^4 + a*b*c^4 - a*c^5 - 2*b*c^5) : :

X(44121) lies on these lines: {4, 14925}, {6, 25}, {19, 10535}, {28, 6759}, {31, 2208}, {56, 3937}, {110, 37254}, {182, 33849}, {578, 4222}, {1092, 13730}, {1147, 20831}, {1437, 37260}, {1498, 37245}, {1503, 37432}, {1614, 17562}, {2192, 11406}, {2324, 26885}, {2360, 28348}, {3270, 11383}, {4185, 26883}, {4186, 11424}, {4224, 9306}, {5651, 25934}, {10282, 14017}, {10539, 39271}, {10984, 37034}, {11206, 37394}, {13323, 28376}, {13346, 28029}, {16252, 37376}, {20986, 20991}, {33810, 37397}, {37366, 43650}

X(44121) = isogonal conjugate of isotomic conjugate of X(1012)
X(44121) = crosssum of X(i) and X(j) for these (i,j): {2, 6925}, {8, 6350}
X(44121) = barycentric product X(6)*X(1012)
X(44121) = barycentric quotient X(1012)/X(76)
X(44121) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 2208, 23204}, {154, 2194, 184}

X(44122) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1080)

Barycentrics    a^2*(Sqrt[3]*(a^8 - a^6*b^2 + 3*a^4*b^4 - 3*a^2*b^6 - a^6*c^2 + 4*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 2*b^6*c^2 + 3*a^4*c^4 + 3*a^2*b^2*c^4 + 4*b^4*c^4 - 3*a^2*c^6 - 2*b^2*c^6) + 2*(a^2 + b^2 + c^2)*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + 4*b^2*c^2 - 2*c^4)*S) : :

X(44122) lies on these lines: {6, 25}, {15, 237}, {16, 3148}, {61, 20897}, {182, 3130}, {263, 3458}, {418, 11515}, {460, 5318}, {462, 5480}, {463, 1503}, {511, 3129}, {1352, 33530}, {1976, 3457}, {2871, 11086}, {3098, 3131}, {3132, 5092}, {5191, 41406}, {5335, 6620}, {6641, 11516}, {10645, 41275}, {10646, 37457}, {11485, 41266}, {34098, 37775}

X(44122) = isogonal conjugate of isotomic conjugate of X(1080)
X(44122) = barycentric product X(6)*X(1080)
X(44122) = barycentric quotient X(1080)/X(76)

X(44123) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1113)

Barycentrics    a^2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4 + a^2*(-a^2 + b^2 + c^2)*J) : :

X(44123) lies on the cubic K1067 and these lines: {6, 25}, {23, 24650}, {110, 1113}, {182, 1345}, {186, 31954}, {468, 13414}, {685, 39241}, {692, 2576}, {1114, 19128}, {1177, 2575}, {1312, 1503}, {1492, 2580}, {1576, 42668}, {1976, 8106}, {2105, 15460}, {4577, 15164}, {14500, 36201}, {15167, 42671}, {32717, 39298}, {40352, 42667}

X(44123) = reflection of X(44124) in X(206)
X(44123) = isogonal conjugate of X(22339)
X(44123) = isogonal conjugate of anticomplement of X(8105)
X(44123) = isogonal conjugate of isotomic conjugate of X(1113)
X(44123) = X(i)-Ceva conjugate of X(j) for these (i,j): {15461, 6}, {41941, 32}
X(44123) = X(i)-cross conjugate of X(j) for these (i,j): {32, 41941}, {42668, 25}
X(44123) = X(i)-isoconjugate of X(j) for these (i,j): {1, 22339}, {2, 2582}, {63, 2592}, {69, 2588}, {75, 2574}, {76, 2578}, {264, 2584}, {304, 8105}, {525, 2581}, {561, 42668}, {656, 15165}, {850, 1823}, {1114, 14208}, {1577, 8116}, {2577, 3267}, {2587, 3265}, {4592, 39240}, {20902, 39299}
X(44123) = cevapoint of X(184) and X(42668)
X(44123) = crosssum of X(2) and X(14807)
X(44123) = trilinear pole of line {32, 42667}
X(44123) = trilinear product X(i)*X(j) for these {i,j}: {6, 2576}, {25, 1822}, {31, 1113}, {32, 2580}, {112, 2579}, {163, 8106}, {184, 2586}, {560, 15164}, {1576, 2589}, {1973, 8115}
X(44123) = barycentric product X(i)*X(j) for these {i,j}: {1, 2576}, {6, 1113}, {19, 1822}, {25, 8115}, {31, 2580}, {32, 15164}, {48, 2586}, {110, 8106}, {112, 2575}, {162, 2579}, {163, 2589}, {512, 39298}, {648, 42667}, {1576, 2593}, {1989, 44067}, {2574, 41941}, {2583, 32676}, {2585, 24019}, {8105, 15461}, {23357, 39241}
X(44123) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 22339}, {25, 2592}, {31, 2582}, {32, 2574}, {112, 15165}, {560, 2578}, {1113, 76}, {1501, 42668}, {1576, 8116}, {1822, 304}, {1973, 2588}, {1974, 8105}, {2489, 39240}, {2575, 3267}, {2576, 75}, {2579, 14208}, {2580, 561}, {2586, 1969}, {2589, 20948}, {8106, 850}, {8115, 305}, {9247, 2584}, {15164, 1502}, {32676, 2581}, {39241, 23962}, {39298, 670}, {41941, 15164}, {42667, 525}, {44067, 7799}
X(44123) = {X(6),X(18374)}-harmonic conjugate of X(44124)
X(44123) = {X(25),X(34397)}-harmonic conjugate of X(44124)

X(44124) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1114)

Barycentrics    a^2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4 - a^2*(-a^2 + b^2 + c^2)*J) : :

X(44124) lies on the cubic K1067 and these lines: {6, 25}, {23, 24651}, {110, 1114}, {182, 1344}, {186, 31955}, {468, 13415}, {685, 39240}, {692, 2577}, {1113, 19128}, {1177, 2574}, {1313, 1503}, {1492, 2581}, {1576, 42667}, {1976, 8105}, {2104, 15461}, {4577, 15165}, {14499, 36201}, {15166, 42671}, {32717, 39299}, {40352, 42668}

X(44124) = reflection of X(44123) in X(206)
X(44124) = isogonal conjugate of X(22340)
X(44124) = isogonal conjugate of anticomplement of X(8106)
X(44124) = isogonal conjugate of isotomic conjugate of X(1114)
X(44124) = X(i)-Ceva conjugate of X(j) for these (i,j): {15460, 6}, {41942, 32}
X(44124) = X(i)-cross conjugate of X(j) for these (i,j): {32, 41942}, {42667, 25}
X(44124) = X(i)-isoconjugate of X(j) for these (i,j): {1, 22340}, {2, 2583}, {63, 2593}, {69, 2589}, {75, 2575}, {76, 2579}, {264, 2585}, {304, 8106}, {525, 2580}, {561, 42667}, {656, 15164}, {850, 1822}, {1113, 14208}, {1577, 8115}, {2576, 3267}, {2586, 3265}, {4592, 39241}, {20902, 39298}
X(44124) = cevapoint of X(184) and X(42667)
X(44124) = crosssum of X(2) and X(14808)
X(44124) = trilinear pole of line {32, 42668}
X(44124) = trilinear product X(i)*X(j) for these {i,j}: {6, 2577}, {25, 1823}, {31, 1114}, {32, 2581}, {112, 2578}, {163, 8105}, {184, 2587}, {560, 15165}, {1576, 2588}, {1973, 8116}
X(44124) = barycentric product X(i)*X(j) for these {i,j}: {1, 2577}, {6, 1114}, {19, 1823}, {25, 8116}, {31, 2581}, {32, 15165}, {48, 2587}, {110, 8105}, {112, 2574}, {162, 2578}, {163, 2588}, {512, 39299}, {648, 42668}, {1576, 2592}, {1989, 44068}, {2575, 41942}, {2582, 32676}, {2584, 24019}, {8106, 15460}, {23357, 39240}
X(44124) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 22340}, {25, 2593}, {31, 2583}, {32, 2575}, {112, 15164}, {560, 2579}, {1114, 76}, {1501, 42667}, {1576, 8115}, {1823, 304}, {1973, 2589}, {1974, 8106}, {2489, 39241}, {2574, 3267}, {2577, 75}, {2578, 14208}, {2581, 561}, {2587, 1969}, {2588, 20948}, {8105, 850}, {8116, 305}, {9247, 2585}, {15165, 1502}, {32676, 2580}, {39240, 23962}, {39299, 670}, {41942, 15165}, {42668, 525}, {44068, 7799}
X(44124) = {X(6),X(18374)}-harmonic conjugate of X(44123)
X(44124) = {X(25),X(34397)}-harmonic conjugate of X(44123)

X(44125) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1312)

Barycentrics    a^2*(a^2*(-a^2 + b^2 + c^2)*(-1 + J) + (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(1 + J)) : :

X(44125) lies on the orthic inconic and these lines: {4, 41519}, {6, 25}, {125, 1312}, {237, 15166}, {373, 1345}, {511, 1113}, {524, 20405}, {895, 15461}, {1344, 12294}, {1976, 41941}, {2574, 5095}, {3978, 15164}, {6000, 31955}, {6784, 8106}, {8115, 8681}, {15167, 20975}

X(44125) = midpoint of X(1113) and X(24650)
X(44125) = reflection of X(44126) in X(6)
X(44125) = isogonal conjugate of isotomic conjugate of X(1312)
X(44125) = polar conjugate of isotomic conjugate of X(15167)
X(44125) = orthic isogonal conjugate of X(8106)
X(44125) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 8106}, {25, 42667}, {1113, 647}, {1312, 15167}
X(44125) = X(i)-isoconjugate of X(j) for these (i,j): {75, 15460}, {304, 41942}, {1313, 24041}, {1823, 15165}, {2581, 8116}, {2582, 39299}
X(44125) = crosspoint of X(i) and X(j) for these (i,j): {4, 8106}, {6, 2575}
X(44125) = crosssum of X(i) and X(j) for these (i,j): {2, 1114}, {3, 8116}
X(44125) = crossdifference of every pair of points on line {525, 8116}
X(44125) = barycentric product X(i)*X(j) for these {i,j}: {4, 15167}, {6, 1312}, {115, 15461}, {125, 41941}, {2575, 8106}, {2579, 2589}, {2593, 42667}, {8749, 14500}
X(44125) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 15460}, {1312, 76}, {1974, 41942}, {3124, 1313}, {8106, 15165}, {15167, 69}, {15461, 4590}, {41941, 18020}, {42667, 8116}
X(44125) = {X(25),X(44084)}-harmonic conjugate of X(44126)
X(44125) = {X(51),X(1495)}-harmonic conjugate of X(44126)

X(44126) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1313)

Barycentrics    a^2*((a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(1 - J) - a^2*(-a^2 + b^2 + c^2)*(1 + J)) : :

X(44126) lies on the orthic inconic and these lines: {4, 41518}, {6, 25}, {125, 1313}, {237, 15167}, {373, 1344}, {511, 1114}, {524, 20406}, {895, 15460}, {1345, 12294}, {1976, 41942}, {2575, 5095}, {3978, 15165}, {6000, 31954}, {6784, 8105}, {8116, 8681}, {15166, 20975}

X(44126) = midpoint of X(1114) and X(24651)
X(44126) = reflection of X(44125) in X(6)
X(44126) = isogonal conjugate of isotomic conjugate of X(1313)
X(44126) = polar conjugate of isotomic conjugate of X(15166)
X(44126) = orthic isogonal conjugate of X(8105)
X(44126) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 8105}, {25, 42668}, {1114, 647}, {1313, 15166}
X(44126) = X(i)-isoconjugate of X(j) for these (i,j): {75, 15461}, {304, 41941}, {1312, 24041}, {1822, 15164}, {2580, 8115}, {2583, 39298}
X(44126) = crosspoint of X(i) and X(j) for these (i,j): {4, 8105}, {6, 2574}
X(44126) = crosssum of X(i) and X(j) for these (i,j): {2, 1113}, {3, 8115}
X(44126) = crossdifference of every pair of points on line {525, 8115}
X(44126) = barycentric product X(i)*X(j) for these {i,j}: {4, 15166}, {6, 1313}, {115, 15460}, {125, 41942}, {2574, 8105}, {2578, 2588}, {2592, 42668}, {8749, 14499}
X(44126) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 15461}, {1313, 76}, {1974, 41941}, {3124, 1312}, {8105, 15164}, {15166, 69}, {15460, 4590}, {41942, 18020}, {42668, 8115}
X(44126) = {X(25),X(44084)}-harmonic conjugate of X(44125)
X(44126) = {X(51),X(1495)}-harmonic conjugate of X(44125)

X(44127) = ISOGONAL CONJUGATE OF ISOTOMIC CONJUGATE OF X(1316)

Barycentrics    a^2*(a^8 - a^6*b^2 - a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 - 2*b^4*c^4 + b^2*c^6) : :

X(44127) lies on these lines: {4, 23582}, {6, 25}, {32, 512}, {110, 34383}, {115, 14574}, {182, 7418}, {263, 32716}, {511, 37930}, {525, 36156}, {1501, 2086}, {1976, 6784}, {2421, 9306}, {2679, 2715}, {2682, 7737}, {3053, 10568}, {3231, 23200}, {3506, 9149}, {3511, 19576}, {3575, 43278}, {3767, 40373}, {4558, 6786}, {5167, 10317}, {5467, 5651}, {6785, 14355}, {6793, 8754}, {7735, 41932}, {9218, 36182}, {10312, 40951}, {11645, 39750}, {14898, 41412}, {17932, 30226}, {22146, 39846}

X(44127) = isogonal conjugate of isotomic conjugate of X(1316)
X(44127) = X(i)-isoconjugate of X(j) for these (i,j): {75, 9513}, {1934, 40077}
X(44127) = crosssum of X(2) and X(36163)
X(44127) = crossdifference of every pair of points on line {325, 525}
X(44127) = barycentric product X(i)*X(j) for these {i,j}: {6, 1316}, {512, 40866}, {1691, 38947}, {2715, 31953}, {3569, 43113}
X(44127) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 9513}, {1316, 76}, {14602, 40077}, {38947, 18896}, {40866, 670}, {43113, 43187}
X(44127) = {X(25),X(2445)}-harmonic conjugate of X(1974)

X(44128) = ISOTOMIC CONJUGATE OF X(70)

Barycentrics    a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 2*b^6*c^2 - 2*b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8 : :

X(44128) lies on these lines: {2, 571}, {3, 39113}, {4, 69}, {6, 41237}, {20, 1273}, {22, 160}, {66, 14957}, {86, 37156}, {95, 7558}, {141, 41231}, {183, 5133}, {290, 18124}, {297, 8745}, {343, 6748}, {394, 467}, {1007, 7494}, {1176, 20022}, {1225, 31723}, {1238, 1975}, {1369, 15589}, {2373, 13398}, {2393, 41757}, {3547, 32816}, {3785, 7404}, {3926, 31305}, {3933, 7553}, {3964, 7387}, {5392, 13579}, {5596, 25046}, {6527, 13219}, {7403, 7767}, {7500, 37668}, {7503, 7750}, {7512, 7763}, {7773, 13160}, {7788, 34603}, {12220, 41761}, {12225, 20477}, {12605, 41005}, {14165, 37669}, {14790, 28706}, {14907, 35921}, {15760, 41008}, {17907, 22151}, {20563, 37444}, {27377, 41614}, {28419, 41253}, {28712, 37448}, {35296, 42406}

X(44128) = isotomic conjugate of X(70)
X(44128) = anticomplement of X(571)
X(44128) = anticomplement of isogonal conjugate of X(5392)
X(44128) = isotomic conjugate of anticomplement of X(34116)
X(44128) = isotomic conjugate of isogonal conjugate of X(26)
X(44128) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {68, 6360}, {75, 40697}, {91, 2}, {92, 6193}, {96, 17479}, {847, 5905}, {925, 4560}, {1820, 3164}, {2165, 192}, {5392, 8}, {14593, 21216}, {20563, 4329}, {20571, 69}, {30450, 7253}, {34385, 21271}, {36145, 31296}
X(44128) = X(34116)-cross conjugate of X(2)
X(44128) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2158}, {31, 70}, {560, 20564}, {810, 1288}
X(44128) = crosssum of X(20975) and X(34952)
X(44128) = X(19)-of-dual-of-orthic-triangle if ABC is acute
X(44128) = barycentric product X(i)*X(j) for these {i,j}: {26, 76}, {305, 8746}, {1502, 44078}
X(44128) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2158}, {2, 70}, {26, 6}, {76, 20564}, {648, 1288}, {8746, 25}, {34116, 571}, {36418, 44078}, {44078, 32}
X(44128) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 69, 311}, {315, 317, 69}, {340, 14615, 69}, {637, 638, 11412}, {32002, 38434, 69}

X(44129) = ISOTOMIC CONJUGATE OF X(71)

Barycentrics    b^2*(a + b)*c^2*(a + c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2) : :
Barycentrics    (csc 2A)/(b + c) : :

X(44129) lies on these lines: {4, 69}, {27, 310}, {29, 811}, {58, 21207}, {86, 8747}, {92, 304}, {99, 917}, {274, 278}, {324, 26541}, {333, 349}, {337, 16747}, {447, 33954}, {469, 18152}, {648, 43093}, {799, 37203}, {823, 37214}, {1043, 35517}, {1172, 30940}, {1396, 8033}, {1838, 10471}, {2064, 27801}, {2700, 22456}, {2973, 17982}, {6331, 6336}, {6528, 18025}, {6999, 26166}, {7379, 30737}, {16749, 23989}, {17911, 17913}, {18134, 40011}, {36659, 41009}, {40071, 40445}

X(44129) = isogonal conjugate of X(2200)
X(44129) = isotomic conjugate of X(71)
X(44129) = polar conjugate of X(42)
X(44129) = isotomic conjugate of anticomplement of X(34830)
X(44129) = isotomic conjugate of complement of X(17220)
X(44129) = isotomic conjugate of isogonal conjugate of X(27)
X(44129) = anticomplement of isotomic conjugate of polar conjugate of X(40954)
X(44129) = anticomplement of crosspoint of X(2) and X(71)
X(44129) = anticomplement of crosssum of X(6) and X(27)
X(44129) = anticomplement of X(2)-Ceva conjugate of X(34830)
X(44129) = pole wrt polar circle of trilinear polar of X(42) (line X(512)X(798))
X(44129) = perspector of ABC and orthoanticevian triangle of X(310)
X(44129) = polar conjugate of isotomic conjugate of X(310)
X(44129) = polar conjugate of isogonal conjugate of X(86)
X(44129) = X(i)-cross conjugate of X(j) for these (i,j): {85, 274}, {86, 310}, {92, 286}, {1848, 273}, {5249, 75}, {17167, 86}, {17171, 27}, {18161, 81}, {18650, 15467}, {19786, 1240}, {21137, 514}, {34830, 2}
X(44129) = cevapoint of X(i) and X(j) for these (i,j): {2, 17220}, {4, 17911}, {6, 23339}, {27, 86}, {75, 18134}, {85, 331}, {92, 264}, {286, 31623}, {514, 21207}
X(44129) = crosssum of X(3) and X(23176)
X(44129) = trilinear pole of line {3261, 4025}
X(44129) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2200}, {3, 213}, {6, 228}, {10, 9247}, {19, 4055}, {25, 3990}, {31, 71}, {32, 72}, {37, 184}, {41, 73}, {42, 48}, {55, 1409}, {63, 1918}, {69, 2205}, {100, 3049}, {101, 810}, {181, 2193}, {212, 1400}, {219, 1402}, {220, 1410}, {248, 5360}, {255, 2333}, {295, 41333}, {306, 560}, {307, 9447}, {321, 14575}, {512, 906}, {577, 1824}, {603, 1334}, {604, 2318}, {607, 22341}, {647, 692}, {656, 32739}, {661, 32656}, {667, 4574}, {669, 1332}, {798, 1331}, {822, 8750}, {872, 1790}, {904, 22061}, {1042, 1802}, {1176, 21814}, {1214, 2175}, {1231, 9448}, {1258, 23212}, {1333, 3690}, {1397, 3694}, {1437, 1500}, {1439, 14827}, {1444, 7109}, {1501, 20336}, {1783, 39201}, {1794, 40978}, {1880, 6056}, {1917, 40071}, {1924, 4561}, {1946, 4559}, {1973, 3682}, {1974, 3998}, {1976, 42702}, {2176, 22381}, {2187, 41087}, {2194, 2197}, {2196, 3747}, {2204, 7066}, {2206, 3949}, {2212, 40152}, {2281, 7085}, {2332, 7138}, {2359, 3725}, {3063, 23067}, {3198, 14642}, {3709, 36059}, {3954, 10547}, {3955, 40729}, {4041, 32660}, {4079, 4575}, {4557, 22383}, {4601, 23216}, {4705, 32661}, {7084, 23620}, {7116, 20964}, {7123, 22363}, {8606, 21741}, {14533, 21807}, {14573, 42698}, {14585, 41013}, {14908, 21839}, {15389, 21877}, {17743, 22364}, {18098, 20775}, {18210, 23990}, {20683, 32658}, {20760, 21759}, {21046, 23995}, {21805, 32659}, {21874, 40319}, {22080, 28615}, {27801, 40373}, {34055, 41267}, {36057, 39258}
X(44129) = barycentric product X(i)*X(j) for these {i,j}: {4, 310}, {19, 6385}, {27, 76}, {28, 561}, {29, 6063}, {34, 40072}, {58, 18022}, {75, 286}, {81, 1969}, {85, 31623}, {86, 264}, {92, 274}, {162, 40495}, {225, 18021}, {273, 314}, {276, 17167}, {278, 28660}, {305, 8747}, {308, 17171}, {331, 333}, {514, 6331}, {648, 3261}, {670, 7649}, {689, 21108}, {693, 811}, {799, 17924}, {823, 15413}, {873, 41013}, {1172, 20567}, {1396, 28659}, {1434, 7017}, {1474, 1502}, {1790, 18027}, {1848, 40827}, {1896, 7182}, {1928, 2203}, {1978, 17925}, {2052, 17206}, {2299, 41283}, {2973, 4600}, {3112, 16747}, {4025, 6528}, {4602, 6591}, {4610, 14618}, {4623, 24006}, {5317, 40364}, {6335, 7199}, {6628, 7141}, {15149, 18031}, {15352, 30805}, {18020, 21207}, {18026, 18155}, {18827, 40717}, {18895, 31905}, {36419, 40071}
X(44129) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 228}, {2, 71}, {3, 4055}, {4, 42}, {6, 2200}, {7, 73}, {8, 2318}, {10, 3690}, {19, 213}, {21, 212}, {25, 1918}, {27, 6}, {28, 31}, {29, 55}, {34, 1402}, {57, 1409}, {58, 184}, {63, 3990}, {69, 3682}, {75, 72}, {76, 306}, {77, 22341}, {81, 48}, {85, 1214}, {86, 3}, {87, 22381}, {92, 37}, {99, 1331}, {107, 8750}, {110, 32656}, {112, 32739}, {158, 1824}, {162, 692}, {189, 41087}, {190, 4574}, {225, 181}, {226, 2197}, {240, 5360}, {242, 3747}, {261, 283}, {264, 10}, {269, 1410}, {270, 2194}, {273, 65}, {274, 63}, {278, 1400}, {281, 1334}, {283, 6056}, {285, 2188}, {286, 1}, {304, 3998}, {307, 7066}, {310, 69}, {312, 3694}, {313, 3695}, {314, 78}, {318, 210}, {321, 3949}, {324, 21011}, {331, 226}, {332, 1259}, {333, 219}, {338, 21046}, {342, 227}, {348, 40152}, {349, 26942}, {393, 2333}, {423, 17735}, {427, 21035}, {513, 810}, {514, 647}, {561, 20336}, {614, 22363}, {645, 4587}, {648, 101}, {649, 3049}, {653, 4559}, {662, 906}, {664, 23067}, {670, 4561}, {693, 656}, {757, 1437}, {799, 1332}, {811, 100}, {823, 1783}, {850, 4064}, {873, 1444}, {894, 22061}, {905, 822}, {1010, 7085}, {1014, 603}, {1019, 22383}, {1043, 1260}, {1088, 1439}, {1111, 18210}, {1119, 1042}, {1125, 22080}, {1172, 41}, {1210, 3611}, {1235, 15523}, {1269, 41014}, {1333, 9247}, {1396, 604}, {1414, 36059}, {1430, 44112}, {1434, 222}, {1439, 7138}, {1441, 201}, {1442, 22342}, {1444, 255}, {1446, 37755}, {1459, 39201}, {1474, 32}, {1502, 40071}, {1509, 1790}, {1790, 577}, {1812, 2289}, {1824, 872}, {1826, 1500}, {1829, 3725}, {1838, 40952}, {1839, 20970}, {1841, 40978}, {1842, 40984}, {1843, 41267}, {1847, 1427}, {1848, 2092}, {1851, 40934}, {1855, 21795}, {1860, 40954}, {1861, 20683}, {1870, 3724}, {1895, 3198}, {1896, 33}, {1897, 4557}, {1920, 4019}, {1959, 42702}, {1969, 321}, {1973, 2205}, {2052, 1826}, {2185, 2193}, {2201, 41333}, {2203, 560}, {2204, 9447}, {2206, 14575}, {2287, 1802}, {2299, 2175}, {2309, 23212}, {2322, 220}, {2332, 14827}, {2333, 7109}, {2501, 4079}, {2669, 20796}, {2905, 18755}, {2969, 3122}, {2970, 21043}, {2973, 3120}, {3064, 3709}, {3120, 20975}, {3194, 2187}, {3261, 525}, {3596, 3710}, {3615, 8606}, {3662, 20727}, {3668, 1425}, {3673, 17441}, {3720, 22369}, {3737, 1946}, {3794, 20753}, {3944, 22169}, {4000, 23620}, {4025, 520}, {4091, 32320}, {4146, 7591}, {4183, 1253}, {4233, 21059}, {4241, 2426}, {4248, 3052}, {4357, 22076}, {4359, 3958}, {4391, 8611}, {4466, 3269}, {4556, 32661}, {4560, 652}, {4565, 32660}, {4573, 1813}, {4610, 4558}, {4623, 4592}, {4625, 6516}, {5089, 39258}, {5125, 209}, {5209, 17977}, {5249, 18591}, {5317, 1973}, {5342, 37593}, {5379, 1110}, {6063, 307}, {6331, 190}, {6335, 1018}, {6385, 304}, {6528, 1897}, {6591, 798}, {6625, 15377}, {6626, 22139}, {6629, 3292}, {7009, 20964}, {7017, 2321}, {7032, 22364}, {7058, 2327}, {7101, 4515}, {7141, 6535}, {7191, 23203}, {7192, 1459}, {7199, 905}, {7257, 4571}, {7282, 2594}, {7292, 23230}, {7649, 512}, {8025, 22054}, {8743, 21034}, {8747, 25}, {8748, 607}, {8822, 7078}, {11125, 9409}, {13149, 1020}, {14006, 2330}, {14012, 26924}, {14534, 2359}, {14616, 1807}, {14618, 4024}, {15149, 672}, {15413, 24018}, {15419, 4091}, {15466, 8804}, {15467, 28786}, {16082, 2250}, {16099, 43693}, {16696, 4020}, {16704, 22356}, {16705, 22097}, {16709, 3916}, {16727, 3942}, {16732, 3708}, {16738, 22065}, {16747, 38}, {16749, 26934}, {16750, 7289}, {16887, 3917}, {16891, 20819}, {17103, 3955}, {17139, 22350}, {17167, 216}, {17168, 22052}, {17169, 22053}, {17170, 22057}, {17171, 39}, {17172, 14961}, {17173, 22058}, {17174, 22059}, {17175, 22060}, {17176, 22062}, {17177, 22064}, {17178, 22066}, {17179, 22067}, {17180, 22068}, {17181, 22069}, {17182, 22071}, {17183, 22072}, {17184, 22073}, {17185, 22074}, {17186, 22075}, {17187, 20775}, {17192, 22077}, {17193, 22078}, {17194, 22079}, {17195, 22082}, {17196, 22083}, {17197, 7117}, {17198, 22084}, {17199, 22085}, {17200, 22352}, {17202, 22447}, {17204, 22087}, {17205, 3937}, {17206, 394}, {17208, 22412}, {17209, 3289}, {17211, 22420}, {17212, 22093}, {17215, 22089}, {17216, 2972}, {17217, 22090}, {17218, 22091}, {17219, 1364}, {17220, 40591}, {17442, 21814}, {17515, 2361}, {17555, 22276}, {17731, 17976}, {17770, 20754}, {17863, 18673}, {17907, 4456}, {17911, 40586}, {17921, 20979}, {17923, 2245}, {17924, 661}, {17925, 649}, {17926, 657}, {17982, 2054}, {17984, 4039}, {18020, 4570}, {18021, 332}, {18022, 313}, {18026, 4551}, {18155, 521}, {18157, 25083}, {18169, 22389}, {18206, 20752}, {18604, 4100}, {18605, 563}, {18609, 2315}, {18645, 22055}, {18646, 22056}, {18648, 22401}, {18653, 3284}, {18792, 20777}, {18827, 295}, {19804, 4047}, {20567, 1231}, {20883, 3954}, {21102, 15451}, {21108, 3005}, {21109, 42665}, {21172, 42658}, {21178, 8673}, {21191, 2524}, {21205, 9517}, {21207, 125}, {23788, 8677}, {23989, 4466}, {23999, 5379}, {24006, 4705}, {24046, 43218}, {26818, 22088}, {26860, 22357}, {26871, 836}, {26959, 22409}, {28660, 345}, {29767, 22126}, {30939, 5440}, {30940, 20769}, {30941, 1818}, {30966, 3781}, {31008, 22370}, {31623, 9}, {31900, 2308}, {31905, 1914}, {31906, 21764}, {31908, 5332}, {31909, 2276}, {31912, 21793}, {31917, 2275}, {31926, 2280}, {32010, 7015}, {32014, 1796}, {33295, 7193}, {33296, 20760}, {33947, 3784}, {33955, 7293}, {36419, 1474}, {36421, 2332}, {36797, 3939}, {37128, 2196}, {37168, 902}, {38462, 21805}, {39915, 23079}, {40011, 40161}, {40072, 3718}, {40149, 2171}, {40395, 2259}, {40411, 7123}, {40412, 1794}, {40414, 2983}, {40432, 7116}, {40495, 14208}, {40684, 21012}, {40717, 740}, {40836, 2357}, {40940, 44093}, {40975, 21753}, {41013, 756}, {41083, 198}, {41364, 205}, {41629, 20818}, {42394, 21022}, {42396, 4628}, {43925, 1919}

X(44130) = ISOTOMIC CONJUGATE OF X(73)

Barycentrics    b^2*(a + b)*c^2*(a + c)*(-a + b + c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2) : :
Barycentrics    (csc A)/(sec B + sec C) : :
Barycentrics    (csc 2A)/(cos B + cos C) : :

X(44130) lies on these lines: {4, 69}, {27, 1240}, {29, 332}, {75, 158}, {86, 811}, {99, 7436}, {273, 310}, {274, 40836}, {281, 345}, {313, 1043}, {318, 3718}, {333, 1948}, {799, 43764}, {1441, 14009}, {1896, 30479}, {2708, 22456}, {6528, 34393}, {7019, 40717}, {7141, 17927}, {7498, 30022}, {8822, 35516}, {18697, 40703}, {30737, 37443}

X(44130) = isotomic conjugate of X(73)
X(44130) = polar conjugate of X(1400)
X(44130) = anticomplement of isogonal conjugate of polar conjugate of X(3142)
X(44130) = anticomplement of crosspoint of X(2) and X(73)
X(44130) = anticomplement of crosssum of X(6) and X(29)
X(44130) = anticomplement of X(2)-Ceva conjugate of X(34831)
X(44130) = pole wrt polar circle of trilinear polar of X(1400) (line X(512)X(810))
X(44130) = isotomic conjugate of anticomplement of X(34831)
X(44130) = isotomic conjugate of isogonal conjugate of X(29)
X(44130) = polar conjugate of isotomic conjugate of X(28660)
X(44130) = polar conjugate of isogonal conjugate of X(333)
X(44130) = X(i)-cross conjugate of X(j) for these (i,j): {75, 314}, {318, 31623}, {333, 28660}, {6734, 312}, {18155, 811}, {24430, 21}, {34831, 2}, {37774, 18031}
X(44130) = cevapoint of X(i) and X(j) for these (i,j): {29, 333}, {75, 264}, {92, 17555}, {318, 7017}
X(44130) = trilinear pole of line {3064, 6332}
X(44130) = X(i)-isoconjugate of X(j) for these (i,j): {3, 1402}, {6, 1409}, {25, 22341}, {31, 73}, {32, 1214}, {34, 4055}, {42, 603}, {48, 1400}, {55, 1410}, {56, 228}, {57, 2200}, {65, 184}, {71, 604}, {72, 1397}, {77, 1918}, {108, 39201}, {109, 810}, {181, 1437}, {201, 2206}, {212, 1042}, {213, 222}, {226, 9247}, {296, 44112}, {307, 560}, {348, 2205}, {512, 36059}, {577, 1880}, {608, 3990}, {647, 1415}, {651, 3049}, {661, 32660}, {667, 23067}, {669, 6516}, {798, 1813}, {822, 32674}, {906, 7180}, {1037, 22363}, {1106, 2318}, {1231, 1501}, {1333, 2197}, {1334, 7099}, {1395, 3682}, {1403, 22381}, {1408, 3690}, {1425, 2194}, {1426, 6056}, {1439, 2175}, {1441, 14575}, {1824, 7335}, {1949, 42669}, {1973, 40152}, {2199, 41087}, {2203, 7066}, {2281, 2286}, {2299, 7138}, {2333, 7125}, {2357, 7114}, {3949, 16947}, {4017, 32656}, {4559, 22383}, {6186, 22342}, {14585, 40149}, {14642, 30456}, {20336, 41280}
X(44130) = barycentric product X(i)*X(j) for these {i,j}: {4, 28660}, {19, 40072}, {21, 1969}, {27, 3596}, {28, 28659}, {29, 76}, {33, 6385}, {75, 31623}, {86, 7017}, {92, 314}, {264, 333}, {270, 27801}, {274, 318}, {281, 310}, {283, 18027}, {284, 18022}, {286, 312}, {304, 1896}, {305, 8748}, {331, 1043}, {332, 2052}, {522, 6331}, {561, 1172}, {648, 35519}, {670, 3064}, {811, 4391}, {823, 35518}, {1474, 40363}, {1502, 2299}, {1826, 18021}, {1928, 2204}, {2322, 6063}, {2332, 41283}, {3261, 36797}, {4183, 20567}, {4572, 17926}, {4602, 18344}, {4620, 21666}, {4631, 24006}, {5931, 15466}, {6332, 6528}, {6335, 18155}, {7257, 17924}, {14024, 18895}, {36800, 40717}
X(44130) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1409}, {2, 73}, {4, 1400}, {8, 71}, {9, 228}, {10, 2197}, {19, 1402}, {21, 48}, {27, 56}, {28, 604}, {29, 6}, {33, 213}, {55, 2200}, {57, 1410}, {63, 22341}, {69, 40152}, {75, 1214}, {76, 307}, {78, 3990}, {81, 603}, {85, 1439}, {86, 222}, {92, 65}, {99, 1813}, {107, 32674}, {110, 32660}, {158, 1880}, {162, 1415}, {190, 23067}, {219, 4055}, {226, 1425}, {243, 42669}, {261, 1790}, {264, 226}, {270, 1333}, {273, 1427}, {274, 77}, {278, 1042}, {280, 41087}, {281, 42}, {283, 577}, {284, 184}, {286, 57}, {306, 7066}, {310, 348}, {312, 72}, {313, 26942}, {314, 63}, {318, 37}, {321, 201}, {331, 3668}, {332, 394}, {333, 3}, {341, 3694}, {345, 3682}, {346, 2318}, {349, 6356}, {415, 17966}, {497, 23620}, {521, 822}, {522, 647}, {556, 7591}, {561, 1231}, {607, 1918}, {643, 906}, {645, 1331}, {648, 109}, {650, 810}, {652, 39201}, {662, 36059}, {663, 3049}, {799, 6516}, {811, 651}, {823, 108}, {950, 44093}, {1010, 2286}, {1014, 7099}, {1021, 1946}, {1039, 2281}, {1043, 219}, {1098, 2193}, {1172, 31}, {1214, 7138}, {1396, 1106}, {1434, 7053}, {1441, 37755}, {1444, 7125}, {1474, 1397}, {1790, 7335}, {1792, 2289}, {1812, 255}, {1817, 7114}, {1826, 181}, {1857, 2333}, {1859, 40978}, {1895, 30456}, {1896, 19}, {1897, 4559}, {1948, 851}, {1969, 1441}, {2052, 225}, {2082, 22363}, {2185, 1437}, {2189, 2206}, {2194, 9247}, {2202, 44112}, {2204, 560}, {2212, 2205}, {2287, 212}, {2299, 32}, {2319, 22381}, {2321, 3690}, {2322, 55}, {2326, 2194}, {2327, 6056}, {2332, 2175}, {2907, 2305}, {3064, 512}, {3194, 2199}, {3219, 22342}, {3261, 17094}, {3559, 2178}, {3596, 306}, {3686, 22080}, {3687, 22076}, {3691, 22369}, {3699, 4574}, {3701, 3949}, {3702, 3958}, {3705, 20727}, {3718, 3998}, {3737, 22383}, {4183, 41}, {4391, 656}, {4397, 8611}, {4560, 1459}, {4563, 6517}, {4612, 4575}, {4631, 4592}, {4636, 32661}, {4673, 4047}, {4858, 18210}, {5081, 2245}, {5249, 39791}, {5317, 1395}, {5379, 2149}, {5546, 32656}, {5931, 1073}, {6198, 21741}, {6331, 664}, {6332, 520}, {6335, 4551}, {6385, 7182}, {6514, 1092}, {6528, 653}, {6708, 2658}, {6734, 18591}, {7003, 2357}, {7017, 10}, {7020, 1903}, {7046, 1334}, {7058, 283}, {7081, 22061}, {7101, 210}, {7253, 652}, {7256, 4587}, {7257, 1332}, {7258, 4571}, {7452, 2425}, {7649, 7180}, {8735, 3122}, {8747, 608}, {8748, 25}, {8822, 7011}, {11107, 2174}, {11393, 21744}, {14006, 172}, {14024, 1914}, {14331, 42658}, {14361, 8803}, {14400, 9409}, {15146, 1951}, {15149, 1458}, {15352, 36127}, {15466, 5930}, {16713, 22053}, {17167, 30493}, {17171, 1401}, {17182, 23154}, {17185, 22345}, {17197, 3937}, {17206, 1804}, {17515, 7113}, {17555, 40590}, {17923, 1464}, {17924, 4017}, {17925, 43924}, {17926, 663}, {18021, 17206}, {18022, 349}, {18026, 1020}, {18155, 905}, {18163, 22344}, {18344, 798}, {20665, 22364}, {21044, 20975}, {21300, 22443}, {21666, 21044}, {23661, 18675}, {25128, 2524}, {27398, 7078}, {27509, 22057}, {27527, 22090}, {27958, 3955}, {28659, 20336}, {28660, 69}, {30713, 3695}, {31623, 1}, {31631, 3157}, {31905, 1428}, {31909, 1469}, {31917, 7248}, {31926, 1471}, {33950, 23203}, {34387, 4466}, {35145, 296}, {35196, 14533}, {35518, 24018}, {35519, 525}, {36421, 2299}, {36797, 101}, {36800, 295}, {37142, 1949}, {37168, 1404}, {37908, 9454}, {40011, 28786}, {40072, 304}, {40149, 1254}, {40363, 40071}, {40411, 1037}, {40414, 951}, {40571, 3215}, {40717, 16609}, {40882, 17975}, {40979, 23204}, {40987, 21750}, {41013, 2171}, {41083, 221}

X(44131) = ISOTOMIC CONJUGATE OF ISOGONAL CONJUGATE OF X(235)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 4*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

X(44131) lies on these lines: {4, 69}, {6, 37778}, {24, 20477}, {25, 30737}, {53, 338}, {74, 8795}, {95, 3520}, {185, 19166}, {235, 41005}, {273, 34387}, {297, 26156}, {318, 34388}, {324, 3580}, {339, 1596}, {393, 41760}, {427, 11197}, {458, 26206}, {459, 2052}, {800, 41678}, {1249, 21447}, {1593, 26166}, {1885, 41008}, {2322, 26592}, {2373, 20626}, {3089, 6527}, {3542, 40680}, {9308, 40318}, {15066, 40684}, {27377, 40316}

X(44131) = polar conjugate of X(41890)
X(44131) = isotomic conjugate of isogonal conjugate of X(235)
X(44131) = polar conjugate of isogonal conjugate of X(13567)
X(44131) = X(264)-Ceva conjugate of X(41005)
X(44131) = X(i)-isoconjugate of X(j) for these (i,j): {48, 41890}, {184, 775}, {801, 9247}, {821, 23606}
X(44131) = cevapoint of X(235) and X(13567)
X(44131) = crosssum of X(184) and X(23606)
X(44131) = barycentric product X(i)*X(j) for these {i,j}: {76, 235}, {92, 17858}, {185, 18027}, {264, 13567}, {324, 19166}, {774, 1969}, {800, 18022}, {850, 41678}, {1502, 44079}, {2052, 41005}
X(44131) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 41890}, {92, 775}, {185, 577}, {235, 6}, {264, 801}, {774, 48}, {800, 184}, {820, 4100}, {1624, 32661}, {2052, 1105}, {2883, 15905}, {6508, 255}, {6509, 1092}, {6521, 821}, {13567, 3}, {14091, 1660}, {16035, 14533}, {17773, 22089}, {17858, 63}, {18022, 40830}, {18603, 1437}, {19166, 97}, {19180, 19210}, {36424, 44079}, {41005, 394}, {41580, 10316}, {41602, 23115}, {41603, 14961}, {41678, 110}, {44079, 32}
X(44131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 264, 32000}, {264, 311, 1235}, {264, 317, 3260}, {21447, 40814, 1249}

X(44132) = ISOTOMIC CONJUGATE X(248)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4) : :
Barycentrics    csc A csc 2A cos(A + ω) : :

X(44132) lies on these lines: {4, 69}, {276, 308}, {290, 41074}, {297, 6393}, {305, 2052}, {324, 8024}, {325, 2967}, {339, 15980}, {384, 26166}, {393, 3926}, {436, 37894}, {648, 41363}, {687, 40832}, {1297, 5999}, {1502, 18027}, {1629, 16276}, {1972, 18024}, {1975, 33971}, {1990, 35549}, {2211, 39931}, {2799, 3267}, {2987, 16081}, {3266, 6331}, {4121, 6747}, {4176, 6820}, {4590, 15014}, {5025, 40822}, {7763, 17907}, {7769, 34349}, {7799, 37765}, {10002, 32816}, {11547, 34254}, {12215, 41204}, {14165, 37804}, {16264, 32819}, {30506, 33798}, {31636, 34137}, {32830, 43981}, {39998, 40684}, {43710, 43714}

X(44132) = isogonal conjugate of X(14600)
X(44132) = isotomic conjugate of X(248)
X(44132) = polar conjugate of X(1976)
X(44132) = isotomic conjugate of isogonal conjugate of X(297)
X(44132) = polar conjugate of isogonal conjugate of X(325)
X(44132) = X(41174)-Ceva conjugate of X(6331)
X(44132) = X(i)-cross conjugate of X(j) for these (i,j): {2799, 877}, {35088, 850}
X(44132) = cevapoint of X(297) and X(325)
X(44132) = crosspoint of X(6331) and X(41174)
X(44132) = trilinear pole of line {6333, 16230}
X(44132) = crossdifference of every pair of points on line {3049, 14575}
X(44132) = pole wrt polar circle of trilinear polar of X(1976) (line X(32)X(512), or PU(39))
X(44132) = perspector of circumconic through the polar conjugates of PU(39)
X(44132) = trilinear product X(i)*X(j) for these {i,j}: {75, 297}, {76, 240}, {92, 325}, {158, 6393}, {232, 561}, {264, 1959}, {304, 6530}, {511, 1969}, {811, 2799}, {823, 6333}, {877, 1577}, {1235, 3405}, {1928, 2211}
X(44132) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14600}, {31, 248}, {32, 293}, {48, 1976}, {63, 14601}, {98, 9247}, {163, 878}, {184, 1910}, {287, 560}, {336, 1501}, {798, 43754}, {810, 2715}, {822, 32696}, {1821, 14575}, {1924, 17932}, {1933, 15391}, {1973, 17974}, {2422, 4575}, {3049, 36084}, {3404, 10547}, {14585, 36120}, {36104, 39201}
X(44132) = barycentric product X(i)*X(j) for these {i,j}: {75, 40703}, {76, 297}, {232, 1502}, {240, 561}, {264, 325}, {286, 42703}, {305, 6530}, {511, 18022}, {670, 16230}, {850, 877}, {1235, 20022}, {1959, 1969}, {2052, 6393}, {2211, 40362}, {2396, 14618}, {2799, 6331}, {2967, 18024}, {4609, 17994}, {6333, 6528}, {16081, 32458}, {18027, 36212}, {18896, 39931}, {34384, 39569}, {34854, 40050}, {35088, 41174}
X(44132) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 248}, {4, 1976}, {6, 14600}, {25, 14601}, {69, 17974}, {75, 293}, {76, 287}, {92, 1910}, {99, 43754}, {107, 32696}, {132, 42671}, {232, 32}, {237, 14575}, {240, 31}, {264, 98}, {297, 6}, {305, 6394}, {325, 3}, {340, 14355}, {511, 184}, {523, 878}, {561, 336}, {648, 2715}, {670, 17932}, {684, 39201}, {811, 36084}, {823, 36104}, {850, 879}, {868, 20975}, {877, 110}, {1235, 20021}, {1755, 9247}, {1916, 15391}, {1959, 48}, {1969, 1821}, {2052, 6531}, {2211, 1501}, {2396, 4558}, {2421, 32661}, {2450, 40947}, {2501, 2422}, {2799, 647}, {2967, 237}, {2973, 43920}, {3260, 35912}, {3289, 14585}, {3569, 3049}, {4230, 1576}, {5968, 14908}, {6331, 2966}, {6333, 520}, {6393, 394}, {6528, 685}, {6530, 25}, {7017, 15628}, {8754, 15630}, {8840, 43722}, {9155, 23200}, {9418, 40373}, {14618, 2395}, {15352, 20031}, {15595, 8779}, {16081, 41932}, {16089, 32545}, {16230, 512}, {17875, 8766}, {17907, 11610}, {17984, 40820}, {17994, 669}, {18022, 290}, {18027, 16081}, {20022, 1176}, {20883, 3404}, {22456, 41173}, {30737, 34156}, {32458, 36212}, {33752, 42659}, {34765, 35909}, {34854, 1974}, {35088, 41172}, {35140, 15407}, {35142, 2065}, {35908, 40352}, {35910, 18877}, {36212, 577}, {36426, 232}, {36790, 3289}, {39569, 51}, {39931, 1691}, {40703, 1}, {40810, 17970}, {40887, 1968}, {41167, 39469}, {42703, 72}, {42717, 906}, {42751, 23220}
X(44132) = {X(324),X(8024)}-harmonic conjugate of X(18022)
X(44132) = {P,U}-harmonic conjugate of X(76), where P, U are the polar conjugates of X(5638) and X(5639)

X(44133) = ISOTOMIC CONJUGATE X(3426)

Barycentrics    b^2*c^2*(-5*a^4 + 4*a^2*b^2 + b^4 + 4*a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(44133) lies on these lines: {4, 69}, {95, 16035}, {99, 43660}, {183, 11284}, {290, 35179}, {305, 670}, {322, 3264}, {325, 11059}, {338, 15533}, {394, 648}, {524, 40814}, {1273, 7871}, {3262, 33933}, {3266, 37668}, {6148, 11057}, {6527, 30698}, {8681, 37190}, {9307, 20819}, {9464, 10513}, {15066, 34289}, {15589, 26235}, {16284, 35516}, {32831, 40680}, {34386, 43752}, {37671, 40022}, {40341, 41760}, {40996, 41009}

X(44133) = isotomic conjugate of X(3426)
X(44133) = isotomic conjugate of isogonal conjugate of X(376)
X(44133) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3426}, {560, 36889}, {810, 9064}
X(44133) = cevapoint of X(15066) and X(21312)
X(44133) = barycentric product X(i)*X(j) for these {i,j}: {76, 376}, {305, 40138}, {670, 9209}, {1502, 26864}, {6331, 9007}, {32833, 39263}
X(44133) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3426}, {76, 36889}, {376, 6}, {648, 9064}, {9007, 647}, {9209, 512}, {26864, 32}, {36427, 26864}, {39263, 34288}, {40138, 25}
X(44133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 315, 340}, {69, 3260, 76}, {69, 14615, 264}, {76, 3260, 264}, {76, 14615, 3260}

X(44134) = ISOTOMIC CONJUGATE X(4846)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 4*b^2*c^2 + c^4) : :
X(44134) = 3 X[458] - 2 X[6749]

X(44134) lies on these lines: {2, 648}, {4, 69}, {5, 40996}, {25, 37671}, {53, 3631}, {95, 253}, {99, 35485}, {140, 41005}, {141, 1990}, {183, 468}, {193, 36794}, {231, 41770}, {232, 16990}, {273, 319}, {290, 5486}, {297, 599}, {298, 471}, {299, 470}, {318, 320}, {325, 5094}, {376, 36889}, {378, 32833}, {393, 3620}, {427, 7788}, {458, 524}, {550, 20477}, {670, 18022}, {1007, 37803}, {1078, 35486}, {1093, 11487}, {1119, 42696}, {1249, 3619}, {1272, 14558}, {1273, 37119}, {1585, 32809}, {1586, 32808}, {1656, 40995}, {1897, 4389}, {1899, 2992}, {2322, 17234}, {3087, 20080}, {3096, 41361}, {3516, 3964}, {3522, 6527}, {3535, 32811}, {3536, 32810}, {3541, 7796}, {3618, 5702}, {3630, 6748}, {3642, 6111}, {3643, 6110}, {3785, 37460}, {4232, 15589}, {5081, 17360}, {5117, 38294}, {6148, 35481}, {7046, 42697}, {7282, 17361}, {7408, 40002}, {7750, 37196}, {7758, 37337}, {7763, 37118}, {7767, 37458}, {7811, 18533}, {7868, 16318}, {7879, 27376}, {7896, 27371}, {8795, 42021}, {9723, 35477}, {10295, 14907}, {11008, 40065}, {11109, 17378}, {11547, 37636}, {13577, 18816}, {15454, 40423}, {16063, 30737}, {16263, 41465}, {16264, 33878}, {17271, 17555}, {17297, 37448}, {17346, 26003}, {18384, 34405}, {21356, 37765}, {24206, 41371}, {27377, 40341}, {31635, 41359}, {31886, 41374}, {32817, 35483}, {35142, 35179}, {35510, 40410}, {37645, 43530}

X(44134) = isotomic conjugate of X(4846)
X(44134) = anticomplement of X(5158)
X(44134) = polar conjugate of X(34288)
X(44134) = anticomplement of isogonal conjugate of X(43530)
X(44134) = isotomic conjugate of anticomplement of X(4550)
X(44134) = isotomic conjugate of isogonal conjugate of X(378)
X(44134) = polar conjugate of isotomic conjugate of X(32833)
X(44134) = polar conjugate of isogonal conjugate of X(15066)
X(44134) = pole wrt polar circle of trilinear polar of X(34288) (line X(512)X(1637))
X(44134) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {92, 18387}, {3431, 6360}, {16263, 5905}, {22455, 18668}, {43530, 8}
X(44134) = X(i)-cross conjugate of X(j) for these (i,j): {4550, 2}, {5891, 15066}, {15066, 32833}
X(44134) = X(i)-isoconjugate of X(j) for these (i,j): {31, 4846}, {48, 34288}, {647, 36149}, {656, 32738}, {810, 1302}, {2631, 32681}, {9247, 34289}, {9409, 36083}
X(44134) = cevapoint of X(i) and X(j) for these (i,j): {376, 37645}, {378, 15066}
X(44134) = crossdifference of every pair of points on line {3049, 9409}
X(44134) = barycentric product X(i)*X(j) for these {i,j}: {4, 32833}, {76, 378}, {264, 15066}, {276, 5891}, {286, 42704}, {648, 30474}, {1502, 44080}, {5063, 18022}, {6331, 8675}
X(44134) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 4846}, {4, 34288}, {112, 32738}, {162, 36149}, {264, 34289}, {378, 6}, {648, 1302}, {1304, 32681}, {4550, 5158}, {5063, 184}, {5891, 216}, {8675, 647}, {10564, 3284}, {11653, 248}, {15066, 3}, {30474, 525}, {32833, 69}, {36429, 44080}, {42660, 3049}, {42704, 72}, {44080, 32}
X(44134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 69, 340}, {4, 340, 317}, {69, 264, 317}, {69, 3260, 315}, {69, 32000, 264}, {141, 1990, 11331}, {141, 9308, 17907}, {264, 340, 4}, {1235, 3260, 264}, {1990, 11331, 17907}, {2992, 2993, 1899}, {9308, 11331, 1990}, {32001, 32002, 317}

X(44135) = ISOTOMIC CONJUGATE X(3431)

Barycentrics    b^2*c^2*(-a^4 - a^2*b^2 + 2*b^4 - a^2*c^2 - 4*b^2*c^2 + 2*c^4) : :
Barycentrics    A-power of anti-orthocentroidal circle : :
Barycentrics    A-power of polar circle of A-altimedial triangle : :
Barycentrics    A'-power of circumcircle : : , where A'B'C' = orthocentroidal triangle
Barycentrics    A'-power of nine-point circle : : , where A'B'C' = orthocentroidal triangle
Barycentrics    A'-power of polar circle : : , where A'B'C' = orthocentroidal triangle
Barycentrics    A'-power of polar circle : : , where A'B'C' = reflection triangle

The anti-orthocentroidal circle is here defined as the circumcircle of the anti-orthocentroidal triangle, with center X(399). (Randy Hutson, August 24, 2021)

X(44135) lies on the cubic K504 and these lines: {2, 94}, {4, 69}, {23, 183}, {99, 13530}, {290, 5967}, {308, 14387}, {313, 27558}, {325, 5169}, {327, 18023}, {458, 22151}, {1007, 3266}, {1078, 7556}, {1273, 7752}, {1975, 7527}, {3262, 3701}, {3549, 32838}, {3618, 41760}, {3702, 30596}, {5392, 11427}, {7488, 20477}, {7493, 26235}, {7519, 15589}, {7526, 9723}, {7540, 7767}, {7552, 32832}, {7565, 7773}, {7578, 11004}, {8754, 21243}, {8797, 20563}, {9220, 18375}, {10024, 41005}, {11059, 34803}, {15574, 26284}, {18300, 18387}, {18563, 41008}, {18581, 43086}, {18582, 43085}, {20023, 40074}, {32805, 34391}, {32806, 34392}, {32829, 40697}, {34289, 37643}, {34387, 42697}, {34388, 42696}, {37669, 40684}

X(44135) = isotomic conjugate of X(3431)
X(44135) = anticomplement of X(566)
X(44135) = anticomplement of isogonal conjugate of X(7578)
X(44135) = isotomic conjugate of complement of X(18387)
X(44135) = isotomic conjugate of isogonal conjugate of X(381)
X(44135) = polar conjugate of isogonal conjugate of X(37638)
X(44135) = X(7578)-anticomplementary conjugate of X(8)
X(44135) = cevapoint of X(i) and X(j) for these (i,j): {2, 18387}, {381, 37638}, {10298, 11004}
X(44135) = crosssum of X(18117) and X(20975)
X(44135) = crossdifference of every pair of points on line {3049, 14270}
X(44135) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3431}, {9247, 43530}
X(44135) = trilinear product X(i)*X(j) for these {i,j}: {2, 80067}, {75, 381}, {92, 37638}, {264, 18477}, {561, 34417}, {1494, 18486}, {1928, 34416}, {1969, 5158}, {4993, 14213}, {18487, 33805}
X(44135) = trilinear quotient X(i)/X(j) for these (i,j): (75, 3431), (381, 31), (1969, 43530), (4993, 2148), (5158, 9247), (18477, 184), (18486, 1495), (18487, 9406), (34416, 1917), (34417, 560), (37638, 48)
X(44135) = barycentric product X(i)*X(j) for these {i,j}: {76, 381}, {264, 37638}, {311, 4993}, {1502, 34417}, {1969, 18477}, {3581, 20573}, {5158, 18022}, {18023, 32225}, {18486, 33805}, {34416, 40362}
X(44135) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3431}, {94, 18316}, {264, 43530}, {381, 6}, {1531, 3284}, {2052, 16263}, {3581, 50}, {4550, 5063}, {4993, 54}, {5158, 184}, {16080, 22455}, {18477, 48}, {18484, 18487}, {18486, 2173}, {18487, 1495}, {21970, 3053}, {32225, 187}, {34416, 1501}, {34417, 32}, {36430, 34417}, {37638, 3}
X(44135) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 264, 3260}, {76, 3260, 69}, {264, 311, 69}, {300, 301, 2}, {311, 3260, 76}, {1232, 14615, 69}, {9220, 18375, 34827}

X(44136) = ISOTOMIC CONJUGATE X(11270)

Barycentrics    b^2*c^2*(-3*a^4 + a^2*b^2 + 2*b^4 + a^2*c^2 - 4*b^2*c^2 + 2*c^4) : :

X(44136) lies on these lines: {4, 69}, {99, 20480}, {183, 13595}, {193, 338}, {253, 328}, {324, 37669}, {325, 13481}, {339, 32827}, {393, 28408}, {1007, 30737}, {1272, 32837}, {1992, 41760}, {2071, 20477}, {2072, 41005}, {3548, 32839}, {3964, 18354}, {6527, 32835}, {9308, 22151}, {9723, 12084}, {14570, 40896}, {20563, 36889}, {28419, 43981}, {32810, 34391}, {32811, 34392}

X(44136) = isotomic conjugate of X(11270)
X(44136) = isotomic conjugate of isogonal conjugate of X(382)
X(44136) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {12092, 4560}, {16867, 6360}
X(44136) = X(i)-isoconjugate of X(j) for these (i,j): {31, 11270}, {810, 33640}
X(44136) = barycentric product X(i)*X(j) for these {i,j}: {75, 14212}, {76, 382}, {1502, 44082}
X(44136) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 11270}, {382, 6}, {648, 33640}, {14212, 1}, {36431, 44082}, {44082, 32}
X(44136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {264, 3260, 69}, {264, 14615, 311}, {311, 3260, 14615}, {311, 14615, 69}

X(44137) = ISOTOMIC CONJUGATE X(1987)

Barycentrics    b^2*c^2*(a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 + a^4*c^4 - 2*b^4*c^4 + b^2*c^6) : :

X(44137) lies on the cubic K779 and these lines: {2, 40815}, {4, 69}, {6, 40822}, {147, 30737}, {276, 34850}, {287, 3978}, {290, 3564}, {323, 23962}, {325, 14941}, {394, 18022}, {670, 6393}, {2456, 14382}, {2896, 26166}, {3267, 7799}, {5661, 7769}, {6331, 11064}, {6374, 6389}, {8783, 32458}, {9308, 18027}, {16089, 41204}, {32428, 39682}, {36901, 41724}

X(44137) = isotomic conjugate of X(1987)
X(44137) = isotomic conjugate of isogonal conjugate of X(401)
X(44137) = isotomic conjugate of polar conjugate of X(16089)
X(44137) = X(325)-Ceva conjugate of X(3978)
X(44137) = X(401)-cross conjugate of X(16089)
X(44137) = crossdifference of every pair of points on line {3049, 40981}
X(44137) = X(i)-isoconjugate of X(j) for these (i,j): {31, 1987}, {32, 1956}, {560, 1972}, {1298, 2179}, {1967, 32542}, {1973, 14941}, {3402, 39683}
X(44137) = barycentric product X(i)*X(j) for these {i,j}: {69, 16089}, {76, 401}, {305, 41204}, {561, 1955}, {670, 6130}, {1502, 1971}, {20023, 39682}, {32428, 34384}
X(44137) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 1987}, {69, 14941}, {75, 1956}, {76, 1972}, {95, 1298}, {183, 39683}, {325, 40804}, {385, 32542}, {401, 6}, {1955, 31}, {1971, 32}, {2313, 2179}, {6130, 512}, {16089, 4}, {32428, 51}, {32545, 1976}, {39682, 263}, {41204, 25}, {42405, 41210}
X(44137) = {X(8920),X(14615)}-harmonic conjugate of X(315)

X(44138) = ISOTOMIC CONJUGATE X(5504)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :
Barycentrics    (csc 2A) (1 + cos 2B + cos 2C) : :

The trilinear polar of X(44138) passes through X(6334).

X(44138) lies on these lines: {4, 69}, {23, 30716}, {26, 20477}, {94, 16080}, {95, 14118}, {186, 328}, {290, 685}, {297, 338}, {300, 470}, {301, 471}, {325, 37981}, {339, 11799}, {421, 18020}, {648, 37778}, {850, 6368}, {1272, 37943}, {3003, 16237}, {5392, 11547}, {7527, 26166}, {8795, 43689}, {15761, 41005}, {16077, 40423}, {16089, 41203}, {17907, 41760}

X(44138) = isotomic conjugate of X(5504)
X(44138) = polar conjugate of X(14910)
X(44138) = isotomic conjugate of isogonal conjugate of X(403)
X(44138) = polar conjugate of isogonal conjugate of X(3580)
X(44138) = X(38534)-anticomplementary conjugate of X(6360)
X(44138) = X(16077)-Ceva conjugate of X(850)
X(44138) = X(16221)-cross conjugate of X(14618)
X(44138) = cevapoint of X(i) and X(j) for these (i,j): {403, 3580}, {35235, 41079}
X(44138) = crosspoint of X(264) and X(18817)
X(44138) = crossdifference of every pair of points on line {3049, 14585}
X(44138) = pole wrt polar circle of trilinear polar of X(14910) (line X(184)X(512))
X(44138) = X(i)-isoconjugate of X(j) for these (i,j): {31, 5504}, {48, 14910}, {184, 36053}, {798, 43755}, {810, 10420}, {822, 32708}, {2986, 9247}, {36114, 39201}
X(44138) = barycentric product X(i)*X(j) for these {i,j}: {76, 403}, {264, 3580}, {850, 16237}, {1502, 44084}, {1725, 1969}, {1986, 20573}, {3003, 18022}, {6334, 6528}, {12828, 18023}, {13754, 18027}, {18817, 34834}
X(44138) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 5504}, {4, 14910}, {92, 36053}, {94, 12028}, {99, 43755}, {107, 32708}, {113, 3284}, {264, 2986}, {403, 6}, {648, 10420}, {686, 39201}, {823, 36114}, {850, 15421}, {1725, 48}, {1986, 50}, {2052, 1300}, {3003, 184}, {3580, 3}, {6331, 18878}, {6334, 520}, {6515, 15478}, {6528, 687}, {11557, 9380}, {12824, 10317}, {12827, 14961}, {12828, 187}, {13754, 577}, {14165, 38936}, {14264, 18877}, {14618, 15328}, {14920, 39371}, {15329, 32661}, {16080, 10419}, {16221, 2088}, {16237, 110}, {18020, 18879}, {18022, 40832}, {18609, 1437}, {18817, 40427}, {21731, 3049}, {23290, 35361}, {34834, 22115}, {39985, 32663}, {41512, 32662}, {41665, 14889}, {44084, 32}
X(44138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {264, 340, 3260}, {15164, 15165, 317}

X(44139) = ISOTOMIC CONJUGATE OF ISOGONAL CONJUGATE OF X(404)

Barycentrics    b*c*(a^3 - a*b^2 + a*b*c + b^2*c - a*c^2 + b*c^2) : :

X(44139) lies on these lines: {2, 34283}, {4, 69}, {6, 18144}, {7, 3596}, {9, 20917}, {75, 537}, {77, 4554}, {85, 3718}, {86, 13741}, {141, 3770}, {142, 3975}, {183, 16434}, {190, 18040}, {261, 799}, {274, 4283}, {312, 17296}, {313, 320}, {319, 1269}, {321, 17287}, {341, 5290}, {350, 3879}, {527, 17787}, {572, 18048}, {645, 37659}, {646, 3729}, {894, 4503}, {1078, 1444}, {1107, 25538}, {1230, 32863}, {1240, 20245}, {1264, 6063}, {1654, 20913}, {1746, 14829}, {1909, 4357}, {3264, 7321}, {3662, 3765}, {3664, 6381}, {3688, 17794}, {3758, 18044}, {3875, 24524}, {3945, 18135}, {3948, 17300}, {3963, 6646}, {4001, 19810}, {4043, 17295}, {4110, 4659}, {4358, 17312}, {4360, 39995}, {4363, 30473}, {4377, 17345}, {4410, 17239}, {4441, 32099}, {4648, 30830}, {4690, 20174}, {4710, 32857}, {4869, 28809}, {4967, 25280}, {5232, 34284}, {6173, 30090}, {6376, 10436}, {6385, 33769}, {10401, 31643}, {11353, 28014}, {14548, 18153}, {14828, 18052}, {16709, 17210}, {17117, 25298}, {17178, 31026}, {17277, 18143}, {17279, 30866}, {17283, 18150}, {17288, 20891}, {17297, 18137}, {17298, 20923}, {17310, 22016}, {17361, 30596}, {17365, 17790}, {17375, 31060}, {17378, 18145}, {17392, 25660}, {17483, 28654}, {18152, 30941}, {18697, 20955}, {19768, 37492}, {20336, 20924}, {21226, 26149}, {21299, 35892}, {21352, 36856}, {24437, 24688}, {25278, 32087}, {27184, 30710}, {29447, 41681}, {31008, 37632}, {32911, 40013}, {34020, 37678}

X(44139) = isotomic conjugate of isogonal conjugate of X(404)
X(44139) = cevapoint of X(i) and X(j) for these (i,j): {69, 18133}, {32911, 35998}
X(44139) = X(1397)-isoconjugate of X(44040)
X(44139) = barycentric product X(i)*X(j) for these {i,j}: {75, 32939}, {76, 404}, {286, 42705}, {1502, 44085}, {4554, 20293}, {4623, 21721}
X(44139) = barycentric quotient X(i)/X(j) for these {i,j}: {312, 44040}, {404, 6}, {6516, 40518}, {20293, 650}, {21721, 4705}, {32939, 1}, {42705, 72}, {44085, 32}
X(44139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 76, 314}, {69, 21287, 7768}, {86, 18133, 18140}, {319, 1269, 17143}, {1232, 1234, 76}, {3729, 17786, 646}, {3761, 17272, 75}

X(44140) = ISOTOMIC CONJUGATE OF ISOGONAL CONJUGATE OF X(405)

Barycentrics    b*c*(-a^3 + a*b^2 + 2*a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2) : :

X(44140) lies on these lines: {2, 37}, {4, 69}, {7, 349}, {8, 313}, {9, 4044}, {28, 19838}, {86, 964}, {141, 33736}, {183, 4220}, {193, 3770}, {273, 1231}, {274, 37037}, {310, 30962}, {319, 5016}, {322, 4673}, {386, 3875}, {387, 4385}, {579, 3729}, {941, 27042}, {966, 3948}, {1089, 1714}, {1228, 2478}, {1230, 5739}, {1240, 1246}, {1265, 3596}, {1284, 5695}, {1441, 3485}, {1444, 1975}, {1654, 31060}, {1766, 16574}, {1909, 5716}, {1930, 24204}, {1992, 34283}, {2303, 19281}, {3216, 17151}, {3262, 5761}, {3264, 32087}, {3620, 18144}, {3701, 38057}, {3760, 4357}, {3761, 3879}, {3765, 5839}, {3945, 30939}, {3963, 17314}, {4066, 20083}, {4360, 19767}, {4373, 40010}, {4377, 17299}, {4431, 4494}, {4648, 20913}, {4869, 18143}, {4967, 32104}, {5019, 24271}, {5051, 5224}, {5165, 17351}, {5232, 18133}, {5317, 9308}, {5747, 20236}, {6381, 17270}, {7253, 20948}, {7283, 13726}, {8062, 17893}, {8822, 14829}, {10436, 20888}, {16752, 25504}, {17144, 20018}, {17220, 17751}, {17277, 28809}, {17861, 18697}, {17907, 18685}, {18040, 29616}, {18044, 29611}, {18065, 29594}, {19766, 39731}, {20477, 36029}, {26045, 27269}, {26243, 36744}, {30882, 36022}

X(44140) = isotomic conjugate of isogonal conjugate of X(405)
X(44140) = anticomplement of X(4261)
X(44140) = X(839)-anticomplementary conjugate of X(20295)
X(44140) = X(5295)-cross conjugate of X(5271)
X(44140) = cevapoint of X(7520) and X(37685)
X(44140) = crossdifference of every pair of points on line {667, 3049}
X(44140) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2215}, {604, 2335}, {649, 36080}, {810, 36077}
X(44140) = barycentric product X(i)*X(j) for these {i,j}: {75, 5271}, {76, 405}, {274, 5295}, {286, 42706}, {304, 39585}, {668, 23882}, {1451, 28659}, {1502, 5320}, {3596, 37543}, {3952, 15417}, {14549, 18152}
X(44140) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2215}, {8, 2335}, {100, 36080}, {405, 6}, {648, 36077}, {1451, 604}, {1882, 1880}, {5271, 1}, {5295, 37}, {5320, 32}, {14549, 2350}, {15417, 7192}, {23882, 513}, {37543, 56}, {39585, 19}, {42706, 72}
X(44140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 69, 21287}, {75, 312, 20336}, {75, 350, 17321}, {75, 18147, 2}, {76, 264, 1234}, {76, 314, 69}, {312, 19792, 2}, {321, 17863, 75}, {3596, 17143, 42696}, {3760, 10447, 4357}

X(44141) = ISOTOMIC CONJUGATE OF ISOGONAL CONJUGATE OF X(426)

Barycentrics    (a^2 - b^2 - c^2)^3*(a^4 + b^4 - 2*b^2*c^2 + c^4) : :

X(44141) lies on these lines: {4, 69}, {68, 339}, {394, 441}, {525, 15075}, {1092, 3926}, {1181, 41005}, {1568, 32816}, {1899, 41009}, {3289, 7758}, {3964, 16391}, {6389, 39643}, {6390, 35602}, {6527, 34781}, {7800, 22416}, {8779, 28696}, {10984, 40680}, {12164, 40995}, {14216, 30737}, {15595, 41361}, {32817, 34403}, {32818, 37669}

X(44141) = isotomic conjugate of isogonal conjugate of X(426)
X(44141) = isotomic conjugate of polar conjugate of X(6389)
X(44141) = X(69)-Ceva conjugate of X(1899)
X(44141) = X(426)-cross conjugate of X(6389)
X(44141) = crosspoint of X(69) and X(4176)
X(44141) = barycentric product X(i)*X(j) for these {i,j}: {69, 6389}, {76, 426}, {305, 39643}, {394, 41009}, {1102, 17871}, {1632, 4143}, {1899, 3926}, {3767, 4176}, {3964, 41760}
X(44141) = barycentric quotient X(i)/X(j) for these {i,j}: {426, 6}, {1632, 6529}, {1899, 393}, {2083, 1096}, {3767, 6524}, {3926, 34405}, {4176, 42407}, {6389, 4}, {6751, 3199}, {17871, 6520}, {39643, 25}, {40947, 2207}, {41009, 2052}, {41760, 1093}, {41762, 36434}

X(44142) = ISOTOMIC CONJUGATE OF X(41435)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(2*a^2 + b^2 + c^2) : :

X(44142) lies on these lines: {2, 40674}, {4, 69}, {5, 30737}, {25, 26235}, {30, 26166}, {83, 8744}, {94, 41253}, {99, 14865}, {183, 10594}, {186, 43459}, {232, 6683}, {276, 35474}, {290, 1173}, {297, 14129}, {305, 32823}, {324, 458}, {325, 15559}, {338, 7745}, {339, 546}, {427, 3266}, {428, 7767}, {472, 41000}, {473, 41001}, {1078, 3518}, {1870, 25303}, {1883, 16747}, {1907, 3933}, {1975, 35502}, {2052, 18841}, {3088, 32831}, {3091, 41009}, {3199, 31239}, {3541, 32829}, {3542, 32838}, {3785, 37122}, {4911, 34387}, {5015, 34388}, {5064, 7776}, {5395, 41370}, {5523, 14770}, {7141, 40717}, {7378, 9464}, {7509, 20477}, {7576, 7750}, {7714, 40022}, {7762, 41628}, {7773, 28706}, {7780, 10985}, {7782, 35475}, {7793, 10986}, {7802, 18559}, {7841, 26214}, {7859, 37765}, {8370, 26164}, {8753, 18023}, {8889, 11059}, {11361, 26179}, {14387, 18027}, {15355, 28407}, {27376, 37778}, {32450, 41676}, {37337, 39575}, {41361, 43981}

X(44142) = isotomic conjugate of X(41435)
X(44142) = polar conjugate of X(3108)
X(44142) = isotomic conjugate of isogonal conjugate of X(428)
X(44142) = polar conjugate of isotomic conjugate of X(39998)
X(44142) = polar conjugate of isogonal conjugate of X(3589)
X(44142) = pole wrt polar circle of trilinear polar of X(3108) (line X(523)X(2076))
X(44142) = X(3589)-cross conjugate of X(39998)
X(44142) = cevapoint of X(428) and X(3589)
X(44142) = crosssum of X(184) and X(20775)
X(44142) = X(i)-isoconjugate of X(j) for these (i,j): {31, 41435}, {48, 3108}, {810, 7953}, {9247, 10159}
X(44142) = barycentric product X(i)*X(j) for these {i,j}: {4, 39998}, {76, 428}, {264, 3589}, {331, 4030}, {1502, 44091}, {1969, 17469}, {2052, 7767}, {5007, 18022}, {6331, 7927}, {7017, 7198}, {10330, 14618}, {16707, 41013}, {18027, 22352}, {18062, 24006}, {32085, 42554}
X(44142) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 41435}, {4, 3108}, {264, 10159}, {428, 6}, {648, 7953}, {3589, 3}, {4030, 219}, {5007, 184}, {6292, 3917}, {6331, 35137}, {7198, 222}, {7767, 394}, {7927, 647}, {8664, 3049}, {10330, 4558}, {11205, 20775}, {14618, 31065}, {16707, 1444}, {17200, 1790}, {17457, 4020}, {17469, 48}, {18062, 4592}, {21802, 228}, {22352, 577}, {28666, 8041}, {39998, 69}, {42554, 3933}, {44091, 32}
X(44142) = {X(4),X(264)}-harmonic conjugate of X(1235)

X(44143) = ISOTOMIC CONJUGATE OF ISOGONAL CONJUGATE OF X(430)

Barycentrics    b^2*c^2*(b + c)*(2*a + b + c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2) : :

X(44143) lies on these lines: {4, 69}, {25, 26266}, {318, 860}, {324, 17555}, {338, 1834}, {339, 21665}, {387, 41760}, {407, 38462}, {429, 3695}, {430, 1230}, {451, 31623}, {942, 34387}, {1577, 23104}, {1826, 21070}, {1893, 5295}, {6998, 30737}, {8747, 37778}, {11109, 40684}, {16589, 17911}, {17905, 27040}, {36672, 41009}

X(44143) = isotomic conjugate of isogonal conjugate of X(430)
X(44143) = polar conjugate of X(1171)
X(44143) = polar conjugate of isotomic conjugate of X(1230)
X(44143) = polar conjugate of isogonal conjugate of X(1213)
X(44143) = pole wrt polar circle of trilinear polar of X(1171) (line X(512)X(1326))
X(44143) = X(1213)-cross conjugate of X(1230)
X(44143) = X(i)-isoconjugate of X(j) for these (i,j): {48, 1171}, {184, 40438}, {810, 6578}, {1126, 1437}, {1333, 1796}, {1790, 28615}, {4629, 22383}, {9247, 32014}
X(44143) = cevapoint of X(430) and X(1213)
X(44143) = barycentric product X(i)*X(j) for these {i,j}: {4, 1230}, {76, 430}, {92, 4647}, {264, 1213}, {313, 1839}, {331, 4046}, {1269, 1826}, {1962, 1969}, {2052, 41014}, {2355, 27801}, {3649, 7017}, {3702, 40149}, {4359, 41013}, {4427, 14618}, {6331, 6367}, {6335, 30591}, {7141, 8025}, {18022, 20970}, {18027, 22080}, {28654, 31900}
X(44143) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 1171}, {10, 1796}, {92, 40438}, {264, 32014}, {430, 6}, {648, 6578}, {1100, 1437}, {1125, 1790}, {1213, 3}, {1230, 69}, {1269, 17206}, {1824, 28615}, {1826, 1126}, {1839, 58}, {1897, 4629}, {1962, 48}, {2355, 1333}, {3649, 222}, {3683, 2193}, {3686, 283}, {3702, 1812}, {3916, 18604}, {3958, 255}, {4046, 219}, {4115, 1331}, {4359, 1444}, {4427, 4558}, {4647, 63}, {4976, 23189}, {4977, 7254}, {4983, 22383}, {4988, 1459}, {4990, 23090}, {4992, 23092}, {6335, 4596}, {6367, 647}, {7141, 6539}, {8013, 71}, {8040, 22054}, {8663, 3049}, {14618, 4608}, {20970, 184}, {21816, 228}, {22080, 577}, {30591, 905}, {31900, 593}, {35327, 32661}, {35342, 4575}, {41013, 1255}, {41014, 394}

X(44144) = ISOTOMIC CONJUGATE OF X(43718)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-a^4 + a^2*b^2 + a^2*c^2 + 2*b^2*c^2) : :
Barycentrics    csc A csc 2A cos(A - ω) : :

X(44144) lies on these lines: {2, 6331}, {4, 69}, {25, 42394}, {183, 33971}, {276, 1502}, {290, 6776}, {308, 393}, {324, 39998}, {327, 40330}, {339, 37348}, {458, 20023}, {670, 10008}, {1629, 1799}, {2052, 37187}, {2211, 9308}, {3087, 33769}, {6528, 10002}, {7750, 16264}, {7763, 37125}, {7791, 26166}, {8024, 40684}, {11056, 14165}, {12215, 37124}, {16089, 34229}, {17907, 32832}, {18911, 36901}, {28706, 40073}, {30737, 37182}, {32834, 43981}

X(44144) = isotomic conjugate of X(43718)
X(44144) = polar conjugate of X(263)
X(44144) = isotomic conjugate of isogonal conjugate of X(458)
X(44144) = polar conjugate of isotomic conjugate of X(20023)
X(44144) = polar conjugate of isogonal conjugate of X(183)
X(44144) = X(183)-cross conjugate of X(20023)
X(44144) = cevapoint of X(183) and X(458)
X(44144) = X(i)-isoconjugate of X(j) for these (i,j): {3, 3402}, {31, 43718}, {48, 263}, {184, 2186}, {262, 9247}, {560, 42313}, {810, 26714}, {4020, 42288}, {36132, 39469}
X(44144) = barycentric product X(i)*X(j) for these {i,j}: {4, 20023}, {76, 458}, {92, 3403}, {182, 18022}, {183, 264}, {286, 42711}, {305, 33971}, {1502, 10311}, {6331, 23878}, {8842, 17984}, {34384, 39530}
X(44144) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 43718}, {4, 263}, {19, 3402}, {76, 42313}, {92, 2186}, {182, 184}, {183, 3}, {264, 262}, {276, 42300}, {458, 6}, {648, 26714}, {685, 32716}, {3288, 3049}, {3403, 63}, {8842, 36214}, {10311, 32}, {14096, 20775}, {14994, 3917}, {16089, 39682}, {18022, 327}, {20023, 69}, {22456, 6037}, {23878, 647}, {32085, 42288}, {33971, 25}, {34396, 14575}, {39530, 51}, {42711, 72}
X(44144) = {X(264),X(17984)}-harmonic conjugate of X(4)

X(44145) = ISOTOMIC CONJUGATE OF X(43705)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(44145) lies on these lines: {4, 69}, {5, 23635}, {24, 157}, {25, 324}, {68, 41757}, {93, 32085}, {94, 35265}, {98, 39644}, {107, 37777}, {110, 421}, {186, 30716}, {237, 32428}, {338, 1503}, {393, 847}, {403, 523}, {419, 685}, {427, 40684}, {458, 39588}, {460, 3564}, {468, 2970}, {935, 1300}, {1093, 6622}, {1513, 30737}, {1594, 3001}, {1692, 14265}, {2052, 6353}, {2974, 10011}, {3089, 43981}, {3563, 22456}, {5201, 10594}, {6240, 16264}, {6344, 17983}, {6531, 41363}, {6756, 14978}, {6776, 41760}, {7505, 17907}, {8754, 39569}, {10608, 30549}, {14767, 37121}, {14912, 40814}, {15466, 38282}, {16868, 18114}, {34334, 37984}, {35360, 44084}, {37114, 42329}, {37446, 40822}, {37765, 37943}

X(44145) = isogonal conjugate of X(42065)
X(44145) = isotomic conjugate of X(43705)
X(44145) = polar conjugate of X(2987)
X(44145) = polar-circle-inverse of X(31848)
X(44145) = pole wrt polar circle of trilinear polar of X(2987) (line X(3)X(512))
X(44145) = isotomic conjugate of isogonal conjugate of X(460)
X(44145) = polar conjugate of isogonal conjugate of X(230)
X(44145) = X(22456)-Ceva conjugate of X(14618)
X(44145) = X(114)-cross conjugate of X(4)
X(44145) = cevapoint of X(230) and X(460)
X(44145) = crosspoint of X(264) and X(16081)
X(44145) = crosssum of X(184) and X(3289)
X(44145) = crossdifference of every pair of points on line {577, 3049}
X(44145) = X(i)-isoconjugate of X(j) for these (i,j): {1, 42065}, {3, 36051}, {31, 43705}, {48, 2987}, {63, 32654}, {184, 8773}, {255, 3563}, {293, 34157}, {810, 10425}, {822, 32697}, {4575, 35364}, {8781, 9247}, {36105, 39201}
X(44145) = barycentric product X(i)*X(j) for these {i,j}: {76, 460}, {92, 1733}, {114, 16081}, {230, 264}, {297, 14265}, {1502, 44099}, {1692, 18022}, {1969, 8772}, {2052, 3564}, {4226, 14618}, {10011, 42298}
X(44145) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 43705}, {4, 2987}, {6, 42065}, {19, 36051}, {25, 32654}, {92, 8773}, {107, 32697}, {114, 36212}, {230, 3}, {232, 34157}, {264, 8781}, {393, 3563}, {460, 6}, {648, 10425}, {823, 36105}, {1692, 184}, {1733, 63}, {2052, 35142}, {2501, 35364}, {3564, 394}, {4226, 4558}, {5477, 3292}, {6531, 2065}, {8772, 48}, {14265, 287}, {16081, 40428}, {36875, 14919}, {42663, 3049}, {44099, 32}
X(44145) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 3186, 6403}, {264, 43976, 4}, {419, 41204, 19128}, {847, 3542, 13450}, {1352, 41762, 4}, {1843, 39530, 4}, {6248, 40325, 4}

X(44146) = ISOTOMIC CONJUGATE OF X(895)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-2*a^2 + b^2 + c^2) : :
Barycentrics    csc 2A (2 a^2 - b^2 - c^2) : :

X(44146) lies on these lines: {2, 14961}, {4, 69}, {5, 26166}, {20, 41009}, {23, 935}, {24, 1975}, {25, 8024}, {27, 1230}, {28, 1228}, {30, 339}, {33, 3761}, {34, 3760}, {74, 290}, {95, 7550}, {99, 186}, {112, 385}, {148, 40889}, {183, 378}, {187, 4235}, {193, 41370}, {194, 39575}, {232, 538}, {235, 3933}, {242, 38457}, {274, 451}, {276, 4994}, {287, 13509}, {297, 525}, {305, 6353}, {308, 32581}, {310, 4213}, {323, 41253}, {325, 403}, {350, 1870}, {384, 10312}, {406, 34284}, {419, 18020}, {420, 3978}, {427, 39998}, {429, 16747}, {458, 15066}, {460, 14052}, {468, 3266}, {470, 41000}, {471, 41001}, {475, 18135}, {524, 37778}, {648, 8744}, {732, 2211}, {892, 8753}, {1078, 3520}, {1172, 3770}, {1861, 6381}, {1885, 7767}, {1909, 6198}, {1968, 7751}, {2052, 5485}, {2967, 32515}, {2973, 40717}, {2996, 43678}, {3088, 32834}, {3089, 32830}, {3144, 28660}, {3147, 6337}, {3263, 37989}, {3541, 32828}, {3542, 3926}, {3734, 10311}, {3934, 37125}, {3948, 15149}, {4212, 18152}, {4232, 9464}, {5025, 26179}, {5081, 34387}, {5094, 26235}, {5641, 6528}, {5971, 37962}, {6240, 32819}, {6344, 35139}, {6392, 41361}, {6527, 34621}, {6622, 32818}, {6623, 37668}, {6656, 26156}, {6664, 27376}, {7282, 34388}, {7500, 18018}, {7505, 7763}, {7750, 18560}, {7752, 16868}, {7754, 8743}, {7762, 40316}, {7769, 14940}, {7770, 14965}, {7771, 35473}, {7773, 35488}, {7776, 37197}, {7782, 21844}, {7799, 37943}, {8267, 40938}, {8370, 27377}, {8889, 40022}, {9466, 33843}, {10313, 15013}, {10317, 40856}, {11054, 37765}, {12082, 20477}, {12215, 19128}, {12243, 16089}, {14711, 33842}, {14712, 40890}, {14907, 35481}, {17555, 26541}, {18533, 32815}, {20880, 25987}, {23115, 26226}, {26592, 37448}, {28809, 37382}, {31276, 37337}, {32225, 36890}, {32269, 36793}, {32832, 37119}, {34664, 41008}, {35940, 37667}, {37118, 37688}, {37643, 40814}, {37912, 44089}, {38664, 41377}, {40894, 42811}, {40895, 42812}, {41760, 43448}

X(44146) = reflection of X(i) in X(j) for these {i,j}: {30737, 339}, {41676, 232}
X(44146) = isogonal conjugate of X(14908)
X(44146) = isotomic conjugate of X(895)
X(44146) = anticomplement of X(14961)
X(44146) = polar conjugate of X(111)
X(44146) = isogonal conjugate of anticomplement of X(34517)
X(44146) = isogonal conjugate of complement of X(34518)
X(44146) = isotomic conjugate of anticomplement of X(5181)
X(44146) = isotomic conjugate of isogonal conjugate of X(468)
X(44146) = isotomic conjugate of polar conjugate of X(37778)
X(44146) = polar conjugate of isotomic conjugate of X(3266)
X(44146) = polar conjugate of isogonal conjugate of X(524)
X(44146) = pole wrt polar circle of trilinear polar of X(111) (line X(6)X(512))
X(44146) = {P,U}-harmonic conjugate of X(264), where P, U are the polar conjugates of X(5638) and X(5639)
X(44146) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {92, 2892}, {158, 34163}, {1177, 6360}, {2373, 4329}, {10423, 4560}, {36095, 523}, {37220, 1370}
X(44146) = X(264)-Ceva conjugate of X(34336)
X(44146) = X(i)-cross conjugate of X(j) for these (i,j): {468, 37778}, {524, 3266}, {690, 4235}, {5181, 2}, {5642, 43084}, {34336, 264}, {41586, 524}
X(44146) = cevapoint of X(i) and X(j) for these (i,j): {23, 37784}, {468, 524}, {2393, 3291}
X(44146) = crosssum of X(i) and X(j) for these (i,j): {184, 23200}, {20975, 42665}
X(44146) = trilinear pole of line {126, 1560}
X(44146) = crossdifference of every pair of points on line {184, 3049}
X(44146) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14908}, {3, 923}, {6, 36060}, {31, 895}, {48, 111}, {63, 32740}, {163, 10097}, {184, 897}, {212, 7316}, {255, 8753}, {304, 19626}, {560, 30786}, {577, 36128}, {603, 5547}, {647, 36142}, {656, 32729}, {671, 9247}, {691, 810}, {922, 15398}, {3049, 36085}, {4575, 9178}, {6091, 38252}, {23894, 32661}, {34055, 41272}
X(44146) = barycentric product X(i)*X(j) for these {i,j}: {4, 3266}, {69, 37778}, {76, 468}, {92, 14210}, {187, 18022}, {264, 524}, {276, 41586}, {286, 42713}, {331, 3712}, {340, 43084}, {648, 35522}, {670, 14273}, {671, 34336}, {690, 6331}, {850, 4235}, {896, 1969}, {1502, 44102}, {2052, 6390}, {3292, 18027}, {5095, 18023}, {5468, 14618}, {6528, 14417}, {7017, 7181}, {10604, 24855}, {12828, 40832}, {16741, 41013}, {17924, 42721}, {17983, 36792}, {24006, 24039}
X(44146) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36060}, {2, 895}, {4, 111}, {6, 14908}, {19, 923}, {25, 32740}, {76, 30786}, {92, 897}, {112, 32729}, {126, 8681}, {158, 36128}, {162, 36142}, {187, 184}, {193, 6091}, {264, 671}, {278, 7316}, {281, 5547}, {297, 5968}, {351, 3049}, {393, 8753}, {468, 6}, {523, 10097}, {524, 3}, {648, 691}, {671, 15398}, {690, 647}, {811, 36085}, {850, 14977}, {896, 48}, {922, 9247}, {1235, 31125}, {1560, 2393}, {1648, 20975}, {1843, 41272}, {1974, 19626}, {2052, 17983}, {2373, 41511}, {2374, 15387}, {2393, 34158}, {2482, 3292}, {2501, 9178}, {2642, 810}, {3266, 69}, {3292, 577}, {3712, 219}, {3793, 3796}, {4062, 71}, {4235, 110}, {4750, 1459}, {4760, 7193}, {5094, 42007}, {5095, 187}, {5181, 14961}, {5203, 8770}, {5467, 32661}, {5468, 4558}, {5642, 3284}, {5967, 248}, {6331, 892}, {6335, 5380}, {6390, 394}, {6593, 10317}, {6629, 1790}, {7181, 222}, {7267, 3955}, {7664, 22151}, {7813, 3917}, {8753, 41936}, {9155, 3289}, {9717, 18877}, {11053, 22143}, {12828, 3003}, {14210, 63}, {14273, 512}, {14417, 520}, {14419, 22383}, {14432, 652}, {14559, 32662}, {14567, 14575}, {14618, 5466}, {15471, 1384}, {16080, 9139}, {16081, 9154}, {16230, 8430}, {16702, 1437}, {16741, 1444}, {17925, 43926}, {17983, 10630}, {18022, 18023}, {18311, 9517}, {18872, 17970}, {19577, 8869}, {21839, 228}, {23200, 14585}, {23287, 30491}, {23889, 4575}, {24006, 23894}, {24039, 4592}, {24855, 10602}, {30247, 35188}, {30737, 36894}, {31013, 1796}, {31068, 41435}, {32225, 5158}, {32459, 3167}, {34163, 19330}, {34336, 524}, {35282, 8779}, {35522, 525}, {36306, 9206}, {36309, 9207}, {36792, 6390}, {36890, 14919}, {37765, 14246}, {37778, 4}, {37784, 39169}, {37855, 1995}, {39689, 23200}, {41586, 216}, {41616, 41336}, {41676, 36827}, {42713, 72}, {42721, 1332}, {42760, 8677}, {43084, 265}, {44102, 32}
X(44146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 76, 1235}, {76, 316, 1236}, {76, 11185, 311}, {316, 1236, 3260}, {317, 11185, 4}, {385, 15014, 112}, {15164, 15165, 4}

X(44147) = ISOTOMIC CONJUGATE OF ISOGONAL CONJUGATE OF X(474)

Barycentrics    b*c*(a^3 - a*b^2 + 2*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :

X(44147) lies on these lines: {2, 3770}, {4, 69}, {7, 313}, {8, 1269}, {75, 3617}, {85, 20336}, {86, 5192}, {183, 1444}, {319, 4441}, {320, 30596}, {341, 4208}, {344, 20917}, {346, 18040}, {668, 42696}, {894, 41316}, {966, 20913}, {1909, 17321}, {1975, 37328}, {3264, 31995}, {3596, 42697}, {3618, 34283}, {3672, 39995}, {3718, 20925}, {3729, 29716}, {3760, 3879}, {3761, 4357}, {3765, 4000}, {3945, 18147}, {3948, 4648}, {3963, 4419}, {4033, 4461}, {4043, 29616}, {4044, 17296}, {4202, 5224}, {4371, 25298}, {4377, 17276}, {4410, 17303}, {4869, 18137}, {5564, 25278}, {5749, 18044}, {6381, 10436}, {6385, 20023}, {9965, 19807}, {14552, 19792}, {17014, 29764}, {17234, 28809}, {17270, 20888}, {17300, 31060}, {17355, 18065}, {18142, 37668}, {18152, 30962}, {18749, 28808}, {19825, 40603}, {24599, 29756}, {29484, 37681}

X(44147) = isotomic conjugate of isogonal conjugate of X(474)
X(44147) = anticomplement of X(5069)
X(44147) = barycentric product X(i)*X(j) for these {i,j}: {76, 474}, {1502, 44104}
X(44147) = barycentric quotient X(i)/X(j) for these {i,j}: {474, 6}, {44104, 32}
X(44147) = {X(3770),X(18144)}-harmonic conjugate of X(2)

X(44148) = ISOTOMIC CONJUGATE OF X(14483)

Barycentrics    b^2*c^2*(4*a^4 - 5*a^2*b^2 + b^4 - 5*a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(44148) lies on these lines: {4, 69}, {183, 3266}, {290, 42367}, {298, 41001}, {299, 41000}, {325, 26235}, {338, 22165}, {343, 36789}, {1273, 3933}, {3917, 25051}, {6148, 8024}, {7788, 39998}, {9464, 15589}, {11059, 34229}, {17271, 26541}, {17297, 26592}, {17360, 34387}, {17361, 34388}, {21356, 40814}, {28975, 30939}, {32814, 34392}, {32840, 40697}

X(44148) = isotomic conjugate of X(14483)
X(44148) = isotomic conjugate of isogonal conjugate of X(549)
X(44148) = X(31)-isoconjugate of X(14483)
X(44148) = crosssum of X(32) and X(34416)
X(44148) = barycentric product X(i)*X(j) for these {i,j}: {76, 549}, {305, 6749}, {1502, 44109}
X(44148) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 14483}, {549, 6}, {6749, 25}, {44109, 32}
X(44148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 76, 3260}, {69, 1232, 311}, {76, 3260, 311}, {1232, 3260, 76}

X(44149) = ISOTOMIC CONJUGATE OF X(3527)

Barycentrics    b^2*c^2*(3*a^4 - 4*a^2*b^2 + b^4 - 4*a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(44149) lies on these lines: {4, 69}, {75, 6735}, {95, 183}, {141, 40814}, {290, 34817}, {322, 1269}, {325, 37439}, {339, 18536}, {343, 15466}, {394, 36794}, {599, 41760}, {1078, 9723}, {1230, 37655}, {1494, 40032}, {1975, 37198}, {4869, 26592}, {5232, 26541}, {7667, 37671}, {7752, 34939}, {7796, 39113}, {8024, 15589}, {11059, 37688}, {11257, 22062}, {15394, 42333}, {15574, 16276}, {20775, 22712}, {21296, 34388}, {30596, 35516}, {32085, 37491}, {32099, 34387}, {32808, 34392}, {32809, 34391}, {32830, 40680}, {32833, 40697}, {37668, 39998}, {41008, 41009}

X(44149) = isotomic conjugate of X(3527)
X(44149) = polar conjugate of X(34818)
X(44149) = isotomic conjugate of isogonal conjugate of X(631)
X(44149) = cevapoint of X(5422) and X(11414)
X(44149) = crosssum of X(32) and X(33578)
X(44149) = pole wrt polar circle of trilinear polar of X(34818) (line X(512)X(30442))
X(44149) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3527}, {48, 34818}, {560, 8797}, {8796, 9247}
X(44149) = barycentric product X(i)*X(j) for these {i,j}: {76, 631}, {305, 3087}, {1502, 11402}, {18022, 36748}
X(44149) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3527}, {4, 34818}, {76, 8797}, {264, 8796}, {631, 6}, {3087, 25}, {6755, 3199}, {11402, 32}, {26907, 217}, {36748, 184}
X(44149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 76, 264}, {69, 311, 14615}, {69, 1232, 76}, {76, 14615, 311}, {183, 3964, 95}, {311, 14615, 264}

X(44150) = ISOTOMIC CONJUGATE OF X(37142)

Barycentrics    b*c*(b + c)*(-a^4 + a^2*b^2 - a^2*b*c + b^3*c + a^2*c^2 - 2*b^2*c^2 + b*c^3) : :

X(44150) lies on these lines: {2, 3002}, {4, 69}, {5, 18738}, {10, 307}, {65, 17867}, {72, 349}, {85, 442}, {140, 29477}, {169, 17739}, {274, 25446}, {333, 36019}, {348, 37154}, {379, 1150}, {440, 18750}, {514, 661}, {517, 35517}, {664, 16090}, {668, 16086}, {758, 21207}, {851, 5088}, {860, 23674}, {948, 43059}, {1230, 34255}, {1231, 17864}, {1834, 3673}, {1944, 1948}, {3142, 17181}, {3177, 27021}, {3212, 10974}, {3661, 26605}, {3732, 39690}, {3761, 11679}, {3933, 21596}, {4223, 37670}, {5051, 26563}, {5763, 16284}, {6376, 18749}, {6554, 16589}, {6734, 17866}, {7112, 14505}, {15988, 17499}, {16091, 18026}, {16552, 25002}, {16749, 24883}, {16822, 27966}, {18641, 40702}, {20347, 34387}, {20888, 30101}, {20943, 38298}, {27022, 30694}, {27049, 30695}, {27250, 27267}, {29962, 29981}, {30011, 34847}, {30031, 30034}, {30809, 30828}, {30879, 44081}, {31042, 31060}

X(44150) = anticomplement of X(3002)
X(44150) = isotomic conjugate of X(37142)
X(44150) = isotomic conjugate of isogonal conjugate of X(851)
X(44150) = crosssum of X(31) and X(44112)
X(44150) = crossdifference of every pair of points on line {31, 3049}
X(44150) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2249}, {31, 37142}, {32, 35145}, {284, 1945}, {296, 2299}, {1172, 1949}, {1937, 2194}, {2204, 40843}, {2713, 21761}, {3063, 41206}
X(44150) = barycentric product X(i)*X(j) for these {i,j}: {75, 8680}, {76, 851}, {243, 1231}, {307, 1948}, {321, 5088}, {349, 1936}, {523, 15418}, {561, 42669}, {1430, 40071}, {1441, 1944}, {1446, 7360}, {1502, 44112}, {1981, 14208}, {3267, 23353}, {6331, 9391}, {26884, 27801}
X(44150) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2249}, {2, 37142}, {65, 1945}, {73, 1949}, {75, 35145}, {226, 1937}, {243, 1172}, {307, 40843}, {664, 41206}, {851, 6}, {1214, 296}, {1430, 1474}, {1441, 1952}, {1936, 284}, {1944, 21}, {1948, 29}, {1951, 2194}, {1981, 162}, {2202, 2299}, {5088, 81}, {6518, 283}, {7360, 2287}, {8680, 1}, {9391, 647}, {15146, 2326}, {15418, 99}, {18026, 41207}, {23353, 112}, {26884, 1333}, {35075, 851}, {39035, 2651}, {39036, 2659}, {42669, 31}, {44112, 32}
X(44150) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {72, 349, 21403}, {1231, 41013, 17864}

X(44151) = ISOTOMIC CONJUGATE OF ISOGONAL CONJUGATE OF X(863)

Barycentrics    a*(b + c)*(a^4*b^2 - a^2*b^4 - a^4*b*c + a^2*b^3*c + a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 + a^2*b*c^3 - 2*b^3*c^3 - a^2*c^4 + b^2*c^4) : :

X(44151) lies on these lines: {4, 69}, {7, 40954}, {44, 513}, {73, 1284}, {651, 44112}, {1716, 1745}, {1742, 22369}, {1985, 30945}, {3136, 26892}, {3286, 13738}, {3888, 3948}, {3962, 20718}, {4644, 40952}, {5360, 8680}, {5698, 22076}, {10974, 24695}, {13724, 28350}, {21246, 22412}, {23212, 32462}, {26027, 26041}, {36287, 41333}

X(44151) = isotomic conjugate of isogonal conjugate of X(863)
X(44151) = crossdifference of every pair of points on line {1, 3049}
X(44151) = barycentric product X(76)*X(863)
X(44151) = barycentric quotient X(863)/X(6)

X(44152) = ISOTOMIC CONJUGATE OF ISOGONAL CONJUGATE OF X(1003)

Barycentrics    b^2*c^2*(3*a^4 - a^2*b^2 - a^2*c^2 + 2*b^2*c^2) : :

X(44152) lies on these lines: {2, 670}, {4, 69}, {6, 30736}, {193, 1502}, {308, 3620}, {524, 20023}, {1992, 3978}, {3117, 6379}, {3266, 7774}, {3618, 6374}, {4470, 40087}, {4577, 9544}, {4644, 18891}, {6331, 40138}, {7736, 11059}, {7779, 9464}, {14033, 16084}, {16989, 35524}, {16990, 26235}, {20080, 33769}, {20105, 40907}, {35906, 43187}, {36794, 40405}

X(44152) = isotomic conjugate of isogonal conjugate of X(1003)
X(44152) = crossdifference of every pair of points on line {887, 3049}
X(44152) = barycentric product X(i)*X(j) for these {i,j}: {76, 1003}, {1502, 44116}
X(44152) = barycentric quotient X(i)/X(j) for these {i,j}: {1003, 6}, {44116, 32}

X(44153) = ISOTOMIC CONJUGATE OF X(1244)

Barycentrics    b*c*(a^4*b - a^2*b^3 + a^4*c + 2*a^3*b*c + b^4*c + b^3*c^2 - a^2*c^3 + b^2*c^3 + b*c^4) : :

X(44153) lies on these lines: {4, 69}, {6, 3948}, {10, 24162}, {75, 141}, {193, 31060}, {305, 30962}, {313, 518}, {350, 1965}, {668, 30893}, {942, 40071}, {3263, 18139}, {3596, 4260}, {3618, 30830}, {3765, 16973}, {3912, 20336}, {8024, 30941}, {13728, 39731}, {16085, 32939}, {18052, 37664}, {29841, 30963}, {29983, 41240}

X(44153) = isotomic conjugate of X(1244)
X(44153) = isotomic conjugate of isogonal conjugate of X(1009)
X(44153) = X(31)-isoconjugate of X(1244)
X(44153) = barycentric product X(76)*X(1009)
X(44153) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 1244}, {1009, 6}

X(44154) = ISOTOMIC CONJUGATE OF X(1245)

Barycentrics    b^2*(a + b)*c^2*(a + c)*(a^2 + b^2 + 2*b*c + c^2) : :

X(44154) lies on these lines: {4, 69}, {38, 75}, {86, 313}, {274, 3596}, {332, 1065}, {1230, 17778}, {1269, 17273}, {1920, 20336}, {1978, 37842}, {3761, 10455}, {3765, 27644}, {3770, 28369}, {3948, 26110}, {3963, 40773}, {4377, 16696}, {4476, 21080}, {5224, 34265}, {17321, 31008}, {18147, 18152}, {20891, 30965}, {28604, 28654}, {30596, 30939}

X(44154) = isotomic conjugate of X(1245)
X(44154) = isotomic conjugate of isogonal conjugate of X(1010)
X(44154) = crossdifference of every pair of points on line {1924, 3049}
X(44154) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2281}, {31, 1245}, {42, 1472}, {213, 2221}, {669, 1310}, {810, 32691}, {1036, 1402}, {1924, 37215}, {3049, 36099}
X(44154) = barycentric product X(i)*X(j) for these {i,j}: {76, 1010}, {274, 4385}, {286, 19799}, {310, 2345}, {388, 28660}, {561, 2303}, {612, 6385}, {670, 6590}, {799, 2517}, {1502, 44119}, {2285, 40072}, {2484, 4609}, {4206, 40364}, {4602, 8678}, {5323, 28659}, {6331, 23874}
X(44154) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2281}, {2, 1245}, {81, 1472}, {86, 2221}, {314, 2339}, {333, 1036}, {388, 1400}, {612, 213}, {648, 32691}, {670, 37215}, {799, 1310}, {811, 36099}, {1010, 6}, {1038, 1409}, {2285, 1402}, {2303, 31}, {2345, 42}, {2484, 669}, {2517, 661}, {2522, 810}, {3610, 3690}, {3974, 1334}, {4206, 1973}, {4385, 37}, {5227, 228}, {5286, 40934}, {5323, 604}, {6590, 512}, {7085, 2200}, {7102, 2333}, {7365, 1042}, {7386, 23620}, {8646, 1924}, {8678, 798}, {14594, 4559}, {19799, 72}, {23874, 647}, {28660, 30479}, {31623, 1039}, {44119, 32}
X(44154) = {X(86),X(313)}-harmonic conjugate of X(28660)

X(44155) = ISOTOMIC CONJUGATE OF X(9513)

Barycentrics    b^2*c^2*(a^8 - a^6*b^2 - a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 - 2*b^4*c^4 + b^2*c^6) : :

X(44155) is the intersection of the 1st and 2nd isobarycs of the Brocard axis (lines P(11)P(38) and U(11)U(38)). (Randy Hutson, August 24, 2021)

X(44155) lies on these lines: {2, 647}, {4, 69}, {99, 37991}, {110, 23962}, {141, 34359}, {182, 14382}, {183, 7418}, {290, 542}, {325, 36183}, {327, 5641}, {338, 11646}, {339, 6033}, {880, 1502}, {3448, 36901}, {3788, 28407}, {5972, 6331}, {6375, 7746}, {6390, 30736}, {6776, 14265}, {7761, 35923}, {9306, 18020}, {10479, 35044}, {10684, 14966}, {14356, 35139}, {15595, 16081}, {18024, 36213}, {24206, 39058}, {26276, 34098}, {30737, 43460}, {31636, 41255}

X(44155) = midpoint of X(i) and X(j) for these {i,j}: {69, 30226}, {15164, 15165}
X(44155) = reflection of X(34359) in X(141)
X(44155) = isotomic conjugate of X(9513)
X(44155) = anticomplement of X(5661)
X(44155) = antitomic conjugate of X(40866)
X(44155) = isotomic conjugate of isogonal conjugate of X(1316)
X(44155) = crossdifference of every pair of points on line {237, 3049}
X(44155) = X(i)-isoconjugate of X(j) for these (i,j): {31, 9513}, {1967, 40077}, {36084, 43112}
X(44155) = barycentric product X(i)*X(j) for these {i,j}: {76, 1316}, {850, 40866}, {1502, 44127}, {3978, 38947}, {31953, 43187}
X(44155) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 9513}, {385, 40077}, {1316, 6}, {3569, 43112}, {31953, 3569}, {38947, 694}, {40866, 110}, {43113, 2715}, {44127, 32}

X(44156) = X(230)X(577)∩X(1092)X(3564)

Barycentrics    (a^2 - b^2 - c^2)*(a^6 + b^6 - 2*a^4*c^2 + a^2*b^2*c^2 - 2*b^4*c^2 + a^2*c^4 + b^2*c^4)*(a^6 - 2*a^4*b^2 + a^2*b^4 + a^2*b^2*c^2 + b^4*c^2 - 2*b^2*c^4 + c^6) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1971.

X(44156) lies on these lines: {230, 577}, {1092, 3564}, {2790, 40082}, {3546, 19210}

X(44156) = cevapoint of X(i) and X(j) for these (i,j): {3, 30771}, {125, 22089}

X(44157) = X(549)X(1147)∩X(571)X(6749)

Barycentrics    (a^8 - 5*a^6*b^2 + 8*a^4*b^4 - 5*a^2*b^6 + b^8 - 3*a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 - 3*b^6*c^2 + 3*a^4*c^4 + 5*a^2*b^2*c^4 + 3*b^4*c^4 - a^2*c^6 - b^2*c^6)*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - 5*a^6*c^2 + a^4*b^2*c^2 + 5*a^2*b^4*c^2 - b^6*c^2 + 8*a^4*c^4 + a^2*b^2*c^4 + 3*b^4*c^4 - 5*a^2*c^6 - 3*b^2*c^6 + c^8) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1972.

X(44157) lies on these lines: {549, 1147}, {571, 6749}, {5961, 7525}, {14533, 26937}

X(44158) = X(2)X(12163)∩X(3)X(68)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^8 - a^6*b^2 - 5*a^4*b^4 + 5*a^2*b^6 - b^8 - a^6*c^2 + 6*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + 4*b^6*c^2 - 5*a^4*c^4 - 5*a^2*b^2*c^4 - 6*b^4*c^4 + 5*a^2*c^6 + 4*b^2*c^6 - c^8) : :
X(44158) =3 X[2] + X[12163], 3 X[3] + X[68], 5 X[3] - X[12118], 7 X[3] + X[12429], X[20] + 3 X[14852], 5 X[68] + 3 X[12118], X[68] - 3 X[12359], 7 X[68] - 3 X[12429], 3 X[140] - 2 X[43839], X[155] - 5 X[631], X[156] - 3 X[34477], 3 X[376] + X[12293], 3 X[549] - X[1147], X[2883] - 3 X[10201], 3 X[3167] - 11 X[15720], X[3521] + 3 X[43689], 7 X[3523] + X[11411], 9 X[3524] - X[6193], 7 X[3526] - 3 X[5654], 9 X[5054] - X[12164], X[5504] - 5 X[38728], 3 X[6699] - X[15115], X[6759] - 3 X[34351], X[9820] - 4 X[20191], 3 X[9820] - 4 X[43839], 3 X[10192] - X[32139], X[12084] - 3 X[23328], 4 X[12108] - X[41597], X[12118] + 5 X[12359], 7 X[12118] + 5 X[12429], 7 X[12359] - X[12429], 3 X[14070] + X[14216], X[14790] - 5 X[40686], 7 X[14869] - X[15083], 3 X[15061] - X[23306], 3 X[18324] + X[32140], 3 X[18324] - X[34782], X[18569] - 3 X[23332], 3 X[20191] - X[43839], 3 X[23329] - X[23335]

See Antreas Hatzipolakis and Peter Moses, euclid 1972.

X(44158) lies on these lines: {2, 12163}, {3, 68}, {5, 4550}, {20, 14852}, {26, 6247}, {30, 5449}, {54, 15136}, {125, 12605}, {140, 9729}, {141, 19908}, {155, 631}, {156, 34477}, {185, 7542}, {186, 12134}, {376, 12293}, {378, 41587}, {382, 32269}, {403, 11440}, {428, 18488}, {468, 12162}, {511, 25563}, {539, 10213}, {546, 20193}, {548, 13470}, {549, 1147}, {550, 9927}, {858, 43608}, {912, 3678}, {1154, 20376}, {1192, 18420}, {1204, 15760}, {1216, 6699}, {1368, 20302}, {1503, 1658}, {2070, 16655}, {2777, 15114}, {2883, 10201}, {2888, 37941}, {2931, 7512}, {3089, 11472}, {3147, 18451}, {3167, 15720}, {3448, 38448}, {3520, 3580}, {3521, 10024}, {3523, 11411}, {3524, 6193}, {3526, 5654}, {3530, 3564}, {3538, 12318}, {3541, 37489}, {3547, 15740}, {3549, 10605}, {3575, 32110}, {3579, 12259}, {3589, 12006}, {3628, 5448}, {5010, 12428}, {5054, 12164}, {5204, 10055}, {5217, 10071}, {5432, 7352}, {5433, 6238}, {5504, 34483}, {5562, 10257}, {5663, 10020}, {5889, 37118}, {5893, 13406}, {5907, 16238}, {6000, 13383}, {6101, 15122}, {6102, 23292}, {6221, 19061}, {6240, 23293}, {6398, 19062}, {6643, 22661}, {6676, 40647}, {6759, 34351}, {6804, 32620}, {7280, 18970}, {7526, 13567}, {10018, 12111}, {10192, 32139}, {10264, 12893}, {10298, 34224}, {11064, 18436}, {11381, 37971}, {11425, 18951}, {11430, 13292}, {11442, 32534}, {11454, 18560}, {11457, 38444}, {12084, 23328}, {12108, 41597}, {12161, 18580}, {12225, 23294}, {12235, 15644}, {12241, 18570}, {12421, 38727}, {13474, 32223}, {13909, 42216}, {13970, 42215}, {14070, 14216}, {14118, 26879}, {14130, 16657}, {14516, 21844}, {14788, 15053}, {14790, 40686}, {14806, 41523}, {14869, 15083}, {15061, 23306}, {15123, 43577}, {15311, 15761}, {15873, 31861}, {16618, 20417}, {16621, 37440}, {16654, 18378}, {16836, 32348}, {18324, 32140}, {18475, 18914}, {18562, 21400}, {18569, 23332}, {18916, 37506}, {18917, 19357}, {19128, 43894}, {21243, 31833}, {23329, 23335}, {31829, 43589}, {32358, 43394}, {33547, 40685}, {34664, 43817}, {37481, 37649},

X(44158) = complement of X(22660)
X(44158) = midpoint of X(i) and X(j) for these {i,j}: {3, 12359}, {5, 7689}, {26, 6247}, {550, 9927}, {3579, 12259}, {10264, 12893}, {12163, 22660}, {12235, 15644}, {15761, 32138}, {32140, 34782}
X(44158) = reflection of X(i) in X(j) for these {i,j}: {140, 20191}, {5448, 3628}, {5893, 13406}, {9820, 140}, {12038, 3530}, {16252, 10020}, {33547, 40685}
X(44158) = crosspoint of X(69) and X(42410)
X(44158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12163, 22660}, {1216, 6699, 16196}, {18324, 32140, 34782}

leftri

Isogonal conjugates and isotomic conjugates: X(44159)-X(44173)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, August 10-12, 2021.

For any triangle center P, let gP and tP denote the isogonal conjugate of P and the isotomic conjugate of P, respectively. Centers X(44159)-X(44173) are members of chains of points

X, gX, tgX, gtgX, tgtgX, gtgtgX, ...

Following is a list of such chains, in which 0 signifies a point that is not in ETC:

(41288, 0, 41286, 0, 41281, 44159, 41280, 40363, 1397, 3596, 56, 8, 7, 55, 6063, 2175, 41283, 9448, 41287, 0, 41289, 0, 41290)

(9233, 40362, 1501, 1502, 32, 76, 6, 2, 2, 6, 76, 32, 1502, 1501, 40362, 9233, 40359)

(18903, 0, 14604, 18901, 8789, 14603, 9468, 3978, 694, 385, 1916, 1691, 18896, 14602, 44160, 18902)

(1917, 1928, 560, 561, 31, 75, 1, 1, 75, 31, 561, 560, 1928, 1917)

(8023, 44163, 44164, 44165, 8265, 38830, 20859, 40416, 626, 38826, 44166, 44167, 8039)

(40372, 0, 20968, 40421, 206, 18018, 22, 66, 315, 2353, 40073, 40146)

(23963, 23962, 23357, 338, 249, 115, 4590, 3124, 34537, 1084, 44168, 9427)

(18897, 44169, 1922, 1921, 292, 239, 335, 1914, 18895, 14599, 44170, 18894)

(18893, 44171, 14598, 18891, 1911, 350, 291, 238, 334, 2210, 44172, 18892)

(14574, 44173, 1576, 850, 110, 523, 99, 512, 670, 669, 4609, 9426)

(1691, 1916, 385, 694, 3978, 9468, 14603, 8789, 18901, 14604, 0, 18903)

X(44159) = ISOGONAL CONJUGATE OF X(41281)

Barycentrics    b^6*c^6*(-a + b + c) : :

X(44159) lies on these lines: {561, 4920}, {1228, 40367}, {1928, 35523}, {4136, 28659}, {33788, 35527}, {40360, 41287}

X(44159) = isogonal conjugate of X(41281)
X(44159) = isotomic conjugate of X(41280)
X(44159) = isotomic conjugate of the isogonal conjugate of X(40363)
X(44159) = X(i)-isoconjugate of X(j) for these (i,j): {1, 41281}, {31, 41280}, {34, 40373}, {56, 1917}, {57, 9233}, {75, 41286}, {560, 1397}, {561, 41288}, {604, 1501}, {1106, 9448}, {1356, 23995}, {1395, 14575}, {1428, 18893}, {2205, 16947}
X(44159) = barycentric product X(i)*X(j) for these {i,j}: {8, 40362}, {55, 40359}, {76, 40363}, {220, 41289}, {281, 40360}, {312, 1928}, {346, 41287}, {561, 28659}, {1502, 3596}, {7017, 40050}, {14827, 41290}, {27801, 40072}
X(44159) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 41280}, {6, 41281}, {8, 1501}, {9, 1917}, {32, 41286}, {55, 9233}, {76, 1397}, {219, 40373}, {310, 16947}, {312, 560}, {338, 1356}, {341, 9447}, {345, 14575}, {346, 9448}, {561, 604}, {645, 14574}, {1264, 14585}, {1501, 41288}, {1502, 56}, {1928, 57}, {1969, 1395}, {3596, 32}, {3685, 18894}, {3700, 9426}, {3701, 2205}, {3703, 41331}, {3718, 9247}, {3975, 18892}, {4086, 1924}, {4087, 14599}, {4092, 9427}, {4136, 8022}, {4391, 1980}, {4518, 18897}, {4609, 4565}, {4876, 18893}, {6064, 23963}, {6385, 1408}, {6386, 1415}, {7017, 1974}, {18022, 608}, {18027, 7337}, {20567, 1106}, {27801, 1402}, {28659, 31}, {28660, 2206}, {30713, 1918}, {34387, 1977}, {35519, 1919}, {40050, 222}, {40072, 1333}, {40073, 7251}, {40359, 6063}, {40360, 348}, {40362, 7}, {40363, 6}, {40364, 603}, {40367, 1403}, {41283, 1407}, {41287, 279}

X(44160) = ISOGONAL CONJUGATE OF X(18902)

Barycentrics    b^4*c^4*(b^2 - a*c)*(b^2 + a*c)*(a*b - c^2)*(a*b + c^2) : :

X(44160) lies on these lines: {76, 694}, {305, 8842}, {308, 9468}, {338, 1502}, {384, 14604}, {1916, 4609}, {2970, 18022}, {8039, 23962}, {14603, 18024}, {16081, 39292}, {18829, 40074}, {20023, 20027}, {35549, 42822}, {36214, 40073}

X(44160) = isogonal conjugate of X(18902)
X(44160) = isotomic conjugate of X(14602)
X(44160) = isotomic conjugate of the isogonal conjugate of X(18896)
X(44160) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18902}, {31, 14602}, {32, 1933}, {171, 18894}, {172, 18892}, {385, 1917}, {560, 1691}, {1501, 1580}, {1966, 9233}, {2086, 23995}, {7122, 14599}, {9247, 44089}
X(44160) = trilinear product X(i)*X(j) for these {i,j}: {76, 1934}, {561, 1916}, {694, 1928}, {1502, 1581}
X(44160) = barycentric product X(i)*X(j) for these {i,j}: {76, 18896}, {561, 1934}, {694, 40362}, {1502, 1916}, {1581, 1928}, {9468, 40359}, {17980, 40360}, {18022, 40708}, {18901, 41517}, {23962, 39292}
X(44160) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 14602}, {6, 18902}, {75, 1933}, {76, 1691}, {256, 18892}, {257, 14599}, {264, 44089}, {334, 7122}, {338, 2086}, {561, 1580}, {694, 1501}, {805, 14574}, {850, 5027}, {882, 9426}, {893, 18894}, {1502, 385}, {1581, 560}, {1916, 32}, {1928, 1966}, {1934, 31}, {1967, 1917}, {3493, 19556}, {4609, 17941}, {5207, 19575}, {7018, 2210}, {8024, 8623}, {8842, 34396}, {9468, 9233}, {14603, 4027}, {17970, 40373}, {18022, 419}, {18024, 40820}, {18829, 1576}, {18895, 172}, {18896, 6}, {36214, 14575}, {36897, 14601}, {39292, 23357}, {40050, 12215}, {40359, 14603}, {40362, 3978}, {40495, 4164}, {40708, 184}, {40810, 9418}, {41209, 4630}, {41517, 8789}

X(44161) = ISOGONAL CONJUGATE OF X(40373)

Barycentrics    b^6*c^6*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2) : :

X(44161) lies on these lines: {76, 22416}, {183, 41488}, {1235, 5117}, {1502, 18027}, {6331, 39575}, {14603, 44144}, {18024, 41009}, {22456, 38907}, {23128, 43187}, {40016, 43678}, {40359, 40360}

X(44161) = isogonal conjugate of X(40373)
X(44161) = isotomic conjugate of X(14575)
X(44161) = polar conjugate of X(1501)
X(44161) = isotomic conjugate of the isogonal conjugate of X(18022)
X(44161) = polar conjugate of the isotomic conjugate of X(40362)
X(44161) = polar conjugate of the isogonal conjugate of X(1502)
X(44161) = X(1502)-cross conjugate of X(40362)
X(44161) = cevapoint of X(1502) and X(18022)
X(44161) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40373}, {3, 1917}, {31, 14575}, {32, 9247}, {48, 1501}, {63, 9233}, {78, 41281}, {184, 560}, {212, 41280}, {603, 9448}, {810, 14574}, {1101, 23216}, {1923, 10547}, {1924, 32661}, {1973, 14585}, {1980, 32656}, {2196, 18894}, {3718, 41286}, {4100, 36417}, {4575, 9426}, {7193, 18893}, {9417, 14600}
X(44161) = barycentric product X(i)*X(j) for these {i,j}: {4, 40362}, {25, 40359}, {76, 18022}, {92, 1928}, {264, 1502}, {281, 41287}, {305, 18027}, {331, 40363}, {393, 40360}, {561, 1969}, {607, 41289}, {826, 42395}, {1235, 40016}, {2052, 40050}, {4609, 14618}, {7017, 41283}, {18024, 44132}
X(44161) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 14575}, {4, 1501}, {6, 40373}, {19, 1917}, {25, 9233}, {69, 14585}, {75, 9247}, {76, 184}, {92, 560}, {115, 23216}, {242, 18894}, {264, 32}, {275, 14573}, {278, 41280}, {281, 9448}, {290, 14600}, {297, 9418}, {305, 577}, {308, 10547}, {311, 217}, {313, 2200}, {315, 22075}, {318, 9447}, {324, 40981}, {331, 1397}, {340, 19627}, {343, 44088}, {419, 18902}, {427, 41331}, {561, 48}, {608, 41281}, {626, 23209}, {648, 14574}, {670, 32661}, {850, 3049}, {1093, 36417}, {1235, 3051}, {1502, 3}, {1928, 63}, {1969, 31}, {1978, 32656}, {2052, 1974}, {2501, 9426}, {2967, 36425}, {2970, 1084}, {2973, 1977}, {3266, 23200}, {3267, 39201}, {3926, 23606}, {3964, 36433}, {4572, 32660}, {4602, 4575}, {4609, 4558}, {5117, 18899}, {6331, 1576}, {6385, 1437}, {6386, 906}, {7017, 2175}, {7141, 7109}, {8024, 20775}, {8039, 20819}, {8743, 40372}, {8754, 9427}, {14618, 669}, {15415, 15451}, {16081, 14601}, {17907, 20968}, {17924, 1980}, {17980, 14604}, {17983, 19626}, {17984, 14602}, {18020, 23963}, {18022, 6}, {18023, 14908}, {18024, 248}, {18027, 25}, {18817, 11060}, {18896, 17970}, {18901, 12215}, {20234, 22364}, {20567, 603}, {20883, 1923}, {20948, 810}, {23962, 20975}, {23989, 22096}, {24006, 1924}, {27801, 228}, {28659, 212}, {28706, 418}, {34384, 14533}, {36793, 34980}, {40016, 1176}, {40050, 394}, {40071, 4055}, {40072, 2193}, {40073, 10316}, {40074, 10317}, {40162, 15389}, {40359, 305}, {40360, 3926}, {40362, 69}, {40363, 219}, {40364, 255}, {40367, 20760}, {40495, 22383}, {40703, 9417}, {40717, 14599}, {41013, 2205}, {41283, 222}, {41287, 348}, {41530, 14642}, {42395, 4577}, {43678, 40146}, {44129, 2206}, {44132, 237}, {44144, 34396}, {44146, 14567}

X(44162) = ISOGONAL CONJUGATE OF X(40050)

Barycentrics    a^6*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) : :

X(44162) lies on these lines: {3, 19118}, {4, 3398}, {6, 15257}, {24, 2967}, {25, 251}, {32, 682}, {39, 9515}, {76, 37912}, {110, 19597}, {112, 699}, {186, 9821}, {237, 10316}, {264, 3115}, {468, 7767}, {827, 6179}, {1501, 40372}, {1576, 3053}, {1843, 5007}, {2205, 9448}, {2207, 2971}, {2353, 20975}, {2868, 10423}, {3080, 36417}, {3199, 44099}, {5008, 44091}, {5095, 7890}, {6287, 16868}, {7487, 41371}, {9418, 14585}, {10317, 20960}, {11470, 30270}, {12167, 43136}, {14001, 37893}, {14581, 40325}, {15270, 18374}, {20993, 40947}, {23216, 40351}, {39575, 44090}, {42671, 44079}

X(44162) = isogonal conjugate of X(40050)
X(44162) = isotomic conjugate of X(40360)
X(44162) = polar conjugate of X(40362)
X(44162) = isogonal conjugate of the isotomic conjugate of X(1974)
X(44162) = isogonal conjugate of the polar conjugate of X(36417)
X(44162) = polar conjugate of the isotomic conjugate of X(1501)
X(44162) = polar conjugate of the isogonal conjugate of X(9233)
X(44162) = X(1974)-Ceva conjugate of X(1501)
X(44162) = X(i)-cross conjugate of X(j) for these (i,j): {9233, 1501}, {23216, 9426}
X(44162) = cevapoint of X(9426) and X(23216)
X(44162) = crosspoint of X(1974) and X(36417)
X(44162) = crosssum of X(i) and X(j) for these (i,j): {69, 34254}, {125, 3267}
X(44162) = crossdifference of every pair of points on line {2525, 3267}
X(44162) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40050}, {2, 40364}, {3, 1928}, {31, 40360}, {48, 40362}, {63, 1502}, {69, 561}, {75, 305}, {76, 304}, {77, 40363}, {78, 41283}, {212, 41287}, {274, 40071}, {306, 6385}, {307, 40072}, {310, 20336}, {326, 18022}, {337, 18891}, {339, 24037}, {345, 20567}, {348, 28659}, {525, 4602}, {656, 4609}, {670, 14208}, {799, 3267}, {1102, 18027}, {1231, 28660}, {1926, 40708}, {1969, 3926}, {1978, 15413}, {2525, 37204}, {3596, 7182}, {3718, 6063}, {3933, 18833}, {4025, 6386}, {4561, 40495}, {4563, 20948}, {4572, 35518}, {9247, 40359}, {17206, 27801}, {18695, 34384}, {18837, 43714}, {20902, 34537}, {33778, 36952}
X(44162) = barycentric product X(i)*X(j) for these {i,j}: {3, 36417}, {4, 1501}, {6, 1974}, {19, 560}, {25, 32}, {28, 2205}, {30, 40351}, {31, 1973}, {34, 9447}, {41, 1395}, {53, 14573}, {92, 1917}, {112, 669}, {162, 1924}, {184, 2207}, {213, 2203}, {232, 14601}, {242, 18897}, {249, 42068}, {250, 1084}, {251, 27369}, {264, 9233}, {278, 9448}, {281, 41280}, {393, 14575}, {419, 8789}, {468, 19626}, {604, 2212}, {607, 1397}, {608, 2175}, {648, 9426}, {798, 32676}, {878, 34859}, {1096, 9247}, {1398, 14827}, {1402, 2204}, {1474, 1918}, {1495, 40354}, {1576, 2489}, {1783, 1980}, {1919, 8750}, {1976, 2211}, {2052, 40373}, {2201, 14598}, {2206, 2333}, {2353, 17409}, {2491, 32696}, {2501, 14574}, {2971, 23357}, {2998, 41293}, {3049, 32713}, {3172, 33581}, {6524, 14585}, {6531, 9418}, {6620, 40823}, {7017, 41281}, {8743, 40146}, {8749, 9407}, {8751, 9455}, {8752, 9459}, {8753, 14567}, {8754, 23963}, {8882, 40981}, {9427, 18020}, {9468, 44089}, {9494, 42396}, {11060, 34397}, {13854, 20968}, {14398, 32715}, {14581, 40352}, {14600, 34854}, {14602, 17980}, {14604, 17984}, {18384, 19627}, {20975, 41937}, {23216, 23582}, {23606, 36434}, {23975, 34980}, {23990, 42067}, {32085, 41331}, {32654, 44099}, {32740, 44102}, {40372, 43678}
X(44162) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 40360}, {4, 40362}, {6, 40050}, {19, 1928}, {25, 1502}, {31, 40364}, {32, 305}, {112, 4609}, {264, 40359}, {278, 41287}, {331, 41289}, {419, 18901}, {560, 304}, {607, 40363}, {608, 41283}, {669, 3267}, {1084, 339}, {1395, 20567}, {1501, 69}, {1917, 63}, {1918, 40071}, {1924, 14208}, {1973, 561}, {1974, 76}, {1980, 15413}, {2203, 6385}, {2204, 40072}, {2205, 20336}, {2207, 18022}, {2212, 28659}, {2971, 23962}, {4117, 20902}, {8023, 20819}, {8789, 40708}, {9233, 3}, {9418, 6393}, {9426, 525}, {9427, 125}, {9447, 3718}, {9448, 345}, {9494, 2525}, {14573, 34386}, {14574, 4563}, {14575, 3926}, {14585, 4176}, {14604, 36214}, {17409, 40073}, {18897, 337}, {18902, 12215}, {18903, 17970}, {19626, 30786}, {20968, 34254}, {23216, 15526}, {27369, 8024}, {32676, 4602}, {36417, 264}, {40351, 1494}, {40372, 20806}, {40373, 394}, {40981, 28706}, {41280, 348}, {41281, 222}, {41293, 194}, {41331, 3933}, {42068, 338}, {44089, 14603}
X(44162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 1974, 27369}, {32, 20968, 14575}, {10547, 30435, 34396}, {11380, 44089, 4}

X(44163) = ISOGONAL CONJUGATE OF X(8023)

Barycentrics    b^6*(a^4 + b^4)*c^6*(a^4 + c^4) : :

X(44163) lies on these lines: {6, 35530}, {39, 14603}, {141, 18901}, {2353, 38842}, {6664, 40016}

X(44163) = isogonal conjugate of X(8023)
X(44163) = isotomic conjugate of X(44164)
X(44163) = X(76)-cross conjugate of X(38830)
X(44163) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8023}, {560, 8265}, {1501, 2085}, {1917, 20859}, {1973, 23209}, {4118, 9233}
X(44163) = cevapoint of X(i) and X(j) for these (i,j): {76, 40362}, {38830, 38842}
X(44163) = barycentric product X(i)*X(j) for these {i,j}: {1502, 38830}, {1928, 38847}, {38826, 40359}, {38842, 40421}, {40362, 40416}
X(44163) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 8023}, {69, 23209}, {76, 8265}, {305, 4173}, {561, 2085}, {1502, 20859}, {1928, 4118}, {6385, 16717}, {8024, 3118}, {38826, 9233}, {38830, 32}, {38842, 206}, {38847, 560}, {40050, 20819}, {40360, 4121}, {40362, 626}, {40416, 1501}, {41287, 7217}

X(44164) = ISOTOMIC CONJUGATE OF ISOGONAL CONJUGATE OF X(8023)

Barycentrics    a^6*(b^4 + c^4) : :

X(44164) lies on these lines: {6, 76}, {32, 8789}, {39, 32748}, {217, 1692}, {575, 6310}, {711, 827}, {1084, 27374}, {1207, 3329}, {1501, 20968}, {1613, 6179}, {1691, 15926}, {2086, 7755}, {2387, 14820}, {3051, 3229}, {3118, 4173}, {3224, 3972}, {3231, 7780}, {5012, 14885}, {8023, 23209}, {8619, 21751}

X(44164) = isogonal conjugate of X(44165)
X(44164) = isotomic conjugate of X(44163)
X(44164) = isotomic conjugate of the isogonal conjugate of X(8023)
X(44164) = isogonal conjugate of the isotomic conjugate of X(8265)
X(44164) = polar conjugate of the isotomic conjugate of X(23209)
X(44164) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 20859}, {827, 9494}, {8265, 23209}
X(44164) = X(i)-isoconjugate of X(j) for these (i,j): {1, 44165}, {75, 38830}, {76, 38847}, {561, 40416}, {1928, 38826}, {1930, 3115}
X(44164) = crosspoint of X(6) and X(1501)
X(44164) = crosssum of X(2) and X(1502)
X(44164) = crossdifference of every pair of points on line {688, 14295}
X(44164) = trilinear product X(i)*X(j) for these {i,j}: {19, 23209}, {31, 8265}, {32, 2085}, {75, 8023}, {560, 20859}, {626, 1917}, {1501, 4118}, {1918, 16717}, {1973, 4173}, {9233, 20627}
X(44164) = barycentric product X(i)*X(j) for these {i,j}: {4, 23209}, {6, 8265}, {25, 4173}, {31, 2085}, {32, 20859}, {76, 8023}, {213, 16717}, {251, 3118}, {560, 4118}, {626, 1501}, {1917, 20627}, {1974, 20819}, {2205, 18167}, {4178, 41280}, {7217, 9448}, {16890, 41331}
X(44164) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 38830}, {206, 38842}, {560, 38847}, {626, 40362}, {1501, 40416}, {2085, 561}, {3118, 8024}, {4118, 1928}, {4121, 40360}, {4173, 305}, {7217, 41287}, {8023, 6}, {8265, 76}, {9233, 38826}, {16717, 6385}, {20819, 40050}, {20859, 1502}, {23209, 69}
X(44164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1186, 42548}, {6, 3499, 7760}, {6, 33786, 76}, {3051, 9490, 5007}, {4173, 8265, 3118}

X(44165) = ISOTOMIC CONJUGATE OF X(8265)

Barycentrics    b^4*(a^4 + b^4)*c^4*(a^4 + c^4) : :

X(44165) lies on these lines: {2, 40359}, {32, 710}, {39, 14603}, {626, 14946}, {3051, 3978}, {4609, 7909}, {7832, 18901}, {9230, 38821}, {17984, 27369}, {40146, 40421}

X(44165) = isogonal conjugate of X(44164)
X(44165) = isotomic conjugate of X(8265)
X(44165) = isotomic conjugate of the complement of X(1502)
X(44165) = isotomic conjugate of the isogonal conjugate of X(38830)
X(44165) = X(i)-cross conjugate of X(j) for these (i,j): {2, 40416}, {826, 42371}, {31296, 670}
X(44165) = X(i)-isoconjugate of X(j) for these (i,j): {1, 44164}, {19, 23209}, {31, 8265}, {32, 2085}, {75, 8023}, {560, 20859}, {626, 1917}, {1501, 4118}, {1918, 16717}, {1973, 4173}, {9233, 20627}
X(44165) = cevapoint of X(2) and X(1502)
X(44165) = trilinear pole of line {688, 14295}
X(44165) = trilinear product X(i)*X(j) for these {i,j}: {75, 38830}, {76, 38847}, {561, 40416}, {1928, 38826}, {1930, 3115}
X(44165) = barycentric product X(i)*X(j) for these {i,j}: {76, 38830}, {561, 38847}, {1502, 40416}, {3115, 8024}, {18018, 38842}, {38826, 40362}
X(44165) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8265}, {3, 23209}, {32, 8023}, {69, 4173}, {75, 2085}, {76, 20859}, {141, 3118}, {274, 16717}, {305, 20819}, {561, 4118}, {1502, 626}, {1928, 20627}, {3115, 251}, {6385, 18167}, {33515, 4630}, {38826, 1501}, {38830, 6}, {38842, 22}, {38847, 31}, {40016, 16890}, {40050, 4121}, {40359, 8039}, {40363, 4178}, {40416, 32}, {41283, 7217}

X(44166) = ISOTOMIC CONJUGATE OF X(38826)

Barycentrics    b^2*c^2*(b^4 + c^4) : :

X(44166) lies on these lines: {6, 76}, {53, 44132}, {69, 2871}, {141, 35542}, {305, 7778}, {311, 325}, {313, 35551}, {321, 35547}, {338, 1502}, {736, 41331}, {1989, 32833}, {3721, 35537}, {4159, 9233}, {5976, 8266}, {6664, 34294}, {7763, 13351}, {7792, 39998}, {8039, 16893}, {9230, 40074}, {16890, 20859}, {16894, 20627}, {17500, 33798}

X(44166) = isogonal conjugate of X(44167)
X(44166) = isotomic conjugate of X(38826)
X(44166) = isotomic conjugate of the isogonal conjugate of X(626)
X(44166) = isogonal conjugate of the isotomic conjugate of X(8039)
X(44166) = polar conjugate of the isogonal conjugate of X(4121)
X(44166) = X(76)-Ceva conjugate of X(20859)
X(44166) = X(16893)-cross conjugate of X(626)
X(44166) = X(i)-isoconjugate of X(j) for these (i,j): {1, 44167}, {31, 38826}, {560, 40416}, {1501, 38847}, {1917, 38830}
X(44166) = cevapoint of X(626) and X(4121)
X(44166) = crosspoint of X(76) and X(40362)
X(44166) = crosssum of X(32) and X(9233)
X(44166) = trilinear product X(i)*X(j) for these {i,j}: {2, 20627}, {31, 8039}, {75, 626}, {76, 4118}, {85, 4178}, {92, 4121}, {274, 16894}, {312, 7217}, {313, 18167}, {321, 16891}, {561, 20859}, {668, 21110}, {1502, 2085}, {1928, 8265}, {1930, 16890}, {1969, 20819}, {3112, 16893}
X(44166) = barycentric product X(i)*X(j) for these {i,j}: {6, 8039}, {75, 20627}, {76, 626}, {264, 4121}, {308, 16893}, {310, 16894}, {313, 16891}, {561, 4118}, {1502, 20859}, {1928, 2085}, {1978, 21110}, {3596, 7217}, {4178, 6063}, {8024, 16890}, {8265, 40362}, {18022, 20819}, {18167, 27801}, {35530, 40847}
X(44166) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 38826}, {76, 40416}, {561, 38847}, {626, 6}, {689, 33515}, {1502, 38830}, {2085, 560}, {3118, 41331}, {4118, 31}, {4121, 3}, {4173, 14575}, {4178, 55}, {7217, 56}, {8039, 76}, {8264, 38838}, {8265, 1501}, {16890, 251}, {16891, 58}, {16893, 39}, {16894, 42}, {18167, 1333}, {20627, 1}, {20819, 184}, {20859, 32}, {21110, 649}, {23209, 40373}, {35530, 16985}, {40016, 3115}, {40847, 711}
X(44166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 40073, 35549}, {76, 40035, 33769}, {76, 40073, 6}

X(44167) = ISOTOMIC CONJUGATE OF X(8039)

Barycentrics    a^4*(a^4 + b^4)*(a^4 + c^4) : :

X(44167) lies on these lines: {2, 9233}, {32, 40366}, {39, 5012}, {3051, 18902}, {4630, 8023}, {33515, 43094}

X(44167) = isogonal conjugate of X(44166)
X(44167) = isotomic conjugate of X(8039)
X(44167) = isogonal conjugate of the isotomic conjugate of X(38826)
X(44167) = X(32)-cross conjugate of X(40416)
X(44167) = X(i)-isoconjugate of X(j) for these (i,j): {1, 44166}, {2, 20627}, {31, 8039}, {75, 626}, {76, 4118}, {85, 4178}, {92, 4121}, {274, 16894}, {312, 7217}, {313, 18167}, {321, 16891}, {561, 20859}, {668, 21110}, {1502, 2085}, {1928, 8265}, {1930, 16890}, {1969, 20819}, {3112, 16893}
X(44167) = cevapoint of X(32) and X(9233)
X(44167) = crosssum of X(626) and X(4121)
X(44167) = trilinear product X(i)*X(j) for these {i,j}: {31, 38826}, {560, 40416}, {1501, 38847}, {1917, 38830}
X(44167) = barycentric product X(i)*X(j) for these {i,j}: {6, 38826}, {32, 40416}, {560, 38847}, {688, 33515}, {1501, 38830}, {3115, 41331}
X(44167) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8039}, {31, 20627}, {32, 626}, {184, 4121}, {560, 4118}, {1397, 7217}, {1501, 20859}, {1917, 2085}, {1918, 16894}, {1919, 21110}, {2175, 4178}, {2206, 16891}, {3051, 16893}, {9233, 8265}, {14575, 20819}, {33515, 42371}, {38826, 76}, {38830, 40362}, {38838, 19562}, {38847, 1928}, {40373, 4173}, {40416, 1502}

X(44168) = ISOTOMIC CONJUGATE OF X(1084)

Barycentrics    (a - b)^2*b^4*(a + b)^2*(a - c)^2*c^4*(a + c)^2 : :
X(44168) = 2 X[670] + X[886], 3 X[3228] - 4 X[31646], 15 X[31639] - 16 X[40507]

X(44168) lies on these lines: {99, 9491}, {512, 670}, {538, 14603}, {799, 21763}, {1502, 14609}, {3228, 31646}, {3231, 3978}, {6374, 30229}, {14382, 40050}, {16084, 17984}, {18829, 42371}, {31639, 40507}

X(44168) = midpoint of X(670) and X(9428)
X(44168) = reflection of X(886) in X(9428)
X(44168) = isogonal conjugate of X(9427)
X(44168) = isotomic conjugate of X(1084)
X(44168) = polar conjugate of X(42068)
X(44168) = isotomic conjugate of the anticomplement of X(36950)
X(44168) = isotomic conjugate of the complement of X(670)
X(44168) = isotomic conjugate of the isogonal conjugate of X(34537)
X(44168) = barycentric square of X(670)
X(44168) = X(i)-cross conjugate of X(j) for these (i,j): {2, 670}, {76, 42371}, {194, 99}, {538, 886}, {1502, 4609}, {1655, 668}, {6392, 6528}, {8267, 4577}, {10010, 9063}, {19570, 35139}, {31088, 42367}, {34022, 799}, {36950, 2}, {40858, 18829}
X(44168) = cevapoint of X(i) and X(j) for these (i,j): {2, 670}, {99, 7760}, {668, 32026}, {1502, 4609}, {1613, 1634}
X(44168) = trilinear pole of line {670, 888} (the tangent to the Steiner circumellipse at X(670))
X(44168) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9427}, {6, 4117}, {19, 23216}, {31, 1084}, {41, 1356}, {48, 42068}, {115, 1917}, {163, 23099}, {512, 1924}, {560, 3124}, {604, 7063}, {661, 9426}, {662, 23610}, {669, 798}, {872, 1977}, {1109, 9233}, {1501, 2643}, {1918, 3121}, {1927, 2086}, {1980, 4079}, {2151, 41993}, {2152, 41994}, {2205, 3122}, {2971, 9247}, {3248, 7109}, {9417, 15630}, {33918, 36133}
X(44168) = barycentric product X(i)*X(j) for these {i,j}: {76, 34537}, {99, 4609}, {249, 40362}, {250, 40360}, {561, 24037}, {670, 670}, {799, 4602}, {1502, 4590}, {1928, 24041}, {4576, 42371}, {4601, 6385}, {4623, 6386}, {6064, 41283}, {7340, 40363}, {14603, 39292}, {18020, 40050}, {23357, 40359}
X(44168) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4117}, {2, 1084}, {3, 23216}, {4, 42068}, {6, 9427}, {7, 1356}, {8, 7063}, {13, 41993}, {14, 41994}, {76, 3124}, {99, 669}, {110, 9426}, {249, 1501}, {264, 2971}, {274, 3121}, {290, 15630}, {305, 20975}, {310, 3122}, {512, 23610}, {523, 23099}, {538, 1645}, {561, 2643}, {662, 1924}, {670, 512}, {689, 18105}, {799, 798}, {850, 22260}, {873, 3248}, {880, 5027}, {888, 33918}, {1016, 7109}, {1101, 1917}, {1502, 115}, {1509, 1977}, {1634, 9494}, {1920, 21823}, {1928, 1109}, {1978, 4079}, {2396, 2491}, {3266, 21906}, {3978, 2086}, {4176, 34980}, {4563, 3049}, {4567, 2205}, {4576, 688}, {4590, 32}, {4600, 1918}, {4601, 213}, {4602, 661}, {4609, 523}, {4610, 1919}, {4623, 667}, {4631, 3063}, {6064, 2175}, {6331, 2489}, {6385, 3125}, {6386, 4705}, {7035, 872}, {7304, 21762}, {7340, 1397}, {7760, 38996}, {8033, 21755}, {9428, 38237}, {16084, 865}, {18020, 1974}, {18021, 3271}, {18022, 8754}, {18829, 881}, {20023, 6784}, {23342, 887}, {23357, 9233}, {23582, 36417}, {24037, 31}, {24041, 560}, {27801, 21833}, {31008, 21835}, {31614, 1576}, {31625, 1500}, {31639, 31646}, {34537, 6}, {35073, 39010}, {35540, 41178}, {39292, 9468}, {40016, 34294}, {40050, 125}, {40072, 4516}, {40359, 23962}, {40360, 339}, {40362, 338}, {40363, 4092}, {40364, 3708}, {41283, 1365}, {43187, 2422}

X(44169) = ISOTOMIC CONJUGATE OF X(1922)

Barycentrics    b^4*c^4*(-a^2 + b*c) : :

X(44169) lies on these lines: {75, 4493}, {76, 1928}, {313, 561}, {321, 40016}, {350, 1926}, {768, 3261}, {1909, 1925}, {3263, 6386}, {3978, 41250}, {4602, 20924}, {6385, 16703}, {7242, 33788}, {18833, 33941}, {18837, 33930}, {18891, 35544}, {28659, 40367}, {33778, 33939}

X(44169) = isogonal conjugate of X(18897)
X(44169) = isotomic conjugate of X(1922)
X(44169) = isotomic conjugate of the isogonal conjugate of X(1921)
X(44169) = X(20630)-cross conjugate of X(75)
X(44169) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18897}, {2, 18893}, {6, 14598}, {31, 1922}, {32, 1911}, {171, 8789}, {172, 1927}, {291, 1501}, {292, 560}, {334, 9233}, {335, 1917}, {604, 18265}, {741, 2205}, {813, 1980}, {875, 32739}, {1909, 14604}, {1914, 18267}, {1918, 18268}, {1919, 34067}, {1974, 2196}, {4584, 9426}, {4876, 41280}, {7122, 9468}, {18263, 18266}, {18894, 30663}
X(44169) = cevapoint of X(75) and X(20644)
X(44169) = trilinear product X(i)*X(j) for these {i,j}: {75, 1921}, {76, 350}, {85, 4087}, {238, 1502}, {239, 561}, {256, 14603}, {257, 1926}, {310, 3948}, {312, 18033}, {740, 6385}, {812, 6386}, {871, 3797}, {874, 3261}, {1914, 1928}, {1978, 3766}, {3596, 10030}, {3975, 6063}, {3978, 7018}, {4010, 4602}, {7260, 14295}, {18032, 18035}, {18036, 18037}
X(44169) = barycentric product X(i)*X(j) for these {i,j}: {75, 18891}, {76, 1921}, {238, 1928}, {239, 1502}, {242, 40050}, {257, 14603}, {305, 40717}, {310, 35544}, {350, 561}, {874, 40495}, {893, 18901}, {1447, 40363}, {1914, 40362}, {1926, 7018}, {3261, 27853}, {3596, 18033}, {3685, 41283}, {3766, 6386}, {3948, 6385}, {3975, 20567}, {4010, 4609}, {4087, 6063}, {10030, 28659}, {14599, 40359}, {27801, 30940}, {39914, 40367}
X(44169) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14598}, {2, 1922}, {6, 18897}, {8, 18265}, {31, 18893}, {75, 1911}, {76, 292}, {238, 560}, {239, 32}, {242, 1974}, {256, 1927}, {257, 9468}, {274, 18268}, {291, 18267}, {304, 2196}, {305, 295}, {310, 741}, {350, 31}, {561, 291}, {659, 1980}, {668, 34067}, {693, 875}, {740, 1918}, {812, 1919}, {874, 692}, {893, 8789}, {1281, 18262}, {1428, 41280}, {1447, 1397}, {1502, 335}, {1914, 1501}, {1921, 6}, {1926, 171}, {1928, 334}, {1966, 7122}, {1978, 813}, {2210, 1917}, {2238, 2205}, {3261, 3572}, {3263, 40730}, {3570, 32739}, {3596, 7077}, {3684, 9447}, {3685, 2175}, {3766, 667}, {3783, 18900}, {3797, 40728}, {3948, 213}, {3975, 41}, {3978, 172}, {4010, 669}, {4037, 7109}, {4087, 55}, {4366, 14599}, {4432, 9459}, {4455, 9426}, {4594, 17938}, {4602, 4584}, {4609, 4589}, {4760, 14567}, {6385, 37128}, {6386, 660}, {6650, 18263}, {7018, 1967}, {7019, 17970}, {7104, 14604}, {7193, 14575}, {8299, 9455}, {8300, 18892}, {10030, 604}, {14295, 7234}, {14599, 9233}, {14603, 894}, {17493, 7104}, {17755, 9454}, {18033, 56}, {18035, 17735}, {18036, 30648}, {18037, 19554}, {18277, 18278}, {18891, 1}, {18901, 1920}, {18904, 21751}, {20769, 9247}, {21832, 1924}, {24459, 3049}, {27853, 101}, {27918, 1977}, {28659, 4876}, {28660, 2311}, {30665, 8630}, {30940, 1333}, {33295, 2206}, {35538, 40155}, {35544, 42}, {39044, 2210}, {40050, 337}, {40362, 18895}, {40363, 4518}, {40367, 40848}, {40495, 876}, {40717, 25}, {41283, 7233}

X(44170) = ISOTOMIC CONJUGATE OF X(14599)

Barycentrics    b^4*c^4*(b^2 - a*c)*(a*b - c^2) : :

X(44170) lies on these lines: {292, 1920}, {334, 561}, {335, 6385}, {18895, 27801}, {40367, 41283}

X(44170) = isogonal conjugate of X(18894)
X(44170) = isotomic conjugate of X(14599)
X(44170) = isotomic conjugate of the isogonal conjugate of X(18895)
X(44170) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18894}, {6, 18892}, {31, 14599}, {32, 2210}, {238, 1501}, {239, 1917}, {256, 18902}, {350, 9233}, {560, 1914}, {904, 14602}, {1428, 9447}, {1429, 9448}, {1933, 7104}, {2201, 14575}, {2205, 5009}, {2206, 41333}, {3684, 41280}, {3975, 41281}, {4366, 18893}, {8300, 18897}, {14574, 21832}
X(44170) = trilinear product X(i)*X(j) for these {i,j}: {76, 334}, {291, 1502}, {292, 1928}, {335, 561}, {337, 1969}, {850, 4639}, {1920, 1934}, {3261, 4583}, {4444, 6386}
X(44170) = barycentric product X(i)*X(j) for these {i,j}: {76, 18895}, {291, 1928}, {292, 40362}, {334, 561}, {335, 1502}, {337, 18022}, {1920, 18896}, {1922, 40359}, {4518, 41283}, {4583, 40495}, {4609, 35352}, {4639, 20948}, {7077, 41287}, {7233, 40363}, {18265, 41289}, {27801, 40017}, {30870, 41072}
X(44170) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18892}, {2, 14599}, {6, 18894}, {75, 2210}, {76, 1914}, {172, 18902}, {291, 560}, {292, 1501}, {295, 14575}, {305, 7193}, {310, 5009}, {313, 3747}, {321, 41333}, {334, 31}, {335, 32}, {337, 184}, {561, 238}, {850, 4455}, {876, 1980}, {894, 14602}, {1502, 239}, {1909, 1933}, {1911, 1917}, {1916, 7104}, {1920, 1691}, {1922, 9233}, {1928, 350}, {1934, 904}, {1969, 2201}, {3261, 8632}, {3864, 18900}, {4444, 1919}, {4518, 2175}, {4562, 32739}, {4583, 692}, {4589, 1576}, {4639, 163}, {4876, 9447}, {6063, 1428}, {6386, 3573}, {7077, 9448}, {7233, 1397}, {17789, 18038}, {18022, 242}, {18033, 12835}, {18275, 18274}, {18827, 2206}, {18891, 8300}, {18895, 6}, {18896, 893}, {19567, 30634}, {20567, 1429}, {20908, 38367}, {20948, 21832}, {22116, 9455}, {27801, 2238}, {28659, 3684}, {30663, 14598}, {30870, 30665}, {35352, 669}, {35538, 20663}, {40017, 1333}, {40098, 1922}, {40217, 9454}, {40362, 1921}, {40363, 3685}, {40364, 20769}, {40495, 659}, {41072, 34069}, {41283, 1447}, {41287, 18033}, {43534, 1918}

X(44171) = ISOTOMIC CONJUGATE OF X(14598)

Barycentrics    b^5*c^5*(-a^2 + b*c) : :

X(44171) lies on these lines: {561, 2887}, {1502, 1928}, {1921, 14603}, {4609, 40075}, {7034, 33165}, {35559, 40495}

X(44171) = isogonal conjugate of X(18893)
X(44171) = isotomic conjugate of X(14598)
X(44171) = isotomic conjugate of the isogonal conjugate of X(18891)
X(44171) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18893}, {6, 18897}, {31, 14598}, {32, 1922}, {172, 8789}, {291, 1917}, {292, 1501}, {335, 9233}, {560, 1911}, {894, 14604}, {1397, 18265}, {1920, 18903}, {1927, 7122}, {1980, 34067}, {2205, 18268}, {2210, 18267}, {4518, 41281}, {7077, 41280}
X(44171) = trilinear product X(i)*X(j) for these {i,j}: {76, 1921}, {238, 1928}, {239, 1502}, {257, 14603}, {350, 561}, {1926, 7018}, {3596, 18033}, {3766, 6386}, {3948, 6385}, {4010, 4609}, {4087, 6063}
X(44171) = barycentric product X(i)*X(j) for these {i,j}: {76, 18891}, {238, 40362}, {239, 1928}, {256, 18901}, {350, 1502}, {561, 1921}, {2201, 40360}, {2210, 40359}, {3684, 41287}, {3975, 41283}, {4087, 20567}, {6385, 35544}, {7018, 14603}, {10030, 40363}, {18033, 28659}, {27853, 40495}, {40364, 40717}
X(44171) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18897}, {2, 14598}, {6, 18893}, {75, 1922}, {76, 1911}, {238, 1501}, {239, 560}, {256, 8789}, {257, 1927}, {305, 2196}, {310, 18268}, {312, 18265}, {335, 18267}, {350, 32}, {561, 292}, {740, 2205}, {812, 1980}, {874, 32739}, {904, 14604}, {1429, 41280}, {1502, 291}, {1914, 1917}, {1921, 31}, {1926, 172}, {1928, 335}, {1978, 34067}, {2210, 9233}, {3261, 875}, {3684, 9448}, {3685, 9447}, {3766, 1919}, {3797, 18900}, {3948, 1918}, {3975, 2175}, {3978, 7122}, {4010, 1924}, {4087, 41}, {4366, 18892}, {4486, 8630}, {4609, 4584}, {6385, 741}, {6386, 813}, {7018, 9468}, {7260, 17938}, {8300, 18894}, {10030, 1397}, {14603, 171}, {17755, 9455}, {18032, 18263}, {18033, 604}, {18035, 18266}, {18037, 18262}, {18891, 6}, {18901, 1909}, {18904, 8022}, {20769, 14575}, {21832, 9426}, {27853, 692}, {28659, 7077}, {30870, 30671}, {30940, 2206}, {35544, 213}, {39044, 14599}, {40072, 2311}, {40362, 334}, {40363, 4876}, {40364, 295}, {40367, 41531}, {40495, 3572}, {40717, 1973}

X(44172) = ISOTOMIC CONJUGATE OF X(2210)

Barycentrics    b^3*c^3*(b^2 - a*c)*(a*b - c^2) : :

X(44172) lies on these lines: {76, 335}, {291, 310}, {305, 4518}, {313, 334}, {561, 8024}, {1909, 1911}, {1926, 18034}, {3761, 18787}, {4583, 40075}, {17755, 25758}, {18037, 37133}, {20567, 34388}

X(44172) = isogonal conjugate of X(18892)
X(44172) = isotomic conjugate of X(2210)
X(44172) = isotomic conjugate of the isogonal conjugate of X(334)
X(44172) = X(20629)-cross conjugate of X(75)
X(44172) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18892}, {2, 18894}, {6, 14599}, {31, 2210}, {32, 1914}, {238, 560}, {239, 1501}, {242, 14575}, {257, 18902}, {350, 1917}, {893, 14602}, {904, 1933}, {1333, 41333}, {1428, 2175}, {1429, 9447}, {1447, 9448}, {1576, 4455}, {1691, 7104}, {1918, 5009}, {1921, 9233}, {1974, 7193}, {1980, 3573}, {2201, 9247}, {2206, 3747}, {3685, 41280}, {4010, 14574}, {4087, 41281}, {4366, 18897}, {4760, 19626}, {8300, 14598}, {8632, 32739}, {12835, 18265}, {18893, 39044}, {40373, 40717}
X(44172) = cevapoint of X(i) and X(j) for these (i,j): {75, 20643}, {16892, 21140}
X(44172) = trilinear pole of line {23100, 23596}
X(44172) = trilinear product X(i)*X(j) for these {i,j}: {75, 334}, {76, 335}, {264, 337}, {291, 561}, {292, 1502}, {295, 18022}, {313, 18827}, {693, 4583}, {850, 4589}, {871, 3864}, {876, 6386}, {1577, 4639}, {1909, 1934}, {1911, 1928}, {1916, 1920}, {1978, 4444}, {3261, 4562}, {3596, 7233}, {4518, 6063}
X(44172) = barycentric product X(i)*X(j) for these {i,j}: {75, 18895}, {76, 334}, {291, 1502}, {292, 1928}, {313, 40017}, {335, 561}, {337, 1969}, {850, 4639}, {1909, 18896}, {1911, 40362}, {1920, 1934}, {3261, 4583}, {4444, 6386}, {4518, 20567}, {4562, 40495}, {4589, 20948}, {4602, 35352}, {4876, 41283}, {6385, 43534}, {7233, 28659}, {14598, 40359}, {18275, 30633}, {18827, 27801}, {18891, 40098}, {30870, 37207}
X(44172) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14599}, {2, 2210}, {6, 18892}, {10, 41333}, {31, 18894}, {75, 1914}, {76, 238}, {85, 1428}, {171, 14602}, {264, 2201}, {274, 5009}, {291, 32}, {292, 560}, {295, 9247}, {304, 7193}, {305, 20769}, {313, 2238}, {321, 3747}, {334, 6}, {335, 31}, {337, 48}, {349, 1284}, {561, 239}, {660, 32739}, {693, 8632}, {850, 21832}, {876, 1919}, {894, 1933}, {1502, 350}, {1577, 4455}, {1581, 7104}, {1909, 1691}, {1911, 1501}, {1916, 904}, {1920, 1580}, {1921, 8300}, {1922, 1917}, {1928, 1921}, {1934, 893}, {1969, 242}, {1978, 3573}, {2196, 14575}, {3252, 9455}, {3261, 659}, {3572, 1980}, {3596, 3684}, {3837, 38367}, {3862, 18900}, {3864, 40728}, {4444, 667}, {4518, 41}, {4562, 692}, {4583, 101}, {4584, 1576}, {4589, 163}, {4639, 110}, {4645, 18038}, {4876, 2175}, {5378, 23990}, {6063, 1429}, {6383, 34252}, {6385, 33295}, {6386, 3570}, {7077, 9447}, {7122, 18902}, {7233, 604}, {10030, 12835}, {14598, 9233}, {15413, 22384}, {17789, 19561}, {18034, 2112}, {18275, 19580}, {18827, 1333}, {18891, 4366}, {18895, 1}, {18896, 256}, {19565, 30634}, {19567, 18274}, {20567, 1447}, {20643, 39029}, {20948, 4010}, {21207, 39786}, {22116, 9454}, {23596, 788}, {23989, 27846}, {27801, 740}, {28659, 3685}, {30663, 1922}, {30669, 7122}, {30671, 8630}, {30713, 4433}, {30870, 4486}, {33931, 16514}, {35352, 798}, {35519, 4435}, {35538, 17475}, {36800, 2194}, {36806, 4636}, {37128, 2206}, {37207, 34069}, {40017, 58}, {40075, 27950}, {40093, 2220}, {40094, 4251}, {40095, 33882}, {40098, 1911}, {40217, 2223}, {40362, 18891}, {40363, 3975}, {40495, 812}, {40708, 7116}, {40834, 38813}, {40848, 2209}, {41072, 825}, {41283, 10030}, {43534, 213}

X(44173) = ISOTOMIC CONJUGATE OF X(1576)

Barycentrics    b^4*(b - c)*c^4*(b + c) : :
Barycentrics    (directed distance from A to Brocard axis)*(directed distance from A to Lemoine axis) : : (Randy Hutson, November 30, 2021)

X(44173) lies on these lines: {76, 525}, {99, 22089}, {305, 30474}, {512, 14295}, {523, 14603}, {670, 14221}, {689, 1287}, {778, 9494}, {804, 30492}, {826, 850}, {1078, 39201}, {2531, 23301}, {2799, 3267}, {7771, 39228}, {8029, 40362}, {17415, 42291}, {23285, 30870}

X(44173) = reflection of X(i) in X(j) for these {i,j}: {2531, 23301}, {17415, 42291}
X(44173) = isogonal conjugate of X(14574)
X(44173) = isotomic conjugate of X(1576)
X(44173) = isotomic conjugate of the isogonal conjugate of X(850)
X(44173) = polar conjugate of the isogonal conjugate of X(3267)
X(44173) = X(2980)-anticomplementary conjugate of X(21220)
X(44173) = X(i)-Ceva conjugate of X(j) for these (i,j): {1502, 23962}, {4609, 1502}, {40362, 338}
X(44173) = X(i)-cross conjugate of X(j) for these (i,j): {338, 40362}, {339, 76}, {868, 18896}, {8029, 338}, {21430, 75}, {23285, 850}, {23962, 1502}
X(44173) = cevapoint of X(i) and X(j) for these (i,j): {75, 21603}, {338, 8029}, {523, 33294}, {850, 3267}
X(44173) = crosspoint of X(i) and X(j) for these (i,j): {308, 6331}, {670, 34384}, {1502, 4609}
X(44173) = crosssum of X(i) and X(j) for these (i,j): {669, 40981}, {1501, 9426}, {3049, 3051}
X(44173) = trilinear pole of line {338, 23962}
X(44173) = pole wrt polar circle of line X(32)X(682)
X(44173) = crossdifference of every pair of points on line {1501, 9233}
X(44173) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14574}, {31, 1576}, {32, 163}, {99, 1917}, {110, 560}, {112, 9247}, {162, 14575}, {184, 32676}, {249, 1924}, {512, 23995}, {643, 41280}, {661, 23963}, {662, 1501}, {669, 1101}, {692, 2206}, {798, 23357}, {799, 9233}, {811, 40373}, {822, 41937}, {827, 1923}, {922, 32729}, {1333, 32739}, {1414, 9448}, {1933, 17938}, {1964, 4630}, {1973, 32661}, {1974, 4575}, {1980, 4570}, {2179, 14586}, {2203, 32656}, {2204, 32660}, {2205, 4556}, {2617, 14573}, {2715, 9417}, {3051, 34072}, {4565, 9447}, {4584, 18894}, {4599, 41331}, {7257, 41281}, {9406, 32640}, {9407, 36034}, {9418, 36084}, {9426, 24041}, {14567, 36142}, {14585, 24019}, {14601, 23997}, {18902, 37134}, {19626, 23889}, {19627, 32678}, {36134, 40981}
X(44173) = trilinear product X(i)*X(j) for these {i,j}: {75, 850}, {76, 1577}, {92, 3267}, {115, 4602}, {264, 14208}, {310, 4036}, {313, 693}, {321, 3261}, {338, 799}, {339, 811}, {349, 4391}, {512, 1928}, {523, 561}, {525, 1969}, {661, 1502}, {670, 1109}, {871, 4122}, {1934, 14295}, {2643, 4609}, {3120, 6386}, {3596, 4077}, {3801, 7034}, {4024, 6385}, {4086, 6063}, {4143, 6521}
X(44173) = barycentric product X(i)*X(j) for these {i,j}: {75, 20948}, {76, 850}, {95, 15415}, {99, 23962}, {115, 4609}, {264, 3267}, {305, 14618}, {308, 23285}, {313, 3261}, {321, 40495}, {338, 670}, {339, 6331}, {349, 35519}, {512, 40362}, {523, 1502}, {525, 18022}, {561, 1577}, {661, 1928}, {669, 40359}, {693, 27801}, {799, 23994}, {826, 40016}, {882, 18901}, {1109, 4602}, {1969, 14208}, {1978, 21207}, {2489, 40360}, {2501, 40050}, {2799, 18024}, {3265, 18027}, {3268, 20573}, {3700, 41283}, {3709, 41287}, {4036, 6385}, {4077, 28659}, {4086, 20567}, {6386, 16732}, {6528, 36793}, {7178, 40363}, {14295, 18896}, {18023, 35522}, {18314, 34384}, {23105, 34537}, {23989, 27808}, {24006, 40364}, {33294, 40421}, {39691, 42371}
X(44173) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 1576}, {6, 14574}, {10, 32739}, {69, 32661}, {75, 163}, {76, 110}, {83, 4630}, {92, 32676}, {94, 14560}, {95, 14586}, {99, 23357}, {107, 41937}, {110, 23963}, {115, 669}, {125, 3049}, {264, 112}, {276, 933}, {290, 2715}, {300, 5995}, {301, 5994}, {304, 4575}, {305, 4558}, {306, 32656}, {307, 32660}, {308, 827}, {310, 4556}, {311, 1625}, {313, 101}, {321, 692}, {325, 14966}, {327, 26714}, {328, 32662}, {338, 512}, {339, 647}, {340, 14591}, {349, 109}, {512, 1501}, {514, 2206}, {520, 14585}, {523, 32}, {525, 184}, {526, 19627}, {561, 662}, {647, 14575}, {656, 9247}, {661, 560}, {662, 23995}, {669, 9233}, {670, 249}, {671, 32729}, {690, 14567}, {693, 1333}, {798, 1917}, {799, 1101}, {804, 14602}, {826, 3051}, {850, 6}, {868, 2491}, {879, 14600}, {881, 14604}, {882, 8789}, {1109, 798}, {1230, 35327}, {1231, 36059}, {1232, 35324}, {1235, 35325}, {1441, 1415}, {1494, 32640}, {1502, 99}, {1577, 31}, {1637, 9407}, {1916, 17938}, {1928, 799}, {1969, 162}, {1978, 4570}, {2052, 32713}, {2394, 40352}, {2395, 14601}, {2485, 20968}, {2501, 1974}, {2525, 20775}, {2592, 44124}, {2593, 44123}, {2618, 2179}, {2623, 14573}, {2643, 1924}, {2799, 237}, {2970, 2489}, {2973, 43925}, {3005, 41331}, {3049, 40373}, {3112, 34072}, {3120, 1919}, {3124, 9426}, {3125, 1980}, {3260, 2420}, {3261, 58}, {3265, 577}, {3266, 5467}, {3267, 3}, {3268, 50}, {3569, 9418}, {3596, 5546}, {3676, 16947}, {3700, 2175}, {3709, 9448}, {3952, 23990}, {4010, 14599}, {4024, 1918}, {4033, 1110}, {4036, 213}, {4041, 9447}, {4064, 2200}, {4077, 604}, {4080, 32719}, {4086, 41}, {4088, 9454}, {4120, 9459}, {4122, 40728}, {4143, 1092}, {4391, 2194}, {4455, 18894}, {4566, 23979}, {4580, 10547}, {4602, 24041}, {4609, 4590}, {4705, 2205}, {5027, 18902}, {5392, 32734}, {5466, 32740}, {6063, 4565}, {6330, 32649}, {6331, 250}, {6333, 3289}, {6368, 217}, {6386, 4567}, {6528, 23964}, {6530, 34859}, {6563, 571}, {7178, 1397}, {7180, 41280}, {7199, 849}, {8024, 1634}, {8029, 1084}, {8061, 1923}, {8673, 22075}, {9148, 33875}, {9178, 19626}, {9464, 9145}, {9979, 18374}, {10412, 11060}, {11140, 32737}, {12077, 40981}, {14208, 48}, {14295, 1691}, {14316, 19558}, {14417, 23200}, {14603, 17941}, {14616, 32671}, {14618, 25}, {14638, 14379}, {14977, 14908}, {15413, 1437}, {15414, 19210}, {15415, 5}, {15449, 2531}, {15526, 39201}, {16080, 32715}, {16081, 32696}, {16230, 2211}, {16732, 667}, {17096, 7342}, {17434, 44088}, {17879, 822}, {17924, 2203}, {18022, 648}, {18023, 691}, {18024, 2966}, {18027, 107}, {18155, 2150}, {18160, 17104}, {18312, 5191}, {18314, 51}, {18808, 40354}, {18833, 4599}, {18896, 805}, {18901, 880}, {20336, 906}, {20567, 1414}, {20571, 36145}, {20573, 476}, {20902, 810}, {20948, 1}, {21178, 17186}, {21207, 649}, {21832, 18892}, {22260, 9427}, {23105, 3124}, {23107, 2972}, {23285, 39}, {23290, 3199}, {23616, 34980}, {23870, 34394}, {23871, 34395}, {23878, 34396}, {23881, 23208}, {23962, 523}, {23978, 21789}, {23989, 3733}, {23994, 661}, {24002, 1408}, {24006, 1973}, {24290, 9455}, {26235, 35357}, {27801, 100}, {27808, 1252}, {28654, 4557}, {28659, 643}, {28660, 4636}, {28706, 23181}, {30474, 5063}, {30713, 3939}, {30730, 6066}, {30735, 40825}, {30736, 5118}, {30870, 40773}, {33294, 206}, {33805, 36034}, {34087, 32717}, {34289, 32738}, {34384, 18315}, {34385, 32692}, {34386, 15958}, {34387, 7252}, {34388, 4559}, {34389, 16806}, {34390, 16807}, {34391, 39383}, {34392, 39384}, {34767, 18877}, {35352, 1922}, {35442, 42293}, {35518, 2193}, {35519, 284}, {35522, 187}, {35524, 41337}, {35550, 1983}, {36035, 9406}, {36793, 520}, {36901, 3050}, {39691, 688}, {40016, 4577}, {40050, 4563}, {40071, 1331}, {40072, 4612}, {40073, 4611}, {40359, 4609}, {40362, 670}, {40363, 645}, {40364, 4592}, {40495, 81}, {40822, 35278}, {40826, 11636}, {40828, 931}, {40832, 10420}, {41000, 35329}, {41001, 35330}, {41079, 1495}, {41167, 9419}, {41283, 4573}, {41298, 2965}, {42331, 1970}, {42761, 23220}, {43665, 1976}, {44132, 4230}

X(44174) = ISOGONAL CONJUGATE OF X(136)

Barycentrics    a^2*(a - b)^2*(a + b)^2*(a - c)^2*(a + c)^2*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*b^2*c^2 + c^4)*(a^4 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(44174) lies on the cubic K568, the curve Q120, and these lines: {68, 39170}, {249, 14587}, {250, 403}, {523, 925}, {924, 4558}, {3003, 23357}, {3564, 13557}, {14264, 14366}

X(44174) = isogonal conjugate of X(136)
X(44174) = isogonal conjugate of the anticomplement of X(34844)
X(44174) = isogonal conjugate of the complement of X(925)
X(44174) = anticomplement of complementary conjugate of X(34844)
X(44174) = X(i)-cross conjugate of X(j) for these (i,j): {3, 925}, {6, 4558}, {155, 110}, {184, 32692}, {3564, 43754}, {10132, 39384}, {10133, 39383}, {10661, 38414}, {10662, 38413}, {13557, 10420}, {23128, 4563}
X(44174) = X(i)-isoconjugate of X(j) for these (i,j): {1, 136}, {24, 1109}, {25, 17881}, {47, 2970}, {91, 34338}, {115, 1748}, {135, 921}, {317, 2643}, {924, 24006}, {1577, 6753}, {3708, 11547}, {6754, 20571}, {8745, 20902}, {23994, 44077}
X(44174) = cevapoint of X(i) and X(j) for these (i,j): {6, 32734}, {110, 5889}, {1576, 1609}
X(44174) = trilinear pole of line {686, 23181}
X(44174) = barycentric product X(i)*X(j) for these {i,j}: {68, 249}, {925, 4558}, {1820, 24041}, {2351, 4590}, {4563, 32734}, {4592, 36145}, {16391, 23582}, {20563, 23357}
X(44174) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 136}, {63, 17881}, {68, 338}, {249, 317}, {250, 11547}, {571, 34338}, {925, 14618}, {1101, 1748}, {1576, 6753}, {1609, 135}, {1820, 1109}, {2165, 2970}, {2351, 115}, {4558, 6563}, {16391, 15526}, {20563, 23962}, {23357, 24}, {23963, 44077}, {32661, 924}, {32662, 43088}, {32734, 2501}, {36145, 24006}

X(44175) = ISOGONAL CONJUGATE OF X(157)

Barycentrics    (a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 - b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*(a^6 - a^4*b^2 + a^2*b^4 - b^6 - a^4*c^2 + b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :
X(44175) = 3 X[2] - 4 X[14725]

X(44174) lies on these lines: {2, 11610}, {22, 160}, {69, 41765}, {110, 34405}, {297, 1993}, {315, 2979}, {317, 3060}, {850, 1899}, {4463, 42703}, {9544, 13485}, {11442, 18022}

X(44175) = reflection of X(22391) in X(14725)
X(44175) = isogonal conjugate of X(157)
X(44175) = isotomic conjugate of X(11442)
X(44175) = anticomplement of X(22391)
X(44175) = isogonal conjugate of the anticomplement of X(23333)
X(44175) = isogonal conjugate of the complement of X(41761)
X(44175) = isotomic conjugate of the anticomplement of X(184)
X(44175) = isotomic conjugate of the isogonal conjugate of X(1485)
X(44175) = X(184)-cross conjugate of X(2)
X(44175) = X(i)-isoconjugate of X(j) for these (i,j): {1, 157}, {6, 21374}, {19, 23128}, {31, 11442}, {32, 21593}, {75, 2909}, {92, 22391}
X(44175) = cevapoint of X(i) and X(j) for these (i,j): {127, 520}, {524, 34517}, {35088, 39469}
X(44175) = crosssum of X(2909) and X(22391)
X(44175) = trilinear pole of line {2485, 2799}
X(44175) = barycentric product X(76)*X(1485)
X(44175) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 21374}, {2, 11442}, {3, 23128}, {6, 157}, {32, 2909}, {75, 21593}, {184, 22391}, {1485, 6}, {41765, 41760}
X(44175) = {X(14725),X(22391)}-harmonic conjugate of X(2)

X(44176) = ISOGONAL CONJUGATE OF X(160)

Barycentrics    b^2*c^2*(a^4 + a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(-a^4 + a^2*b^2 - a^2*c^2 + b^2*c^2 - c^4) : :

X(44176) lies on these lines: {2, 40588}, {22, 157}, {25, 36901}, {251, 41760}, {264, 5012}, {290, 3060}, {315, 2387}, {324, 458}, {338, 1501}, {850, 1853}, {1297, 18018}, {2979, 34384}, {4463, 42711}, {11550, 23962}

X(44176) = isogonal conjugate of X(160)
X(44176) = isotomic conjugate of X(2979)
X(44176) = anticomplement of X(40588)
X(44176) = polar conjugate of X(39575)
X(44176) = isogonal conjugate of the anticomplement of X(34845)
X(44176) = isotomic conjugate of the anticomplement of X(51)
X(44176) = isotomic conjugate of the isogonal conjugate of X(2980)
X(44176) = X(i)-cross conjugate of X(j) for these (i,j): {51, 2}, {5007, 308}, {27366, 2980}, {34396, 42354}, {42671, 16081}
X(44176) = X(i)-isoconjugate of X(j) for these (i,j): {1, 160}, {31, 2979}, {48, 39575}, {75, 3202}, {560, 7796}, {2148, 41480}, {2167, 40588}
X(44176) = cevapoint of X(i) and X(j) for these (i,j): {127, 6368}, {338, 512}
X(44176) = crosssum of X(23208) and X(34452)
X(44176) = trilinear pole of line {2485, 18314}
X(44176) = barycentric product X(i)*X(j) for these {i,j}: {76, 2980}, {308, 27366}
X(44176) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2979}, {4, 39575}, {5, 41480}, {6, 160}, {32, 3202}, {51, 40588}, {76, 7796}, {1676, 1670}, {1677, 1671}, {2980, 6}, {3199, 15897}, {16732, 18188}, {27366, 39}

X(44177) = ISOGONAL CONJUGATE OF X(161)

Barycentrics    (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - a^8*c^2 + 2*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 2*a^2*b^6*c^2 - b^8*c^2 - 2*a^6*c^4 - 2*a^4*b^2*c^4 - 2*a^2*b^4*c^4 - 2*b^6*c^4 + 2*a^4*c^6 + 2*a^2*b^2*c^6 + 2*b^4*c^6 + a^2*c^8 + b^2*c^8 - c^10)*(a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - 3*a^8*c^2 + 2*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 2*a^2*b^6*c^2 + b^8*c^2 + 2*a^6*c^4 - 2*a^4*b^2*c^4 - 2*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 2*a^2*b^2*c^6 - 2*b^4*c^6 - 3*a^2*c^8 - b^2*c^8 + c^10) : :

X(44177) lies on these lines: {69, 7488}, {253, 7487}, {264, 7544}, {317, 20564}, {328, 13219}, {11090, 11417}, {11091, 11418}, {15526, 36416}, {18019, 32001}, {20563, 37444}

X(44177) = isogonal conjugate of X(161)
X(44177) = isotomic conjugate of X(37444)
X(44177) = isotomic conjugate of the anticomplement of X(24)
X(44177) = isotomic conjugate of the complement of X(31304)
X(44177) = isotomic conjugate of the isogonal conjugate of X(34438)
X(44177) = X(i)-cross conjugate of X(j) for these (i,j): {24, 2}, {70, 13579}
X(44177) = X(i)-isoconjugate of X(j) for these (i,j): {1, 161}, {6, 18595}, {31, 37444}, {41, 18628}
X(44177) = cevapoint of X(i) and X(j) for these (i,j): {2, 31304}, {924, 15526}
X(44177) = trilinear pole of line {525, 16040}
X(44177) = barycentric product X(76)*X(34438)
X(44177) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18595}, {2, 37444}, {6, 161}, {7, 18628}, {1993, 8907}, {34438, 6}

X(44178) = ISOGONAL CONJUGATE OF X(169)

Barycentrics    a*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - b^2*c + a*c^2 + b*c^2 - c^3)*(a^3 - a^2*b + a*b^2 - b^3 - a^2*c + b^2*c - a*c^2 - b*c^2 + c^3) : :

X(44178) lies on these lines: {1, 36057}, {3, 518}, {9, 34847}, {19, 14377}, {27, 21370}, {57, 5236}, {58, 30733}, {63, 3730}, {85, 169}, {101, 7131}, {103, 26706}, {116, 7079}, {218, 222}, {295, 22116}, {514, 2082}, {1445, 4253}, {1790, 18206}, {2725, 35185}, {4251, 39273}, {8257, 36949}, {17206, 18157}, {17758, 40131}, {26934, 42467}, {32462, 39344}

X(44178) = isogonal conjugate of X(169)
X(44178) = isotomic conjugate of X(20927)
X(44178) = isogonal conjugate of the anticomplement of X(34847)
X(44178) = isogonal conjugate of the complement of X(17170)
X(44178) = X(41)-cross conjugate of X(1)
X(44178) = X(i)-isoconjugate of X(j) for these (i,j): {1, 169}, {2, 1486}, {3, 17905}, {4, 22131}, {6, 3434}, {7, 5452}, {9, 34036}, {25, 28420}, {31, 20927}, {37, 4228}, {55, 37800}, {58, 21073}, {81, 21867}, {101, 21185}, {218, 14268}, {650, 40576}, {651, 11934}, {692, 26546}, {2298, 41581}, {3052, 27826}, {18098, 41582}
X(44178) = cevapoint of X(i) and X(j) for these (i,j): {6, 1473}, {650, 17463}, {657, 7004}, {798, 17476}, {3433, 40141}
X(44178) = crosssum of X(1486) and X(5452)
X(44178) = trilinear pole of line {1459, 2254}
X(44178) = barycentric product X(i)*X(j) for these {i,j}: {1, 13577}, {75, 3433}, {85, 40141}, {100, 26721}, {4025, 26706}, {7123, 41788}
X(44178) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3434}, {2, 20927}, {6, 169}, {19, 17905}, {31, 1486}, {37, 21073}, {41, 5452}, {42, 21867}, {48, 22131}, {56, 34036}, {57, 37800}, {58, 4228}, {63, 28420}, {109, 40576}, {513, 21185}, {514, 26546}, {663, 11934}, {1193, 41581}, {2191, 14268}, {3433, 1}, {8056, 27826}, {13577, 75}, {17187, 41582}, {26706, 1897}, {26721, 693}, {35185, 36086}, {40141, 9}

X(44179) = ISOTOMIC CONJUGATE OF X(91)

Barycentrics    a*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4) : :
Barycentrics    cos A cot 2A : :
Trilinears    cot A cot 2A : :

X(44179) lies on these lines: {1, 75}, {19, 662}, {48, 1760}, {63, 2148}, {69, 1442}, {77, 320}, {78, 319}, {92, 31631}, {273, 664}, {306, 19795}, {318, 20570}, {344, 26668}, {560, 17467}, {610, 16568}, {914, 28793}, {997, 5224}, {1332, 27396}, {1444, 3869}, {1953, 1958}, {1969, 20571}, {1993, 42700}, {2324, 17336}, {3083, 32791}, {3084, 32792}, {3553, 3758}, {3554, 3759}, {3666, 26625}, {3811, 17377}, {3872, 5564}, {3879, 22836}, {3912, 28738}, {4000, 26639}, {4357, 30144}, {4861, 42696}, {5552, 7318}, {5738, 34772}, {6350, 28935}, {6505, 17923}, {6510, 28965}, {7190, 7321}, {7269, 42697}, {16678, 18614}, {16876, 18611}, {17073, 37796}, {17134, 17139}, {17136, 17220}, {17181, 21276}, {17221, 20245}, {17263, 25930}, {17322, 19861}, {17776, 37645}, {17791, 25716}, {18049, 18596}, {18151, 27384}, {18161, 20769}, {19860, 28653}, {20883, 21593}, {21277, 37700}, {25538, 30140}, {26637, 28606}

X(44179) = isotomic conjugate of X(91)
X(44179) = isotomic conjugate of the isogonal conjugate of X(47)
X(44179) = isotomic conjugate of the polar conjugate of X(1748)
X(44179) = X(7130)-anticomplementary conjugate of X(2475)
X(44179) = X(i)-Ceva conjugate of X(j) for these (i,j): {1969, 63}, {40440, 75}
X(44179) = X(i)-cross conjugate of X(j) for these (i,j): {47, 1748}, {42700, 7763}
X(44179) = X(i)-isoconjugate of X(j) for these (i,j): {3, 14593}, {4, 2351}, {5, 41271}, {6, 2165}, {19, 1820}, {25, 68}, {31, 91}, {32, 5392}, {51, 96}, {184, 847}, {485, 8576}, {486, 8577}, {512, 925}, {523, 32734}, {560, 20571}, {661, 36145}, {1799, 27367}, {1953, 2168}, {1974, 20563}, {3049, 30450}, {3426, 40348}, {6413, 41516}, {6414, 41515}, {6524, 16391}, {11060, 37802}, {12077, 32692}, {34385, 40981}, {34428, 39111}, {34853, 39109}
X(44179) = crosspoint of X(811) and X(24041)
X(44179) = crosssum of X(810) and X(2643)
X(44179) = barycentric product X(i)*X(j) for these {i,j}: {1, 7763}, {24, 304}, {47, 76}, {63, 317}, {69, 1748}, {75, 1993}, {86, 42700}, {92, 9723}, {249, 17881}, {313, 18605}, {326, 11547}, {561, 571}, {563, 18022}, {662, 6563}, {799, 924}, {1147, 1969}, {1959, 31635}, {1978, 34948}, {2167, 39113}, {2180, 34384}, {4602, 34952}, {14208, 41679}, {40364, 44077}
X(44179) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2165}, {2, 91}, {3, 1820}, {19, 14593}, {24, 19}, {47, 6}, {48, 2351}, {52, 1953}, {54, 2168}, {63, 68}, {75, 5392}, {76, 20571}, {92, 847}, {110, 36145}, {163, 32734}, {304, 20563}, {317, 92}, {563, 184}, {571, 31}, {662, 925}, {811, 30450}, {924, 661}, {1147, 48}, {1599, 3378}, {1600, 3377}, {1748, 4}, {1993, 1}, {2148, 41271}, {2167, 96}, {2180, 51}, {3133, 2180}, {6507, 16391}, {6563, 1577}, {7763, 75}, {8745, 1096}, {8907, 18595}, {9723, 63}, {11547, 158}, {12095, 2314}, {14576, 2181}, {17881, 338}, {18605, 58}, {18883, 2166}, {30451, 810}, {31635, 1821}, {33808, 39116}, {34948, 649}, {34952, 798}, {36134, 32692}, {39113, 14213}, {41679, 162}, {41770, 17871}, {42700, 10}, {44077, 1973}
X(44179) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 326, 75}, {48, 1959, 1760}, {75, 18156, 33808}, {610, 18713, 16568}, {662, 18041, 19}, {1442, 4511, 69}, {14210, 17859, 18695}, {17859, 18695, 75}

X(44180) = ISOTOMIC CONJUGATE OF X(93)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - b^2*c^2 + c^4) : :
Barycentrics    csc A cos 3A : :

X(44180) lies on these lines: {2, 9609}, {3, 69}, {6, 35296}, {22, 1007}, {25, 34803}, {26, 32829}, {75, 4996}, {95, 99}, {141, 15109}, {160, 33801}, {183, 15246}, {186, 317}, {193, 8553}, {216, 4558}, {253, 35493}, {264, 3520}, {302, 11141}, {303, 11142}, {325, 6636}, {340, 17506}, {343, 34433}, {577, 22151}, {1078, 1232}, {1176, 43705}, {1273, 15620}, {1583, 32812}, {1584, 32813}, {1599, 32805}, {1600, 32806}, {1609, 1992}, {1975, 37126}, {1994, 2965}, {2071, 20477}, {3432, 7488}, {3518, 7769}, {3629, 11063}, {4357, 14792}, {5224, 37293}, {5562, 20574}, {6148, 22468}, {6467, 14060}, {6503, 37068}, {7393, 36948}, {7485, 34229}, {7496, 14360}, {7506, 32839}, {7512, 7763}, {7514, 32815}, {7516, 32828}, {7550, 11185}, {7752, 12088}, {7771, 44149}, {8266, 39099}, {8797, 9818}, {9734, 11188}, {10323, 32006}, {10607, 36751}, {12083, 32827}, {13154, 32867}, {13595, 37647}, {14118, 44135}, {14558, 14615}, {14793, 17321}, {15031, 40410}, {17500, 35919}, {20572, 20573}, {20806, 36748}, {21844, 32001}, {22052, 36212}, {22085, 37893}, {23333, 36163}, {27377, 41758}, {28408, 37188}, {32000, 35473}, {32835, 38435}, {43459, 44148}

X(44180) = isotomic conjugate of X(93)
X(44180) = isotomic conjugate of the anticomplement of X(34833)
X(44180) = isotomic conjugate of the isogonal conjugate of X(49)
X(44180) = isotomic conjugate of the polar conjugate of X(1994)
X(44180) = isogonal conjugate of the polar conjugate of X(7769)
X(44180) = X(i)-Ceva conjugate of X(j) for these (i,j): {7769, 1994}, {20573, 323}
X(44180) = X(i)-cross conjugate of X(j) for these (i,j): {49, 1994}, {34833, 2}
X(44180) = X(i)-isoconjugate of X(j) for these (i,j): {19, 2963}, {25, 2962}, {31, 93}, {252, 2181}, {560, 20572}, {798, 38342}, {1096, 3519}, {1973, 11140}, {2501, 36148}, {24006, 32737}
X(44180) = crosssum of X(512) and X(41221)
X(44180) = barycentric product X(i)*X(j) for these {i,j}: {3, 7769}, {49, 76}, {69, 1994}, {143, 34386}, {304, 2964}, {305, 2965}, {394, 32002}, {1510, 4563}, {3518, 3926}, {4558, 41298}, {6331, 37084}, {25044, 28706}
X(44180) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 93}, {3, 2963}, {49, 6}, {61, 8742}, {62, 8741}, {63, 2962}, {69, 11140}, {76, 20572}, {97, 252}, {99, 38342}, {143, 53}, {323, 562}, {343, 25043}, {394, 3519}, {1493, 6748}, {1510, 2501}, {1993, 14111}, {1994, 4}, {2964, 19}, {2965, 25}, {3518, 393}, {4558, 930}, {4575, 36148}, {7769, 264}, {14129, 13450}, {14577, 14569}, {20577, 23290}, {25044, 8882}, {30529, 6344}, {31626, 1487}, {32002, 2052}, {32661, 32737}, {37084, 647}, {41298, 14618}
X(44180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9723, 69}, {95, 99, 311}, {99, 311, 18354}, {4996, 7279, 75}, {10607, 36751, 41614}

X(44181) = ISOTOMIC CONJUGATE OF X(122)

Barycentrics    (a - b)^2*(a + b)^2*(a - c)^2*(a + c)^2*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*(a^4 - 2*a^2*b^2 + b^4 + 2*a^2*c^2 + 2*b^2*c^2 - 3*c^4)*(a^4 + 2*a^2*b^2 - 3*b^4 - 2*a^2*c^2 + 2*b^2*c^2 + c^4) : :

X(44181) lies on these lines: {2, 23590}, {107, 3265}, {253, 42308}, {441, 23582}, {1301, 22456}, {6528, 39464}, {6529, 14341}, {15384, 18020}, {16096, 32230}, {34407, 39297}

X(44181) = isotomic conjugate of X(122)
X(44181) = polar conjugate of X(1562)
X(44181) = isotomic conjugate of the anticomplement of X(6716)
X(44181) = isotomic conjugate of the complement of X(107)
X(44181) = isotomic conjugate of the isogonal conjugate of X(15384)
X(44181) = X(i)-cross conjugate of X(j) for these (i,j): {20, 648}, {69, 6528}, {2060, 36841}, {2897, 18026}, {6527, 99}, {6716, 2}, {20477, 18831}, {32230, 23582}, {34170, 15459}
X(44181) = X(i)-isoconjugate of X(j) for these (i,j): {31, 122}, {48, 1562}, {154, 2632}, {204, 2972}, {610, 3269}, {656, 42658}, {798, 20580}, {810, 8057}, {822, 6587}, {1249, 37754}, {1895, 34980}, {2155, 39020}, {2643, 35602}, {3708, 15905}, {14249, 42080}, {17898, 39201}
X(44181) = cevapoint of X(i) and X(j) for these (i,j): {2, 107}, {20, 648}, {459, 1301}, {1968, 32713}
X(44181) = trilinear pole of line {648, 2404}
X(44181) = barycentric product X(i)*X(j) for these {i,j}: {76, 15384}, {253, 23582}, {459, 18020}, {1301, 6331}, {2184, 23999}, {4590, 6526}, {15394, 34538}, {23964, 41530}, {32230, 34403}
X(44181) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 122}, {4, 1562}, {20, 39020}, {64, 3269}, {99, 20580}, {107, 6587}, {112, 42658}, {249, 35602}, {250, 15905}, {253, 15526}, {459, 125}, {648, 8057}, {823, 17898}, {1073, 2972}, {1301, 647}, {2184, 2632}, {4240, 14345}, {6526, 115}, {6616, 13613}, {13157, 35442}, {14379, 35071}, {14572, 13611}, {14642, 34980}, {15384, 6}, {18020, 37669}, {19614, 37754}, {23582, 20}, {23590, 6525}, {23964, 154}, {23999, 18750}, {24000, 610}, {32230, 1249}, {34538, 14249}, {38956, 39008}, {41489, 20975}, {41530, 36793}

X(44182) = ISOTOMIC CONJUGATE OF X(126)

Barycentrics    (a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2)*(a^4 - 4*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2)*(a^4 + a^2*b^2 - 4*a^2*c^2 + b^2*c^2 + c^4) : :

X(44182) lies on these lines: {2, 34161}, {111, 3266}, {468, 691}, {523, 15398}, {524, 9225}, {892, 3291}, {4590, 10418}, {5967, 40132}, {8585, 40826}, {9172, 18823}

X(44182) = isotomic conjugate of X(126)
X(44182) = isotomic conjugate of the anticomplement of X(6719)
X(44182) = isotomic conjugate of the complement of X(111)
X(44182) = isotomic conjugate of the isogonal conjugate of X(15387)
X(44182) = X(i)-cross conjugate of X(j) for these (i,j): {69, 671}, {512, 892}, {6388, 5466}, {6719, 2}, {34161, 41909}
X(44182) = X(i)-isoconjugate of X(j) for these (i,j): {6, 17466}, {31, 126}, {662, 21905}, {896, 3291}, {2642, 11634}, {14263, 42081}
X(44182) = cevapoint of X(i) and X(j) for these (i,j): {2, 111}, {115, 14977}, {34161, 41909}
X(44182) = trilinear pole of line {690, 895}
X(44182) = barycentric product X(i)*X(j) for these {i,j}: {76, 15387}, {671, 41909}, {2374, 30786}, {9154, 36892}
X(44182) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17466}, {2, 126}, {111, 3291}, {512, 21905}, {691, 11634}, {895, 8681}, {2374, 468}, {5466, 9134}, {8753, 5140}, {9154, 36874}, {10630, 14263}, {15387, 6}, {34161, 2482}, {41909, 524}

X(44183) = ISOTOMIC CONJUGATE OF X(127)

Barycentrics    (a - b)^2*(a + b)^2*(a - c)^2*(a + c)^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 + b^4 - c^4)*(a^4 - b^4 + c^4) : :

X(44183) lies on these lines: {2, 41937}, {112, 3267}, {249, 15388}, {250, 858}, {691, 1289}, {2966, 41679}, {4143, 15639}, {5649, 16237}, {15013, 23582}, {17907, 32230}, {39295, 43678}

X(44183) = isogonal conjugate of X(38356)
X(44183) = isotomic conjugate of X(127)
X(44183) = isotomic conjugate of the anticomplement of X(6720)
X(44183) = isotomic conjugate of the complement of X(112)
X(44183) = isotomic conjugate of the isogonal conjugate of X(15388)
X(44183) = X(i)-cross conjugate of X(j) for these (i,j): {69, 648}, {1370, 99}, {2979, 18831}, {6720, 2}, {10316, 110}, {11442, 6528}, {12220, 4577}, {13854, 1289}, {28696, 4563}, {28766, 4554}, {30737, 2966}, {41363, 685}
X(44183) = X(i)-isoconjugate of X(j) for these (i,j): {1, 38356}, {22, 3708}, {31, 127}, {42, 18187}, {125, 2172}, {206, 20902}, {339, 17453}, {656, 2485}, {661, 8673}, {810, 33294}, {1109, 10316}, {1760, 20975}, {2632, 8743}, {2643, 20806}, {4456, 18210}, {17409, 17879}, {22075, 23994}
X(44183) = cevapoint of X(i) and X(j) for these (i,j): {2, 112}, {3, 35325}, {110, 10316}, {441, 15639}, {1289, 13854}, {1560, 4235}, {4558, 28419}, {14966, 15595}
X(44183) = trilinear pole of line {110, 1289}
X(44183) = trilinear product X(i)*X(j) for these {i,j}: {75, 15388}, {662, 1289}
X(44183) = barycentric product X(i)*X(j) for these {i,j}: {66, 18020}, {76, 15388}, {99, 1289}, {249, 43678}, {250, 18018}, {4590, 13854}, {14376, 23582}
X(44183) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 127}, {6, 38356}, {66, 125}, {81, 18187}, {110, 8673}, {112, 2485}, {249, 20806}, {250, 22}, {648, 33294}, {1289, 523}, {2156, 3708}, {2353, 20975}, {2420, 14396}, {4590, 34254}, {5379, 4463}, {13854, 115}, {14376, 15526}, {15388, 6}, {18018, 339}, {18020, 315}, {23357, 10316}, {23582, 17907}, {23963, 22075}, {23964, 8743}, {41168, 35442}, {41676, 23881}, {41937, 17409}, {43678, 338}

X(44184) = ISOTOMIC CONJUGATE OF X(150)

Barycentrics    (a^4 - a^3*b - a*b^3 + b^4 - a^3*c + a^2*b*c + a*b^2*c - b^3*c - a*b*c^2 + a*c^3 + b*c^3 - c^4)*(a^4 - a^3*b + a*b^3 - b^4 - a^3*c + a^2*b*c - a*b^2*c + b^3*c + a*b*c^2 - a*c^3 - b*c^3 + c^4) : :

X(44184) lies on these lines: {2, 39026}, {149, 7253}, {150, 3261}, {513, 33650}, {517, 16086}, {518, 1875}, {521, 25048}, {859, 34179}, {1457, 1818}, {2183, 3006}, {4388, 36278}, {5730, 6790}

X(44184) = isogonal conjugate of X(20999)
X(44184) = isotomic conjugate of X(150)
X(44184) = anticomplement of X(39026)
X(44184) = cyclocevian conjugate of X(190)
X(44184) = isotomic conjugate of the anticomplement of X(101)
X(44184) = isotomic conjugate of the complement of X(20096)
X(44184) = isotomic conjugate of the isogonal conjugate of X(34179)
X(44184) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {100, 14888}, {34179, 17494}
X(44184) = X(101)-cross conjugate of X(2)
X(44184) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20999}, {6, 16560}, {19, 22145}, {31, 150}, {32, 20940}, {58, 22321}, {100, 8578}, {244, 14887}, {292, 27943}, {513, 39026}, {692, 21202}, {1333, 21091}
X(44184) = cevapoint of X(i) and X(j) for these (i,j): {2, 20096}, {8, 17777}, {101, 40150}, {519, 3259}
X(44184) = trilinear pole of line {3310, 13006}
X(44184) = barycentric product X(i)*X(j) for these {i,j}: {76, 34179}, {3261, 40150}
X(44184) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16560}, {2, 150}, {3, 22145}, {6, 20999}, {10, 21091}, {37, 22321}, {75, 20940}, {101, 39026}, {238, 27943}, {514, 21202}, {649, 8578}, {1252, 14887}, {34179, 6}, {40150, 101}

X(44185) = ISOTOMIC CONJUGATE OF X(160)

Barycentrics    b^4*c^4*(a^4 + a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(-a^4 + a^2*b^2 - a^2*c^2 + b^2*c^2 - c^4) : :

X(44185) lies on these lines: {32, 23962}, {76, 41480}, {315, 2387}, {1078, 18022}, {1502, 7917}, {3001, 40073}, {4150, 4174}, {7752, 18024}, {17907, 32832}, {35140, 40421}

X(44185) = isogonal conjugate of X(3202)
X(44185) = isotomic conjugate of X(160)
X(44185) = isotomic conjugate of the anticomplement of X(34845)
X(44185) = X(i)-cross conjugate of X(j) for these (i,j): {5, 76}, {3589, 40016}, {23300, 2052}, {23333, 5392}, {34845, 2}
X(44185) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3202}, {31, 160}, {560, 2979}, {1917, 7796}, {2148, 40588}, {2169, 15897}, {9247, 39575}
X(44185) = cevapoint of X(i) and X(j) for these (i,j): {76, 7814}, {523, 23962}, {1676, 1677}
X(44185) = trilinear pole of line {15415, 33294}
X(44185) = barycentric product X(i)*X(j) for these {i,j}: {1502, 2980}, {27366, 40016}
X(44185) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 160}, {5, 40588}, {6, 3202}, {53, 15897}, {76, 2979}, {264, 39575}, {311, 41480}, {1502, 7796}, {1676, 41379}, {1677, 41378}, {2980, 32}, {27366, 3051}

X(44186) = ISOTOMIC CONJUGATE OF X(165)

Barycentrics    b*c*(a^2 - 2*a*b + b^2 + 2*a*c + 2*b*c - 3*c^2)*(-a^2 - 2*a*b + 3*b^2 + 2*a*c - 2*b*c - c^2) : :

X(44186) lies on these lines: {75, 31627}, {312, 10405}, {314, 3062}, {1088, 24026}, {1699, 18025}, {3596, 35517}, {18738, 34258}, {18743, 19605}, {20935, 42034}, {20942, 33677}, {25507, 31623}, {33672, 40422}

X(44186) = isotomic conjugate of X(165)
X(44186) = isotomic conjugate of the anticomplement of X(3817)
X(44186) = isotomic conjugate of the complement of X(9812)
X(44186) = isotomic conjugate of the isogonal conjugate of X(3062)
X(44186) = X(i)-cross conjugate of X(j) for these (i,j): {85, 75}, {3817, 2}, {20905, 76}, {32023, 6384}
X(44186) = X(i)-isoconjugate of X(j) for these (i,j): {6, 3207}, {25, 22117}, {31, 165}, {32, 144}, {41, 1419}, {560, 16284}, {1253, 17106}, {1333, 21872}, {1475, 33634}, {2175, 3160}, {2206, 21060}, {7658, 32739}, {9447, 31627}, {9533, 14827}, {13609, 23979}
X(44186) = cevapoint of X(i) and X(j) for these (i,j): {2, 9812}, {693, 24026}
X(44186) = trilinear pole of line {4391, 20907}
X(44186) = barycentric product X(i)*X(j) for these {i,j}: {75, 10405}, {76, 3062}, {312, 36620}, {561, 11051}, {6063, 19605}
X(44186) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3207}, {2, 165}, {7, 1419}, {10, 21872}, {63, 22117}, {75, 144}, {76, 16284}, {85, 3160}, {279, 17106}, {321, 21060}, {693, 7658}, {1088, 9533}, {2346, 33634}, {3062, 6}, {6063, 31627}, {10405, 1}, {11051, 31}, {17862, 41561}, {19605, 55}, {20905, 43182}, {24026, 13609}, {36620, 57}, {42872, 221}

X(44187) = ISOTOMIC CONJUGATE OF X(172)

Barycentrics    b^2*c^2*(b^2 + a*c)*(a*b + c^2) : :

X(44187) lies on these lines: {75, 256}, {76, 20236}, {239, 7104}, {257, 1921}, {304, 1432}, {313, 1934}, {314, 4594}, {561, 35524}, {789, 17797}, {1228, 28659}, {1240, 1441}, {1916, 18895}, {1930, 3865}, {1969, 44132}, {3261, 21110}, {3596, 6382}, {4451, 20895}, {6383, 33930}, {6385, 16732}, {7019, 40717}, {9230, 17788}, {18891, 21442}, {20892, 27447}

X(44187) = isotomic conjugate of X(172)
X(44187) = isotomic conjugate of the isogonal conjugate of X(257)
X(44187) = polar conjugate of the isogonal conjugate of X(7019)
X(44187) = X(i)-cross conjugate of X(j) for these (i,j): {18891, 18895}, {21442, 75}
X(44187) = X(i)-isoconjugate of X(j) for these (i,j): {6, 7122}, {31, 172}, {32, 171}, {163, 7234}, {184, 7119}, {291, 14602}, {292, 1933}, {334, 18902}, {385, 14598}, {560, 894}, {604, 2330}, {692, 20981}, {1101, 21823}, {1333, 20964}, {1397, 2329}, {1501, 1909}, {1580, 1922}, {1691, 1911}, {1917, 1920}, {1919, 4579}, {1927, 27982}, {1966, 18897}, {1973, 3955}, {1980, 18047}, {2175, 7175}, {2196, 44089}, {2203, 22061}, {2205, 17103}, {2206, 2295}, {3978, 18893}, {4367, 32739}, {4570, 21755}, {7009, 9247}, {7176, 9447}, {7196, 9448}, {14599, 18787}, {17787, 41280}, {18262, 41534}, {18892, 30669}, {18900, 40745}, {21725, 23357}
X(44187) = cevapoint of X(i) and X(j) for these (i,j): {75, 17788}, {257, 7019}, {312, 33938}, {3004, 21138}, {3261, 16732}
X(44187) = trilinear pole of line {29017, 35519}
X(44187) = barycentric product X(i)*X(j) for these {i,j}: {75, 7018}, {76, 257}, {239, 18896}, {256, 561}, {264, 7019}, {313, 32010}, {350, 1934}, {694, 44169}, {850, 4594}, {893, 1502}, {904, 1928}, {1431, 40363}, {1432, 28659}, {1577, 7260}, {1581, 18891}, {1914, 44160}, {1916, 1921}, {1920, 40099}, {1967, 44171}, {3261, 27805}, {3596, 7249}, {3865, 7034}, {3903, 40495}, {4451, 6063}, {4603, 20948}, {6382, 27447}, {7015, 18022}, {7104, 40362}, {17493, 18895}, {18786, 44172}, {20234, 40835}, {27801, 40432}, {30670, 30870}, {40708, 40717}
X(44187) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 7122}, {2, 172}, {8, 2330}, {10, 20964}, {69, 3955}, {75, 171}, {76, 894}, {85, 7175}, {92, 7119}, {115, 21823}, {238, 1933}, {239, 1691}, {242, 44089}, {256, 31}, {257, 6}, {264, 7009}, {306, 22061}, {310, 17103}, {312, 2329}, {313, 1215}, {321, 2295}, {334, 18787}, {349, 4032}, {350, 1580}, {514, 20981}, {523, 7234}, {561, 1909}, {668, 4579}, {693, 4367}, {694, 1922}, {850, 2533}, {893, 32}, {904, 560}, {1089, 21803}, {1109, 21725}, {1178, 2206}, {1228, 27697}, {1269, 4697}, {1431, 1397}, {1432, 604}, {1502, 1920}, {1581, 1911}, {1914, 14602}, {1916, 292}, {1920, 6645}, {1921, 385}, {1927, 18893}, {1934, 291}, {1967, 14598}, {1978, 18047}, {3120, 4128}, {3125, 21755}, {3261, 4369}, {3263, 4447}, {3264, 4434}, {3266, 7267}, {3596, 7081}, {3766, 4164}, {3865, 7032}, {3903, 692}, {3954, 21752}, {3978, 27982}, {4010, 5027}, {4025, 22093}, {4391, 3287}, {4397, 4477}, {4451, 55}, {4486, 30654}, {4496, 2241}, {4572, 6649}, {4594, 110}, {4603, 163}, {6063, 7176}, {6382, 17752}, {6385, 8033}, {7015, 184}, {7018, 1}, {7019, 3}, {7081, 10799}, {7104, 1501}, {7116, 9247}, {7199, 18200}, {7249, 56}, {7260, 662}, {7303, 849}, {8024, 16720}, {9468, 18897}, {14599, 18902}, {15523, 40936}, {16732, 16592}, {17493, 1914}, {17788, 40597}, {18036, 7061}, {18210, 22373}, {18786, 2210}, {18835, 17797}, {18891, 1966}, {18895, 30669}, {18896, 335}, {20234, 18905}, {20567, 7196}, {20906, 24533}, {20911, 28369}, {23989, 7200}, {27447, 2162}, {27801, 3963}, {27805, 101}, {28654, 21021}, {28659, 17787}, {28660, 27958}, {30643, 18786}, {30670, 34069}, {30713, 4095}, {30966, 40731}, {32010, 58}, {33930, 7184}, {33931, 40790}, {34387, 4459}, {34388, 7211}, {35519, 3907}, {35544, 4039}, {37137, 1415}, {40071, 4019}, {40098, 30657}, {40099, 893}, {40106, 40096}, {40432, 1333}, {40495, 4374}, {40708, 295}, {40717, 419}, {40729, 2205}, {40738, 40746}, {40845, 41534}, {40849, 18278}, {40873, 19554}, {41283, 7205}, {41532, 18262}, {43263, 7031}, {44130, 14006}, {44160, 18895}, {44169, 3978}, {44171, 1926}

X(44188) = ISOTOMIC CONJUGATE OF X(191)

Barycentrics    b*c*(-a^3 - a^2*b + a*b^2 + b^3 - a^2*c - a*b*c + b^2*c - a*c^2 - b*c^2 - c^3)*(a^3 + a^2*b + a*b^2 + b^3 + a^2*c + a*b*c + b^2*c - a*c^2 - b*c^2 - c^3) : :

X(44188) lies on these lines: {75, 267}, {92, 17394}, {313, 502}, {319, 321}, {561, 20450}, {757, 1109}, {1441, 17095}, {18040, 20648}, {18133, 20939}, {18151, 25660}

X(44188) = isotomic conjugate of X(191)
X(44188) = isotomic conjugate of the anticomplement of X(11263)
X(44188) = isotomic conjugate of the complement of X(14450)
X(44188) = isotomic conjugate of the isogonal conjugate of X(267)
X(44188) = X(i)-cross conjugate of X(j) for these (i,j): {86, 75}, {502, 1029}, {11263, 2}, {30690, 85}
X(44188) = X(i)-isoconjugate of X(j) for these (i,j): {3, 44097}, {6, 1030}, {25, 22136}, {31, 191}, {32, 2895}, {42, 501}, {55, 8614}, {110, 42653}, {184, 451}, {213, 40592}, {228, 2906}, {560, 20932}, {692, 31947}, {1333, 21873}, {2175, 41808}, {2206, 21081}, {21192, 32739}
X(44188) = cevapoint of X(i) and X(j) for these (i,j): {2, 14450}, {514, 1109}, {693, 17886}, {39149, 41910}
X(44188) = trilinear pole of line {1577, 4467}
X(44188) = barycentric product X(i)*X(j) for these {i,j}: {75, 1029}, {76, 267}, {274, 502}, {310, 21353}, {313, 40143}, {561, 3444}, {30602, 33939}
X(44188) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1030}, {2, 191}, {10, 21873}, {19, 44097}, {27, 2906}, {57, 8614}, {63, 22136}, {75, 2895}, {76, 20932}, {81, 501}, {85, 41808}, {86, 40592}, {92, 451}, {267, 6}, {313, 42710}, {321, 21081}, {502, 37}, {514, 31947}, {661, 42653}, {693, 21192}, {1029, 1}, {3444, 31}, {21353, 42}, {30602, 2160}, {39149, 2245}, {40143, 58}, {41493, 2294}, {41910, 34586}

X(44189) = ISOTOMIC CONJUGATE OF X(196)

Barycentrics    (a - b - c)*(a^2 - b^2 - c^2)*(a^3 - a^2*b - a*b^2 + b^3 + a^2*c + 2*a*b*c + b^2*c - a*c^2 - b*c^2 - c^3)*(a^3 + a^2*b - a*b^2 - b^3 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + b*c^2 + c^3) : :

X(44189) lies on these lines: {2, 23982}, {69, 189}, {271, 1265}, {280, 285}, {304, 7055}, {314, 7003}, {326, 345}, {346, 394}, {348, 34403}, {1422, 30701}, {1433, 20745}, {6225, 7219}, {7101, 34413}

X(44189) = isogonal conjugate of X(3209)
X(44189) = isotomic conjugate of X(196)
X(44189) = isotomic conjugate of the isogonal conjugate of X(268)
X(44189) = isotomic conjugate of the polar conjugate of X(280)
X(44189) = X(i)-cross conjugate of X(j) for these (i,j): {8, 69}, {63, 345}, {268, 280}
X(44189) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3209}, {4, 2199}, {6, 208}, {19, 221}, {25, 223}, {31, 196}, {32, 342}, {33, 6611}, {34, 198}, {40, 608}, {56, 2331}, {57, 3195}, {227, 1474}, {278, 2187}, {329, 1395}, {347, 1973}, {393, 7114}, {560, 40701}, {604, 7952}, {1096, 7011}, {1398, 2324}, {1400, 3194}, {1402, 41083}, {1407, 40971}, {1435, 7074}, {1880, 2360}, {1974, 40702}, {2149, 38362}, {2207, 7013}, {2212, 14256}, {3213, 41088}, {6087, 32667}, {6129, 32674}, {7151, 40212}
X(44189) = cevapoint of X(i) and X(j) for these (i,j): {63, 41081}, {6332, 23983}
X(44189) = barycentric product X(i)*X(j) for these {i,j}: {63, 34404}, {69, 280}, {75, 271}, {76, 268}, {78, 309}, {84, 3718}, {189, 345}, {282, 304}, {285, 20336}, {305, 2192}, {312, 41081}, {326, 7020}, {332, 39130}, {346, 34400}, {561, 2188}, {1264, 40836}, {1265, 1440}, {1433, 3596}, {3926, 7003}, {7118, 40364}, {13138, 35518}, {15416, 37141}, {28660, 41087}
X(44189) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 208}, {2, 196}, {3, 221}, {6, 3209}, {8, 7952}, {9, 2331}, {11, 38362}, {21, 3194}, {48, 2199}, {55, 3195}, {63, 223}, {69, 347}, {72, 227}, {75, 342}, {76, 40701}, {78, 40}, {84, 34}, {189, 278}, {200, 40971}, {212, 2187}, {219, 198}, {222, 6611}, {255, 7114}, {268, 6}, {271, 1}, {280, 4}, {282, 19}, {283, 2360}, {285, 28}, {304, 40702}, {309, 273}, {326, 7013}, {332, 8822}, {333, 41083}, {345, 329}, {348, 14256}, {394, 7011}, {521, 6129}, {1259, 7078}, {1260, 7074}, {1265, 7080}, {1413, 1398}, {1422, 1435}, {1433, 56}, {1436, 608}, {1440, 1119}, {1565, 38374}, {1809, 15501}, {1812, 1817}, {1903, 1880}, {2188, 31}, {2192, 25}, {2208, 1395}, {2968, 38357}, {3341, 207}, {3692, 2324}, {3694, 21871}, {3710, 21075}, {3718, 322}, {6081, 36067}, {6332, 14837}, {6355, 6046}, {7003, 393}, {7008, 1096}, {7020, 158}, {7118, 1973}, {7151, 7337}, {7154, 2207}, {7358, 3318}, {7367, 607}, {13138, 108}, {23983, 16596}, {34162, 42451}, {34400, 279}, {34404, 92}, {35518, 17896}, {36049, 32674}, {37141, 32714}, {39130, 225}, {39471, 6087}, {40836, 1118}, {41081, 57}, {41087, 1400}

X(44190) = ISOTOMIC CONJUGATE OF X(198)

Barycentrics    b^2*c^2*(a^3 - a^2*b - a*b^2 + b^3 + a^2*c + 2*a*b*c + b^2*c - a*c^2 - b*c^2 - c^3)*(-a^3 - a^2*b + a*b^2 + b^3 + a^2*c - 2*a*b*c + b^2*c + a*c^2 - b*c^2 - c^3) : :

X(44190) lies on these lines: {76, 7182}, {189, 28660}, {274, 40836}, {279, 23978}, {282, 30022}, {304, 309}, {305, 28659}, {348, 7017}, {1240, 1440}, {1969, 6063}

X(44190) = isotomic conjugate of X(198)
X(44190) = polar conjugate of X(3195)
X(44190) = isotomic conjugate of the anticomplement of X(21239)
X(44190) = isotomic conjugate of the complement of X(21279)
X(44190) = isotomic conjugate of the isogonal conjugate of X(189)
X(44190) = X(i)-cross conjugate of X(j) for these (i,j): {85, 76}, {264, 6063}, {1226, 561}, {21239, 2}
X(44190) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2187}, {31, 198}, {32, 40}, {41, 221}, {48, 3195}, {55, 2199}, {184, 2331}, {212, 3209}, {213, 2360}, {223, 2175}, {322, 1501}, {329, 560}, {347, 9447}, {604, 7074}, {607, 7114}, {1106, 7368}, {1253, 6611}, {1397, 2324}, {1817, 1918}, {1973, 7078}, {2200, 3194}, {2205, 8822}, {2206, 21871}, {2212, 7011}, {6129, 32739}, {7952, 9247}, {9448, 40702}
X(44190) = cevapoint of X(i) and X(j) for these (i,j): {2, 21279}, {75, 20921}, {309, 34404}, {693, 23978}
X(44190) = trilinear pole of line {15413, 17896}
X(44190) = barycentric product X(i)*X(j) for these {i,j}: {75, 309}, {76, 189}, {84, 561}, {85, 34404}, {280, 6063}, {282, 20567}, {305, 40836}, {310, 39130}, {1413, 40363}, {1422, 28659}, {1433, 18022}, {1436, 1502}, {1440, 3596}, {1903, 6385}, {1928, 2208}, {1969, 41081}, {2192, 41283}, {7017, 34400}, {7020, 7182}, {7129, 40364}, {7151, 40050}, {8808, 28660}, {13138, 40495}, {41084, 41530}
X(44190) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2187}, {2, 198}, {4, 3195}, {7, 221}, {8, 7074}, {57, 2199}, {69, 7078}, {75, 40}, {76, 329}, {77, 7114}, {84, 31}, {85, 223}, {86, 2360}, {92, 2331}, {189, 6}, {253, 41088}, {264, 7952}, {271, 212}, {273, 208}, {274, 1817}, {278, 3209}, {279, 6611}, {280, 55}, {282, 41}, {285, 2194}, {286, 3194}, {309, 1}, {310, 8822}, {312, 2324}, {313, 21075}, {318, 40971}, {321, 21871}, {322, 1103}, {331, 196}, {332, 1819}, {346, 7368}, {348, 7011}, {561, 322}, {693, 6129}, {1226, 6260}, {1256, 2208}, {1413, 1397}, {1422, 604}, {1433, 184}, {1436, 32}, {1440, 56}, {1441, 227}, {1903, 213}, {2192, 2175}, {2208, 560}, {2357, 1918}, {2973, 38362}, {3261, 14837}, {3596, 7080}, {4391, 14298}, {6063, 347}, {6332, 10397}, {6355, 1425}, {7003, 607}, {7008, 2212}, {7020, 33}, {7118, 9447}, {7129, 1973}, {7151, 1974}, {7182, 7013}, {7367, 14827}, {8808, 1400}, {13138, 692}, {13156, 1475}, {18816, 15501}, {20567, 40702}, {23978, 5514}, {28660, 27398}, {34387, 38357}, {34400, 222}, {34404, 9}, {34413, 42019}, {35519, 8058}, {36049, 32739}, {37141, 1415}, {39130, 42}, {40495, 17896}, {40702, 40212}, {40836, 25}, {41081, 48}, {41084, 154}, {41087, 2200}, {42549, 20228}, {44129, 41083}

X(44191) = (name pending)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - b^2*c^2 + c^4)*(a^12 - 4*a^10*b^2 + 5*a^8*b^4 - 5*a^4*b^8 + 4*a^2*b^10 - b^12 - 4*a^10*c^2 + 8*a^8*b^2*c^2 - 4*a^6*b^4*c^2 + 4*a^4*b^6*c^2 - 8*a^2*b^8*c^2 + 4*b^10*c^2 + 5*a^8*c^4 - 4*a^6*b^2*c^4 - a^4*b^4*c^4 + 4*a^2*b^6*c^4 - 7*b^8*c^4 + 4*a^4*b^2*c^6 + 4*a^2*b^4*c^6 + 8*b^6*c^6 - 5*a^4*c^8 - 8*a^2*b^2*c^8 - 7*b^4*c^8 + 4*a^2*c^10 + 4*b^2*c^10 - c^12)*(2*a^16 - 11*a^14*b^2 + 23*a^12*b^4 - 19*a^10*b^6 - 5*a^8*b^8 + 23*a^6*b^10 - 19*a^4*b^12 + 7*a^2*b^14 - b^16 - 11*a^14*c^2 + 42*a^12*b^2*c^2 - 57*a^10*b^4*c^2 + 38*a^8*b^6*c^2 - 31*a^6*b^8*c^2 + 36*a^4*b^10*c^2 - 21*a^2*b^12*c^2 + 4*b^14*c^2 + 23*a^12*c^4 - 57*a^10*b^2*c^4 + 36*a^8*b^4*c^4 - a^6*b^6*c^4 - 18*a^4*b^8*c^4 + 21*a^2*b^10*c^4 - 4*b^12*c^4 - 19*a^10*c^6 + 38*a^8*b^2*c^6 - a^6*b^4*c^6 + 2*a^4*b^6*c^6 - 7*a^2*b^8*c^6 - 4*b^10*c^6 - 5*a^8*c^8 - 31*a^6*b^2*c^8 - 18*a^4*b^4*c^8 - 7*a^2*b^6*c^8 + 10*b^8*c^8 + 23*a^6*c^10 + 36*a^4*b^2*c^10 + 21*a^2*b^4*c^10 - 4*b^6*c^10 - 19*a^4*c^12 - 21*a^2*b^2*c^12 - 4*b^4*c^12 + 7*a^2*c^14 + 4*b^2*c^14 - c^16) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1999.

X(44191) lies on this line: {125, 1493}

leftri

Points associated with Vijay orthic polar triangle of circumcircle: X(44192)-X(44200)

rightri

This preamble is contributed by Dasari Naga Vijay Krishna, July 26, 2021.

In the plane of a triangle ABC, O = circumcircle of triangle ABC. let
Oa = circle with diameter BC, and define Ob and Oc cyclically;
La = The perpendicular from X(3) of triangle ABC to side BC, define Lb and Lc cyclically;
A1, A2 = La ∩Oa such that A2 is nearer to A than A1, and define B1, B2, C1, C2 cyclically;
Ta, T'a = polar of A1, A2 wrt Oa, define Tb, T'b, Tc, T'c cyclically;
Pa, P'a = polar of A1, A2 wrt O, define Pb, P'b, Pc and P'c cyclically;
A3 = Tb ∩ Tc, B3 = Tc ∩ Ta, C3 = Ta ∩ Tb;
A4 = T'b ∩ T'c, B4= T'c ∩ T'a, C4 = T'a ∩ T'b;
A5 = Pb ∩ Pc, B5= Pc ∩ Pa, C5 = Pa ∩ Pb;
A6 = P'b ∩ P'c, B6= P'c ∩ P'a, C6 = P'a ∩ P'b;

Barycentrics:

A1 = -a^2 : S + SC : S + SB
A3 = -(2S + b^2 + c^2) : b^2 : c^2
A5 = -(2*S*(S + SB)*(S + SC) + b^2*(S - SB)*(S + SC) + c^2*(S - SC)*(S + SB)) : b^2*(S - SB)*(S + SC) : c^2*(S - SC)*(S + SB)

Barycentrics for A2, A4, A6 are obtained by replacing S by -S in the barycentrics for A1, A3, A5 respectively.

Related triangles are here named as follows:

A1B1C1 = 1st Vijay orthic polar triangle of circumcircle;
A2B2C2 = 2nd Vijay orthic polar trriangle of circumcircle;
A3B3C3 = 3rd Vijay orthic polar trriangle of circumcircle;
A4B4C4 = 4th Vijay orthic polar trriangle of circumcircle;
A5B5C5 = 5th Vijay orthic polar trriangle of circumcircle;
A6B6C6 = 6th Vijay orthic polar trriangle of circumcircle.

The first four of those triangles have been introduced previously:
A1B1C1 is the outer Vecten triangle.
A2B2C2 is the inner Vecten triangle.
A3B3C3 is the 1st anti-Kenmotu-centers triangle.
A4B4C4 is the 2nd anti-Kenmotu-centers triangle.
(Randy Hutson, January 11, 2022)

Collinearities:

A3, A4, A are collinear.
X(485), X(486), X(6) are collinear.
X(6), X(1991), X(591) are collinear.
X(44192), X(44193), X(44200) are collinear.
X(6), X(44193), X(44197), X(44199), are collinear.
X(6), X(44192), X(44196), X(44198), are collinear.

Perspectors :

AA1 ∩ BB1∩ CC1 = X(485);
AA2 ∩ BB2∩ CC2 = X(486);
AA3 ∩ BB3∩ CC3 = AA4 ∩ BB4∩ CC4 = A3A4 ∩ B3B4∩ C3C4 = X(6);
A1A4 ∩ B1B4∩ C1C4 = X(1991);
A2A3 ∩ B2B3 ∩ C2C3 = X(591);
X(44192) = AA5∩ BB5∩ CC5;
X(44193) = AA6∩ BB6∩ CC6;
X(44194) = A1A5∩ B1B5∩ C1C5;
X(44195) = A2A6∩ B2B6∩ C2C6;
X(44196) = A3A5∩ B3B5∩ C3C5;
X(44197) = A3A6∩ B3B6∩ C3C6;
X(44198) = A4A5∩ B4B5∩ C4C5;
X(44199) = A4A6∩ B4B6∩ C4C6;
X(44200) = A5A6∩ B5B6∩ C5C6:

X(44192) = PERSPECTOR OF THESE TRIANGLES: ABC AND 5TH VIJAY ORTHIC POLAR TRIANGLE OF CIRCUMCIRCLE

Barycentrics    a^2*(S-SA)*(S+SB)*(S+SC) : :

X(44192) lies on these lines: {2, 44194}, {3, 485}, {6, 3156}, {22, 13638}, {24, 13440}, {25, 53}, {141, 1584}, {183, 34391}, {237, 45429}, {371, 5417}, {372, 1147}, {491, 1600}, {571, 5412}, {1321, 1593}, {1586, 41770}, {2164, 34125}, {2178, 34121}, {3003, 5413}, {3053, 8946}, {3155, 8553}, {8573, 44599}, {8770, 45596}, {8943, 8944}, {10533, 12968}, {14533, 15846}, {32420, 39383}, {35302, 44393}, {40947, 45428}

X(44192) = perspector of ABC and cross-triangle of ABC and 1st Kenmotu diagonals triangle
X(44192) = {X(25),X(1609)}-harmonic conjugate of X(44193)

X(44193) = PERSPECTOR OF THESE TRIANGLES: ABC AND 6TH VIJAY ORTHIC POLAR TRIANGLE OF CIRCUMCIRCLE

Barycentrics    a^2*(S+SA)*(S-SB)*(S-SC) : :

X(44193) lies on these lines: {2, 44195}, {3, 486}, {6, 3155}, {22, 13758}, {24, 13429}, {25, 53}, {141, 1583}, {183, 34392}, {237, 45428}, {371, 1147}, {372, 5419}, {492, 1599}, {571, 5413}, {1151, 26922}, {1322, 1593}, {1585, 41770}, {2164, 34121}, {2178, 34125}, {3003, 5412}, {3053, 8948}, {3156, 8553}, {8573, 44598}, {8770, 45595}, {8908, 9675}, {8939, 8940}, {10534, 12963}, {14533, 15847}, {32422, 39384}, {35302, 44400}, {40947, 45429}

X(44193) = perspector of ABC and cross-triangle of ABC and 2nd Kenmotu diagonals triangle
X(44193) = {X(25),X(1609)}-harmonic conjugate of X(44192)

X(44194) = PERSPECTOR OF THESE TRIANGLES: 1ST AND 5TH VIJAY ORTHIC POLAR TRIANGLE OF CIRCUMCIRCLE

Barycentrics    (S+SB)*(S+SC)*(c^10+b^2*c^8-4*a^2*c^8+6*S*c^8-2*b^4*c^6+4*a^4*c^6-8*S*a^2*c^6+16*S^2*c^6-2*b^6*c^4+8*a^2*b^4*c^4-12*S*b^4*c^4-8*a^4*b^2*c^4+8*S*a^2*b^2*c^4+2*a^6*c^4+8*S*a^4*c^4-8*S^2*a^2*c^4+32*S^3*c^4+b^8*c^2-8*a^4*b^4*c^2+8*S*a^2*b^4*c^2+12*a^6*b^2*c^2+8*S*a^4*b^2*c^2-16*S^2*a^2*b^2*c^2+32*S^3*b^2*c^2-5*a^8*c^2-16*S*a^6*c^2-24*S^2*a^4*c^2+48*S^4*c^2+b^10-4*a^2*b^8+6*S*b^8+4*a^4*b^6-8*S*a^2*b^6+16*S^2*b^6+2*a^6*b^4+8*S*a^4*b^4-8*S^2*a^2*b^4+32*S^3*b^4-5*a^8*b^2-16*S*a^6*b^2-24*S^2*a^4*b^2+48*S^4*b^2+2*a^10+10*S*a^8+16*S^2*a^6+16*S^3*a^4+32*S^4*a^2+32*S^5) : :

X(44194) lies on these lines: {2, 44192}, {6290, 44198}

X(44195) = PERSPECTOR OF THESE TRIANGLES: 2ND AND 6TH VIJAY ORTHIC POLAR TRIANGLE OF CIRCUMCIRCLE

Barycentrics    (S-SB)*(S-SC)*(c^10+b^2*c^8-4*a^2*c^8-6*S*c^8-2*b^4*c^6+4*a^4*c^6+8*S*a^2*c^6+16*S^2*c^6-2*b^6*c^4+8*a^2*b^4*c^4+12*S*b^4*c^4-8*a^4*b^2*c^4-8*S*a^2*b^2*c^4+2*a^6*c^4-8*S*a^4*c^4-8*S^2*a^2*c^4-32*S^3*c^4+b^8*c^2-8*a^4*b^4*c^2-8*S*a^2*b^4*c^2+12*a^6*b^2*c^2-8*S*a^4*b^2*c^2-16*S^2*a^2*b^2*c^2-32*S^3*b^2*c^2-5*a^8*c^2+16*S*a^6*c^2-24*S^2*a^4*c^2+48*S^4*c^2+b^10-4*a^2*b^8-6*S*b^8+4*a^4*b^6+8*S*a^2*b^6+16*S^2*b^6+2*a^6*b^4-8*S*a^4*b^4-8*S^2*a^2*b^4-32*S^3*b^4-5*a^8*b^2+16*S*a^6*b^2-24*S^2*a^4*b^2+48*S^4*b^2+2*a^10-10*S*a^8+16*S^2*a^6-16*S^3*a^4+32*S^4*a^2-32*S^5) : :

X(44195) lies on these lines: {2, 44193}, {6289, 44197}

X(44196) = PERSPECTOR OF THESE TRIANGLES: 3RD AND 5TH VIJAY ORTHIC POLAR TRIANGLE OF CIRCUMCIRCLE

Barycentrics    a^2*(c^6-b^2*c^4+a^2*c^4+4*S*c^4-b^4*c^2+2*a^2*b^2*c^2-a^4*c^2+4*S^2*c^2+b^6+a^2*b^4+4*S*b^4-a^4*b^2+4*S^2*b^2-a^6-4*S*a^4-4*S^2*a^2) : :

X(44196) lies on these lines: {3, 639}, {6, 3156}, {22, 160}, {25, 8939}, {51, 19358}, {155, 9733}, {157, 492}, {195, 45488}, {1498, 12305}, {1584, 31521}, {1597, 19454}, {1598, 18980}, {1995, 19406}, {3517, 19440}, {7716, 12590}, {8904, 33582}, {8943, 44197}, {10494, 38034}, {10594, 19424}, {11793, 17668}, {15047, 45411}, {15805, 43119}, {18414, 18494}, {19216, 45416}, {40947, 44392}

X(44196) = crosspoint of circumcircle intercepts of outer Vecten circle
X(44196) = {X(22),X(160)}-harmonic conjugate of X(44199)

X(44197) = PERSPECTOR OF THESE TRIANGLES: 3RD AND 6TH VIJAY ORTHIC POLAR TRIANGLE OF CIRCUMCIRCLE

Barycentrics    a^2*(c^6-b^2*c^4-S*c^4-b^4*c^2+2*a^2*b^2*c^2-2*S*b^2*c^2-a^4*c^2+2*S*a^2*c^2+b^6-S*b^4-a^4*b^2+2*S*a^2*b^2-S*a^4+4*S^2*a^2-4*S^3) : :

X(44197) lies on these lines: {2, 44198}, {3, 591}, {6, 3155}, {157, 3069}, {570,18194}, {615, 40947}, {1583, 32621}, {3148, 32788}, {3156, 7669}, {6289, 44195}, {6410, 32071}, {8943, 44196}, {15624, 45416}, {33029, 38997}, {33582, 45428}

X(44198) = PERSPECTOR OF THESE TRIANGLES: 4TH AND 5TH VIJAY ORTHIC POLAR TRIANGLE OF CIRCUMCIRCLE

Barycentrics    a^2*(c^6-b^2*c^4+S*c^4-b^4*c^2+2*a^2*b^2*c^2+2*S*b^2*c^2-a^4*c^2-2*S*a^2*c^2+b^6+S*b^4-a^4*b^2-2*S*a^2*b^2+S*a^4+4*S^2*a^2+4*S^3) : :

X(44198) lies on these lines: {2, 44197}, {3, 1991}, {6, 3156}, {157, 3068}, {590, 40947}, {1584, 32621}, {3148, 32787}, {3155, 7669}, {6290, 44194}, {6409, 32070}, {8939, 44199}, {8969, 33582}, {15624, 45417}

X(44199) = PERSPECTOR OF THESE TRIANGLES: 4TH AND 6TH VIJAY ORTHIC POLAR TRIANGLE OF CIRCUMCIRCLE

Barycentrics    a^2*(c^6-b^2*c^4+a^2*c^4-4*S*c^4-b^4*c^2+2*a^2*b^2*c^2-a^4*c^2+4*S^2*c^2+b^6+a^2*b^4-4*S*b^4-a^4*b^2+4*S^2*b^2-a^6+4*S*a^4-4*S^2*a^2) : :

X(44199) lies on these lines: {3, 640}, {6, 3155}, {22, 160}, {25, 8943}, {51, 19359}, {155, 9732}, {157, 491}, {195, 45489}, {1498, 12306}, {1583, 31521}, {1598, 18981}, {1995, 19407}, {7716, 12591}, {8903, 33582}, {8939, 44198}, {10594, 19425}, {15047, 45410}, {15805, 43118}, {18415, 18494}, {19215, 45417}, {26922, 30427}, {40947, 44394}

X(44199) = crosspoint of circumcircle intercepts of inner Vecten circle
X(44199) = {X(22),X(160)}-harmonic conjugate of X(44196)

X(44200) = PERSPECTOR OF THESE TRIANGLES: 5TH AND 6TH VIJAY ORTHIC POLAR TRIANGLE OF CIRCUMCIRCLE

Barycentrics    a^2*(a^2 - b^2 - c^2)*(3*a^4 - 2*a^2*b^2 + 3*b^4 - 2*a^2*c^2 - 6*b^2*c^2 + 3*c^4) : :

X(44200) lies on these lines: {3, 69}, {22, 33974}, {25, 53}, {50, 34777}, {98, 20477}, {159, 7669}, {184, 36751}, {186, 16312}, {216, 19125}, {237, 33582}, {511, 10608}, {570, 11402}, {571, 12167}, {577, 10602}, {1151, 19358}, {1152, 19359}, {1593, 35717}, {1599, 19422}, {1600, 19423}, {1843, 3053}, {1899, 34828}, {2974, 20563}, {3003, 19118}, {3148, 8573}, {3155, 13889}, {3156, 13943}, {3186, 21445}, {3515, 15653}, {4558, 6391}, {5023, 9924}, {6409, 19430}, {6410, 19431}, {6467, 36748}, {7484, 7778}, {8266, 8667}, {8681, 10607}, {8939, 44198}, {8943, 44196}, {9715, 15512}, {9777, 13345}, {9909, 27364}, {11063, 20987}, {11284, 33980}, {13558, 33801}, {14060, 20806}, {14615, 34473}, {15655, 34106}, {15905, 20975}, {21312, 38749}, {23200, 38292}, {33580, 40981}, {37183, 37491}, {41489, 44096}

X(44200) = X(34208)-Ceva conjugate of X(6)
X(44200) = crosssum of X(4) and X(32001)
X(44200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 19588, 9723}, {3, 39653, 40321}, {3, 40947, 19459}, {157, 1609, 25}, {7669, 8553, 159}, {15512, 31381, 9715}, {19446, 19447, 9723}

X(44201) = X(3)X(68)∩X(140)X(389)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^8 - a^6*b^2 - 5*a^4*b^4 + 5*a^2*b^6 - b^8 - a^6*c^2 - 2*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + 4*b^6*c^2 - 5*a^4*c^4 - 5*a^2*b^2*c^4 - 6*b^4*c^4 + 5*a^2*c^6 + 4*b^2*c^6 - c^8) : :
X(44201) = 5 X[631] - X[1993], 3 X[10519] + X[41614], 3 X[13394] - X[18445]

See Antreas Hatzipolakis and Peter Moses, euclid 2005.

X(44201) lies these lines: {2, 37489}, {3, 68}, {5, 11745}, {30, 21243}, {140, 389}, {141, 6644}, {182, 524}, {185, 34002}, {186, 37636}, {381, 4549}, {427, 37478}, {468, 5891}, {548, 30522}, {550, 6696}, {568, 37649}, {631, 1199}, {1209, 3575}, {1352, 14070}, {1503, 7502}, {1511, 3631}, {1594, 7691}, {1596, 4550}, {2937, 16655}, {2979, 37118}, {3098, 23300}, {3410, 7488}, {3522, 43607}, {3523, 18916}, {3530, 32165}, {3541, 37486}, {3547, 12163}, {3549, 22660}, {3564, 18475}, {3580, 35921}, {3581, 37347}, {3589, 5946}, {3796, 18917}, {3917, 10257}, {5447, 16196}, {5449, 12362}, {5562, 7542}, {5663, 25337}, {5876, 16252}, {5890, 7495}, {5899, 16654}, {5907, 13383}, {6000, 16618}, {6102, 7568}, {6515, 37506}, {6676, 13754}, {6677, 10170}, {6699, 11574}, {6823, 7689}, {7493, 18451}, {7499, 9730}, {7503, 41587}, {7514, 13567}, {7789, 36952}, {9306, 34351}, {10018, 11444}, {10020, 11591}, {10127, 24206}, {10192, 15068}, {10282, 31831}, {10300, 20397}, {10519, 41614}, {10610, 32358}, {10627, 23336}, {11064, 23039}, {11202, 34507}, {11245, 37513}, {11793, 16238}, {12605, 13851}, {13348, 25563}, {13394, 18445}, {14791, 23332}, {14852, 18918}, {15030, 37971}, {15361, 20582}, {15585, 34776}, {15720, 42021}, {16197, 40647}, {16621, 17714}, {16658, 37913}, {16659, 38435}, {18531, 35254}, {18537, 32620}, {18951, 37476}, {21230, 23358}, {26879, 37126}, {31834, 34577}, {34200, 38726}, {37935, 43586}

X(44201) = midpoint of X(i) and X(j) for these {i,j}: {3, 343}, {427, 37478}
X(44201) = reflection of X(23292) in X(140)
X(44201) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {389, 32348, 140}, {5447, 20191, 16196}, {5562, 7542, 9820}

leftri

Centers of circles through X(24007) and X(24008): X(44202)-X(44205)

rightri

This preamble is contributed by Peter Moses, August 13, 2021.

In addition to the Dao-Moses-Telv circle, {13,14,5000,5001,6104,6105,6106,6107,6108,6109,6110,6111,24007,24008}, the following four circles also pass thorugh X(24007) and X(24008):

{{2,98,112,5913,10295,24007,24008}}, with center X(44202)
{{4,107,111,671,5523,7426,9979,20410,24007,24008,41125}}, with center X(44203)
{{51,115,132,24007,24008}, with center X(44204)}
{{125,187,1560,6055,9730,10162,24007,24008}}, with center X(44205)

X(44202) = MIDPOINT OF X(376) AND X(9979)

Barycentrics    (b^2 - c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(3*a^4 - 4*a^2*b^2 + b^4 - 4*a^2*c^2 + c^4) : :
X(44202) = X[3268] - 3 X[3524]

X(44202) lies on these lines: {3, 2799}, {30, 1637}, {376, 9979}, {541, 14697}, {549, 14417}, {690, 6055}, {1499, 9189}, {2793, 14666}, {3268, 3524}, {3534, 9529}, {5664, 9033}, {6644, 42659}, {9003, 11179}, {9730, 39469}, {11621, 32473}, {15469, 35912}

X(44202) = midpoint of X(376) and X(9979)
X(44202) = reflection of X(14417) in X(549)

X(44203) = MIDPOINT OF X(4) AND X(9979)

Barycentrics    (a^4-b^4+4*b^2*c^2-c^4)*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*(b^2-c^2) : :
X(44203) = X[3268] - 3 X[3545], 2 X[9126] - 3 X[9189]

X(44203) lies on these lines: {3, 9529}, {4, 9979}, {5, 14417}, {30, 1637}, {113, 133}, {381, 2799}, {525, 16229}, {690, 9880}, {2780, 9134}, {2793, 6094}, {3268, 3545}, {5512, 14672}, {7530, 42659}, {9003, 20423}, {9126, 9189}, {12083, 25644}, {14697, 17702}, {30209, 37855}

X(44203) = midpoint of X(4) and X(9979)
X(44203) = reflection of X(14417) in X(5)
X(44203) = X(i)-isoconjugate of X(j) for these (i,j): {5486, 36034}, {18877, 37217}, {30247, 35200}
X(44203) = crossdifference of every pair of points on line {9717, 18877}
X(44203) = X(9979)-of-Euler-triangle
X(44203) = X(14417)-of-Johnson-triangle
X(44203) = barycentric product X(i)*X(j) for these {i,j}: {1637, 11185}, {1784, 14209}, {1995, 41079}
X(44203) = barycentric quotient X(i)/X(j) for these {i,j}: {1637, 5486}, {1784, 37217}, {1990, 30247}, {19136, 32640}, {30209, 14919}

X(44204) = MIDPOINT OF X(381) AND X(9979)

Barycentrics    (b^2 - c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^2*b^2 - b^4 + a^2*c^2 + 3*b^2*c^2 - c^4) : :
X(44204) = X[3268] - 3 X[5055]

X(44204) lies on these lines: {5, 2799}, {30, 1637}, {381, 9979}, {547, 14417}, {2780, 10278}, {3268, 5055}, {8029, 19912}, {8703, 9529}, {10189, 16235}, {24978, 39491}

X(44204) = midpoint of X(i) and X(j) for these {i,j}: {381, 9979}, {8029, 19912}, {24978, 39491}
X(44204) = reflection of X(i) in X(j) for these {i,j}: {14417, 547}, {16235, 10189}
X(44204) = barycentric product X(5640)*X(41079)
X(44204) = barycentric quotient X(33885)/X(1304)

X(44205) = MIDPOINT OF X(9979) AND X(44206)

Barycentrics    (b^2 - c^2)*(a^2 - b^2 - c^2)*(2*a^8 + 2*a^6*b^2 - 3*a^4*b^4 - 2*a^2*b^6 + b^8 + 2*a^6*c^2 - 2*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 3*b^6*c^2 - 3*a^4*c^4 + 3*a^2*b^2*c^4 + 4*b^4*c^4 - 2*a^2*c^6 - 3*b^2*c^6 + c^8) : :

X(44205) lies on this line: {2799, 12042}

X(44205) = midpoint of X(9979) and X(44205)

X(44206) = REFLECTION OF X(9979) IN X(44205)

Barycentrics    (b^2 - c^2)*(5*a^10 + a^8*b^2 - 13*a^6*b^4 + a^4*b^6 + 8*a^2*b^8 - 2*b^10 + a^8*c^2 - 13*a^6*b^2*c^2 + 25*a^4*b^4*c^2 - 17*a^2*b^6*c^2 + 4*b^8*c^2 - 13*a^6*c^4 + 25*a^4*b^2*c^4 - 2*a^2*b^4*c^4 - 2*b^6*c^4 + a^4*c^6 - 17*a^2*b^2*c^6 - 2*b^4*c^6 + 8*a^2*c^8 + 4*b^2*c^8 - 2*c^10) : :
X(44206) = 3 X[3] - 2 X[18311], 3 X[381] - 4 X[18310]

X(44206) lies on these lines: {3, 18311}, {30, 14977}, {381, 18310}, {523, 3534}, {525, 33878}, {2799, 14830}, {9979, 44205}

X(44206) = reflection of X(9979) in X(44205)

X(44207) = (name pending)

Barycentrics    (a^10 - a^8*b^2 - a^2*b^8 + b^10 - 3*a^8*c^2 + 2*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 2*a^2*b^6*c^2 - 3*b^8*c^2 + 4*a^6*c^4 + 2*a^4*b^2*c^4 + 2*a^2*b^4*c^4 + 4*b^6*c^4 - 4*a^4*c^6 - 6*a^2*b^2*c^6 - 4*b^4*c^6 + 3*a^2*c^8 + 3*b^2*c^8 - c^10)*(a^10 - 3*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 + 3*a^2*b^8 - b^10 - a^8*c^2 + 2*a^6*b^2*c^2 + 2*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^4*b^2*c^4 + 2*a^2*b^4*c^4 - 4*b^6*c^4 + 2*a^2*b^2*c^6 + 4*b^4*c^6 - a^2*c^8 - 3*b^2*c^8 + c^10) : :

See Antreas Hatzipolakis and Peter Moses, euclid 2016.

X(44207) lies on the Jerabek circumhyperbola and these lines: { }

X(44207) = isogonal conjugate of X(44208)

X(44208) = 61ST HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    a^2*(a^10 - 3*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 + 3*a^2*b^8 - b^10 - 3*a^8*c^2 + 6*a^6*b^2*c^2 - 2*a^4*b^4*c^2 - 2*a^2*b^6*c^2 + b^8*c^2 + 4*a^6*c^4 - 2*a^4*b^2*c^4 + 2*a^2*b^4*c^4 - 4*a^4*c^6 - 2*a^2*b^2*c^6 + 3*a^2*c^8 + b^2*c^8 - c^10) : :

See Antreas Hatzipolakis and Peter Moses, euclid 2016.

X(44208) lies on these lines: {2,3}, {2351,11442}

X(44208) = isogonal conjugate of X(44207)

X(44209) = 62ND HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^16 - 9*a^14*b^2 + 17*a^12*b^4 - 19*a^10*b^6 + 15*a^8*b^8 - 7*a^6*b^10 - a^4*b^12 + 3*a^2*b^14 - b^16 - 9*a^14*c^2 + 22*a^12*b^2*c^2 - 19*a^10*b^4*c^2 + 10*a^8*b^6*c^2 - 7*a^6*b^8*c^2 + 10*a^4*b^10*c^2 - 13*a^2*b^12*c^2 + 6*b^14*c^2 + 17*a^12*c^4 - 19*a^10*b^2*c^4 - 2*a^8*b^4*c^4 + 6*a^6*b^6*c^4 - 7*a^4*b^8*c^4 + 21*a^2*b^10*c^4 - 16*b^12*c^4 - 19*a^10*c^6 + 10*a^8*b^2*c^6 + 6*a^6*b^4*c^6 - 4*a^4*b^6*c^6 - 11*a^2*b^8*c^6 + 26*b^10*c^6 + 15*a^8*c^8 - 7*a^6*b^2*c^8 - 7*a^4*b^4*c^8 - 11*a^2*b^6*c^8 - 30*b^8*c^8 - 7*a^6*c^10 + 10*a^4*b^2*c^10 + 21*a^2*b^4*c^10 + 26*b^6*c^10 - a^4*c^12 - 13*a^2*b^2*c^12 - 16*b^4*c^12 + 3*a^2*c^14 + 6*b^2*c^14 - c^16 : :

See Antreas Hatzipolakis and Peter Moses, euclid 2016.

X(44209) lies on this line: {2,3}

leftri

Midpoints on the Euler line: X(44210)-X(44290)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, August 16, 2021.

If U and V are points on the Euler line, then their midpoint, given by the combo U + V, also lies on the Euler line.

X(44210) = MIDPOINT OF X(2) AND X(22)

Barycentrics    4*a^6 - a^4*b^2 - 4*a^2*b^4 + b^6 - a^4*c^2 - b^4*c^2 - 4*a^2*c^4 - b^2*c^4 + c^6 : :

X(44210) lies on these lines: {2, 3}, {51, 597}, {69, 26864}, {74, 32227}, {113, 35254}, {141, 1495}, {154, 599}, {160, 15652}, {182, 32269}, {184, 524}, {343, 542}, {511, 13394}, {612, 4995}, {614, 5298}, {1112, 9967}, {1177, 34319}, {1194, 3003}, {1353, 11003}, {1494, 1799}, {1503, 35268}, {1879, 3054}, {1899, 43273}, {1992, 11402}, {2781, 3917}, {2916, 23300}, {2979, 40112}, {3058, 5310}, {3098, 11064}, {3163, 40938}, {3564, 6800}, {3580, 15080}, {3589, 34417}, {3629, 44109}, {3763, 41424}, {3796, 11179}, {3815, 35345}, {3933, 26233}, {5012, 15360}, {5063, 9300}, {5090, 34712}, {5092, 32223}, {5181, 22165}, {5191, 7664}, {5322, 5434}, {5370, 7354}, {5476, 37649}, {5486, 15534}, {5640, 38110}, {5650, 21167}, {5651, 15448}, {5943, 10168}, {5972, 14810}, {6030, 9140}, {6031, 14929}, {6090, 10519}, {6284, 7302}, {6723, 33751}, {6781, 15820}, {7749, 40350}, {7750, 37804}, {7788, 34254}, {7799, 33651}, {7810, 42671}, {8192, 34667}, {8193, 34656}, {8263, 40114}, {8550, 41586}, {8584, 13366}, {8588, 24855}, {9157, 10718}, {9306, 35266}, {9591, 34657}, {10601, 38064}, {11056, 32819}, {11180, 11206}, {11396, 34730}, {11513, 13937}, {11514, 13884}, {11574, 44084}, {11645, 21243}, {12017, 21970}, {13567, 22352}, {14389, 15107}, {14569, 37765}, {14826, 21356}, {15880, 43618}, {16316, 40879}, {16317, 21843}, {16331, 19221}, {19121, 34397}, {19126, 41584}, {20423, 33586}, {20582, 44082}, {24206, 32237}, {25406, 26869}, {26881, 37636}, {32218, 37283}, {33878, 37645}, {37775, 42121}, {37776, 42124}, {41587, 43573}

X(44210) = midpoint of X(2) and X(22)
X(44210) = complement of X(31133)

X(44211) = MIDPOINT OF X(2) AND X(24)

Barycentrics    4*a^10 - 9*a^8*b^2 + 2*a^6*b^4 + 8*a^4*b^6 - 6*a^2*b^8 + b^10 - 9*a^8*c^2 + 12*a^6*b^2*c^2 - 12*a^4*b^4*c^2 + 12*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 12*a^4*b^2*c^4 - 12*a^2*b^4*c^4 + 2*b^6*c^4 + 8*a^4*c^6 + 12*a^2*b^2*c^6 + 2*b^4*c^6 - 6*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44211) lies on these lines: {2, 3}, {343, 43586}, {539, 33563}, {542, 20771}, {800, 3163}, {1353, 9703}, {5642, 14831}, {5651, 44201}, {5892, 13394}, {5943, 10182}, {6148, 39113}, {8780, 18917}, {9730, 10192}, {11179, 23041}, {11449, 43595}, {11597, 19138}, {16194, 23328}, {18475, 37648}, {21850, 38794}, {22115, 41588}, {23324, 23515}, {32062, 38727}, {34782, 43817}, {41628, 43572}

X(44211) = midpoint of X(2) and X(24)
X(44211) = complement of X(31180)

X(44212) = MIDPOINT OF X(2) AND X(25)

Barycentrics    4*a^6 - a^4*b^2 - 4*a^2*b^4 + b^6 - a^4*c^2 + 12*a^2*b^2*c^2 - b^4*c^2 - 4*a^2*c^4 - b^2*c^4 + c^6 : :

X(44212) lies on these lines: {2, 3}, {51, 5642}, {69, 21970}, {110, 1353}, {125, 39884}, {141, 32223}, {154, 11179}, {182, 15448}, {184, 35266}, {343, 32225}, {373, 13394}, {524, 8263}, {542, 13567}, {597, 2393}, {1084, 1196}, {1494, 40413}, {1495, 37648}, {1992, 3167}, {2790, 6055}, {3054, 36412}, {3060, 40112}, {3066, 18583}, {3564, 35259}, {3580, 10546}, {4995, 5268}, {5012, 40114}, {5050, 35260}, {5254, 40350}, {5272, 5298}, {5309, 34481}, {5476, 23292}, {5480, 5972}, {5651, 32269}, {6090, 34380}, {6593, 8584}, {6688, 10168}, {7713, 34643}, {7718, 34713}, {8185, 34634}, {8262, 22165}, {8770, 16310}, {8780, 11433}, {8854, 32787}, {8855, 32788}, {9300, 33871}, {10272, 32227}, {10418, 18907}, {10545, 14389}, {11064, 21850}, {11245, 35264}, {11427, 14848}, {11439, 43903}, {11746, 41714}, {12294, 13416}, {13846, 18289}, {13847, 18290}, {13857, 44106}, {14908, 19661}, {14929, 26276}, {15060, 15361}, {15082, 21167}, {17810, 20423}, {17825, 38064}, {18358, 37638}, {18440, 37643}, {23332, 36201}, {31670, 31860}, {31804, 43573}, {32819, 37803}, {33552, 33962}, {33651, 37671}, {34224, 43836}, {34319, 38851}, {37488, 40917}, {37649, 38079}

X(44212) = midpoint of X(2) and X(25)
X(44212) = complement of X(31152)

X(44213) = MIDPOINT OF X(2) AND X(26)

Barycentrics    4*a^10 - 9*a^8*b^2 + 2*a^6*b^4 + 8*a^4*b^6 - 6*a^2*b^8 + b^10 - 9*a^8*c^2 + 4*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 10*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 2*a^4*b^2*c^4 - 8*a^2*b^4*c^4 + 2*b^6*c^4 + 8*a^4*c^6 + 10*a^2*b^2*c^6 + 2*b^4*c^6 - 6*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44213) lies on these lines:s {2, 3}, {49, 41628}, {395, 11267}, {396, 11268}, {524, 19154}, {539, 10282}, {542, 20773}, {1154, 10192}, {1989, 42459}, {4995, 8144}, {5298, 32047}, {5944, 41587}, {5946, 13394}, {9707, 32358}, {9971, 38110}, {11265, 32788}, {11266, 32787}, {15448, 44201}, {15806, 31802}, {18475, 32223}, {19153, 34380}, {36987, 38793}

X(44213) = midpoint of X(2) and X(26)
X(44213) = complement of X(31181)

X(44214) = MIDPOINT OF X(2) AND X(186)

Barycentrics    4*a^10 - 9*a^8*b^2 + 2*a^6*b^4 + 8*a^4*b^6 - 6*a^2*b^8 + b^10 - 9*a^8*c^2 + 14*a^6*b^2*c^2 - 10*a^4*b^4*c^2 + 8*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 10*a^4*b^2*c^4 - 4*a^2*b^4*c^4 + 2*b^6*c^4 + 8*a^4*c^6 + 8*a^2*b^2*c^6 + 2*b^4*c^6 - 6*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44214) lies on these lines: {2, 3}, {182, 32113}, {187, 16760}, {511, 16222}, {524, 15462}, {541, 21663}, {568, 16227}, {1154, 15361}, {1353, 11935}, {1495, 6699}, {1503, 15061}, {1511, 3580}, {1514, 20127}, {1531, 12900}, {3003, 3163}, {3564, 32609}, {3581, 11064}, {4995, 10149}, {5181, 11693}, {5642, 13754}, {5972, 32110}, {6795, 16321}, {9730, 10182}, {10168, 11649}, {10193, 16194}, {10540, 20126}, {10564, 32223}, {11657, 14934}, {11694, 40111}, {12028, 14993}, {12041, 32111}, {12893, 32123}, {13289, 32125}, {13367, 43573}, {13394, 40280}, {13857, 14156}, {14693, 38613}, {14805, 37648}, {14915, 38727}, {15034, 41724}, {15360, 43574}, {15448, 38728}, {18350, 44158}, {26879, 32171}, {32269, 37477}, {38227, 38704}, {40352, 40630}

X(44214) = midpoint of X(2) and X(186)
X(44214) = X(44452)-of-anti-Euler-triangle

X(44215) = MIDPOINT OF X(2) AND X(237)

Barycentrics    4*a^6*b^2 - 5*a^4*b^4 + a^2*b^6 + 4*a^6*c^2 + b^6*c^2 - 5*a^4*c^4 - 2*b^4*c^4 + a^2*c^6 + b^2*c^6 : :

X(44215) lies on these lines: {2, 3}, {230, 5106}, {373, 40108}, {512, 11176}, {524, 36213}, {620, 32223}, {1495, 12042}, {1625, 3231}, {3117, 5306}, {4995, 40790}, {5968, 16329}, {9155, 32515}, {10168, 34236}, {11673, 40112}, {16237, 16330}, {22329, 35146}, {35278, 38225}

X(44215) = midpoint of X(2) and X(237)

X(44216) = MIDPOINT OF X(2) AND X(297)

Barycentrics    2*a^8 + a^6*b^2 - 3*a^4*b^4 - 5*a^2*b^6 + 5*b^8 + a^6*c^2 + 2*a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 8*b^6*c^2 - 3*a^4*c^4 + 5*a^2*b^2*c^4 + 6*b^4*c^4 - 5*a^2*c^6 - 8*b^2*c^6 + 5*c^8 : :

X(44216) lies on these lines: {2, 3}, {317, 20204}, {524, 3163}, {525, 1637}, {1494, 6330}, {1503, 41145}, {1990, 40996}, {5309, 13567}, {5641, 22329}, {7615, 34360}, {7753, 23292}, {8859, 39359}, {15526, 18487}, {16076, 16080}, {16321, 38393}, {34573, 36412}

X(44216) = midpoint of X(2) and X(297)
X(44216) = complement of X(40884)
X(44216) = anticomplement of X(44346)

X(44217) = MIDPOINT OF X(2) AND X(377)

Barycentrics    a^4 + a^2*b^2 - 2*b^4 + 6*a^2*b*c + 6*a*b^2*c + a^2*c^2 + 6*a*b*c^2 + 4*b^2*c^2 - 2*c^4 : :

X(44217) lies on these lines: {1, 21949}, {2, 3}, {10, 553}, {56, 3841}, {72, 4654}, {78, 3824}, {142, 3419}, {274, 7788}, {392, 31162}, {518, 599}, {540, 19723}, {551, 31140}, {940, 3017}, {956, 3925}, {958, 41859}, {997, 4870}, {999, 33108}, {1125, 11238}, {1376, 3584}, {1478, 3826}, {1698, 3916}, {2094, 38058}, {2886, 10072}, {3219, 18541}, {3336, 3928}, {3421, 40333}, {3434, 15170}, {3582, 25524}, {3583, 8167}, {3586, 20195}, {3634, 10895}, {3653, 24541}, {3654, 24987}, {3697, 5290}, {3822, 4413}, {3828, 31141}, {3940, 31019}, {4002, 9578}, {4292, 5325}, {4995, 10198}, {5131, 19876}, {5250, 28198}, {5253, 31493}, {5260, 9655}, {5275, 5309}, {5284, 9668}, {5298, 26363}, {5362, 42974}, {5367, 42975}, {5440, 25525}, {5550, 9669}, {5587, 10167}, {5687, 10056}, {5730, 12609}, {6739, 15668}, {6767, 33110}, {7610, 7621}, {7811, 16992}, {7989, 9841}, {8583, 38021}, {9654, 9780}, {9709, 26060}, {9782, 11024}, {10390, 38024}, {10707, 32558}, {10711, 34122}, {10712, 34124}, {10894, 31423}, {10896, 19862}, {11231, 21165}, {11235, 17614}, {11648, 16589}, {12699, 24564}, {15934, 27186}, {16118, 41872}, {16483, 33109}, {16763, 17057}, {17757, 26040}, {19860, 28204}, {25973, 34697}, {31473, 35823}, {32833, 37664}, {34648, 38204}

X(44217) = midpoint of X(2) and X(377)
X(44217) = complement of X(31156)

X(44218) = MIDPOINT OF X(2) AND X(378)

Barycentrics    4*a^10 - 9*a^8*b^2 + 2*a^6*b^4 + 8*a^4*b^6 - 6*a^2*b^8 + b^10 - 9*a^8*c^2 + 20*a^6*b^2*c^2 - 4*a^4*b^4*c^2 - 4*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 4*a^4*b^2*c^4 + 20*a^2*b^4*c^4 + 2*b^6*c^4 + 8*a^4*c^6 - 4*a^2*b^2*c^6 + 2*b^4*c^6 - 6*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44218) lies on these lines: {2, 3}, {39, 3163}, {49, 43894}, {74, 14389}, {141, 10564}, {373, 38727}, {511, 30539}, {524, 13352}, {542, 11430}, {567, 5622}, {569, 6696}, {575, 20417}, {597, 2781}, {599, 37497}, {1503, 39242}, {3581, 21850}, {3589, 37470}, {4550, 11064}, {5476, 11438}, {5480, 32110}, {5642, 15030}, {5943, 10193}, {6699, 37648}, {8550, 12506}, {8589, 36412}, {9140, 12022}, {10168, 16836}, {10192, 16194}, {10249, 11179}, {10625, 40929}, {11424, 44158}, {11459, 40112}, {13394, 14915}, {13434, 43607}, {13482, 41628}, {13630, 43896}, {16165, 43586}, {16789, 37480}, {18488, 34782}, {20423, 37489}, {37477, 41721}, {37487, 38072}, {38110, 40280}, {43608, 43836}

X(44218) = midpoint of X(2) and X(378)

X(44219) = MIDPOINT OF X(2) AND X(383)

Barycentrics    (3*a^2 - b^2 - c^2)*(b^2 - c^2)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(3*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - 4*(Sqrt[3]*a^2 - S)*S) - (2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*((a^2 - c^2)*(a^2 - b^2 + c^2)*(3*(a^2 + b^2 - c^2)*(-a^2 + b^2 + c^2) - 4*(Sqrt[3]*b^2 - S)*S) - (a^2 - b^2)*(a^2 + b^2 - c^2)*(3*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2) - 4*(Sqrt[3]*c^2 - S)*S)) : :

X(44219) lies on these lines: {2, 3}, {13, 3815}, {14, 230}, {16, 41043}, {98, 42063}, {114, 530}, {302, 18358}, {303, 21850}, {325, 11128}, {395, 542}, {396, 5476}, {397, 32907}, {524, 5613}, {531, 7685}, {597, 9749}, {1352, 9761}, {1499, 9195}, {3054, 16809}, {3055, 16808}, {3564, 37785}, {3818, 23303}, {5321, 6109}, {5460, 6055}, {5480, 33475}, {5617, 33474}, {5979, 23234}, {6774, 11645}, {7610, 22491}, {7735, 42975}, {7736, 42974}, {8550, 36383}, {9113, 43274}, {9762, 9771}, {9763, 20423}, {11184, 22492}, {11489, 18440}, {11537, 14356}, {14848, 37640}, {15597, 20428}, {16644, 38072}, {19130, 23302}, {20112, 22576}, {21159, 41025}, {22796, 43101}, {22797, 42943}, {23698, 41047}, {37689, 42816}, {37835, 41042}

X(44219) = midpoint of X(2) and X(383)

X(44220) = MIDPOINT OF X(3) AND X(28)

Barycentrics    a*(2*a^9 - 4*a^7*b^2 + 4*a^3*b^6 - 2*a*b^8 + a^5*b^3*c - a^4*b^4*c - 2*a^3*b^5*c + 2*a^2*b^6*c + a*b^7*c - b^8*c - 4*a^7*c^2 + 8*a^5*b^2*c^2 - a^4*b^3*c^2 - 6*a^3*b^4*c^2 + 2*a*b^6*c^2 + b^7*c^2 + a^5*b*c^3 - a^4*b^2*c^3 - 2*a^2*b^4*c^3 - a*b^5*c^3 + 3*b^6*c^3 - a^4*b*c^4 - 6*a^3*b^2*c^4 - 2*a^2*b^3*c^4 - 3*b^5*c^4 - 2*a^3*b*c^5 - a*b^3*c^5 - 3*b^4*c^5 + 4*a^3*c^6 + 2*a^2*b*c^6 + 2*a*b^2*c^6 + 3*b^3*c^6 + a*b*c^7 + b^2*c^7 - 2*a*c^8 - b*c^8) : :

X(44220) lies on these lines: {2, 3}, {284, 5453}, {942, 1511}, {2828, 38602}, {2838, 38603}, {3601, 37729}, {5267, 6708}, {7280, 37695}, {7740, 18115}, {9895, 11259}, {15803, 37697}, {15943, 18481}, {30282, 37696}, {38606, 38612}, {40111, 41608}

X(44220) = midpoint of X(3) and X(28)

X(44221) = MIDPOINT OF X(3) AND X(237)

Barycentrics    a^2*(2*a^8*b^2 - 6*a^6*b^4 + 6*a^4*b^6 - 2*a^2*b^8 + 2*a^8*c^2 - 6*a^6*b^2*c^2 + 3*a^4*b^4*c^2 + 2*a^2*b^6*c^2 - b^8*c^2 - 6*a^6*c^4 + 3*a^4*b^2*c^4 - 4*a^2*b^4*c^4 + b^6*c^4 + 6*a^4*c^6 + 2*a^2*b^2*c^6 + b^4*c^6 - 2*a^2*c^8 - b^2*c^8) : :

X(44221) lies on these lines: {2, 3}, {39, 5946}, {50, 15462}, {187, 1511}, {249, 2080}, {327, 7771}, {511, 34990}, {512, 5926}, {1154, 36212}, {1634, 3564}, {2387, 13335}, {2482, 15361}, {3003, 14984}, {3580, 36829}, {5504, 41336}, {5892, 13334}, {7789, 36952}, {9826, 14961}, {10317, 12228}, {23217, 32269}, {32219, 37470}

X(44221) = midpoint of X(3) and X(237)

X(44222) = MIDPOINT OF X(3) AND X(377)

Barycentrics    a^5*b^2 - a^4*b^3 - 2*a^3*b^4 + 2*a^2*b^5 + a*b^6 - b^7 + 8*a^5*b*c - a^4*b^2*c - 8*a^3*b^3*c + b^6*c + a^5*c^2 - a^4*b*c^2 - 2*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 - a^4*c^3 - 8*a^3*b*c^3 - 2*a^2*b^2*c^3 - 3*b^4*c^3 - 2*a^3*c^4 - a*b^2*c^4 - 3*b^3*c^4 + 2*a^2*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :

X(44222) lies on these lines: {2, 3}, {10, 13369}, {46, 495}, {119, 16209}, {496, 3612}, {518, 5690}, {960, 41540}, {1385, 3813}, {1698, 7171}, {2886, 13624}, {3576, 10943}, {3579, 25466}, {3653, 37722}, {3654, 15888}, {3820, 5302}, {3826, 18480}, {3925, 18481}, {5122, 15844}, {5249, 37585}, {5433, 14803}, {5794, 37705}, {7280, 26481}, {7680, 31663}, {7987, 26470}, {8273, 37820}, {9710, 28204}, {9956, 31805}, {10198, 35238}, {10942, 21031}, {11231, 18242}, {11246, 16139}, {11698, 26066}, {12609, 22791}, {12616, 38042}, {12625, 18443}, {15325, 22768}, {17647, 31419}, {26475, 37616}, {30389, 37726}

X(44222) = midpoint of X(3) and X(377)
X(44222) = complement of X(37234)

X(44223) = MIDPOINT OF X(3) AND X(383)

Barycentrics    (b^2 - c^2)*(3*a^6 - 4*a^4*b^2 + 2*a^2*b^4 - b^6 - 4*a^4*c^2 + 3*a^2*b^2*c^2 + 2*a^2*c^4 - c^6)*(Sqrt[3]*((a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) + a^2*(-a^2 + b^2 + c^2)) - 2*(b^2 + c^2)*S) + (2*a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4)*(-((a^2 - b^2)*(a^2 + b^2 - c^2)*(Sqrt[3]*(c^2*(a^2 + b^2 - c^2) + (a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)) - 2*(a^2 + b^2)*S)) + (a^2 - c^2)*(a^2 - b^2 + c^2)*(Sqrt[3]*(b^2*(a^2 - b^2 + c^2) + (a^2 + b^2 - c^2)*(-a^2 + b^2 + c^2)) - 2*(a^2 + c^2)*S)) : :

X(44223) lies on these lines: {2, 3}, {14, 38230}, {16, 5613}, {182, 33390}, {187, 6114}, {299, 5615}, {303, 20425}, {395, 11135}, {396, 3106}, {511, 619}, {617, 20426}, {618, 24206}, {620, 624}, {636, 7880}, {1353, 42634}, {1503, 33389}, {2080, 5978}, {2782, 6108}, {3564, 42913}, {3643, 9736}, {5237, 37825}, {5321, 20253}, {5476, 13083}, {5617, 16242}, {5872, 42149}, {5873, 22238}, {5979, 15561}, {6109, 14693}, {6672, 6774}, {6771, 33479}, {11178, 13084}, {11543, 19781}, {13103, 14145}, {13349, 41023}, {16626, 42489}, {16627, 42158}, {16964, 36959}, {16966, 23005}, {18581, 21843}, {18583, 42912}, {20252, 37832}, {20428, 30560}, {20429, 36968}, {22509, 22998}, {33416, 36765}

X(44223) = midpoint of X(3) and X(383)
X(44223) = outer-Napoleon-circle-inverse of X(44462)

X(44224) = MIDPOINT OF X(3) AND X(384)

Barycentrics    2*a^8 - 2*a^6*b^2 + a^4*b^4 - a^2*b^6 - 2*a^6*c^2 - 2*a^4*b^2*c^2 - 4*a^2*b^4*c^2 + b^6*c^2 + a^4*c^4 - 4*a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + b^2*c^6 : :

X(44224) lies on these lines: {2, 3}, {32, 32521}, {76, 26316}, {83, 35002}, {99, 12054}, {141, 32151}, {182, 698}, {325, 34885}, {511, 32134}, {736, 7780}, {1503, 35422}, {1511, 37890}, {2023, 37512}, {3095, 7878}, {3098, 42534}, {3398, 7760}, {3734, 14880}, {3934, 12042}, {3972, 9821}, {5031, 7830}, {5092, 7816}, {5116, 43456}, {5149, 7789}, {5162, 7745}, {5206, 42535}, {6033, 7832}, {6292, 38749}, {7804, 14881}, {7822, 9996}, {7847, 38730}, {7861, 22515}, {7944, 10722}, {8290, 35464}, {10357, 14712}, {10359, 32447}, {10583, 43453}, {10796, 30270}, {11272, 18860}, {11842, 12251}, {12176, 40238}, {12188, 17128}, {13334, 33813}, {18358, 24273}, {18769, 35701}, {21167, 43152}

X(44224) = midpoint of X(3) and X(384)
X(44224) = complement of X(37243)

X(44225) = MIDPOINT OF X(4) AND X(29)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^5*b + a^4*b^2 - 4*a^3*b^3 - 2*a^2*b^4 + 2*a*b^5 + b^6 + 2*a^5*c - 2*a^4*b*c - 2*a*b^4*c + 2*b^5*c + a^4*c^2 - b^4*c^2 - 4*a^3*c^3 - 4*b^3*c^3 - 2*a^2*c^4 - 2*a*b*c^4 - b^2*c^4 + 2*a*c^5 + 2*b*c^5 + c^6) : :

X(44225) lies on these lines: {2, 3}, {34, 7100}, {92, 22791}, {113, 20620}, {124, 133}, {158, 39542}, {240, 5492}, {243, 37737}, {278, 18493}, {281, 12702}, {355, 39531}, {517, 39574}, {946, 39529}, {1159, 3176}, {1547, 13474}, {1784, 3649}, {1838, 9955}, {1844, 2771}, {1859, 31937}, {1895, 6147}, {5174, 18357}, {5708, 40836}, {7070, 18492}, {10572, 42387}, {12047, 42385}, {12699, 39585}, {21666, 34334}

X(44225) = midpoint of X(4) and X(29)
X(44225) = X(29)-of-Euler-triangle

X(44226) = MIDPOINT OF X(4) AND X(235)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^6 - a^4*b^2 - 4*a^2*b^4 + 3*b^6 - a^4*c^2 + 12*a^2*b^2*c^2 - 3*b^4*c^2 - 4*a^2*c^4 - 3*b^2*c^4 + 3*c^6) : :

X(44226) lies on these lines: {2, 3}, {113, 22970}, {185, 1514}, {389, 5893}, {1829, 40273}, {1902, 18357}, {1968, 43291}, {2883, 18390}, {3564, 11470}, {6225, 26944}, {6746, 13451}, {6748, 39590}, {7687, 13474}, {8537, 39871}, {8548, 39884}, {9820, 12897}, {10110, 43392}, {10575, 44079}, {10641, 42136}, {10642, 42137}, {11245, 43602}, {11363, 28186}, {11473, 18538}, {11474, 18762}, {11475, 42146}, {11476, 42143}, {11572, 16654}, {11801, 12133}, {12294, 18358}, {12295, 20771}, {13093, 23291}, {13142, 22660}, {13346, 18418}, {13403, 16252}, {13419, 15125}, {13567, 22802}, {13568, 43589}, {13630, 44084}, {13851, 16655}, {14864, 15153}, {15114, 15473}, {15120, 30522}, {16621, 18383}, {16657, 43831}, {16658, 18394}, {18918, 34780}, {18945, 32063}, {20427, 26958}, {22115, 22750}, {26879, 43806}, {35764, 42283}, {35765, 42284}

X(44226) = midpoint of X(4) and X(235)
X(44226) = X(235)-of-Euler-triangle

X(44227) = MIDPOINT OF X(4) AND X(237)

Barycentrics    a^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10 + 4*a^8*b^2*c^2 - 5*a^4*b^6*c^2 + 2*a^2*b^8*c^2 - b^10*c^2 + a^8*c^4 + 4*a^4*b^4*c^4 - a^2*b^6*c^4 + 4*b^8*c^4 - 3*a^6*c^6 - 5*a^4*b^2*c^6 - a^2*b^4*c^6 - 6*b^6*c^6 + 3*a^4*c^8 + 2*a^2*b^2*c^8 + 4*b^4*c^8 - a^2*c^10 - b^2*c^10 : :

X(44227) lies on these lines: {2, 3}, {113, 2679}, {133, 38974}, {217, 5305}, {512, 6130}, {1503, 7668}, {2387, 18388}, {2790, 3003}, {3331, 43291}, {3767, 32445}, {6530, 15352}, {13881, 38297}, {15048, 43718}, {16330, 35908}, {23039, 32521}, {30258, 43976}

X(44227) = midpoint of X(2) and X(237)
X(44227) = X(237)-of-Euler-triangle

X(44228) = MIDPOINT OF X(4) AND X(297)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^8 - 3*a^6*b^2 + 3*a^4*b^4 - 5*a^2*b^6 + 3*b^8 - 3*a^6*c^2 + 6*a^4*b^2*c^2 + a^2*b^4*c^2 - 4*b^6*c^2 + 3*a^4*c^4 + a^2*b^2*c^4 + 2*b^4*c^4 - 5*a^2*c^6 - 4*b^2*c^6 + 3*c^8) : :

X(44228) lies on these lines: {2, 3}, {53, 3818}, {113, 38970}, {133, 36471}, {264, 18358}, {265, 5523}, {317, 21850}, {393, 18440}, {399, 8744}, {525, 16229}, {542, 1990}, {648, 3564}, {1249, 39899}, {1351, 10002}, {1353, 41371}, {1503, 39569}, {2207, 18451}, {2966, 39663}, {5254, 18390}, {5476, 6749}, {6531, 43291}, {6748, 19130}, {7745, 18388}, {8743, 18445}, {11442, 14569}, {13142, 43995}, {13754, 34854}, {15262, 39562}, {16077, 35142}, {16240, 32225}, {16326, 36875}, {18437, 42459}, {18474, 27376}, {31670, 42854}, {33971, 39884}, {34334, 44146}

X(44228) = midpoint of X(4) and X(297)
X(44228) = X(297)-of-Euler-triangle

X(44229) = MIDPOINT OF X(4) AND X(377)

Barycentrics    a^7 - a^6*b - a^5*b^2 + a^4*b^3 - a^3*b^4 + a^2*b^5 + a*b^6 - b^7 - a^6*c - a^4*b^2*c - 2*a^3*b^3*c + a^2*b^4*c + 2*a*b^5*c + b^6*c - a^5*c^2 - a^4*b*c^2 + 2*a^3*b^2*c^2 - 2*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 + a^4*c^3 - 2*a^3*b*c^3 - 2*a^2*b^2*c^3 - 4*a*b^3*c^3 - 3*b^4*c^3 - a^3*c^4 + a^2*b*c^4 - a*b^2*c^4 - 3*b^3*c^4 + a^2*c^5 + 2*a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :

X(44229) lies on these lines: {1, 18406}, {2, 3}, {6, 13408}, {8, 20886}, {10, 37584}, {12, 18491}, {57, 3585}, {68, 1243}, {80, 18962}, {119, 10894}, {142, 31673}, {225, 37696}, {278, 18447}, {355, 518}, {388, 15934}, {495, 18518}, {496, 18544}, {497, 18493}, {515, 30143}, {579, 32431}, {942, 1478}, {946, 12437}, {952, 10532}, {960, 12699}, {1056, 18526}, {1060, 1838}, {1068, 37729}, {1466, 13273}, {1479, 9955}, {1483, 10597}, {1699, 10525}, {1728, 9579}, {1836, 31937}, {2550, 12702}, {3085, 18524}, {3193, 15068}, {3434, 5730}, {3436, 18357}, {3583, 3601}, {3587, 41869}, {3600, 12773}, {3818, 4260}, {3925, 35239}, {4292, 10395}, {4293, 26321}, {4295, 40266}, {4857, 38021}, {5082, 8148}, {5138, 19130}, {5229, 5708}, {5251, 35250}, {5270, 11518}, {5290, 18528}, {5302, 5791}, {5396, 5713}, {5492, 24248}, {5587, 5709}, {5654, 41608}, {5691, 18443}, {5706, 18451}, {5707, 5721}, {5715, 5720}, {5755, 5816}, {5777, 37826}, {5778, 5798}, {5787, 6256}, {5800, 18440}, {5886, 24299}, {5891, 10441}, {5901, 12116}, {6245, 37612}, {6246, 9946}, {6253, 10267}, {6326, 33594}, {7354, 18761}, {7680, 11499}, {7688, 41859}, {7741, 37583}, {7951, 10953}, {7956, 11928}, {7965, 11826}, {9654, 10629}, {9945, 22938}, {10283, 10806}, {10531, 38034}, {10805, 28224}, {11459, 41723}, {12667, 38107}, {13151, 18481}, {13226, 22799}, {15171, 18499}, {15803, 18513}, {15888, 34746}, {18343, 18345}, {18483, 21616}, {18514, 30282}, {18519, 18990}, {19925, 37532}, {22753, 26470}, {22793, 31793}, {22798, 41697}, {26333, 33596}, {28204, 37724}, {37534, 41698}, {37623, 38140}, {37697, 40950}

X(44229) = midpoint of X(4) and X(377)
X(44229) = X(377)-of-Euler-triangle

X(44230) = MIDPOINT OF X(4) AND X(384)

Barycentrics    3*a^6*b^2 - a^4*b^4 - a^2*b^6 - b^8 + 3*a^6*c^2 + 4*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - a^4*c^4 + 3*a^2*b^2*c^4 + 2*b^4*c^4 - a^2*c^6 - c^8 : :

X(44230) lies on these lines: {2, 3}, {32, 3818}, {39, 19130}, {76, 9993}, {83, 43460}, {98, 20576}, {113, 35971}, {114, 6249}, {115, 13357}, {141, 9821}, {325, 14881}, {511, 7794}, {542, 5007}, {698, 3095}, {736, 6248}, {1352, 14023}, {1503, 3398}, {2080, 6287}, {3098, 7822}, {3589, 12054}, {3933, 18906}, {3972, 9873}, {5092, 7889}, {5103, 7789}, {5188, 24206}, {5207, 7767}, {5305, 12188}, {5475, 13356}, {5476, 7772}, {6033, 7745}, {6054, 7858}, {6393, 40252}, {7750, 9996}, {7758, 20423}, {7761, 10356}, {7792, 14880}, {7795, 31670}, {7799, 14492}, {7810, 25561}, {7826, 43150}, {7854, 11178}, {7855, 37517}, {7860, 34733}, {8721, 14561}, {9478, 12042}, {9863, 10788}, {9971, 18375}, {11842, 39884}, {12176, 12206}, {13754, 27374}, {17128, 43453}, {18440, 30435}, {18501, 18907}, {22681, 39663}, {32447, 38136}, {37479, 38317}, {39899, 43136}

X(44230) = midpoint of X(4) and X(384)
X(44230) = midpoint of X(37332) and X(37333)
X(44230) = complement of X(7470)
X(44230) = X(384)-of-Euler-triangle

X(44231) = MIDPOINT OF X(4) AND X(401)

Barycentrics    (a^2 - b^2 - c^2)*(3*a^8*b^2 - 4*a^6*b^4 + b^10 + 3*a^8*c^2 + 2*a^6*b^2*c^2 - 2*a^2*b^6*c^2 - 3*b^8*c^2 - 4*a^6*c^4 + 4*a^2*b^4*c^4 + 2*b^6*c^4 - 2*a^2*b^2*c^6 + 2*b^4*c^6 - 3*b^2*c^8 + c^10) : :

X(44231) lies on these lines: {2, 3}, {6, 18437}, {32, 18390}, {39, 18388}, {113, 11672}, {131, 2679}, {157, 18382}, {187, 7687}, {216, 19130}, {248, 265}, {316, 6394}, {399, 13509}, {511, 15526}, {525, 684}, {542, 3284}, {577, 3818}, {1503, 1576}, {1568, 36212}, {2055, 12134}, {3564, 22143}, {5158, 5476}, {5480, 30258}, {5523, 9475}, {6389, 31670}, {6530, 32428}, {10110, 10600}, {10316, 18474}, {10745, 35002}, {12022, 34396}, {12241, 36245}, {15905, 18440}, {18358, 41008}, {18400, 42671}, {18445, 22120}, {18451, 23115}, {20208, 33878}, {21850, 41005}, {38292, 39899}

X(44231) = midpoint of X(4) and X(401)
X(44231) = X(401)-of-Euler-triangle

X(44232) = MIDPOINT OF X(5) AND X(24)

Barycentrics    2*a^10 - 5*a^8*b^2 + 2*a^6*b^4 + 4*a^4*b^6 - 4*a^2*b^8 + b^10 - 5*a^8*c^2 + 4*a^6*b^2*c^2 - 6*a^4*b^4*c^2 + 10*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 6*a^4*b^2*c^4 - 12*a^2*b^4*c^4 + 2*b^6*c^4 + 4*a^4*c^6 + 10*a^2*b^2*c^6 + 2*b^4*c^6 - 4*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44232) lies on these lines: {2, 3}, {110, 32358}, {143, 9820}, {154, 18952}, {156, 13567}, {973, 22051}, {1216, 32223}, {1495, 43817}, {3564, 33563}, {3580, 18350}, {5446, 5972}, {6101, 32269}, {6696, 32137}, {6699, 13474}, {8254, 18583}, {10095, 23292}, {10110, 43839}, {10192, 32046}, {10263, 11064}, {10540, 26879}, {11255, 41585}, {11572, 23515}, {12241, 32171}, {13292, 34116}, {13451, 20193}, {13598, 14156}, {13630, 16252}, {14128, 44201}, {16654, 34128}, {16657, 43394}, {20771, 32423}, {25738, 35264}, {26958, 32140}, {35265, 43808}

X(44232) = midpoint of X(5) and X(24)

X(44233) = MIDPOINT OF X(5) AND X(25)

Barycentrics    2*a^10 - 5*a^8*b^2 + 2*a^6*b^4 + 4*a^4*b^6 - 4*a^2*b^8 + b^10 - 5*a^8*c^2 - 8*a^4*b^4*c^2 + 16*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 8*a^4*b^2*c^4 - 24*a^2*b^4*c^4 + 2*b^6*c^4 + 4*a^4*c^6 + 16*a^2*b^2*c^6 + 2*b^4*c^6 - 4*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44233) lies on these lines: {2, 3}, {1147, 15873}, {1568, 44106}, {1660, 32046}, {2386, 20576}, {2393, 13364}, {3564, 19136}, {5448, 11745}, {5462, 16252}, {5654, 17810}, {5891, 32269}, {8263, 34380}, {9820, 10110}, {9969, 10272}, {10539, 13292}, {10540, 11245}, {14845, 37649}, {14862, 15012}, {15053, 32111}, {15068, 41588}, {15448, 18475}, {16655, 43817}, {16658, 26913}, {20304, 36201}, {20772, 32423}, {31831, 41587}, {32223, 44201}

X(44233) = midpoint of X(5) and X(25)
X(44233) = complement of complement of X(18534)

X(44234) = 1ST HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    2*a^10 - 5*a^8*b^2 + 2*a^6*b^4 + 4*a^4*b^6 - 4*a^2*b^8 + b^10 - 5*a^8*c^2 + 6*a^6*b^2*c^2 - 5*a^4*b^4*c^2 + 7*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 5*a^4*b^2*c^4 - 6*a^2*b^4*c^4 + 2*b^6*c^4 + 4*a^4*c^6 + 7*a^2*b^2*c^6 + 2*b^4*c^6 - 4*a^2*c^8 - 3*b^2*c^8 + c^10 : :
X(44899) = X[1495]+2*X[40685], 3*X[5943]-X[11692], X[10264]+X[10540], X[13445]-5*X[38728], X[14157]+3*X[15061], 5*X[38794]-X[43574]

See Antreas Hatzipolakis and Francisco Javier García Capitán, Euclid 2479 .

X(44234) lies on these lines: {2, 3}, {49, 32165}, {143, 43839}, {389, 15806}, {523, 31667}, {1154, 5972}, {1495, 40685}, {3580, 11597}, {3589, 11649}, {5462, 8254}, {5943, 11692}, {5944, 43817}, {6689, 13365}, {10110, 20193}, {10264, 10540}, {10272, 11561}, {11801, 30522}, {11803, 16625}, {13367, 43575}, {13391, 14156}, {13445, 38728}, {14157, 15061}, {16243, 40630}, {16881, 22051}, {17433, 31945}, {18400, 20304}, {22104, 34837}, {23292, 32411}, {25563, 32137}, {32218, 40670}, {38794, 43574}

X(44234) = midpoint of X(5) and X(186)
X(44234) = complement of X(37938)

X(44235) = MIDPOINT OF X(5) AND X(235)

Barycentrics    a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 + 2*a^6*b^2*c^2 + a^4*b^4*c^2 - 7*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 + a^4*b^2*c^4 + 10*a^2*b^4*c^4 - 2*b^6*c^4 - 7*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44235) lies on these lines: {2, 3}, {113, 6102}, {143, 5448}, {156, 18390}, {184, 43575}, {576, 11803}, {578, 15806}, {1147, 10272}, {1568, 10263}, {1614, 43821}, {3292, 18555}, {3521, 15053}, {3567, 18504}, {3574, 13368}, {5946, 43831}, {5972, 12897}, {7687, 18379}, {7730, 20424}, {9544, 36966}, {10095, 18388}, {10112, 16534}, {10113, 20771}, {10264, 18439}, {10539, 32423}, {11430, 15807}, {11439, 11704}, {11805, 32339}, {13403, 32171}, {13445, 43866}, {13451, 15873}, {13491, 43817}, {13630, 32050}, {13754, 15887}, {14643, 34148}, {14862, 18128}, {15002, 15038}, {15030, 34826}, {18356, 18451}, {18445, 32165}, {20299, 20304}, {21659, 43865}, {22251, 38942}, {22660, 33563}

X(44235) = midpoint of X(5) and X(235)

X(44236) = MIDPOINT OF X(5) AND X(378)

Barycentrics    2*a^10 - 5*a^8*b^2 + 2*a^6*b^4 + 4*a^4*b^6 - 4*a^2*b^8 + b^10 - 5*a^8*c^2 + 12*a^6*b^2*c^2 - 2*a^4*b^4*c^2 - 2*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 2*a^4*b^2*c^4 + 12*a^2*b^4*c^4 + 2*b^6*c^4 + 4*a^4*c^6 - 2*a^2*b^2*c^6 + 2*b^4*c^6 - 4*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(442) lies on these lines: {2, 3}, {143, 44158}, {578, 43588}, {2781, 18583}, {3815, 19220}, {5462, 25563}, {5663, 23292}, {5943, 6699}, {5944, 16655}, {6247, 32046}, {6696, 13630}, {7706, 11204}, {10110, 20191}, {10193, 19130}, {10264, 11245}, {11064, 15060}, {11425, 32140}, {11550, 39242}, {12134, 43394}, {12233, 32138}, {12241, 13561}, {12834, 15057}, {13366, 16003}, {13367, 18488}, {13391, 44201}, {13482, 41724}, {13568, 32210}, {15739, 22051}, {16252, 32137}, {18356, 43595}, {18952, 40686}, {32358, 37472}, {37477, 37636}, {37481, 43607}

X(44236) = midpoint of X(5) and X(378)

X(44237) = MIDPOINT OF X(5) AND X(384)

Barycentrics    2*a^8 - 5*a^6*b^2 + 2*a^4*b^4 + b^8 - 5*a^6*c^2 - 6*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + b^6*c^2 + 2*a^4*c^4 - 7*a^2*b^2*c^4 - 4*b^4*c^4 + b^2*c^6 + c^8 : :

X(44237) lies on these lines: {2, 3}, {620, 42788}, {698, 18583}, {736, 20576}, {2782, 7829}, {3314, 18501}, {3564, 42421}, {3589, 32516}, {3972, 32151}, {7759, 10796}, {7820, 14881}, {7832, 18502}, {7888, 10358}, {10583, 12188}, {32515, 35437}

X(44237) = midpoint of X(5) and X(384)

X(44238) = MIDPOINT OF X(20) AND X(21)

Barycentrics    4*a^7 - 4*a^6*b - 7*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 + a*b^6 - b^7 - 4*a^6*c - 2*a^5*b*c - a^4*b^2*c + 2*a^3*b^3*c + 4*a^2*b^4*c + b^6*c - 7*a^5*c^2 - a^4*b*c^2 + 8*a^3*b^2*c^2 - 2*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 + 7*a^4*c^3 + 2*a^3*b*c^3 - 2*a^2*b^2*c^3 - 3*b^4*c^3 + 2*a^3*c^4 + 4*a^2*b*c^4 - a*b^2*c^4 - 3*b^3*c^4 - 2*a^2*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :

X(44238) lies on these lines: {2, 3}, {7, 16137}, {11, 17009}, {46, 5441}, {63, 16139}, {65, 4304}, {74, 43354}, {79, 3612}, {84, 191}, {224, 16006}, {515, 21677}, {516, 35016}, {517, 39772}, {758, 1071}, {950, 41547}, {1259, 35250}, {2077, 33961}, {2245, 40979}, {2646, 3649}, {2771, 3650}, {2777, 16164}, {2795, 38738}, {2829, 35204}, {3184, 9528}, {3576, 11281}, {3647, 15823}, {3655, 11520}, {3868, 34773}, {4313, 6361}, {4324, 41853}, {5249, 13624}, {5427, 6284}, {5731, 34195}, {5732, 16113}, {5787, 21165}, {5794, 18253}, {7987, 26725}, {10391, 41549}, {10884, 33858}, {11491, 31799}, {11544, 37606}, {11604, 38693}, {11826, 12511}, {12512, 24466}, {12664, 40661}, {16155, 37618}, {16465, 37585}, {26066, 35242}, {28628, 41869}, {33594, 34123}, {35252, 43740}, {37623, 41574}

X(44238) = midpoint of X(20) and X(21)

X(44239) = MIDPOINT OF X(20) AND X(22)

Barycentrics    4*a^10 - 7*a^8*b^2 - 2*a^6*b^4 + 8*a^4*b^6 - 2*a^2*b^8 - b^10 - 7*a^8*c^2 + 4*a^6*b^2*c^2 + 3*b^8*c^2 - 2*a^6*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 + 8*a^4*c^6 - 2*b^4*c^6 - 2*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44239) lies on these lines: {2, 3}, {54, 31802}, {66, 10606}, {74, 41464}, {99, 18401}, {112, 42459}, {343, 18400}, {477, 11635}, {827, 1294}, {1141, 3565}, {1287, 2693}, {1295, 26712}, {1297, 44061}, {1350, 36989}, {1503, 16789}, {1568, 10192}, {2777, 16165}, {2781, 3313}, {4549, 18451}, {5562, 34782}, {5889, 31804}, {5890, 12220}, {5891, 35254}, {5966, 20187}, {6243, 43595}, {7691, 14516}, {8550, 14831}, {9019, 19161}, {9538, 10386}, {10313, 15048}, {10605, 26926}, {10619, 14531}, {10984, 13568}, {11064, 11202}, {11245, 37489}, {11381, 35240}, {11417, 42216}, {11418, 42215}, {11420, 42118}, {11421, 42117}, {11425, 14542}, {11605, 38717}, {11750, 12359}, {12022, 41588}, {12118, 37486}, {12160, 18925}, {12226, 36966}, {13394, 18388}, {14907, 20477}, {15033, 19121}, {17712, 43604}, {17834, 19467}, {18390, 32269}, {18474, 44201}, {18907, 22240}, {19127, 29181}, {24466, 36984}, {26864, 41465}, {30264, 36986}, {41468, 41469}

X(44239) = midpoint of X(20) and X(22)

X(44240) = MIDPOINT OF X(20) AND X(24)

Barycentrics    (a^2 - b^2 - c^2)*(4*a^8 - 3*a^6*b^2 - 5*a^4*b^4 + 3*a^2*b^6 + b^8 - 3*a^6*c^2 + 14*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 4*b^6*c^2 - 5*a^4*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 + 3*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(44240) lies on these lines: {2, 3}, {49, 38723}, {74, 14516}, {113, 43898}, {131, 33553}, {185, 16163}, {1060, 15338}, {1062, 15326}, {1941, 5667}, {2777, 20771}, {3053, 15075}, {3357, 12134}, {4846, 19357}, {5663, 43896}, {5890, 43595}, {5894, 12162}, {6696, 18474}, {6781, 22401}, {7723, 14677}, {7747, 40349}, {8263, 38885}, {9934, 22955}, {10539, 15311}, {10575, 34782}, {10605, 12118}, {12022, 43601}, {12038, 38726}, {12041, 43903}, {12121, 43616}, {12293, 26937}, {12359, 21663}, {12363, 43581}, {13142, 37490}, {13352, 13568}, {13445, 16659}, {14855, 40928}, {15034, 43599}, {15055, 43607}, {17702, 33563}, {18350, 20127}, {18451, 20427}, {23328, 43907}, {31802, 37495}, {35240, 35254}, {37511, 40929}

X(44240) = midpoint of X(20) and X(24)

X(44241) = MIDPOINT OF X(20) AND X(25)

Barycentrics    (a^2 - b^2 - c^2)*(4*a^8 - 3*a^6*b^2 - 5*a^4*b^4 + 3*a^2*b^6 + b^8 - 3*a^6*c^2 + 18*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 4*b^6*c^2 - 5*a^4*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 + 3*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(44241) lies on these lines: {2, 3}, {99, 22468}, {112, 41890}, {141, 11598}, {343, 21663}, {974, 6467}, {1038, 15338}, {1040, 15326}, {1060, 4319}, {1062, 4320}, {1181, 34966}, {1209, 43907}, {1285, 38292}, {1352, 10606}, {1353, 5890}, {1503, 8263}, {1578, 42260}, {1579, 42261}, {2777, 20772}, {2790, 3184}, {2883, 22966}, {3564, 10605}, {3815, 40349}, {5305, 15075}, {5651, 20725}, {5656, 8780}, {5891, 13416}, {5894, 5907}, {5925, 32602}, {9306, 15311}, {9722, 34866}, {9786, 13142}, {9967, 36987}, {10386, 18447}, {10602, 14914}, {11438, 41588}, {11454, 37636}, {12118, 12421}, {12162, 30443}, {12358, 14677}, {12359, 43604}, {12429, 18913}, {13346, 13568}, {13562, 34778}, {13630, 43595}, {14855, 34750}, {14907, 41008}, {14961, 18907}, {15644, 31807}, {15740, 27082}, {17814, 20427}, {18475, 38726}, {18850, 36876}, {19136, 29181}, {19467, 22663}, {21243, 23328}, {22581, 22833}, {22660, 43577}, {31730, 37613}, {31804, 40647}, {32817, 40995}, {32833, 40996}, {39120, 39812}

X(44241) = midpoint of X(20) and X(25)
X(44241) = complement of X(44438)
X(44241) = anticomplement of X(44920)

X(44242) = MIDPOINT OF X(20) AND X(26)

Barycentrics    4*a^10 - 7*a^8*b^2 - 2*a^6*b^4 + 8*a^4*b^6 - 2*a^2*b^8 - b^10 - 7*a^8*c^2 + 12*a^6*b^2*c^2 - 6*a^4*b^4*c^2 - 2*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 6*a^4*b^2*c^4 + 8*a^2*b^4*c^4 - 2*b^6*c^4 + 8*a^4*c^6 - 2*a^2*b^2*c^6 - 2*b^4*c^6 - 2*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44242) lies on these lines: {2, 3}, {50, 42459}, {74, 41482}, {511, 32903}, {1192, 18952}, {1503, 32138}, {2777, 20773}, {4351, 9630}, {5663, 16775}, {5891, 35240}, {5944, 34798}, {6247, 32210}, {7689, 34785}, {8144, 15338}, {9934, 15132}, {10625, 11562}, {11265, 42259}, {11266, 42258}, {11267, 42088}, {11268, 42087}, {11597, 38723}, {11660, 36966}, {11750, 21663}, {12359, 30522}, {13561, 41362}, {13568, 32046}, {15326, 32047}, {15807, 15873}, {16111, 21650}, {17845, 32140}, {18350, 18442}, {18383, 20191}, {19154, 29181}, {19467, 43588}, {21659, 32110}, {22660, 32171}, {25487, 38726}, {32142, 35254}, {32330, 32423}

X(44242) = midpoint of X(20) and X(26)
X(44242) = 1st-Droz-Farny-circle-inverse of X(44905)

X(44243) = MIDPOINT OF X(20) AND X(27)

Barycentrics    (a^2 - b^2 - c^2)*(4*a^8 - 2*a^7*b - 3*a^6*b^2 + 4*a^5*b^3 - 5*a^4*b^4 - 2*a^3*b^5 + 3*a^2*b^6 + b^8 - 2*a^7*c - 2*a^6*b*c + 4*a^5*b^2*c + 4*a^4*b^3*c - 2*a^3*b^4*c - 2*a^2*b^5*c - 3*a^6*c^2 + 4*a^5*b*c^2 + 18*a^4*b^2*c^2 + 4*a^3*b^3*c^2 - 3*a^2*b^4*c^2 - 4*b^6*c^2 + 4*a^5*c^3 + 4*a^4*b*c^3 + 4*a^3*b^2*c^3 + 4*a^2*b^3*c^3 - 5*a^4*c^4 - 2*a^3*b*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^3*c^5 - 2*a^2*b*c^5 + 3*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(44243) lies on these lines: {2, 3}, {63, 15941}, {84, 1762}, {1060, 7675}, {1214, 4304}, {1565, 16163}, {2328, 15311}, {2822, 3184}, {4653, 18643}, {6356, 24929}, {8680, 30271}, {10543, 41393}, {15326, 23207}

X(44243) = midpoint of X(20) and X(27)

X(44244) = MIDPOINT OF X(20) AND X(29)

Barycentrics    (a^2 - b^2 - c^2)*(4*a^8 + 2*a^7*b - 3*a^6*b^2 - 4*a^5*b^3 - 5*a^4*b^4 + 2*a^3*b^5 + 3*a^2*b^6 + b^8 + 2*a^7*c - 2*a^6*b*c - 2*a^3*b^4*c + 2*a^2*b^5*c - 3*a^6*c^2 + 10*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 4*b^6*c^2 - 4*a^5*c^3 - 4*a^2*b^3*c^3 - 5*a^4*c^4 - 2*a^3*b*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 + 2*a^3*c^5 + 2*a^2*b*c^5 + 3*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(44244) lies on these lines: {2, 3}, {77, 1062}, {390, 38290}, {1214, 31730}, {2360, 15311}, {2816, 3184}, {2968, 3916}, {3345, 5732}, {4294, 7011}, {10386, 38284}, {15326, 40946}, {15338, 22341}, {16553, 23058}, {17073, 41869}, {17102, 18593}

X(44244) = midpoint of X(20) and X(29)

X(44245) = MIDPOINT OF X(20) AND X(140)

Barycentrics    14*a^4 - 11*a^2*b^2 - 3*b^4 - 11*a^2*c^2 + 6*b^2*c^2 - 3*c^4 : :

X(44245) lies on these lines: {2, 3}, {61, 42123}, {62, 42122}, {156, 8717}, {371, 43321}, {372, 43320}, {395, 42996}, {396, 42997}, {397, 42529}, {398, 42528}, {952, 12512}, {1125, 28182}, {1385, 28216}, {1483, 9778}, {1503, 32903}, {1587, 6519}, {1588, 6522}, {2777, 13392}, {3098, 32138}, {3411, 42792}, {3412, 42791}, {3579, 28224}, {3592, 42261}, {3594, 42260}, {3746, 15326}, {3819, 32137}, {4297, 5844}, {4324, 15325}, {5237, 42087}, {5238, 42088}, {5351, 11543}, {5352, 11542}, {5355, 35007}, {5563, 15172}, {5609, 16111}, {5663, 13348}, {5901, 31666}, {6053, 38726}, {6101, 14855}, {6102, 36987}, {6390, 7917}, {6409, 13925}, {6410, 13993}, {6425, 42216}, {6426, 42215}, {6427, 9541}, {6429, 42643}, {6430, 42644}, {6445, 43787}, {6446, 43788}, {6447, 19117}, {6448, 19116}, {6453, 42259}, {6454, 42258}, {6455, 43407}, {6456, 43408}, {6496, 23249}, {6497, 23259}, {6684, 28190}, {6781, 31652}, {7991, 34773}, {8960, 43209}, {10095, 17704}, {10222, 28212}, {10541, 21850}, {10575, 31834}, {10645, 42165}, {10646, 42164}, {10721, 15023}, {11495, 32153}, {11591, 14641}, {11801, 38729}, {12046, 13570}, {12121, 15021}, {13353, 43576}, {13391, 16625}, {13624, 28178}, {14094, 14677}, {14915, 32142}, {15012, 16881}, {15034, 20127}, {15044, 38728}, {15048, 22331}, {15054, 34153}, {15178, 28174}, {15513, 43291}, {16192, 38042}, {16808, 42590}, {16809, 42591}, {16962, 43207}, {16963, 43208}, {16964, 42497}, {16965, 42496}, {17502, 40273}, {17508, 42785}, {17712, 30522}, {17852, 43323}, {18510, 43884}, {18512, 43883}, {18907, 22332}, {20125, 22250}, {20190, 29181}, {22236, 42091}, {22238, 42090}, {22251, 38790}, {22676, 32448}, {22791, 30389}, {23235, 38731}, {23302, 42889}, {23303, 42888}, {28186, 31663}, {32423, 37853}, {35255, 42267}, {35256, 42266}, {36836, 42118}, {36843, 42117}, {36967, 43233}, {36968, 43232}, {38664, 38742}, {38668, 38766}, {38669, 38754}, {38674, 38778}, {38688, 38798}, {42099, 42163}, {42100, 42166}, {42108, 43102}, {42109, 43103}, {42115, 43307}, {42116, 43306}, {42121, 42160}, {42124, 42161}, {42136, 42599}, {42137, 42598}, {42144, 42159}, {42145, 42162}, {42150, 42625}, {42151, 42626}, {42157, 42913}, {42158, 42912}, {42429, 42936}, {42430, 42937}, {42431, 43372}, {42432, 43373}, {42433, 42924}, {42434, 42925}, {42488, 43401}, {42489, 43402}, {42641, 43568}, {42642, 43569}, {42795, 42939}, {42796, 42938}, {42896, 42966}, {42897, 42967}, {42916, 43465}, {42917, 43466}, {42922, 43777}, {42923, 43778}, {42944, 43417}, {42945, 43416}, {42970, 43005}, {42971, 43004}, {42990, 43109}, {42991, 43108}, {43110, 43645}, {43111, 43646}, {43292, 43643}, {43293, 43638}, {43304, 43635}, {43305, 43634}, {43463, 43648}, {43464, 43647}, {43483, 43546}, {43484, 43547}

X(44245) = midpoint of X(20) and X(140)
X(44245) = anticomplement of X(3856)

X(44246) = MIDPOINT OF X(20) AND X(186)

Barycentrics    (a^2 - b^2 - c^2)*(4*a^8 - 3*a^6*b^2 - 5*a^4*b^4 + 3*a^2*b^6 + b^8 - 3*a^6*c^2 + 12*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 4*b^6*c^2 - 5*a^4*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 + 3*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(44246) lies on these lines: {2, 3}, {97, 19651}, {127, 32456}, {1204, 44076}, {1272, 40996}, {1288, 2693}, {1503, 38788}, {1531, 14156}, {3184, 12091}, {4351, 15326}, {4354, 10149}, {5447, 35240}, {5894, 18439}, {6000, 7723}, {6699, 13851}, {6781, 14961}, {9730, 32411}, {9934, 10540}, {10620, 25740}, {11204, 18474}, {11468, 12278}, {11649, 37511}, {12041, 30522}, {13367, 43577}, {13376, 17704}, {13557, 14934}, {13568, 37472}, {13754, 16163}, {14516, 32138}, {14677, 22584}, {15055, 25739}, {15075, 16306}, {15905, 16303}, {17702, 21663}, {18400, 37853}, {18430, 23332}, {18914, 43807}, {20299, 24572}, {21659, 43604}, {22115, 38723}, {32110, 32282}, {32710, 44062}, {35254, 35257}

X(44246) = midpoint of X(20) and X(186)
X(44246) = anticomplement of X(23323)
X(44246) = circumcircle-inverse of X(12084)

X(44247) = MIDPOINT OF X(20) AND X(235)

Barycentrics    (a^2 - b^2 - c^2)*(6*a^8 - 5*a^6*b^2 - 7*a^4*b^4 + 5*a^2*b^6 + b^8 - 5*a^6*c^2 + 22*a^4*b^2*c^2 - 5*a^2*b^4*c^2 - 4*b^6*c^2 - 7*a^4*c^4 - 5*a^2*b^2*c^4 + 6*b^4*c^4 + 5*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(44247) lies on these lines: {2, 3}, {1192, 41588}, {1204, 3564}, {1352, 8567}, {3532, 15069}, {5893, 5972}, {5894, 9306}, {5907, 13416}, {6146, 16163}, {6225, 8780}, {6776, 27082}, {7745, 40349}, {9307, 30262}, {9820, 43577}, {11245, 43601}, {11438, 13142}, {11442, 43903}, {12235, 16270}, {12429, 18931}, {12512, 37613}, {15074, 37511}, {15647, 22966}, {16111, 20771}, {19126, 23326}, {22581, 32223}, {31802, 37497}, {31831, 32138}, {32820, 40996}, {38726, 40647}

X(44247) = midpoint of X(20) and X(235)

X(44248) = MIDPOINT OF X(20) AND X(297)

Barycentrics    (a^2 - b^2 - c^2)*(6*a^10 - 3*a^8*b^2 - 4*a^6*b^4 - 6*a^4*b^6 + 6*a^2*b^8 + b^10 - 3*a^8*c^2 + 8*a^6*b^2*c^2 + 6*a^4*b^4*c^2 - 8*a^2*b^6*c^2 - 3*b^8*c^2 - 4*a^6*c^4 + 6*a^4*b^2*c^4 + 4*a^2*b^4*c^4 + 2*b^6*c^4 - 6*a^4*c^6 - 8*a^2*b^2*c^6 + 2*b^4*c^6 + 6*a^2*c^8 - 3*b^2*c^8 + c^10) : :

X(442) lies on these lines: {2, 3}, {32, 41369}, {74, 2867}, {122, 15448}, {187, 3184}, {525, 42658}, {542, 40996}, {1294, 32646}, {1503, 15526}, {1990, 9530}, {3098, 41008}, {3793, 40948}, {6390, 16163}, {6776, 34815}, {10991, 34109}, {15311, 42671}, {15312, 41204}, {39874, 40995}

X(44248) = midpoint of X(20) and X(297)

X(44249) = MIDPOINT OF X(20) AND X(378)

Barycentrics    (a^2 - b^2 - c^2)*(4*a^8 - 3*a^6*b^2 - 5*a^4*b^4 + 3*a^2*b^6 + b^8 - 3*a^6*c^2 + 6*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 4*b^6*c^2 - 5*a^4*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 + 3*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(44249) lies on these lines: {2, 3}, {49, 18442}, {113, 10192}, {216, 6781}, {343, 17702}, {394, 4549}, {516, 24301}, {569, 13568}, {577, 19220}, {1060, 15326}, {1062, 15338}, {2781, 9967}, {3098, 16789}, {3284, 14836}, {3581, 41588}, {3796, 4846}, {3917, 12358}, {5562, 35240}, {5889, 43595}, {5894, 10575}, {6146, 7689}, {6247, 11750}, {7706, 37649}, {7723, 34153}, {8717, 20725}, {9019, 37511}, {10317, 15048}, {10610, 34798}, {10634, 42088}, {10635, 42087}, {10897, 42259}, {10898, 42258}, {11003, 34796}, {11440, 34224}, {11472, 31383}, {11597, 20127}, {11793, 32903}, {12134, 34785}, {12162, 34782}, {12163, 19467}, {12359, 21659}, {13367, 22660}, {13403, 41587}, {13470, 32210}, {13491, 31807}, {13567, 32110}, {14675, 23240}, {14983, 38699}, {15062, 16659}, {15063, 44110}, {16165, 38726}, {18438, 35257}, {18457, 42216}, {18459, 42215}, {18468, 42118}, {18470, 42117}, {19129, 21850}, {19131, 29181}, {22165, 32275}, {22815, 36966}, {23292, 39242}, {26881, 32111}, {31802, 37472}, {31804, 34783}, {32423, 41730}

X(44249) = midpoint of X(20) and X(378)

X(44250) = MIDPOINT OF X(20) AND X(383)

Barycentrics    Sqrt[3]*(4*a^8 - 15*a^6*b^2 + 13*a^4*b^4 - a^2*b^6 - b^8 - 15*a^6*c^2 + 10*a^4*b^2*c^2 + 5*a^2*b^4*c^2 + 4*b^6*c^2 + 13*a^4*c^4 + 5*a^2*b^2*c^4 - 6*b^4*c^4 - a^2*c^6 + 4*b^2*c^6 - c^8) + 2*(a^2 + b^2 + c^2)*(8*a^4 - 7*a^2*b^2 - b^4 - 7*a^2*c^2 + 2*b^2*c^2 - c^4)*S : :

X(44250) lies on these lines: {2, 3}, {14, 21159}, {16, 5474}, {62, 22843}, {182, 42942}, {299, 36995}, {395, 13349}, {396, 9735}, {511, 25179}, {617, 3564}, {1296, 34376}, {1350, 42625}, {5085, 42626}, {5321, 6774}, {5479, 6672}, {5865, 42151}, {5979, 21166}, {6036, 31710}, {6108, 23698}, {11543, 13102}, {14538, 42528}, {14539, 16529}, {14541, 42433}, {20425, 42118}, {20426, 42913}, {21156, 23005}, {21157, 36970}, {21401, 42791}, {32553, 38749}, {33517, 36756}

X(44250) = midpoint of X(20) and X(383)

X(44251) = MIDPOINT OF X(20) AND X(384)

Barycentrics    4*a^8 - a^6*b^2 + a^4*b^4 - 3*a^2*b^6 - b^8 - a^6*c^2 - 5*a^2*b^4*c^2 + 2*b^6*c^2 + a^4*c^4 - 5*a^2*b^2*c^4 - 2*b^4*c^4 - 3*a^2*c^6 + 2*b^2*c^6 - c^8 : :

X(44251) lies on these lines: {2, 3}, {141, 9873}, {698, 11257}, {736, 5188}, {1350, 36998}, {2794, 7873}, {3098, 6393}, {5305, 43453}, {5976, 38749}, {7738, 40825}, {7759, 30270}, {7767, 9862}, {7787, 21850}, {7789, 43460}, {9983, 32521}, {12110, 29181}, {14712, 35456}, {14810, 32152}, {15048, 38905}, {16111, 38650}, {16163, 38641}, {20065, 33878}, {24466, 38646}, {32134, 40238}, {32476, 32516}, {32830, 39874}, {33706, 35700}, {38642, 38738}, {38643, 38761}, {38644, 38773}, {38651, 38805}

X(44251) = midpoint of X(20) and X(384)

X(44252) = MIDPOINT OF X(20) AND X(401)

Barycentrics    4*a^12 - 9*a^10*b^2 + 7*a^8*b^4 - 6*a^6*b^6 + 6*a^4*b^8 - a^2*b^10 - b^12 - 9*a^10*c^2 + 16*a^8*b^2*c^2 - 2*a^6*b^4*c^2 - 4*a^4*b^6*c^2 - 5*a^2*b^8*c^2 + 4*b^10*c^2 + 7*a^8*c^4 - 2*a^6*b^2*c^4 - 4*a^4*b^4*c^4 + 6*a^2*b^6*c^4 - 7*b^8*c^4 - 6*a^6*c^6 - 4*a^4*b^2*c^6 + 6*a^2*b^4*c^6 + 8*b^6*c^6 + 6*a^4*c^8 - 5*a^2*b^2*c^8 - 7*b^4*c^8 - a^2*c^10 + 4*b^2*c^10 - c^12 : :

X(44252) lies on these lines: {2, 3}, {511, 34980}, {1294, 2715}, {1503, 1632}, {1975, 44141}, {3284, 9530}, {3564, 39352}, {6527, 39874}, {6530, 23583}, {10605, 36998}, {16163, 43952}, {36988, 42329}

X(44252) = midpoint of X(20) and X(401)

X(44253) = MIDPOINT OF X(21) AND X(28)

Barycentrics    a*(a + b)*(a + c)*(a^7 - a^6*b - a^5*b^2 + a^4*b^3 - a^3*b^4 + a^2*b^5 + a*b^6 - b^7 - a^6*c - a^5*b*c + a^4*b^2*c + a*b^5*c - a^5*c^2 + a^4*b*c^2 + 2*a^3*b^2*c^2 - 3*a^2*b^3*c^2 - a*b^4*c^2 + 2*b^5*c^2 + a^4*c^3 - 3*a^2*b^2*c^3 - 2*a*b^3*c^3 - b^4*c^3 - a^3*c^4 - a*b^2*c^4 - b^3*c^4 + a^2*c^5 + a*b*c^5 + 2*b^2*c^5 + a*c^6 - c^7) : :

X(44253) lies on these lines: {2, 3}, {110, 24475}, {229, 24470}, {270, 18455}, {1780, 41697}, {2328, 16139}, {2360, 33858}, {16164, 18180}, {17188, 33592}, {39772, 41608}

X(44253) = midpoint of X(21) and X(28)

X(44254) = MIDPOINT OF X(21) AND X(140)

Barycentrics    6*a^7 - 6*a^6*b - 13*a^5*b^2 + 13*a^4*b^3 + 8*a^3*b^4 - 8*a^2*b^5 - a*b^6 + b^7 - 6*a^6*c + 2*a^5*b*c + a^4*b^2*c + 3*a^3*b^3*c + 6*a^2*b^4*c - 5*a*b^5*c - b^6*c - 13*a^5*c^2 + a^4*b*c^2 + 12*a^3*b^2*c^2 + 2*a^2*b^3*c^2 + a*b^4*c^2 - 3*b^5*c^2 + 13*a^4*c^3 + 3*a^3*b*c^3 + 2*a^2*b^2*c^3 + 10*a*b^3*c^3 + 3*b^4*c^3 + 8*a^3*c^4 + 6*a^2*b*c^4 + a*b^2*c^4 + 3*b^3*c^4 - 8*a^2*c^5 - 5*a*b*c^5 - 3*b^2*c^5 - a*c^6 - b*c^6 + c^7 : :

X(44254) lies on these lines: {2, 3}, {191, 38028}, {2771, 13392}, {5426, 5690}, {5844, 35016}, {5901, 22937}, {10165, 22936}, {10543, 11545}, {21677, 34352}, {37737, 41542}

X(44254) = midpoint of X(21) and X(140)

X(44255) = MIDPOINT OF X(21) AND X(376)

Barycentrics    8*a^7 - 8*a^6*b - 15*a^5*b^2 + 15*a^4*b^3 + 6*a^3*b^4 - 6*a^2*b^5 + a*b^6 - b^7 - 8*a^6*c - 2*a^5*b*c - a^4*b^2*c + 4*a^3*b^3*c + 8*a^2*b^4*c - 2*a*b^5*c + b^6*c - 15*a^5*c^2 - a^4*b*c^2 + 16*a^3*b^2*c^2 - 2*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 + 15*a^4*c^3 + 4*a^3*b*c^3 - 2*a^2*b^2*c^3 + 4*a*b^3*c^3 - 3*b^4*c^3 + 6*a^3*c^4 + 8*a^2*b*c^4 - a*b^2*c^4 - 3*b^3*c^4 - 6*a^2*c^5 - 2*a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :

X(44255) lies on these lines: {2, 3}, {541, 16164}, {553, 13151}, {3058, 5427}, {3189, 34718}, {3579, 10543}, {3649, 13624}, {3650, 4511}, {3653, 11281}, {3655, 16139}, {4677, 10268}, {5441, 35242}, {7987, 16113}, {10122, 37585}, {11237, 35250}, {12702, 15174}, {17502, 38033}, {18253, 18481}, {21677, 28204}, {28194, 35016}, {35459, 41549}

X(44255) = midpoint of X(21) and X(376)

X(44256) = MIDPOINT OF X(21) AND X(377)

Barycentrics    a^5*b^2 - a^4*b^3 - 2*a^3*b^4 + 2*a^2*b^5 + a*b^6 - b^7 + 6*a^5*b*c - a^4*b^2*c - 10*a^3*b^3*c + 4*a*b^5*c + b^6*c + a^5*c^2 - a^4*b*c^2 - 12*a^3*b^2*c^2 - 14*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 - a^4*c^3 - 10*a^3*b*c^3 - 14*a^2*b^2*c^3 - 8*a*b^3*c^3 - 3*b^4*c^3 - 2*a^3*c^4 - a*b^2*c^4 - 3*b^3*c^4 + 2*a^2*c^5 + 4*a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :

X(44256) lies on these lines: {2, 3}, {7, 11684}, {10, 10122}, {12, 5302}, {63, 10404}, {224, 33857}, {518, 8261}, {960, 3649}, {1259, 10198}, {1837, 3826}, {3647, 4292}, {3683, 31936}, {3841, 4304}, {3925, 10543}, {4313, 33108}, {5427, 24953}, {5441, 41859}, {5730, 16137}, {5745, 41547}, {5784, 17637}, {6598, 37723}, {6701, 21616}, {8583, 26725}, {9710, 19860}, {11031, 21674}, {11064, 25526}, {11281, 19861}, {15174, 31419}, {15823, 41542}, {24541, 37722}, {24982, 34501}, {26531, 27483}, {31446, 37719}, {40661, 41571}

X(44256) = midpoint of X(21) and X(377)

X(44257) = MIDPOINT OF X(21) AND X(381)

Barycentrics    2*a^7 - 2*a^6*b - 6*a^5*b^2 + 6*a^4*b^3 + 6*a^3*b^4 - 6*a^2*b^5 - 2*a*b^6 + 2*b^7 - 2*a^6*c + 4*a^5*b*c + 2*a^4*b^2*c + a^3*b^3*c + 2*a^2*b^4*c - 5*a*b^5*c - 2*b^6*c - 6*a^5*c^2 + 2*a^4*b*c^2 + 4*a^3*b^2*c^2 + 4*a^2*b^3*c^2 + 2*a*b^4*c^2 - 6*b^5*c^2 + 6*a^4*c^3 + a^3*b*c^3 + 4*a^2*b^2*c^3 + 10*a*b^3*c^3 + 6*b^4*c^3 + 6*a^3*c^4 + 2*a^2*b*c^4 + 2*a*b^2*c^4 + 6*b^3*c^4 - 6*a^2*c^5 - 5*a*b*c^5 - 6*b^2*c^5 - 2*a*c^6 - 2*b*c^6 + 2*c^7 : :

X(44257) lies on these lines: {2, 3}, {191, 38021}, {499, 11544}, {1125, 22798}, {2771, 3742}, {3582, 3649}, {3584, 10543}, {3647, 9955}, {3652, 8227}, {3656, 3899}, {5441, 5560}, {6701, 26202}, {10056, 15174}, {10072, 16137}, {10171, 34126}, {10199, 33668}, {11281, 38022}, {11684, 18493}, {16139, 31162}, {16140, 23708}, {16141, 37692}, {18253, 22791}, {19919, 33592}, {25055, 33858}, {28204, 35016}, {38114, 38140}

X(44257) = midpoint of X(21) and X(381)

X(44258) = MIDPOINT OF X(21) AND X(382)

Barycentrics    2*a^7 - 2*a^6*b - 2*a^5*b^2 + 2*a^4*b^3 - 2*a^3*b^4 + 2*a^2*b^5 + 2*a*b^6 - 2*b^7 - 2*a^6*c - 4*a^5*b*c - 2*a^4*b^2*c + a^3*b^3*c + 2*a^2*b^4*c + 3*a*b^5*c + 2*b^6*c - 2*a^5*c^2 - 2*a^4*b*c^2 + 4*a^3*b^2*c^2 - 4*a^2*b^3*c^2 - 2*a*b^4*c^2 + 6*b^5*c^2 + 2*a^4*c^3 + a^3*b*c^3 - 4*a^2*b^2*c^3 - 6*a*b^3*c^3 - 6*b^4*c^3 - 2*a^3*c^4 + 2*a^2*b*c^4 - 2*a*b^2*c^4 - 6*b^3*c^4 + 2*a^2*c^5 + 3*a*b*c^5 + 6*b^2*c^5 + 2*a*c^6 + 2*b*c^6 - 2*c^7 : :

X(44258) lies on these lines: {2, 3}, {79, 5561}, {758, 22793}, {1478, 15174}, {1479, 15935}, {1539, 2771}, {1699, 33858}, {2795, 22505}, {3583, 3649}, {3585, 5719}, {3678, 18480}, {5427, 10483}, {5441, 11374}, {5806, 16125}, {9581, 16118}, {11281, 38034}, {12679, 16159}, {16139, 41869}, {18483, 33592}, {19919, 22798}, {21677, 28174}, {28160, 35016}

X(44258) = midpoint of X(21) and X(382)

X(44259) = MIDPOINT OF X(22) AND X(24)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^12 - 2*a^10*b^2 - a^8*b^4 + 4*a^6*b^6 - a^4*b^8 - 2*a^2*b^10 + b^12 - 2*a^10*c^2 + 2*a^8*b^2*c^2 - 2*a^6*b^4*c^2 + 2*a^4*b^6*c^2 + 4*a^2*b^8*c^2 - 4*b^10*c^2 - a^8*c^4 - 2*a^6*b^2*c^4 - 6*a^4*b^4*c^4 - 2*a^2*b^6*c^4 + 7*b^8*c^4 + 4*a^6*c^6 + 2*a^4*b^2*c^6 - 2*a^2*b^4*c^6 - 8*b^6*c^6 - a^4*c^8 + 4*a^2*b^2*c^8 + 7*b^4*c^8 - 2*a^2*c^10 - 4*b^2*c^10 + c^12) : :

X(44259) lies on these lines: {2, 3}, {156, 8907}, {2781, 20771}, {2931, 10605}, {7723, 10117}, {9699, 14961}, {9932, 34783}, {12358, 40914}, {16165, 18445}, {25738, 33563}, {32048, 44076}

X(44259) = midpoint of X(22) and X(24)
X(44259) = harmonic center of circumcircle and tangential circle
X(44259) = center of circle {{X(22),X(24),PU(4)}}
X(44259) = tangential-circle-inverse of X(11810)
X(44259) = X(8069)-of-tangential-triangle if ABC is acute

X(44260) = MIDPOINT OF X(22) AND X(25)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^8 - 2*a^4*b^4 + b^8 + 4*a^4*b^2*c^2 + a^2*b^4*c^2 - 3*b^6*c^2 - 2*a^4*c^4 + a^2*b^2*c^4 + 4*b^4*c^4 - 3*b^2*c^6 + c^8) : :

X(44260) lies on these lines: {2, 3}, {182, 11746}, {184, 14984}, {1352, 10117}, {1383, 22121}, {1495, 37511}, {1660, 15582}, {2393, 19127}, {2781, 9306}, {2931, 4846}, {3060, 18449}, {5651, 13416}, {6776, 12310}, {9019, 11511}, {15080, 19129}, {15107, 18438}, {19126, 41579}, {19131, 35268}, {19220, 34481}, {21243, 36201}, {21849, 37827}, {26881, 40114}, {31804, 32048}

X(44260) = midpoint of X(22) and X(25)

X(44261) = MIDPOINT OF X(22) AND X(376)

Barycentrics    8*a^10 - 15*a^8*b^2 - 2*a^6*b^4 + 16*a^4*b^6 - 6*a^2*b^8 - b^10 - 15*a^8*c^2 + 4*a^6*b^2*c^2 + 4*a^4*b^4*c^2 + 4*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 + 4*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 + 16*a^4*c^6 + 4*a^2*b^2*c^6 - 2*b^4*c^6 - 6*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44261) lies on these lines: {2, 3}, {32, 14836}, {52, 8584}, {524, 37478}, {541, 16165}, {542, 16789}, {597, 37513}, {1495, 35254}, {3933, 6148}, {9019, 9730}, {11179, 37489}, {11430, 19924}, {11464, 40112}, {12022, 15360}, {13352, 19127}, {14805, 21850}, {15534, 17834}, {18317, 28724}, {18472, 42459}, {20423, 37506}, {22165, 34782}, {29181, 39242}, {30714, 31729}, {37853, 40291}

X(44261) = midpoint of X(22) and X(376)

X(44262) = MIDPOINT OF X(22) AND X(381)

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 - 4*a^6*b^2*c^2 + 5*a^4*b^4*c^2 + 5*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 + 5*a^4*b^2*c^4 - 4*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 5*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44262) lies on these lines: {2, 3}, {113, 33533}, {155, 15533}, {265, 15080}, {542, 19127}, {568, 15360}, {599, 15068}, {2781, 15067}, {3767, 18573}, {5305, 14836}, {5476, 9019}, {5609, 31744}, {5655, 11459}, {6795, 34209}, {6800, 32423}, {7998, 14643}, {9730, 32225}, {10264, 37638}, {10272, 15066}, {11438, 15361}, {11645, 34514}, {12161, 15534}, {13339, 15362}, {14852, 43273}, {14880, 39170}, {15072, 20126}, {16534, 40107}, {17702, 34513}, {21230, 32139}, {21357, 32063}

X(44262) = midpoint of X(22) and X(381)

X(44263) = MIDPOINT OF X(22) AND X(382)

Barycentrics    a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - a^8*c^2 + 4*a^6*b^2*c^2 - 3*a^4*b^4*c^2 - 3*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 3*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 + 2*a^4*c^6 - 3*a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44263) lies on these lines: {2, 3}, {49, 12278}, {146, 18550}, {156, 43831}, {184, 30522}, {265, 5890}, {1204, 13561}, {1511, 19479}, {1531, 5891}, {1539, 2781}, {3521, 6241}, {3583, 37729}, {4846, 18434}, {5654, 40111}, {5663, 18474}, {5944, 34785}, {5946, 7706}, {6000, 34514}, {6102, 9927}, {6288, 12111}, {7689, 34798}, {7699, 12121}, {7703, 20127}, {7728, 12281}, {9220, 38872}, {9703, 12383}, {9730, 13851}, {9826, 13364}, {10264, 10605}, {10574, 18394}, {10575, 11572}, {10606, 14677}, {10610, 32365}, {10733, 12228}, {10749, 14983}, {10984, 13470}, {11472, 32316}, {12041, 19506}, {12042, 39847}, {12161, 12293}, {12233, 12370}, {12902, 15087}, {13403, 34114}, {13491, 18381}, {13630, 18379}, {14356, 18380}, {14644, 15053}, {15026, 43865}, {15043, 43821}, {15111, 20957}, {15800, 32338}, {17702, 18388}, {18356, 34783}, {18383, 40647}, {18430, 25739}, {18435, 41171}, {18445, 32423}, {18513, 37697}, {18514, 37696}, {19127, 29012}, {20299, 43577}, {20424, 36747}, {21400, 43816}, {21659, 32046}, {22802, 22804}, {32767, 43604}, {33813, 39818}, {36753, 43575}

X(44263) = midpoint of X(22) and X(382)
X(44263) = reflection of X(18570) in X(5)
X(44263) = X(18570)-of-Johnson-triangle
X(44263) = orthocentroidal-circle-inverse of X(18403)
X(44263) = {X(2),X(4)}-harmonic conjugate of X(18403)
X(44263) = {X(3),X(4)}-harmonic conjugate of X(18377)

X(44264) = MIDPOINT OF X(23) AND X(140)

Barycentrics    6*a^10 - 13*a^8*b^2 + 2*a^6*b^4 + 12*a^4*b^6 - 8*a^2*b^8 + b^10 - 13*a^8*c^2 + 6*a^6*b^2*c^2 - 7*a^4*b^4*c^2 + 17*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 7*a^4*b^2*c^4 - 18*a^2*b^4*c^4 + 2*b^6*c^4 + 12*a^4*c^6 + 17*a^2*b^2*c^6 + 2*b^4*c^6 - 8*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44264) lies on these lines: {2, 3}, {143, 40632}, {511, 13392}, {3564, 32218}, {7286, 38458}, {10610, 20193}, {13353, 43579}, {14979, 33505}, {22251, 37496}, {29012, 40685}, {32217, 34380}, {32223, 32423}

X(44264) = midpoint of X(23) and X(140)
X(44264) = X(468)-of-Napoleon-Feuerbach-triangle

X(44265) = MIDPOINT OF X(23) AND X(376)

Barycentrics    8*a^10 - 15*a^8*b^2 - 2*a^6*b^4 + 16*a^4*b^6 - 6*a^2*b^8 - b^10 - 15*a^8*c^2 + 22*a^6*b^2*c^2 - 14*a^4*b^4*c^2 + 4*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 14*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 + 16*a^4*c^6 + 4*a^2*b^2*c^6 - 2*b^4*c^6 - 6*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44265) lies on these lines: {2, 3}, {187, 3018}, {511, 15303}, {524, 3581}, {541, 1495}, {542, 32110}, {568, 8584}, {597, 14805}, {1384, 16303}, {1503, 20126}, {1511, 40112}, {2080, 14934}, {2777, 32267}, {3580, 15361}, {5476, 39242}, {5655, 35266}, {7728, 15448}, {8547, 11179}, {8705, 40280}, {9730, 11649}, {10564, 19924}, {12121, 32269}, {14653, 16320}, {15462, 32217}, {15534, 37489}, {16111, 32237}, {16279, 16324}, {16760, 31173}, {17702, 32225}, {18316, 34209}, {18317, 18876}, {21158, 34314}, {21159, 34313}, {22151, 37496}, {32111, 32124}, {32417, 42671}

X(44265) = midpoint of X(23) and X(376)
X(44265) = circumcircle-inverse of X(31861)
X(44265) = nine-point-circle-inverse of X(7579)
X(44265) = orthocentroidal-circle-inverse of X(39484)
X(44265) = {X(2),X(4)}-harmonic conjugate of X(39484)

X(44266) = MIDPOINT OF X(23) AND X(381)

Barycentrics    2*a^10 - 6*a^8*b^2 + 4*a^6*b^4 + 4*a^4*b^6 - 6*a^2*b^8 + 2*b^10 - 6*a^8*c^2 - 8*a^6*b^2*c^2 + a^4*b^4*c^2 + 19*a^2*b^6*c^2 - 6*b^8*c^2 + 4*a^6*c^4 + a^4*b^2*c^4 - 26*a^2*b^4*c^4 + 4*b^6*c^4 + 4*a^4*c^6 + 19*a^2*b^2*c^6 + 4*b^4*c^6 - 6*a^2*c^8 - 6*b^2*c^8 + 2*c^10 : :

X(44266) lies on these lines: {2, 3}, {511, 25566}, {523, 11622}, {524, 19140}, {541, 15361}, {542, 32217}, {2682, 32219}, {3581, 10706}, {3582, 7286}, {3584, 5160}, {5309, 16308}, {5476, 8705}, {5655, 15360}, {5663, 32225}, {9140, 15362}, {10113, 32237}, {10272, 40112}, {15068, 15533}, {15448, 34153}, {16252, 41149}, {17702, 32267}

X(44266) = midpoint of X(23) and X(381)
X(44266) = {X(13626),X(13627)}-harmonic conjugate of X(5)

X(44267) = MIDPOINT OF X(23) AND X(382)

Barycentrics    2*a^10 - 2*a^8*b^2 - 4*a^6*b^4 + 4*a^4*b^6 + 2*a^2*b^8 - 2*b^10 - 2*a^8*c^2 + 16*a^6*b^2*c^2 - 7*a^4*b^4*c^2 - 13*a^2*b^6*c^2 + 6*b^8*c^2 - 4*a^6*c^4 - 7*a^4*b^2*c^4 + 22*a^2*b^4*c^4 - 4*b^6*c^4 + 4*a^4*c^6 - 13*a^2*b^2*c^6 - 4*b^4*c^6 + 2*a^2*c^8 + 6*b^2*c^8 - 2*c^10 : :

X(44267) lies on these lines: {2, 3}, {323, 38789}, {511, 1539}, {1154, 16105}, {1503, 9976}, {1531, 41673}, {1533, 12295}, {3521, 16881}, {3564, 16176}, {3581, 10721}, {3583, 7286}, {3585, 5160}, {5270, 10149}, {5446, 43392}, {7748, 16308}, {10113, 14915}, {12112, 12902}, {13382, 43585}, {13851, 16270}, {15118, 29012}, {15125, 15647}, {16534, 40111}, {32110, 34584}, {32111, 32423}, {32220, 32255}

X(44267) = midpoint of X(23) and X(382)

X(44268) = MIDPOINT OF X(24) AND X(376)

Barycentrics    8*a^10 - 15*a^8*b^2 - 2*a^6*b^4 + 16*a^4*b^6 - 6*a^2*b^8 - b^10 - 15*a^8*c^2 + 36*a^6*b^2*c^2 - 24*a^4*b^4*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 24*a^4*b^2*c^4 + 12*a^2*b^4*c^4 - 2*b^6*c^4 + 16*a^4*c^6 - 2*b^4*c^6 - 6*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44268) lies on these lines: {2, 3}, {541, 20771}, {5085, 10169}, {8584, 19161}, {12134, 43903}, {13567, 16163}, {16270, 27365}, {22660, 43898}, {23332, 38727}, {31804, 43601}

X(44268) = midpoint of X(24) and X(376)

X(44269) = MIDPOINT OF X(24) AND X(378)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 8*a^6*b^2*c^2 - 6*a^4*b^4*c^2 + b^8*c^2 + 2*a^6*c^4 - 6*a^4*b^2*c^4 + 10*a^2*b^4*c^4 - 2*b^6*c^4 + 2*a^4*c^6 - 2*b^4*c^6 - 3*a^2*c^8 + b^2*c^8 + c^10) : :

X(44269) lies on these lines: {2, 3}, {74, 18532}, {230, 21397}, {232, 19220}, {974, 38534}, {1204, 43896}, {1619, 12112}, {1853, 19457}, {1993, 15463}, {2904, 6102}, {3043, 3167}, {3060, 15472}, {8537, 13482}, {9938, 14516}, {11550, 32607}, {12111, 19908}, {12140, 12901}, {12290, 32321}, {13171, 35450}, {15473, 25564}, {20771, 35264}

X(44269) = midpoint of X(24) and X(378)
X(44269) = X(45179)-of-anti-Euler-triangle

X(44270) = MIDPOINT OF X(24) AND X(381)

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 - 3*a^4*b^4*c^2 + 9*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 3*a^4*b^2*c^4 - 12*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 9*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44270) lies on these lines: {2, 3}, {1993, 10272}, {3060, 14643}, {9707, 43575}, {10264, 26958}, {11455, 15061}, {11550, 20304}, {14576, 18487}, {15534, 19139}, {26882, 43821}, {32423, 35264}, {34785, 43865}, {34796, 38789}

X(44270) = midpoint of X(24) and X(381)

X(44271) = MIDPOINT OF X(24) AND X(382)

Barycentrics    a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - a^8*c^2 + 8*a^6*b^2*c^2 - 3*a^4*b^4*c^2 - 7*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 3*a^4*b^2*c^4 + 12*a^2*b^4*c^4 - 2*b^6*c^4 + 2*a^4*c^6 - 7*a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44271) lies on these lines: {2, 3}, {64, 10264}, {155, 22972}, {265, 12290}, {569, 15807}, {1533, 11750}, {1539, 10263}, {2883, 12370}, {3521, 3567}, {5889, 7728}, {6102, 22802}, {6288, 11439}, {8548, 36990}, {10113, 18381}, {11550, 18379}, {13203, 21970}, {13423, 15800}, {13474, 34514}, {13491, 18390}, {15072, 43821}, {15811, 19458}, {18356, 18439}, {18383, 31978}, {18474, 32137}, {18550, 43891}, {22968, 43577}, {26883, 30522}, {32111, 44076}

X(44271) = midpoint of X(24) and X(382)

X(44272) = MIDPOINT OF X(25) AND X(186)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^10 - 6*a^8*b^2 + 4*a^6*b^4 + 4*a^4*b^6 - 6*a^2*b^8 + 2*b^10 - 6*a^8*c^2 + 16*a^6*b^2*c^2 - 17*a^4*b^4*c^2 + 10*a^2*b^6*c^2 - 3*b^8*c^2 + 4*a^6*c^4 - 17*a^4*b^2*c^4 + 4*a^2*b^4*c^4 + b^6*c^4 + 4*a^4*c^6 + 10*a^2*b^2*c^6 + b^4*c^6 - 6*a^2*c^8 - 3*b^2*c^8 + 2*c^10) : :

X(44272) lies on these lines: {2, 3}, {184, 16227}, {974, 1495}, {1511, 44084}, {2493, 14581}, {5140, 38611}, {5926, 41357}, {11062, 40135}, {12584, 15471}, {13754, 20772}, {14984, 44102}

X(44272) = midpoint of X(25) and X(186)

X(44273) = MIDPOINT OF X(25) AND X(376)

Barycentrics    8*a^10 - 15*a^8*b^2 - 2*a^6*b^4 + 16*a^4*b^6 - 6*a^2*b^8 - b^10 - 15*a^8*c^2 + 40*a^6*b^2*c^2 - 32*a^4*b^4*c^2 + 4*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 32*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 + 16*a^4*c^6 + 4*a^2*b^2*c^6 - 2*b^4*c^6 - 6*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44273) lies on these lines: {2, 3}, {389, 8584}, {524, 11438}, {541, 20772}, {542, 8263}, {597, 11430}, {599, 37487}, {1192, 15533}, {2393, 16836}, {3053, 34288}, {9730, 14984}, {9786, 15534}, {10564, 21850}, {11179, 37475}, {11180, 18931}, {12022, 43804}, {14389, 15051}, {14836, 14910}, {16163, 37648}, {19136, 37480}, {20423, 37497}, {23328, 36201}, {38110, 39242}, {43601, 43897}

X(44273) = midpoint of X(25) and X(376)

X(44274) = MIDPOINT OF X(25) AND X(378)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 8*a^6*b^2*c^2 - 7*a^4*b^4*c^2 + 2*a^2*b^6*c^2 + 2*a^6*c^4 - 7*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - b^6*c^4 + 2*a^4*c^6 + 2*a^2*b^2*c^6 - b^4*c^6 - 3*a^2*c^8 + c^10) : :

X(44274) lies on these lines: {2, 3}, {32, 39176}, {1511, 44080}, {1843, 10564}, {1974, 37470}, {2393, 11430}, {2781, 11438}, {2790, 3455}, {6403, 37477}, {8541, 13352}, {9019, 37480}, {9730, 44102}, {10986, 40115}, {11464, 40114}, {12168, 37645}, {12294, 32110}, {15655, 41758}, {16836, 19127}, {19124, 39242}, {19128, 40280}

X(44274) = midpoint of X(25) and X(378)

X(44275) = MIDPOINT OF X(25) AND X(381)

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 - 4*a^6*b^2*c^2 - 4*a^4*b^4*c^2 + 14*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 4*a^4*b^2*c^4 - 22*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 14*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44275) lies on these lines: {2, 3}, {113, 34417}, {155, 15534}, {399, 37644}, {524, 15068}, {541, 11438}, {542, 19136}, {567, 40114}, {568, 5655}, {576, 16534}, {1533, 37470}, {1989, 3767}, {2393, 5476}, {3199, 18487}, {4550, 32223}, {5609, 34319}, {5642, 13352}, {5648, 5654}, {6759, 43573}, {8584, 12161}, {9220, 43620}, {10264, 37643}, {10272, 37645}, {10602, 14848}, {11004, 20125}, {11179, 18374}, {11459, 15360}, {12228, 44080}, {15030, 32225}, {15533, 17814}, {16657, 35266}, {18952, 26883}, {23325, 36201}, {26937, 32137}, {31860, 40909}

X(44275) = midpoint of X(25) and X(381)

X(44276) = MIDPOINT OF X(25) AND X(382)

Barycentrics    a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - a^8*c^2 + 12*a^6*b^2*c^2 - 4*a^4*b^4*c^2 - 10*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 4*a^4*b^2*c^4 + 18*a^2*b^4*c^4 - 2*b^6*c^4 + 2*a^4*c^6 - 10*a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44276) lies on these lines: {2, 3}, {1353, 41735}, {1478, 9629}, {1498, 12370}, {1539, 9973}, {2790, 22515}, {2883, 12161}, {4846, 5946}, {5446, 22802}, {5878, 6102}, {6225, 18951}, {6759, 12897}, {9927, 13474}, {10575, 18952}, {11381, 32140}, {11744, 12236}, {12174, 43588}, {12290, 25738}, {12293, 15811}, {13419, 22661}, {13491, 39571}, {13598, 31815}, {14677, 18933}, {14915, 18390}, {18382, 36201}, {18445, 32111}, {18474, 32062}, {19136, 29012}, {21850, 34777}, {22660, 34966}, {30522, 31383}

X(44276) = midpoint of X(25) and X(382)

X(44277) = MIDPOINT OF X(26) AND X(140)

Barycentrics    6*a^10 - 13*a^8*b^2 + 2*a^6*b^4 + 12*a^4*b^6 - 8*a^2*b^8 + b^10 - 13*a^8*c^2 + 8*a^6*b^2*c^2 - 4*a^4*b^4*c^2 + 12*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 4*a^4*b^2*c^4 - 8*a^2*b^4*c^4 + 2*b^6*c^4 + 12*a^4*c^6 + 12*a^2*b^2*c^6 + 2*b^4*c^6 - 8*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44277) lies on these lines: {2, 3}, {1147, 19154}, {2883, 16775}, {3564, 10282}, {5907, 15448}, {5944, 13292}, {10619, 32225}, {12164, 35260}, {12241, 32223}, {12359, 34776}, {13142, 13367}, {16621, 32237}, {19357, 41588}

X(44277) = midpoint of X(26) and X(140)

X(44278) = MIDPOINT OF X(26) AND X(381)

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 - 2*a^6*b^2*c^2 + a^4*b^4*c^2 + 7*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 + a^4*b^2*c^4 - 8*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 7*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44278) lies on these lines: {2, 3}, {13, 11268}, {14, 11267}, {154, 32423}, {156, 539}, {265, 26881}, {394, 10272}, {542, 19154}, {2979, 14643}, {3582, 32047}, {3584, 8144}, {6759, 18356}, {8254, 10982}, {11265, 35823}, {11266, 35822}, {15806, 36747}, {19347, 32165}, {26883, 34826}, {35237, 40685}

X(44278) = midpoint of X(26) and X(381)

X(44279) = MIDPOINT OF X(26) AND X(382)

Barycentrics    a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - a^8*c^2 + 6*a^6*b^2*c^2 - 3*a^4*b^4*c^2 - 5*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 3*a^4*b^2*c^4 + 8*a^2*b^4*c^4 - 2*b^6*c^4 + 2*a^4*c^6 - 5*a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44279) lies on these lines: {2, 3}, {156, 17702}, {265, 6241}, {974, 10113}, {1514, 12134}, {1531, 10625}, {1539, 5876}, {1614, 10733}, {2777, 5449}, {3357, 13561}, {3521, 5890}, {3583, 32047}, {3585, 8144}, {4846, 18952}, {5663, 9927}, {5878, 32140}, {5895, 14852}, {6288, 15305}, {6759, 30522}, {7706, 10095}, {7728, 7731}, {10540, 12278}, {10574, 43821}, {10575, 13851}, {10721, 11440}, {11265, 35821}, {11266, 35820}, {11267, 19107}, {11268, 19106}, {11381, 34514}, {11449, 12121}, {11468, 20127}, {11598, 19506}, {11704, 15061}, {12279, 18394}, {12290, 18392}, {12293, 17824}, {12295, 21659}, {12897, 18388}, {12902, 34799}, {13403, 32046}, {13630, 18390}, {14643, 18504}, {14831, 18555}, {14915, 18383}, {18379, 18381}, {18418, 22816}, {19154, 29012}, {19479, 20773}, {26881, 40242}

X(44279) = midpoint of X(26) and X(382)
X(44279) = reflection of X(18377) in X(4)
X(44279) = reflection of X(18569) in X(18567)
X(44279) = complement of X(34350)
X(44279) = anticomplement of X(10226)
X(44279) = {X(4),X(20)}-harmonic conjugate of X(18403)

X(44280) = MIDPOINT OF X(186) AND X(376)

Barycentrics    8*a^10 - 15*a^8*b^2 - 2*a^6*b^4 + 16*a^4*b^6 - 6*a^2*b^8 - b^10 - 15*a^8*c^2 + 34*a^6*b^2*c^2 - 20*a^4*b^4*c^2 - 2*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 20*a^4*b^2*c^4 + 16*a^2*b^4*c^4 - 2*b^6*c^4 + 16*a^4*c^6 - 2*a^2*b^2*c^6 - 2*b^4*c^6 - 6*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44280) lies on these lines: {2, 3}, {542, 21663}, {1350, 32220}, {1495, 37853}, {1503, 15055}, {3060, 16227}, {3580, 16163}, {5023, 16306}, {6091, 16092}, {8584, 37473}, {11064, 15051}, {11693, 39083}, {15136, 43572}, {15311, 35266}, {15448, 20725}, {16111, 32111}, {16226, 32411}, {32110, 38726}, {38699, 38701}, {38702, 38718}

X(44280) = midpoint of X186) and X(376)

X(44281) = MIDPOINT OF X(186) AND X(378)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^10 - 6*a^8*b^2 + 4*a^6*b^4 + 4*a^4*b^6 - 6*a^2*b^8 + 2*b^10 - 6*a^8*c^2 + 16*a^6*b^2*c^2 - 11*a^4*b^4*c^2 - 2*a^2*b^6*c^2 + 3*b^8*c^2 + 4*a^6*c^4 - 11*a^4*b^2*c^4 + 16*a^2*b^4*c^4 - 5*b^6*c^4 + 4*a^4*c^6 - 2*a^2*b^2*c^6 - 5*b^4*c^6 - 6*a^2*c^8 + 3*b^2*c^8 + 2*c^10) : :

X(44281) lies on these lines: {2, 3}, {74, 34397}, {1112, 32110}, {1495, 12133}, {1503, 32607}, {1514, 13289}, {1968, 16308}, {2781, 21663}, {3003, 39176}, {3581, 15472}, {8705, 19124}, {11204, 44077}, {11438, 16227}, {11807, 25564}, {12294, 32217}, {15055, 19128}, {16013, 16659}, {22455, 40352}, {32113, 39871}

X(44281) = midpoint of X(186) and X(378)

X(44282) = MIDPOINT OF X(186) AND X(381)

Barycentrics    2*a^10 - 6*a^8*b^2 + 4*a^6*b^4 + 4*a^4*b^6 - 6*a^2*b^8 + 2*b^10 - 6*a^8*c^2 + 4*a^6*b^2*c^2 - 5*a^4*b^4*c^2 + 13*a^2*b^6*c^2 - 6*b^8*c^2 + 4*a^6*c^4 - 5*a^4*b^2*c^4 - 14*a^2*b^4*c^4 + 4*b^6*c^4 + 4*a^4*c^6 + 13*a^2*b^2*c^6 + 4*b^4*c^6 - 6*a^2*c^8 - 6*b^2*c^8 + 2*c^10 : :

X(44282) lies on these lines: {2, 3}, {524, 34155}, {1154, 32225}, {1495, 20304}, {1514, 14677}, {3580, 10272}, {3584, 10149}, {5099, 14693}, {5642, 40111}, {7746, 16308}, {8705, 38317}, {9140, 10540}, {11062, 18487}, {11649, 16776}, {12900, 32223}, {13391, 13857}, {14915, 34128}, {14993, 18883}, {15311, 16219}, {15362, 22115}, {15826, 25555}, {16310, 18285}, {16319, 34209}, {18583, 32113}, {24206, 32217}, {35265, 38724}, {38795, 41586}

X(44282) = midpoint of X(186) and X(381)

X(44283) = MIDPOINT OF X(186) AND X(382)

Barycentrics    2*a^10 - 2*a^8*b^2 - 4*a^6*b^4 + 4*a^4*b^6 + 2*a^2*b^8 - 2*b^10 - 2*a^8*c^2 + 12*a^6*b^2*c^2 - 5*a^4*b^4*c^2 - 11*a^2*b^6*c^2 + 6*b^8*c^2 - 4*a^6*c^4 - 5*a^4*b^2*c^4 + 18*a^2*b^4*c^4 - 4*b^6*c^4 + 4*a^4*c^6 - 11*a^2*b^2*c^6 - 4*b^4*c^6 + 2*a^2*c^8 + 6*b^2*c^8 - 2*c^10 : :

X(44283) lies on these lines: {2, 3}, {113, 40111}, {539, 38791}, {974, 13851}, {1531, 13391}, {1539, 11807}, {3585, 10149}, {5893, 12370}, {6000, 10113}, {10110, 22833}, {10264, 15311}, {10540, 10733}, {10688, 23956}, {11381, 18379}, {11455, 18430}, {12295, 30522}, {13321, 18550}, {21663, 34584}, {40647, 43865}

X(44283) = midpoint of X(186) and X(382)
X(44283) = center of the Vu pedal-centroidal circle of X(23)

X(44284) = MIDPOINT OF X(376) AND X(377)

Barycentrics    a^7 - a^6*b - 3*a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 - 3*a^2*b^5 - a*b^6 + b^7 - a^6*c - 16*a^5*b*c + a^4*b^2*c + 14*a^3*b^3*c + a^2*b^4*c + 2*a*b^5*c - b^6*c - 3*a^5*c^2 + a^4*b*c^2 + 2*a^3*b^2*c^2 + 2*a^2*b^3*c^2 + a*b^4*c^2 - 3*b^5*c^2 + 3*a^4*c^3 + 14*a^3*b*c^3 + 2*a^2*b^2*c^3 - 4*a*b^3*c^3 + 3*b^4*c^3 + 3*a^3*c^4 + a^2*b*c^4 + a*b^2*c^4 + 3*b^3*c^4 - 3*a^2*c^5 + 2*a*b*c^5 - 3*b^2*c^5 - a*c^6 - b*c^6 + c^7 : :

X(44284) lies on these lines: {2, 3}, {518, 3654}, {553, 37584}, {3579, 10056}, {3584, 35242}, {3587, 4654}, {3655, 11260}, {3656, 10179}, {4677, 30503}, {4745, 43151}, {4995, 35238}, {5434, 35239}, {10072, 13624}, {10178, 26446}, {10525, 35202}, {16192, 26487}, {37496, 37685}

X(44284) = midpoint of X(376) and X(377)

X(44285) = MIDPOINT OF X(376) AND X(378)

Barycentrics    8*a^10 - 15*a^8*b^2 - 2*a^6*b^4 + 16*a^4*b^6 - 6*a^2*b^8 - b^10 - 15*a^8*c^2 + 28*a^6*b^2*c^2 - 8*a^4*b^4*c^2 - 8*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 8*a^4*b^2*c^4 + 28*a^2*b^4*c^4 - 2*b^6*c^4 + 16*a^4*c^6 - 8*a^2*b^2*c^6 - 2*b^4*c^6 - 6*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44285) lies on these lines: {2, 3}, {141, 16163}, {541, 18475}, {2777, 13394}, {2781, 15303}, {5063, 14836}, {5092, 37853}, {8584, 14831}, {9019, 36987}, {10564, 35254}, {10605, 11179}, {10606, 43273}, {11202, 35266}, {11440, 31804}, {15472, 19129}

X(44285) = midpoint of X(376) and X(378)

X(44286) = MIDPOINT OF X(377) AND X(382)

Barycentrics    4*a^7 - 4*a^6*b - 5*a^5*b^2 + 5*a^4*b^3 - 2*a^3*b^4 + 2*a^2*b^5 + 3*a*b^6 - 3*b^7 - 4*a^6*c - 8*a^5*b*c - 3*a^4*b^2*c + 4*a^2*b^4*c + 8*a*b^5*c + 3*b^6*c - 5*a^5*c^2 - 3*a^4*b*c^2 + 8*a^3*b^2*c^2 - 6*a^2*b^3*c^2 - 3*a*b^4*c^2 + 9*b^5*c^2 + 5*a^4*c^3 - 6*a^2*b^2*c^3 - 16*a*b^3*c^3 - 9*b^4*c^3 - 2*a^3*c^4 + 4*a^2*b*c^4 - 3*a*b^2*c^4 - 9*b^3*c^4 + 2*a^2*c^5 + 8*a*b*c^5 + 9*b^2*c^5 + 3*a*c^6 + 3*b*c^6 - 3*c^7 : :

X(44286) lies on these lines: {2, 3}, {518, 39884}, {3874, 31673}, {5557, 37723}, {5761, 10248}, {5806, 26201}, {10404, 12433}, {10572, 15935}, {17098, 37730}, {18482, 25557}

X(44286) = midpoint of X(377) and X(382)

X(44287) = MIDPOINT OF X(377) AND X(381)

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 8*a^6*b^2*c^2 - a^4*b^4*c^2 - a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - a^4*b^2*c^4 + 8*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 - a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44287) lies on these lines: {2, 3}, {6, 10264}, {156, 18488}, {182, 20113}, {265, 7703}, {541, 18388}, {1511, 3818}, {2781, 5476}, {3574, 32138}, {5640, 15061}, {5655, 15305}, {5890, 20126}, {5891, 13857}, {6699, 19130}, {7699, 7728}, {7706, 12041}, {8548, 15534}, {9140, 15033}, {9143, 9703}, {10168, 19127}, {10546, 38794}, {11424, 13561}, {11430, 34514}, {11645, 18475}, {11935, 14683}, {12163, 20424}, {14643, 16261}, {18356, 37472}, {20299, 43573}, {21230, 37498}, {29012, 34513}, {31840, 41731}

X(44287) = midpoint of X(377) and X(381)

X(44288) = MIDPOINT OF X(378) AND X(382)

Barycentrics    a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - a^8*c^2 - a^4*b^4*c^2 - a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - a^4*b^2*c^4 - 2*b^6*c^4 + 2*a^4*c^6 - a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(44288) lies on these lines: {2, 3}, {52, 11572}, {68, 31815}, {195, 34799}, {265, 3060}, {568, 25739}, {569, 13470}, {1154, 18474}, {1353, 11216}, {1531, 16194}, {1539, 19479}, {1853, 10264}, {1993, 32423}, {2781, 10113}, {3167, 12319}, {3357, 34798}, {3521, 12279}, {3574, 11750}, {3581, 23293}, {3818, 9019}, {5446, 18383}, {5448, 13419}, {5663, 11550}, {5889, 15800}, {6101, 22804}, {6102, 11262}, {6288, 11412}, {7699, 26881}, {7728, 11455}, {9707, 15806}, {9781, 43821}, {9927, 10263}, {10272, 35264}, {10620, 34796}, {11605, 12918}, {12161, 17824}, {12278, 37495}, {12289, 37472}, {12295, 32235}, {12370, 41362}, {13203, 35450}, {13352, 30522}, {13754, 34514}, {16789, 18358}, {16881, 18912}, {17505, 17711}, {18382, 21850}, {18396, 39522}, {19127, 19130}, {19139, 36990}, {20299, 32393}, {22505, 22823}, {22515, 39847}, {23039, 41171}, {31802, 32358}, {32346, 36966}, {32533, 38433}, {34785, 43394}

X(44288) = midpoint of X(378) and X(382)
X(44288) = Johnson-circle-inverse of X(23)

X(44289) = MIDPOINT OF X(381) AND X(383)

Barycentrics    3*a^10 - 12*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - 6*b^10 - 12*a^6*b^2*c^2 - 30*a^4*b^4*c^2 + 24*a^2*b^6*c^2 + 18*b^8*c^2 - 12*a^6*c^4 - 30*a^4*b^2*c^4 - 66*a^2*b^4*c^4 - 12*b^6*c^4 + 6*a^4*c^6 + 24*a^2*b^2*c^6 - 12*b^4*c^6 + 9*a^2*c^8 + 18*b^2*c^8 - 6*c^10 + 2*Sqrt[3]*(a^8 + 7*a^4*b^4 - 9*a^2*b^6 + b^8 + 10*a^4*b^2*c^2 + 10*a^2*b^4*c^2 - 9*b^6*c^2 + 7*a^4*c^4 + 10*a^2*b^2*c^4 + 16*b^4*c^4 - 9*a^2*c^6 - 9*b^2*c^6 + c^8)*S : :

X(44289) lies on these lines: {2, 3}, {530, 22566}, {542, 7685}, {623, 25561}, {624, 19924}, {2548, 41112}, {3767, 41113}, {5459, 19130}, {5460, 11645}, {5873, 15534}, {6298, 8176}, {14881, 33483}, {16268, 36382}, {22496, 36362}, {22568, 22575}, {22796, 33477}, {22803, 33484}, {25164, 41037}, {43291, 43417}

X(44289) = midpoint of X(381) and X(383)

X(44290) = MIDPOINT OF X(28) AND X(29)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^7 - 2*a^5*b^2 - a^4*b^3 - 2*a^3*b^4 + 2*a^2*b^5 + 2*a*b^6 - b^7 - 2*a^5*b*c + 3*a^4*b^2*c - 2*a^2*b^4*c + 2*a*b^5*c - b^6*c - 2*a^5*c^2 + 3*a^4*b*c^2 + 4*a^3*b^2*c^2 - 4*a^2*b^3*c^2 - 2*a*b^4*c^2 + b^5*c^2 - a^4*c^3 - 4*a^2*b^2*c^3 - 4*a*b^3*c^3 + b^4*c^3 - 2*a^3*c^4 - 2*a^2*b*c^4 - 2*a*b^2*c^4 + b^3*c^4 + 2*a^2*c^5 + 2*a*b*c^5 + b^2*c^5 + 2*a*c^6 - b*c^6 - c^7) : :
X(44290) = X(28) + X(29)

X(44290) lies on these lines: {2, 3}, {162, 34753}, {14192, 15171}

X(44290) = midpoint of X(28) and X(29)

X(44291) = (pending)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(3*a^7 - a^6*b - 3*a^5*b^2 - 3*a^3*b^4 + 3*a^2*b^5 + 3*a*b^6 - 2*b^7 - a^6*c - 3*a^5*b*c + 6*a^4*b^2*c - 3*a^2*b^4*c + 3*a*b^5*c - 2*b^6*c - 3*a^5*c^2 + 6*a^4*b*c^2 + 6*a^3*b^2*c^2 - 8*a^2*b^3*c^2 - 3*a*b^4*c^2 + 2*b^5*c^2 - 8*a^2*b^2*c^3 - 6*a*b^3*c^3 + 2*b^4*c^3 - 3*a^3*c^4 - 3*a^2*b*c^4 - 3*a*b^2*c^4 + 2*b^3*c^4 + 3*a^2*c^5 + 3*a*b*c^5 + 2*b^2*c^5 + 3*a*c^6 - 2*b*c^6 - 2*c^7) : :
X(44291) = X(28) + 2 X(29)

X(44291) lies on this line: {2, 3}

X(44291) = midpoint of X(29) and X(44293)
X(44291) = reflection of X(i) in X(j) for these (i, j): (28, 44293), (44293, 44290)
X(44291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (29, 44290, 28), (4248, 15763, 28)

X(44292) = (pending)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^7 - 3*a^6*b - a^5*b^2 + 4*a^4*b^3 - a^3*b^4 + a^2*b^5 + a*b^6 - 2*b^7 - 3*a^6*c - a^5*b*c + 6*a^4*b^2*c - a^2*b^4*c + a*b^5*c - 2*b^6*c - a^5*c^2 + 6*a^4*b*c^2 + 2*a^3*b^2*c^2 - 8*a^2*b^3*c^2 - a*b^4*c^2 + 2*b^5*c^2 + 4*a^4*c^3 - 8*a^2*b^2*c^3 - 2*a*b^3*c^3 + 2*b^4*c^3 - a^3*c^4 - a^2*b*c^4 - a*b^2*c^4 + 2*b^3*c^4 + a^2*c^5 + a*b*c^5 + 2*b^2*c^5 + a*c^6 - 2*b*c^6 - 2*c^7) : :
X(44292) = X(28) - 2 X(29)

X(44292) lies on this line: {2, 3}

X(44293) = X(2)X(3)∩X(3058)X(14192)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(3*a^6 - 2*a^5*b - a^4*b^2 - 2*a^3*b^3 - a^2*b^4 + 4*a*b^5 - b^6 - 2*a^5*c + a^4*b*c + 3*a^3*b^2*c - a^2*b^3*c - a*b^4*c - a^4*c^2 + 3*a^3*b*c^2 - 3*a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 - a^2*b*c^3 - 3*a*b^2*c^3 - a^2*c^4 - a*b*c^4 + b^2*c^4 + 4*a*c^5 - c^6) : :
X(44293) = 2 X(28) + X(29)

X(44293) lies on these lines: {2, 3}, {3058, 14192}

X(44294) = X(2)X(3)∩X(270)X(18653)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^7 + 3*a^6*b - a^5*b^2 - 5*a^4*b^3 - a^3*b^4 + a^2*b^5 + a*b^6 + b^7 + 3*a^6*c - a^5*b*c - 3*a^4*b^2*c - a^2*b^4*c + a*b^5*c + b^6*c - a^5*c^2 - 3*a^4*b*c^2 + 2*a^3*b^2*c^2 + 4*a^2*b^3*c^2 - a*b^4*c^2 - b^5*c^2 - 5*a^4*c^3 + 4*a^2*b^2*c^3 - 2*a*b^3*c^3 - b^4*c^3 - a^3*c^4 - a^2*b*c^4 - a*b^2*c^4 - b^3*c^4 + a^2*c^5 + a*b*c^5 - b^2*c^5 + a*c^6 + b*c^6 + c^7) : :
X(44294) = 2 X(28) - X(29)

X(44294) lies on these lines: {2, 3}, {270, 18653}, {7354, 14192}

X(44295) = (pending)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^9 + a^7*b^2 - a^6*b^3 - 4*a^5*b^4 + a^4*b^5 + a^3*b^6 + a^2*b^7 + a*b^8 - b^9 + 2*a^7*b*c + a^6*b^2*c - 4*a^5*b^3*c - a^4*b^4*c + a^2*b^6*c + 2*a*b^7*c - b^8*c + a^7*c^2 + a^6*b*c^2 - a^5*b^2*c^2 + 2*a^4*b^3*c^2 - a^3*b^4*c^2 - 3*a^2*b^5*c^2 + a*b^6*c^2 - a^6*c^3 - 4*a^5*b*c^3 + 2*a^4*b^2*c^3 - 7*a^2*b^4*c^3 - 2*a*b^5*c^3 - 4*a^5*c^4 - a^4*b*c^4 - a^3*b^2*c^4 - 7*a^2*b^3*c^4 - 4*a*b^4*c^4 + 2*b^5*c^4 + a^4*c^5 - 3*a^2*b^2*c^5 - 2*a*b^3*c^5 + 2*b^4*c^5 + a^3*c^6 + a^2*b*c^6 + a*b^2*c^6 + a^2*c^7 + 2*a*b*c^7 + a*c^8 - b*c^8 - c^9) : :
X(44295) = (a*b + a*c + b*c)X(28) + (a^2 + b^2 + c^2)X(29)

X(44295) lies on this line: {2, 3}

X(44296) = (pending)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^9 - 2*a^8*b - a^7*b^2 + a^6*b^3 + 3*a^4*b^5 - a^3*b^6 - a^2*b^7 + a*b^8 - b^9 - 2*a^8*c - 4*a^7*b*c + 3*a^6*b^2*c + 2*a^5*b^3*c + 5*a^4*b^4*c + 2*a^3*b^5*c - 5*a^2*b^6*c - b^8*c - a^7*c^2 + 3*a^6*b*c^2 + a^5*b^2*c^2 - 2*a^4*b^3*c^2 + a^3*b^4*c^2 - a^2*b^5*c^2 - a*b^6*c^2 + a^6*c^3 + 2*a^5*b*c^3 - 2*a^4*b^2*c^3 - 4*a^3*b^3*c^3 - a^2*b^4*c^3 + 5*a^4*b*c^4 + a^3*b^2*c^4 - a^2*b^3*c^4 + 2*b^5*c^4 + 3*a^4*c^5 + 2*a^3*b*c^5 - a^2*b^2*c^5 + 2*b^4*c^5 - a^3*c^6 - 5*a^2*b*c^6 - a*b^2*c^6 - a^2*c^7 + a*c^8 - b*c^8 - c^9) : :
X(44296) = (a*b + a*c + b*c)X(28) - (a^2 + b^2 + c^2)X(29)

X(44296) lies on this line: {2, 3}

X(44297) = (pending)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^9 + 2*a^8*b - a^7*b^2 - 2*a^6*b^3 - a^5*b^4 - 2*a^4*b^5 + a^3*b^6 + 2*a^2*b^7 + 2*a^8*c - 2*a^7*b*c - 2*a^6*b^2*c + 2*a^5*b^3*c - a^4*b^4*c + 2*a^2*b^6*c - b^8*c - a^7*c^2 - 2*a^6*b*c^2 + 5*a^5*b^2*c^2 + 3*a^4*b^3*c^2 - 5*a^3*b^4*c^2 + a*b^6*c^2 - b^7*c^2 - 2*a^6*c^3 + 2*a^5*b*c^3 + 3*a^4*b^2*c^3 - 8*a^3*b^3*c^3 - 8*a^2*b^4*c^3 + b^6*c^3 - a^5*c^4 - a^4*b*c^4 - 5*a^3*b^2*c^4 - 8*a^2*b^3*c^4 - 2*a*b^4*c^4 + b^5*c^4 - 2*a^4*c^5 + b^4*c^5 + a^3*c^6 + 2*a^2*b*c^6 + a*b^2*c^6 + b^3*c^6 + 2*a^2*c^7 - b^2*c^7 - b*c^8) : :
X(44297) = (a^2 + b^2 + c^2)X(28) + (a*b + a*c + b*c)X(29)

X(44297) lies on this line: {2, 3}

X(44298) = (pending)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 - a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - a^4*b^4 + a^3*b^5 - 2*a^2*b^6 + 2*a*b^7 - a^7*c + 2*a^6*b*c - 2*a^4*b^3*c + 2*a^3*b^4*c - a^2*b^5*c - a*b^6*c + b^7*c + 2*a^6*c^2 - 5*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 2*a^5*c^3 - 2*a^4*b*c^3 + 4*a^2*b^3*c^3 - a*b^4*c^3 - b^5*c^3 - a^4*c^4 + 2*a^3*b*c^4 + 3*a^2*b^2*c^4 - a*b^3*c^4 + a^3*c^5 - a^2*b*c^5 - b^3*c^5 - 2*a^2*c^6 - a*b*c^6 + 2*a*c^7 + b*c^7) : :
X(44297) = (a^2 + b^2 + c^2)X(28) - (a*b + a*c + b*c)X(29)

X(44298) lies on this line: {2, 3}

X(44299) = X(2)X(51)∩X(110)X(7484)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 - 7*b^2*c^2 - c^4) : :
X(44299) = 9 X[2] - 2 X[51], 13 X[2] - 6 X[373], 6 X[2] + X[2979], 8 X[2] - X[3060], 3 X[2] + 4 X[3819], 5 X[2] + 2 X[3917], 10 X[2] - 3 X[5640], X[2] + 6 X[5650], 11 X[2] - 4 X[5943], 15 X[2] - 8 X[6688], 4 X[2] + 3 X[7998], 23 X[2] - 16 X[10219], 17 X[2] - 3 X[11002], 12 X[2] - 5 X[11451], 31 X[2] - 24 X[12045], 5 X[2] - 12 X[15082], 31 X[2] - 3 X[16981], 25 X[2] - 4 X[21849], 23 X[2] - 2 X[21969], 2 X[2] - 9 X[33879], 11 X[2] + 3 X[33884], 16 X[3] + 5 X[11439], 6 X[3] + X[11455], 17 X[3] + 4 X[32137], 13 X[51] - 27 X[373], 4 X[51] + 3 X[2979], 16 X[51] - 9 X[3060], X[51] + 6 X[3819], 5 X[51] + 9 X[3917], 20 X[51] - 27 X[5640], X[51] + 27 X[5650], 11 X[51] - 18 X[5943], 5 X[51] - 12 X[6688], 8 X[51] + 27 X[7998], 23 X[51] - 72 X[10219], 34 X[51] - 27 X[11002], 8 X[51] - 15 X[11451], 31 X[51] - 108 X[12045]

See Francisco Javier García Capitán and Peter Moses, euclid 2027.

X(44299) lies on these lines: {2, 51}, {3, 11439}, {9, 26910}, {25, 41462}, {54, 13154}, {57, 26911}, {110, 7484}, {140, 5890}, {141, 26913}, {154, 5888}, {394, 5646}, {549, 15072}, {568, 10124}, {573, 16057}, {631, 5891}, {632, 11412}, {1154, 3526}, {1180, 21001}, {1194, 8617}, {1216, 3533}, {1368, 7703}, {1401, 9330}, {1613, 15302}, {1994, 22112}, {2393, 3619}, {3091, 36987}, {3522, 32062}, {3523, 6000}, {3524, 10170}, {3525, 5889}, {3530, 15058}, {3567, 32142}, {3620, 40673}, {3688, 9335}, {3763, 12220}, {3784, 35595}, {3843, 11592}, {5012, 10541}, {5020, 21766}, {5054, 11459}, {5067, 5447}, {5068, 13348}, {5070, 13364}, {5092, 44108}, {5644, 15019}, {5651, 15246}, {5663, 15701}, {6030, 35259}, {6101, 11465}, {6241, 15720}, {6617, 39243}, {6636, 10546}, {7486, 15644}, {7495, 41715}, {7496, 9306}, {7509, 11449}, {8703, 16261}, {9730, 15709}, {9971, 34573}, {10303, 10574}, {10601, 23061}, {11004, 34566}, {11064, 33523}, {11188, 20582}, {11202, 37126}, {11205, 36650}, {11402, 15066}, {11422, 43650}, {11539, 23039}, {12279, 15717}, {12290, 15712}, {13340, 15699}, {13363, 15723}, {13391, 15703}, {13595, 16187}, {13754, 15702}, {14449, 41992}, {14915, 15698}, {15024, 16239}, {15030, 15692}, {15045, 15067}, {15060, 15693}, {15100, 38794}, {15531, 21356}, {15713, 40280}, {15721, 16836}, {15801, 15805}, {16194, 19708}, {16658, 43934}, {17534, 37482}, {17582, 41723}, {18950, 41724}, {20859, 39576}, {23293, 30739}, {24206, 31101}, {31255, 40920}, {31274, 39836}, {33540, 35502}

X(44299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2979, 11451}, {2, 3819, 2979}, {2, 3917, 5640}, {2, 7998, 3060}, {2, 33884, 5943}, {631, 5891, 20791}, {1216, 3533, 15028}, {2979, 3819, 7998}, {2979, 11451, 3060}, {3524, 10170, 15305}, {3526, 7999, 15043}, {3819, 6688, 3917}, {3819, 15082, 6688}, {3917, 15082, 2}, {5640, 6688, 11451}, {5640, 33879, 15082}, {5650, 33879, 7998}, {5651, 15246, 26881}, {5891, 20791, 12111}, {7998, 11451, 2979}, {10303, 11793, 10574}, {15067, 15694, 15045}, {17811, 40916, 5012}

X(44300) = X(5)X(113)∩X(20)X(22112)

Barycentrics    -4*a^4*b^2 + 3*a^2*b^4 + b^6 - 4*a^4*c^2 - 22*a^2*b^2*c^2 - b^4*c^2 + 3*a^2*c^4 - b^2*c^4 + c^6 : :

See Francisco Javier García Capitán and Peter Moses, euclid 2033.

X(44300) lies on these lines: {5, 113}, {20, 22112}, {542, 5643}, {631, 34417}, {632, 20192}, {858, 6688}, {1506, 6791}, {2548, 22111}, {3066, 3526}, {3124, 9698}, {3628, 32225}, {3843, 5544}, {5181, 40670}, {5640, 40107}, {5642, 16042}, {5943, 37636}, {5972, 7605}, {7693, 29317}, {10168, 14002}, {11451, 38397}, {15018, 24981}, {16239, 32269}, {16240, 37124}, {25565, 32271}

X(44300) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 13363, 16003}, {16042, 25555, 5642}

leftri

Perspectors involving 1st and 2nd Savin triangles: X(44301)-X(44308)

rightri

This preamble is based on notes from Andrey Savin, August 19, 2021 and Peter Moses, August 20, 2021. Let A' = a : s - a : s - a = 2a : -a + b + c : -a + b + c (barycentrics) , and define B' and C' cyclically. The triangle A'B'C' is introduced here as the 1st Savin triangle.
Let A" = a : s + a : s + a = 2a : 3a + b + c : 3a + b + c (barycentrics), and define B" and C" cyclically. The triangle A"B"C" is introduced here as the 2nd Savin triangle.

1st Savin triangle
2nd Savin triangle

Let T1 = 1st Savin triangle.
T1 is perspective to the following triangles, with perspector X(2): ABC, medial, anticomplementary, circum-medial, Gemini 1,2, 9-14, 20-24, 27, 28, 31-61, 65-70, 72-111.
T2 is perspective to the following triangles with perspector X(2): intouch, intangents, hexyl, infinite altitude, 6th mixtilinear, Hutson intouch, 3rd Conway, Garcia reflection, Gemini 8, Bevan-antipodal (see X(34488)).
The appearance of (T,k) in the following list means that T1 is perspective to T and the perspector is X(k):
(Andromeda, 3677)
(Jenkins, 5530)
(2nd outer Soddy, 31582)
(2nd inner Soddy, 31583)
(anticevian of X(8051), 44301)
(pedal of X(24851), 44302)

Let T2 = 2nd Savin triangle.
T2 is perspective to the following triangles, with perspector X(1): ABC, medial, anticomplementary, circum-medial, Gemini 1,2, 9-14, 20-24, 27, 28, 31-61, 65-70, 72-111.
The appearance of (T,k) in the following list means that T2 is perspective to T and the perspector is X(k):
(excentral, 7308)
(Gemini 7, 25430)
(Soddy, 44303) (2nd Sharygin, 44304)
(Aquila, 44305)
(2nd extouch, 44306)
(Gemini 15, 44307)
(9th Vijay-Paasche-Hutson, 44308)

X(44301) = PERSPECTOR OF THESE TRIANGLES: 1ST SAVIN AND ANTICEVIAN OF X(8051)

Barycentrics    (3*a - b - c)*(a + b - c)*(a - b + c)*(a^2 + 2*a*b + b^2 - 6*a*c + 2*b*c + c^2)*(a^2 - 6*a*b + b^2 + 2*a*c + 2*b*c + c^2) : :

X(44301) lies on the cubic K365 and these lines: {56, 15519}, {57, 145}, {1420, 24150}, {3340, 35577}, {6049, 37743}

Construction: X(44301)

X(44301) = X(i)-cross conjugate of X(j) for these (i,j): {1, 145}, {3161, 5435}, {24150, 8051}
X(44301) = cevapoint of X(1) and X(2137)
X(44301) = X(i)-isoconjugate of X(j) for these (i,j): {6, 24151}, {41, 27828}, {1616, 3680}, {2136, 3445}, {6552, 16945}, {8055, 38266}
X(44301) = barycentric product X(i)*X(j) for these {i,j}: {7, 24150}, {145, 8051}, {2137, 18743}, {5435, 6553}
X(44301) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 24151}, {7, 27828}, {145, 8055}, {1420, 23511}, {1743, 2136}, {2137, 8056}, {3161, 6552}, {5435, 4452}, {6553, 6557}, {8051, 4373}, {24150, 8}, {39126, 33780}
X(44301) = {X(2137),X(6553)}-harmonic conjugate of X(8051)

X(44302) = PERSPECTOR OF THESE TRIANGLES: 1ST SAVIN AND PEDAL OF X(24851)

Barycentrics    a*(a^4 - a^2*b^2 + a*b^3 + b^4 + a^2*b*c - a^2*c^2 + a*c^3 + c^4) : :

X(44302) lies on these lines: {1, 256}, {6, 1959}, {37, 1332}, {81, 593}, {257, 27958}, {319, 31089}, {894, 33946}, {1442, 37596}, {1790, 18202}, {1958, 3959}, {2277, 44179}, {2650, 23928}, {3570, 41779}, {3672, 20090}, {3924, 28365}, {3936, 4851}, {7083, 23193}, {7113, 18179}, {8424, 8772}, {11683, 27970}, {15903, 27691}, {17231, 30831}, {17778, 21287}, {25898, 27697}, {26639, 28358}, {37549, 40765}

X(44302) = crossdifference of every pair of points on line {3287, 4705}
X(44302) = barycentric product X(81)*X(27688)
X(44302) = barycentric quotient X(27688)/X(321)

X(44303) = PERSPECTOR OF THESE TRIANGLES: 2ND SAVIN AND SODDY

Barycentrics    (a + b - c)*(a - b + c)*(3*a^4 + 12*a^3*b - 2*a^2*b^2 - 12*a*b^3 - b^4 + 12*a^3*c + 24*a^2*b*c - 36*a*b^2*c - 2*a^2*c^2 - 36*a*b*c^2 + 2*b^2*c^2 - 12*a*c^3 - c^4) : :

X44303 is also the perspector of the 2nd Savin triangle and the Soddy triangle.

X(44303) lies on these lines: {7, 25430}, {279, 5226}, {3666, 5435}, {5273, 16578}, {18230, 18623}

X(44304) = PERSPECTOR OF THESE TRIANGLES: 2ND SAVIN AND 2ND SHARYGIN

Barycentrics    a*(a^3*b - a^2*b^2 + a^3*c + 2*a^2*b*c - 3*a*b^2*c + 3*b^3*c - a^2*c^2 - 3*a*b*c^2 - 2*b^2*c^2 + 3*b*c^3) : :

Construction: X(44304)

X(44304) lies on these lines: {2, 11}, {37, 244}, {42, 17477}, {291, 3677}, {344, 30947}, {350, 21404}, {354, 4712}, {659, 4728}, {899, 1279}, {1282, 7308}, {1284, 3911}, {2108, 25502}, {2238, 21341}, {3008, 4433}, {3675, 24036}, {3932, 29824}, {3937, 24494}, {4011, 36538}, {4124, 21232}, {4370, 24405}, {4422, 21320}, {4436, 40480}, {4447, 17266}, {4465, 9318}, {4869, 36635}, {5251, 29637}, {7484, 20871}, {8300, 17123}, {8849, 25507}, {9024, 16494}, {9345, 24512}, {9451, 10582}, {16373, 20999}, {16468, 37676}, {17279, 30942}, {17357, 30970}, {17754, 35341}, {17777, 30997}, {21010, 29627}, {21580, 30963}, {23407, 29629}, {24330, 31005}, {29677, 37319}

X(44305) = PERSPECTOR OF THESE TRIANGLES: 2ND SAVIN AND AQUILA

Barycentrics    3*a^3 + 20*a^2*b + 27*a*b^2 + 6*b^3 + 20*a^2*c + 82*a*b*c + 26*b^2*c + 27*a*c^2 + 26*b*c^2 + 6*c^3 : :

X(44305) lies on these lines: {1698, 37548}, {5316, 12047}

X(44306) = PERSPECTOR OF THESE TRIANGLES: 2ND SAVIN AND 2ND EXTOUCH

Barycentrics    a*(a^5 + 4*a^4*b + 2*a^3*b^2 - 4*a^2*b^3 - 3*a*b^4 + 4*a^4*c + 6*a^3*b*c - 14*a^2*b^2*c - 18*a*b^3*c - 2*b^4*c + 2*a^3*c^2 - 14*a^2*b*c^2 - 30*a*b^2*c^2 - 14*b^3*c^2 - 4*a^2*c^3 - 18*a*b*c^3 - 14*b^2*c^3 - 3*a*c^4 - 2*b*c^4) : :

X(44306) lies on these lines: {2, 1901}, {3, 1750}, {9, 940}, {329, 15668}, {386, 405}, {965, 3305}, {1211, 37169}, {1213, 37185}, {3683, 9816}, {4422, 5737}, {4877, 11347}, {6913, 21363}, {9612, 16456}, {12572, 16458}, {16053, 19701}, {17123, 19758}, {18230, 19645}

X(44306) = {X(3306),X(37323)}-harmonic conjugate of X(965)

X(44307) = PERSPECTOR OF THESE TRIANGLES: 2ND SAVIN AND GEMINI 15

Barycentrics    a*(a*b + b^2 + a*c + 4*b*c + c^2) : :
Barycentrics    c a (2 b + c + a) + a b (2 c + a + b) : :
X(44307) = 3 X[2] + X[3995], 2 X[756] + X[4883]

X(44307) lies on these lines: {1, 210}, {2, 37}, {5, 37528}, {6, 3305}, {9, 940}, {10, 3706}, {31, 4682}, {35, 20988}, {38, 3742}, {42, 3740}, {43, 37593}, {44, 81}, {45, 63}, {55, 5020}, {57, 3731}, {86, 27064}, {142, 3782}, {171, 3683}, {223, 43064}, {226, 241}, {227, 10588}, {238, 1961}, {239, 34064}, {244, 3848}, {278, 17916}, {306, 5743}, {329, 4648}, {333, 17260}, {354, 984}, {392, 30116}, {405, 975}, {469, 1841}, {517, 21363}, {518, 756}, {519, 4113}, {551, 4090}, {612, 1001}, {614, 8167}, {650, 4500}, {748, 1386}, {750, 4640}, {846, 1155}, {899, 1962}, {905, 4944}, {908, 16585}, {910, 37675}, {936, 16416}, {960, 22275}, {966, 34255}, {968, 1376}, {980, 25066}, {982, 25502}, {991, 5927}, {1089, 25512}, {1100, 17019}, {1104, 5047}, {1107, 16826}, {1125, 1215}, {1203, 5506}, {1211, 3912}, {1212, 5308}, {1214, 5219}, {1255, 3723}, {1279, 3920}, {1407, 8545}, {1427, 5226}, {1465, 16577}, {1468, 5302}, {1500, 24603}, {1573, 29574}, {1621, 5297}, {1698, 3931}, {1724, 37594}, {1736, 11018}, {1738, 4854}, {1754, 31658}, {1757, 4038}, {1848, 5089}, {1920, 18140}, {1999, 17277}, {2256, 17825}, {2292, 3812}, {2295, 4520}, {2352, 16058}, {2895, 17374}, {2999, 3247}, {3008, 27800}, {3091, 15852}, {3187, 17348}, {3218, 33761}, {3219, 16814}, {3242, 4666}, {3246, 17469}, {3306, 16675}, {3452, 5718}, {3616, 27538}, {3624, 37592}, {3634, 3743}, {3661, 41015}, {3663, 40688}, {3681, 9330}, {3687, 5241}, {3689, 3750}, {3696, 26037}, {3698, 37598}, {3700, 25084}, {3702, 19874}, {3703, 4078}, {3714, 31339}, {3715, 3751}, {3741, 3842}, {3748, 3961}, {3765, 24656}, {3816, 29639}, {3823, 4972}, {3826, 3914}, {3828, 4868}, {3834, 17184}, {3836, 4425}, {3844, 29687}, {3846, 29653}, {3925, 24210}, {3938, 42819}, {3965, 11679}, {3967, 32771}, {3971, 24325}, {3974, 39581}, {3985, 5750}, {3991, 16832}, {4001, 17332}, {4003, 17063}, {4023, 4028}, {4042, 39594}, {4413, 17594}, {4414, 17124}, {4415, 5249}, {4419, 9776}, {4422, 5294}, {4503, 29418}, {4512, 37540}, {4518, 25531}, {4646, 9780}, {4651, 28581}, {4653, 5440}, {4670, 26223}, {4675, 5905}, {4679, 26098}, {4702, 32945}, {4706, 4970}, {4719, 27627}, {4849, 17018}, {4851, 5739}, {4864, 29817}, {4871, 6682}, {4875, 14555}, {4886, 6542}, {4891, 17135}, {4903, 5550}, {4914, 32847}, {4981, 29824}, {5069, 28640}, {5087, 33105}, {5129, 5716}, {5135, 26885}, {5256, 16777}, {5259, 5266}, {5262, 17536}, {5271, 17259}, {5272, 17599}, {5283, 16831}, {5293, 37080}, {5316, 37663}, {5333, 16696}, {5393, 9646}, {5405, 8965}, {5432, 9371}, {5437, 16676}, {5492, 40296}, {5710, 31435}, {5745, 37634}, {5847, 41002}, {6354, 21617}, {6536, 32781}, {6666, 40940}, {6685, 10180}, {6687, 29833}, {6706, 26100}, {7069, 10391}, {7174, 10582}, {7226, 21342}, {7262, 37604}, {7365, 8232}, {8055, 25082}, {8580, 37553}, {8609, 37662}, {8758, 29640}, {9047, 20961}, {9345, 15481}, {9347, 17127}, {9791, 33068}, {10436, 30568}, {14996, 15492}, {15082, 40649}, {15485, 17716}, {16569, 17592}, {16578, 25080}, {16583, 17308}, {16600, 25086}, {16604, 29612}, {16669, 37685}, {16673, 23511}, {16699, 27398}, {16700, 25507}, {16823, 32926}, {16830, 32942}, {16975, 29597}, {17012, 37687}, {17013, 39260}, {17017, 17125}, {17074, 29007}, {17120, 42028}, {17140, 28582}, {17231, 32782}, {17234, 27184}, {17237, 33172}, {17239, 41809}, {17244, 18134}, {17256, 37653}, {17257, 18141}, {17258, 26840}, {17261, 32939}, {17267, 39982}, {17287, 41816}, {17300, 33066}, {17317, 17778}, {17335, 37652}, {17337, 26723}, {17338, 29841}, {17344, 32863}, {17365, 17781}, {17376, 32859}, {17381, 41850}, {17448, 29570}, {17449, 42039}, {17450, 42041}, {17529, 23537}, {17603, 24430}, {17605, 33111}, {17721, 26105}, {18139, 26580}, {18607, 31053}, {19684, 28639}, {19717, 41241}, {19730, 21371}, {20106, 25081}, {20138, 20166}, {20195, 23681}, {20487, 24239}, {20691, 29576}, {20716, 32772}, {20917, 27269}, {21611, 27193}, {21838, 31336}, {21870, 42042}, {21949, 33134}, {21965, 25007}, {23632, 31052}, {24331, 32920}, {24471, 28387}, {24575, 25420}, {24697, 33085}, {25068, 25089}, {25069, 43063}, {25072, 35466}, {25098, 31250}, {25109, 27044}, {25614, 29593}, {25760, 29854}, {25960, 29643}, {25961, 32776}, {26627, 32933}, {27186, 33151}, {27253, 30854}, {27255, 30830}, {28626, 39956}, {29610, 41817}, {29624, 40133}, {29654, 31289}, {29837, 33118}, {29845, 33115}, {29851, 32775}, {30567, 37660}, {30615, 36479}, {30710, 32009}, {30821, 39957}, {30823, 41878}, {31445, 37522}, {32017, 37870}, {37597, 41867}, {39703, 39738}

X(44307) = midpoint of X(i) and X(j) for these {i,j}: {756, 3720}, {3995, 4359}
X(44307) = reflection of X(4883) in X(3720)
X(44307) = complement of X(4359)
X(44307) = complement of the isogonal conjugate of X(28615)
X(44307) = complement of the isotomic conjugate of X(1255)
X(44307) = isotomic conjugate of the polar conjugate of X(1900)
X(44307) = X(i)-complementary conjugate of X(j) for these (i,j): {1126, 141}, {1171, 3741}, {1255, 2887}, {1268, 626}, {1796, 1368}, {1919, 35076}, {2206, 41820}, {4596, 42327}, {4629, 512}, {4632, 23301}, {6540, 21262}, {8701, 3835}, {28615, 10}, {32018, 21235}, {32635, 21244}, {32739, 4988}, {33635, 1329}, {37212, 21260}, {40438, 21240}
X(44307) = X(i)-Ceva conjugate of X(j) for these (i,j): {4967, 4662}, {6540, 513}
X(44307) = crosspoint of X(2) and X(1255)
X(44307) = crosssum of X(6) and X(1100)
X(44307) = crossdifference of every pair of points on line {667, 4790}
X(44307) = barycentric product X(i)*X(j) for these {i,j}: {1, 4967}, {7, 4662}, {69, 1900}, {40438, 42437}
X(44307) = barycentric quotient X(i)/X(j) for these {i,j}: {1900, 4}, {4662, 8}, {4967, 75}, {27597, 6533}, {42437, 4647}
X(44307) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7308, 4383}, {2, 37, 3666}, {2, 192, 19804}, {2, 312, 31993}, {2, 321, 3739}, {2, 344, 32777}, {2, 3666, 16610}, {2, 3995, 4359}, {2, 4704, 17490}, {2, 4850, 16602}, {2, 17147, 24589}, {2, 17280, 19808}, {2, 18743, 30818}, {2, 19785, 17278}, {2, 28606, 3752}, {2, 31035, 321}, {2, 32774, 17356}, {2, 33155, 26724}, {2, 41839, 75}, {6, 5287, 37595}, {9, 940, 4641}, {9, 17022, 940}, {10, 6051, 37548}, {10, 27784, 6051}, {37, 3752, 28606}, {38, 3742, 3999}, {38, 30950, 3742}, {45, 37674, 63}, {63, 37674, 37520}, {75, 41839, 3175}, {81, 27065, 44}, {142, 4656, 3782}, {192, 19804, 42051}, {238, 1961, 3745}, {321, 31035, 35652}, {405, 975, 37539}, {612, 1001, 3744}, {748, 5311, 1386}, {846, 17122, 1155}, {968, 1376, 4689}, {984, 26102, 354}, {1255, 17011, 3723}, {1255, 37680, 17011}, {1698, 27785, 3931}, {2999, 3247, 20182}, {3305, 5287, 6}, {3739, 35652, 321}, {3740, 15569, 42}, {3752, 28606, 3666}, {3920, 5284, 1279}, {3961, 16484, 3748}, {3971, 25501, 24325}, {4415, 17245, 5249}, {4422, 6703, 5294}, {4682, 15254, 31}, {4687, 18743, 2}, {4688, 22034, 28605}, {5283, 16831, 37596}, {5308, 18228, 5712}, {5743, 17243, 306}, {7174, 10582, 17597}, {7308, 25430, 1}, {9330, 29814, 3681}, {10180, 24003, 6685}, {16601, 29571, 241}, {16777, 37679, 5256}, {17019, 32911, 1100}, {17019, 35595, 32911}, {17021, 27065, 81}, {17341, 19812, 2}, {17720, 25067, 16610}, {25089, 25092, 25068}, {25507, 40773, 16700}, {26037, 32915, 3696}

X(44308) = PERSPECTOR OF THESE TRIANGLES: 2ND SAVIN AND 9TH VIJAY-PAASCHE-HUTSON

Barycentrics    5*a^5*b + a^4*b^2 - 10*a^3*b^3 - 2*a^2*b^4 + 5*a*b^5 + b^6 + 5*a^5*c + 14*a^4*b*c - 10*a^3*b^2*c - 20*a^2*b^3*c + 5*a*b^4*c + 6*b^5*c + a^4*c^2 - 10*a^3*b*c^2 - 52*a^2*b^2*c^2 - 10*a*b^3*c^2 - b^4*c^2 - 10*a^3*c^3 - 20*a^2*b*c^3 - 10*a*b^2*c^3 - 12*b^3*c^3 - 2*a^2*c^4 + 5*a*b*c^4 - b^2*c^4 + 5*a*c^5 + 6*b*c^5 + c^6 + 2*(a + b + c)*(a^3 + a^2*b - 3*a*b^2 + b^3 + a^2*c - 18*a*b*c - b^2*c - 3*a*c^2 - b*c^2 + c^3)*S : :

X(44308) lies on these lines: {2, 30416}, {1123, 5405}

X(44309) = EULER LINE INTERCEPT OF X(1503)X(15461)

Barycentrics   (8*OH*((-a^2+b^2+c^2)^2-b^2*c^2)*S*a^3*b*c+(b^2+c^2)*a^10-3*(b^4+4*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(b^4+7*b^2*c^2+c^4)*a^6+2*(b^4+3*b^2*c^2+c^4)*(b^4-4*b^2*c^2+c^4)*a^4-(b^4-c^4)*(b^2-c^2)*(3*b^4+4*b^2*c^2+3*c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
Barycentrics    (2*(3*R^2-SB-SC)*OH*R-6*(3*R^2+SA)*R^2+S^2+SA^2-SB*SC+SW^2)*SB*SC : :
X(44309) = X(858)+2*X(20408)

See Antreas Hatzipolakis and César Lozada, euclid 2048.

X(44309) lies on these lines: {2, 3}, {1503, 15461}, {6000, 14500}

X(44309) = midpoint of X(i) and X(j) for these {i, j}: {2071, 14808}, {15154, 18403}
X(44309) = reflection of X(i) in X(j) for these (i, j): {403, 1312}, {1114, 10257}, {10736, 13473}, {10750, 23323}, {15646, 31681}, {44214, 13626}, {44246, 35231}
X(44309) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): {1113, 10736, 20}, {1312, 20408, 1113}

X(44310) = EULER LINE INTERCEPT OF X(1503)X(15460)

Barycentrics    (-8*OH*((-a^2+b^2+c^2)^2-b^2*c^2)*S*a^3*b*c+(b^2+c^2)*a^10-3*(b^4+4*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(b^4+7*b^2*c^2+c^4)*a^6+2*(b^4+3*b^2*c^2+c^4)*(b^4-4*b^2*c^2+c^4)*a^4-(b^4-c^4)*(b^2-c^2)*(3*b^4+4*b^2*c^2+3*c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
Barycentrics    (-2*(3*R^2-SB-SC)*OH*R-6*(3*R^2+SA)*R^2+S^2+SA^2-SB*SC+SW^2)*SB*SC : :
X(44310) = X(858)+2*X(20409)

See Antreas Hatzipolakis and César Lozada, euclid 2048.

X(44310) lies on these lines: {2, 3}, {1503, 15460}, {6000, 14499}

X(44310) = midpoint of X(i) and X(j) for these {i, j}: {2071, 14807}, {15155, 18403}
X(44310) = reflection of X(i) in X(j) for these (i, j): {403, 1313}, {1113, 10257}, {10737, 13473}, {10751, 23323}, {15646, 31682}, {44214, 13627}, {44246, 35232}
X(44310) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): {1114, 10737, 20}, {1313, 20409, 1114}

leftri

Points associated with the Moses-Soddy triangle: X(44301)-X(44305)

rightri

This preamble is based on notes from Peter Moses, August 21, 2021. Let A' = pole of Soddy line in the Soddy A-circle, and define B' and C' cyclically, so that A' = b - c : a - c : b - a
B' = c - b : c - a : b - a
C' = c - b : a - c : a - b

The triangle A'B'C' is here named the Moses-Soddy triangle. This triangle is also the complement of the Yff contact triangle. The vertices A', B', C' lie on the cubic K927.

The appearance of (T,n) in the following list means that A'B'C' is perspective to T, and the perspector is X(k): (ABC, 514), (medial, 1086), (orthic, 116), (incentral, 17761), (intouch, 11), (extouch, 4904), (McBeath, 44311), (symmedial, 44312), (Steiner, 1125), (3rd Euler, 11), (2nd Hatzipolakis, 44313), (Yff contact,2), (Garcia reflection, 3667), (Gemini 7, 7658), (Gemini 8, 3667), (anti-Ursa-minor, 44316), (Lemoine, 44317), (Ursa-major, 44318), (Ursa-minor, 44319), (24th Vijay-Paasche-Hutson, 44320)

The Moses-Soddy triangle is also perspective to the Wasat triangle.

X(2)-of-A'B'C' = X(21204)
X(3)-of-A'B'C' = X(44314)
X(4)-of-A'B'C' = X(1)
X(5)-of-A'B'C' = X(44315)

X(44311) = PERSPECTOR OF THESE TRIANGLES: MOSES-SODDY AND MACBEATH

Barycentrics    (a - b - c)*(b - c)^2*(a^3 - a*b^2 + a*b*c + b^2*c - a*c^2 + b*c^2) : :

X(44311) lies on these lines: {8, 596}, {10, 1772}, {11, 522}, {116, 136}, {200, 17155}, {244, 17888}, {318, 24046}, {514, 3937}, {537, 14740}, {726, 6745}, {900, 38390}, {982, 17860}, {1086, 2968}, {1111, 24031}, {1125, 34834}, {1357, 23772}, {1421, 24410}, {1845, 4292}, {2611, 4151}, {3159, 27385}, {3190, 3210}, {3663, 18690}, {3667, 38389}, {3670, 23661}, {3705, 31075}, {3953, 23528}, {4025, 23989}, {4075, 27529}, {4193, 44040}, {4467, 40619}, {4765, 14936}, {4847, 20882}, {4853, 9457}, {4858, 7004}, {4957, 28623}, {4976, 38347}, {5515, 40626}, {5552, 24068}, {6734, 24176}, {7649, 21666}, {10538, 30117}, {17205, 17880}, {18210, 24237}, {21196, 38987}, {21208, 24186}, {21318, 40687}, {22084, 23820}, {22148, 36205}, {24177, 24218}, {24431, 41797}, {27009, 27486}, {34467, 39210}

X(44311) = polar conjugate of the isogonal conjugate of X(39006)
X(44311) = X(i)-complementary conjugate of X(j) for these (i,j): {54, 513}, {95, 21260}, {513, 1209}, {667, 233}, {1333, 18314}, {2148, 514}, {2167, 3835}, {2169, 20315}, {2190, 20316}, {2203, 17434}, {2616, 3454}, {2623, 1211}, {6591, 34836}, {15412, 21245}, {18210, 20625}, {23224, 10600}, {23286, 21530}, {34948, 34835}, {39177, 21246}
X(44311) = X(i)-Ceva conjugate of X(j) for these (i,j): {264, 514}, {40010, 4391}, {40012, 3239}
X(44311) = X(i)-isoconjugate of X(j) for these (i,j): {1783, 40518}, {24027, 44040}
X(44311) = crosspoint of X(75) and X(4560)
X(44311) = crosssum of X(31) and X(4559)
X(44311) = barycentric product X(i)*X(j) for these {i,j}: {11, 32939}, {264, 39006}, {404, 4858}, {514, 20293}, {2170, 44139}
X(44311) = barycentric quotient X(i)/X(j) for these {i,j}: {404, 4564}, {1146, 44040}, {1459, 40518}, {20293, 190}, {32939, 4998}, {39006, 3}, {44085, 2149}

X(44312) = PERSPECTOR OF THESE TRIANGLES: MOSES-SODDY AND SYMMEDIAL

Barycentrics    (b - c)^2*(-(a^3*b) + a^2*b^2 - a^3*c + a^2*b*c + a^2*c^2 + b^2*c^2) : :
X(44312) = 3 X[2] + X[25049]

X(44312) lies on these lines: {2, 25049}, {11, 3835}, {75, 7239}, {116, 125}, {141, 36951}, {226, 34253}, {244, 38995}, {514, 20974}, {649, 27009}, {661, 40619}, {675, 32739}, {812, 38347}, {1084, 1086}, {1125, 38998}, {2140, 5773}, {3120, 4107}, {3124, 21208}, {3741, 39080}, {3937, 4932}, {4904, 38992}, {6593, 34830}, {20295, 26846}, {20999, 24279}, {21196, 38987}, {23638, 24787}, {23803, 24198}, {24220, 29658}, {24237, 38991}, {29654, 36213}, {40601, 40940}

X(44312) = midpoint of X(20974) and X(23989)
X(44312) = complement of X(46148)
X(44312) = complement of the isogonal conjugate of X(10566)
X(44312) = X(i)-complementary conjugate of X(j) for these (i,j): {28, 23285}, {81, 3005}, {82, 514}, {83, 513}, {251, 650}, {308, 21260}, {513, 6292}, {514, 21249}, {649, 16587}, {693, 21248}, {3112, 3835}, {3121, 35971}, {3125, 15449}, {3669, 17055}, {4580, 21530}, {4628, 24036}, {10566, 10}, {18070, 3454}, {18082, 4129}, {18098, 661}, {18101, 26932}, {18105, 16589}, {18107, 34832}, {18108, 2}, {18113, 40617}, {18833, 21262}, {34055, 20315}, {39179, 1125}, {39276, 9508}
X(44312) = X(6)-Ceva conjugate of X(514)
X(44312) = crosspoint of X(6) and X(21791)
X(44312) = barycentric product X(i)*X(j) for these {i,j}: {514, 21225}, {3261, 21791}, {7199, 21901}
X(44312) = barycentric quotient X(i)/X(j) for these {i,j}: {21225, 190}, {21791, 101}, {21901, 1018}, {23093, 1331}

X(44313) = PERSPECTOR OF THESE TRIANGLES: MOSES-SODDY AND 2ND HATZIPOLAKIS

Barycentrics    (b - c)^2*(-2*a^4 + a^3*b + a^2*b^2 - a*b^3 + b^4 + a^3*c - a^2*b*c - a*b^2*c + b^3*c + a^2*c^2 - a*b*c^2 - a*c^3 + b*c^3 + c^4) : :

X(44313) lies on these lines: {10, 2840}, {11, 1357}, {116, 5521}, {117, 2829}, {124, 513}, {514, 2968}, {867, 3937}, {946, 15528}, {1364, 6003}, {3667, 38357}, {3825, 12014}, {4292, 7683}, {5190, 39006}, {7192, 40618}, {8226, 40687}, {10167, 40677}, {11028, 21621}

X(44313) = X(1119)-Ceva conjugate of X(514)

X(44314) = X(3)-OF-MOSES-SODDY TRIANGLE

Barycentrics    (b - c)*(a^3 - 2*a^2*b + 2*a*b^2 + b^3 - 2*a^2*c + a*b*c - 2*b^2*c + 2*a*c^2 - 2*b*c^2 + c^3) : :
X(44314) = X[1] - 3 X[21204], X[8] + 3 X[6545], X[145] - 9 X[6548], 5 X[1698] - 3 X[10196], 5 X[3616] - 9 X[14475], 3 X[4049] - X[21201], 9 X[6544] - 13 X[19877], 3 X[6546] - 7 X[9780]

X(44314) lies on these lines: {1, 21204}, {2, 5592}, {4, 2457}, {8, 6545}, {10, 514}, {145, 6548}, {513, 3812}, {676, 28521}, {942, 37998}, {1027, 1722}, {1698, 10196}, {2785, 3837}, {2789, 3960}, {3309, 5806}, {3616, 14475}, {3676, 10106}, {3835, 12047}, {4406, 33944}, {4778, 6133}, {6544, 19877}, {6546, 9780}, {7192, 17589}, {7658, 11512}, {8713, 40551}, {13464, 28292}, {19950, 21211}, {19951, 21143}, {21188, 28470}, {21198, 28225}, {21212, 29066}, {25380, 29240}

X(44314) = reflection of X(1) in X(44315)
X(44314) = reflection of X(32212) in X(10)
X(44314) = complement of X(5592)
X(44314) = crossdifference of every pair of points on line {1914, 22356}
X(44314) = Moses-Soddy-isogonal conjugate of X(1)

X(44315) = X(5)-OF-MOSES-SODDY TRIANGLE

Barycentrics    (b - c)*(3*a^3 - 2*a^2*b - 2*a*b^2 - b^3 - 2*a^2*c + 3*a*b*c + 2*b^2*c - 2*a*c^2 + 2*b*c^2 - c^3) : :
X(44315) = X[1] + 3 X[21204], X[8] - 9 X[14475], 5 X[3616] - X[5592], 5 X[3616] + 3 X[6545], 7 X[3622] + 9 X[6548], 7 X[3624] - 3 X[10196], 11 X[5550] - 3 X[6546], X[5592] + 3 X[6545]

X(44315) lies on these lines: {1, 21204}, {2, 32212}, {8, 14475}, {514, 1125}, {522, 19947}, {946, 3667}, {3616, 5592}, {3622, 6548}, {3624, 10196}, {3835, 13407}, {4449, 5293}, {4786, 26839}, {5045, 37998}, {5550, 6546}, {6789, 36205}, {7658, 24174}, {11726, 38019}, {19884, 28161}, {19949, 21196}, {23345, 28225}, {29350, 33815}

X(44315) = midpoint of X(1) and X(44314)
X(44315) = midpoint of X(11726) and X(38019)
X(44315) = complement of X(32212)
X(44315) = {X(3616),X(6545)}-harmonic conjugate of X(5592)

X(44316) = PERSPECTOR OF THESE TRIANGLES: MOSES-SODDY AND ANTI-URSA-MINOR

Barycentrics    ((b^2+c^2)*a^2+(b+c)*(b^2+c^2)*a-(b+c)^2*b*c)*(b-c) : :
X(44316) = X(3777)+2*X(21714) = 2*X(4472)+X(24698)

Centers X(44316)-X(44320) were contributed by César Lozada, August 21, 2021.

X(44316) lies on these lines: {2, 4057}, {5, 3667}, {11, 42312}, {12, 43924}, {86, 21304}, {140, 39225}, {141, 21191}, {325, 523}, {427, 7649}, {514, 40086}, {594, 17458}, {656, 14288}, {834, 17072}, {900, 21189}, {1213, 20979}, {1368, 20315}, {1595, 16231}, {1919, 17398}, {2530, 4036}, {3733, 21301}, {3777, 21714}, {3814, 3836}, {4472, 24698}, {4665, 23886}, {4802, 23815}, {4926, 23809}, {4977, 21051}, {6004, 24959}, {9002, 20316}, {11681, 23345}, {17303, 21389}, {21053, 21123}, {21187, 21193}, {21261, 42327}, {30795, 31003}, {31096, 31097}

X(44316) = midpoint of X(i) and X(j) for these {i, j}: {656, 14288}, {2530, 4036}, {3733, 21301}
X(44316) = reflection of X(i) in X(j) for these (i, j): (5, 39508), (31946, 21260), (39225, 140)
X(44316) = complement of X(4057)
X(44316) = complementary conjugate of X(8054)
X(44316) = barycentric product X(514)*X(24068)
X(44316) = barycentric quotient X(514)/X(39693)
X(44316) = trilinear product X(513)*X(24068)
X(44316) = trilinear quotient X(693)/X(39693)
X(44316) = pole of the Nagel line wrt the nine-point circle
X(44316) = pole of the trilinear polar of X(20295) with respect to circumhyperbola dual of Yff parabola
X(44316) = crossdifference of every pair of points on line {X(32), X(16685)}
X(44316) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 8054), (100, 4075), (596, 11)
X(44316) = X(692)-isoconjugate-of-X(39693)
X(44316) = X(514)-reciprocal conjugate of-X(39693)

X(44317) = PERSPECTOR OF THESE TRIANGLES: MOSES-SODDY AND LEMOINE

Barycentrics    (b-c)^2*(a^2-3*(b+c)*a+4*b^2+3*b*c+4*c^2) : :

X(44317) lies on these lines: {115, 116}, {6789, 30790}, {38988, 44312}

X(44317) = pole of the trilinear polar of X(598) with respect to circumhyperbola dual of Yff parabola
X(44317) = X(598)-Ceva conjugate of-X(514)
X(44317) = X(1333)-complementary conjugate of-X(17436)

X(44318) = PERSPECTOR OF THESE TRIANGLES: MOSES-SODDY AND URSA-MAJOR

Barycentrics    a*((b+c)*a^6-(3*b^2+4*b*c+3*c^2)*a^5+(b+c)*(2*b^2+9*b*c+2*c^2)*a^4+2*(b^4+c^4-2*(3*b^2+4*b*c+3*c^2)*b*c)*a^3-(b+c)*(3*b^4+3*c^4-2*(3*b^2+4*b*c+3*c^2)*b*c)*a^2+(b^6+c^6+(7*b^2-24*b*c+7*c^2)*b^2*c^2)*a+(b^2-c^2)*(b-c)*(b^2-4*b*c+c^2)*b*c)*(b-c) : :

X(44318) lies on these lines: {2254, 13252}, {3676, 17625}, {3835, 17618}, {3900, 23813}

X(44319) = PERSPECTOR OF THESE TRIANGLES: MOSES-SODDY AND URSA-MINOR

Barycentrics    a*((b+c)*a^3-2*(b^2+b*c+c^2)*a^2+(b^3+c^3)*a+(b-c)^2*b*c)*(b-c) : :
X(44319) = 3*X(210)-2*X(4468) = 3*X(354)-4*X(3676) = 3*X(1638)-2*X(2488) = 3*X(30724)-2*X(39541)

X(44319) lies on these lines: {210, 4468}, {354, 3676}, {512, 20507}, {926, 21104}, {1638, 2488}, {1836, 8049}, {2223, 4905}, {3057, 28292}, {3309, 4077}, {3474, 26853}, {3835, 17605}, {6003, 40467}, {6006, 31391}, {15636, 43921}, {17660, 37998}, {18071, 21302}, {23806, 42325}, {30724, 39541}

X(44319) = crossdifference of every pair of points on line {X(1), X(14746)}
X(44319) = crosspoint of X(651) and X(42311)
X(44319) = crosssum of X(i) and X(j) for these (i, j): {55, 4040}, {354, 4905}
X(44319) = barycentric product X(513)*X(28742)
X(44319) = trilinear product X(649)*X(28742)

X(44320) = PERSPECTOR OF THESE TRIANGLES: MOSES-SODDY AND 24TH VIJAY-PAASCHE-HUTSON

Barycentrics    (-a^2+b*c+(b+c)*a+2*S)*(b-c)^2 : :

X(44320) lies on these lines: {514, 22107}, {812, 1015}

X(44320) = pole of the trilinear polar of X(1123) with respect to circumhyperbola dual of Yff parabola
X(44320) = X(1123)-Ceva conjugate of-X(514)

X(44321) = X(51)X(15059)∩X(125)X(3819)

Barycentrics    ((b^2+c^2)*a^8+7*(b^2+c^2)*a^4*b^2*c^2-2*(b^4+3*b^2*c^2+c^4)*a^6+(2*b^8+2*c^8+(7*b^4-24*b^2*c^2+7*c^4)*b^2*c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4+10*b^2*c^2+c^4))*a^2 : :
Barycentrics    (SB+SC)*((33*R^2-10*SA-8*SW)*S^2+(3*(12*SA+5*SW)*R^2-10*SA^2+10*SB*SC-2*SW^2)*SA) : :
X(44321) = X(51)-5*X(15059), X(3448)+7*X(44299), X(5447)+2*X(20396), X(5642)-3*X(15082), 3*X(5650)+X(9140), X(5891)+3*X(15061), X(5892)-3*X(34128), X(5907)+5*X(38729), 4*X(6723)-X(41671), X(9143)-9*X(33879), 5*X(11451)-X(13417), X(11793)+2*X(20397), X(11807)-3*X(14845), 3*X(14644)+X(36987), X(14855)-5*X(38728), 3*X(15055)+X(32062), X(15738)+2*X(17704), 3*X(20791)+X(21650)

See Antreas Hatzipolakis and César Lozada, euclid 2058.

X(44321) lies on these lines: {51, 15059}, {125, 3819}, {511, 12099}, {1154, 40685}, {2393, 6698}, {2777, 10127}, {2781, 6688}, {2979, 11800}, {3448, 44299}, {5447, 20396}, {5642, 15082}, {5650, 9140}, {5663, 10124}, {5891, 15061}, {5892, 10628}, {5907, 38729}, {6000, 6699}, {9143, 33879}, {10219, 41670}, {11451, 13417}, {11793, 20397}, {11807, 14845}, {14644, 36987}, {14855, 38728}, {15055, 32062}, {15738, 17704}, {17855, 18435}, {20791, 21650}

X(44321) = midpoint of X(i) and X(j) for these {i, j}: {125, 3819}, {2979, 11800}, {17855, 18435}
X(44321) = reflection of X(i) in X(j) for these (i, j): (6688, 6723), (41670, 10219), (41671, 6688)

X(44322) = X(49)X(41586)∩X(54)X(37644)

Barycentrics    ((b^2+c^2)*a^4-2*(b^4+b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*(2*a^10-5*(b^2+c^2)*a^8+2*(b^4+b^2*c^2+c^4)*a^6+2*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^4-4*(b^4+c^4)*(b^2-c^2)^2*a^2+(b^4-c^4)*(b^2-c^2)^3) : :

See Antreas Hatzipolakis and César Lozada, euclid 2058.

X(44322) lies on these lines: {49, 41586}, {54, 37644}, {206, 5965}, {382, 6288}, {539, 2917}, {1154, 15761}, {1209, 1216}, {2888, 31304}, {3574, 10254}, {5449, 34751}, {6689, 10601}, {7689, 18400}, {7691, 35481}, {8254, 8262}, {13419, 15605}, {18580, 32348}

X(44322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1209, 41599, 6153), (41594, 41598, 1209)

X(44323) = X(6)X(6636)∩X(51)X(6329)

Barycentrics    a^2*(2*(b^2+c^2)*a^4-10*b^2*c^2*a^2-(b^2+c^2)*(2*b^4-b^2*c^2+2*c^4)) : :
X(44323) = 5*X(141)-7*X(44299), 5*X(575)-2*X(16881), 5*X(597)-3*X(5640), 3*X(597)-X(9971), 5*X(3589)-4*X(6688), 7*X(3589)-4*X(9822), 3*X(3589)-2*X(40670), 5*X(3589)-2*X(41579), X(3631)+2*X(32366), 3*X(3917)+5*X(40673), 9*X(5640)-5*X(9971), 2*X(6329)+X(17710), X(6467)+2*X(34573), 7*X(6688)-5*X(9822), 6*X(6688)-5*X(40670), 5*X(8550)+X(18436), 6*X(9822)-7*X(40670), 10*X(9822)-7*X(41579), 6*X(15082)-5*X(20582), 5*X(40670)-3*X(41579)

See Antreas Hatzipolakis and César Lozada, euclid 2058.

X(44323) lies on these lines: {6, 6636}, {51, 6329}, {141, 26913}, {182, 15646}, {511, 20583}, {524, 3917}, {575, 16881}, {597, 5640}, {1154, 12007}, {2393, 3589}, {2781, 40647}, {2854, 15082}, {2979, 3629}, {3631, 3819}, {6467, 34573}, {6656, 16175}, {8550, 18436}, {9019, 21849}, {9973, 11451}, {10541, 40929}, {11574, 32455}, {15531, 22165}, {37283, 41614}

X(44323) = midpoint of X(i) and X(j) for these {i, j}: {51, 17710}, {2979, 3629}, {3819, 32366}, {15531, 22165}
X(44323) = reflection of X(i) in X(j) for these (i, j): (51, 6329), (3631, 3819), (41579, 6688)

X(44324) = X(3)X(9544)∩X(5)X(2979)

Barycentrics    a^2*(2*(b^2+c^2)*a^6-2*(3*b^4+5*b^2*c^2+3*c^4)*a^4+3*(b^2+c^2)*(2*b^4+b^2*c^2+2*c^4)*a^2-(b^2-c^2)^2*(b^2+2*c^2)*(2*b^2+c^2)) : :
X(44324) = 7*X(2)-3*X(13321), 2*X(3)+X(31834), X(5)-7*X(7999), 5*X(5)+X(37484), X(2979)+7*X(7999), 5*X(2979)-X(37484), 3*X(3917)+X(5891), 7*X(3917)+X(15030), 5*X(3917)+X(15060), 11*X(3917)+X(16194), 15*X(3917)+X(32062), 9*X(3917)-X(36987), 7*X(5891)-3*X(15030), 5*X(5891)-3*X(15060), X(5891)-3*X(15067), 11*X(5891)-3*X(16194), 5*X(5891)-X(32062), 3*X(5891)+X(36987), 5*X(15030)-7*X(15060), X(15030)-7*X(15067), 11*X(15030)-7*X(16194), 15*X(15030)-7*X(32062), 9*X(15030)+7*X(36987)

See Antreas Hatzipolakis and César Lozada, euclid 2058.

X(44324) lies on these lines: {2, 13321}, {3, 9544}, {5, 2979}, {30, 3917}, {51, 3628}, {52, 16239}, {140, 389}, {141, 39504}, {143, 6688}, {154, 7525}, {381, 33884}, {511, 547}, {546, 10627}, {548, 5447}, {549, 5890}, {550, 11444}, {568, 11539}, {632, 11412}, {2781, 10272}, {3060, 15699}, {3530, 5562}, {3845, 13340}, {3850, 10625}, {3853, 14128}, {3859, 13598}, {5066, 10170}, {5446, 12812}, {5650, 5946}, {5663, 34200}, {5876, 14855}, {5889, 14869}, {5907, 12103}, {6102, 12108}, {6243, 11451}, {6592, 34828}, {7496, 15087}, {7502, 15066}, {7516, 11402}, {7555, 9306}, {8703, 11459}, {9730, 11812}, {9820, 34004}, {10201, 10519}, {10226, 43652}, {10263, 14845}, {11002, 15703}, {11455, 15704}, {11465, 41992}, {11592, 40647}, {11801, 41673}, {12100, 13754}, {12106, 17811}, {12162, 44245}, {14915, 15691}, {15045, 15713}, {15305, 15686}, {15712, 18436}, {16261, 35404}, {16836, 41983}, {18445, 21766}, {21230, 37452}, {21357, 37636}, {32137, 40247}, {34006, 35265}

X(44324) = midpoint of X(i) and X(j) for these {i, j}: {5, 2979}, {51, 6101}, {549, 23039}, {550, 18435}, {1216, 3819}, {3845, 13340}, {3917, 15067}, {5876, 14855}, {6688, 15606}, {8703, 11459}, {11455, 15704}, {15305, 15686}
X(44324) = reflection of X(i) in X(j) for these (i, j): (51, 3628), (140, 3819), (143, 6688), (3819, 32142), (5066, 10170), (5946, 10124), (9730, 11812), (13451, 547), (14449, 51), (14855, 33923)
X(44324) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (632, 11412, 16881), (1216, 32142, 140), (3628, 6101, 14449), (5447, 11591, 548), (5650, 5946, 10124), (5891, 32062, 15060), (7998, 23039, 549), (10627, 11793, 546), (14128, 15644, 3853)

X(44325) = X(3)X(54)∩X(51)X(8254)

Barycentrics    a^2*((b^2+c^2)*a^12-2*(b^2+2*c^2)*(2*b^2+c^2)*a^10+(b^2+c^2)*(5*b^4+16*b^2*c^2+5*c^4)*a^8-3*(5*b^4+4*b^2*c^2+5*c^4)*b^2*c^2*a^6-(b^2+c^2)*(5*b^8+5*c^8-(9*b^4-17*b^2*c^2+9*c^4)*b^2*c^2)*a^4+(b^6-c^6)*(b^2-c^2)*(4*b^4+b^2*c^2+4*c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3*(b^4+b^2*c^2+c^4)) : :
Barycentrics    (SB+SC)*((11*R^2+2*SA-2*SW)*S^2+(6*R^4-(11*SA+10*SW)*R^2+2*SA^2-2*SB*SC+4*SW^2)*SA) : :
X(44325) = 2*X(140)+X(21660), 2*X(143)+X(12226), 2*X(1209)+X(15532), 2*X(1493)+X(6101), X(1493)+2*X(12363), 5*X(1656)+X(12291), X(3519)-4*X(32142), 7*X(3526)-X(12280), X(5876)+2*X(10619), X(6101)-4*X(12363), X(6102)+2*X(12606), 2*X(6152)-5*X(15026), X(6242)-4*X(12006), 4*X(6689)-X(13368), 4*X(8254)-X(32196), X(10263)-4*X(12242), X(10625)+2*X(11803), 2*X(10627)+X(15801), 2*X(13630)+X(22815), X(21230)+2*X(40632)

See Antreas Hatzipolakis and César Lozada, euclid 2058.

X(44325) lies on these lines: {3, 54}, {51, 8254}, {140, 21660}, {141, 21357}, {143, 12226}, {539, 15067}, {1209, 15532}, {1656, 12291}, {2781, 11702}, {3519, 15108}, {3526, 12280}, {3819, 21230}, {5876, 10619}, {5891, 32423}, {5946, 15330}, {6152, 15026}, {6153, 6688}, {6242, 12006}, {6689, 13368}, {10263, 12242}, {10625, 11803}, {11451, 13365}, {12234, 36153}, {12254, 18435}, {13364, 37943}, {14855, 43581}, {15089, 35921}, {18376, 22804}, {18475, 38898}, {23048, 38317}, {37649, 44234}

X(44325) = midpoint of X(i) and X(j) for these {i, j}: {195, 2979}, {3819, 40632}, {12254, 18435}, {14855, 43581}
X(44325) = reflection of X(i) in X(j) for these (i, j): (51, 8254), (6153, 6688), (21230, 3819), (32196, 51)
X(44325) = {X(1493), X(12363)}-harmonic conjugate of X(6101)

X(44326) = ISOTOMIC CONJUGATE OF X(6587)

Barycentrics    (a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*(a^2-c^2)*(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))*(a^2-b^2) : :

See Antreas Hatzipolakis and César Lozada, euclid 2060.

X(44326) lies on these lines: {2, 20313}, {99, 1301}, {107, 3265}, {110, 35571}, {122, 35140}, {253, 30769}, {325, 16096}, {459, 8781}, {1073, 41530}, {4561, 7256}, {4563, 34211}, {7763, 34403}, {8858, 33581}, {34410, 40995}

X(44326) = isotomic conjugate of X(6587)
X(44326) = isogonal conjugate of PK-transform of X(20)
X(44326) = isogonal conjugate of PK-transform of X(64)
X(44326) = polar conjugate of X(44705)
X(44326) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(107)}} and {{A, B, C, X(99), X(4554)}}
X(44326) = trilinear pole of the line {20, 64}
X(44326) = barycentric product X(i)*X(j) for these {i, j}: {64, 670}, {99, 253}, {110, 41530}, {305, 1301}, {459, 4563}, {648, 34403}
X(44326) = barycentric quotient X(i)/X(j) for these (i, j): (3, 42658), (8, 14308), (64, 512), (75, 17898), (86, 21172), (99, 20)
X(44326) = trilinear product X(i)*X(j) for these {i, j}: {64, 799}, {99, 2184}, {162, 34403}, {163, 41530}, {253, 662}, {304, 1301}
X(44326) = trilinear quotient X(i)/X(j) for these (i, j): (63, 42658), (64, 798), (76, 17898), (99, 610), (162, 3172), (190, 3198)

X(44327) = ISOTOMIC CONJUGATE OF X(14837)

Barycentrics    (a-c)*(a^3+(b-c)*a^2-(b-c)^2*a-(b+c)*(b^2-c^2))*(a-b)*(a^3-(b-c)*a^2-(b-c)^2*a+(b+c)*(b^2-c^2)) : :

See Antreas Hatzipolakis and César Lozada, euclid 2060.

X(44327) lies on these lines: {2, 23982}, {84, 36798}, {189, 1997}, {190, 2406}, {282, 309}, {336, 41087}, {645, 4592}, {646, 4561}, {653, 6332}, {662, 7452}, {664, 6335}, {1310, 40117}, {1332, 3699}, {1422, 36805}, {1436, 36799}, {1440, 28753}, {1461, 3239}, {1903, 36800}, {4626, 15413}, {6081, 9056}, {7020, 8777}, {8059, 8707}, {9376, 19582}, {16596, 34393}, {18743, 34404}

X(44327) = isotomic conjugate of X(14837)
X(44327) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(1461)}} and {{A, B, C, X(2), X(653)}}
X(44327) = trilinear pole of the line {8, 20} (the line through X(8) perpendicular to the trilinear polar of X(8))
X(44327) = barycentric product X(i)*X(j) for these {i, j}: {75, 13138}, {76, 36049}, {84, 668}, {99, 39130}, {100, 309}, {101, 44190}
X(44327) = barycentric quotient X(i)/X(j) for these (i, j): (1, 6129), (9, 14298), (75, 17896), (84, 513), (99, 8822), (100, 40)
X(44327) = trilinear product X(i)*X(j) for these {i, j}: {2, 13138}, {8, 37141}, {69, 40117}, {75, 36049}, {76, 32652}, {84, 190}
X(44327) = trilinear quotient X(i)/X(j) for these (i, j): (2, 6129), (8, 14298), (76, 17896), (78, 10397), (84, 649), (99, 1817)

leftri

Steiner-ellipse-inverses of points on the Euler line: X(44328)-X(44349)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, August 23, 2021.

Suppose that P is a point on the Euler line. Then P is given by the combo X(2) + t*x(3) for some t, and the Steiner-circumellipse-inverse of P is given by the following combo:

(3*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 - 2*b^4*c^4 + a^2*c^6 + b^2*c^6)*k - 16*S^4)*X[2] + 16*(1 + k)*S^4*X[3]

The appearance of (i,j) in the following list means that X(j) = Steiner-circumellipse-inverse of X(i):

(2,30), (3,401), (4,297), (5,40853), (20,441), (21,448), (22,15013), (23,40856), (24,44328), (25,15014), (26,44329), (27,447), (28,44330), (29,44331), (237,10684), (376,40884), (381,40885), (384,6660), (427,40889), (449,452), (458,35474), (468,40890), (472,11093), (473,11094), (858,35923), (2479, 2479), (2480,2480), (3543,44216), (4235,7473), (6655,21536), (8613,15781), (1113,44332), (1114,44333), (14953,37045), (37174,44228), (37188,44252)

Continuing with a point P on the Euler line, with combo X(2) + t*x(3) for some t, the Steiner-inellipse-inverse of P is given by the following combo:

(3*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 - 2*b^4*c^4 + a^2*c^6 + b^2*c^6)*k - 16*S^4)*X[2] + 16*(1 + k)*S^4*X[3]

The appearance of (i,j) in the following list means that X(j) = Steiner-inellipse-inverse of X(i):

(2,30), (3,441), (4,44334), (5,297), (20,44335), (21,44336), (22,44337), (23,44338), (24,44339), (25,44340), (26,44341), (27,44342), (28,44343), (29,44344), (140,401), (237,44345), (376,44346), (381,44216), (384,44347), (447,6678), (448,6675), (449,11108), (468,40856), (547,40885), (549,40884), (1113,44348), (1114,44349), (1375,37045), (2454,2454), (2455, 2455), (3628,40853), (5159,35923), (6656,21536), (6660,7819), (6676,15013), (6677,15014), (37911,40890)

X(44328) = STEINER-CIRCUMELLIPSE-INVERSE OF X(24)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6 - 3*a^8*c^2 + 5*a^6*b^2*c^2 - 4*a^4*b^4*c^2 + 3*a^2*b^6*c^2 - b^8*c^2 + 3*a^6*c^4 - 4*a^4*b^2*c^4 - 2*a^2*b^4*c^4 + b^6*c^4 - a^4*c^6 + 3*a^2*b^2*c^6 + b^4*c^6 - b^2*c^8) : :

X(44328) lies on these lines: {2, 3}, {287, 34146}, {4558, 37778}, {20563, 36416}, {36212, 41253}, {37784, 41678}, {41679, 44138}

X(44328) = anticomplement of anticomplement of X(44339)
X(44328) = {X(2479),X(2480)}-harmonic conjugate of X(24)

X(44329) = STEINER-CIRCUMELLIPSE-INVERSE OF X(26)

Barycentrics    a^14 - 3*a^12*b^2 + 2*a^10*b^4 + 2*a^8*b^6 - 3*a^6*b^8 + a^4*b^10 - 3*a^12*c^2 + 5*a^10*b^2*c^2 - 3*a^8*b^4*c^2 + 2*a^6*b^6*c^2 + a^4*b^8*c^2 - 3*a^2*b^10*c^2 + b^12*c^2 + 2*a^10*c^4 - 3*a^8*b^2*c^4 - 2*a^4*b^6*c^4 + 6*a^2*b^8*c^4 - 3*b^10*c^4 + 2*a^8*c^6 + 2*a^6*b^2*c^6 - 2*a^4*b^4*c^6 - 6*a^2*b^6*c^6 + 2*b^8*c^6 - 3*a^6*c^8 + a^4*b^2*c^8 + 6*a^2*b^4*c^8 + 2*b^6*c^8 + a^4*c^10 - 3*a^2*b^2*c^10 - 3*b^4*c^10 + b^2*c^12 : :

X(44329) lies on these lines: {2, 3}, {20564, 36418}

X(44329) = anticomplement of anticomplement of X(44341)
X(44329) = {X(2479),X(2480)}-harmonic conjugate of X(26)

X(44330) = STEINER-CIRCUMELLIPSE-INVERSE OF X(28)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^5 - a^3*b^2 - a^3*b*c + a^2*b^2*c + a*b^3*c - b^4*c - a^3*c^2 + a^2*b*c^2 + 2*a*b^2*c^2 - b^3*c^2 + a*b*c^3 - b^2*c^3 - b*c^4) : :

X(44330) lies on these lines: {2, 3}, {162, 239}, {525, 17498}, {536, 648}, {894, 2326}, {3227, 16077}, {4567, 23582}, {20336, 36420}, {25257, 41676}

X(44330) = anticomplement of anticomplement of X(44343)
X(44330) = antitomic conjugate of X(16085)
X(44330) = {X(2479),X(2480)}-harmonic conjugate of X(28)

X(44331) = STEINER-CIRCUMELLIPSE-INVERSE OF X(29)

Barycentrics    (a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^5 - a^3*b^2 - a^2*b^3 + b^5 - a^3*b*c + a*b^3*c - a^3*c^2 + 2*a*b^2*c^2 - b^3*c^2 - a^2*c^3 + a*b*c^3 - b^2*c^3 + c^5) : :

X(44331) lies on these lines: {2, 3}, {307, 36421}, {525, 17926}, {527, 648}, {823, 1948}, {1121, 16077}, {2326, 7282}, {3496, 31623}, {3912, 36797}, {8748, 8822}, {40843, 41207}

X(44331) = anticomplement of anticomplement of X(44344)
X(44331) = {X(2479),X(2480)}-harmonic conjugate of X(29)

X(44332) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1113)

Barycentrics    a^8 - a^6*b^2 - a^2*b^6 + b^8 - a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + a^2*b^2*c^4 - a^2*c^6 - b^2*c^6 + c^8 - (a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 + a^4*c^4 - 2*b^4*c^4 + b^2*c^6)*J : :

X(44332) lies on these lines: {2, 3}, {112, 2592}, {287, 2575}, {525, 8115}, {2966, 15164}, {22339, 41941}, {23582, 39299}

X(44332) = relfection of X(44333) in X(40856)
X(44332) = anticomplement of anticomplement of X(44348)
X(44332) = {X(2),X(401)}-harmonic conjugate of X(44333)
X(44332) = {X(2479),X(2480)}-harmonic conjugate of X(1113)

X(44333) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1114)

Barycentrics    a^8 - a^6*b^2 - a^2*b^6 + b^8 - a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + a^2*b^2*c^4 - a^2*c^6 - b^2*c^6 + c^8 + (a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 + a^4*c^4 - 2*b^4*c^4 + b^2*c^6)*J : :

X(44333) lies on these lines: {2, 3}, {112, 2593}, {287, 2574}, {525, 8116}, {2966, 15165}, {22340, 41942}, {23582, 39298}

X(44333) = reflection of X(44332) in X(40856)
X(44333) = anticomplement of anticomplement of X(44349)
X(44333) = {X(2),X(401)}-harmonic conjugate of X(44332)
X(44333) = {X(2479),X(2480)}-harmonic conjugate of X(1114)

X(44334) = STEINER-INELLIPSE-INVERSE OF X(4)

Barycentrics    2*a^8 - a^6*b^2 - a^4*b^4 - 3*a^2*b^6 + 3*b^8 - a^6*c^2 + 2*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 4*b^6*c^2 - a^4*c^4 + 3*a^2*b^2*c^4 + 2*b^4*c^4 - 3*a^2*c^6 - 4*b^2*c^6 + 3*c^8 : :

X(44334) lies on these lines: {2, 3}, {6, 20204}, {98, 9476}, {230, 23976}, {253, 33630}, {393, 20208}, {524, 23583}, {525, 3239}, {648, 40996}, {1249, 40995}, {1503, 40542}, {1990, 15526}, {3564, 15595}, {3767, 20207}, {3912, 15252}, {5305, 13567}, {6330, 6530}, {6389, 42459}, {7776, 37669}, {10002, 34815}, {14572, 38253}, {14725, 23292}, {14743, 17282}, {14767, 34573}, {15466, 41009}, {16318, 43717}, {17907, 41005}, {23967, 41139}, {32001, 38292}, {34360, 43620}

X(44334) = complement of X(441)
X(44334) = anticomplement of X(44335)
X(44334) = {X(2454),X(2455)}-harmonic conjugate of X(4)

X(44335) = STEINER-INELLIPSE-INVERSE OF X(20)

Barycentrics    6*a^8 - 7*a^6*b^2 + a^4*b^4 - 5*a^2*b^6 + 5*b^8 - 7*a^6*c^2 + 6*a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 4*b^6*c^2 + a^4*c^4 + 5*a^2*b^2*c^4 - 2*b^4*c^4 - 5*a^2*c^6 - 4*b^2*c^6 + 5*c^8 : :

X(44335) lies on these lines: {2, 3}, {524, 40484}, {525, 7658}, {3788, 20203}, {6389, 20204}, {11064, 40512}, {18440, 42287}

X(44335) = complement of X(44334)
X(44335) = {X(2454),X(2455)}-harmonic conjugate of X(20)

X(44336) = STEINER-INELLIPSE-INVERSE OF X(21)

Barycentrics    2*a^8 - 3*a^6*b^2 + a^4*b^4 - a^2*b^6 + b^8 - 2*a^6*b*c - 2*a^5*b^2*c + a^4*b^3*c + a^3*b^4*c + a^2*b^5*c + a*b^6*c - 3*a^6*c^2 - 2*a^5*b*c^2 + 2*a^4*b^2*c^2 + a^3*b^3*c^2 + a^2*b^4*c^2 + a*b^5*c^2 + a^4*b*c^3 + a^3*b^2*c^3 - 2*a^2*b^3*c^3 - 2*a*b^4*c^3 + a^4*c^4 + a^3*b*c^4 + a^2*b^2*c^4 - 2*a*b^3*c^4 - 2*b^4*c^4 + a^2*b*c^5 + a*b^2*c^5 - a^2*c^6 + a*b*c^6 + c^8 : :

X(44336) lies on these lines: {2, 3}, {525, 14838}

X(44336) = {X(2454),X(2455)}-harmonic conjugate of X(21)

X(44337) = STEINER-INELLIPSE-INVERSE OF X(22)

Barycentrics    2*a^10 - a^8*b^2 - 2*a^6*b^4 + b^10 - a^8*c^2 + 2*a^4*b^4*c^2 - 2*a^2*b^6*c^2 + b^8*c^2 - 2*a^6*c^4 + 2*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 - 2*a^2*b^2*c^6 - 2*b^4*c^6 + b^2*c^8 + c^10 : :

X(44337) lies on these lines: {2, 3}, {525, 7630}, {754, 40484}, {3564, 41255}

X(44337) = {X(2454),X(2455)}-harmonic conjugate of X(22)

X(44338) = STEINER-INELLIPSE-INVERSE OF X(23)

Barycentrics    2*a^10 - a^8*b^2 - 2*a^6*b^4 + b^10 - a^8*c^2 + 2*a^6*b^2*c^2 + a^4*b^4*c^2 - 3*a^2*b^6*c^2 + b^8*c^2 - 2*a^6*c^4 + a^4*b^2*c^4 + 6*a^2*b^4*c^4 - 2*b^6*c^4 - 3*a^2*b^2*c^6 - 2*b^4*c^6 + b^2*c^8 + c^10 : :

X(44338) lies on these lines: {2, 3}, {525, 3589}, {15595, 32423}

X(44338) = midpoint of X(44348) and X(44349)
X(44338) = complement of complement of X(40856)
X(44338) = {X(2454),X(2455)}-harmonic conjugate of X(23)

X(44339) = STEINER-INELLIPSE-INVERSE OF X(24)

Barycentrics    2*a^14 - 5*a^12*b^2 + 2*a^10*b^4 + 3*a^8*b^6 - 2*a^6*b^8 + a^4*b^10 - 2*a^2*b^12 + b^14 - 5*a^12*c^2 + 8*a^10*b^2*c^2 - 5*a^8*b^4*c^2 + 2*a^6*b^6*c^2 + 3*a^4*b^8*c^2 - 2*a^2*b^10*c^2 - b^12*c^2 + 2*a^10*c^4 - 5*a^8*b^2*c^4 - 4*a^4*b^6*c^4 + 10*a^2*b^8*c^4 - 3*b^10*c^4 + 3*a^8*c^6 + 2*a^6*b^2*c^6 - 4*a^4*b^4*c^6 - 12*a^2*b^6*c^6 + 3*b^8*c^6 - 2*a^6*c^8 + 3*a^4*b^2*c^8 + 10*a^2*b^4*c^8 + 3*b^6*c^8 + a^4*c^10 - 2*a^2*b^2*c^10 - 3*b^4*c^10 - 2*a^2*c^12 - b^2*c^12 + c^14 : :

X(44339) lies on these lines: {2, 3}, {525, 16040}

X(44339) = complement of complement of X(44328)
X(44339) = {X(2454),X(2455)}-harmonic conjugate of X(24)

X(44340) = STEINER-INELLIPSE-INVERSE OF X(25)

Barycentrics    2*a^10 - a^8*b^2 - 2*a^6*b^4 + b^10 - a^8*c^2 + 4*a^6*b^2*c^2 - 4*a^2*b^6*c^2 + b^8*c^2 - 2*a^6*c^4 + 8*a^2*b^4*c^4 - 2*b^6*c^4 - 4*a^2*b^2*c^6 - 2*b^4*c^6 + b^2*c^8 + c^10 : :

X(44340) lies on these lines: {2, 3}, {230, 6720}, {339, 16318}, {525, 2485}, {538, 23583}, {1575, 40561}, {2207, 14376}, {14581, 15526}, {15048, 20204}

X(44340) = {X(2454),X(2455)}-harmonic conjugate of X(25)

X(44341) = STEINER-INELLIPSE-INVERSE OF X(26)

Barycentrics    2*a^14 - 5*a^12*b^2 + 2*a^10*b^4 + 3*a^8*b^6 - 2*a^6*b^8 + a^4*b^10 - 2*a^2*b^12 + b^14 - 5*a^12*c^2 + 4*a^10*b^2*c^2 + a^8*b^4*c^2 + 5*a^4*b^8*c^2 - 4*a^2*b^10*c^2 - b^12*c^2 + 2*a^10*c^4 + a^8*b^2*c^4 - 4*a^6*b^4*c^4 - 6*a^4*b^6*c^4 + 10*a^2*b^8*c^4 - 3*b^10*c^4 + 3*a^8*c^6 - 6*a^4*b^4*c^6 - 8*a^2*b^6*c^6 + 3*b^8*c^6 - 2*a^6*c^8 + 5*a^4*b^2*c^8 + 10*a^2*b^4*c^8 + 3*b^6*c^8 + a^4*c^10 - 4*a^2*b^2*c^10 - 3*b^4*c^10 - 2*a^2*c^12 - b^2*c^12 + c^14 : :

X(44341) lies on these lines: {2, 3}

X(44341) = complement of complement of X(44329)
X(44341) = {X(2454),X(2455)}-harmonic conjugate of X(26)

X(44342) = STEINER-INELLIPSE-INVERSE OF X(27)

Barycentrics    2*a^10 + 2*a^9*b - a^8*b^2 - a^7*b^3 - 2*a^6*b^4 - a^5*b^5 - 3*a^3*b^7 + 3*a*b^9 + b^10 + 2*a^9*c + 2*a^8*b*c - a^7*b^2*c - a^6*b^3*c - a^5*b^4*c - a^4*b^5*c - 3*a^3*b^6*c - 3*a^2*b^7*c + 3*a*b^8*c + 3*b^9*c - a^8*c^2 - a^7*b*c^2 + 4*a^6*b^2*c^2 + 2*a^5*b^3*c^2 + 3*a^3*b^5*c^2 - 4*a^2*b^6*c^2 - 4*a*b^7*c^2 + b^8*c^2 - a^7*c^3 - a^6*b*c^3 + 2*a^5*b^2*c^3 + 2*a^4*b^3*c^3 + 3*a^3*b^4*c^3 + 3*a^2*b^5*c^3 - 4*a*b^6*c^3 - 4*b^7*c^3 - 2*a^6*c^4 - a^5*b*c^4 + 3*a^3*b^3*c^4 + 8*a^2*b^4*c^4 + 2*a*b^5*c^4 - 2*b^6*c^4 - a^5*c^5 - a^4*b*c^5 + 3*a^3*b^2*c^5 + 3*a^2*b^3*c^5 + 2*a*b^4*c^5 + 2*b^5*c^5 - 3*a^3*b*c^6 - 4*a^2*b^2*c^6 - 4*a*b^3*c^6 - 2*b^4*c^6 - 3*a^3*c^7 - 3*a^2*b*c^7 - 4*a*b^2*c^7 - 4*b^3*c^7 + 3*a*b*c^8 + b^2*c^8 + 3*a*c^9 + 3*b*c^9 + c^10 : :

X(44342) lies on these lines: {2, 3}, {519, 23583}, {525, 8062}, {30117, 35122}

X(44342) = complement of isotomic conjugate of cevapoint of X(2) and X(447)
X(44342) = complement of complement of X(447)
X(44342) = {X(2454),X(2455)}-harmonic conjugate of X(27)

X(44343) = STEINER-INELLIPSE-INVERSE OF X(28)

Barycentrics    2*a^11 + 2*a^10*b - a^9*b^2 - a^8*b^3 - 2*a^7*b^4 - 2*a^6*b^5 + a*b^10 + b^11 + 2*a^10*c + 2*a^9*b*c - a^8*b^2*c - a^7*b^3*c - 2*a^6*b^4*c - a^5*b^5*c - 3*a^3*b^7*c + 3*a*b^9*c + b^10*c - a^9*c^2 - a^8*b*c^2 + 4*a^7*b^2*c^2 + 4*a^6*b^3*c^2 - 4*a^3*b^6*c^2 - 4*a^2*b^7*c^2 + a*b^8*c^2 + b^9*c^2 - a^8*c^3 - a^7*b*c^3 + 4*a^6*b^2*c^3 + 2*a^5*b^3*c^3 + 3*a^3*b^5*c^3 - 4*a^2*b^6*c^3 - 4*a*b^7*c^3 + b^8*c^3 - 2*a^7*c^4 - 2*a^6*b*c^4 + 8*a^3*b^4*c^4 + 8*a^2*b^5*c^4 - 2*a*b^6*c^4 - 2*b^7*c^4 - 2*a^6*c^5 - a^5*b*c^5 + 3*a^3*b^3*c^5 + 8*a^2*b^4*c^5 + 2*a*b^5*c^5 - 2*b^6*c^5 - 4*a^3*b^2*c^6 - 4*a^2*b^3*c^6 - 2*a*b^4*c^6 - 2*b^5*c^6 - 3*a^3*b*c^7 - 4*a^2*b^2*c^7 - 4*a*b^3*c^7 - 2*b^4*c^7 + a*b^2*c^8 + b^3*c^8 + 3*a*b*c^9 + b^2*c^9 + a*c^10 + b*c^10 + c^11 : :

X(44343) lies on these lines: {2, 3}, {525, 16612}, {536, 23583}, {3008, 40532}

X(44343) = complement of complement of X(44330)
X(44343) = {X(2454),X(2455)}-harmonic conjugate of X(28)

X(44344) = STEINER-INELLIPSE-INVERSE OF X(29)

Barycentrics    2*a^11 - 3*a^9*b^2 - a^7*b^4 - a^6*b^5 + a^5*b^6 + 3*a^4*b^7 + 3*a^3*b^8 - 3*a^2*b^9 - 2*a*b^10 + b^11 - 2*a^9*b*c - 2*a^8*b^2*c + a^7*b^3*c + a^5*b^5*c + 4*a^4*b^6*c + 3*a^3*b^7*c - 3*a*b^9*c - 2*b^10*c - 3*a^9*c^2 - 2*a^8*b*c^2 + 6*a^7*b^2*c^2 + 3*a^6*b^3*c^2 - a^5*b^4*c^2 - 2*a^4*b^5*c^2 - 4*a^3*b^6*c^2 + 3*a^2*b^7*c^2 + 2*a*b^8*c^2 - 2*b^9*c^2 + a^7*b*c^3 + 3*a^6*b^2*c^3 - 2*a^5*b^3*c^3 - 5*a^4*b^4*c^3 - 3*a^3*b^5*c^3 - 3*a^2*b^6*c^3 + 4*a*b^7*c^3 + 5*b^8*c^3 - a^7*c^4 - a^5*b^2*c^4 - 5*a^4*b^3*c^4 + 2*a^3*b^4*c^4 + 3*a^2*b^5*c^4 + 2*b^7*c^4 - a^6*c^5 + a^5*b*c^5 - 2*a^4*b^2*c^5 - 3*a^3*b^3*c^5 + 3*a^2*b^4*c^5 - 2*a*b^5*c^5 - 4*b^6*c^5 + a^5*c^6 + 4*a^4*b*c^6 - 4*a^3*b^2*c^6 - 3*a^2*b^3*c^6 - 4*b^5*c^6 + 3*a^4*c^7 + 3*a^3*b*c^7 + 3*a^2*b^2*c^7 + 4*a*b^3*c^7 + 2*b^4*c^7 + 3*a^3*c^8 + 2*a*b^2*c^8 + 5*b^3*c^8 - 3*a^2*c^9 - 3*a*b*c^9 - 2*b^2*c^9 - 2*a*c^10 - 2*b*c^10 + c^11 : :

X(44344) lies on this line {2, 3}, {527, 23583}

X(44344) = complement of complement of X(44331)
X(44344) = {X(2454),X(2455)}-harmonic conjugate of X(29)

X(44345) = STEINER-INELLIPSE-INVERSE OF X(237)

Barycentrics    2*a^10*b^2 - 3*a^8*b^4 + a^6*b^6 - a^4*b^8 + a^2*b^10 + 2*a^10*c^2 - 2*a^8*b^2*c^2 + a^6*b^4*c^2 - a^4*b^6*c^2 - a^2*b^8*c^2 + b^10*c^2 - 3*a^8*c^4 + a^6*b^2*c^4 + 4*a^4*b^4*c^4 + a^6*c^6 - a^4*b^2*c^6 - 2*b^6*c^6 - a^4*c^8 - a^2*b^2*c^8 + a^2*c^10 + b^2*c^10 : :

X(44345) lies on these lines: {2, 3}, {39, 525}, {83, 2966}, {141, 14966}, {339, 9475}, {1506, 35088}, {1576, 41255}, {2421, 3933}, {3589, 5661}, {5013, 34360}

X(44345) = {X(2454),X(2455)}-harmonic conjugate of X(237)

X(44346) = STEINER-INELLIPSE-INVERSE OF X(376)

Barycentrics    10*a^8 - 13*a^6*b^2 + 3*a^4*b^4 - 7*a^2*b^6 + 7*b^8 - 13*a^6*c^2 + 10*a^4*b^2*c^2 + 7*a^2*b^4*c^2 - 4*b^6*c^2 + 3*a^4*c^4 + 7*a^2*b^2*c^4 - 6*b^4*c^4 - 7*a^2*c^6 - 4*b^2*c^6 + 7*c^8 : :

X(44346) lies on these lines: {2, 3}, {525, 14345}, {2966, 41133}, {3564, 41145}, {11180, 42287}, {22110, 23967}

X(44346) = complement of X(44216)
X(44346) = {X(2454),X(2455)}-harmonic conjugate of X(376)

X(44347) = STEINER-INELLIPSE-INVERSE OF X(384)

Barycentrics    2*a^8 - a^6*b^2 - 2*a^2*b^6 + b^8 - a^6*c^2 + 2*a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + a^2*b^2*c^4 - 2*a^2*c^6 - b^2*c^6 + c^8 : :

X(44347) lies on these lines: {2, 3}, {325, 19576}, {525, 5113}, {3506, 3564}, {9019, 40559}, {41273, 43291}

X(44347) = complement of X(21536)
X(44347) = {X(2454),X(2455)}-harmonic conjugate of X(384)

X(44348) = STEINER-INELLIPSE-INVERSE OF X(1113)

Barycentrics    4*(a^8 - a^6*b^2 - a^2*b^6 + b^8 - a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + a^2*b^2*c^4 - a^2*c^6 - b^2*c^6 + c^8) - (a^2 - b^2 - c^2)*(2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6)*J : :

X(44348) lies on this line: {2, 3}

X(44348) = reflection of X(44349) in X(44338)
X(44348) = complement of complement of X(44332)
X(44348) = {X(2),X(441)}-harmonic conjugate of X(44349)
X(44348) = {X(2454),X(2455)}-harmonic conjugate of X(1113)

X(44349) = STEINER-INELLIPSE-INVERSE OF X(1114)

Barycentrics    4*(a^8 - a^6*b^2 - a^2*b^6 + b^8 - a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + a^2*b^2*c^4 - a^2*c^6 - b^2*c^6 + c^8) + (a^2 - b^2 - c^2)*(2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6)*J : :

X(44349) lies on this line: {2, 3}

X(44349) = reflection of X(44348) in X(44338)
X(44349) = complement of complement of X(44333)
X(44349) = {X(2),X(441)}-harmonic conjugate of X(44348)
X(44349) = {X(2454),X(2455)}-harmonic conjugate of X(1114)

leftri

Steiner-ellipse-inverses of points on the line X(1)X(3): X(44350)-X(44360)

rightri

This preamble is contributed by Peter Moses, August 24, 2021.

Let f(a,b,c,x,y,z) = b c (b - c) (b + c - a) (x2 - y z). The inverse of the line X(1)X(3) in the Steiner circumellipse is the ellipse given by

f(a,b,c,x,y,z) + f(b,c,a,y,z x) + f(c,a,b,z,x,y) = 0.

Let g(a,b,c,x,y,z) = (b - c) (a3 - a b2 - a c2 - 2 a b c + 2 b2 c + 2 b c2) (x2 - y z). The inverse of the line X(1)X(3) in the Steiner inellipse is the ellipse given by

g(a,b,c,x,y,z) + g(b,c,a,y,z x) + g(c,a,b,z,x,y) = 0.

The appearance of (j,.k) in the following list means that X(j) lies on the line X(1)X(3) and the X(k) = Steiner-circumellipse-inverse of X(j):

(1,239), (3,401), (55,40861), (57,40862), (65, 44350), (241,44351), (517,2), (940,44352), (982,44353), (1214,44354), (5662,17496)

The appearance of (j,.k) in the following list means that X(j) lies on the line X(1)X(3) and the X(k) = Steiner-inellipse-inverse of X(j):

(1,3008), (3,441), (55,44355), (57,44356), (241,44357), (942, 44358), (982,44359), (1214,44360), (517,2), (5662,905)

X(44350) = STEINER-CIRCUMELLIPSE-INVERSE OF X(65)

Barycentrics    (a + b - c)*(a - b + c)*(a^4*b^2 - a^2*b^4 + a^4*b*c + a^3*b^2*c + a^2*b^3*c - a*b^4*c + a^4*c^2 + a^3*b*c^2 + 3*a^2*b^2*c^2 - a*b^3*c^2 - b^4*c^2 + a^2*b*c^3 - a*b^2*c^3 - 2*b^3*c^3 - a^2*c^4 - a*b*c^4 - b^2*c^4) : :

X(44350) lies on these lines: {2, 65}, {73, 1999}, {239, 1457}, {241, 350}, {348, 4352}, {693, 3669}, {948, 1909}, {1284, 26113}, {3911, 25510}, {11349, 40861}, {15149, 17985}, {17139, 17950}, {17321, 40784}, {26048, 40663}, {26801, 41245}

X(44351) = STEINER-CIRCUMELLIPSE-INVERSE OF X(241)

Barycentrics    (a + b - c)*(a - b + c)*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5 + a^5*b*c - a^4*b^2*c - a^2*b^4*c + a*b^5*c + a^5*c^2 - a^4*b*c^2 + a^3*b^2*c^2 + a^2*b^3*c^2 - 3*a*b^4*c^2 + b^5*c^2 - 3*a^4*c^3 + a^2*b^2*c^3 + 4*a*b^3*c^3 - b^4*c^3 + 3*a^3*c^4 - a^2*b*c^4 - 3*a*b^2*c^4 - b^3*c^4 - a^2*c^5 + a*b*c^5 + b^2*c^5) : :

X(44351) lies on these lines: {2, 85}, {145, 3900}, {651, 40861}, {664, 39350}, {1025, 3501}, {6604, 35167}, {7056, 21218}, {24410, 40862}

X(44352) = STEINER-CIRCUMELLIPSE-INVERSE OF X(940)

Barycentrics    a^5 + a^4*b + a^4*c + 4*a^3*b*c - 2*a*b^3*c - a*b^2*c^2 - b^3*c^2 - 2*a*b*c^3 - b^2*c^3 : :
X(44352) = 3 X[13586] - 4 X[16702]

X(44352) lies on these lines: {2, 6}, {314, 24271}, {523, 17496}, {1227, 4366}, {1943, 7175}, {5019, 34282}, {5327, 20077}, {13586, 16702}

X(44352) = reflection of X(385) in X(19623)
X(44352) = crossdifference of every pair of points on line {512, 4263}
X(44352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 940}

X(44353) = STEINER-CIRCUMELLIPSE-INVERSE OF X(982)

Barycentrics    -a^2*b^4 + a^4*b*c - a^3*b^2*c + 3*a^2*b^3*c - a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 + 3*a^2*b*c^3 - a*b^2*c^3 + b^3*c^3 - a^2*c^4 : :

X(44353) lies on these lines: {2, 38}, {7, 9263}, {190, 2275}, {239, 2810}, {330, 4440}, {668, 3662}, {812, 17496}, {894, 1015}, {1086, 1909}, {1469, 32029}, {5299, 24815}, {9055, 40875}, {10027, 14839}, {17291, 27076}, {17368, 27195}

X(44354) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1214)

Barycentrics    (a + b - c)*(a - b + c)*(a^7*b^2 - a^6*b^3 - 2*a^5*b^4 + 2*a^4*b^5 + a^3*b^6 - a^2*b^7 + a^7*b*c - a^6*b^2*c - a^5*b^3*c + 2*a^4*b^4*c - a^3*b^5*c - a^2*b^6*c + a*b^7*c + a^7*c^2 - a^6*b*c^2 + a^5*b^2*c^2 - a^4*b^3*c^2 - a^3*b^4*c^2 + a^2*b^5*c^2 - a*b^6*c^2 + b^7*c^2 - a^6*c^3 - a^5*b*c^3 - a^4*b^2*c^3 + 2*a^3*b^3*c^3 + a^2*b^4*c^3 - a*b^5*c^3 + b^6*c^3 - 2*a^5*c^4 + 2*a^4*b*c^4 - a^3*b^2*c^4 + a^2*b^3*c^4 + 2*a*b^4*c^4 - 2*b^5*c^4 + 2*a^4*c^5 - a^3*b*c^5 + a^2*b^2*c^5 - a*b^3*c^5 - 2*b^4*c^5 + a^3*c^6 - a^2*b*c^6 - a*b^2*c^6 + b^3*c^6 - a^2*c^7 + a*b*c^7 + b^2*c^7) : :

X(44354) lies on these lines: {2, 92}, {7, 3164}, {226, 18667}, {401, 651}, {416, 2659}, {521, 17496}, {1943, 40152}, {6180, 20477}, {6516, 40888}, {7361, 20078}, {8680, 40843}, {10538, 40862}, {17483, 43988}, {17950, 35145}

X(44354) = anticomplement of X(1948)
X(44354) = anticomplement of the isogonal conjugate of X(1949)
X(44354) = anticomplement of the isotomic conjugate of X(40843)
X(44354) = isotomic conjugate of the anticomplement of X(39036)
X(44354) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {296, 69}, {1937, 21270}, {1945, 4}, {1949, 8}, {1952, 11442}, {40843, 6327}, {41206, 21300}
X(44354) = X(i)-Ceva conjugate of X(j) for these (i,j): {8680, 17950}, {40843, 2}
X(44354) = X(39036)-cross conjugate of X(2)
X(44354) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2656}, {1172, 2660}
X(44354) = barycentric product X(i)*X(j) for these {i,j}: {75, 2655}, {307, 2659}, {416, 1441}, {39036, 40843}
X(44354) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2656}, {73, 2660}, {416, 21}, {2655, 1}, {2659, 29}, {39036, 1948}

X(44355) = STEINER-INELLIPSE-INVERSE OF X(55)

Barycentrics    2*a^6 - 4*a^5*b + 3*a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 - 2*a*b^5 + b^6 - 4*a^5*c + 4*a^4*b*c + 2*a*b^4*c - 2*b^5*c + 3*a^4*c^2 - 4*a^2*b^2*c^2 + 3*b^4*c^2 - 2*a^3*c^3 - 4*b^3*c^3 + 2*a^2*c^4 + 2*a*b*c^4 + 3*b^2*c^4 - 2*a*c^5 - 2*b*c^5 + c^6 : :
X(44355) = 3 X[2] + X[40861]

X(44355) lies on these lines: {2, 11}, {664, 17352}, {905, 918}, {1086, 20269}, {1146, 17337}, {3589, 17044}, {4422, 7789}, {14827, 18214}, {28850, 31289}

X(44355) = crossdifference of every pair of points on line {665, 1486}

X(44356) = STEINER-INELLIPSE-INVERSE OF X(57)

Barycentrics    2*a^5 - a^4*b - 2*a^3*b^2 + b^5 - a^4*c + 4*a^3*b*c - 4*a*b^3*c + b^4*c - 2*a^3*c^2 + 8*a*b^2*c^2 - 2*b^3*c^2 - 4*a*b*c^3 - 2*b^2*c^3 + b*c^4 + c^5 : :
X(44356) = 3 X[2] + X[40862], X[10025] + 3 X[40892]

X(44356) lies on these lines: {2, 7}, {269, 281}, {519, 6510}, {522, 905}, {536, 17044}, {651, 26001}, {1111, 37805}, {1125, 25375}, {1146, 6610}, {1407, 20205}, {1420, 24565}, {1422, 7003}, {2325, 16578}, {3008, 36949}, {3663, 17073}, {3664, 16608}, {3752, 20201}, {3942, 8756}, {4021, 17043}, {4472, 6706}, {4670, 21258}, {4858, 43035}, {4887, 18644}, {6180, 20262}, {6907, 25365}, {7190, 24553}, {8074, 34371}, {10106, 24537}, {15149, 17197}, {17067, 24781}, {17862, 18652}, {17917, 23681}, {20206, 24213}, {23986, 35094}, {26011, 34050}

X(44356) = midpoint of X(i) and X(j) for these {i,j}: {1146, 6610}, {1944, 9436}, {40862, 40880}
X(44356) = complement of X(40880)
X(44356) = X(9372)-complementary conjugate of X(141)
X(44356) = crossdifference of every pair of points on line {198, 663}
X(44356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 40862, 40880}

X(44357) = STEINER-INELLIPSE-INVERSE OF X(241)

Barycentrics    a*(a^6*b^2 - 3*a^5*b^3 + 2*a^4*b^4 + 2*a^3*b^5 - 3*a^2*b^6 + a*b^7 + a^5*b^2*c - a^4*b^3*c - 2*a^3*b^4*c + 2*a^2*b^5*c + a*b^6*c - b^7*c + a^6*c^2 + a^5*b*c^2 - 5*a^2*b^4*c^2 - a*b^5*c^2 + 4*b^6*c^2 - 3*a^5*c^3 - a^4*b*c^3 + 12*a^2*b^3*c^3 - a*b^4*c^3 - 7*b^5*c^3 + 2*a^4*c^4 - 2*a^3*b*c^4 - 5*a^2*b^2*c^4 - a*b^3*c^4 + 8*b^4*c^4 + 2*a^3*c^5 + 2*a^2*b*c^5 - a*b^2*c^5 - 7*b^3*c^5 - 3*a^2*c^6 + a*b*c^6 + 4*b^2*c^6 + a*c^7 - b*c^7) : :

X(44357) lies on these lines: {1, 905}, {2, 85}, {142, 5701}, {220, 1025}, {5662, 29571}, {6184, 17044}, {21258, 35094}, {25242, 42719}

X(44357) = crossdifference of every pair of points on line {910, 8641}

X(44358) = STEINER-INELLIPSE-INVERSE OF X(942)

Barycentrics    a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*b*c + 2*a^5*b^2*c - a^4*b^3*c - 3*a^3*b^4*c + a*b^6*c + a^6*c^2 + 2*a^5*b*c^2 + 3*a^4*b^2*c^2 + a^3*b^3*c^2 - a^2*b^4*c^2 + a*b^5*c^2 + b^6*c^2 - a^4*b*c^3 + a^3*b^2*c^3 - 2*a*b^4*c^3 - 2*a^4*c^4 - 3*a^3*b*c^4 - a^2*b^2*c^4 - 2*a*b^3*c^4 - 2*b^4*c^4 + a*b^2*c^5 + a^2*c^6 + a*b*c^6 + b^2*c^6 : :

X(44358) lies on these lines: {2, 72}, {36, 448}, {241, 16090}, {350, 25083}, {441, 15325}, {693, 905}, {17095, 19786}, {20935, 31997}, {26971, 27334}

X(44359) = STEINER-INELLIPSE-INVERSE OF X(982)

Barycentrics    a^4*b^2 - a^3*b^3 + 2*a^2*b^4 - 2*a^4*b*c - 4*a^2*b^3*c - a*b^4*c + a^4*c^2 + 8*a^2*b^2*c^2 + b^4*c^2 - a^3*c^3 - 4*a^2*b*c^3 - 2*b^3*c^3 + 2*a^2*c^4 - a*b*c^4 + b^2*c^4 : :

X(44359) lies on these lines: {2, 38}, {142, 1015}, {668, 17282}, {812, 905}, {1086, 4920}, {2810, 3008}, {5750, 40479}, {10436, 27195}, {27191, 31997}

X(44359) = crossdifference of every pair of points on line {8632, 34247}

X(44360) = STEINER-INELLIPSE-INVERSE OF X(1214)

Barycentrics    a*(a^2 - b^2 - c^2)*(a^6*b^2 - a^5*b^3 - 2*a^4*b^4 + 2*a^3*b^5 + a^2*b^6 - a*b^7 + a^4*b^3*c - 2*a^2*b^5*c + b^7*c + a^6*c^2 + 2*a^4*b^2*c^2 - 2*a^3*b^3*c^2 - a^2*b^4*c^2 + 2*a*b^5*c^2 - 2*b^6*c^2 - a^5*c^3 + a^4*b*c^3 - 2*a^3*b^2*c^3 + 4*a^2*b^3*c^3 - a*b^4*c^3 - b^5*c^3 - 2*a^4*c^4 - a^2*b^2*c^4 - a*b^3*c^4 + 4*b^4*c^4 + 2*a^3*c^5 - 2*a^2*b*c^5 + 2*a*b^2*c^5 - b^3*c^5 + a^2*c^6 - 2*b^2*c^6 - a*c^7 + b*c^7) : :

X(44360) lies on these lines: {2, 92}, {142, 216}, {226, 6509}, {394, 7364}, {441, 36949}, {521, 656}, {527, 35072}, {6617, 34048}, {16608, 41005}, {25365, 42353}

X(44360) = complement of X(1948)
X(44360) = complement of the isogonal conjugate of X(1949)
X(44360) = complement of the isotomic conjugate of X(40843)
X(44360) = X(i)-complementary conjugate of X(j) for these (i,j): {296, 141}, {1937, 20305}, {1945, 5}, {1949, 10}, {1952, 21243}, {2249, 34831}, {40843, 2887}, {41206, 21259}
X(44360) = X(6)-isoconjugate of X(8764)
X(44360) = crosspoint of X(2) and X(40843)
X(44360) = crosssum of X(6) and X(2202)
X(44360) = crossdifference of every pair of points on line {19, 1946}
X(44360) = barycentric product X(75)*X(8763)
X(44360) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8764}, {8763, 1}

X(44361) = STEINER-CIRCUMELLIPSE-INVERSE OF X(302)

Barycentrics    a^2*b^2 - b^4 + a^2*c^2 - c^4 + 2*Sqrt[3]*(2*a^2 - b^2 - c^2)*S : :
X(44361) = 4 X[230] - 3 X[37785], 3 X[298] - 4 X[325], 3 X[299] - 2 X[325], 2 X[385] - 3 X[37786], 4 X[6671] - 3 X[16530], 2 X[6781] - 3 X[8594], 3 X[8595] - 4 X[32456]

X(44361) lies on these lines: {2, 6}, {61, 22737}, {76, 22701}, {99, 532}, {316, 533}, {340, 23712}, {511, 22509}, {621, 20425}, {892, 11117}, {5965, 5983}, {6671, 16530}, {6781, 8594}, {8595, 32456}, {11132, 16529}, {18813, 34389}

X(44361) = midpoint of X(3180) and X(40899)
X(44361) = reflection of X(i) in X(j) for these {i,j}: {298, 299}, {3181, 396}
X(44361) = isotomic conjugate of X(11602)
X(44361) = isotomic conjugate of the isogonal conjugate of X(39554)
X(44361) = X(31)-isoconjugate of X(11602)
X(44361) = barycentric product X(76)*X(39554)
X(44361) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 11602}, {39554, 6}
X(44361) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 302}, {33459, 37647, 302}, {39365, 39366, 40900}

X(44362) = STEINER-CIRCUMELLIPSE-INVERSE OF X(303)

Barycentrics    a^2*b^2 - b^4 + a^2*c^2 - c^4 - 2*Sqrt[3]*(2*a^2 - b^2 - c^2)*S : :
X(44362) = 4 X[230] - 3 X[37786], 3 X[298] - 2 X[325], 3 X[299] - 4 X[325], 2 X[385] - 3 X[37785], 4 X[6672] - 3 X[16529], 2 X[6781] - 3 X[8595], 3 X[8594] - 4 X[32456]

X(44362) lies on these lines: {2, 6}, {62, 22736}, {76, 22702}, {99, 533}, {316, 532}, {340, 23713}, {511, 22507}, {622, 20426}, {892, 11118}, {5965, 5982}, {6672, 16529}, {6781, 8595}, {8594, 32456}, {11133, 16530}, {18814, 34390}

X(44362) = midpoint of X(3181) and X(40898)
X(44362) = reflection of X(i) in X(j) for these {i,j}: {299, 298}, {3180, 395}
X(44362) = isotomic conjugate of X(11603)
X(44362) = isotomic conjugate of the isogonal conjugate of X(39555)
X(44362) = X(31)-isoconjugate of X(11603)
X(44362) = barycentric product X(76)*X(39555)
X(44362) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 11603}, {39555, 6}
X(44362) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 303}, {33458, 37647, 303}, {39365, 39366, 40901}

X(44363) = STEINER-CIRCUMELLIPSE-INVERSE OF X(343)

Barycentrics    a^8 - a^6*b^2 - 2*a^4*b^4 + 3*a^2*b^6 - b^8 - a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + 3*a^2*c^6 + b^2*c^6 - c^8 : :

X(44363) lies on these lines: {2, 6}, {147, 2393}, {311, 17035}, {340, 36212}, {523, 3153}, {1273, 4558}, {3164, 44128}, {3260, 39352}, {7577, 36207}, {9019, 40236}, {14570, 40853}, {18420, 32515}, {22087, 35922}, {40074, 44144}, {40897, 44180}

X(44363) = reflection of X(40888) in X(325)
X(44363) = isotomic conjugate of the polar conjugate of X(41203)
X(44363) = isotomic conjugate of antigonal conjugate of X(275)
X(44363) = barycentric product X(i)*X(j) for these {i,j}: {69, 41203}, {670, 42651}
X(44363) = barycentric quotient X(i)/X(j) for these {i,j}: {41203, 4}, {42651, 512}
X(44363) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 343}

X(44364) = STEINER-CIRCUMELLIPSE-INVERSE OF X(491)

Barycentrics    a^2*b^2 - b^4 + a^2*c^2 - c^4 - 2*(2*a^2 - b^2 - c^2)*S : :
X(44364) lies on these lines: {2, 6}, {99, 32419}, {316, 32421}, {317, 41516}, {372, 6229}, {487, 21445}, {489, 12256}, {511, 6231}, {637, 8982}, {3564, 9867}, {5491, 13939}, {7771, 41490}, {8036, 18820}, {8598, 13797}, {12323, 26331}, {22623, 42009}, {24243, 38294}, {32515, 33434}

X(44364) = isotomic conjugate of the isogonal conjugate of X(2460)
X(44364) = isotomic conjugate of antigonal conjugate of X(486)
X(44364) = crossdifference of every pair of points on line {512, 5058}
X(44364) = barycentric product X(76)*X(2460)
X(44364) = barycentric quotient X(2460)/X(6)
X(44364) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 385, 44365}, {69, 3069, 491}, {1007, 5861, 491}, {6189, 6190, 491}

X(44365) = STEINER-CIRCUMELLIPSE-INVERSE OF X(492)

Barycentrics    a^2*b^2 - b^4 + a^2*c^2 - c^4 + 2*(2*a^2 - b^2 - c^2)*S : :

X(44365) lies on these lines: {2, 6}, {99, 32421}, {316, 32419}, {317, 41515}, {371, 6228}, {488, 21445}, {490, 12257}, {511, 6230}, {638, 26441}, {3564, 9868}, {5490, 13886}, {7771, 41491}, {8035, 18819}, {8598, 13677}, {8960, 42009}, {12322, 26330}, {22594, 42060}, {24244, 38294}, {32515, 33435}

X(44365) = isotomic conjugate of the isogonal conjugate of X(2459)
X(44365) = isotomic conjugate of antigonal conjugate of X(485)
X(44365) = crossdifference of every pair of points on line {512, 5062}
X(44365) = barycentric product X(76)*X(2459)
X(44365) = barycentric quotient X(2459)/X(6)
X(44365) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 385, 44364}, {69, 3068, 492}, {1007, 5860, 492}, {6189, 6190, 492}

X(44366) = STEINER-CIRCUMELLIPSE-INVERSE OF X(591)

Barycentrics    a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4 - 2*(2*a^2 - b^2 - c^2)*S : :

X(44366) lies on these lines: {2, 6}, {187, 13640}, {1585, 38294}, {5107, 13773}, {9855, 33343}, {11054, 13676}, {13586, 32421}, {14041, 32419}, {26289, 33017}, {33273, 41491}

X(44366) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3068, 5861, 1992}, {6189, 6190, 591}

X(44367) = STEINER-CIRCUMELLIPSE-INVERSE OF X(597)

Barycentrics    5*a^4 + a^2*b^2 - b^4 + a^2*c^2 - 5*b^2*c^2 - c^4 : :
X(44367) = 7 X[2] - 8 X[230], 5 X[2] - 4 X[325], 11 X[2] - 10 X[7925], 5 X[2] - 6 X[8859], X[2] - 8 X[15480], 9 X[2] - 8 X[22110], 3 X[2] - 4 X[22329], 13 X[2] - 12 X[41133], 4 X[2] - 3 X[41136], 23 X[2] - 24 X[41139], 10 X[230] - 7 X[325], 4 X[230] - 7 X[385], 16 X[230] - 7 X[7779], 12 X[230] - 7 X[7840], 44 X[230] - 35 X[7925], 20 X[230] - 21 X[8859], X[230] - 7 X[15480], 9 X[230] - 7 X[22110], 6 X[230] - 7 X[22329], 26 X[230] - 21 X[41133], 32 X[230] - 21 X[41136], 23 X[230] - 21 X[41139], 2 X[316] - 3 X[41135], 2 X[325] - 5 X[385], 8 X[325] - 5 X[7779], 6 X[325] - 5 X[7840], 22 X[325] - 25 X[7925], 2 X[325] - 3 X[8859], X[325] - 10 X[15480], 9 X[325] - 10 X[22110], 3 X[325] - 5 X[22329], 13 X[325] - 15 X[41133], 16 X[325] - 15 X[41136], 23 X[325] - 30 X[41139], 4 X[385] - X[7779], 3 X[385] - X[7840], 11 X[385] - 5 X[7925], 5 X[385] - 3 X[8859], X[385] - 4 X[15480], 9 X[385] - 4 X[22110], 3 X[385] - 2 X[22329], 13 X[385] - 6 X[41133], 8 X[385] - 3 X[41136], 23 X[385] - 12 X[41139], 2 X[671] - 3 X[19570], 3 X[5032] - 2 X[39099], 4 X[5461] - 3 X[7809], 3 X[7779] - 4 X[7840], 11 X[7779] - 20 X[7925], 5 X[7779] - 12 X[8859], X[7779] - 16 X[15480], 9 X[7779] - 16 X[22110], 3 X[7779] - 8 X[22329], 13 X[7779] - 24 X[41133], 2 X[7779] - 3 X[41136], 23 X[7779] - 48 X[41139], 2 X[7813] - 3 X[41134], 11 X[7840] - 15 X[7925], 5 X[7840] - 9 X[8859], X[7840] - 12 X[15480], 3 X[7840] - 4 X[22110], 13 X[7840] - 18 X[41133], 8 X[7840] - 9 X[41136], 23 X[7840] - 36 X[41139], 25 X[7925] - 33 X[8859], 5 X[7925] - 44 X[15480], 45 X[7925] - 44 X[22110], 15 X[7925] - 22 X[22329], 65 X[7925] - 66 X[41133], 40 X[7925] - 33 X[41136], 115 X[7925] - 132 X[41139], 2 X[8591] - 3 X[33265], 3 X[8859] - 20 X[15480], 27 X[8859] - 20 X[22110], 9 X[8859] - 10 X[22329], 13 X[8859] - 10 X[41133], 8 X[8859] - 5 X[41136], 23 X[8859] - 20 X[41139], 4 X[11054] - X[40246], 3 X[14568] - 2 X[31173], 9 X[15480] - X[22110], 6 X[15480] - X[22329], 26 X[15480] - 3 X[41133], 32 X[15480] - 3 X[41136], 23 X[15480] - 3 X[41139], 5 X[15692] - 6 X[21445], 2 X[22110] - 3 X[22329], 26 X[22110] - 27 X[41133], 32 X[22110] - 27 X[41136], 23 X[22110] - 27 X[41139], 13 X[22329] - 9 X[41133], 16 X[22329] - 9 X[41136], 23 X[22329] - 18 X[41139], 3 X[26613] - 2 X[39785], 16 X[41133] - 13 X[41136], 23 X[41133] - 26 X[41139], 23 X[41136] - 32 X[41139]

X(44367) lies on these lines: {2, 6}, {30, 5984}, {76, 34604}, {114, 10487}, {148, 3849}, {316, 41135}, {376, 32515}, {511, 11177}, {519, 1281}, {523, 37901}, {538, 8591}, {542, 40236}, {543, 14712}, {671, 754}, {736, 19686}, {2482, 4027}, {2896, 7805}, {3552, 32824}, {3793, 8598}, {4577, 18823}, {5189, 25051}, {5211, 26280}, {5368, 32027}, {5461, 7809}, {5965, 6054}, {5976, 8787}, {5992, 28558}, {6034, 9866}, {6179, 7801}, {6194, 11179}, {6392, 33192}, {6653, 37857}, {6655, 9939}, {6995, 38294}, {7751, 7812}, {7754, 7833}, {7758, 33259}, {7760, 7810}, {7762, 33013}, {7768, 7817}, {7775, 7877}, {7780, 13571}, {7793, 34511}, {7797, 7826}, {7811, 41748}, {7813, 41134}, {7823, 34505}, {7839, 8359}, {7841, 7893}, {7855, 7870}, {7890, 34506}, {7900, 33006}, {7926, 8176}, {7929, 33190}, {7939, 8360}, {8370, 17129}, {8587, 35005}, {9164, 31068}, {9855, 20094}, {10162, 11056}, {10353, 12151}, {14568, 31173}, {14907, 32480}, {15527, 35087}, {15692, 21445}, {20065, 32826}, {20081, 32822}, {22253, 35955}, {26613, 39785}, {32833, 37809}

X(44367) = reflection of X(i) in X(j) for these {i,j}: {2, 385}, {148, 11054}, {7779, 2}, {7840, 22329}, {8598, 3793}, {8782, 22564}, {20094, 9855}, {40246, 148}
X(44367) = anticomplement of X(7840)
X(44367) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(9169)
X(44367) = anticomplement of the isotomic conjugate of X(43535)
X(44367) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {32694, 7192}, {43535, 6327}
X(44367) = X(43535)-Ceva conjugate of X(2)
X(44367) = crosssum of X(3124) and X(9208)
X(44367) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7779, 41136}, {193, 9740, 2}, {325, 8859, 2}, {385, 7840, 22329}, {5032, 15589, 2}, {6189, 6190, 597}, {7610, 7777, 2}, {7837, 8667, 2}, {7840, 22329, 2}, {7875, 21358, 2}, {9770, 17008, 2}, {9771, 17006, 2}, {11184, 17004, 2}, {15597, 17005, 2}, {16989, 21356, 2}, {39107, 39108, 3589}, {39365, 39366, 1992}

X(44368) = STEINER-CIRCUMELLIPSE-INVERSE OF X(615)

Barycentrics    a^4 - b^2*c^2 - 2*(2*a^2 - b^2 - c^2)*S : :
X(44368) = 4 X[230] - 3 X[44374], 2 X[325] - 3 X[44366]

X(44368) lies on these lines: {2, 6}, {148, 32419}, {511, 33431}, {5965, 6231}, {8591, 13797}, {14712, 32421}, {35944, 43133}

X(44368) = anticomplement of X(44364)
X(44368) = reflection of X(7779) in X(44365)
X(44368) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {325, 44365, 1271}, {6189, 6190, 615}

X(44369) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1007)

Barycentrics    4*a^6 - 9*a^4*b^2 + 8*a^2*b^4 - 3*b^6 - 9*a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 + 8*a^2*c^4 + b^2*c^4 - 3*c^6 : :
X(44369) = 3 X[69] - X[39099], 3 X[325] - 2 X[39099], 4 X[599] - 3 X[41133], 2 X[1351] - 3 X[39663], 3 X[1570] - 4 X[6722], 2 X[5107] - 3 X[33228], 2 X[5477] - 3 X[35297], 4 X[15993] - 3 X[22329]

X(44369) lies on these lines: {2, 6}, {99, 3564}, {340, 892}, {511, 39809}, {1351, 39663}, {1570, 6722}, {5107, 33228}, {5477, 35297}, {5965, 6393}, {6394, 40996}, {9146, 41724}, {10008, 21445}, {10553, 35266}, {14929, 32515}, {15069, 32819}, {32001, 34208}, {40074, 44149}

X(44369) = midpoint of X(385) and X(20080)
X(44369) = reflection of X(i) in X(j) for these {i,j}: {193, 230}, {325, 69}, {41146, 22165}
X(44369) = crossdifference of every pair of points on line {512, 39764}
X(44369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {298, 299, 22110}, {325, 37688, 41133}, {6189, 6190, 1007}

X(44370) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1211)

Barycentrics    a^5 + a^4*b + a^3*b^2 + a^2*b^3 - a*b^4 - b^5 + a^4*c + 4*a^3*b*c + a^2*b^2*c - 2*a*b^3*c - b^4*c + a^3*c^2 + a^2*b*c^2 - a*b^2*c^2 - b^3*c^2 + a^2*c^3 - 2*a*b*c^3 - b^2*c^3 - a*c^4 - b*c^4 - c^5 : :

X(44370) lies on these lines: {2, 6}, {148, 536}, {239, 26081}, {740, 20558}, {894, 21076}, {984, 36223}, {986, 1330}, {3770, 17788}, {3912, 26147}, {4053, 6542}, {4363, 6625}, {4440, 20349}, {20654, 28604}, {35511, 42713}, {39356, 39360}

X(44370) = reflection of X(40882) in X(10026)
X(44370) = anticomplement of X(19623)
X(44370) = anticomplement of the isotomic conjugate of X(11611)
X(44370) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2703, 7192}, {11609, 20245}, {11611, 6327}, {17929, 17159}, {17939, 17161}, {17946, 17135}, {17954, 75}, {17961, 1}, {17971, 17134}, {17981, 17220}, {18002, 4440}, {18015, 150}, {35147, 17217}
X(44370) = X(11611)-Ceva conjugate of X(2)
X(44370) = crosspoint of X(4590) and X(35147)
X(44370) = crosssum of X(3124) and X(5040)
X(44370) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 1211}, {39365, 39366, 2895}

X(44371) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1613)

Barycentrics    a^6*b^2 + a^6*c^2 - 3*a^4*b^2*c^2 + a^2*b^4*c^2 + a^2*b^2*c^4 - b^4*c^4 : :

X(44371) lies on these lines: {2, 6}, {99, 6379}, {237, 25054}, {670, 33875}, {706, 12215}, {1916, 2393}, {4590, 39927}, {8264, 20794}

X(44371) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 1613}

X(44372) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1641)

Barycentrics    5*a^8 - 10*a^6*b^2 + 5*a^2*b^6 - b^8 - 10*a^6*c^2 + 30*a^4*b^2*c^2 - 15*a^2*b^4*c^2 - b^6*c^2 - 15*a^2*b^2*c^4 + 9*b^4*c^4 + 5*a^2*c^6 - b^2*c^6 - c^8 : :
X(44372) = X[671] - 3 X[31998], 2 X[2482] - 3 X[4590], 3 X[4590] - X[18823], 8 X[9164] - 3 X[35511], 3 X[9166] - 4 X[40553], 2 X[14588] + X[31372], 2 X[23992] - 3 X[41134], 3 X[31998] - 2 X[35087]

X(44372) lies on these lines: {2, 6}, {148, 17948}, {523, 8591}, {543, 892}, {671, 31998}, {2482, 4590}, {9164, 35511}, {9166, 40553}, {9180, 33915}, {14588, 31372}, {23992, 41134}

X(44372) = reflection of X(i) in X(j) for these {i,j}: {2, 9182}, {148, 17948}, {671, 35087}, {18823, 2482}
X(44372) = barycentric product X(670)*X(39527)
X(44372) = barycentric quotient X(39527)/X(512)
X(44372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {671, 31998, 35087}, {4590, 18823, 2482}, {6189, 6190, 1641}, {39107, 39108, 11053}

X(44373) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1648)

Barycentrics    a^8 - 2*a^6*b^2 - 2*a^4*b^4 + 3*a^2*b^6 - b^8 - 2*a^6*c^2 + 10*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + b^6*c^2 - 2*a^4*c^4 - 5*a^2*b^2*c^4 + b^4*c^4 + 3*a^2*c^6 + b^2*c^6 - c^8 : :
X(44373) = X[148] + 3 X[35511], 4 X[620] - 3 X[4590], 3 X[9166] - 2 X[35087], 5 X[14061] - 6 X[23991], 5 X[14061] - 3 X[31998], 5 X[14061] - 4 X[40553], 2 X[17948] - 3 X[41135], 3 X[23991] - 2 X[40553], 3 X[31998] - 4 X[40553], 3 X[35511] - X[39356]

X(44373) lies on these lines: {2, 6}, {99, 23992}, {115, 892}, {148, 523}, {543, 18823}, {620, 4590}, {888, 31513}, {9166, 35087}, {9170, 41176}, {9180, 33921}, {14061, 23991}, {17948, 41135}

X(44373) = midpoint of X(148) and X(39356)
X(44373) = reflection of X(i) in X(j) for these {i,j}: {99, 23992}, {892, 115}, {31998, 23991}
X(44373) = anticomplement of X(9182)
X(44373) = anticomplement of the isotomic conjugate of X(9180)
X(44373) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {843, 7192}, {9180, 6327}, {18823, 17217}
X(44373) = X(9180)-Ceva conjugate of X(2)
X(44373) = crosspoint of X(4590) and X(18823)
X(44373) = crosssum of X(2502) and X(3124)
X(44373) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {148, 35511, 39356}, {325, 5912, 2}, {325, 22329, 24855}, {6189, 6190, 1648}, {14061, 31998, 40553}, {23991, 40553, 14061}

X(44374) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1991)

Barycentrics    a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4 + 2*(2*a^2 - b^2 - c^2)*S : :

X(44374) lies on these lines: {2, 6}, {187, 13760}, {1586, 38294}, {5107, 13653}, {9855, 33342}, {11054, 13796}, {13586, 32419}, {14041, 32421}, {26288, 33017}, {33273, 41490}

X(44374) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3069, 5860, 1992}, {6189, 6190, 1991}

X(44375) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1993)

Barycentrics    a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + a^4*b^2*c^2 - b^6*c^2 + a^4*c^4 + 2*b^4*c^4 - b^2*c^6 : :
X(44375) = X[385] + 2 X[40879], 3 X[21445] + X[38294]

X(44375) lies on these lines: {2, 6}, {50, 338}, {95, 570}, {98, 2393}, {112, 37778}, {157, 3186}, {186, 523}, {231, 340}, {237, 9512}, {264, 571}, {297, 16310}, {317, 2165}, {389, 19179}, {419, 1576}, {577, 41760}, {648, 3003}, {687, 2966}, {1316, 23200}, {1609, 9308}, {1879, 32002}, {1989, 40885}, {3018, 37765}, {3164, 8553}, {5063, 40814}, {5999, 9019}, {6644, 36207}, {7514, 32515}, {7793, 19221}, {9722, 27377}, {9755, 32621}, {11676, 39231}, {14570, 35296}, {18533, 33971}, {41679, 44138}

X(44375) = midpoint of X(385) and X(40888)
X(44375) = reflection of X(i) in X(j) for these {i,j}: {11676, 39231}, {40888, 40879}
X(44375) = isotomic conjugate of the polar conjugate of X(421)
X(44375) = crossdifference of every pair of points on line {216, 512}
X(44375) = barycentric product X(69)*X(421)
X(44375) = barycentric quotient X(421)/X(4)
X(44375) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {50, 338, 401}, {6189, 6190, 1993}, {39022, 39023, 23292}, {41679, 44138, 44328}

X(44376) = STEINER-CIRCUMELLIPSE-INVERSE OF X(1994)

Barycentrics    a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 - a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 + 2*b^4*c^4 - b^2*c^6 : :
X(44376) = 2 X[385] + X[40879], 3 X[385] + X[40888], 3 X[40879] - 2 X[40888]

X(44376) lies on these lines: {2, 6}, {98, 9019}, {311, 2965}, {523, 2070}, {648, 11062}, {2782, 39231}, {2966, 11077}, {5201, 9512}, {11063, 14570}

X(44376) = crossdifference of every pair of points on line {512, 570}
X(44376) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 1994}, {39022, 39023, 37649}

X(44377) = STEINER-INELLIPSE-INVERSE OF X(69)

Barycentrics    2*a^4 - 3*a^2*b^2 + 3*b^4 - 3*a^2*c^2 - 2*b^2*c^2 + 3*c^4 : :
X(44377) = 3 X[2] + X[325], 9 X[2] - X[385], 15 X[2] + X[7779], 7 X[2] + X[7840], 3 X[2] + 5 X[7925], 11 X[2] - 3 X[8859], 15 X[2] - X[15480], 5 X[2] - X[22329], X[2] + 3 X[41133], 13 X[2] + 3 X[41136], 5 X[2] - 3 X[41139], X[3] - 3 X[10256], X[98] - 5 X[40336], X[99] + 3 X[33228], X[115] - 5 X[31275], X[187] - 5 X[31274], 3 X[230] - X[385], 5 X[230] + X[7779], 7 X[230] + 3 X[7840], X[230] + 5 X[7925], 11 X[230] - 9 X[8859], 5 X[230] - X[15480], X[230] + 3 X[22110], 5 X[230] - 3 X[22329], X[230] + 9 X[41133], 13 X[230] + 9 X[41136], 5 X[230] - 9 X[41139], X[316] + 3 X[35297], 3 X[325] + X[385], 5 X[325] - X[7779], 7 X[325] - 3 X[7840], X[325] - 5 X[7925], 11 X[325] + 9 X[8859], 5 X[325] + X[15480], X[325] - 3 X[22110], 5 X[325] + 3 X[22329], X[325] - 9 X[41133], 13 X[325] - 9 X[41136], 5 X[325] + 9 X[41139], 5 X[385] + 3 X[7779], 7 X[385] + 9 X[7840], X[385] + 15 X[7925], 11 X[385] - 27 X[8859], 5 X[385] - 3 X[15480], X[385] + 9 X[22110], 5 X[385] - 9 X[22329], X[385] + 27 X[41133], 13 X[385] + 27 X[41136], 5 X[385] - 27 X[41139], 3 X[620] - X[32456], 3 X[625] + X[32456], 2 X[625] + X[32459], 7 X[3090] - 3 X[39663], 11 X[3525] - 3 X[21445], 7 X[3619] + X[39099], 5 X[3763] - X[15993], X[5026] + 3 X[5031], X[5461] - 3 X[10150], 3 X[5461] + X[14148], 3 X[5461] - X[32457], X[6390] + 5 X[31275], 3 X[6393] + X[10754], X[6781] - 9 X[9167], X[6781] - 3 X[27088], X[6781] + 3 X[31173], 7 X[7779] - 15 X[7840], X[7779] - 25 X[7925], 11 X[7779] + 45 X[8859], X[7779] - 15 X[22110], X[7779] + 3 X[22329], X[7779] - 45 X[41133], 13 X[7779] - 45 X[41136], X[7779] + 9 X[41139], 3 X[7799] + 5 X[14061], 3 X[7840] - 35 X[7925], 11 X[7840] + 21 X[8859], 15 X[7840] + 7 X[15480], X[7840] - 7 X[22110], 5 X[7840] + 7 X[22329], X[7840] - 21 X[41133], 13 X[7840] - 21 X[41136], 5 X[7840] + 21 X[41139], 55 X[7925] + 9 X[8859], 25 X[7925] + X[15480], 5 X[7925] - 3 X[22110], 25 X[7925] + 3 X[22329], 5 X[7925] - 9 X[41133], 65 X[7925] - 9 X[41136], 25 X[7925] + 9 X[41139], X[8352] + 3 X[41134], 45 X[8859] - 11 X[15480], 3 X[8859] + 11 X[22110], 15 X[8859] - 11 X[22329], X[8859] + 11 X[41133], 13 X[8859] + 11 X[41136], 5 X[8859] - 11 X[41139], 3 X[9167] - X[27088], 3 X[9167] + X[31173], 9 X[10150] + X[14148], 9 X[10150] - X[32457], X[13449] + 3 X[38748], 3 X[14971] + X[39785], X[15480] + 15 X[22110], X[15480] - 3 X[22329], X[15480] + 45 X[41133], 13 X[15480] + 45 X[41136], X[15480] - 9 X[41139], 3 X[15561] + X[15980], X[18860] + 3 X[36519], 3 X[21358] + X[41146], 5 X[22110] + X[22329], X[22110] - 3 X[41133], 13 X[22110] - 3 X[41136], 5 X[22110] + 3 X[41139], X[22329] + 15 X[41133], 13 X[22329] + 15 X[41136], X[22329] - 3 X[41139], 9 X[23234] - X[43460], 2 X[32456] - 3 X[32459], 13 X[41133] - X[41136], 5 X[41133] + X[41139], 5 X[41136] + 13 X[41139]

X(44377) lies on these lines: {2, 6}, {3, 7694}, {5, 3734}, {30, 620}, {39, 8361}, {53, 42406}, {76, 33249}, {98, 13196}, {99, 33228}, {114, 1503}, {115, 6390}, {126, 3258}, {127, 10257}, {140, 626}, {187, 31274}, {232, 34990}, {287, 40428}, {315, 33233}, {316, 35297}, {441, 35067}, {468, 14052}, {511, 6721}, {523, 4885}, {538, 6722}, {543, 8355}, {546, 7816}, {547, 7880}, {548, 7842}, {549, 7761}, {550, 7825}, {574, 33184}, {631, 7784}, {632, 7815}, {698, 2023}, {736, 6683}, {858, 16320}, {1368, 23333}, {1447, 7238}, {1506, 7819}, {1513, 5103}, {1656, 7795}, {1975, 32961}, {2482, 37350}, {2548, 32954}, {2549, 11318}, {2896, 16923}, {2996, 39143}, {3035, 20541}, {3053, 32816}, {3090, 39663}, {3266, 40511}, {3525, 21445}, {3526, 7800}, {3529, 39142}, {3530, 7830}, {3564, 6036}, {3628, 3934}, {3705, 4399}, {3767, 22253}, {3785, 32977}, {3793, 7845}, {3849, 22247}, {3926, 13881}, {3933, 7746}, {3972, 7745}, {4045, 8360}, {4048, 13860}, {4478, 7081}, {4643, 36407}, {5013, 14064}, {5023, 32006}, {5024, 33240}, {5210, 33216}, {5254, 7763}, {5286, 32955}, {5305, 7764}, {5461, 10150}, {5475, 8369}, {5480, 37071}, {5866, 34866}, {5988, 28530}, {6337, 32972}, {6389, 30771}, {6393, 8781}, {6656, 7769}, {6667, 20530}, {6676, 14725}, {6781, 9167}, {7179, 7228}, {7499, 15822}, {7603, 7820}, {7737, 11288}, {7738, 32835}, {7749, 7767}, {7750, 7907}, {7762, 7814}, {7773, 16925}, {7775, 18907}, {7782, 33229}, {7785, 33245}, {7786, 8363}, {7799, 14061}, {7803, 9606}, {7804, 8368}, {7808, 33185}, {7832, 32992}, {7834, 31406}, {7835, 8370}, {7836, 32967}, {7844, 15048}, {7848, 34506}, {7849, 16239}, {7851, 9607}, {7852, 9698}, {7853, 8359}, {7863, 39565}, {7865, 11539}, {7866, 31401}, {7867, 8362}, {7881, 32832}, {7885, 33259}, {7891, 32819}, {7898, 33274}, {7934, 8356}, {7938, 33015}, {7945, 16921}, {8352, 41134}, {8354, 8589}, {8357, 37512}, {8716, 43448}, {8787, 25486}, {9306, 19156}, {9752, 11477}, {9767, 13785}, {9768, 13665}, {10155, 18840}, {11286, 31415}, {11812, 40344}, {13449, 38748}, {14069, 31404}, {14971, 39785}, {15483, 15561}, {15815, 32974}, {15819, 15850}, {16043, 32839}, {17045, 24239}, {18584, 32983}, {18860, 36519}, {22998, 38412}, {23234, 43460}, {30103, 31460}, {30739, 30747}, {30749, 37454}, {31400, 32951}, {32815, 32984}, {32817, 34505}, {32818, 32958}, {32823, 32959}, {32827, 32985}, {32828, 32976}, {32871, 33202}, {35387, 37451}, {37450, 43461}

X(44377) = midpoint of X(i) and X(j) for these {i,j}: {2, 22110}, {115, 6390}, {230, 325}, {441, 35088}, {620, 625}, {858, 16320}, {2482, 37350}, {3793, 7845}, {7779, 15480}, {14148, 32457}, {27088, 31173}, {44382, 44383}, {44384, 44385}, {44390, 44391} to midpoints
X(44377) = reflection of X(i) in X(j) for these {i,j}: {10011, 6721}, {32459, 620}, {43291, 6722}
X(44377) = complement of X(230)
X(44377) = orthoptic-circle-of-Steiner-inellipe-inverse of X(38940)
X(44377) = complement of the isogonal conjugate of X(2987)
X(44377) = complement of the isotomic conjugate of X(8781)
X(44377) = isotomic conjugate of the isogonal conjugate of X(1570)
X(44377) = X(i)-complementary conjugate of X(j) for these (i,j): {48, 35067}, {63, 31842}, {661, 36472}, {2065, 16609}, {2987, 10}, {3563, 226}, {8773, 141}, {8781, 2887}, {10425, 4369}, {32654, 37}, {32697, 8062}, {34157, 16591}, {35142, 20305}, {35364, 8287}, {36051, 2}, {36105, 30476}, {42065, 1214}, {43705, 18589}
X(44377) = X(4226)-Ceva conjugate of X(2799)
X(44377) = crosspoint of X(2) and X(8781)
X(44377) = crosssum of X(6) and X(1692)
X(44377) = crossdifference of every pair of points on line {512, 3053}
X(44377) = barycentric product X(76)*X(1570)
X(44377) = barycentric quotient X(1570)/X(6)
X(44377) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 69, 37637}, {2, 183, 3054}, {2, 325, 230}, {2, 599, 15597}, {2, 1007, 6}, {2, 3314, 37688}, {2, 3815, 3589}, {2, 7777, 7792}, {2, 7778, 141}, {2, 7897, 17004}, {2, 7925, 325}, {2, 11184, 597}, {2, 22329, 41139}, {2, 30760, 1211}, {2, 30761, 1213}, {2, 31489, 15491}, {2, 34803, 31489}, {2, 37647, 3055}, {2, 37690, 7778}, {2, 41133, 22110}, {5, 3788, 7789}, {69, 37637, 13468}, {230, 15480, 22329}, {230, 22110, 325}, {325, 7925, 22110}, {325, 22329, 7779}, {325, 41133, 7925}, {599, 34229, 15598}, {1506, 7874, 7819}, {3788, 7862, 5}, {3926, 32969, 13881}, {5306, 7774, 32455}, {5461, 14148, 32457}, {6189, 6190, 20080}, {7735, 9766, 3629}, {7746, 7888, 3933}, {7749, 7821, 7767}, {7752, 7807, 7745}, {7752, 7940, 7807}, {7763, 7887, 5254}, {7764, 7886, 5305}, {7769, 7899, 6656}, {7777, 7792, 9300}, {7779, 22329, 15480}, {7792, 9300, 6329}, {7814, 7857, 7762}, {7867, 31455, 8362}, {7891, 32966, 32819}, {7897, 17004, 37671}, {7907, 7912, 7750}, {8667, 37668, 3630}, {9167, 31173, 27088}, {9771, 15491, 31489}, {14064, 32829, 5013}, {15480, 41139, 230}, {15597, 15598, 34229}, {31406, 33186, 7834}, {31489, 34803, 9771}, {32006, 32989, 5023}, {32816, 32970, 3053}, {32835, 33199, 7738}, {39022, 39023, 69}, {39107, 39108, 11160}

X(44378) = STEINER-INELLIPSE-INVERSE OF X(81)

Barycentrics    2*a^5 + 2*a^4*b - a^3*b^2 - a^2*b^3 + a*b^4 + b^5 + 2*a^4*c + 2*a^3*b*c - a^2*b^2*c - a*b^3*c + b^4*c - a^3*c^2 - a^2*b*c^2 - 2*a*b^2*c^2 - 2*b^3*c^2 - a^2*c^3 - a*b*c^3 - 2*b^2*c^3 + a*c^4 + b*c^4 + c^5 : :
X(44378) = 3 X[2] + X[19623]

X(44378) lies on these lines: {2, 6}, {115, 16702}, {523, 8043}, {536, 620}, {1931, 24957}, {3008, 40539}, {4665, 24384}, {8609, 34990}, {24636, 37756}, {36953, 42713}

X(44378) = midpoint of X(115) and X(16702)
X(44378) = crosssum of X(6) and X(5164)
X(44378) = crossdifference of every pair of points on line {512, 1030}
X(44378) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 20086}, {39022, 39023, 81}

X(44379) = STEINER-INELLIPSE-INVERSE OF X(86)

Barycentrics    2*a^4 + 2*a^3*b - a^2*b^2 - a*b^3 + b^4 + 2*a^3*c + 2*a^2*b*c - a*b^2*c - b^3*c - a^2*c^2 - a*b*c^2 - 2*b^2*c^2 - a*c^3 - b*c^3 + c^4 : :
X(44379) = X[2] + X[17731], 9 X[2] - X[20536], 3 X[10026] - X[20536], 3 X[17731] + X[20536], 5 X[29590] - X[35148]

X(44379) lies on these lines: {2, 6}, {8, 24384}, {115, 6629}, {239, 24636}, {519, 620}, {523, 2487}, {540, 625}, {1834, 35916}, {1931, 23947}, {4062, 36953}, {4399, 24374}, {4434, 4478}, {4987, 25383}, {5209, 25472}, {6626, 23905}, {6682, 17045}, {6690, 17390}, {8608, 34990}, {11599, 17768}, {13174, 28530}, {17103, 23897}, {17290, 36223}, {17366, 35960}, {20530, 40546}, {24345, 34824}, {24366, 24883}, {29590, 35148}

X(44379) = midpoint of X(i) and X(j) for these {i,j}: {115, 6629}, {239, 35080}, {10026, 17731}
X(44379) = complement of X(10026)
X(44379) = X(i)-complementary conjugate of X(j) for these (i,j): {1333, 35114}, {28482, 1211}, {35162, 21245}
X(44379) = crosssum of X(6) and X(20666)
X(44379) = crossdifference of every pair of points on line {512, 18755}
X(44379) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17731, 10026}, {6189, 6190, 20090}, {39022, 39023, 86}

X(44380) = STEINER-INELLIPSE-INVERSE OF X(183)

Barycentrics    2*a^6 - 3*a^4*b^2 + 2*a^2*b^4 + b^6 - 3*a^4*c^2 - 4*a^2*b^2*c^2 + b^4*c^2 + 2*a^2*c^4 + b^2*c^4 + c^6 : :
X(44380) = 3 X[2] + X[39099], X[2] + 3 X[41137], X[69] - 5 X[7925], X[148] + 3 X[12215], X[316] + 3 X[5182], X[385] - 5 X[3618], X[599] - 3 X[41133], X[1352] + 3 X[22525], 3 X[1692] + X[7845], 3 X[2456] + X[6033], X[5104] - 3 X[35297], 3 X[7799] + X[10754], X[11646] + 3 X[12151], X[11646] - 3 X[33228], X[15993] + 9 X[41137], X[15993] + 3 X[41146], X[39099] - 9 X[41137], X[39099] - 3 X[41146], 3 X[41137] - X[41146]

X(44380) lies on these lines: {2, 6}, {30, 5026}, {126, 13857}, {148, 12215}, {182, 7761}, {316, 5182}, {511, 620}, {523, 24284}, {542, 625}, {575, 626}, {576, 3788}, {732, 2025}, {754, 2030}, {1352, 22525}, {1503, 2456}, {1692, 7845}, {1990, 39931}, {2882, 35060}, {3001, 38987}, {3095, 7789}, {3564, 5031}, {3734, 5476}, {3934, 25555}, {4048, 5480}, {4364, 36405}, {5034, 7913}, {5038, 6656}, {5104, 35297}, {5111, 6393}, {5112, 32217}, {5969, 6390}, {6593, 34827}, {7745, 10349}, {7750, 39560}, {7799, 10754}, {7807, 13330}, {7830, 20190}, {7835, 22486}, {7862, 34507}, {8705, 16320}, {9132, 25328}, {9830, 37350}, {10256, 22677}, {11173, 11288}, {11245, 40379}, {11646, 12151}, {11676, 29181}, {15118, 40553}, {15483, 32459}, {18583, 24256}, {18800, 31173}, {19924, 32456}, {31636, 34369}, {40074, 41760}

X(44380) = midpoint of X(i) and X(j) for these {i,j}: {2, 41146}, {6, 325}, {5103, 13196}, {5111, 6393}, {12151, 33228}, {12177, 15980}, {15993, 39099}, {18800, 31173}
X(44380) = reflection of X(230) in X(3589)
X(44380) = complement of X(15993)
X(44380) = crosssum of X(6) and X(2021)
X(44380) = crossdifference of every pair of points on line {512, 5017}
X(44380) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 39099, 15993}, {2, 41137, 41146}, {15483, 37461, 32459}, {15993, 41146, 39099}, {39022, 39023, 183}

X(44381) = STEINER-INELLIPSE-INVERSE OF X(193)

Barycentrics    6*a^4 - 5*a^2*b^2 + 5*b^4 - 5*a^2*c^2 - 6*b^2*c^2 + 5*c^4 : :
X(44381) = 3 X[2] + X[230], 9 X[2] - X[325], 15 X[2] + X[385], 33 X[2] - X[7779], 17 X[2] - X[7840], 21 X[2] - 5 X[7925], 13 X[2] + 3 X[8859], 27 X[2] + X[15480], 5 X[2] - X[22110], 7 X[2] + X[22329], 11 X[2] - 3 X[41133], 35 X[2] - 3 X[41136], X[2] + 3 X[41139], 3 X[230] + X[325], 5 X[230] - X[385], 11 X[230] + X[7779], 17 X[230] + 3 X[7840], 7 X[230] + 5 X[7925], 13 X[230] - 9 X[8859], 9 X[230] - X[15480], 5 X[230] + 3 X[22110], 7 X[230] - 3 X[22329], 11 X[230] + 9 X[41133], 35 X[230] + 9 X[41136], X[230] - 9 X[41139], 5 X[325] + 3 X[385], 11 X[325] - 3 X[7779], 17 X[325] - 9 X[7840], 7 X[325] - 15 X[7925], 13 X[325] + 27 X[8859], 3 X[325] + X[15480], 5 X[325] - 9 X[22110], 7 X[325] + 9 X[22329], 11 X[325] - 27 X[41133], 35 X[325] - 27 X[41136], X[325] + 27 X[41139], 11 X[385] + 5 X[7779], 17 X[385] + 15 X[7840], 7 X[385] + 25 X[7925], 13 X[385] - 45 X[8859], 9 X[385] - 5 X[15480], X[385] + 3 X[22110], 7 X[385] - 15 X[22329], 11 X[385] + 45 X[41133], 7 X[385] + 9 X[41136], X[385] - 45 X[41139], 5 X[620] - X[15301], 3 X[620] + X[32457], 5 X[631] + 3 X[39663], 7 X[3526] - 3 X[10256], 13 X[5067] + 3 X[21445], 9 X[5215] - X[6781], 3 X[5215] + X[37350], 3 X[5461] + X[32456], X[6390] - 5 X[31274], X[6781] + 3 X[37350], 17 X[7779] - 33 X[7840], 7 X[7779] - 55 X[7925], 13 X[7779] + 99 X[8859], 9 X[7779] + 11 X[15480], 5 X[7779] - 33 X[22110], 7 X[7779] + 33 X[22329], X[7779] - 9 X[41133], 35 X[7779] - 99 X[41136], X[7779] + 99 X[41139], 21 X[7840] - 85 X[7925], 13 X[7840] + 51 X[8859], 27 X[7840] + 17 X[15480], 5 X[7840] - 17 X[22110], 7 X[7840] + 17 X[22329], 11 X[7840] - 51 X[41133], 35 X[7840] - 51 X[41136], X[7840] + 51 X[41139], 65 X[7925] + 63 X[8859], 45 X[7925] + 7 X[15480], 25 X[7925] - 21 X[22110], 5 X[7925] + 3 X[22329], 55 X[7925] - 63 X[41133], 25 X[7925] - 9 X[41136], 5 X[7925] + 63 X[41139], 81 X[8859] - 13 X[15480], 15 X[8859] + 13 X[22110], 21 X[8859] - 13 X[22329], 11 X[8859] + 13 X[41133], 35 X[8859] + 13 X[41136], X[8859] - 13 X[41139], 5 X[14061] + 3 X[35297], 3 X[14971] + X[27088], 3 X[15301] + 5 X[32457], X[15301] + 5 X[43291], 5 X[15480] + 27 X[22110], 7 X[15480] - 27 X[22329], 11 X[15480] + 81 X[41133], 35 X[15480] + 81 X[41136], X[15480] - 81 X[41139], 7 X[22110] + 5 X[22329], 11 X[22110] - 15 X[41133], 7 X[22110] - 3 X[41136], X[22110] + 15 X[41139], 11 X[22329] + 21 X[41133], 5 X[22329] + 3 X[41136], X[22329] - 21 X[41139], X[32457] - 3 X[43291], 3 X[34127] + X[37459], 3 X[38227] + 5 X[40336], 35 X[41133] - 11 X[41136], X[41133] + 11 X[41139], X[41136] + 35 X[41139]

X(44381) lies on these lines: {2, 6}, {30, 6722}, {115, 32459}, {140, 4045}, {439, 39143}, {468, 40511}, {523, 14341}, {547, 7804}, {549, 7844}, {620, 15301}, {631, 39663}, {632, 7834}, {1503, 6036}, {3053, 32827}, {3526, 10256}, {3530, 7861}, {3564, 6721}, {3628, 6680}, {5013, 32977}, {5023, 32972}, {5066, 32414}, {5067, 21445}, {5210, 16041}, {5215, 6781}, {5254, 33233}, {5461, 32456}, {5585, 33272}, {6390, 31274}, {6683, 16239}, {6719, 22104}, {7612, 15069}, {7745, 7857}, {7746, 7789}, {7749, 7853}, {7784, 32955}, {7815, 33186}, {7851, 33000}, {7872, 15712}, {7887, 14907}, {7914, 33212}, {11288, 43620}, {11318, 21843}, {11539, 15482}, {13881, 32815}, {14061, 35297}, {14971, 27088}, {32817, 32959}, {32838, 33222}, {34127, 37459}, {34369, 40428}, {38227, 40336}, {40477, 40486}

X(44381) = midpoint of X(i) and X(j) for these {i,j}: {115, 32459}, {620, 43291}, {6036, 10011}
X(44381) = crosssum of X(6) and X(1570)
X(44381) = crossdifference of every pair of points on line {512, 5023}
X(44381) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7792, 3055}, {2, 7806, 37647}, {2, 15597, 20582}, {2, 23053, 21358}, {2, 37637, 141}, {230, 22110, 385}, {385, 7925, 41136}, {7778, 13468, 3631}, {7806, 37647, 9300}, {7857, 33249, 7745}, {39022, 39023, 193}

X(44382) = STEINER-INELLIPSE-INVERSE OF X(298)

Barycentrics    Sqrt[3]*(b^2 + c^2) - 4*S : :
X(44382) = 3 X[2] + X[299], 9 X[2] - X[3181], 5 X[2] - X[37785], 15 X[2] + X[40899], X[14] - 5 X[40335], X[16] + 3 X[21360], X[298] - 5 X[7925], 3 X[299] + X[3181], 5 X[299] + 3 X[37785], 5 X[299] - X[40899], 3 X[395] - X[3181], 5 X[395] - 3 X[37785], 5 X[395] + X[40899], 5 X[1656] - X[20426], 5 X[3181] - 9 X[37785], 5 X[3181] + 3 X[40899], 3 X[5464] + X[36970], X[9115] - 5 X[31274], 3 X[14971] - X[22574], X[22998] - 5 X[36770], 3 X[31694] - X[36970], 3 X[35303] - X[36968], 3 X[37785] + X[40899]


X(44382) lies on these lines: {2, 6}, {5, 3642}, {13, 7789}, {14, 40335}, {15, 37351}, {16, 21360}, {30, 619}, {140, 618}, {383, 29181}, {397, 11308}, {398, 628}, {466, 34828}, {530, 620}, {531, 625}, {532, 6672}, {533, 6670}, {547, 623}, {549, 3643}, {617, 5321}, {622, 42943}, {626, 42912}, {629, 16239}, {633, 42599}, {634, 16773}, {635, 3628}, {641, 34551}, {642, 34552}, {1503, 5613}, {1656, 20426}, {3564, 6774}, {3788, 34509}, {3934, 6669}, {4399, 40713}, {4478, 40714}, {5031, 6109}, {5103, 5978}, {5237, 33386}, {5318, 11300}, {5464, 31694}, {6292, 22892}, {6673, 42590}, {6694, 7849}, {7761, 13083}, {7799, 40706}, {7862, 34508}, {7865, 42124}, {7880, 11542}, {8355, 33476}, {9115, 31274}, {10410, 33507}, {10653, 11302}, {10654, 11306}, {11085, 40710}, {11092, 11120}, {11121, 44032}, {11129, 22847}, {11132, 22893}, {11289, 42598}, {11290, 16772}, {11298, 18582}, {11301, 42092}, {11304, 42942}, {11305, 42911}, {11310, 42149}, {11312, 42152}, {14539, 41017}, {14905, 33228}, {14971, 22574}, {15685, 33618}, {16241, 37340}, {18586, 23311}, {18587, 23312}, {18840, 43554}, {20429, 44250}, {22511, 36763}, {22573, 39785}, {22845, 42993}, {22998, 36770}, {32459, 35303}, {32515, 33479}, {33560, 42146}, {33615, 33617}, {34827, 41888}, {37170, 42098}, {37171, 42154}, {37173, 42155}, {37177, 43238}, {37178, 42156}, {37352, 37832}, {38745, 41022}, {41887, 43962}

X(44382) = midpoint of X(i) and X(j) for these {i,j}: {299, 395}, {325, 396}, {617, 5321}, {619, 624}, {622, 42943}, {5464, 31694}, {10410, 33507}, {11132, 22893}, {14539, 41017}, {20429, 44250}, {22573, 39785}, {22797, 36756}, {41887, 43962}
X(44382) = reflection of X(i) in X(j) for these {i,j}: {11543, 6670}, {42913, 6672}, {43417, 33561}, {44383, 44377}
X(44382) = complement of X(395)
X(44382) = circumcircle-of-outer-Napoleon-triangle inverse of X(38940)
X(44382) = complement of the isogonal conjugate of X(6151)
X(44382) = complement of the isotomic conjugate of X(40706)
X(44382) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 22848}, {163, 35444}, {661, 15610}, {2154, 16537}, {6151, 10}, {10410, 4369}, {19301, 40580}, {38427, 20305}, {40706, 2887}
X(44382) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 22848}, {35315, 23871}
X(44382) = crosspoint of X(2) and X(40706)
X(44382) = crosssum of X(32) and X(11134)
X(44382) = crossdifference of every pair of points on line {512, 19780}
X(44382) = barycentric product X(i)*X(j) for these {i,j}: {16022, 34390}, {22848, 40706}
X(44382) = barycentric quotient X(i)/X(j) for these {i,j}: {16022, 62}, {22848, 395}
X(44382) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 69, 16645}, {2, 141, 44383}, {2, 298, 23303}, {2, 299, 395}, {2, 303, 396}, {2, 396, 3589}, {2, 599, 33474}, {2, 9763, 597}, {2, 34541, 298}, {69, 16645, 33459}, {299, 37785, 40899}, {630, 636, 140}, {3180, 43229, 32455}, {5859, 37641, 3629}, {6189, 6190, 40898}, {11092, 11120, 34326}, {15685, 33620, 33618}, {23303, 34541, 3631}, {39022, 39023, 298}

X(44383) = STEINER-INELLIPSE-INVERSE OF X(299)

Barycentrics    Sqrt[3]*(b^2 + c^2) + 4*S : :
X(44383) = 3 X[2] + X[298], 9 X[2] - X[3180], 5 X[2] - X[37786], 15 X[2] + X[40898], X[13] - 5 X[40334], X[15] + 3 X[21359], X[15] - 5 X[36770], 3 X[298] + X[3180], 5 X[298] + 3 X[37786], 5 X[298] - X[40898], X[299] - 5 X[7925], 3 X[396] - X[3180], 5 X[396] - 3 X[37786], 5 X[396] + X[40898], 5 X[1656] - X[20425], 5 X[3180] - 9 X[37786], 5 X[3180] + 3 X[40898], 3 X[5463] + X[36969], X[9117] - 5 X[31274], X[14538] + 3 X[36765], 3 X[14971] - X[22573], 3 X[21359] + 5 X[36770], 3 X[31693] - X[36969], 3 X[35304] - X[36967], 3 X[36765] - X[41016], 3 X[37786] + X[40898]

X(44383) lies on these lines: {2, 6}, {5, 3643}, {13, 40334}, {14, 7789}, {15, 21359}, {16, 37352}, {30, 618}, {140, 619}, {397, 627}, {398, 11307}, {465, 34828}, {530, 625}, {531, 620}, {532, 6669}, {533, 6671}, {547, 624}, {549, 3642}, {616, 5318}, {621, 42942}, {626, 42913}, {630, 16239}, {633, 16772}, {634, 42598}, {636, 3628}, {641, 34552}, {642, 34551}, {1080, 29181}, {1503, 5617}, {1656, 20425}, {3564, 6771}, {3788, 34508}, {3934, 6670}, {4399, 40714}, {4478, 40713}, {5031, 6108}, {5103, 5979}, {5238, 33387}, {5321, 11299}, {5463, 31693}, {6292, 22848}, {6674, 42591}, {6695, 7849}, {7761, 13084}, {7799, 40707}, {7862, 34509}, {7865, 42121}, {7880, 11543}, {8355, 33477}, {9117, 31274}, {10409, 33506}, {10653, 11305}, {10654, 11301}, {11078, 11119}, {11080, 40709}, {11122, 44030}, {11128, 22893}, {11133, 22847}, {11289, 16773}, {11290, 42599}, {11297, 18581}, {11302, 42089}, {11303, 42943}, {11306, 42910}, {11309, 42152}, {11311, 42149}, {14538, 36765}, {14904, 33228}, {14971, 22573}, {15685, 33619}, {16242, 37341}, {18586, 23312}, {18587, 23311}, {18840, 43555}, {22510, 42489}, {22574, 39785}, {22844, 42992}, {32459, 35304}, {32515, 33478}, {33561, 42143}, {33614, 33616}, {34827, 41887}, {37170, 42155}, {37171, 42095}, {37172, 42154}, {37177, 42153}, {37178, 43239}, {37351, 37835}, {38745, 41023}, {41888, 43961}

X(44383) = midpoint of X(i) and X(j) for these {i,j}: {298, 396}, {325, 395}, {616, 5318}, {618, 623}, {621, 42942}, {5463, 31693}, {10409, 33506}, {11133, 22847}, {14538, 41016}, {22574, 39785}, {22796, 36755}, {41888, 43961}
X(44383) = reflection of X(i) in X(j) for these {i,j}: {11542, 6669}, {42912, 6671}, {43416, 33560}, {44382, 44377}
X(44383) = complement of X(396)
X(44383) = circumcircle of inner Napoleon triangle inverse of X(38940)
X(44383) = complement of the isogonal conjugate of X(2981)
X(44383) = complement of the isotomic conjugate of X(40707)
X(44383) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 22892}, {163, 35443}, {661, 15609}, {2153, 16536}, {2981, 10}, {10409, 4369}, {19300, 40581}, {38428, 20305}, {40707, 2887}
X(44383) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 22892}, {35314, 23870}
X(44383) = crosspoint of X(2) and X(40707)
X(44383) = crosssum of X(32) and X(11137)
X(44383) = crossdifference of every pair of points on line {512, 19781}
X(44383) = barycentric product X(i)*X(j) for these {i,j}: {16021, 34389}, {22892, 40707}
X(44383) = barycentric quotient X(i)/X(j) for these {i,j}: {16021, 61}, {22892, 396}
X(44383) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 69, 16644}, {2, 141, 44382}, {2, 298, 396}, {2, 299, 23302}, {2, 302, 395}, {2, 395, 3589}, {2, 599, 33475}, {2, 9761, 597}, {2, 34540, 299}, {69, 16644, 33458}, {298, 37786, 40898}, {629, 635, 140}, {3181, 43228, 32455}, {5858, 37640, 3629}, {6189, 6190, 40899}, {11078, 11119, 34325}, {14538, 36765, 41016}, {15685, 33621, 33619}, {21359, 36770, 15}, {23302, 34540, 3631}, {39022, 39023, 299}

X(44384) = STEINER-INELLIPSE-INVERSE OF X(302)

Barycentrics    2*a^4 - 3*a^2*b^2 + 3*b^4 - 3*a^2*c^2 - 2*b^2*c^2 + 3*c^4 - 2*Sqrt[3]*(2*a^2 - b^2 - c^2)*S : :
X(44384) = 3 X[299] + X[385], X[385] - 3 X[396], X[7779] + 3 X[37786], 3 X[21360] + X[22997]

X(44384) lies on these lines: {2, 6}, {30, 32552}, {530, 32456}, {532, 620}, {533, 625}, {1503, 22509}, {3564, 25560}, {3734, 34509}, {5026, 6783}, {6779, 32459}, {8598, 33376}, {13196, 22508}, {21360, 22997}, {32515, 33462}

X(44384) = midpoint of X(299) and X(396)
X(44384) = reflection of X(44385) in X(44377)
X(44384) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 385, 44385}, {6189, 6190, 40900}, {39022, 39023, 302}

X(44385) = STEINER-INELLIPSE-INVERSE OF X(303)

Barycentrics    2*a^4 - 3*a^2*b^2 + 3*b^4 - 3*a^2*c^2 - 2*b^2*c^2 + 3*c^4 + 2*Sqrt[3]*(2*a^2 - b^2 - c^2)*S : :
X(44385) = 3 X[298] + X[385], X[385] - 3 X[395], X[7779] + 3 X[37785], 3 X[21359] + X[22998]

X(44385) lies on these lines: {2, 6}, {30, 32553}, {531, 32456}, {532, 625}, {533, 620}, {1503, 22507}, {3564, 25559}, {3734, 34508}, {5026, 6782}, {6780, 32459}, {8598, 33377}, {13196, 22506}, {21359, 22998}, {32515, 33463}

X(44385) = midpoint of X(298) and X(395)
X(44385) = reflection of X(44384) in X(44377)
X(44385) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 385, 44384}, {6189, 6190, 40901}, {39022, 39023, 303}

X(44386) = STEINER-INELLIPSE-INVERSE OF X(323)

Barycentrics    2*a^8 - 5*a^6*b^2 + 5*a^4*b^4 - 3*a^2*b^6 + b^8 - 5*a^6*c^2 + 4*a^4*b^2*c^2 - 4*b^6*c^2 + 5*a^4*c^4 + 6*b^4*c^4 - 3*a^2*c^6 - 4*b^2*c^6 + c^8 : :
X(44386) = 3 X[2] + X[40879], 7 X[3526] + X[36207], X[9142] - 5 X[38739], X[9145] + 3 X[38224]

X(44386) lies on these lines: {2, 6}, {140, 523}, {2854, 6036}, {3018, 34990}, {3526, 36207}, {3934, 36597}, {4558, 34989}, {6748, 14590}, {7495, 16320}, {7499, 16316}, {7789, 36953}, {7847, 40429}, {9142, 38739}, {9145, 38224}, {11594, 37459}, {19221, 33233}, {37283, 37451}

X(44386) = midpoint of X(18122) and X(40879)
X(44386) = complement of X(18122)
X(44386) = X(39448)-complementary conjugate of X(4369)
X(44386) = crosssum of X(6) and X(15544)
X(44386) = crossdifference of every pair of points on line {512, 11063}
X(44386) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 24975, 3589}, {2, 40879, 18122}, {39022, 39023, 323}

X(44387) = STEINER-INELLIPSE-INVERSE OF X(333)

Barycentrics    2*a^5 - 3*a^3*b^2 + 2*a*b^4 + b^5 - 2*a^3*b*c - 2*a^2*b^2*c + a*b^3*c + 2*b^4*c - 3*a^3*c^2 - 2*a^2*b*c^2 - b^3*c^2 + a*b*c^3 - b^2*c^3 + 2*a*c^4 + 2*b*c^4 + c^5 : :
X(44387) = 3 X[2] + X[40882]

X(44387) lies on these lines: {2, 6}, {523, 8045}, {527, 620}, {662, 20337}, {1944, 35086}, {3834, 40539}, {4363, 24384}, {8607, 34990}, {23947, 24957}

X(44387) = midpoint of X(i) and X(j) for these {i,j}: {1944, 35086}, {10026, 19623}
X(44387) = crossdifference of every pair of points on line {512, 2305}
X(44387) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39022, 39023, 333}

X(44388) = STEINER-INELLIPSE-INVERSE OF X(343)

Barycentrics    a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 - 3*a^4*c^4 - a^2*b^2*c^4 - 2*b^4*c^4 + 3*a^2*c^6 + 2*b^2*c^6 - c^8 : :
X(44388) = X[325] + 2 X[18122], 5 X[7925] - X[40888]

X(44388) lies on these lines: {2, 6}, {114, 2393}, {297, 11062}, {317, 42406}, {523, 2072}, {566, 41237}, {868, 22087}, {1513, 9019}, {2450, 3001}, {8553, 44128}, {16320, 37980}, {18531, 42353}, {37347, 41169}, {37459, 39231}, {40074, 40822}

X(44388) = reflection of X(39231) in X(37459)
X(44388) = crossdifference of every pair of points on line {512, 571}
X(44388) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {34827, 34990, 297}, {39022, 39023, 343}

X(44389) = STEINER-INELLIPSE-INVERSE OF X(394)

Barycentrics    2*a^8 - 5*a^6*b^2 + 5*a^4*b^4 - 3*a^2*b^6 + b^8 - 5*a^6*c^2 + 6*a^4*b^2*c^2 - a^2*b^4*c^2 - 4*b^6*c^2 + 5*a^4*c^4 - a^2*b^2*c^4 + 6*b^4*c^4 - 3*a^2*c^6 - 4*b^2*c^6 + c^8 : :
X(44389) = 3 X[2] + X[40888]

X(44389) lies on these lines: {2, 6}, {523, 7663}, {1990, 34990}, {2165, 3964}, {6036, 8681}, {9308, 42406}, {16310, 36212}, {16320, 16387}, {36953, 37778}

X(44389) = crossdifference of every pair of points on line {512, 1609}
X(44389) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39022, 39023, 394}

X(44390) = STEINER-INELLIPSE-INVERSE OF X(491)

Barycentrics    2*a^4 - 3*a^2*b^2 + 3*b^4 - 3*a^2*c^2 - 2*b^2*c^2 + 3*c^4 + 2*(2*a^2 - b^2 - c^2)*S : :

X(44390) lies on these lines: {2, 6}, {620, 32419}, {625, 32421}, {639, 43121}, {641, 9738}, {1503, 6231}, {7751, 13880}, {7761, 41490}, {13748, 35944}, {14230, 23311}

X(44390) = relection of X(44391) in X(44377)
X(44390) = crossdifference of every pair of points on line {512, 12963}
X(44390) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 230, 44391}, {492, 13758, 591}, {39022, 39023, 491}

X(44391) = STEINER-INELLIPSE-INVERSE OF X(492)

Barycentrics    2*a^4 - 3*a^2*b^2 + 3*b^4 - 3*a^2*c^2 - 2*b^2*c^2 + 3*c^4 - 2*(2*a^2 - b^2 - c^2)*S : :

X(44391) lies on these lines: {2, 6}, {620, 32421}, {625, 32419}, {640, 43120}, {642, 9739}, {1503, 6230}, {7751, 13921}, {7761, 41491}, {13749, 35945}, {14233, 23312}

X(44391) = relection of X(44390) in X(44377)
X(44391) = crossdifference of every pair of points on line {512, 12968}
X(44391) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 230, 44390}, {491, 13638, 1991}, {39022, 39023, 492}

X(44392) = STEINER-INELLIPSE-INVERSE OF X(590)

Barycentrics    2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4 + 2*(2*a^2 - b^2 - c^2)*S : :

X(44392) lies on these lines: {2, 6}, {115, 32421}, {187, 13989}, {316, 19108}, {523, 17431}, {574, 41490}, {637, 12968}, {639, 5062}, {641, 1504}, {1503, 33430}, {3070, 6289}, {3071, 9733}, {3102, 7584}, {3564, 6230}, {6423, 13644}, {6560, 13771}, {7746, 13880}, {7799, 19109}, {12256, 13748}, {12305, 35945}, {12962, 39387}, {13677, 33342}, {13934, 13961}, {13935, 21445}, {13988, 18362}, {22594, 35684}, {22616, 42276}, {26288, 43448}, {32494, 39679}, {39663, 42262}, {40947, 44196}

X(44392) = relection of X(44394) in X(230)
X(44392) = crosssum of X(6) and X(2459)
X(44392) = crossdifference of every pair of points on line {371, 512}
X(44392) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 325, 44394}, {6, 13847, 13758}, {1991, 37637, 590}, {3069, 5860, 7735}, {39022, 39023, 590}, {39107, 39108, 13637}

X(44393) = STEINER-INELLIPSE-INVERSE OF X(591)

Barycentrics    2*(a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4) - (2*a^2 - b^2 - c^2)*S : :

X(44393) lies on these lines: {2, 6}, {3, 11157}, {3070, 35306}, {3933, 13921}, {12158, 13785}, {13665, 13669}, {32419, 32435}, {33184, 41491}, {35302, 44192}

X(44393) = reflection of X(44400) in X(2)
X(44393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39022, 39023, 591}, {39107, 39108, 5860}

X(44394) = STEINER-INELLIPSE-INVERSE OF X(615)

Barycentrics    2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4 - 2*(2*a^2 - b^2 - c^2)*S : :

X(44394) lies on these lines: {2, 6}, {115, 32419}, {187, 8997}, {316, 19109}, {523, 17432}, {574, 41491}, {638, 12963}, {640, 5058}, {642, 1505}, {1503, 33431}, {3070, 9732}, {3071, 6290}, {3103, 7583}, {3564, 6231}, {6424, 13763}, {6561, 13650}, {7746, 13921}, {7799, 19108}, {9540, 21445}, {12257, 13749}, {12306, 35944}, {12969, 39388}, {13797, 33343}, {13848, 18362}, {13882, 13903}, {22623, 35685}, {22645, 42275}, {26289, 43448}, {31454, 32497}, {39663, 42265}, {40947, 44199}

X(44394) = relection of X(44392) in X(230)
X(44394) = crosssum of X(6) and X(2460)
X(44394) = crossdifference of every pair of points on line {372, 512}
X(44394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 325, 44392}, {6, 13846, 13638}, {591, 37637, 615}, {3068, 5861, 7735}, {39022, 39023, 615}, {39107, 39108, 13757}

X(44395) = STEINER-INELLIPSE-INVERSE OF X(1007)

Barycentrics    2*a^6 - 9*a^4*b^2 + 8*a^2*b^4 - 5*b^6 - 9*a^4*c^2 + 8*a^2*b^2*c^2 + b^4*c^2 + 8*a^2*c^4 + b^2*c^4 - 5*c^6 : :
X(44395) = X[325] - 5 X[3620], 3 X[599] + X[15993], X[1992] - 3 X[41139], 3 X[21356] - X[22110], 9 X[21356] - X[39099], 3 X[22110] - X[39099]

X(44395) lies on these lines: {2, 6}, {542, 32459}, {620, 3564}, {1503, 38749}, {7789, 34507}, {14645, 43291}, {15069, 39647}, {41585, 41762}

X(44395) = midpoint of X(69) and X(230)
X(44395) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15271, 21356, 141}, {39022, 39023, 1007}

X(44396) = STEINER-INELLIPSE-INVERSE OF X(1211)

Barycentrics    (b + c)*(-(a^3*b) - a^2*b^2 + a*b^3 + b^4 - a^3*c - a^2*c^2 + a*c^3 + c^4) : :

X(44396) lies on these lines: {2, 6}, {75, 5949}, {115, 536}, {338, 3262}, {442, 28611}, {523, 1577}, {620, 16702}, {740, 20546}, {1030, 21287}, {1086, 20337}, {2092, 21245}, {3454, 25374}, {3695, 14873}, {3712, 33329}, {3729, 8818}, {3834, 17058}, {3842, 24348}, {3912, 8287}, {3943, 23947}, {3948, 18151}, {4665, 23897}, {4708, 6537}, {5164, 41179}, {5695, 37049}, {13466, 23992}, {15526, 35083}, {17318, 23903}, {17790, 35147}, {20654, 27697}, {20975, 35552}, {21076, 27691}, {23980, 35088}, {23991, 25357}, {24345, 33159}, {28654, 42710}, {30860, 41310}

X(44396) = midpoint of X(17790) and X(35147)
X(44396) = reflection of X(16702) in X(620)
X(44396) = complement of X(19623)
X(44396) = complement of the isotomic conjugate of X(11611)
X(44396) = isotomic conjugate of the isogonal conjugate of X(5164)
X(44396) = isotomic conjugate of the polar conjugate of X(424)
X(44396) = isotomic conjugate of antigonal conjugate of X(1029)
X(44396) = X(i)-complementary conjugate of X(j) for these (i,j): {798, 35079}, {2703, 4369}, {4079, 41179}, {11609, 21246}, {11611, 2887}, {17939, 21196}, {17946, 3741}, {17954, 3739}, {17961, 1125}, {17981, 34830}, {18002, 1086}, {18015, 116}, {35147, 42327}
X(44396) = X(i)-Ceva conjugate of X(j) for these (i,j): {35147, 523}, {43189, 525}
X(44396) = X(5164)-cross conjugate of X(424)
X(44396) = crosspoint of X(2) and X(11611)
X(44396) = crosssum of X(6) and X(5006)
X(44396) = crossdifference of every pair of points on line {512, 1333}
X(44396) = barycentric product X(i)*X(j) for these {i,j}: {69, 424}, {76, 5164}
X(44396) = barycentric quotient X(i)/X(j) for these {i,j}: {424, 4}, {5164, 6}
X(44396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 2895}, {27556, 27688, 6}, {39022, 39023, 1211}, {39107, 39108, 31143}

X(44397) = STEINER-INELLIPSE-INVERSE OF X(1641)

Barycentrics    8*a^8 - 16*a^6*b^2 + 9*a^4*b^4 - a^2*b^6 + 2*b^8 - 16*a^6*c^2 + 30*a^4*b^2*c^2 - 15*a^2*b^4*c^2 - 7*b^6*c^2 + 9*a^4*c^4 - 15*a^2*b^2*c^4 + 18*b^4*c^4 - a^2*c^6 - 7*b^2*c^6 + 2*c^8 : :
X(44397) = X[671] + 3 X[4590], 2 X[671] - 3 X[31644], X[892] + 3 X[41134], 2 X[4590] + X[31644], X[8591] - 3 X[14588], 2 X[9164] + X[35087], 4 X[9165] - 3 X[23991], 3 X[9167] - X[23992], X[18823] + 3 X[31998], X[18823] - 6 X[36953], X[31998] + 2 X[36953]

X(44397) lies on these lines: {2, 6}, {99, 17948}, {523, 2482}, {543, 40553}, {671, 4590}, {892, 41134}, {6786, 9044}, {8591, 14588}, {8598, 34205}, {9165, 23991}, {9167, 23992}, {10717, 16092}, {14120, 31173}, {18823, 31998}

X(44397) = midpoint of X(i) and X(j) for these {i,j}: {2, 9182}, {99, 17948}, {2482, 35087}
X(44397) = reflection of X(2482) in X(9164)
X(44397) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39022, 39023, 1641}, {39107, 39108, 5468}

X(44398) = STEINER-INELLIPSE-INVERSE OF X(1648)

Barycentrics    (b - c)^2*(b + c)^2*(5*a^4 - 5*a^2*b^2 + 2*b^4 - 5*a^2*c^2 + b^2*c^2 + 2*c^4) : :
X(44398) = X[115] - 3 X[23991], 4 X[115] - 3 X[31644], X[892] - 5 X[14061], 2 X[9164] - 3 X[9167], 4 X[9165] - 3 X[14971], 4 X[9165] - X[35087], 3 X[9166] - X[17948], 3 X[9166] + X[18823], 3 X[14971] - X[35087], 3 X[23991] + X[23992], 4 X[23991] - X[31644], 4 X[23992] + 3 X[31644], X[35511] + 4 X[40511]

X(44398) lies on these lines: {2, 6}, {115, 523}, {125, 9193}, {526, 14113}, {542, 5915}, {620, 40486}, {892, 14061}, {2679, 9009}, {2872, 44011}, {4590, 36953}, {5914, 10418}, {5996, 8288}, {6722, 40553}, {6784, 9044}, {6791, 9209}, {9007, 41181}, {9012, 15630}, {9164, 9167}, {9165, 14971}, {9166, 17948}, {16320, 36168}, {17416, 35078}, {28209, 41180}, {35088, 35133}, {35511, 40511}, {39689, 41102}

X(44398) = midpoint of X(i) and X(j) for these {i,j}: {115, 23992}, {17948, 18823}
X(44398) = reflection of X(i) in X(j) for these {i,j}: {620, 40486}, {4590, 36953}, {40553, 6722}
X(44398) = complement of X(9182)
X(44398) = complement of the isotomic conjugate of X(9180)
X(44398) = X(i)-complementary conjugate of X(j) for these (i,j): {798, 35087}, {843, 4369}, {9180, 2887}, {18823, 42327}
X(44398) = X(i)-Ceva conjugate of X(j) for these (i,j): {9166, 8371}, {18823, 523}, {41134, 9168}
X(44398) = crosspoint of X(i) and X(j) for these (i,j): {2, 9180}, {523, 9164}, {9168, 41134}
X(44398) = crosssum of X(6) and X(9181)
X(44398) = crossdifference of every pair of points on line {512, 5467}
X(44398) = barycentric product X(i)*X(j) for these {i,j}: {115, 41134}, {523, 9168}
X(44398) = barycentric quotient X(i)/X(j) for these {i,j}: {9168, 99}, {41134, 4590}, {41177, 1641}
X(44398) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5912, 230}, {230, 22110, 24855}, {9166, 18823, 17948}, {23991, 23992, 115}, {39022, 39023, 1648}

X(44399) = STEINER-INELLIPSE-INVERSE OF X(1654)

Barycentrics    2*a^4 - 2*a^3*b - 3*a^2*b^2 + a*b^3 + 3*b^4 - 2*a^3*c - 2*a^2*b*c + a*b^2*c + b^3*c - 3*a^2*c^2 + a*b*c^2 - 2*b^2*c^2 + a*c^3 + b*c^3 + 3*c^4 : :
X(44399) = 3 X[2] + X[10026], 9 X[2] - X[17731], 15 X[2] + X[20536], X[6629] - 5 X[31274], 3 X[10026] + X[17731], 5 X[10026] - X[20536], 5 X[17266] - X[35080], 5 X[17731] + 3 X[20536]

X(44399) lies on these lines: {2, 6}, {519, 6722}, {523, 25666}, {4062, 40511}, {6629, 31274}, {11599, 28530}, {17266, 35080}, {20337, 24617}, {24348, 31285}

X(44399) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39022, 39023, 1654}

X(44400) = STEINER-INELLIPSE-INVERSE OF X(1991)

Barycentrics    2*(a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4) + (2*a^2 - b^2 - c^2)*S : :

X(44400) lies on these lines: {2, 6}, {3, 11158}, {3071, 35305}, {3933, 13880}, {12159, 13665}, {13785, 13789}, {32421, 32432}, {33184, 41490}, {35302, 44193}

X(44400) = reflection of X(44393) in X(2)
X(44400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39022, 39023, 1991}, {39107, 39108, 5861}

X(44401) = STEINER-INELLIPSE-INVERSE OF X(1992)

Barycentrics    10*a^4 - 7*a^2*b^2 + 7*b^4 - 7*a^2*c^2 - 10*b^2*c^2 + 7*c^4 : :
X(44401) = 5 X[2] - X[325], 7 X[2] + X[385], 17 X[2] - X[7779], 9 X[2] - X[7840], 13 X[2] - 5 X[7925], 5 X[2] + 3 X[8859], 13 X[2] + X[15480], 3 X[2] + X[22329], 7 X[2] - 3 X[41133], 19 X[2] - 3 X[41136], X[2] - 3 X[41139], X[115] + 3 X[5215], X[187] + 3 X[14971], 5 X[230] + X[325], 7 X[230] - X[385], 17 X[230] + X[7779], 9 X[230] + X[7840], 13 X[230] + 5 X[7925], 5 X[230] - 3 X[8859], 13 X[230] - X[15480], 3 X[230] + X[22110], 3 X[230] - X[22329], 7 X[230] + 3 X[41133], 19 X[230] + 3 X[41136], X[230] + 3 X[41139], 7 X[325] + 5 X[385], 17 X[325] - 5 X[7779], 9 X[325] - 5 X[7840], 13 X[325] - 25 X[7925], X[325] + 3 X[8859], 13 X[325] + 5 X[15480], 3 X[325] - 5 X[22110], 3 X[325] + 5 X[22329], 7 X[325] - 15 X[41133], 19 X[325] - 15 X[41136], X[325] - 15 X[41139], X[376] + 3 X[39663], 17 X[385] + 7 X[7779], 9 X[385] + 7 X[7840], 13 X[385] + 35 X[7925], 5 X[385] - 21 X[8859], 13 X[385] - 7 X[15480], 3 X[385] + 7 X[22110], 3 X[385] - 7 X[22329], X[385] + 3 X[41133], 19 X[385] + 21 X[41136], X[385] + 21 X[41139], X[671] + 3 X[35297], X[3793] + 5 X[31275], 5 X[5071] + 3 X[21445], 3 X[5215] - X[27088], X[6390] - 3 X[9167], 9 X[7779] - 17 X[7840], 13 X[7779] - 85 X[7925], 5 X[7779] + 51 X[8859], 13 X[7779] + 17 X[15480], 3 X[7779] - 17 X[22110], 3 X[7779] + 17 X[22329], 7 X[7779] - 51 X[41133], 19 X[7779] - 51 X[41136], X[7779] - 51 X[41139], 13 X[7840] - 45 X[7925], 5 X[7840] + 27 X[8859], 13 X[7840] + 9 X[15480], X[7840] - 3 X[22110], X[7840] + 3 X[22329], 7 X[7840] - 27 X[41133], 19 X[7840] - 27 X[41136], X[7840] - 27 X[41139], 25 X[7925] + 39 X[8859], 5 X[7925] + X[15480], 15 X[7925] - 13 X[22110], 15 X[7925] + 13 X[22329], 35 X[7925] - 39 X[41133], 95 X[7925] - 39 X[41136], 5 X[7925] - 39 X[41139], X[8352] - 5 X[14061], X[8352] + 3 X[26613], X[8598] + 3 X[9166], 39 X[8859] - 5 X[15480], 9 X[8859] + 5 X[22110], 9 X[8859] - 5 X[22329], 7 X[8859] + 5 X[41133], 19 X[8859] + 5 X[41136], X[8859] + 5 X[41139], 3 X[10256] - 5 X[15694], 5 X[14061] + 3 X[26613], 3 X[14971] - X[37350], 3 X[15480] + 13 X[22110], 3 X[15480] - 13 X[22329], 7 X[15480] + 39 X[41133], 19 X[15480] + 39 X[41136], X[15480] + 39 X[41139], 7 X[22110] - 9 X[41133], 19 X[22110] - 9 X[41136], X[22110] - 9 X[41139], 7 X[22329] + 9 X[41133], 19 X[22329] + 9 X[41136], X[22329] + 9 X[41139], 5 X[31274] - X[39785], X[32459] + 2 X[43291], X[37461] + 3 X[38224], 19 X[41133] - 7 X[41136], X[41133] - 7 X[41139], X[41136] - 19 X[41139]

X(44401) lies on these lines: {2, 6}, {30, 5461}, {98, 10153}, {114, 8787}, {115, 5215}, {140, 7817}, {187, 14971}, {376, 39663}, {381, 37809}, {468, 8754}, {538, 22247}, {542, 10011}, {543, 32459}, {549, 9734}, {671, 35297}, {858, 34989}, {1153, 4045}, {1503, 6055}, {2030, 19662}, {2549, 11157}, {3053, 32984}, {3291, 34990}, {3734, 16509}, {3793, 31275}, {3849, 6722}, {3934, 8365}, {5071, 21445}, {5077, 21843}, {5159, 9165}, {5475, 19661}, {5569, 7844}, {6390, 9167}, {6680, 8367}, {7612, 11180}, {7622, 15048}, {7746, 8369}, {7749, 8359}, {7810, 8361}, {7812, 33249}, {7829, 16239}, {7857, 8370}, {7886, 8360}, {7902, 14869}, {8176, 18907}, {8352, 14061}, {8366, 32832}, {8598, 9166}, {9607, 33000}, {10124, 32515}, {10162, 37454}, {10256, 15694}, {11159, 20112}, {13665, 13681}, {13785, 13801}, {13881, 32826}, {14726, 40478}, {15525, 35087}, {16092, 16320}, {19130, 32414}, {22331, 32988}, {23583, 37911}, {23967, 44216}, {29181, 38227}, {31274, 39785}, {32456, 36523}, {32457, 36521}, {32822, 34505}, {32824, 32970}, {37461, 38224}

X(44401) = midpoint of X(i) and X(j) for these {i,j}: {2, 230}, {115, 27088}, {187, 37350}, {2030, 19662}, {16092, 16320}, {22110, 22329}, {23967, 44216}, {32456, 36523}, {32457, 36521}
X(44401) = reflection of X(8355) in X(6722)
X(44401) = complement of X(22110)
X(44401) = crosssum of X(6) and X(5107)
X(44401) = crossdifference of every pair of points on line {512, 5210}
X(44401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 9771}, {2, 385, 41133}, {2, 5032, 34803}, {2, 7610, 141}, {2, 7735, 11184}, {2, 8859, 325}, {2, 8860, 11168}, {2, 9740, 37690}, {2, 11168, 20582}, {2, 22329, 22110}, {2, 23055, 599}, {2, 34229, 21358}, {2, 37637, 15597}, {2, 37689, 9770}, {115, 5215, 27088}, {187, 14971, 37350}, {230, 22110, 22329}, {230, 41139, 2}, {599, 23055, 13468}, {3055, 7806, 6329}, {5306, 11163, 20583}, {7735, 11184, 8584}, {7886, 34506, 8360}, {11159, 43620, 20112}, {13663, 13783, 1992}, {14061, 26613, 8352}, {39022, 39023, 1992}, {39107, 39108, 193}

X(44402) = X(2)X(94)∩X(69)X(5621)

Barycentrics    a^14 - 5*a^12*b^2 + 9*a^10*b^4 - 5*a^8*b^6 - 5*a^6*b^8 + 9*a^4*b^10 - 5*a^2*b^12 + b^14 - 5*a^12*c^2 + 15*a^10*b^2*c^2 - 23*a^8*b^4*c^2 + 30*a^6*b^6*c^2 - 27*a^4*b^8*c^2 + 11*a^2*b^10*c^2 - b^12*c^2 + 9*a^10*c^4 - 23*a^8*b^2*c^4 - 2*a^6*b^4*c^4 + 10*a^4*b^6*c^4 + 9*a^2*b^8*c^4 - 3*b^10*c^4 - 5*a^8*c^6 + 30*a^6*b^2*c^6 + 10*a^4*b^4*c^6 - 30*a^2*b^6*c^6 + 3*b^8*c^6 - 5*a^6*c^8 - 27*a^4*b^2*c^8 + 9*a^2*b^4*c^8 + 3*b^6*c^8 + 9*a^4*c^10 + 11*a^2*b^2*c^10 - 3*b^4*c^10 - 5*a^2*c^12 - b^2*c^12 + c^14 : :

See Antreas Hatzipolakis and Peter Moses, euclid 2094.

X(44402) lies on these lines: {2, 94}, {69, 5621}, {99, 40680}, {253, 35520}, {1494, 3926}, {6148, 10304}

X(44402) = isotomic conjugate of the isogonal conjugate of X(17838)
X(44402) = barycentric product X(76)*X(17838)
X(44402) = barycentric quotient X(17838)/X(6)

X(44403) = X(65)X(74)∩X(165)X(2836)

Barycentrics    a*(a^10*b - 2*a^9*b^2 - a^8*b^3 + 4*a^7*b^4 - 2*a^6*b^5 + 2*a^4*b^7 - 4*a^3*b^8 + a^2*b^9 + 2*a*b^10 - b^11 + a^10*c + 2*a^9*b*c - 3*a^7*b^3*c - 5*a^6*b^4*c - 7*a^5*b^5*c + 9*a^4*b^6*c + 15*a^3*b^7*c - 8*a^2*b^8*c - 7*a*b^9*c + 3*b^10*c - 2*a^9*c^2 + 7*a^6*b^3*c^2 - 2*a^5*b^4*c^2 + a^4*b^5*c^2 - 4*a^3*b^6*c^2 - 7*a^2*b^7*c^2 + 8*a*b^8*c^2 - b^9*c^2 - a^8*c^3 - 3*a^7*b*c^3 + 7*a^6*b^2*c^3 + 18*a^5*b^3*c^3 - 12*a^4*b^4*c^3 - 15*a^3*b^5*c^3 + 11*a^2*b^6*c^3 - 5*b^8*c^3 + 4*a^7*c^4 - 5*a^6*b*c^4 - 2*a^5*b^2*c^4 - 12*a^4*b^3*c^4 + 16*a^3*b^4*c^4 + 3*a^2*b^5*c^4 - 10*a*b^6*c^4 + 6*b^7*c^4 - 2*a^6*c^5 - 7*a^5*b*c^5 + a^4*b^2*c^5 - 15*a^3*b^3*c^5 + 3*a^2*b^4*c^5 + 14*a*b^5*c^5 - 2*b^6*c^5 + 9*a^4*b*c^6 - 4*a^3*b^2*c^6 + 11*a^2*b^3*c^6 - 10*a*b^4*c^6 - 2*b^5*c^6 + 2*a^4*c^7 + 15*a^3*b*c^7 - 7*a^2*b^2*c^7 + 6*b^4*c^7 - 4*a^3*c^8 - 8*a^2*b*c^8 + 8*a*b^2*c^8 - 5*b^3*c^8 + a^2*c^9 - 7*a*b*c^9 - b^2*c^9 + 2*a*c^10 + 3*b*c^10 - c^11) : :
X(44403) = (OI - 5*R^2)*X[65] + (3*OI - 11*R^2)*X[74]

See Antreas Hatzipolakis, Francisco Javier García Capitán and Peter Moses, euclid 2098 and euclid 2099 .

X(44403) lies on these lines: {65, 74}, {165, 2836}, {2771, 20417}, {2779, 15151}, {12041, 31793}

X(44404) = (name pending)

Barycentrics    a*(3*a^11*b - 3*a^10*b^2 - 9*a^9*b^3 + 9*a^8*b^4 + 6*a^7*b^5 - 6*a^6*b^6 + 6*a^5*b^7 - 6*a^4*b^8 - 9*a^3*b^9 + 9*a^2*b^10 + 3*a*b^11 - 3*b^12 + 3*a^11*c + 4*a^9*b^2*c - 26*a^7*b^4*c - 4*a^6*b^5*c + 24*a^5*b^6*c + 12*a^4*b^7*c - a^3*b^8*c - 12*a^2*b^9*c - 4*a*b^10*c + 4*b^11*c - 3*a^10*c^2 + 4*a^9*b*c^2 - 8*a^8*b^2*c^2 + 20*a^7*b^3*c^2 + 6*a^6*b^4*c^2 - 48*a^5*b^5*c^2 + 24*a^4*b^6*c^2 + 20*a^3*b^7*c^2 - 19*a^2*b^8*c^2 + 4*a*b^9*c^2 - 9*a^9*c^3 + 20*a^7*b^2*c^3 + 24*a^6*b^3*c^3 + 26*a^5*b^4*c^3 - 4*a^4*b^5*c^3 - 36*a^3*b^6*c^3 - 8*a^2*b^7*c^3 - a*b^8*c^3 - 12*b^9*c^3 + 9*a^8*c^4 - 26*a^7*b*c^4 + 6*a^6*b^2*c^4 + 26*a^5*b^3*c^4 - 52*a^4*b^4*c^4 + 26*a^3*b^5*c^4 + 10*a^2*b^6*c^4 - 26*a*b^7*c^4 + 27*b^8*c^4 + 6*a^7*c^5 - 4*a^6*b*c^5 - 48*a^5*b^2*c^5 - 4*a^4*b^3*c^5 + 26*a^3*b^4*c^5 + 40*a^2*b^5*c^5 + 24*a*b^6*c^5 + 8*b^7*c^5 - 6*a^6*c^6 + 24*a^5*b*c^6 + 24*a^4*b^2*c^6 - 36*a^3*b^3*c^6 + 10*a^2*b^4*c^6 + 24*a*b^5*c^6 - 48*b^6*c^6 + 6*a^5*c^7 + 12*a^4*b*c^7 + 20*a^3*b^2*c^7 - 8*a^2*b^3*c^7 - 26*a*b^4*c^7 + 8*b^5*c^7 - 6*a^4*c^8 - a^3*b*c^8 - 19*a^2*b^2*c^8 - a*b^3*c^8 + 27*b^4*c^8 - 9*a^3*c^9 - 12*a^2*b*c^9 + 4*a*b^2*c^9 - 12*b^3*c^9 + 9*a^2*c^10 - 4*a*b*c^10 + 3*a*c^11 + 4*b*c^11 - 3*c^12) : :

See Antreas Hatzipolakis and Peter Moses, euclid 2100.

X(44404) lies on these lines: { }

X(44405) = X(95)X(3549)∩X(454)X(3964)

Barycentrics    a^4*(a^2 - b^2 - c^2)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 2*a^6*c^2 + 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 2*b^6*c^2 - 4*a^2*b^2*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 4*a^6*c^2 + 2*a^4*b^2*c^2 - 4*a^2*b^4*c^2 + 2*b^6*c^2 + 6*a^4*c^4 + 2*a^2*b^2*c^4 - 4*a^2*c^6 - 2*b^2*c^6 + c^8) : :

See Antreas Hatzipolakis and Peter Moses, euclid 2106.

X(44405) lies on these lines: {95, 3549}, {454, 3964}, {924, 10539}, {11585, 44156}, {13754, 16391}

X(44405) = X(158)-isoconjugate of X(3548)
X(44405) = barycentric quotient X(577)/X(3548)

X(44406) = X(5)X(13558)∩X(185)X(567)

Barycentrics    a^2 (a^20-5 a^18 b^2+9 a^16 b^4-6 a^14 b^6+6 a^6 b^14-9 a^4 b^16+5 a^2 b^18-b^20-5 a^18 c^2+20 a^16 b^2 c^2-26 a^14 b^4 c^2+6 a^12 b^6 c^2+9 a^10 b^8 c^2+5 a^8 b^10 c^2-20 a^6 b^12 c^2+16 a^4 b^14 c^2-6 a^2 b^16 c^2+b^18 c^2+9 a^16 c^4-26 a^14 b^2 c^4+21 a^12 b^4 c^4-14 a^8 b^8 c^4+24 a^6 b^10 c^4-9 a^4 b^12 c^4-14 a^2 b^14 c^4+9 b^16 c^4-6 a^14 c^6+6 a^12 b^2 c^6+2 a^8 b^6 c^6-10 a^6 b^8 c^6+4 a^4 b^10 c^6+28 a^2 b^12 c^6-24 b^14 c^6+9 a^10 b^2 c^8-14 a^8 b^4 c^8-10 a^6 b^6 c^8-4 a^4 b^8 c^8-13 a^2 b^10 c^8+24 b^12 c^8+5 a^8 b^2 c^10+24 a^6 b^4 c^10+4 a^4 b^6 c^10-13 a^2 b^8 c^10-18 b^10 c^10-20 a^6 b^2 c^12-9 a^4 b^4 c^12+28 a^2 b^6 c^12+24 b^8 c^12+6 a^6 c^14+16 a^4 b^2 c^14-14 a^2 b^4 c^14-24 b^6 c^14-9 a^4 c^16-6 a^2 b^2 c^16+9 b^4 c^16+5 a^2 c^18+b^2 c^18-c^20) : :

See Francisco Javier García Capitán, euclid 2114

X(44406) lies on these lines: {5,13558}, {185,567}, {3520,5667}, {7503,14687}

X(44407) = X(3)X(2918)∩X(4)X(569)

Barycentrics    -2 a^10+4 a^8 b^2-a^6 b^4-a^4 b^6-a^2 b^8+b^10+4 a^8 c^2-a^4 b^4 c^2-3 b^8 c^2-a^6 c^4-a^4 b^2 c^4+2 a^2 b^4 c^4+2 b^6 c^4-a^4 c^6+2 b^4 c^6-a^2 c^8-3 b^2 c^8+c^10 : :

See Francisco Javier García Capitán, euclid 2114

X(44407) lies on these lines: {3,2918}, {4,569}, {5,13419}, {20,3410}, {22,18474}, {26,5449}, {30,511}, {51,7540}, {52,10116}, {113,3153}, {125,2070}, {182,11818}, {186,6699}, {265,5899}, {381,3796}, {382,1181}, {389,11819}, {427,18475}, {546,13470}, {858,14156}, {1112,11692}, {1147,9833}, {1209,7512}, {1216,12134}, {1495,2072}, {1568,7574}, {1658,20191}, {1853,14070}, {3146,12289}, {3529,12278}, {3627,12233}, {3818,7514}, {5157,18420}, {5446,6146}, {5448,6759}, {5462,6756}, {5576,6689}, {5654,11206}, {5943,13490}, {6240,10575}, {6288,13564}, {6688,23410}, {7387,9927}, {7391,13352}, {7502,21243}, {7530,18390}, {7544,13336}, {7556,23293}, {7575,20397}, {7576,9730}, {7687,11563}, {7689,14216}, {7706,18494}, {8717,14927}, {9306,14791}, {9909,14852}, {9934,19479}, {10024,11572}, {10096,20304}, {10112,10263}, {10201,23325}, {10282,13371}, {10313,15340}, {10625,14516}, {11202,18281}, {11264,14449}, {11381,18563}, {11799,13851}, {12038,23335}, {12046,23409}, {12102,15807}, {12107,13561}, {12162,12225}, {12370,13598}, {13445,13619}, {14118,18488}, {15072,18559}, {15761,18383}, {18324,23329}, {18396,18534}

X(44408) = CIRCUMCIRCLE-POLE OF SODDY LINE

Barycentrics    a^2*(b - c)*(a^4 - a^3*b - a^2*b^2 + a*b^3 - a^3*c + a^2*b*c + a*b^2*c - b^3*c - a^2*c^2 + a*b*c^2 + 2*b^2*c^2 + a*c^3 - b*c^3) : :
X(44408) = 3 X[4057] - 4 X[39200], 3 X[39199] - 2 X[39200]

X(44408) lies on these lines: {3, 514}, {6, 22090}, {36, 238}, {55, 4449}, {56, 663}, {58, 22154}, {523, 2071}, {650, 22091}, {664, 14723}, {958, 17072}, {1011, 4379}, {1376, 4147}, {1486, 14878}, {1491, 23361}, {1597, 39532}, {1946, 3669}, {2975, 21302}, {3433, 26721}, {3960, 22160}, {4083, 9441}, {4091, 8676}, {4191, 4893}, {4367, 8638}, {4724, 5204}, {4778, 39226}, {5267, 23789}, {6003, 23187}, {6545, 16064}, {8071, 21185}, {8641, 43932}, {9029, 22769}, {20834, 21204}, {20835, 21183}, {21118, 37564}, {21791, 33863}, {23394, 23867}, {23864, 43067}, {28209, 39478}, {28225, 39225}

X(44408) = reflection of X(i) in X(j) for these {i,j}: {3, 39476}, {3733, 23224}, {4057, 39199}
X(44408) = isogonal conjugate of isotomic conjugate X(46402)
X(44408) = isogonal conjugate of the anticomplement of X(14714)
X(44408) = X(658)-Ceva conjugate of X(6)
X(44408) = crosspoint of X(i) and X(j) for these (i,j): {58, 934}, {109, 3449}, {15380, 24016}
X(44408) = crosssum of X(i) and X(j) for these (i,j): {10, 3900}, {512, 1834}, {513, 11019}, {514, 21258}, {521, 34822}, {522, 2886}, {8058, 20307}
X(44408) = crossdifference of every pair of points on line {37, 800}
X(44408) = barycentric product X(i)*X(j) for these {i,j}: {513, 37659}, {658, 14714}, {905, 4219}
X(44408) = barycentric quotient X(i)/X(j) for these {i,j}: {4219, 6335}, {14714, 3239}, {37659, 668}

X(44409) = INCIRCLE-POLE OF EULER LINE

Barycentrics    (b - c)*(-2*a^4 + a^3*b + a^2*b^2 - a*b^3 + b^4 + a^3*c - a*b^2*c + a^2*c^2 - a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4) : :
X(44409) = 3 X[354] - 2 X[34954], X[656] - 3 X[11125], 2 X[656] - 3 X[41800]

X(44409) lies on these lines: {1, 523}, {57, 5583}, {354, 34954}, {425, 2501}, {447, 525}, {513, 5570}, {521, 7649}, {522, 905}, {656, 11125}, {676, 21189}, {900, 5533}, {1021, 6587}, {2815, 40467}, {2826, 43924}, {3667, 3676}, {3700, 16612}, {3738, 21179}, {3800, 4581}, {3900, 21186}, {4017, 34958}, {4885, 28590}, {6003, 7178}, {6362, 21173}, {6615, 11031}, {7655, 21188}, {8672, 39541}, {21180, 35057}, {21182, 43042}

X(44409) = reflection of X(i) in X(j) for these {i,j}: {1, 39540}, {905, 21172}, {4017, 34958}, {7655, 21188}, {10015, 7649}, {21189, 676}, {41800, 11125}
X(44409) = incircle-inverse of X(3109)
X(44409) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {28, 34548}, {112, 8055}, {162, 42020}, {8056, 13219}, {34080, 3151}, {38266, 39352}, {38828, 2897}
X(44409) = X(i)-complementary conjugate of X(j) for these (i,j): {56, 42425}, {604, 40622}, {6011, 1329}
X(44409) = crosspoint of X(7) and X(648)
X(44409) = crosssum of X(55) and X(647)
X(44409) = crossdifference of every pair of points on line {198, 2245}
X(44409) = barycentric product X(21452)*X(43728)

X(44410) = INCIRCLE-POLE OF BROCARD AXIS

Barycentrics    a^2*(b - c)*(a^3*b - a^2*b^2 - a*b^3 + b^4 + a^3*c - a*b^2*c - a^2*c^2 - a*b*c^2 - a*c^3 + c^4) : :
X(44410) = 3 X[354] - 2 X[34958]

X(44410) lies on these lines: {1, 512}, {65, 28473}, {354, 34958}, {513, 5570}, {520, 3737}, {654, 22160}, {663, 928}, {905, 8676}, {924, 2605}, {926, 1734}, {942, 7178}, {1210, 4129}, {1401, 38370}, {1737, 21051}, {2488, 4040}, {2774, 14838}, {3022, 7266}, {3309, 4897}, {3738, 4142}, {4017, 34954}, {4807, 31397}, {7215, 11918}, {7252, 8673}, {10122, 42325}, {17899, 21300}, {21259, 24353}, {22093, 42662}, {23599, 39790}, {24472, 40459}

X(44410) = reflection of X(i) in X(j) for these {i,j}: {1, 39541}, {4017, 34954}, {4040, 2488}, {7178, 942}
X(44410) = incircle-inverse of X(3110)
X(44410) = crosspoint of X(7) and X(110)
X(44410) = crosssum of X(55) and X(523)
X(44410) = crossdifference of every pair of points on line {2238, 2911}
X(44410) = barycentric product X(i)*X(j) for these {i,j}: {4556, 21947}, {4570, 23762}
X(44410) = barycentric quotient X(23762)/X(21207)

X(44411) = NINE-POINT-CIRCLE-POLE OF ANTI-ORTHIC AXIS

Barycentrics    (b + c)*(a^3*b^2 - a*b^4 + a*b^3*c - b^4*c + a^3*c^2 + b^3*c^2 + a*b*c^3 + b^2*c^3 - a*c^4 - b*c^4) : :

X(44411) lies on these lines: {2, 16678}, {5, 10}, {11, 42}, {12, 73}, {35, 37357}, {55, 1985}, {71, 1213}, {100, 14008}, {235, 1869}, {313, 325}, {427, 1826}, {442, 16828}, {523, 21318}, {692, 17188}, {908, 22275}, {1220, 14011}, {1746, 20986}, {2476, 19874}, {2486, 3914}, {3035, 37365}, {3120, 21936}, {3214, 7173}, {3293, 7741}, {3613, 15523}, {3816, 37355}, {3829, 4685}, {4193, 26115}, {4417, 11681}, {4651, 5233}, {4847, 22271}, {4884, 21080}, {5432, 37354}, {5433, 28268}, {5711, 19754}, {6690, 37370}, {7354, 28377}, {7951, 33111}, {8804, 23305}, {10592, 15666}, {10886, 30827}, {14321, 23301}, {14973, 15281}, {15974, 37619}, {17530, 19870}, {20486, 21025}, {20531, 21098}, {20718, 22000}, {21020, 21801}, {21028, 21920}, {21045, 21911}, {21051, 34964}, {21892, 21949}, {22301, 31330}, {30980, 32943}, {30981, 32918}, {31084, 37353}

X(44411) = reflection of X(5) in X(39505)
X(44411) = complement of X(16678)
X(44411) = nine-point-circle-inverse of X(38472)
X(44411) = medial isogonal conjugate of X(40600)
X(44411) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 40600}, {40516, 1213}
X(44411) = X(4559)-Ceva conjugate of X(523)
X(44411) = barycentric product X(i)*X(j) for these {i,j}: {1, 40564}, {10, 24220}, {14618, 23161}
X(44411) = barycentric quotient X(i)/X(j) for these {i,j}: {23161, 4558}, {24220, 86}, {40564, 75}
X(44411) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 946, 22300}, {10, 39583, 5}, {1329, 2886, 5743}, {2051, 41797, 38472}, {2540, 2541, 2051}

X(44412) = NINE-POINT-CIRCLE-POLE OF GERGONNE LINE

Barycentrics    a^3*b^2 - b^5 + a^3*c^2 + b^3*c^2 + b^2*c^3 - c^5 : :

X(44412) lies on these lines: {2, 1631}, {5, 516}, {11, 4336}, {141, 9018}, {427, 1826}, {523, 41007}, {673, 7678}, {674, 20305}, {857, 8053}, {858, 17134}, {1268, 33108}, {1486, 30808}, {1836, 2160}, {1953, 21045}, {2886, 27798}, {4364, 21536}, {6284, 27555}, {8068, 34845}, {8287, 21746}, {17243, 20531}, {17792, 21237}, {20470, 37050}, {21239, 40646}, {21252, 24220}, {21275, 30882}, {22277, 26012}

X(44412) = reflection of X(5) in X(39507)
X(44412) = complement of X(1631)
X(44412) = complement of the isogonal conjugate of X(7357)
X(44412) = medial isogonal conjugate of X(32664)
X(44412) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 32664}, {7087, 37}, {7096, 2}, {7213, 1}, {7357, 10}, {40145, 39}
X(44412) = crosssum of X(6) and X(40370)

X(44413) = 2ND-LEMOINE-CIRCLE-POLE OF ORTHIC AXIS

Barycentrics    a^2*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 4*a^6*c^2 + 12*a^4*b^2*c^2 - 8*b^6*c^2 + 6*a^4*c^4 + 14*b^4*c^4 - 4*a^2*c^6 - 8*b^2*c^6 + c^8) : :
X(44413) = 7 X[6] - X[33534], 4 X[6] - X[35237], 2 X[1351] + X[11472], 4 X[9818] - 3 X[32620], X[11477] + 2 X[31861], 4 X[21850] - X[40909], 4 X[33534] - 7 X[35237], X[33534] - 14 X[39522], X[35237] - 8 X[39522]

X(44413) lies on these lines: {2, 37483}, {3, 51}, {4, 155}, {5, 17811}, {6, 30}, {20, 34545}, {22, 15033}, {25, 13352}, {26, 11425}, {52, 1593}, {64, 6102}, {68, 1595}, {143, 9786}, {154, 7530}, {182, 35243}, {184, 18534}, {185, 37493}, {195, 5076}, {323, 3839}, {376, 5422}, {378, 3060}, {381, 394}, {382, 1181}, {389, 12085}, {399, 38335}, {427, 14852}, {511, 9813}, {539, 18440}, {541, 39562}, {546, 16266}, {549, 17825}, {550, 37514}, {567, 3796}, {568, 10605}, {569, 11414}, {576, 6000}, {578, 7387}, {1092, 7529}, {1112, 12302}, {1147, 1598}, {1154, 9972}, {1192, 11250}, {1199, 33703}, {1204, 19360}, {1216, 11479}, {1350, 7514}, {1351, 1597}, {1498, 3627}, {1511, 31860}, {1539, 17838}, {1596, 5654}, {1620, 10226}, {1657, 36753}, {1994, 3543}, {1995, 43574}, {2071, 11002}, {2323, 18540}, {2931, 15472}, {2935, 12236}, {3066, 37477}, {3088, 12359}, {3089, 9820}, {3146, 7592}, {3167, 18535}, {3357, 16625}, {3426, 38263}, {3431, 37939}, {3517, 12002}, {3534, 15038}, {3541, 41587}, {3545, 15066}, {3567, 11413}, {3830, 18445}, {3845, 15068}, {3853, 15811}, {5012, 12082}, {5054, 21970}, {5055, 13857}, {5064, 18474}, {5073, 14627}, {5093, 14915}, {5102, 5663}, {5198, 10539}, {5480, 18420}, {5504, 20772}, {5707, 37406}, {5889, 35502}, {5943, 37480}, {5944, 14528}, {5946, 37475}, {6247, 18951}, {6642, 10110}, {6644, 17810}, {6756, 12118}, {6800, 37925}, {6985, 36742}, {7391, 12022}, {7393, 15644}, {7395, 10625}, {7503, 37486}, {7506, 35602}, {7517, 19357}, {7526, 10263}, {7553, 19467}, {8909, 35764}, {9645, 19365}, {9714, 13367}, {9730, 9777}, {9781, 17928}, {9833, 43595}, {9909, 18475}, {10113, 17847}, {10116, 34780}, {10304, 15018}, {10323, 13434}, {10594, 34148}, {11003, 37945}, {11284, 14845}, {11403, 12160}, {11410, 32110}, {11426, 39568}, {11430, 14070}, {11432, 40647}, {11438, 21849}, {11439, 15801}, {11464, 13482}, {11591, 33537}, {11807, 12412}, {11819, 17845}, {12241, 14790}, {12295, 19504}, {13202, 19456}, {13292, 14216}, {13321, 18859}, {13336, 37198}, {13488, 19458}, {15019, 20791}, {15032, 15682}, {15037, 15681}, {15045, 43576}, {16473, 41869}, {16657, 18531}, {17702, 18494}, {17821, 37440}, {18281, 26958}, {18396, 31723}, {18400, 19149}, {18405, 44288}, {20424, 44271}, {21971, 34417}, {22115, 35259}, {22505, 39820}, {22515, 39849}, {23060, 32046}, {23335, 39571}, {25739, 31133}, {32276, 34802}, {36750, 37411}, {37784, 39588}, {39806, 39841}, {39809, 39839}, {39810, 39838}, {39812, 39835}

X(44413) = midpoint of X(1351) and X(1597)
X(44413) = reflection of X(i) in X(j) for these {i,j}: {6, 39522}, {1350, 7514}, {11472, 1597}, {18420, 5480}, {35243, 182}
X(44413) = 2nd-Lemoine-circle-inverse of X(16303)
X(44413) = X(18852)-Ceva conjugate of X(3)
X(44413) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3527, 5462}, {4, 1993, 18451}, {4, 36747, 155}, {22, 15033, 37506}, {52, 1593, 12163}, {143, 12084, 9786}, {378, 3060, 37489}, {382, 36749, 1181}, {546, 16266, 17814}, {567, 12083, 3796}, {578, 13598, 7387}, {1595, 13142, 68}, {1993, 18451, 155}, {1994, 3543, 11456}, {3627, 12161, 1498}, {3853, 32139, 15811}, {7506, 37495, 35602}, {7517, 37472, 19357}, {7526, 10263, 17834}, {9777, 21312, 9730}, {10110, 13346, 6642}, {11403, 12160, 12162}, {15316, 22660, 155}, {17810, 37497, 6644}, {18451, 36747, 1993}, {36987, 43650, 3}

X(44414) = 2ND-LEMOINE-CIRCLE-POLE OF ANTI-ORTHIC AXIS

Barycentrics    a^2*(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5 + a^4*c - 4*a^2*b^2*c + 3*b^4*c - 2*a^3*c^2 - 4*a^2*b*c^2 + 2*a*b^2*c^2 - 4*b^3*c^2 - 2*a^2*c^3 - 4*b^2*c^3 + a*c^4 + 3*b*c^4 + c^5) : :
X(44414) = 4 X[6] - X[1480], X[1480] - 8 X[39523], 2 X[3751] + X[7986]

X(44414) lies on these lines: {1, 6883}, {3, 42}, {5, 33137}, {6, 517}, {10, 5707}, {31, 10679}, {40, 36742}, {43, 6911}, {55, 5398}, {56, 5399}, {58, 11248}, {65, 921}, {81, 5657}, {212, 1497}, {218, 6913}, {219, 9708}, {222, 36279}, {355, 5706}, {386, 11249}, {392, 10601}, {394, 3753}, {495, 37543}, {500, 5584}, {580, 10267}, {581, 1126}, {582, 2334}, {595, 37622}, {601, 35448}, {602, 16202}, {607, 7497}, {613, 5844}, {912, 3751}, {940, 26446}, {999, 1450}, {1006, 17018}, {1060, 41539}, {1069, 10573}, {1159, 23071}, {1191, 10222}, {1193, 10680}, {1201, 12001}, {1203, 7982}, {1385, 36745}, {1482, 16466}, {1616, 33179}, {1656, 24892}, {1834, 10526}, {1870, 7672}, {2003, 2093}, {2323, 9623}, {3193, 5554}, {3240, 6905}, {3293, 11499}, {3428, 5396}, {3526, 29678}, {3560, 5247}, {3576, 16474}, {3579, 36746}, {3877, 5422}, {3914, 37826}, {3915, 12000}, {3931, 26921}, {4252, 26285}, {4255, 26286}, {4295, 8757}, {4383, 5886}, {4663, 6001}, {5173, 37697}, {5312, 11012}, {5315, 16200}, {5603, 32911}, {5690, 5711}, {5697, 16472}, {5790, 21696}, {5903, 16473}, {6583, 17054}, {6829, 33139}, {6830, 33142}, {6882, 11269}, {6985, 37699}, {7074, 24929}, {10247, 16483}, {10982, 12672}, {11230, 37679}, {11231, 37674}, {11929, 21935}, {12702, 36750}, {18481, 37537}, {25413, 36749}, {28466, 42042}, {31663, 37501}, {31786, 37514}, {31788, 37498}, {34046, 37582}, {34048, 39542}, {35238, 37469}, {36747, 37562}

X(44414) = reflection of X(6) in X(39523)
X(44414) = crossdifference of every pair of points on line {9001, 13401}
X(44414) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1482, 37509, 16466}, {3293, 37530, 11499}, {5247, 37529, 3560}, {35774, 35775, 21853}

X(44415) = 2ND-LEMOINE-CIRCLE-POLE OF DE LONGCHAMPS AXIS

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^4*b^4 - 2*a^2*b^6 + b^8 - 2*a^6*c^2 + 2*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - 4*b^6*c^2 + 2*a^4*c^4 - 4*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(44415) lies on these lines: {3, 20859}, {4, 34945}, {6, 30}, {323, 33251}, {394, 33184}, {1003, 5422}, {1180, 15033}, {1184, 37483}, {1194, 13352}, {1501, 12083}, {1915, 7530}, {1993, 7841}, {1994, 33017}, {3094, 7514}, {3981, 6644}, {5017, 13391}, {5028, 13754}, {5254, 23128}, {6800, 37902}, {8360, 17811}, {8368, 17825}, {8369, 10601}, {9465, 43574}, {11004, 33278}, {15018, 33255}, {15045, 39024}, {15066, 33219}, {33007, 34545}, {34481, 43586}, {35243, 40825}

X(44415) = reflection of X(6) in X(39524)

X(44416) = SPIEKER-CIRCLE-POLE OF ORTHIC AXIS

Barycentrics    2*a^3 - a*b^2 + b^3 + b^2*c - a*c^2 + b*c^2 + c^3 : :
X(44416) = 3 X[2] + X[32933], 3 X[31] + X[32854], X[31] + 3 X[33161], 3 X[3703] - X[32854], X[3703] - 3 X[33161], X[3744] - 3 X[35263], 5 X[31237] - X[33098], X[32854] - 9 X[33161], X[32912] + 3 X[33156], X[32929] + 3 X[33114]

X(44416) lies on these lines: {1, 4884}, {2, 45}, {6, 345}, {8, 3052}, {9, 5743}, {10, 30}, {11, 32930}, {31, 3703}, {37, 6703}, {38, 29686}, {42, 3712}, {44, 3687}, {55, 33163}, {57, 17279}, {58, 3695}, {63, 141}, {71, 15985}, {81, 17390}, {100, 33166}, {171, 3932}, {226, 17351}, {238, 33167}, {306, 524}, {312, 17340}, {321, 35466}, {333, 594}, {344, 37674}, {346, 37642}, {527, 20106}, {528, 29673}, {536, 40940}, {537, 29656}, {553, 3834}, {597, 5256}, {726, 6679}, {846, 4026}, {894, 17056}, {896, 15523}, {902, 4030}, {940, 17243}, {958, 5835}, {1018, 18163}, {1125, 39544}, {1211, 3219}, {1213, 19808}, {1215, 6690}, {1329, 30448}, {1376, 24320}, {1621, 33170}, {1707, 3416}, {1757, 33160}, {1762, 24335}, {1812, 17796}, {1817, 30906}, {1834, 7283}, {1836, 29857}, {1999, 3943}, {2194, 17977}, {2308, 32848}, {2325, 35652}, {2345, 5273}, {2886, 3923}, {2887, 17768}, {3058, 33120}, {3159, 6693}, {3187, 4971}, {3210, 17366}, {3218, 33157}, {3550, 33165}, {3589, 3666}, {3631, 4001}, {3685, 33121}, {3704, 5247}, {3705, 4676}, {3710, 37539}, {3729, 3772}, {3744, 9053}, {3752, 17353}, {3769, 3790}, {3771, 32935}, {3816, 4011}, {3826, 3980}, {3914, 28530}, {3925, 4418}, {3928, 17284}, {3929, 4643}, {3938, 9041}, {3969, 16704}, {3994, 29683}, {4028, 4663}, {4046, 32864}, {4062, 4722}, {4078, 4682}, {4104, 15481}, {4141, 29819}, {4234, 16086}, {4358, 37634}, {4376, 5845}, {4383, 17740}, {4387, 11269}, {4395, 26723}, {4414, 26061}, {4417, 17350}, {4427, 4972}, {4428, 36479}, {4432, 29655}, {4445, 14552}, {4450, 31079}, {4650, 29674}, {4664, 29841}, {4665, 5271}, {4672, 29671}, {4697, 29653}, {4854, 29631}, {4918, 17016}, {4957, 20919}, {4966, 32913}, {5057, 29872}, {5222, 42049}, {5235, 24146}, {5241, 27065}, {5249, 7228}, {5432, 32931}, {5433, 25591}, {5695, 33137}, {5718, 26223}, {5745, 17355}, {5852, 33064}, {5905, 30811}, {6057, 17763}, {6284, 36568}, {6542, 41629}, {6682, 24295}, {6691, 25079}, {7227, 31993}, {7232, 9965}, {7262, 32778}, {7263, 24789}, {7277, 17778}, {7789, 25083}, {8369, 30108}, {8616, 33169}, {9021, 40959}, {9776, 17265}, {10327, 37540}, {11246, 25957}, {11679, 17281}, {12572, 39559}, {13742, 17054}, {14555, 16885}, {14829, 17280}, {16468, 32855}, {16579, 24036}, {17022, 41313}, {17045, 28606}, {17126, 32862}, {17127, 33089}, {17140, 24542}, {17165, 17724}, {17233, 37683}, {17246, 19786}, {17247, 19812}, {17248, 19827}, {17267, 18141}, {17269, 34255}, {17276, 25527}, {17289, 38000}, {17314, 37666}, {17334, 27184}, {17337, 19804}, {17339, 18743}, {17352, 17490}, {17356, 24177}, {17362, 21793}, {17365, 18134}, {17484, 30831}, {17526, 37549}, {17594, 38047}, {17596, 33159}, {17602, 32925}, {17775, 30834}, {19732, 19822}, {20017, 28337}, {20292, 29873}, {21000, 35261}, {24358, 36483}, {24443, 25992}, {24851, 36499}, {24943, 36263}, {25453, 32934}, {25557, 29642}, {26685, 37679}, {27064, 32851}, {27539, 34524}, {28333, 32859}, {29632, 32940}, {29672, 42055}, {29846, 32938}, {29850, 32845}, {29856, 33154}, {29858, 33103}, {29861, 33095}, {29862, 33097}, {29865, 32856}, {29867, 33145}, {31237, 33098}, {32911, 33168}, {32912, 33156}, {32929, 33114}, {32932, 33118}, {33117, 34612}, {37759, 41806}

X(44416) = midpoint of X(i) and X(j) for these {i,j}: {31, 3703}, {306, 4641}, {3782, 32933}, {19542, 21375}
X(44416) = reflection of X(i) in X(j) for these {i,j}: {17061, 6679}, {39544, 1125}
X(44416) = complement of X(3782)
X(44416) = Spieker-circle-inverse of X(16305)
X(44416) = complement of the isotomic conjugate of X(2985)
X(44416) = isotomic conjugate of the polar conjugate of X(12135)
X(44416) = X(i)-complementary conjugate of X(j) for these (i,j): {2985, 2887}, {3450, 142}
X(44416) = crosspoint of X(2) and X(2985)
X(44416) = crosssum of X(6) and X(17053)
X(44416) = barycentric product X(69)*X(12135)
X(44416) = barycentric quotient X(12135)/X(4)
X(44416) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 190, 4415}, {2, 32933, 3782}, {2, 32939, 1086}, {2, 40688, 40480}, {31, 33161, 3703}, {63, 32777, 141}, {171, 33164, 3932}, {345, 26065, 6}, {846, 32780, 4026}, {894, 33116, 17056}, {902, 33162, 4030}, {940, 17776, 17243}, {1211, 3219, 17332}, {1999, 42033, 3943}, {2325, 39595, 35652}, {2345, 5273, 5737}, {3219, 32779, 1211}, {3666, 5294, 3589}, {3923, 4438, 2886}, {3977, 5294, 3666}, {4418, 33115, 3925}, {17340, 37646, 312}, {26223, 33113, 5718}, {26723, 42051, 4395}, {27064, 32851, 37662}, {29631, 32936, 4854}, {32913, 33158, 4966}, {32930, 33119, 11}

X(44417) = SPIEKER-CIRCLE-POLE OF ANTI-ORTHIC AXIS

Barycentrics    a^2*b + a*b^2 + a^2*c + 2*b^2*c + a*c^2 + 2*b*c^2 : :
X(44417) = 3 X[2] + X[321], 9 X[2] - X[17147], X[38] - 5 X[31241], X[42] - 5 X[31264], 3 X[321] + X[17147], 5 X[1698] - X[4424], 3 X[3666] - X[17147], X[3706] + 5 X[31264], 3 X[3740] - X[22325], 3 X[3971] + X[36862], X[11611] - 5 X[14061]

X(44417) lies on these lines: {1, 3714}, {2, 37}, {5, 10}, {6, 11679}, {8, 4849}, {9, 1764}, {38, 28582}, {42, 3706}, {43, 3696}, {44, 333}, {45, 30568}, {55, 29828}, {57, 4363}, {63, 17351}, {72, 10479}, {141, 226}, {190, 38000}, {210, 31330}, {220, 27411}, {241, 16720}, {274, 16736}, {306, 5718}, {329, 4643}, {354, 30942}, {386, 5295}, {518, 1215}, {553, 7228}, {594, 3687}, {712, 3934}, {726, 6682}, {740, 6685}, {756, 4009}, {824, 4885}, {894, 14829}, {899, 3725}, {908, 1211}, {910, 26244}, {940, 4670}, {958, 37415}, {964, 37539}, {965, 27413}, {966, 18228}, {968, 4387}, {975, 2049}, {982, 29827}, {984, 3967}, {1089, 19863}, {1100, 1999}, {1104, 13740}, {1107, 21902}, {1125, 17061}, {1150, 4641}, {1155, 4418}, {1279, 3757}, {1376, 3185}, {1386, 4362}, {1465, 6358}, {1698, 4424}, {1766, 2050}, {1836, 26034}, {1861, 37362}, {2176, 4384}, {2352, 16405}, {2783, 3035}, {2887, 3838}, {2999, 4361}, {3008, 6704}, {3120, 32781}, {3212, 5226}, {3219, 41242}, {3305, 19732}, {3416, 26098}, {3589, 9022}, {3619, 26132}, {3634, 17070}, {3661, 4417}, {3683, 32917}, {3689, 32945}, {3700, 30864}, {3702, 26115}, {3703, 29639}, {3704, 5530}, {3723, 34064}, {3742, 3840}, {3744, 24552}, {3745, 17763}, {3748, 32943}, {3750, 4702}, {3758, 37683}, {3763, 25527}, {3773, 29671}, {3782, 4054}, {3812, 3831}, {3823, 3925}, {3834, 5249}, {3848, 4871}, {3911, 7227}, {3912, 17056}, {3923, 4640}, {3944, 32784}, {3952, 4981}, {3971, 36862}, {3982, 7238}, {3989, 3994}, {3999, 17140}, {4001, 4715}, {4003, 17155}, {4011, 15254}, {4026, 24210}, {4031, 7231}, {4035, 29594}, {4113, 21805}, {4357, 4415}, {4364, 4656}, {4383, 5271}, {4426, 41236}, {4429, 21949}, {4519, 32915}, {4644, 37655}, {4654, 7232}, {4663, 32853}, {4675, 18141}, {4682, 29649}, {4689, 32929}, {4690, 5739}, {4708, 25345}, {4717, 4868}, {4851, 5712}, {4852, 5256}, {4883, 29824}, {4906, 29668}, {4914, 32844}, {4970, 28484}, {4972, 26251}, {5057, 33083}, {5219, 17293}, {5235, 27065}, {5241, 28633}, {5263, 7081}, {5287, 19701}, {5294, 5830}, {5296, 8055}, {5333, 17021}, {5435, 7229}, {5437, 25590}, {5461, 27076}, {5695, 17594}, {5745, 17355}, {5749, 37642}, {5750, 6703}, {5905, 17345}, {5955, 26364}, {6048, 31327}, {6533, 19847}, {6535, 29688}, {6557, 9780}, {6679, 24295}, {6706, 17284}, {7222, 21454}, {7263, 24177}, {7283, 19270}, {7308, 17259}, {8727, 12618}, {9478, 26582}, {10129, 25958}, {10436, 30567}, {11354, 37817}, {11611, 14061}, {11680, 29667}, {13741, 16817}, {13881, 17308}, {14534, 19623}, {14555, 17275}, {15523, 33105}, {15569, 43223}, {15668, 17022}, {16669, 37652}, {16700, 30599}, {16826, 25130}, {17019, 37869}, {17120, 41629}, {17122, 24342}, {17231, 18134}, {17237, 27184}, {17251, 31142}, {17265, 41867}, {17272, 28609}, {17285, 41878}, {17290, 23681}, {17316, 24656}, {17317, 26109}, {17344, 33066}, {17369, 37646}, {17374, 17778}, {17381, 29841}, {17592, 29825}, {17599, 29826}, {17605, 25760}, {17717, 32778}, {17718, 33171}, {17719, 32783}, {17722, 32866}, {17723, 33088}, {17889, 33174}, {18142, 26563}, {19684, 37595}, {19742, 41241}, {20292, 33086}, {20317, 28468}, {20436, 26035}, {20593, 22230}, {21071, 29571}, {21241, 28595}, {21242, 29673}, {21342, 24349}, {21611, 27346}, {21857, 34258}, {24003, 27798}, {24178, 25914}, {24627, 32939}, {24725, 33080}, {24892, 26061}, {24943, 33127}, {25107, 39143}, {25109, 29610}, {25383, 30566}, {25502, 40328}, {25591, 25917}, {26105, 39581}, {27483, 32011}, {28107, 30617}, {28570, 41011}, {29633, 33135}, {29637, 33130}, {29640, 33158}, {29650, 32921}, {29651, 42819}, {29652, 32920}, {29657, 33092}, {29659, 33141}, {29663, 33128}, {29664, 32862}, {29670, 32941}, {29674, 33111}, {29676, 33169}, {29678, 33156}, {29679, 33108}, {29680, 33089}, {29690, 33162}, {29857, 31245}, {30811, 31266}, {30823, 30831}, {30824, 30852}, {31019, 33172}, {31053, 32782}, {32780, 33140}, {32914, 32944}, {33074, 33104}, {33075, 33107}, {33076, 33106}, {33078, 33112}, {33079, 33109}, {33082, 33096}, {33085, 33097}, {33137, 38047}, {33138, 33159}, {37594, 43531}

X(44417) = midpoint of X(i) and X(j) for these {i,j}: {42, 3706}, {321, 3666}, {1215, 3741}, {4717, 4868}
X(44417) = complement of X(3666)
X(44417) = Spieker-circle-inverse of X(38472)
X(44417) = complement of the isogonal conjugate of X(2298)
X(44417) = complement of the isotomic conjugate of X(30710)
X(44417) = X(i)-complementary conjugate of X(j) for these (i,j): {649, 15611}, {961, 142}, {1169, 1125}, {1220, 141}, {1240, 626}, {1791, 18589}, {1919, 39015}, {2298, 10}, {2359, 3}, {2363, 3739}, {4581, 116}, {6648, 17072}, {8687, 522}, {8707, 3835}, {14534, 3741}, {14624, 3454}, {30710, 2887}, {31643, 17046}, {32736, 514}, {36098, 4885}, {36147, 513}, {40454, 12610}
X(44417) = X(10455)-Ceva conjugate of X(10459)
X(44417) = crosspoint of X(2) and X(30710)
X(44417) = crosssum of X(6) and X(2300)
X(44417) = barycentric product X(i)*X(j) for these {i,j}: {10, 10455}, {75, 10459}, {313, 10457}, {3596, 10475}
X(44417) = barycentric quotient X(i)/X(j) for these {i,j}: {10455, 86}, {10457, 58}, {10459, 1}, {10475, 56}
X(44417) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 75, 3752}, {2, 312, 37}, {2, 321, 3666}, {2, 4359, 16610}, {2, 4671, 28606}, {2, 17280, 33116}, {2, 19786, 17384}, {2, 19804, 16602}, {2, 24789, 17356}, {2, 26591, 25091}, {2, 28605, 4850}, {2, 31025, 4359}, {2, 31993, 3739}, {2, 37759, 19786}, {9, 18229, 5737}, {10, 3452, 5743}, {37, 312, 35652}, {192, 42034, 22034}, {333, 27064, 44}, {594, 37662, 3687}, {960, 5836, 34434}, {1150, 26223, 4641}, {2887, 25385, 3838}, {3175, 28606, 4681}, {3210, 42029, 4686}, {3452, 6708, 34852}, {3702, 26115, 37548}, {3757, 32942, 1279}, {3838, 3844, 2887}, {3840, 24325, 3742}, {3923, 32916, 4640}, {4362, 25496, 1386}, {4383, 5271, 17348}, {4418, 32918, 1155}, {4519, 37593, 32915}, {4671, 28606, 3175}, {4688, 16602, 19804}, {4850, 28605, 42051}, {5044, 39564, 10}, {5287, 19701, 28639}, {5712, 34255, 4851}, {5750, 39595, 6703}, {6535, 29688, 32848}, {9780, 19582, 31359}, {10436, 30567, 37674}, {16610, 31025, 4739}, {17763, 32772, 3745}, {24552, 26227, 3744}, {25591, 31339, 25917}, {28605, 42051, 4726}, {30818, 31993, 2}, {30942, 32771, 354}, {31330, 32931, 210}, {32917, 32930, 3683}, {33066, 37653, 17344}

X(44418) = SPIEKER-CIRCLE-POLE OF LEMOINE AXIS

Barycentrics    a^3*b^2 + a^2*b^3 + a^2*b^2*c + a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + 2*b^3*c^2 + a^2*c^3 + 2*b^2*c^3 : :

X(44418) lies on these lines: {2, 32017}, {10, 511}, {39, 3596}, {75, 1574}, {192, 30819}, {313, 538}, {2092, 17790}, {2234, 21022}, {2277, 4494}, {3264, 6683}, {3664, 25102}, {3739, 9055}, {3948, 26764}, {3963, 27102}, {4021, 20530}, {4033, 26979}, {4357, 27076}, {4967, 29991}, {6007, 21238}, {8891, 31130}, {17049, 24327}, {17787, 21796}, {27042, 29388}, {27274, 28653}, {28350, 29381}, {28369, 29511}

X(44418) = {X(3596),X(26042)}-harmonic conjugate of X(39)

X(44419) = SPIEKER-CIRCLE-POLE OF DE LONGCHAMPS AXIS

Barycentrics    2*a^3 - 2*a^2*b - a*b^2 - b^3 - 2*a^2*c - b^2*c - a*c^2 - b*c^2 - c^3 : :
X(44419) = 3 X[2] + X[4450]

X(44419) lies on these lines: {2, 3052}, {8, 4884}, {10, 30}, {11, 32918}, {20, 5793}, {31, 3589}, {38, 4030}, {40, 5835}, {42, 524}, {55, 141}, {100, 1211}, {171, 4026}, {200, 4643}, {210, 17332}, {306, 4689}, {321, 28530}, {511, 22325}, {528, 3741}, {594, 32932}, {612, 4364}, {752, 6685}, {846, 3932}, {899, 41002}, {902, 32781}, {958, 37331}, {966, 42316}, {968, 17243}, {1086, 3757}, {1213, 17735}, {1215, 17768}, {1376, 4192}, {1503, 37619}, {1621, 33086}, {1707, 38047}, {1836, 29828}, {2177, 3631}, {2308, 6329}, {2345, 9778}, {2550, 5737}, {2886, 4660}, {2887, 6690}, {3035, 3846}, {3058, 30942}, {3158, 17272}, {3256, 26942}, {3416, 17594}, {3434, 37660}, {3474, 4363}, {3475, 7232}, {3550, 32784}, {3578, 19998}, {3666, 5846}, {3683, 4422}, {3703, 4414}, {3712, 15523}, {3740, 29349}, {3745, 17045}, {3750, 4966}, {3752, 3883}, {3763, 21000}, {3782, 26227}, {3821, 17061}, {3925, 32917}, {3974, 17262}, {3996, 37653}, {4046, 4478}, {4061, 4690}, {4388, 37662}, {4389, 37671}, {4395, 32914}, {4399, 32860}, {4415, 7081}, {4416, 4849}, {4418, 7227}, {4419, 7172}, {4425, 4434}, {4472, 4797}, {4512, 17279}, {4514, 24627}, {4553, 40966}, {4645, 17056}, {4650, 29659}, {4655, 29670}, {4657, 5269}, {4722, 4831}, {4851, 37553}, {4854, 17763}, {4972, 35466}, {4995, 29846}, {5264, 13728}, {5432, 25760}, {5718, 6327}, {6007, 14973}, {6057, 32936}, {6154, 32945}, {6682, 17766}, {7228, 11246}, {7238, 33067}, {7789, 37586}, {8013, 21047}, {8616, 33174}, {16052, 17734}, {17147, 28472}, {17184, 17724}, {17246, 32926}, {17259, 26040}, {17305, 29838}, {17334, 32937}, {17390, 37593}, {17398, 21793}, {17593, 32866}, {17596, 33076}, {17601, 32778}, {17602, 32776}, {17747, 26244}, {17792, 22276}, {18235, 23845}, {18252, 40635}, {20582, 24943}, {25557, 29651}, {29678, 31134}, {29822, 37631}, {31330, 34612}, {32773, 37646}, {32777, 35258}, {32850, 38000}, {33069, 37703}, {33771, 41014}

X(44419) = midpoint of X(38) and X(4030)
X(44419) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55, 26034, 141}, {100, 33083, 1211}, {171, 4026, 6703}, {846, 33079, 3932}, {3750, 33085, 4966}, {3757, 33068, 1086}, {4414, 33074, 3703}, {4660, 32916, 2886}, {7081, 24723, 4415}, {11246, 32771, 7228}, {26227, 32950, 3782}, {32917, 32948, 3925}, {32918, 32947, 11}

X(44420) = SPIEKER-CIRCLE-POLE OF EULER LINE

Barycentrics    a^2*(2*a^6*b^2 - a^4*b^4 - 2*a^2*b^6 + b^8 + 2*a^6*c^2 - 4*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 4*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 + 8*b^4*c^4 - 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :
X(44420) = 2 X[2493] + X[9149]

X(44420) lies on these lines: {2, 2782}, {6, 110}, {23, 2080}, {98, 6795}, {311, 7495}, {351, 523}, {373, 36213}, {381, 11187}, {543, 9177}, {574, 13233}, {1634, 12093}, {1976, 6800}, {2021, 3291}, {2770, 14480}, {3164, 7493}, {3186, 4232}, {5663, 7418}, {7998, 36790}, {9176, 10418}, {9486, 11580}, {11002, 34098}, {11159, 37811}, {11634, 33962}, {14611, 36168}, {14934, 36166}, {15329, 40283}

X(44420) = midpoint of X(5968) and X(9149)
X(44420) = reflection of X(i) in X(j) for these {i,j}: {351, 39526}, {5968, 2493}
X(44420) = Parry-circle-inverse of X(7426)
X(44420) = crossdifference of every pair of points on line {574, 690}
X(44420) = barycentric product X(598)*X(17430)
X(44420) = barycentric quotient X(17430)/X(599)
X(44420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 111, 1995}, {110, 11422, 39689}, {111, 9465, 3124}, {3124, 39689, 13410}, {37775, 37776, 2502}

X(44421) = BEVAN-CIRCLE-POLE OF EULER LINE

Barycentrics    a*(a^3*b - a*b^3 + a^3*c + 3*a^2*b*c - a*b^2*c - b^3*c - a*b*c^2 + 2*b^2*c^2 - a*c^3 - b*c^3) : :

X(44421) lies on these lines: {1, 20793}, {2, 7}, {6, 37555}, {40, 511}, {46, 1757}, {69, 3501}, {71, 4644}, {75, 21384}, {193, 3169}, {194, 3875}, {219, 7175}, {239, 41834}, {291, 1716}, {314, 3729}, {322, 35102}, {347, 34497}, {583, 17276}, {1002, 4343}, {1014, 9310}, {1044, 10822}, {1334, 3945}, {1409, 1419}, {1429, 5120}, {1475, 3672}, {1697, 2293}, {1743, 20367}, {2171, 24635}, {2260, 4419}, {2264, 4641}, {2323, 23125}, {2663, 17594}, {3000, 3214}, {3208, 3879}, {3217, 11349}, {3247, 18164}, {3663, 4253}, {3664, 3730}, {3786, 3951}, {3886, 6762}, {4650, 20368}, {6210, 24695}, {7201, 40937}, {10456, 21061}, {12526, 35628}, {15803, 20805}, {16549, 17272}, {16552, 25590}, {16572, 20605}, {17207, 29597}, {17364, 22370}, {18161, 21853}, {18162, 36743}, {20358, 36635}, {21746, 24708}, {21866, 34371}, {24328, 37500}, {24342, 41229}, {27544, 36854}, {27623, 39970}

X(44421) = reflection of X(i) in X(j) for these {i,j}: {1, 37507}, {1423, 579}
X(44421) = isogonal conjugate of the isotomic conjugate of X(40493)
X(44421) = X(39741)-Ceva conjugate of X(1)
X(44421) = barycentric product X(i)*X(j) for these {i,j}: {1, 36854}, {6, 40493}, {57, 27544}
X(44421) = barycentric quotient X(i)/X(j) for these {i,j}: {27544, 312}, {36854, 75}, {40493, 76}
X(44421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 672, 27626}, {9, 3928, 16574}, {63, 894, 9}, {329, 27334, 21246}, {3218, 17350, 21371}, {17350, 21371, 9}

X(44422) = GALLATLY-CIRCLE-POLE OF ORTHIC AXIS

Barycentrics    a^6*b^2 + 4*a^4*b^4 - 5*a^2*b^6 + a^6*c^2 + 12*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 2*b^6*c^2 + 4*a^4*c^4 + 3*a^2*b^2*c^4 + 4*b^4*c^4 - 5*a^2*c^6 - 2*b^2*c^6 : :
X(44422) = X[2] - 3 X[262], 7 X[2] - 3 X[6194], 4 X[2] - 3 X[15819], 5 X[2] - 3 X[22712], X[39] + 2 X[14881], 7 X[39] - 4 X[32516], X[76] - 3 X[3545], X[194] + 3 X[3839], 7 X[262] - X[6194], 4 X[262] - X[15819], 5 X[262] - X[22712], 9 X[262] - X[33706], 5 X[381] - X[13108], 7 X[381] + X[32520], 2 X[3095] + X[6248], 5 X[3095] + X[13108], 7 X[3095] - X[32520], 3 X[3524] - 5 X[7786], X[3534] - 3 X[11171], X[3534] + 3 X[22728], 2 X[3818] + X[41622], X[3830] + 3 X[32447], 2 X[3845] - 3 X[22682], 4 X[3860] - 3 X[22681], 2 X[3934] - 3 X[5055], 3 X[5054] - 4 X[6683], 3 X[5054] - X[9821], 4 X[5066] - X[14711], 5 X[5071] - X[12251], X[5188] - 4 X[11272], 4 X[6194] - 7 X[15819], 5 X[6194] - 7 X[22712], 9 X[6194] - 7 X[33706], 5 X[6248] - 2 X[13108], 7 X[6248] + 2 X[32520], 4 X[6683] - X[9821], 3 X[7697] - 5 X[19709], 3 X[7709] + X[15682], 5 X[7921] + X[9873], 2 X[8703] - 3 X[21163], X[9764] - 3 X[9770], X[11055] + 5 X[41099], 2 X[12100] - 3 X[40108], 7 X[13108] + 5 X[32520], 3 X[13331] - X[43273], 3 X[14269] + 2 X[32450], 3 X[14853] - X[22486], 7 X[14881] + 2 X[32516], X[15683] - 5 X[32522], 6 X[15699] - 5 X[31239], 3 X[15699] - X[32521], 5 X[15819] - 4 X[22712], 9 X[15819] - 4 X[33706], 5 X[19708] - 3 X[22676], X[22564] - 3 X[38227], 9 X[22712] - 5 X[33706], 5 X[31239] - 2 X[32521]

X(44422) lies on these lines: {2, 51}, {4, 7757}, {5, 7794}, {30, 39}, {76, 3545}, {98, 5097}, {114, 5480}, {183, 37517}, {194, 3839}, {325, 19130}, {376, 13334}, {381, 538}, {524, 35439}, {542, 38383}, {549, 5188}, {575, 5999}, {576, 13860}, {597, 13354}, {754, 35436}, {1003, 9737}, {1351, 8667}, {1570, 42535}, {1916, 6054}, {2023, 5052}, {2782, 3845}, {2967, 39530}, {3098, 11174}, {3102, 35822}, {3103, 35823}, {3104, 16267}, {3105, 16268}, {3106, 41107}, {3107, 41108}, {3329, 5092}, {3524, 7786}, {3534, 11171}, {3543, 11257}, {3656, 14839}, {3815, 21850}, {3818, 7774}, {3830, 32447}, {3860, 22681}, {3934, 5055}, {5008, 12042}, {5041, 14880}, {5054, 6683}, {5066, 14711}, {5071, 12251}, {5093, 9756}, {7697, 19709}, {7709, 15682}, {7736, 31670}, {7764, 44230}, {7776, 10356}, {7777, 9993}, {7779, 43150}, {7788, 11178}, {7804, 35002}, {7816, 18502}, {7833, 34733}, {7840, 25561}, {7843, 37243}, {7845, 9996}, {7921, 9873}, {7976, 34627}, {8029, 8704}, {8556, 11477}, {8703, 21163}, {8716, 10983}, {8859, 32414}, {9151, 15820}, {9734, 39656}, {9755, 15520}, {9764, 9770}, {10011, 15850}, {10358, 11286}, {10711, 32454}, {10796, 18860}, {11055, 41099}, {11163, 44114}, {11180, 32451}, {11237, 12836}, {11238, 12837}, {12100, 40108}, {12110, 13586}, {12150, 13335}, {12782, 31162}, {12816, 32466}, {12817, 32465}, {13331, 43273}, {14160, 14639}, {14269, 32450}, {15683, 32522}, {15687, 32448}, {15699, 31239}, {18907, 38749}, {19708, 22676}, {22521, 34473}, {25555, 37450}, {35437, 41750}, {39095, 41413}

X(44422) = midpoint of X(i) and X(j) for these {i,j}: {4, 7757}, {381, 3095}, {1916, 6054}, {3543, 11257}, {7833, 34733}, {7976, 34627}, {10711, 32454}, {11171, 22728}, {11180, 32451}, {12782, 31162}, {15687, 32448}, {36384, 36385}
X(44422) = reflection of X(i) in X(j) for these {i,j}: {376, 13334}, {549, 11272}, {5188, 549}, {6055, 2023}, {6248, 381}, {9466, 5}, {13354, 597}, {14994, 11178}
X(44422) = complement of X(33706)
X(44422) = Gallatly-circle-inverse of X(16308)
X(44422) = X(7757)-of-Euler-triangle
X(44422) = X(9466)-of-Johnson-triangle

X(44423) = GALLATLY-CIRCLE-POLE OF LEMOINE AXIS

Barycentrics    a^2*(a^6*b^2 - 2*a^4*b^4 + b^8 + a^6*c^2 - 4*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + b^6*c^2 - 2*a^4*c^4 - 7*a^2*b^2*c^4 - 2*b^4*c^4 + b^2*c^6 + c^8) : :
X(44423) = X[6] + 3 X[32447], 3 X[39] + X[35439], X[69] - 3 X[11261], X[76] - 3 X[38317], X[182] - 3 X[13331], X[194] + 3 X[14561], 3 X[262] - X[3818], X[3095] + 3 X[13331], X[3098] - 3 X[11171], 4 X[3589] - 3 X[32149], 3 X[7697] + X[41747], 3 X[7709] + X[31670], X[9821] - 3 X[17508], X[13330] - 3 X[15520]

X(44423) lies on these lines: {3, 6}, {4, 32429}, {5, 32449}, {69, 11261}, {76, 38317}, {147, 262}, {194, 14561}, {302, 33478}, {303, 33479}, {698, 18583}, {732, 7764}, {2001, 34986}, {2782, 19130}, {3399, 7760}, {3589, 32149}, {5476, 7757}, {5480, 32448}, {7697, 41747}, {7709, 31670}, {7777, 41622}, {7796, 14994}, {7806, 15819}, {10007, 40107}, {11163, 25561}, {12110, 32476}, {13571, 32451}, {14881, 29012}, {24256, 25555}, {29181, 32516}, {30499, 40810}, {34236, 36212}

X(44423) = midpoint of X(i) and X(j) for these {i,j}: {4, 32429}, {5, 32449}, {182, 3095}, {576, 3094}, {5476, 7757}, {5480, 32448}, {32451, 34507}, {32452, 35431}
X(44423) = reflection of X(i) in X(j) for these {i,j}: {5052, 22330}, {14810, 13334}, {24206, 11272}, {24256, 25555}, {40107, 10007}
X(44423) = Gallatly-circle-inverse of X(187)}
X(44423) = X(5) of X(6)PU(1)
X(44423) = X(32429)-of-Euler-triangle
X(44423) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 35436, 13334}, {39, 35437, 3}, {1689, 1690, 2076}, {2026, 2027, 187}, {3095, 13331, 182}, {35426, 43157, 1691}

X(44424) = STEVANOVIC-CIRCLE-POLE OF NAGEL LINE

Barycentrics    a*(a^5*b - 3*a^4*b^2 + 2*a^3*b^3 + 2*a^2*b^4 - 3*a*b^5 + b^6 + a^5*c - 8*a^4*b*c + 4*a^3*b^2*c - 2*a^2*b^3*c + 3*a*b^4*c + 2*b^5*c - 3*a^4*c^2 + 4*a^3*b*c^2 - b^4*c^2 + 2*a^3*c^3 - 2*a^2*b*c^3 - 4*b^3*c^3 + 2*a^2*c^4 + 3*a*b*c^4 - b^2*c^4 - 3*a*c^5 + 2*b*c^5 + c^6) : :

X(44424) lies on these lines: {3, 25068}, {4, 5089}, {5, 25086}, {9, 165}, {20, 25066}, {37, 1699}, {72, 1695}, {210, 573}, {218, 1490}, {226, 1465}, {515, 43065}, {516, 3693}, {517, 3930}, {650, 3667}, {672, 971}, {962, 3991}, {1212, 5691}, {1334, 9856}, {3146, 25082}, {3691, 9947}, {3730, 12688}, {3965, 10443}, {4192, 10157}, {4253, 12680}, {4515, 7991}, {5022, 10085}, {5269, 10382}, {5658, 17756}, {5806, 21808}, {6999, 25083}, {7308, 16435}, {9943, 16549}, {10167, 17754}, {12679, 17732}, {19541, 40131}, {24036, 28164}, {31793, 33299}

X(44425) = STEVANOVIC-CIRCLE-POLE OF LINE X(1)X(6)

Barycentrics    a*(a^5 - 2*a^4*b + 2*a^2*b^3 - a*b^4 - 2*a^4*c + 3*a^3*b*c - 2*a^2*b^2*c - a*b^3*c + 2*b^4*c - 2*a^2*b*c^2 + 4*a*b^2*c^2 - 2*b^3*c^2 + 2*a^2*c^3 - a*b*c^3 - 2*b^2*c^3 - a*c^4 + 2*b*c^4) : :
X(44425) = 3 X[36] - 2 X[104], X[104] - 3 X[6905], 4 X[119] - 3 X[31160], 3 X[165] - 2 X[17613], 3 X[484] - X[12767], 2 X[908] - 3 X[5660], 4 X[1538] - 3 X[1699], 3 X[2077] - 4 X[33814], 4 X[3911] - 3 X[11219], 4 X[5087] - 5 X[15017], X[5537] + 2 X[36002], 4 X[6882] - 5 X[31263], 5 X[7987] - 6 X[35271], 2 X[9952] - 3 X[40663], X[12331] - 3 X[18524]

X(44425) lies on these lines: {1, 227}, {2, 15931}, {3, 1698}, {4, 35}, {5, 5259}, {9, 165}, {10, 411}, {11, 2078}, {12, 20420}, {20, 8165}, {21, 19925}, {30, 119}, {36, 80}, {40, 5692}, {43, 1754}, {46, 1490}, {55, 1538}, {56, 5727}, {57, 11502}, {100, 516}, {109, 2635}, {125, 851}, {153, 535}, {191, 5777}, {200, 15104}, {238, 5400}, {355, 5258}, {381, 32613}, {382, 26285}, {404, 4297}, {405, 7989}, {474, 7987}, {484, 6001}, {497, 8166}, {499, 6927}, {517, 3689}, {518, 5531}, {546, 38109}, {581, 37559}, {631, 35202}, {650, 1734}, {750, 991}, {899, 13329}, {912, 4880}, {919, 29352}, {944, 5563}, {946, 3746}, {956, 37712}, {958, 37714}, {962, 8715}, {971, 1155}, {1001, 7988}, {1004, 5732}, {1006, 10175}, {1012, 5010}, {1013, 39531}, {1071, 3336}, {1125, 6915}, {1158, 37572}, {1203, 3072}, {1283, 8229}, {1325, 1793}, {1385, 37251}, {1479, 6848}, {1532, 3583}, {1621, 3817}, {1657, 37001}, {1697, 11501}, {1735, 3465}, {1736, 1758}, {1745, 1771}, {1770, 6260}, {1826, 4219}, {1836, 3256}, {1837, 37583}, {1936, 4551}, {1995, 39475}, {2003, 5348}, {2095, 3894}, {2346, 11218}, {2646, 40262}, {2752, 6011}, {2800, 3245}, {2801, 3218}, {2829, 4316}, {3035, 37374}, {3058, 7956}, {3090, 25542}, {3091, 5248}, {3100, 24025}, {3216, 37570}, {3219, 15064}, {3295, 11522}, {3337, 12675}, {3428, 3679}, {3474, 5658}, {3560, 18492}, {3576, 6911}, {3579, 12688}, {3584, 7680}, {3585, 18242}, {3586, 8069}, {3624, 6918}, {3632, 22770}, {3634, 6986}, {3651, 6684}, {3658, 18653}, {3667, 13266}, {3683, 10157}, {3814, 6840}, {3822, 6839}, {3825, 6979}, {3871, 4301}, {3913, 11531}, {4192, 29315}, {4299, 12667}, {4311, 13370}, {4312, 37541}, {4421, 42843}, {4428, 30308}, {4434, 28850}, {4857, 7681}, {4995, 7965}, {5087, 15017}, {5089, 5268}, {5284, 10171}, {5288, 5881}, {5312, 5706}, {5424, 14496}, {5432, 8727}, {5440, 5538}, {5445, 12616}, {5450, 6942}, {5534, 12704}, {5584, 9588}, {5659, 25006}, {5687, 7991}, {5709, 5904}, {5787, 24914}, {5805, 17718}, {5806, 37080}, {5816, 37400}, {5818, 6876}, {5883, 18444}, {5886, 34486}, {5902, 18446}, {5903, 6261}, {6244, 31142}, {6256, 6934}, {6690, 8226}, {6763, 14872}, {6830, 14799}, {6834, 7741}, {6835, 10198}, {6836, 26364}, {6841, 31659}, {6863, 18517}, {6882, 31263}, {6889, 41859}, {6895, 27529}, {6906, 31673}, {6909, 28164}, {6924, 18481}, {6941, 14795}, {6946, 10165}, {6960, 25639}, {6962, 26363}, {6980, 18407}, {6988, 19854}, {7081, 20236}, {7280, 12114}, {7411, 10164}, {7489, 38140}, {7503, 39582}, {7688, 26446}, {7967, 37602}, {8071, 9613}, {8227, 10267}, {8273, 16408}, {9318, 29069}, {9352, 11220}, {9578, 26357}, {9579, 11509}, {9581, 37579}, {9589, 10306}, {9612, 11507}, {9614, 11508}, {9624, 16202}, {9778, 31018}, {9841, 16209}, {9856, 37568}, {9897, 22775}, {9943, 16143}, {9952, 40663}, {9955, 37621}, {10085, 15803}, {10310, 37411}, {10434, 19544}, {10679, 31162}, {10708, 34927}, {10786, 26332}, {10826, 36152}, {10857, 37270}, {10966, 37709}, {11009, 40257}, {11010, 12672}, {11248, 41869}, {11372, 35445}, {11849, 22793}, {12116, 37720}, {12512, 33557}, {12650, 37618}, {12680, 37582}, {12699, 32141}, {13257, 17768}, {13743, 33862}, {14204, 34535}, {15622, 16453}, {15624, 27471}, {15626, 20470}, {16117, 22936}, {16132, 34339}, {16139, 31835}, {16192, 37426}, {16208, 31435}, {16371, 34628}, {16489, 32486}, {16858, 38076}, {17549, 34648}, {17763, 29016}, {18450, 37789}, {18525, 26286}, {18839, 37736}, {20330, 37703}, {21031, 31799}, {22765, 28204}, {22935, 35459}, {23961, 28208}, {24982, 35979}, {25485, 41553}, {25524, 30389}, {25882, 33305}, {26086, 33697}, {26333, 37000}, {26487, 44229}, {28146, 35000}, {28172, 34474}, {28234, 38665}, {29046, 40109}, {31159, 37820}, {31231, 37578}, {31434, 40292}, {34462, 38472}, {35986, 36991}, {36475, 37619}, {37240, 38052}, {37530, 37699}, {37625, 37700}, {41561, 41572}

X(44425) = midpoint of X(i) and X(j) for these {i,j}: {100, 36002}, {5531, 5536}
X(44425) = reflection of X(i) in X(j) for these {i,j}: {36, 6905}, {80, 1512}, {1768, 1155}, {3583, 1532}, {4867, 6326}, {4880, 5535}, {5057, 21635}, {5537, 100}, {5538, 5440}, {6840, 3814}, {34462, 38472}, {35459, 22935}, {37374, 3035}
X(44425) = reflection of X(34464) in the anti-orthic axis
X(44425) = Stevanovic-circle-inverse of X(5526)
X(44425) = crosspoint of X(21453) and X(34234)
X(44425) = crosssum of X(2183) and X(2293)
X(44425) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5587, 5251}, {3, 18491, 5587}, {3, 20989, 9590}, {4, 6796, 35}, {5, 10902, 5259}, {40, 5720, 5692}, {46, 1490, 15071}, {55, 19541, 1699}, {165, 1750, 1709}, {165, 7580, 41853}, {165, 41860, 10860}, {200, 41338, 15104}, {355, 11012, 5258}, {946, 11491, 3746}, {1376, 7580, 165}, {1745, 1771, 34043}, {3072, 37732, 1203}, {3149, 11500, 1}, {5584, 9709, 9588}, {5709, 17857, 5904}, {5881, 11249, 5288}, {6256, 6934, 10483}, {6924, 18481, 37561}, {6985, 11499, 40}, {7686, 33597, 1}, {10090, 21578, 36}, {10786, 26332, 37719}, {11249, 18518, 5881}, {14872, 37623, 6763}, {18242, 37468, 3585}, {37625, 37700, 41696}

X(44426) = POLAR-CIRCLE-POLE OF LINE X(1)X(3)

Barycentrics    b*(b - c)*c*(-a + b + c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2) : :
Barycentrics    (sec A) (cos B - cos C) : :

X(44426) lies on the ABC-inscribed parabola having focus X(108) and these lines: {4, 513}, {11, 21666}, {19, 21390}, {107, 2766}, {108, 1309}, {240, 522}, {273, 2400}, {281, 28132}, {318, 7705}, {403, 523}, {451, 33528}, {469, 4776}, {514, 16231}, {521, 1948}, {650, 17926}, {693, 17094}, {811, 17931}, {885, 1863}, {1172, 3063}, {2399, 7020}, {2804, 4397}, {3064, 3239}, {3667, 39532}, {3810, 21108}, {3900, 4036}, {4823, 23595}, {6335, 15742}, {6591, 17737}, {6941, 42769}, {8672, 16229}, {8760, 14294}, {15633, 24026}, {17925, 23880}, {18026, 35157}, {23614, 40165}, {23615, 40149}, {36059, 36113}, {43737, 43742}

X(44426) = reflection of X(4) in X(16228)
X(44426) = isogonal conjugate of X(36059)
X(44426) = isotomic conjugate of X(6516)
X(44426) = polar-circle-inverse of X(31849)
X(44426) = polar conjugate of X(651)
X(44426) = isotomic conjugate of the anticomplement of X(6506)
X(44426) = isotomic conjugate of the isogonal conjugate of X(18344)
X(44426) = polar conjugate of the isotomic conjugate of X(4391)
X(44426) = polar conjugate of the isogonal conjugate of X(650)
X(44426) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {90, 34188}, {7040, 33650}, {36082, 20}
X(44426) = X(i)-Ceva conjugate of X(j) for these (i,j): {273, 4858}, {1897, 41013}, {2052, 1146}, {6335, 281}, {7017, 8735}, {7020, 24026}, {18026, 92}, {40165, 34591}
X(44426) = X(i)-cross conjugate of X(j) for these (i,j): {11, 4}, {523, 522}, {650, 4391}, {1146, 2052}, {2968, 43742}, {3064, 17924}, {3318, 7149}, {4081, 7003}, {4516, 1172}, {5514, 459}, {6506, 2}, {8735, 7017}, {14312, 43728}, {21044, 40149}, {35014, 36121}, {42069, 281}, {42455, 21666}
X(44426) = cevapoint of X(i) and X(j) for these (i,j): {11, 42455}, {523, 24006}, {650, 18344}, {21044, 23615}
X(44426) = crosspoint of X(i) and X(j) for these (i,j): {29, 1897}, {92, 18026}, {264, 6335}
X(44426) = crosssum of X(i) and X(j) for these (i,j): {3, 23187}, {48, 1946}, {73, 1459}, {184, 22383}, {212, 36054}, {520, 22076}, {652, 40945}, {7335, 23224}, {32656, 32660}
X(44426) = trilinear pole of line {1146, 8735}
X(44426) = crossdifference of every pair of points on line {48, 577}
X(44426) = X(i)-isoconjugate of X(j) for these (i,j): {1, 36059}, {2, 32660}, {3, 109}, {6, 1813}, {7, 32656}, {25, 6517}, {31, 6516}, {48, 651}, {56, 1331}, {57, 906}, {58, 23067}, {59, 1459}, {63, 1415}, {65, 4575}, {71, 4565}, {73, 110}, {77, 692}, {100, 603}, {101, 222}, {108, 255}, {112, 40152}, {162, 22341}, {163, 1214}, {184, 664}, {212, 934}, {219, 1461}, {226, 32661}, {228, 1414}, {307, 1576}, {348, 32739}, {394, 32674}, {521, 24027}, {577, 653}, {604, 1332}, {643, 1410}, {644, 7099}, {652, 1262}, {662, 1409}, {905, 2149}, {1020, 2193}, {1025, 32658}, {1092, 36127}, {1106, 4571}, {1260, 6614}, {1397, 4561}, {1400, 4558}, {1402, 4592}, {1407, 4587}, {1412, 4574}, {1425, 4636}, {1437, 4551}, {1783, 7125}, {1790, 4559}, {1795, 23981}, {1796, 36075}, {1802, 4617}, {1803, 35326}, {1804, 8750}, {1818, 32735}, {1897, 7335}, {1946, 7045}, {2197, 4556}, {2200, 4573}, {2283, 36057}, {2289, 32714}, {2701, 17975}, {2720, 22350}, {3049, 4620}, {3157, 36082}, {3215, 13397}, {3451, 23113}, {3784, 8685}, {3939, 7053}, {3955, 29055}, {4091, 7115}, {4303, 15439}, {4554, 9247}, {4564, 22383}, {4572, 14575}, {4619, 7117}, {6056, 36118}, {6332, 23979}, {6510, 36141}, {7011, 36049}, {7012, 23224}, {7013, 32652}, {7078, 8059}, {7114, 13138}, {7128, 36054}, {7352, 33600}, {8687, 22097}, {13486, 22342}, {14578, 24029}, {20752, 36146}, {20818, 38828}, {22128, 32675}, {22345, 36098}, {23071, 34921}, {23207, 36048}, {23225, 39293}, {23703, 36058}
X(44426) = trilinear product X(i)*X(j) for these {i,j}: {2, 3064}, {4, 522}, {8, 7649}, {9, 17924}, {11, 1897}, {19, 4391}, {21, 24006}, {27, 3700}, {28, 4086}, {29, 523}, {33, 693}, {34, 4397}, {75, 18344}, {92, 650}, {108, 24026}, {158, 521}, {190, 8735}, {225, 7253}, {226, 17926}, {264, 663}, {273, 3900}, {278, 3239}, {281, 514}, {284, 14618}, {286, 4041}, {312, 6591}, {318, 513}, {331, 657}, {333, 2501}, {393, 6332}, {525, 8748}, {607, 3261}, {649, 7017}, {652, 2052}, {653, 1146}, {656, 1896}, {661, 31623}, {850, 2299}, {885, 1861}, {1172, 1577}, {1783, 4858}, {1824, 18155}, {1826, 4560}, {1857, 4025}, {1969, 3063}, {2170, 6335}, {2204, 20948}, {2310, 18026}, {2399, 8755}, {2489, 28660}, {6129, 7020}, {7003, 14837}, {7008, 17896}, {8750, 34387}, {23978, 32674}
X(44426) = barycentric product X(i)*X(j) for these {i,j}: {4, 4391}, {8, 17924}, {11, 6335}, {19, 35519}, {21, 14618}, {27, 4086}, {29, 1577}, {33, 3261}, {75, 3064}, {76, 18344}, {92, 522}, {108, 23978}, {158, 6332}, {264, 650}, {273, 3239}, {278, 4397}, {281, 693}, {286, 3700}, {312, 7649}, {314, 2501}, {318, 514}, {331, 3900}, {333, 24006}, {393, 35518}, {513, 7017}, {521, 2052}, {523, 31623}, {525, 1896}, {607, 40495}, {644, 2973}, {646, 2969}, {651, 21666}, {653, 24026}, {661, 44130}, {663, 1969}, {668, 8735}, {811, 21044}, {850, 1172}, {1118, 15416}, {1146, 18026}, {1441, 17926}, {1783, 34387}, {1826, 18155}, {1847, 4163}, {1857, 15413}, {1897, 4858}, {1946, 18027}, {2204, 44173}, {2299, 20948}, {2322, 4077}, {2489, 40072}, {2804, 16082}, {2970, 4612}, {3063, 18022}, {3596, 6591}, {3676, 7101}, {3701, 17925}, {4041, 44129}, {4081, 13149}, {4516, 6331}, {4554, 42069}, {4560, 41013}, {4631, 8754}, {4768, 6336}, {7003, 17896}, {7020, 14837}, {7046, 24002}, {7128, 23104}, {7253, 40149}, {8748, 14208}, {15633, 24035}, {15742, 40166}, {16732, 36797}, {36795, 39534}
X(44426) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1813}, {2, 6516}, {4, 651}, {6, 36059}, {8, 1332}, {9, 1331}, {11, 905}, {19, 109}, {21, 4558}, {25, 1415}, {27, 1414}, {28, 4565}, {29, 662}, {31, 32660}, {33, 101}, {34, 1461}, {37, 23067}, {41, 32656}, {55, 906}, {63, 6517}, {92, 664}, {108, 1262}, {158, 653}, {200, 4587}, {210, 4574}, {225, 1020}, {264, 4554}, {270, 4556}, {273, 658}, {278, 934}, {281, 100}, {284, 4575}, {286, 4573}, {312, 4561}, {314, 4563}, {318, 190}, {331, 4569}, {333, 4592}, {346, 4571}, {393, 108}, {512, 1409}, {513, 222}, {514, 77}, {521, 394}, {522, 63}, {523, 1214}, {607, 692}, {647, 22341}, {649, 603}, {650, 3}, {652, 255}, {653, 7045}, {656, 40152}, {657, 212}, {661, 73}, {663, 48}, {693, 348}, {811, 4620}, {850, 1231}, {884, 32658}, {885, 1814}, {905, 1804}, {926, 20752}, {1021, 283}, {1024, 36057}, {1096, 32674}, {1118, 32714}, {1119, 4617}, {1146, 521}, {1172, 110}, {1435, 6614}, {1459, 7125}, {1577, 307}, {1639, 5440}, {1783, 59}, {1785, 24029}, {1824, 4559}, {1826, 4551}, {1827, 35326}, {1847, 4626}, {1855, 35338}, {1857, 1783}, {1861, 1025}, {1896, 648}, {1897, 4564}, {1946, 577}, {1969, 4572}, {2052, 18026}, {2170, 1459}, {2194, 32661}, {2204, 1576}, {2212, 32739}, {2299, 163}, {2310, 652}, {2322, 643}, {2326, 4636}, {2355, 36075}, {2432, 36055}, {2489, 1402}, {2501, 65}, {2969, 3669}, {2973, 24002}, {3057, 23113}, {3063, 184}, {3064, 1}, {3239, 78}, {3261, 7182}, {3270, 36054}, {3271, 22383}, {3287, 3955}, {3309, 23144}, {3669, 7053}, {3676, 7177}, {3700, 72}, {3709, 228}, {3716, 20769}, {3737, 1790}, {3738, 22128}, {3900, 219}, {4024, 201}, {4025, 7183}, {4036, 26942}, {4041, 71}, {4086, 306}, {4105, 1802}, {4130, 1260}, {4147, 22370}, {4162, 20818}, {4163, 3692}, {4171, 2318}, {4183, 5546}, {4391, 69}, {4397, 345}, {4435, 7193}, {4516, 647}, {4521, 4855}, {4560, 1444}, {4705, 2197}, {4765, 4652}, {4768, 3977}, {4820, 3927}, {4843, 4047}, {4858, 4025}, {4895, 22356}, {4944, 3940}, {4976, 3916}, {4985, 4001}, {5081, 4585}, {5089, 2283}, {5190, 23800}, {5236, 41353}, {6129, 7011}, {6332, 326}, {6335, 4998}, {6366, 6510}, {6520, 36127}, {6590, 1038}, {6591, 56}, {7003, 13138}, {7004, 4091}, {7008, 36049}, {7012, 4619}, {7017, 668}, {7046, 644}, {7079, 3939}, {7101, 3699}, {7117, 23224}, {7129, 8059}, {7140, 21859}, {7154, 32652}, {7178, 1439}, {7180, 1410}, {7252, 1437}, {7253, 1812}, {7649, 57}, {8062, 7364}, {8611, 3682}, {8678, 2286}, {8735, 513}, {8748, 162}, {8750, 2149}, {8751, 32735}, {8756, 23703}, {10581, 22079}, {11124, 22055}, {11193, 22144}, {11934, 22131}, {11998, 23187}, {14298, 7078}, {14571, 23981}, {14618, 1441}, {14775, 2982}, {14837, 7013}, {14936, 1946}, {15313, 3173}, {15413, 7055}, {15416, 1264}, {15742, 31615}, {16228, 34048}, {16732, 17094}, {17115, 7124}, {17420, 22097}, {17880, 30805}, {17905, 40576}, {17924, 7}, {17925, 1014}, {17926, 21}, {18026, 1275}, {18155, 17206}, {18191, 7254}, {18344, 6}, {21044, 656}, {21127, 22053}, {21132, 3942}, {21666, 4391}, {21789, 2193}, {22383, 7335}, {23189, 18604}, {23615, 34591}, {23710, 23890}, {23838, 1797}, {23978, 35518}, {24002, 7056}, {24006, 226}, {24026, 6332}, {26932, 4131}, {31623, 99}, {32674, 24027}, {32714, 7339}, {33525, 23207}, {33573, 14414}, {34387, 15413}, {35518, 3926}, {35519, 304}, {36054, 1092}, {36123, 37136}, {36124, 36146}, {36127, 7128}, {36797, 4567}, {38347, 22160}, {39534, 1465}, {40149, 4566}, {40166, 1565}, {40213, 17219}, {40573, 36048}, {40836, 37141}, {41013, 4552}, {42069, 650}, {42455, 26932}, {42462, 7004}, {43923, 1407}, {43924, 7099}, {43925, 1408}, {43933, 34051}, {44129, 4625}, {44130, 799}
X(44426) = {X(7649),X(24006)}-harmonic conjugate of X(17924)

X(44427) = POLAR-CIRCLE-POLE OF FERMAT LINE

Barycentrics    (b^2 - c^2)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-a^2 + b^2 - b*c + c^2)*(-a^2 + b^2 + b*c + c^2) : :
Barycentrics    sec A sin(B - C) (1 + 2 cos 2A) : :
X(44427) = 4 X[2501] - 3 X[14618], 3 X[3268] - 4 X[8552], 3 X[3268] - 2 X[41078], X[5489] - 3 X[42731], 3 X[5664] - 2 X[8552], 3 X[5664] - X[41078], 2 X[6130] - 3 X[42731], 3 X[9979] - 4 X[24978], 3 X[9979] - 2 X[41079]

X(44427) lies on these lines: {2, 6334}, {4, 690}, {74, 1300}, {99, 112}, {186, 14270}, {246, 2970}, {297, 525}, {338, 3269}, {420, 9208}, {468, 9185}, {523, 9409}, {526, 1986}, {671, 35142}, {685, 935}, {1235, 14295}, {1637, 2394}, {1826, 22037}, {2489, 7624}, {2491, 39575}, {2986, 43756}, {3268, 5664}, {5094, 9191}, {5191, 9131}, {5489, 6130}, {5667, 9033}, {6110, 6782}, {6111, 6783}, {9003, 32234}, {9479, 17994}, {14696, 41203}, {16868, 39509}, {21844, 39477}, {33919, 38294}, {43673, 43717}

X(44427) = reflection of X(i) in X(j) for these {i,j}: {4, 16230}, {2394, 1637}, {3268, 5664}, {5489, 6130}, {41078, 8552}, {41079, 24978}
X(44427) = isogonal conjugate of X(32662)
X(44427) = anticomplement of X(6334)
X(44427) = polar conjugate of X(476)
X(44427) = anticomplement of the isogonal conjugate of X(32708)
X(44427) = anticomplement of the isotomic conjugate of X(687)
X(44427) = polar conjugate of the isotomic conjugate of X(3268)
X(44427) = polar conjugate of the isogonal conjugate of X(526)
X(44427) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {687, 6327}, {1300, 21294}, {10420, 4329}, {32708, 8}, {36053, 13219}, {36114, 69}
X(44427) = isotomic conjugate of trilinear pole of line X(3)X(125)
X(44427) = intersection of trilinear polars of X(470) and X(471)
X(44427) = radical center of circumcircle and X(15)- and X(16)-Fuhrmann circles (aka -Hagge circles)
X(44427) = X(i)-Ceva conjugate of X(j) for these (i,j): {340, 35235}, {648, 14920}, {687, 2}, {9381, 338}, {14590, 14918}, {16077, 4}, {18831, 3043}, {18878, 38936}, {43752, 3134}
X(44427) = X(i)-cross conjugate of X(j) for these (i,j): {526, 3268}, {2081, 526}, {2088, 186}, {35235, 340}
X(44427) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32662}, {3, 32678}, {6, 36061}, {48, 476}, {63, 14560}, {163, 265}, {184, 32680}, {577, 36129}, {810, 39295}, {1101, 14582}, {1789, 32675}, {1989, 4575}, {2153, 38413}, {2154, 38414}, {2166, 32661}, {2437, 36062}, {2617, 11077}, {2631, 15395}, {4592, 11060}, {5961, 36145}, {9247, 35139}, {14559, 36060}, {14592, 23995}, {35200, 41392}
X(44427) = crosspoint of X(i) and X(j) for these (i,j): {76, 18878}, {648, 16080}, {2052, 15459}, {2394, 15412}
X(44427) = crosssum of X(i) and X(j) for these (i,j): {32, 21731}, {577, 1636}, {647, 3284}, {1625, 2420}
X(44427) = trilinear pole of line {3258, 16186}
X(44427) = crossdifference of every pair of points on line {184, 5158}
X(44427) = barycentric product X(i)*X(j) for these {i,j}: {4, 3268}, {92, 32679}, {99, 35235}, {186, 850}, {264, 526}, {275, 41078}, {276, 2081}, {323, 14618}, {338, 14590}, {340, 523}, {470, 23871}, {471, 23870}, {525, 14165}, {562, 41298}, {860, 4467}, {1969, 2624}, {2052, 8552}, {2088, 6331}, {2394, 14920}, {2501, 7799}, {2970, 10411}, {3258, 16077}, {4242, 17886}, {5664, 16080}, {5962, 6563}, {6148, 18808}, {6528, 16186}, {7265, 17923}, {9213, 44146}, {14270, 18022}, {14591, 23962}, {14918, 15412}, {15470, 44138}, {16221, 18878}, {17924, 42701}, {34397, 44173}
X(44427) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36061}, {4, 476}, {6, 32662}, {15, 38413}, {16, 38414}, {19, 32678}, {25, 14560}, {50, 32661}, {92, 32680}, {115, 14582}, {125, 43083}, {136, 43088}, {158, 36129}, {186, 110}, {264, 35139}, {323, 4558}, {338, 14592}, {340, 99}, {403, 41512}, {468, 14559}, {470, 23896}, {471, 23895}, {523, 265}, {526, 3}, {562, 930}, {648, 39295}, {850, 328}, {860, 6742}, {924, 5961}, {1154, 23181}, {1304, 15395}, {1825, 2222}, {1835, 26700}, {1870, 13486}, {1986, 15329}, {1990, 41392}, {2081, 216}, {2088, 647}, {2433, 11079}, {2436, 32663}, {2489, 11060}, {2501, 1989}, {2623, 11077}, {2624, 48}, {2970, 10412}, {3258, 9033}, {3268, 69}, {3738, 1789}, {5664, 11064}, {5962, 925}, {6103, 23968}, {6137, 36297}, {6138, 36296}, {6143, 43965}, {6149, 4575}, {7799, 4563}, {8552, 394}, {8739, 5994}, {8740, 5995}, {8754, 15475}, {9213, 895}, {11062, 1625}, {14165, 648}, {14222, 1300}, {14270, 184}, {14355, 43754}, {14590, 249}, {14591, 23357}, {14618, 94}, {14918, 14570}, {14920, 2407}, {15328, 12028}, {15470, 5504}, {15475, 14595}, {16080, 39290}, {16186, 520}, {16230, 14356}, {18808, 5627}, {20188, 31676}, {23283, 10217}, {23284, 10218}, {23870, 40710}, {23871, 40709}, {24006, 2166}, {32679, 63}, {32710, 35189}, {34397, 1576}, {35057, 1793}, {35235, 523}, {36130, 36047}, {36423, 14591}, {38936, 10420}, {39176, 2420}, {41078, 343}, {42701, 1332}
X(44427) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2592, 2593, 14618}, {5489, 42731, 6130}, {5664, 41078, 8552}, {8552, 41078, 3268}, {24978, 41079, 9979}

X(44428) = POLAR-CIRCLE-POLE OF LINE X(1)X(5)

Barycentrics    (b - c)*(-a + b + c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-a^2 + b^2 - b*c + c^2) : :
Barycentrics    (sec A) (cos(A - B) - cos(A - C)) : :

X(44428) lies on these lines: {4, 900}, {24, 39200}, {100, 108}, {104, 915}, {186, 523}, {240, 522}, {406, 26144}, {427, 31131}, {475, 26078}, {521, 43923}, {676, 14312}, {1119, 43042}, {1172, 4435}, {1845, 3738}, {3064, 4765}, {3144, 28284}, {3904, 6369}, {3907, 21108}, {3910, 17925}, {4194, 27545}, {4213, 4800}, {4560, 14024}, {4858, 7004}, {4926, 16228}, {4962, 16231}, {4976, 17926}, {6089, 16230}, {6353, 26275}, {7577, 39493}, {10015, 39471}, {17555, 25020}, {21192, 23595}, {28114, 37055}, {30091, 31916}, {36121, 36123}

X(44428) = reflection of X(i) in X(j) for these {i,j}: {4, 39534}, {14304, 21180}, {14312, 676}
X(44428) = polar conjugate of X(655)
X(44428) = polar conjugate of the isotomic conjugate of X(3904)
X(44428) = polar conjugate of the isogonal conjugate of X(654)
X(44428) = isotomic conjugate of trilinear pole of line X(63)X(343)
X(44428) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {913, 37781}, {915, 33650}, {32698, 329}, {36052, 34188}, {36106, 3436}
X(44428) = X(i)-Ceva conjugate of X(j) for these (i,j): {1309, 4}, {4242, 860}, {16080, 1146}
X(44428) = X(654)-cross conjugate of X(3904)
X(44428) = crosspoint of X(i) and X(j) for these (i,j): {4242, 17515}, {16082, 18026}
X(44428) = crossdifference of every pair of points on line {48, 216}
X(44428) = X(i)-isoconjugate of X(j) for these (i,j): {3, 2222}, {48, 655}, {63, 32675}, {80, 36059}, {109, 1807}, {184, 35174}, {201, 36069}, {476, 22342}, {759, 23067}, {906, 2006}, {1331, 1411}, {1813, 2161}, {2197, 37140}, {2594, 36061}, {6187, 6516}, {16577, 32662}, {18359, 32660}, {18815, 32656}, {26942, 32671}
X(44428) = barycentric product X(i)*X(j) for these {i,j}: {4, 3904}, {29, 4707}, {92, 3738}, {264, 654}, {275, 6369}, {281, 4453}, {318, 3960}, {320, 3064}, {514, 5081}, {522, 17923}, {860, 4560}, {1577, 17515}, {1870, 4391}, {1969, 8648}, {2600, 40440}, {4242, 4858}, {4511, 17924}, {7649, 32851}, {17926, 41804}, {18344, 20924}, {21828, 44130}
X(44428) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 655}, {19, 2222}, {25, 32675}, {36, 1813}, {92, 35174}, {270, 37140}, {318, 36804}, {650, 1807}, {654, 3}, {860, 4552}, {1021, 1793}, {1835, 1020}, {1845, 24029}, {1870, 651}, {2189, 36069}, {2245, 23067}, {2323, 1331}, {2361, 906}, {2610, 201}, {2624, 22342}, {3064, 80}, {3218, 6516}, {3738, 63}, {3904, 69}, {3960, 77}, {4242, 4564}, {4282, 4575}, {4453, 348}, {4511, 1332}, {4707, 307}, {5081, 190}, {6369, 343}, {6370, 26942}, {6591, 1411}, {7113, 36059}, {7649, 2006}, {8648, 48}, {8882, 36078}, {17515, 662}, {17923, 664}, {17924, 18815}, {17926, 6740}, {18344, 2161}, {21758, 603}, {21828, 73}, {22128, 6517}, {22379, 7125}, {32851, 4561}, {42666, 2197}, {44113, 4559}

X(44429) = ORTHOPTIC-CIRCLE-OF-STEINER-INELLIPSE-POLE OF LINE X(1)X(3)

Barycentrics    (b - c)*(2*a*b^2 + a*b*c - b^2*c + 2*a*c^2 - b*c^2) : :
X(44429) = X[649] - 4 X[25380], 2 X[659] - 5 X[31209], X[661] + 2 X[24720], X[693] + 2 X[1491], X[693] - 4 X[3837], 2 X[905] + X[21301], X[1491] + 2 X[3837], X[2254] + 2 X[3835], X[2526] + 2 X[4885], 2 X[2530] + X[4391], X[2530] + 2 X[21260], 2 X[3126] + X[30804], 2 X[3716] - 5 X[30835], 2 X[3776] + X[4088], 2 X[3777] + X[4462], X[3777] + 2 X[21051], X[4024] + 2 X[4818], 2 X[4129] + X[4905], X[4378] - 4 X[19947], X[4380] - 4 X[9508], X[4380] + 2 X[24719], X[4382] + 2 X[4913], X[4391] - 4 X[21260], X[4462] - 4 X[21051], 2 X[4522] + X[16892], 2 X[4705] + X[4801], X[4705] + 2 X[23815], X[4724] - 4 X[25666], X[4776] + 2 X[36848], X[4801] - 4 X[23815], 2 X[4874] - 5 X[30795], 2 X[4940] + X[7659], 2 X[7662] - 5 X[26985], 2 X[9508] + X[24719], 4 X[10006] - X[13266], 2 X[24718] + X[27469]

X(44429) lies on these lines: {2, 513}, {105, 29348}, {325, 523}, {514, 14430}, {522, 4728}, {649, 25380}, {659, 31209}, {661, 4521}, {663, 28521}, {905, 21301}, {2254, 3667}, {2526, 4885}, {2530, 4391}, {2787, 31149}, {2976, 4806}, {3063, 33854}, {3126, 30804}, {3716, 30835}, {3733, 26249}, {3776, 4088}, {3777, 4462}, {4010, 4926}, {4024, 4818}, {4036, 31096}, {4129, 4905}, {4369, 30764}, {4378, 16830}, {4380, 9508}, {4382, 4913}, {4444, 28851}, {4486, 30519}, {4522, 16892}, {4705, 4801}, {4724, 25666}, {4775, 16823}, {4784, 26277}, {4824, 28199}, {4874, 30795}, {4940, 7659}, {4977, 30792}, {5276, 20980}, {6363, 14426}, {7179, 24002}, {7378, 16228}, {7662, 26985}, {10006, 13266}, {20949, 30758}, {21146, 28195}, {24533, 28399}, {24718, 27469}, {25299, 28374}, {26275, 28217}, {28468, 30574}, {28481, 41800}, {29362, 31150}, {36238, 42722}

X(44429) = midpoint of X(2530) and X(14431)
X(44429) = reflection of X(i) in X(j) for these {i,j}: {4391, 14431}, {14431, 21260}
X(44429) = orthoptic-circle-of-Steiner-inellipe-inverse of X(34583)
X(44429) = isotomic conjugate of X(9067)
X(44429) = isotomic conjugate of the isogonal conjugate of X(9010)
X(44429) = X(31)-isoconjugate of X(9067)
X(44429) = crossdifference of every pair of points on line {32, 3230}
X(44429) = barycentric product X(i)*X(j) for these {i,j}: {76, 9010}, {693, 17756}
X(44429) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 9067}, {9010, 6}, {17756, 100}
X(44429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 3837, 693}, {2530, 21260, 4391}, {3777, 21051, 4462}, {4705, 23815, 4801}, {9508, 24719, 4380}

X(44430) = ORTHOPTIC-CIRCLE-OF-STEINER-INELLIPSE-POLE OF ANTI-ORTHIC AXIS

Barycentrics    2*a^3*b^3 - 2*a*b^5 - 3*a^4*b*c + 4*a^3*b^2*c - b^5*c + 4*a^3*b*c^2 + 2*a*b^3*c^2 + 2*a^3*c^3 + 2*a*b^2*c^3 + 2*b^3*c^3 - 2*a*c^5 - b*c^5 : :
X(44430) = X[75] + 2 X[31395], 4 X[3842] - X[6210], 5 X[4687] - 2 X[31394]

X(44430) lies on these lines: {1, 21554}, {2, 392}, {3, 16830}, {4, 5089}, {10, 262}, {40, 6998}, {75, 31395}, {165, 13634}, {355, 7379}, {381, 29365}, {495, 1565}, {612, 7413}, {944, 39587}, {1447, 36279}, {1482, 16823}, {2783, 4664}, {3576, 13635}, {3842, 6210}, {3920, 5767}, {3940, 5774}, {4385, 15973}, {4648, 39898}, {4687, 31394}, {5587, 24808}, {5711, 9755}, {5790, 29331}, {5818, 7407}, {5988, 37716}, {6361, 7390}, {7385, 12699}, {8158, 19319}, {10306, 19309}, {10595, 16020}, {10679, 26241}, {11248, 19310}, {11249, 19314}, {12245, 39581}, {14853, 38057}, {18788, 36531}, {19313, 22770}, {28915, 36722}, {29641, 37360}, {31359, 31785}

X(44430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 39605, 7380}, {40, 39586, 6998}, {7407, 39570, 5818}

X(44431) = ORTHOPTIC-CIRCLE-OF-STEINER-INELLIPSE-POLE OF GERGONNE LINE

Barycentrics    3*a^5 - 3*a^4*b + 6*a^3*b^2 - 2*a^2*b^3 - a*b^4 - 3*b^5 - 3*a^4*c + 2*a^2*b^2*c + b^4*c + 6*a^3*c^2 + 2*a^2*b*c^2 + 2*a*b^2*c^2 + 2*b^3*c^2 - 2*a^2*c^3 + 2*b^2*c^3 - a*c^4 + b*c^4 - 3*c^5 : :

X(44431) lies on these lines: {2, 165}, {4, 5089}, {7, 43751}, {8, 7985}, {10, 43951}, {40, 7407}, {120, 42356}, {226, 3424}, {262, 13576}, {376, 28897}, {381, 10712}, {390, 7179}, {497, 3666}, {515, 11200}, {612, 1750}, {946, 16020}, {962, 7379}, {1503, 3475}, {1541, 11372}, {2784, 3241}, {3146, 16830}, {3598, 4312}, {3755, 37665}, {3886, 37668}, {4339, 13442}, {4349, 41825}, {4423, 19649}, {5483, 29815}, {5658, 29207}, {5691, 39587}, {5698, 17747}, {5731, 10186}, {6194, 30946}, {6361, 7380}, {7172, 21060}, {7390, 39605}, {7967, 28901}, {9756, 37540}, {9791, 40236}, {18788, 29611}, {19925, 39570}, {24239, 31326}, {25080, 37456}, {28862, 34632}, {28881, 31162}

X(44431) = reflection of X(5731) in X(10186)
X(44431) = anticomplement of X(9746)
X(44431) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {962, 7379, 39581}, {39605, 41869, 7390}

X(44432) = ORTHOPTIC-CIRCLE-OF-STEINER-INELLIPSE-POLE OF SODDY LINE

Barycentrics    (b - c)*(-3*a^2 + 4*a*b + b^2 + 4*a*c - 4*b*c + c^2) : :
X(44432) = 2 X[2487] + X[4940], X[3004] + 5 X[31250], X[3239] + 2 X[21212], X[3676] + 2 X[25666], X[3776] + 2 X[4521], X[3798] + 2 X[3835], X[3798] - 4 X[7658], X[3835] + 2 X[7658], X[4025] + 5 X[30835], X[4120] - 5 X[30835], X[4893] + 3 X[14475], 3 X[4893] + X[21116], X[11068] - 4 X[31287], 9 X[14475] - X[21116], 3 X[14475] - X[21183], X[21116] - 3 X[21183]

X(44432) lies on these lines: {2, 514}, {25, 39476}, {427, 39532}, {522, 4928}, {523, 4885}, {650, 4927}, {663, 5272}, {1638, 28846}, {2254, 3667}, {2487, 4940}, {2826, 10006}, {3004, 31250}, {3239, 21212}, {3676, 25666}, {3705, 4546}, {3742, 9029}, {3776, 4521}, {3960, 40134}, {4025, 4120}, {4106, 4773}, {4107, 28296}, {4369, 4778}, {4449, 5268}, {4468, 21115}, {4777, 30792}, {4786, 31147}, {4926, 17069}, {6006, 26275}, {9209, 21188}, {11068, 14425}, {14837, 28468}, {21196, 30764}, {25084, 43051}, {28478, 41800}

X(44432) = midpoint of X(i) and X(j) for these {i,j}: {650, 4927}, {4025, 4120}, {4106, 4773}, {4468, 21115}, {4786, 31147}, {4893, 21183}
X(44432) = reflection of X(i) in X(j) for these {i,j}: {11068, 14425}, {14425, 31287}
X(44432) = orthoptic-circle-of-Steiner-inellipe-inverse of X(38941)
X(44432) = X(i)-complementary conjugate of X(j) for these (i,j): {3478, 26932}, {9088, 226}
X(44432) = crossdifference of every pair of points on line {902, 3053}
X(44432) = barycentric product X(514)*X(20073)
X(44432) = barycentric quotient X(20073)/X(190)
X(44432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3835, 7658, 3798}, {4893, 14475, 21183}

X(44433) = ORTHOPTIC-CIRCLE-OF-STEINER-INELLIPSE-POLE OF LINE X(1)X(5)

Barycentrics    (b - c)*(3*a^3 - a^2*b + a*b^2 - b^3 - a^2*c - a*b*c + a*c^2 - c^3) : :
X(44433) = 5 X[2] - 4 X[30792], 4 X[1960] - X[3904], X[2254] - 4 X[13246], 5 X[26275] - 2 X[30792], 4 X[26275] - X[31131], 8 X[30792] - 5 X[31131]

X(44433) lies on these lines: {1, 23888}, {2, 900}, {22, 39200}, {23, 385}, {100, 2397}, {104, 105}, {513, 4453}, {522, 1635}, {663, 28468}, {665, 26242}, {676, 4927}, {690, 1281}, {1960, 3904}, {2254, 3667}, {2496, 4926}, {3598, 43042}, {3716, 4120}, {3766, 26234}, {3810, 8643}, {4435, 5276}, {4448, 30565}, {4458, 4778}, {4467, 26277}, {4724, 28851}, {6636, 39478}, {6995, 39534}, {10015, 28294}, {24128, 39567}, {28521, 30574}

X(44433) = reflection of X(i) in X(j) for these {i,j}: {2, 26275}, {3904, 30580}, {4120, 3716}, {4453, 4809}, {4927, 676}, {21115, 4458}, {25020, 28396}, {30565, 4448}, {30580, 1960}, {31131, 2}
X(44433) = anticomplement of the isotomic conjugate of X(9089)
X(44433) = X(9089)-anticomplementary conjugate of X(6327)
X(44433) = X(9089)-Ceva conjugate of X(2)
X(44433) = crossdifference of every pair of points on line {39, 8649}

X(44434) = ORTHOPTIC-CIRCLE-OF-STEINER-CIRCUMLLIPSE-POLE OF LEMOINE AXIS

Barycentrics    3*a^6*b^2 + 2*a^4*b^4 - 5*a^2*b^6 + 3*a^6*c^2 + 11*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 + 2*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 - 5*a^2*c^6 - b^2*c^6 : :
X(44434) = 3 X[2] - 4 X[262], 9 X[2] - 8 X[15819], 5 X[2] - 4 X[22712], 7 X[2] - 4 X[33706], 5 X[4] - 2 X[13108], 4 X[4] - X[20081], X[20] - 4 X[3095], 8 X[39] - 5 X[3522], 4 X[76] - 7 X[3832], 2 X[194] + X[3146], 3 X[262] - 2 X[15819], 5 X[262] - 3 X[22712], 7 X[262] - 3 X[33706], 4 X[1916] - X[5984], 7 X[3090] - 4 X[32521], 5 X[3091] - 4 X[7697], 5 X[3091] - 2 X[12251], 5 X[3091] - 8 X[14881], 5 X[3522] - 4 X[22676], 7 X[3523] - 4 X[9821], 7 X[3523] - 8 X[40108], X[3529] - 4 X[32448], 5 X[3617] - 4 X[22697], 7 X[3622] - 8 X[22475], 5 X[3623] - 4 X[22713], 2 X[3627] + X[32520], 7 X[3832] - 8 X[22682], 9 X[3839] - 8 X[22681], 16 X[3934] - 19 X[15022], X[5059] - 4 X[11257], 13 X[5068] - 10 X[31276], 8 X[5188] - 11 X[15717], 3 X[6194] - 4 X[15819], 5 X[6194] - 6 X[22712], 7 X[6194] - 6 X[33706], 4 X[7757] - X[15683], 4 X[7843] - X[18768], X[8782] - 4 X[38383], 13 X[10303] - 16 X[11272], 3 X[10304] - 4 X[11171], 3 X[10519] - 4 X[11261], X[12251] - 4 X[14881], 4 X[12782] - X[20070], 8 X[13108] - 5 X[20081], X[13108] - 5 X[22728], 16 X[13334] - 13 X[21734], 3 X[14853] - 2 X[31958], X[14927] - 4 X[32449], 10 X[15819] - 9 X[22712], 14 X[15819] - 9 X[33706], 5 X[17538] - 8 X[32516], 5 X[17578] + X[20105], X[20081] - 8 X[22728], 7 X[22712] - 5 X[33706]

X(44434) lies on these lines: {2, 51}, {3, 22521}, {4, 7779}, {8, 7985}, {20, 3095}, {23, 22655}, {30, 32519}, {39, 3522}, {76, 3832}, {98, 37517}, {147, 31670}, {193, 1916}, {194, 3146}, {376, 32447}, {385, 9756}, {390, 12837}, {538, 23334}, {726, 9812}, {1160, 10839}, {1161, 10840}, {1350, 3329}, {1351, 5999}, {1352, 9866}, {1503, 7837}, {1569, 43618}, {1587, 35838}, {1588, 35839}, {2023, 37689}, {2782, 3543}, {3090, 32521}, {3091, 7697}, {3094, 37665}, {3097, 9778}, {3098, 9751}, {3104, 42998}, {3105, 42999}, {3314, 5480}, {3523, 9821}, {3529, 32448}, {3552, 39101}, {3600, 12836}, {3617, 22697}, {3620, 14484}, {3622, 22475}, {3623, 22713}, {3627, 32520}, {3839, 22681}, {3934, 15022}, {5059, 11257}, {5068, 31276}, {5171, 33022}, {5188, 15717}, {5261, 22705}, {5274, 22706}, {5304, 13330}, {5905, 29840}, {5987, 10752}, {6776, 33693}, {6995, 22480}, {7694, 7785}, {7710, 7774}, {7757, 15683}, {7770, 40268}, {7783, 8719}, {7787, 30270}, {7843, 18768}, {7897, 13862}, {7929, 37336}, {8586, 42535}, {8721, 13571}, {8782, 9742}, {9737, 33014}, {9917, 14118}, {10303, 11272}, {10304, 11171}, {10334, 12110}, {10753, 14931}, {10788, 35002}, {10841, 12974}, {10842, 12975}, {12206, 37479}, {12782, 20070}, {13334, 21734}, {14927, 32449}, {14986, 22730}, {17538, 32516}, {17578, 20105}, {18906, 37668}, {21445, 39089}, {22664, 36849}, {22679, 32965}, {23253, 35866}, {23263, 35867}, {23698, 32469}, {29181, 41624}, {32465, 42085}, {32466, 42086}, {32470, 43408}, {32471, 43407}, {32966, 39663}, {33878, 37455}

X(44434) = reflection of X(i) in X(j) for these {i,j}: {4, 22728}, {8, 22650}, {20, 7709}, {76, 22682}, {376, 32447}, {6194, 262}, {7697, 14881}, {7709, 3095}, {8782, 9772}, {9772, 38383}, {9778, 3097}, {9821, 40108}, {12251, 7697}, {22676, 39}
X(44434) = anticomplement of X(6194)
X(44434) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {262, 6194, 2}, {1351, 5999, 7766}, {12251, 14881, 3091}, {22684, 22686, 31958}

X(44435) = ORTHOPTIC-CIRCLE-OF-STEINER-ICIRCUMELLIPSE-POLE OF SODDY LINE

Barycentrics    (b - c)*(a*b + b^2 + a*c - b*c + c^2) : :
X(44435) = X[649] - 4 X[21212], X[661] + 2 X[3776], X[693] + 2 X[3004], 4 X[3239] - 7 X[27138], 4 X[3676] - X[7192], 4 X[3798] - X[26853], 2 X[3835] + X[16892], 4 X[3835] - X[25259], 2 X[4025] + X[20295], 2 X[4106] + X[4467], X[4380] - 4 X[17069], X[4380] + 2 X[23729], X[4382] + 2 X[21196], 3 X[4728] - X[4931], X[4804] + 2 X[4818], 2 X[4932] + X[23731], 3 X[6545] - X[21116], 3 X[6548] - 2 X[21183], 2 X[6590] - 5 X[26985], 8 X[7658] - 5 X[27013], 4 X[11068] - 7 X[27115], 4 X[14425] - 5 X[31209], 2 X[16892] + X[25259], 2 X[17069] + X[23729]

X(44435) lies on these lines: {2, 514}, {325, 523}, {513, 4453}, {522, 21297}, {614, 4040}, {649, 21212}, {661, 3776}, {663, 7191}, {664, 14513}, {675, 953}, {812, 27486}, {824, 4728}, {918, 4776}, {1443, 1447}, {1635, 28882}, {2786, 31147}, {2826, 30804}, {3239, 27138}, {3667, 4025}, {3777, 8034}, {3798, 26853}, {3835, 4120}, {3873, 9029}, {3920, 4449}, {4024, 31094}, {4106, 4467}, {4147, 29679}, {4367, 26249}, {4380, 4773}, {4382, 21196}, {4406, 26234}, {4750, 4785}, {4777, 31131}, {4789, 28894}, {4804, 4818}, {4897, 39386}, {4928, 28863}, {4932, 23731}, {6084, 31150}, {6590, 26985}, {6636, 39476}, {7409, 39532}, {7658, 27013}, {9810, 28840}, {11068, 27115}, {14425, 31209}, {17072, 29667}, {20952, 29427}, {21118, 29680}, {21130, 23888}, {23345, 26240}, {23813, 28205}, {26230, 30580}, {26248, 28195}, {26275, 28209}, {28179, 30792}, {28374, 43051}, {28859, 31148}, {29110, 31149}, {29144, 36848}, {30520, 30565}

X(44435) = midpoint of X(i) and X(j) for these {i,j}: {661, 21115}, {3004, 4927}, {4120, 16892}, {4773, 23729}
X(44435) = reflection of X(i) in X(j) for these {i,j}: {693, 4927}, {4120, 3835}, {4379, 21204}, {4380, 4773}, {4773, 17069}, {21115, 3776}, {25259, 4120}
X(44435) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(38941)
X(44435) = isotomic conjugate of X(9059)
X(44435) = isotomic conjugate of the isogonal conjugate of X(9002)
X(44435) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3478, 37781}, {9088, 5905}
X(44435) = X(20569)-Ceva conjugate of X(1086)
X(44435) = X(i)-isoconjugate of X(j) for these (i,j): {31, 9059}, {44, 32686}, {101, 40401}, {692, 996}, {902, 36091}
X(44435) = crossdifference of every pair of points on line {32, 902}
X(44435) = barycentric product X(i)*X(j) for these {i,j}: {76, 9002}, {513, 33934}, {514, 4389}, {523, 16712}, {693, 4850}, {903, 23888}, {995, 3261}, {3267, 4247}, {3676, 5233}, {3877, 24002}, {4424, 7199}, {7192, 26580}, {21130, 39704}
X(44435) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 9059}, {88, 36091}, {106, 32686}, {513, 40401}, {514, 996}, {995, 101}, {3877, 644}, {4247, 112}, {4266, 3939}, {4389, 190}, {4424, 1018}, {4850, 100}, {5233, 3699}, {9002, 6}, {16712, 99}, {17461, 4752}, {21130, 3679}, {23206, 906}, {23888, 519}, {26580, 3952}, {33934, 668}
X(44435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3835, 16892, 25259}, {17069, 23729, 4380}

X(44436) = MOSES-RADICAL-CIRCLE-POLE OF VAN AUBEL LINE

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 + 4*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 2*b^6*c^2 - 3*a^4*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 + 3*a^2*c^6 - 2*b^2*c^6 - c^8) : :
Barycentrics    (csc A) (sec B cos C (sin 2A - sin 2B) + cos B sec C (sin 2A - sin 2C)) : :

X(44436) lies on these lines: {2, 216}, {3, 1495}, {20, 16253}, {51, 38283}, {110, 34147}, {122, 858}, {126, 38974}, {131, 2072}, {268, 22129}, {323, 3284}, {373, 30258}, {394, 1073}, {401, 39062}, {417, 5907}, {418, 3819}, {426, 9306}, {441, 525}, {511, 852}, {577, 15066}, {800, 37643}, {1214, 6357}, {1304, 2071}, {1350, 33924}, {1531, 10745}, {1624, 34146}, {1971, 17811}, {3218, 35072}, {3580, 15526}, {3917, 6638}, {5421, 23292}, {5562, 14059}, {5943, 13409}, {6000, 40948}, {6760, 8431}, {7386, 43460}, {7485, 26880}, {8798, 12111}, {10257, 16319}, {10601, 15851}, {11413, 14379}, {11427, 13341}, {11589, 13445}, {11695, 42441}, {16419, 26898}, {18890, 37669}, {20208, 37638}, {26895, 33879}, {30739, 42353}, {35071, 40884}, {37648, 41005}

X(44436) = midpoint of X(852) and X(2972)
X(44436) = complement of X(46106)
X(44436) = complement of polar conjugate of X(74)
X(44436) = Moses-radical-circle-inverse of X(15341)
X(44436) = complement of the isogonal conjugate of X(18877)
X(44436) = complement of the isotomic conjugate of X(14919)
X(44436) = isotomic conjugate of the polar conjugate of X(6000)
X(44436) = X(i)-complementary conjugate of X(j) for these (i,j): {48, 113}, {74, 20305}, {822, 16177}, {2159, 5}, {2349, 21243}, {9247, 3163}, {14380, 21253}, {14919, 2887}, {15291, 20308}, {18877, 10}, {32640, 8062}, {35200, 141}, {36034, 30476}, {36131, 520}, {40352, 226}, {40354, 24005}
X(44436) = X(i)-Ceva conjugate of X(j) for these (i,j): {3260, 13754}, {16077, 520}
X(44436) = X(i)-isoconjugate of X(j) for these (i,j): {19, 1294}, {647, 36043}, {656, 32646}, {2430, 36126}, {24019, 43701}
X(44436) = cevapoint of X(3284) and X(12096)
X(44436) = crosspoint of X(i) and X(j) for these (i,j): {2, 14919}, {276, 43767}
X(44436) = crosssum of X(i) and X(j) for these (i,j): {6, 1990}, {1562, 1637}
X(44436) = crossdifference of every pair of points on line {25, 9209}
X(44436) = barycentric product X(i)*X(j) for these {i,j}: {69, 6000}, {511, 36893}, {1494, 40948}, {1559, 15394}, {2442, 4143}, {3260, 39174}, {6148, 39376}
X(44436) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 1294}, {112, 32646}, {162, 36043}, {520, 43701}, {1301, 39464}, {1559, 14249}, {2404, 15352}, {2442, 6529}, {6000, 4}, {32320, 2430}, {36893, 290}, {39174, 74}, {39376, 5627}, {40948, 30}
X(44436) = {X(1073),X(6617)}-harmonic conjugate of X(394)

X(44437) = MOSES-RADICAL-CIRCLE-POLE OF LINE X(2)X(6)

Barycentrics    a^2*(a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10 + a^8*c^2 - 14*a^6*b^2*c^2 + 4*a^4*b^4*c^2 + 6*a^2*b^6*c^2 + 3*b^8*c^2 - 4*a^6*c^4 + 4*a^4*b^2*c^4 - 4*a^2*b^4*c^4 - 4*b^6*c^4 + 6*a^4*c^6 + 6*a^2*b^2*c^6 - 4*b^4*c^6 - 4*a^2*c^8 + 3*b^2*c^8 + c^10) : :

X(44437) lies on these lines: {3, 1495}, {4, 39}, {30, 36212}, {32, 11456}, {187, 12112}, {237, 6000}, {566, 36990}, {647, 1499}, {800, 39874}, {842, 37946}, {1181, 8779}, {1199, 34571}, {1498, 1971}, {1503, 3003}, {1513, 3291}, {1514, 14961}, {1561, 11672}, {3088, 14165}, {3926, 34621}, {5007, 15032}, {5188, 11459}, {5562, 9821}, {10605, 41266}, {10984, 19558}, {11438, 20897}, {12082, 30270}, {12290, 37114}, {14157, 42671}, {15072, 37465}, {15305, 37184}, {15811, 15815}, {16194, 35934}, {16261, 21163}, {16836, 37338}, {32062, 32444}

X(44437) = crossdifference of every pair of points on line {9209, 11284}

X(44438) = 2ND-DROZ-FARNY-CIRCLE-POLE OF ORTHIC AXIS

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6 - 4*a^4*c^2 + 10*a^2*b^2*c^2 - 2*b^4*c^2 - a^2*c^4 - 2*b^2*c^4 + 2*c^6) : :
X(44438) = 2 X[3] - 3 X[16072], 4 X[3] - 5 X[31255], 3 X[4] - 2 X[1596], 3 X[4] - X[18533], 4 X[4] - X[37196], 5 X[4] - 2 X[37458], 3 X[25] - 4 X[1596], 3 X[25] - 2 X[18533], 5 X[25] - 4 X[37458], 2 X[376] - 3 X[32216], 3 X[381] - 2 X[6644], 4 X[403] - 3 X[37917], 8 X[1596] - 3 X[37196], 5 X[1596] - 3 X[37458], 5 X[3091] - 4 X[6677], 3 X[3545] - 2 X[44273], 3 X[3830] - X[18534], 3 X[3830] - 2 X[44276], 3 X[3839] - 2 X[44212], 3 X[3845] - 2 X[44233], X[5073] + 2 X[14791], 5 X[5076] - 2 X[7530], X[7500] - 5 X[17578], 2 X[10605] - 3 X[26869], 3 X[14269] - 2 X[44275], 6 X[16072] - 5 X[31255], 4 X[18390] - 3 X[26869], 4 X[18531] - 3 X[31152], 4 X[18533] - 3 X[37196], 5 X[18533] - 6 X[37458], 2 X[21312] - 3 X[31152], 5 X[37196] - 8 X[37458]

X(44438) lies on these lines: {2, 3}, {6, 1562}, {33, 12943}, {34, 9627}, {64, 13399}, {125, 10606}, {146, 12165}, {148, 9308}, {185, 5895}, {1105, 18848}, {1112, 5890}, {1181, 13403}, {1204, 5925}, {1217, 18846}, {1398, 1479}, {1478, 7071}, {1498, 21659}, {1503, 10602}, {1514, 26864}, {1531, 44080}, {1539, 15472}, {1552, 9717}, {1568, 37497}, {1660, 17845}, {1824, 15942}, {1829, 41869}, {1853, 13851}, {1862, 10728}, {1870, 9668}, {1876, 3586}, {1899, 15311}, {1902, 5691}, {1986, 38790}, {2207, 7748}, {2386, 36997}, {2393, 12294}, {2777, 10605}, {2790, 5186}, {2834, 10729}, {2883, 19467}, {3092, 35820}, {3093, 35821}, {3172, 5254}, {3521, 36753}, {3767, 8778}, {5090, 31673}, {5185, 10727}, {5410, 6561}, {5411, 6560}, {5412, 42263}, {5413, 42264}, {5878, 6146}, {5894, 26937}, {5972, 18418}, {6000, 18396}, {6198, 9655}, {6225, 18945}, {6247, 15153}, {6748, 15433}, {6749, 34288}, {7687, 23329}, {7728, 18445}, {8739, 42155}, {8740, 42154}, {9541, 13884}, {9703, 15463}, {9777, 16657}, {9968, 11470}, {10311, 41336}, {10483, 11399}, {10632, 42130}, {10633, 42131}, {10641, 42096}, {10642, 42097}, {10723, 12131}, {10724, 12138}, {10733, 12133}, {10734, 10735}, {11396, 12699}, {11405, 20423}, {11408, 42085}, {11409, 42086}, {11425, 43831}, {11441, 34966}, {11457, 13093}, {11472, 12295}, {11473, 23251}, {11474, 23261}, {11475, 42094}, {11476, 42093}, {11550, 18405}, {11648, 14581}, {12111, 12282}, {12162, 12293}, {12167, 31670}, {12290, 34780}, {12292, 12902}, {12315, 34224}, {12897, 36747}, {13219, 40995}, {13474, 34786}, {13622, 14490}, {14356, 34233}, {14379, 33553}, {14989, 15111}, {15043, 43823}, {15048, 41370}, {15123, 15127}, {15152, 34782}, {15928, 39809}, {16318, 43448}, {17702, 18451}, {17846, 32340}, {18550, 38534}, {18847, 18852}, {18849, 18851}, {19124, 19136}, {20427, 34469}, {21663, 26958}, {22951, 22970}, {23698, 40801}, {29181, 41585}, {32063, 32111}, {33584, 38956}, {43273, 44102}

X(44438) = midpoint of X(1370) and X(3146)
X(44438) = reflection of X(i) in X(j) for these {i,j}: {20, 1368}, {25, 4}, {10605, 18390}, {17845, 1660}, {18533, 1596}, {18534, 44276}, {21312, 18531}, {37196, 25}
X(44438) = anticomplement of X(44241)
X(44438) = orthocentroidal-circle-inverse of X(10151)
X(44438) = 2nd-Droz-Farny-circle-inverse of X(468)
X(44438) = crosspoint of X(4) and X(18850)
X(44438) = crosssum of X(3) and X(10605)
X(44438) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 10151}, {2, 16386, 3}, {3, 4, 37197}, {3, 25, 37917}, {3, 403, 37453}, {3, 3830, 31726}, {3, 16072, 31255}, {4, 20, 235}, {4, 376, 6623}, {4, 378, 381}, {4, 382, 12173}, {4, 427, 18386}, {4, 1593, 7507}, {4, 1594, 3843}, {4, 1597, 5064}, {4, 1885, 1593}, {4, 3088, 23047}, {4, 3146, 3575}, {4, 3520, 35488}, {4, 3529, 3089}, {4, 3541, 546}, {4, 3542, 44226}, {4, 3575, 5198}, {4, 6240, 1598}, {4, 6869, 431}, {4, 7487, 1906}, {4, 7576, 18535}, {4, 8889, 3839}, {4, 13488, 11403}, {4, 14865, 7547}, {4, 18533, 1596}, {4, 18560, 3}, {4, 30100, 7566}, {4, 33703, 7487}, {4, 34797, 10594}, {4, 35480, 18494}, {4, 35481, 403}, {4, 35485, 37984}, {4, 35490, 382}, {5, 16976, 2}, {5, 34350, 3}, {20, 235, 3515}, {20, 6353, 37931}, {25, 32216, 468}, {235, 37931, 6353}, {376, 6623, 468}, {378, 381, 5094}, {381, 35495, 1656}, {382, 18494, 35480}, {403, 18560, 35481}, {403, 35481, 3}, {427, 13473, 4}, {427, 18386, 7507}, {550, 3542, 15750}, {550, 44226, 3542}, {1344, 1345, 1593}, {1593, 18386, 427}, {1595, 3853, 4}, {1596, 18533, 25}, {1597, 3830, 4}, {1598, 5073, 6240}, {1885, 13473, 427}, {3517, 17800, 35471}, {3520, 35488, 1656}, {3627, 13488, 4}, {3830, 18534, 44276}, {5878, 6146, 12174}, {5899, 18561, 1657}, {6353, 37931, 3515}, {7505, 35491, 3}, {7577, 18533, 6644}, {8703, 37942, 35486}, {10605, 18390, 26869}, {12362, 37201, 37198}, {13403, 22802, 1181}, {16868, 35477, 3526}, {18325, 18564, 12083}, {18494, 35480, 12173}, {18531, 21312, 31152}, {18563, 31725, 7387}, {30771, 34622, 2071}, {31861, 44263, 381}, {37197, 37453, 403}

X(44439) = 2ND-DROZ-FARNY-CIRCLE-POLE OF LEMOINE AXIS

Barycentrics    a^2*(a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 - 3*a^6*b^2*c^2 + 4*a^4*b^4*c^2 - 3*a^2*b^6*c^2 + b^8*c^2 - 2*a^6*c^4 + 4*a^4*b^2*c^4 + 2*a^2*b^4*c^4 - 3*a^2*b^2*c^6 + 2*a^2*c^8 + b^2*c^8 - c^10) : :
X(44439) = 5 X[6] - 4 X[389], 3 X[6] - 2 X[19161], 7 X[6] - 4 X[21851], 2 X[52] - 3 X[5102], 10 X[182] - 9 X[40280], 3 X[381] - 2 X[41714], 6 X[389] - 5 X[19161], 7 X[389] - 5 X[21851], 8 X[389] - 5 X[37473], 3 X[568] - 4 X[5097], 5 X[1352] - 6 X[15060], 5 X[3091] - 4 X[41579], 4 X[3631] - 5 X[11444], 5 X[3843] - 4 X[43129], 3 X[5085] - 2 X[37511], 4 X[5480] - 3 X[9971], 3 X[5890] - 4 X[12007], 8 X[6329] - 7 X[15043], 2 X[6403] - 3 X[9971], 4 X[11574] - 3 X[31884], 5 X[12283] + 3 X[12290], X[12283] - 3 X[15073], X[12290] + 5 X[15073], 5 X[12294] - 3 X[32062], 5 X[18438] - X[37484], 7 X[19161] - 6 X[21851], 4 X[19161] - 3 X[37473], 8 X[21851] - 7 X[37473], 6 X[32062] - 5 X[36990], 5 X[37481] - 6 X[39561]

X(44439) lies on these lines: {2, 11746}, {3, 6}, {4, 9973}, {20, 17710}, {51, 37453}, {69, 22466}, {184, 10117}, {185, 32366}, {206, 11470}, {381, 41714}, {403, 5480}, {427, 34751}, {524, 41716}, {599, 16072}, {974, 35485}, {1154, 4549}, {1352, 10113}, {1503, 12283}, {1593, 34777}, {1843, 37197}, {2393, 12294}, {2781, 6776}, {2854, 5921}, {2929, 43652}, {2979, 13567}, {3056, 9627}, {3060, 23292}, {3091, 41579}, {3589, 40929}, {3629, 5889}, {3631, 11444}, {3843, 43129}, {3917, 26958}, {5486, 11744}, {5562, 40341}, {5622, 15578}, {5890, 12007}, {5965, 13403}, {6101, 39571}, {6293, 19467}, {6329, 15043}, {6467, 30443}, {7505, 14853}, {8550, 35491}, {9306, 12310}, {10201, 20423}, {10628, 10938}, {10752, 32245}, {11412, 12241}, {11649, 31726}, {12220, 29181}, {12236, 18580}, {12902, 18435}, {13310, 19220}, {13367, 41593}, {14157, 15580}, {14913, 15752}, {15069, 34382}, {15072, 20725}, {15074, 34350}, {15140, 15463}, {15577, 18374}, {15761, 21850}, {16386, 32220}, {18390, 23039}, {19128, 35228}, {19136, 37917}, {19151, 38534}, {20987, 34787}, {21243, 32263}, {21660, 26883}, {26913, 32282}, {32246, 40330}, {33884, 37643}

X(44439) = reflection of X(i) in X(j) for these {i,j}: {20, 17710}, {185, 32366}, {1350, 9967}, {5889, 3629}, {6243, 37517}, {6403, 5480}, {9973, 4}, {36990, 12294}, {37473, 6}, {40341, 5562}, {40929, 3589}
X(44439) = 2nd-Droz-Farny-circle-inverse of X(187)
X(44439) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1970, 5111, 6}, {5102, 11425, 6}, {5480, 6403, 9971}

X(44440) = 2ND-DROZ-FARNY-CIRCLE-POLE OF DE LONGCHAMPS LINE

Barycentrics    a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - a^8*c^2 + 10*a^6*b^2*c^2 - 6*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 6*a^4*b^2*c^4 + 10*a^2*b^4*c^4 - 2*b^6*c^4 + 2*a^4*c^6 - 6*a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(44440) = 3 X[2] - 4 X[15760], 5 X[2] - 4 X[44218], 3 X[3] - 4 X[25337], 3 X[4] - 2 X[31723], 3 X[4] - 4 X[44263], 5 X[4] - 4 X[44288], 3 X[20] - 4 X[44239], 3 X[22] - 2 X[44239], 3 X[376] - 4 X[7502], 5 X[378] - 6 X[44218], 4 X[381] - 3 X[31105], 4 X[427] - 5 X[3091], 5 X[631] - 4 X[18570], 5 X[1656] - 4 X[44236], 3 X[2071] - 4 X[16387], X[3146] + 2 X[12082], 5 X[3522] - 8 X[16618], 5 X[3522] - 4 X[44249], 7 X[3523] - 8 X[6676], 3 X[3524] - 4 X[44262], 17 X[3544] - 16 X[13413], 9 X[3545] - 8 X[39504], 3 X[3839] - 2 X[31133], 11 X[5056] - 10 X[31236], 5 X[5071] - 4 X[44287], 3 X[7391] - 4 X[31723], 3 X[7391] - 8 X[44263], 5 X[7391] - 8 X[44288], 8 X[7555] - 5 X[17538], 3 X[10304] - 4 X[44210], 5 X[15692] - 4 X[44285], 5 X[15760] - 3 X[44218], 4 X[19127] - 3 X[25406], X[20062] + 2 X[35480], 8 X[25337] - 3 X[35481], 5 X[31723] - 6 X[44288], 5 X[44263] - 3 X[44288]

X(44440) lies on these lines: {2, 3}, {68, 6241}, {69, 146}, {148, 3164}, {280, 10522}, {343, 15311}, {388, 9538}, {569, 12897}, {1352, 15305}, {1478, 3100}, {1479, 4296}, {1498, 14516}, {1503, 41614}, {1514, 15066}, {1531, 36987}, {1568, 37480}, {1614, 12118}, {1899, 15072}, {2063, 5893}, {2549, 22240}, {2777, 12827}, {2883, 11441}, {2888, 6225}, {3014, 41761}, {3098, 13202}, {3448, 17854}, {3521, 6243}, {3580, 10605}, {3767, 19220}, {3818, 32062}, {4549, 10721}, {4846, 5890}, {5270, 9643}, {5422, 16657}, {5562, 22802}, {5622, 10733}, {5654, 43574}, {5878, 12111}, {5921, 41735}, {6000, 11442}, {6193, 43605}, {6560, 11418}, {6561, 11417}, {6776, 37784}, {7712, 12319}, {7728, 23039}, {7735, 41336}, {7737, 10313}, {8717, 12295}, {8718, 12289}, {9833, 12278}, {9927, 10575}, {10249, 18382}, {10574, 39571}, {10606, 37638}, {10984, 13403}, {11185, 30737}, {11202, 16163}, {11416, 20423}, {11420, 42085}, {11421, 42086}, {11440, 20427}, {11455, 41171}, {12058, 15030}, {12174, 12429}, {12220, 31670}, {12279, 14216}, {12293, 34224}, {12384, 14983}, {13203, 41398}, {13346, 43831}, {13445, 23293}, {13491, 25738}, {14826, 15052}, {14915, 18474}, {15075, 39575}, {15438, 32605}, {15466, 34170}, {15740, 22466}, {16165, 35260}, {18390, 18911}, {18451, 32111}, {18912, 40647}, {19127, 25406}, {22555, 22951}, {34944, 40196}, {36983, 43695}, {41464, 43621}, {41465, 41466}

X(44440) = midpoint of X(i) and X(j) for these {i,j}: {3146, 20062}, {12082, 35480}
X(44440) = reflection of X(i) in X(j) for these {i,j}: {20, 22}, {378, 15760}, {3146, 35480}, {7391, 4}, {12384, 14983}, {20062, 12082}, {31723, 44263}, {35481, 3}, {44249, 16618}
X(44440) = anticomplement of X(378)
X(44440) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(37980)
X(44440) = 2nd-Droz-Farny-circle-inverse of X(858)
X(44440) = circumcircle-of-anticomplementary-triangle-inverse of X(10296)
X(44440) = de Longchamps circle inverse of X(7464)
X(44440) = anticomplement of the isogonal conjugate of X(4846)
X(44440) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1302, 7253}, {4846, 8}, {32738, 17498}, {34288, 5905}, {34289, 21270}, {36083, 9033}, {36149, 525}
X(44440) = crosssum of X(3269) and X(42660)
X(44440) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 2071}, {2, 3543, 37077}, {3, 403, 2}, {3, 15761, 7505}, {4, 20, 37444}, {4, 376, 18531}, {4, 1370, 3153}, {4, 3529, 14790}, {4, 6815, 3091}, {4, 6997, 3839}, {4, 7401, 3832}, {4, 10996, 6816}, {4, 18420, 7394}, {4, 35513, 1370}, {4, 37201, 20}, {5, 31725, 4}, {20, 3153, 1370}, {20, 3839, 7396}, {20, 10298, 376}, {235, 31829, 17928}, {376, 7493, 10298}, {376, 18531, 16063}, {378, 15760, 2}, {381, 18325, 44276}, {381, 21312, 858}, {381, 44276, 4}, {382, 11414, 12225}, {468, 44241, 15078}, {550, 10020, 3}, {550, 44279, 18404}, {1370, 3153, 37444}, {1370, 35513, 20}, {1370, 37201, 35513}, {1885, 6823, 7503}, {3146, 34007, 4}, {3534, 18403, 14791}, {3830, 11818, 4}, {5002, 5003, 16063}, {6240, 7387, 31304}, {6816, 10996, 3523}, {7394, 18420, 7544}, {7500, 34621, 37945}, {7576, 18534, 7519}, {9927, 10575, 11457}, {10024, 12084, 37119}, {10254, 18859, 18281}, {10323, 35490, 12605}, {11414, 12225, 20}, {11744, 12825, 146}, {13383, 44240, 32534}, {14784, 14785, 12084}, {14807, 14808, 10296}, {15760, 31723, 18537}, {15760, 44239, 16387}, {16386, 31726, 3153}, {18404, 44279, 4}, {31723, 44239, 1370}, {31723, 44263, 4}, {35732, 42282, 12086}

X(44441) = 1ST-DROZ-FARNY-CIRCLE-POLE OF ORTHIC AXIS

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 12*a^6*b^2*c^2 - 6*a^4*b^4*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 6*a^4*b^2*c^4 + 6*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :
X(44441) = 9 X[2] - 8 X[34330], 7 X[2] - 8 X[34331], 5 X[2] - X[34621], 7 X[2] - 4 X[44278], 2 X[3] + X[14790], X[3] + 2 X[23335], X[4] + 2 X[12084], X[4] - 4 X[13371], 2 X[5] + X[12085], X[20] - 4 X[11250], X[20] + 2 X[18569], 2 X[26] - 5 X[631], X[26] - 4 X[23336], 2 X[26] + X[34938], X[64] + 2 X[22660], X[68] + 2 X[13346], X[68] - 4 X[20299], 4 X[140] - X[7387], X[155] + 2 X[6247], 4 X[156] - X[34781], X[376] + 2 X[31181], 5 X[631] - 8 X[23336], 5 X[631] - 4 X[34477], 5 X[631] - X[34608], 5 X[631] + X[34938], 2 X[1147] + X[14216], X[1498] - 4 X[9820], 5 X[1656] - 8 X[32144], 4 X[1658] - 7 X[3523], 4 X[1658] - X[31305], X[2935] + 2 X[23306], 7 X[3090] - 4 X[15761], 7 X[3090] - 10 X[31283], 5 X[3091] - 8 X[10224], X[3146] - 4 X[18377], X[3146] + 2 X[34350], 5 X[3522] - 8 X[10226], 7 X[3523] - X[31305], 3 X[3524] - 2 X[18324], 11 X[3525] - 8 X[10020], 7 X[3526] - 4 X[13383], 7 X[3526] - X[39568], 7 X[3528] - 4 X[44242], 7 X[3832] - 4 X[44279], 3 X[5054] - X[9909], 3 X[5054] - 2 X[34351], 11 X[5056] - 8 X[13406], 11 X[5056] - 16 X[34199], 5 X[5071] - 9 X[30775], 4 X[5448] - X[5878], 16 X[5498] - 13 X[10303], 4 X[5498] - X[17714], X[6193] + 2 X[32140], 4 X[6696] - X[12163], X[9833] - 4 X[12038], X[10201] - 3 X[18281], 3 X[10201] - 4 X[34330], 7 X[10201] - 12 X[34331], 10 X[10201] - 3 X[34621], 7 X[10201] - 6 X[44278], 3 X[10245] - 7 X[15701], 13 X[10303] - 4 X[17714], 2 X[11250] + X[18569], X[11411] + 2 X[16266], X[12084] + 2 X[13371], X[12118] + 2 X[18381], X[12302] + 2 X[23315], X[12324] + 2 X[32139], 2 X[12359] + X[37498], 2 X[12359] - 5 X[40686], X[12383] - 4 X[25487], X[13346] + 2 X[20299], 4 X[13383] - X[39568], X[14790] - 4 X[23335], 7 X[14869] - 4 X[44277], 8 X[15330] - 11 X[15721], 8 X[15331] - 11 X[15717], 5 X[15693] - X[34726], 7 X[15702] - 4 X[44213], 11 X[15720] - 5 X[16195], 2 X[15761] - 5 X[31283], 5 X[17578] - 8 X[18567], X[17834] - 4 X[44158], 9 X[18281] - 4 X[34330], 7 X[18281] - 4 X[34331], 10 X[18281] - X[34621], 7 X[18281] - 2 X[44278], 2 X[18377] + X[34350], 8 X[23336] - X[34608], 8 X[23336] + X[34938], 7 X[34330] - 9 X[34331], 40 X[34330] - 9 X[34621], 14 X[34330] - 9 X[44278], 40 X[34331] - 7 X[34621], 4 X[34477] - X[34608], 4 X[34477] + X[34938], 7 X[34621] - 20 X[44278], X[37498] + 5 X[40686], X[39812] + 2 X[39845], 2 X[39816] + X[39841]

X(44441) lies on these lines: {2, 3}, {52, 26937}, {64, 22660}, {66, 542}, {68, 13346}, {155, 6247}, {156, 34781}, {193, 10264}, {343, 37483}, {511, 23048}, {571, 6128}, {1147, 14216}, {1236, 32833}, {1272, 32837}, {1350, 44201}, {1498, 9820}, {1511, 28408}, {1853, 37497}, {1899, 13352}, {1993, 18917}, {2931, 18382}, {2935, 23306}, {3085, 32047}, {3086, 8144}, {3654, 34643}, {4846, 18388}, {5157, 38064}, {5433, 9645}, {5448, 5878}, {5654, 6000}, {5892, 14561}, {5946, 14853}, {6102, 18913}, {6193, 32140}, {6696, 12163}, {6699, 31670}, {9540, 11265}, {9833, 12038}, {10564, 18474}, {11064, 18451}, {11202, 29012}, {11266, 13935}, {11411, 16266}, {11433, 39522}, {11442, 43574}, {11457, 34148}, {11645, 36989}, {12042, 41770}, {12099, 15061}, {12118, 18381}, {12134, 35602}, {12161, 18909}, {12302, 23315}, {12324, 32139}, {12359, 37498}, {12383, 25487}, {13292, 26944}, {14852, 23332}, {15033, 18911}, {15068, 37669}, {15136, 34118}, {16658, 35264}, {17822, 17836}, {17834, 44158}, {18440, 28419}, {18445, 37645}, {18916, 36749}, {18951, 36747}, {19161, 20423}, {21243, 37480}, {25738, 37495}, {39812, 39845}, {39816, 39841}

X(44441) = midpoint of X(i) and X(j) for these {i,j}: {3, 34609}, {1853, 37497}, {3534, 34725}, {3654, 34643}, {3830, 34622}, {34608, 34938}
X(44441) = reflection of X(i) in X(j) for these {i,j}: {2, 18281}, {26, 34477}, {3543, 18568}, {7387, 10154}, {9909, 34351}, {10154, 140}, {13406, 34199}, {14070, 549}, {14790, 34609}, {14852, 23332}, {33591, 11812}, {34477, 23336}, {34608, 26}, {34609, 23335}, {44278, 34331}
X(44441) = anticomplement of X(10201)
X(44441) = 1st-Droz-Farny-circle-inverse of X(468)
X(44441) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 427, 18420}, {3, 5576, 6815}, {3, 23335, 14790}, {3, 31723, 18533}, {5, 44276, 6623}, {20, 37119, 3549}, {26, 23336, 631}, {378, 858, 18531}, {382, 6640, 3542}, {549, 13490, 6644}, {631, 34938, 26}, {1595, 16196, 6642}, {1597, 30771, 5}, {2071, 31074, 4}, {3088, 3546, 5}, {3523, 31305, 1658}, {3526, 39568, 13383}, {5054, 9909, 34351}, {5054, 14787, 2}, {5094, 21312, 15760}, {7500, 35486, 2070}, {11250, 18569, 20}, {12084, 13371, 4}, {13346, 20299, 68}, {13490, 15122, 549}, {15078, 31133, 7576}, {15559, 17928, 7528}, {15761, 31283, 3090}, {15765, 18585, 6642}, {18377, 34350, 3146}, {18533, 31099, 31723}, {18586, 18587, 235}, {34551, 34552, 16197}, {37498, 40686, 12359}

X(44442) = CIRCUMCIRCLE-OF-ANTICOMPLEMENTARY-TRIANGLE-POLE OF ORTHIC AXIS

Barycentrics    3*a^6 + 3*a^4*b^2 - 3*a^2*b^4 - 3*b^6 + 3*a^4*c^2 - 2*a^2*b^2*c^2 + 3*b^4*c^2 - 3*a^2*c^4 + 3*b^2*c^4 - 3*c^6 : :
X(44442) = 5 X[2] - 4 X[10154], 8 X[2] - 9 X[30775], X[4] - 4 X[14790], 13 X[4] - 16 X[18377], 15 X[4] - 16 X[18566], 29 X[4] - 32 X[18567], 7 X[4] - 8 X[18568], 5 X[4] - 8 X[18569], X[4] + 2 X[34938], 19 X[4] - 16 X[44279], 8 X[26] - 11 X[3525], 4 X[140] - 3 X[10245], 5 X[631] - 4 X[14070], 5 X[631] - 8 X[23335], 5 X[631] - 2 X[31305], 10 X[632] - 7 X[10244], 7 X[3090] - 4 X[7387], 5 X[3091] - 2 X[39568], 9 X[3524] - 8 X[18324], X[3529] - 4 X[12085], 13 X[5067] - 16 X[13371], 5 X[5071] - 8 X[31181], 5 X[9909] - 6 X[10154], 16 X[9909] - 27 X[30775], 4 X[9909] - 3 X[34608], X[9909] - 3 X[34609], 32 X[10154] - 45 X[30775], 8 X[10154] - 5 X[34608], 2 X[10154] - 5 X[34609], 13 X[10303] - 10 X[16195], 8 X[12084] - 5 X[17538], 13 X[14790] - 4 X[18377], 15 X[14790] - 4 X[18566], 29 X[14790] - 8 X[18567], 7 X[14790] - 2 X[18568], 5 X[14790] - 2 X[18569], 2 X[14790] + X[34938], 19 X[14790] - 4 X[44279], 32 X[15330] - 35 X[15702], 4 X[15330] - 5 X[18281], 9 X[15330] - 10 X[34478], 5 X[15694] - 4 X[33591], 7 X[15702] - 8 X[18281], 63 X[15702] - 64 X[34478], 9 X[15709] - 8 X[34351], 9 X[18281] - 8 X[34478], 15 X[18377] - 13 X[18566], 29 X[18377] - 26 X[18567], 14 X[18377] - 13 X[18568], 10 X[18377] - 13 X[18569], 8 X[18377] + 13 X[34938], 19 X[18377] - 13 X[44279], 29 X[18566] - 30 X[18567], 14 X[18566] - 15 X[18568], 2 X[18566] - 3 X[18569], 8 X[18566] + 15 X[34938], 19 X[18566] - 15 X[44279], 28 X[18567] - 29 X[18568], 20 X[18567] - 29 X[18569], 16 X[18567] + 29 X[34938], 38 X[18567] - 29 X[44279], 5 X[18568] - 7 X[18569], 4 X[18568] + 7 X[34938], 19 X[18568] - 14 X[44279], 4 X[18569] + 5 X[34938], 19 X[18569] - 10 X[44279], 4 X[23335] - X[31305], 9 X[30775] - 4 X[34608], 9 X[30775] - 16 X[34609], X[34608] - 4 X[34609], 19 X[34938] + 8 X[44279]

X(44442) is the centroid of the 3rd antipedal triangle of X(4), which is also the polar triangle of the anticomplementary circle, and the anticomplement of the Ara triangle. (Randy Hutson, September 30, 2021)

X(44442) lies on these lines: {2, 3}, {39, 15437}, {69, 11550}, {184, 14927}, {305, 32006}, {388, 4348}, {497, 7221}, {511, 32064}, {524, 34944}, {534, 11677}, {541, 12319}, {542, 13203}, {543, 39842}, {551, 34712}, {612, 5229}, {614, 5225}, {1184, 43448}, {1503, 37672}, {1853, 29181}, {1899, 21969}, {1992, 18935}, {1993, 39874}, {3060, 18950}, {3241, 34643}, {3434, 4980}, {3679, 34730}, {3828, 34642}, {3829, 34702}, {4176, 5207}, {5254, 40179}, {5485, 40178}, {6403, 12058}, {7753, 34722}, {8144, 17024}, {8280, 42260}, {8281, 42261}, {8854, 22644}, {8855, 22615}, {9766, 41761}, {10625, 33523}, {11206, 29012}, {11433, 21849}, {11645, 41736}, {12320, 32419}, {12321, 32421}, {14826, 36990}, {14831, 18909}, {15435, 21358}, {18289, 42266}, {18290, 42267}, {20049, 34729}, {21243, 33522}, {23291, 33586}, {29323, 35260}, {29815, 32047}, {30737, 32001}, {31145, 34713}, {31383, 37669}, {37643, 43621}, {37665, 42459}

X(44442) = reflection of X(i) in X(j) for these {i,j}: {2, 34609}, {3241, 34643}, {3543, 34725}, {14070, 23335}, {15683, 34622}, {20049, 34729}, {31145, 34713}, {31305, 14070}, {34608, 2}, {34621, 381}, {34642, 3828}, {34658, 10691}, {34702, 3829}, {34712, 551}, {34722, 7753}, {34726, 549}, {34730, 3679}
X(44442) = anticomplement of X(9909)
X(44442) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(37941)
X(44442) = circumcircle-of-anticomplementary-triangle-inverse of X(468)
X(44442) = anticomplement of the isogonal conjugate of X(16774)
X(44442) = X(16774)-anticomplementary conjugate of X(8)
X(44442) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3543, 428}, {2, 34603, 7714}, {4, 1370, 7386}, {4, 3537, 18420}, {4, 3538, 7401}, {4, 7386, 7392}, {20, 427, 7494}, {22, 31099, 8889}, {25, 7396, 16051}, {376, 15682, 18559}, {381, 10691, 2}, {382, 1368, 6995}, {428, 31152, 2}, {858, 7500, 6353}, {1368, 6995, 40132}, {1370, 6997, 16063}, {1370, 7391, 4}, {2043, 2044, 7400}, {3146, 7396, 25}, {3529, 8889, 22}, {3627, 5020, 7408}, {5064, 7667, 2}, {5159, 21974, 2}, {5189, 7391, 1370}, {6353, 33703, 7500}, {7714, 15682, 34603}, {14790, 34938, 4}, {14807, 14808, 468}, {20062, 31074, 7493}, {23335, 31305, 631}, {34621, 34658, 34608}

X(44443) = CIRCUMCIRCLE-OF-ANTICOMPLEMENTARY-TRIANGLE-POLE OF LEMOINE AXIS

Barycentrics    a^6*b^2 - a^2*b^6 + a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 - a^2*b^2*c^4 + 2*b^4*c^4 - a^2*c^6 - b^2*c^6 : :

X(44443) lies on these lines: {2, 22062}, {4, 69}, {6, 37190}, {20, 20775}, {30, 20794}, {95, 5171}, {193, 14957}, {216, 7386}, {382, 22152}, {393, 3289}, {420, 28408}, {458, 37491}, {1370, 3164}, {3619, 17500}, {5080, 25311}, {5999, 40947}, {6643, 30258}, {6997, 16990}, {7391, 7779}, {7392, 14767}, {7762, 26926}, {7900, 32747}, {9306, 32085}, {9723, 11676}, {9917, 37337}, {11008, 25051}, {32428, 34938}, {32854, 36855}, {33971, 37498}, {37124, 37488}

X(44443) = circumcircle-of-anticomplementary-triangle-inverse of X(5167)
X(44443) = polar conjugate of the isotomic conjugate of X(28441)
X(44443) = barycentric product X(4)*X(28441)
X(44443) = barycentric quotient X(28441)/X(69)
X(44443) = {X(315),X(9230)}-harmonic conjugate of X(69)

X(44444) = CIRCUMCIRCLE-OF-ANTICOMPLEMENTARY-TRIANGLE-POLE OF NAGEL LINE

Barycentrics    (b - c)*(-a^4 - a^3*b - a^2*b^2 - a*b^3 - a^3*c + a^2*b*c - a*b^2*c + b^3*c - a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(44444) = 5 X[631] - 4 X[39225], 7 X[3090] - 8 X[39508], X[4419] - 4 X[24698]

X(44444) lies on these lines: {2, 4057}, {4, 2457}, {69, 21304}, {388, 43924}, {497, 42312}, {513, 2517}, {523, 2528}, {631, 39225}, {659, 25299}, {834, 21302}, {966, 20979}, {1370, 20294}, {1459, 28470}, {2345, 21389}, {2789, 21103}, {3090, 39508}, {3261, 17159}, {3733, 31291}, {3837, 26097}, {4106, 17896}, {4132, 20950}, {4419, 24698}, {4491, 31946}, {4648, 21191}, {7253, 14288}, {7386, 20315}, {9002, 20293}, {10566, 26853}, {17217, 21303}, {17314, 17458}, {20060, 23345}, {21102, 28487}

X(44444) = reflection of X(i) in X(j) for these {i,j}: {4491, 31946}, {7253, 14288}, {31291, 3733}
X(44444) = anticomplement of X(4057)
X(44444) = circumcircle-of-anticomplementary-triangle-inverse of X(6788)
X(44444) = anticomplement of the isogonal conjugate of X(8050)
X(44444) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {100, 24068}, {190, 18133}, {596, 149}, {8050, 8}, {34594, 1}, {37205, 75}, {39798, 4440}, {39949, 17154}, {40013, 150}, {40085, 21221}, {40148, 9263}, {40519, 192}
X(44444) = crossdifference of every pair of points on line {2300, 5007}

X(44445) = CIRCUMCIRCLE-OF-ANTICOMPLEMENTARY-TRIANGLE-POLE OF LINE X(2)X(6)

Barycentrics    (b^2 - c^2)*(-a^4 - a^2*b^2 - a^2*c^2 + b^2*c^2) : :
X(44445) = 3 X[2] - 4 X[23301], 9 X[2] - 10 X[31279], 5 X[631] - 4 X[5926], 2 X[647] - 3 X[5996], 4 X[647] - 3 X[9147], X[669] - 3 X[31176], 3 X[669] - 5 X[31279], 8 X[2501] - 9 X[5466], 7 X[3090] - 8 X[39511], 2 X[3804] - 3 X[4108], 3 X[4108] - 4 X[30476], X[8664] - 3 X[9148], 2 X[8664] - 5 X[31072], 6 X[9148] - 5 X[31072], 3 X[9979] - 4 X[12075], 2 X[23301] - 3 X[31176], 6 X[23301] - 5 X[31279], 4 X[23301] - X[31299], 9 X[31176] - 5 X[31279], 6 X[31176] - X[31299], 10 X[31279] - 3 X[31299]


X(44445) lies on these lines: {2, 669}, {4, 1499}, {69, 9009}, {316, 512}, {523, 2528}, {631, 5926}, {647, 5996}, {688, 14295}, {804, 3005}, {924, 30735}, {1370, 6563}, {3090, 39511}, {3221, 9493}, {3288, 30217}, {3566, 33294}, {3569, 13307}, {3804, 4108}, {3907, 27469}, {4010, 27712}, {4132, 24719}, {4151, 4382}, {4367, 26822}, {4455, 27045}, {4774, 31290}, {6655, 14824}, {6776, 30451}, {7234, 26983}, {7392, 14341}, {7533, 8371}, {7785, 23099}, {8639, 31291}, {8640, 30968}, {8664, 9148}, {9168, 16063}, {9491, 26823}, {9979, 12075}, {10278, 37349}, {10359, 39518}, {11550, 21646}, {12077, 32473}, {17072, 27673}, {18020, 32729}, {18197, 31330}, {20953, 22322}, {20983, 25298}, {24721, 40471}, {28470, 30094}, {34944, 43673}

X(44445) = reflection of X(i) in X(j) for these {i,j}: {2, 31176}, {669, 23301}, {3804, 30476}, {9147, 5996}, {31291, 8639}, {31296, 3005}, {31299, 669}
X(44445) = complement of X(31299)
X(44445) = anticomplement of X(669)
X(44445) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(32531)
X(44445) = circumcircle-of-anticomplementary-triangle-inverse of X(6792)
X(44445) = anticomplement of the isogonal conjugate of X(670)
X(44445) = anticomplement of the isotomic conjugate of X(4609)
X(44445) = isotomic conjugate of the anticomplement of X(38996)
X(44445) = isotomic conjugate of the isogonal conjugate of X(21006)
X(44445) = polar conjugate of the isogonal conjugate of X(22159)
X(44445) = anticomplementary isogonal conjugate of X(25054)
X(44445) = X(4609)-Ceva conjugate of X(2)
X(44445) = X(i)-cross conjugate of X(j) for these (i,j): {8711, 21006}, {38996, 2}
X(44445) = X(i)-isoconjugate of X(j) for these (i,j): {163, 6664}, {1964, 6573}
X(44445) = cevapoint of X(21006) and X(22159)
X(44445) = crosspoint of X(i) and X(j) for these (i,j): {83, 670}, {99, 40416}, {40425, 42371}
X(44445) = crosssum of X(i) and X(j) for these (i,j): {39, 669}, {512, 20859}, {667, 23632}, {9494, 11205}
X(44445) = crossdifference of every pair of points on line {3051, 3229}
X(44445) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 25054}, {2, 21220}, {75, 148}, {76, 21221}, {81, 21224}, {86, 9263}, {99, 192}, {110, 17486}, {163, 8264}, {190, 1655}, {274, 4440}, {304, 39352}, {310, 149}, {314, 39351}, {561, 3448}, {643, 21218}, {645, 3177}, {648, 21216}, {662, 194}, {668, 1654}, {670, 8}, {689, 17165}, {789, 40721}, {799, 2}, {811, 193}, {823, 6392}, {873, 17154}, {874, 39367}, {892, 17497}, {1502, 21294}, {1930, 39346}, {1978, 2895}, {3112, 25047}, {3222, 21223}, {3736, 39347}, {4554, 17778}, {4561, 18666}, {4563, 6360}, {4567, 21225}, {4572, 2475}, {4573, 3210}, {4576, 21217}, {4577, 17489}, {4584, 19565}, {4589, 17759}, {4590, 4560}, {4592, 3164}, {4593, 6}, {4594, 21226}, {4599, 8267}, {4600, 17494}, {4601, 514}, {4602, 69}, {4609, 6327}, {4610, 17147}, {4615, 17495}, {4616, 17480}, {4620, 17496}, {4623, 1}, {4625, 145}, {4631, 63}, {4632, 3995}, {4633, 41839}, {4634, 519}, {4635, 4452}, {4639, 6542}, {6331, 5905}, {6385, 150}, {6386, 1330}, {7035, 31290}, {7257, 144}, {7258, 30695}, {7260, 6646}, {14210, 39356}, {16709, 39348}, {18020, 17498}, {18155, 17036}, {18157, 39353}, {18829, 17493}, {18833, 25051}, {23999, 33294}, {24037, 523}, {24039, 8591}, {24041, 31296}, {28660, 37781}, {30939, 39349}, {30940, 39362}, {31614, 6758}, {32680, 19570}, {34537, 7192}, {35137, 28598}, {36036, 385}, {36806, 1959}, {36860, 21219}, {37134, 40858}, {37204, 76}, {40072, 33650}, {40364, 13219}, {42371, 21278}, {44168, 17217}
X(44445) = barycentric product X(i)*X(j) for these {i,j}: {1, 20953}, {76, 21006}, {264, 22159}, {274, 22322}, {308, 8711}, {523, 7760}, {661, 18064}, {850, 1627}, {1577, 33760}, {3005, 41297}, {4609, 38996}
X(44445) = barycentric quotient X(i)/X(j) for these {i,j}: {83, 6573}, {523, 6664}, {1627, 110}, {7760, 99}, {8711, 39}, {18064, 799}, {20953, 75}, {21006, 6}, {22159, 3}, {22322, 37}, {33760, 662}, {38996, 669}, {41297, 689}
X(44445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 31299, 669}, {669, 23301, 2}, {669, 31176, 23301}, {3804, 30476, 4108}, {24533, 28401, 27677}, {24533, 31003, 2}, {25299, 26148, 2}

X(44446) = INCIRCLE-OF-ANTICOMPLEMENTARY-TRIANGLE-POLE OF ORTHIC AXIS

Barycentrics    5*a^3 - a^2*b - 3*a*b^2 - b^3 - a^2*c + 3*b^2*c - 3*a*c^2 + 3*b*c^2 - c^3 : :
X(44446) = 2 X[33144] - 3 X[35261]

X(44446) lies on these lines: {8, 30}, {46, 2899}, {63, 12717}, {144, 32932}, {190, 3474}, {200, 4480}, {344, 11246}, {345, 17768}, {545, 3052}, {612, 20073}, {1707, 28526}, {1836, 30741}, {2796, 33137}, {3616, 26729}, {3683, 42697}, {3685, 9965}, {3757, 4454}, {4418, 17257}, {4427, 5905}, {4438, 28546}, {4488, 9778}, {5435, 17777}, {5698, 32939}, {9369, 20070}, {9780, 32950}, {10453, 28610}, {17316, 32936}, {17336, 26040}, {17767, 33144}, {20017, 31301}, {20078, 32929}, {24248, 25453}, {24695, 32934}, {25734, 27549}, {26132, 29865}, {29579, 33067}, {29864, 33100}

X(44446) = reflection of X(30699) in X(1707)
X(44446) = incircle-of-anticomplementary-triangle-inverse of X(16304)
X(44446) = {X(4488),X(9778)}-harmonic conjugate of X(32937)

X(44447) = INCIRCLE-OF-ANTICOMPLEMENTARY-TRIANGLE-POLE OF DE LONGCHAMPS AXIS

Barycentrics    3*a^3 - a^2*b - a*b^2 - b^3 - a^2*c + b^2*c - a*c^2 + b*c^2 - c^3 : :
X(44447) = 9 X[2] - 8 X[3838], 3 X[2] - 4 X[4640], 3 X[63] - 2 X[4847], 3 X[210] - 2 X[41871], 2 X[226] - 3 X[35258], 4 X[946] - 5 X[6974], 3 X[1836] - 4 X[3838], 3 X[3434] - 4 X[4847], 5 X[3616] - 6 X[16370], 5 X[3616] - 4 X[39542], 2 X[3838] - 3 X[4640], 3 X[3873] - 4 X[10391], 3 X[5603] - 4 X[6914], 3 X[5657] - 2 X[6923], 2 X[7580] - 3 X[9778], 4 X[8727] - 3 X[9812], 7 X[9780] - 6 X[17532], 4 X[13405] - 3 X[31164], 3 X[16370] - 2 X[39542], 2 X[22791] - 3 X[28444]

X(44447) lies on these lines: {2, 1155}, {3, 11415}, {4, 1748}, {7, 1617}, {8, 30}, {20, 3869}, {21, 4295}, {22, 1633}, {31, 19785}, {40, 3436}, {42, 24695}, {46, 2478}, {55, 5905}, {63, 516}, {65, 6872}, {69, 20291}, {78, 31730}, {79, 10198}, {100, 329}, {144, 3059}, {145, 28646}, {149, 24477}, {162, 17903}, {165, 908}, {190, 10327}, {192, 20069}, {193, 3896}, {200, 17781}, {210, 41871}, {226, 35258}, {283, 1777}, {321, 24280}, {345, 4427}, {346, 33078}, {376, 4511}, {377, 1770}, {390, 3873}, {497, 3218}, {513, 43991}, {517, 6938}, {518, 20075}, {527, 3870}, {529, 12648}, {535, 12647}, {550, 5730}, {553, 4666}, {752, 32934}, {758, 4302}, {896, 33094}, {902, 33098}, {912, 37000}, {944, 14988}, {946, 4652}, {956, 28174}, {960, 4190}, {962, 1012}, {1001, 11246}, {1145, 38756}, {1158, 6836}, {1376, 31018}, {1479, 1727}, {1707, 3914}, {1759, 17732}, {1760, 11677}, {1788, 5046}, {1889, 5278}, {2094, 10580}, {2096, 5731}, {2194, 26830}, {2345, 33083}, {2550, 3219}, {2796, 4362}, {3000, 25941}, {3052, 3782}, {3057, 20076}, {3146, 5086}, {3152, 12940}, {3185, 35980}, {3189, 20066}, {3241, 34740}, {3306, 40998}, {3419, 28146}, {3475, 17483}, {3476, 20067}, {3485, 4189}, {3486, 15680}, {3487, 14450}, {3534, 10609}, {3550, 33099}, {3556, 16049}, {3579, 5552}, {3600, 3890}, {3616, 5303}, {3647, 19854}, {3652, 18517}, {3717, 25734}, {3744, 17276}, {3827, 20243}, {3868, 4294}, {3872, 28194}, {3874, 4309}, {3877, 4293}, {3878, 4299}, {3884, 4317}, {3886, 4001}, {3899, 4316}, {3901, 4330}, {3911, 10584}, {3916, 10527}, {3920, 4419}, {3923, 26034}, {3928, 9580}, {3929, 25006}, {3935, 34607}, {3937, 35645}, {3957, 10385}, {3962, 20013}, {3996, 17347}, {4000, 17127}, {4184, 17139}, {4191, 15507}, {4292, 5250}, {4297, 11682}, {4307, 28606}, {4312, 4512}, {4313, 34195}, {4314, 11520}, {4329, 8822}, {4333, 17647}, {4338, 12609}, {4388, 17740}, {4414, 26098}, {4415, 37540}, {4418, 19822}, {4463, 12530}, {4644, 17018}, {4645, 17776}, {4650, 11269}, {4655, 33171}, {4660, 33163}, {4661, 20095}, {4756, 5423}, {4855, 12512}, {4865, 28494}, {4972, 26065}, {4973, 10072}, {5080, 5657}, {5128, 24982}, {5180, 5603}, {5187, 24914}, {5218, 31053}, {5220, 34612}, {5230, 24851}, {5273, 33108}, {5284, 9776}, {5289, 15326}, {5314, 24309}, {5327, 27174}, {5493, 12527}, {5535, 26333}, {5554, 37567}, {5692, 15228}, {5697, 36977}, {5739, 32932}, {5744, 8727}, {5794, 31295}, {5852, 41711}, {5887, 6934}, {6224, 38753}, {6284, 12649}, {6734, 41869}, {6840, 14647}, {6871, 26066}, {6907, 11681}, {6910, 12047}, {6921, 21616}, {6936, 34339}, {6962, 12608}, {7262, 24715}, {7406, 24633}, {7613, 26724}, {8616, 32857}, {9579, 24987}, {9612, 10585}, {9780, 17532}, {9791, 37327}, {10052, 14798}, {10056, 16152}, {10164, 30852}, {10200, 37524}, {10404, 10587}, {10528, 37568}, {10529, 12701}, {10531, 37532}, {10586, 32636}, {11113, 36279}, {11114, 18391}, {11206, 17134}, {11220, 43161}, {11362, 40264}, {12116, 24467}, {12532, 13199}, {12635, 15338}, {13405, 31164}, {14206, 17860}, {14923, 20070}, {15310, 26893}, {15803, 41012}, {16558, 18513}, {16865, 28629}, {17126, 33100}, {17147, 20064}, {17150, 42058}, {17156, 28580}, {17484, 25568}, {17594, 41011}, {17601, 33096}, {17724, 21000}, {17747, 26258}, {17753, 23407}, {17764, 32853}, {17767, 32920}, {19535, 37737}, {19819, 32914}, {20011, 31301}, {20012, 20072}, {22060, 31394}, {22791, 28444}, {24692, 29642}, {25527, 35263}, {26040, 27065}, {26105, 27003}, {26132, 35261}, {26364, 37572}, {26842, 38053}, {27385, 35242}, {28508, 32946}, {28609, 35445}, {28610, 30332}, {30295, 35977}, {30652, 33155}, {30653, 33150}, {30985, 35270}, {31631, 35997}, {32842, 42049}, {32940, 36479}, {33134, 37642}, {34610, 38460}, {34647, 37600}, {35915, 40214}, {36277, 40940}, {41539, 41563}

X(44447) = midpoint of X(20075) and X(20078)
X(44447) = reflection of X(i) in X(j) for these {i,j}: {962, 1012}, {1836, 4640}, {3434, 63}, {5905, 55}, {6925, 40}, {10431, 1709}, {14450, 37286}, {33088, 32934}
X(44447) = anticomplement of X(1836)
X(44447) = anticomplement of the isogonal conjugate of X(37741)
X(44447) = anticomplement of the isotomic conjugate of X(34409)
X(44447) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {34409, 6327}, {37741, 8}
X(44447) = X(34409)-Ceva conjugate of X(2)
X(44447) = crosssum of X(512) and X(22094)
X(44447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 24248, 19785}, {144, 17784, 3681}, {329, 9778, 100}, {390, 9965, 3873}, {896, 33094, 33137}, {902, 33098, 33144}, {1155, 24703, 2}, {1707, 3914, 24597}, {1770, 12514, 377}, {1836, 4640, 2}, {3052, 3782, 26228}, {3474, 5698, 2}, {3683, 5880, 2}, {3916, 12699, 10527}, {3928, 9580, 26015}, {4312, 4512, 5249}, {4427, 6327, 345}, {4450, 32933, 8}, {4650, 33095, 11269}, {4676, 33068, 2}, {5744, 9812, 11680}, {16370, 39542, 3616}, {17127, 33102, 4000}, {28610, 30332, 36845}, {30332, 36845, 34611}

X(44448) = INCIRCLE-OF-ANTICOMPLEMENTARY-TRIANGLE-POLE OF SODDY LINE

Barycentrics    (b - c)*(-a + b + c)*(a^2 - 2*a*b + b^2 - 2*a*c + c^2) : :
X(44448) = X[4959] - 3 X[14432]

X(44448) lies on these lines: {8, 514}, {10, 21185}, {75, 30181}, {78, 663}, {100, 2730}, {200, 4040}, {522, 3717}, {850, 4151}, {1734, 4025}, {2832, 28591}, {3239, 28058}, {3309, 4468}, {3667, 4498}, {3669, 4925}, {3872, 4449}, {3900, 6332}, {4420, 4794}, {4437, 30188}, {4528, 6362}, {4729, 28478}, {4847, 21183}, {4959, 14432}, {6065, 32094}, {6734, 17072}, {8058, 20294}, {17880, 24010}, {21124, 28161}

X(44448) = reflection of X(i) in X(j) for these {i,j}: {8, 4546}, {3669, 4925}, {4025, 1734}, {4391, 4163}, {21185, 10}
X(44448) = X(41790)-anticomplementary conjugate of X(150)
X(44448) = X(i)-Ceva conjugate of X(j) for these (i,j): {3261, 3239}, {6558, 8}
X(44448) = X(4904)-cross conjugate of X(8)
X(44448) = X(i)-isoconjugate of X(j) for these (i,j): {56, 1292}, {101, 17107}, {109, 2191}, {241, 32644}, {277, 1415}, {604, 37206}, {692, 40154}, {1458, 36041}, {1462, 2428}
X(44448) = crosspoint of X(i) and X(j) for these (i,j): {75, 3699}, {190, 8817}
X(44448) = crosssum of X(i) and X(j) for these (i,j): {31, 43924}, {649, 7083}
X(44448) = barycentric product X(i)*X(j) for these {i,j}: {8, 4468}, {218, 35519}, {312, 3309}, {318, 24562}, {341, 43049}, {344, 522}, {346, 31605}, {645, 21945}, {668, 38375}, {1445, 4397}, {2402, 3717}, {3239, 6604}, {3261, 6600}, {3699, 4904}, {3870, 4391}, {3900, 21609}, {3991, 18155}, {4076, 23760}, {4086, 41610}, {4163, 17093}, {6558, 40615}, {7719, 35518}, {8642, 28659}
X(44448) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 37206}, {9, 1292}, {218, 109}, {294, 36041}, {344, 664}, {513, 17107}, {514, 40154}, {522, 277}, {650, 2191}, {1445, 934}, {1617, 1461}, {2195, 32644}, {2340, 2428}, {2440, 1416}, {3239, 6601}, {3309, 57}, {3717, 2414}, {3870, 651}, {3991, 4551}, {4350, 4617}, {4468, 7}, {4878, 4559}, {4904, 3676}, {6600, 101}, {6604, 658}, {7719, 108}, {8642, 604}, {17093, 4626}, {21059, 1415}, {21609, 4569}, {21945, 7178}, {23760, 1358}, {24562, 77}, {31605, 279}, {31638, 927}, {38375, 513}, {41539, 1020}, {41610, 1414}, {43049, 269}

X(44449) = INCIRCLE-OF-ANTICOMPLEMENTARY-TRIANGLE-POLE OF LINE X(2)X(6)

Barycentrics    (b - c)*(-a^2 - 2*a*b + b^2 - 2*a*c + b*c + c^2) : :
X(44449) 9 X[2] - 8 X[2487], 3 X[2] - 4 X[14321], 2 X[649] - 3 X[30565], 3 X[661] - 2 X[21196], 6 X[1638] - 7 X[27138], 6 X[1639] - 5 X[27013], 4 X[2487] - 3 X[4897], 2 X[2487] - 3 X[14321], 5 X[3616] - 4 X[39545], 4 X[3700] - 3 X[4789], 2 X[3776] - 3 X[31147], 4 X[3798] - 5 X[31209], 4 X[3835] - 3 X[4453], 2 X[4025] - 3 X[4776], 3 X[4120] - 2 X[4369], 3 X[4467] - 4 X[21196], 4 X[4521] - 3 X[4786], 3 X[4750] - 4 X[25666], 3 X[4789] - 2 X[7192], X[14779] - 5 X[31290], 3 X[20295] - 2 X[23729], 2 X[21104] - 3 X[21297]

X(44449) lies on these lines: {2, 2487}, {8, 1499}, {226, 31603}, {513, 4122}, {514, 4838}, {523, 4963}, {649, 28867}, {661, 2786}, {693, 28846}, {824, 4813}, {900, 17494}, {918, 20295}, {1638, 27138}, {1639, 27013}, {3616, 39545}, {3667, 4380}, {3700, 4789}, {3709, 16751}, {3776, 31147}, {3798, 31209}, {3835, 4453}, {3904, 29148}, {4024, 28840}, {4025, 4776}, {4079, 27469}, {4106, 4949}, {4120, 4369}, {4382, 28851}, {4462, 28478}, {4498, 28493}, {4500, 28886}, {4521, 4786}, {4750, 25666}, {4784, 18004}, {4822, 29037}, {4841, 17161}, {4958, 28855}, {4983, 29090}, {5287, 7203}, {7180, 28606}, {7265, 15309}, {21104, 21297}, {23731, 28863}, {25020, 25902}, {26853, 28217}

X(44449) = reflection of X(i) in X(j) for these {i,j}: {4106, 4949}, {4380, 4468}, {4467, 661}, {4784, 18004}, {4897, 14321}, {7192, 3700}, {17161, 4841}
X(44449) = anticomplement of X(4897)
X(44449) = X(8599)-Ceva conjugate of X(4789)
X(44449) = barycentric product X(514)*X(17315)
X(44449) = barycentric quotient X(17315)/X(190)
X(44449) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3700, 7192, 4789}, {4897, 14321, 2}

X(44450) = INCIRCLE-OF-ANTICOMPLEMENTARY-TRIANGLE-POLE OF HATZIPOLAKIS AXIS

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 13*a^6*b^2*c^2 - 8*a^4*b^4*c^2 + a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 8*a^4*b^2*c^4 + 4*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :
X(44450) = 17 X[2] - 8 X[44266], 11 X[2] - 8 X[44282], X[4] + 2 X[18859], X[4] - 4 X[37938], 2 X[5] + X[35452], X[20] + 8 X[858], X[20] - 4 X[2071], X[20] + 2 X[3153], 5 X[20] + 4 X[10296], 5 X[20] - 8 X[16386], X[23] - 4 X[10257], 4 X[23] - 13 X[10303], 4 X[140] - X[5899], X[146] - 4 X[1568], X[146] + 2 X[13445], 4 X[186] - 7 X[3523], 2 X[186] + X[5189], X[186] - 4 X[15122], 8 X[403] - 11 X[5056], 2 X[403] - 5 X[30745], 2 X[403] + X[37944], 4 X[468] - X[37945], 5 X[631] - 2 X[2070], 10 X[631] - X[20063], 25 X[631] - 16 X[22249], 2 X[858] + X[2071], 4 X[858] - X[3153], 10 X[858] - X[10296], 5 X[858] + X[16386], 2 X[1568] + X[13445], 5 X[1656] - 2 X[43893], 4 X[2070] - X[20063], 5 X[2070] - 8 X[22249], 2 X[2071] + X[3153], 5 X[2071] + X[10296], 5 X[2071] - 2 X[16386], 8 X[2072] - 5 X[3091], 2 X[2072] + X[7464], 7 X[3090] - 4 X[11563], 7 X[3090] + 2 X[35001], 5 X[3091] + 4 X[7464], X[3146] - 4 X[18403], X[3146] + 8 X[37950], 5 X[3153] - 2 X[10296], 5 X[3153] + 4 X[16386], X[3448] + 2 X[43574], 5 X[3522] + 4 X[7574], 5 X[3522] - 2 X[13619], 5 X[3522] - 8 X[34152], 7 X[3523] + 2 X[5189], 7 X[3523] - 16 X[15122], 3 X[3524] - 2 X[37955], 11 X[3525] - 2 X[37924], 11 X[3525] - 8 X[44234], 7 X[3526] - 4 X[10096], 7 X[3526] - X[37949], 17 X[3533] - 8 X[25338], 7 X[3832] - 4 X[31726], 7 X[3851] - 4 X[11558], 17 X[3854] - 8 X[44267], 3 X[5054] - 2 X[16532], 3 X[5054] - X[37956], 11 X[5056] - 20 X[30745], 11 X[5056] + 4 X[37944], X[5059] + 8 X[18572], 13 X[5068] - 4 X[18325], X[5189] + 8 X[15122], 17 X[7486] - 8 X[11799], 2 X[7574] + X[13619], X[7574] + 2 X[34152], 4 X[10096] - X[37949], 16 X[10257] - 13 X[10303], X[10296] + 2 X[16386], 3 X[10304] - 4 X[37948], 2 X[10564] + X[25739], 4 X[10989] + 5 X[15692], 2 X[11563] + X[35001], X[13619] - 4 X[34152], 4 X[14156] - X[14157], X[14683] - 4 X[22115], 14 X[14869] - 5 X[37923], 8 X[15646] - 11 X[15717], 5 X[15692] - 4 X[37941], 9 X[15708] - 4 X[37940], 11 X[15721] - 2 X[37901], 11 X[15721] - 4 X[37939], 11 X[15721] - 8 X[44214], 8 X[16531] - 5 X[37953], 8 X[16976] - 5 X[37952], X[18403] + 2 X[37950], X[18859] + 2 X[37938], 5 X[20063] - 32 X[22249], 5 X[30745] + X[37944], 5 X[37760] - 2 X[37925], X[37900] - 4 X[37935], X[37901] - 4 X[44214], X[37924] - 4 X[44234], 17 X[37943] - 12 X[44266], 11 X[37943] - 12 X[44282], 11 X[44266] - 17 X[44282]

X(44450) lies on these lines: {2, 3}, {146, 1568}, {539, 3448}, {1157, 43768}, {2697, 7953}, {2888, 20299}, {2979, 23329}, {3100, 3582}, {3584, 4296}, {5900, 10264}, {7691, 25563}, {7799, 30737}, {7809, 13219}, {8718, 43839}, {9143, 43572}, {9538, 10072}, {9833, 38942}, {10149, 14986}, {10168, 19121}, {10420, 13597}, {10519, 11649}, {10564, 25739}, {10625, 43608}, {10627, 12226}, {11420, 16241}, {11421, 16242}, {12058, 16226}, {12219, 20126}, {13391, 15061}, {13482, 43573}, {13857, 15100}, {14072, 33855}, {14156, 14157}, {14683, 22115}, {23293, 37480}, {37472, 43838}, {37495, 43808}

X(44450) = midpoint of X(10989) and X(37941)
X(44450) = reflection of X(i) in X(j) for these {i,j}: {9143, 43572}, {35489, 3}, {37901, 37939}, {37922, 549}, {37939, 44214}, {37956, 16532}
X(44450) = anticomplement of X(37943)
X(44450) = orthoptic-circle-of-Steiner-inellipe-inverse of X(10691)
X(44450) = de Longchamps circle inverse of X(5)
X(44450) = anticomplement of the isogonal conjugate of X(43704)
X(44450) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1291, 7253}, {2169, 13512}, {13582, 21270}, {14579, 5905}, {43704, 8}
X(44450) = crosssum of X(3269) and X(6140)
X(44450) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 31181, 18559}, {376, 18281, 2}, {858, 2071, 3153}, {1370, 10298, 20}, {1568, 13445, 146}, {2071, 3153, 20}, {2071, 10296, 16386}, {3526, 37949, 10096}, {5002, 5003, 20063}, {5004, 5005, 37920}, {5054, 37956, 16532}, {5189, 15122, 3523}, {7574, 34152, 13619}, {13619, 34152, 3522}, {14787, 15702, 2}, {18859, 37938, 4}, {28447, 28448, 34006}, {30745, 37944, 403}

X(44451) = NINE-POINT-CIRCLE-OF-MEDIAL-TRIANGLE-POLE OF LINE X(2)X(6)

Barycentrics    (b^2 - c^2)*(2*a^4 - a^2*b^2 - a^2*c^2 + b^2*c^2) : :
X(44451) = 3 X[2] + X[669], 5 X[2] - X[31176], 9 X[2] - 5 X[31279], 15 X[2] + X[31299], 3 X[351] + X[850], X[647] - 3 X[11176], 5 X[669] + 3 X[31176], 3 X[669] + 5 X[31279], 5 X[669] - X[31299], X[3005] + 3 X[4108], 3 X[5996] + X[8664], X[6563] - 3 X[10190], 3 X[8644] + 5 X[31277], 3 X[9147] + 5 X[31072], X[9148] + 3 X[15724], 3 X[10189] - 4 X[14341], 5 X[23301] - 3 X[31176], 3 X[23301] - 5 X[31279], 5 X[23301] + X[31299], 9 X[31176] - 25 X[31279], 3 X[31176] + X[31299], 25 X[31279] + 3 X[31299], 3 X[32193] - X[33294]

X(44451) lies on these lines: {2, 669}, {5, 5926}, {140, 1499}, {230, 231}, {351, 850}, {420, 39201}, {423, 23864}, {512, 31286}, {525, 5113}, {659, 26114}, {804, 8651}, {1576, 18020}, {3005, 4108}, {3221, 24675}, {3265, 9479}, {3566, 24284}, {3589, 9009}, {3628, 39511}, {3837, 25511}, {4367, 27527}, {5972, 22103}, {5996, 8664}, {6563, 10190}, {6677, 10189}, {7234, 21051}, {7857, 23099}, {7907, 14824}, {8062, 9508}, {8644, 31277}, {8655, 30968}, {9147, 31072}, {9148, 15724}, {10104, 39518}, {18282, 32204}, {20979, 24674}, {21841, 39533}, {23655, 25636}, {24666, 24755}, {32193, 33294}

X(44451) = midpoint of X(i) and X(j) for these {i,j}: {5, 5926}, {669, 23301}, {8651, 30476}
X(44451) = reflection of X(39511) in X(3628)
X(44451) = complement of X(23301)
X(44451) = complement of the isotomic conjugate of X(3222)
X(44451) = X(i)-complementary conjugate of X(j) for these (i,j): {163, 6374}, {2998, 21253}, {3222, 2887}, {3223, 125}, {3224, 8287}, {3504, 34846}, {15389, 16573}, {34248, 115}
X(44451) = X(662)-isoconjugate of X(30496)
X(44451) = crosspoint of X(2) and X(3222)
X(44451) = crosssum of X(6) and X(3221)
X(44451) = crossdifference of every pair of points on line {3, 3229}
X(44451) = radical center of polar circles of {ABC, 1st Brocard triangle, 1st anti-Brocard triangle}
X(44451) = barycentric product X(523)*X(3552)
X(44451) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 30496}, {3552, 99}
X(44451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 669, 23301}, {2, 24533, 25126}, {669, 31176, 31299}

X(44452) = NINE-POINT-CIRCLE-OF-MEDIAL-TRIANGLE-POLE OF HATZIPOLAKIS AXIS

Barycentrics    2*a^10 - 5*a^8*b^2 + 2*a^6*b^4 + 4*a^4*b^6 - 4*a^2*b^8 + b^10 - 5*a^8*c^2 + 8*a^6*b^2*c^2 - 6*a^4*b^4*c^2 + 6*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 6*a^4*b^2*c^4 - 4*a^2*b^4*c^4 + 2*b^6*c^4 + 4*a^4*c^6 + 6*a^2*b^2*c^6 + 2*b^4*c^6 - 4*a^2*c^8 - 3*b^2*c^8 + c^10 : :
X(44452) = 3 X[2] + X[186], 9 X[2] - X[3153], 3 X[2] + 2 X[16531], 2 X[2] + X[18579], 5 X[2] + X[44265], 3 X[3] - X[16386], 3 X[3] + X[31726], X[4] + 3 X[37941], X[5] - 4 X[37911], X[23] + 11 X[3525], 2 X[140] + X[468], 3 X[140] + X[10096], 4 X[140] - X[15122], 8 X[140] + X[16619], 5 X[140] + X[25338], 6 X[140] + X[37971], 3 X[186] + X[3153], 2 X[186] - 3 X[18579], X[186] - 3 X[44214], 5 X[186] - 3 X[44265], 3 X[403] + X[16386], 3 X[403] - X[31726], 3 X[468] - 2 X[10096], 2 X[468] + X[15122], 4 X[468] - X[16619], 5 X[468] - 2 X[25338], 3 X[468] - X[37971], 3 X[549] + X[11563], 3 X[549] - 2 X[16976], 3 X[549] - X[34152], 3 X[549] + 2 X[37942], X[550] + 2 X[37984], 5 X[631] - X[2071], 5 X[631] + X[11799], 5 X[631] + 3 X[37943], 5 X[632] - 2 X[5159], 5 X[632] + X[7575], 5 X[632] + 3 X[16532], 5 X[632] + 2 X[37935], 5 X[632] - X[37938], X[858] - 7 X[3526], X[1370] + 3 X[37951], 5 X[1656] + X[10295], 5 X[1656] - X[18403], 5 X[1656] + 3 X[37955], X[2070] + 7 X[3526], X[2071] + 3 X[37943], 3 X[2072] - X[3153], X[2072] + 2 X[16531], 2 X[2072] + 3 X[18579], X[2072] + 3 X[44214], 5 X[2072] + 3 X[44265], 7 X[3090] + X[13619], 7 X[3090] - X[18323], 7 X[3090] + 5 X[37952], X[3153] + 6 X[16531], 2 X[3153] + 9 X[18579], X[3153] + 9 X[44214], 5 X[3153] + 9 X[44265], 7 X[3523] - 3 X[37948], 17 X[3533] - 5 X[30745], 17 X[3533] + 3 X[37940], X[3580] + 5 X[38794], 4 X[3628] - X[10297], 2 X[3628] + X[18571], 4 X[3628] + X[37931], 9 X[5054] - X[18859], 13 X[5067] - X[10296], 13 X[5067] + 3 X[35489], 2 X[5159] + X[7575], 2 X[5159] + 3 X[16532], X[5189] + 3 X[37939], X[5899] - 3 X[7426], X[5899] + 15 X[15694], 3 X[6688] - X[13376], X[7426] + 5 X[15694], X[7464] - 13 X[10303], X[7574] + 3 X[37922], X[7575] - 3 X[16532], 2 X[10096] + 3 X[10257], 4 X[10096] + 3 X[15122], 8 X[10096] - 3 X[16619], 5 X[10096] - 3 X[25338], X[10096] - 3 X[44234], X[10151] - 4 X[15350], X[10151] + 2 X[37968], 4 X[10257] + X[16619], 5 X[10257] + 2 X[25338], 3 X[10257] + X[37971], X[10257] + 2 X[44234], X[10295] - 3 X[37955], X[10296] + 3 X[35489], X[10297] + 2 X[18571], X[10540] + 3 X[15061], 9 X[11539] + X[37936], 8 X[11540] + X[37904], X[11558] + 3 X[12100], X[11563] + 2 X[16976], X[11563] - 3 X[44282], X[11799] - 3 X[37943], X[13399] - 5 X[38729], X[13619] - 5 X[37952], X[13851] - 3 X[23515], 7 X[14869] - X[37950], 7 X[14869] + X[43893], 5 X[15059] - X[25739], 2 X[15122] + X[16619], 5 X[15122] + 4 X[25338], 3 X[15122] + 2 X[37971], X[15122] + 4 X[44234], 2 X[15350] + X[37968], 2 X[15646] + X[23323], X[15646] + 4 X[37911], 21 X[15702] - X[37944], 3 X[15709] + X[37907], 27 X[15709] + X[37945], 5 X[15712] + X[44267], 5 X[15713] + X[44266], 11 X[15720] + X[18325], 2 X[16239] + X[22249], 4 X[16531] - 3 X[18579], 2 X[16531] - 3 X[44214], 10 X[16531] - 3 X[44265], 3 X[16532] - 2 X[37935], 3 X[16532] + X[37938], 5 X[16619] - 8 X[25338], 3 X[16619] - 4 X[37971], X[16619] - 8 X[44234], 2 X[16976] + 3 X[44282], X[18323] + 5 X[37952], X[18403] + 3 X[37955], X[18572] + 2 X[37934], 5 X[18579] - 2 X[44265], X[22115] - 5 X[38794], X[23323] - 8 X[37911], 6 X[25338] - 5 X[37971], X[25338] - 5 X[44234], 5 X[30745] + 3 X[37940], 5 X[31255] + 3 X[37917], X[32111] + 5 X[38728], X[34152] + 2 X[37942], X[34152] + 3 X[44282], X[34170] + 3 X[38719], 5 X[37760] - X[37925], X[37899] - 4 X[44264], X[37900] - 3 X[37956], 9 X[37907] - X[37945], 2 X[37935] + X[37938], 3 X[37941] - X[44246], 2 X[37942] - 3 X[44282], X[37971] - 6 X[44234], X[41724] + 3 X[43572], 5 X[44214] - X[44265]

X(44452) lies on these lines: {2, 3}, {49, 26879}, {113, 21663}, {389, 43839}, {511, 14156}, {1147, 32358}, {1154, 9826}, {1503, 34128}, {1568, 32110}, {3564, 15462}, {3580, 12228}, {5432, 10149}, {5462, 32411}, {5876, 44158}, {5907, 20191}, {5946, 23292}, {5972, 13754}, {6000, 6699}, {6102, 9820}, {6146, 32171}, {6688, 13376}, {6689, 11695}, {6716, 31379}, {6720, 16760}, {6723, 18400}, {7740, 39170}, {7749, 16306}, {10182, 18475}, {10272, 12825}, {10540, 15061}, {11449, 26917}, {11464, 26913}, {11589, 18809}, {11704, 12278}, {11744, 14677}, {12028, 34209}, {12038, 12370}, {12041, 15311}, {12095, 16221}, {12134, 13561}, {12241, 43394}, {13348, 13446}, {13363, 37649}, {13367, 43817}, {13391, 32269}, {13399, 38729}, {13491, 16252}, {13851, 23515}, {15059, 25739}, {15067, 44201}, {18439, 43607}, {18952, 19357}, {19129, 26156}, {20304, 30522}, {20376, 22804}, {21243, 43586}, {22104, 34840}, {22151, 34380}, {23332, 34514}, {26937, 32139}, {31945, 39005}, {32111, 38728}, {32415, 32767}, {34170, 38719}, {41724, 43572}

X(44452) = midpoint of X(i) and X(j) for these {i,j}: {2, 44214}, {3, 403}, {4, 44246}, {5, 15646}, {113, 21663}, {140, 44234}, {186, 2072}, {381, 44280}, {468, 10257}, {549, 44282}, {550, 44283}, {858, 2070}, {1368, 44272}, {1568, 32110}, {2071, 11799}, {3580, 22115}, {5159, 37935}, {7575, 37938}, {10295, 18403}, {10297, 37931}, {11563, 34152}, {11589, 18809}, {12095, 16221}, {13348, 13446}, {13619, 18323}, {15760, 44281}, {16386, 31726}, {16976, 37942}, {37950, 43893}
X(44452) = reflection of X(i) in X(j) for these {i,j}: {186, 16531}, {468, 44234}, {7575, 37935}, {10257, 140}, {11563, 37942}, {13473, 546}, {15122, 10257}, {18579, 44214}, {23323, 5}, {32411, 5462}, {34152, 16976}, {37931, 18571}, {37938, 5159}, {37947, 37897}, {37971, 10096}, {44283, 37984}
X(44452) = complement of X(2072)
X(44452) = circumcircle-inverse of X(7517)
X(44452) = nine-point-circle-inverse of X(13371)
X(44452) = polar-circle-inverse of X(7505)
X(44452) = orthoptic-circle-of-Steiner-inellipe-inverse of X(7391)
X(44452) = 2nd-Droz-Farny-circle-inverse of X(382)
X(44452) = ninepoint-circle-of-medial-triangle-inverse of X(5)
X(44452) = complement of the isogonal conjugate of X(38534)
X(44452) = X(38534)-complementary conjugate of X(10)
X(44452) = crossdifference of every pair of points on line {647, 8553}
X(44452) = radical trace of circumcircle and 1st Droz-Farny circle
X(44452) = X(44214)-of-Euler-triangle
X(44452) = X(23323)-of-Johnson-triangle
X(44452) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 186, 2072}, {2, 6644, 5}, {2, 35486, 18531}, {2, 37347, 3628}, {3, 381, 35481}, {3, 7505, 15761}, {3, 10018, 10020}, {3, 31726, 16386}, {3, 37197, 34350}, {3, 37453, 10201}, {4, 37941, 44246}, {5, 549, 18570}, {24, 6640, 13371}, {24, 13371, 11819}, {24, 30744, 31723}, {49, 26879, 43588}, {140, 468, 15122}, {140, 546, 5498}, {140, 6676, 549}, {140, 7542, 7568}, {140, 10020, 3}, {140, 10125, 7542}, {140, 13383, 16196}, {140, 16238, 5}, {140, 34004, 12108}, {140, 34577, 3530}, {140, 44232, 23336}, {186, 7514, 34152}, {186, 16531, 18579}, {186, 44214, 16531}, {381, 37118, 44236}, {403, 16386, 31726}, {427, 12106, 13490}, {427, 44211, 12106}, {468, 7499, 16387}, {468, 15122, 16619}, {468, 37971, 10096}, {549, 11563, 34152}, {549, 34152, 16976}, {631, 37943, 2071}, {632, 7575, 5159}, {632, 16532, 37938}, {1113, 1114, 7517}, {1312, 1313, 13371}, {1368, 34351, 7502}, {1656, 37955, 18403}, {2071, 37943, 11799}, {2072, 44214, 186}, {3090, 37952, 18323}, {3147, 3548, 26}, {3530, 34577, 34002}, {3628, 18571, 10297}, {3628, 31833, 5}, {5054, 9818, 18580}, {6640, 31723, 30744}, {7499, 16387, 16977}, {7568, 15122, 16977}, {7575, 16532, 37935}, {7577, 38321, 546}, {10226, 44235, 1885}, {11449, 26917, 44076}, {11563, 44282, 37942}, {13154, 37943, 37938}, {13383, 16196, 550}, {14070, 30771, 14791}, {14940, 22467, 10024}, {15350, 37968, 10151}, {16532, 37938, 7575}, {18324, 18531, 550}, {18403, 37955, 10295}, {18404, 32534, 44242}, {18531, 35486, 18324}, {23336, 44232, 4}, {30744, 31723, 13371}, {31664, 31665, 15122}, {31681, 31682, 3853}, {34152, 44282, 11563}, {34350, 37197, 3627}, {35231, 35232, 37814}, {42807, 42808, 35477}

X(44453) = 2ND-BROCARD-CIRCLE-POLE OF LEMOINE AXIS

Barycentrics    a^2*(a^2*b^2 - 2*b^4 + a^2*c^2 - b^2*c^2 - 2*c^4) : :
Trilinears    sin A - 2 sin(A + 2ω) : :
X(44453) = 3 X[6] - 4 X[39], 5 X[6] - 4 X[5052], 3 X[6] - 2 X[13330], 5 X[6] - 6 X[13331], 2 X[39] - 3 X[3094], 5 X[39] - 3 X[5052], 10 X[39] - 9 X[13331], 3 X[69] - X[20081], 2 X[76] - 3 X[599], 4 X[140] - 3 X[31958], 6 X[141] - 5 X[31276], 2 X[576] - 3 X[32447], 3 X[1350] - 2 X[9821], 5 X[1656] - 6 X[11261], 5 X[3094] - 2 X[5052], 3 X[3094] - X[13330], 5 X[3094] - 3 X[13331], 3 X[3097] - 2 X[4663], 5 X[3763] - 4 X[24256], 8 X[3934] - 9 X[21358], 6 X[5052] - 5 X[13330], 2 X[5052] - 3 X[13331], 3 X[7709] - 2 X[8550], 5 X[7786] - 3 X[22486], 7 X[10541] - 8 X[13334], 3 X[11160] + X[20105], 3 X[11179] - 4 X[32516], 5 X[13330] - 9 X[13331], 3 X[18906] - 5 X[31276]

X(44453) lies on these lines: {2, 20977}, {3, 6}, {69, 698}, {76, 338}, {115, 40107}, {140, 8179}, {141, 5025}, {183, 1916}, {193, 32449}, {194, 524}, {230, 6194}, {262, 7608}, {320, 33890}, {353, 9716}, {538, 5077}, {542, 7756}, {597, 33274}, {726, 17299}, {732, 33234}, {1078, 10754}, {1196, 36650}, {1569, 38741}, {1613, 2979}, {1656, 11261}, {1992, 14897}, {1993, 10329}, {2023, 22712}, {2162, 7186}, {2176, 3792}, {2393, 10568}, {2493, 40805}, {2549, 32515}, {2781, 32445}, {2782, 15069}, {2810, 38522}, {2854, 38523}, {2882, 4173}, {3056, 23633}, {3060, 8041}, {3097, 4663}, {3124, 7998}, {3231, 33884}, {3269, 15073}, {3291, 3917}, {3297, 12841}, {3298, 12840}, {3314, 8782}, {3399, 11170}, {3589, 7907}, {3618, 33259}, {3629, 33275}, {3763, 7887}, {3764, 23473}, {3767, 32521}, {3864, 5220}, {3906, 10097}, {3934, 7617}, {4643, 17760}, {5026, 7782}, {5108, 16055}, {5254, 12251}, {5475, 22695}, {5476, 31455}, {5480, 37446}, {5976, 7778}, {6034, 7746}, {6144, 32451}, {7492, 14567}, {7709, 8550}, {7747, 19924}, {7748, 11646}, {7757, 15534}, {7767, 31981}, {7776, 8149}, {7779, 10335}, {7783, 39099}, {7786, 22486}, {7788, 9865}, {7830, 14645}, {7866, 18806}, {7873, 37004}, {8288, 38397}, {8705, 36182}, {9009, 14824}, {9024, 38521}, {10007, 33233}, {10488, 11152}, {10766, 14585}, {11160, 20105}, {11179, 32516}, {11257, 32469}, {12837, 31477}, {13192, 16042}, {13881, 22677}, {15066, 20998}, {15080, 20976}, {15915, 16308}, {17042, 30489}, {20423, 31401}, {25235, 32465}, {25236, 32466}, {31670, 40279}, {32429, 39899}, {39024, 41462}

X(44453) = reflection of X(i) in X(j) for these {i,j}: {6, 3094}, {182, 43147}, {193, 32449}, {6144, 32451}, {10488, 11152}, {11477, 3095}, {13108, 34507}, {13330, 39}, {15534, 7757}, {18906, 141}, {33683, 32480}, {39899, 32429}
X(44453) = Brocard-circle-inverse of X(39560)
X(44453) = Ehrmann-circle-inverse of X(5111)
X(44453) = 2nd-Brocard-circle-inverse of X(187)
X(44453) = isogonal conjugate of the isotomic conjugate of X(7897)
X(44453) = crosssum of X(187) and X(8787)
X(44453) = circle-{{X(371),X(372),PU(1),PU(39)}}-inverse of X(11842)
X(44453) = barycentric product X(6)*X(7897)
X(44453) = barycentric quotient X(7897)/X(76)
X(44453) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 39560}, {6, 1350, 2076}, {39, 9821, 3053}, {39, 13330, 6}, {182, 5111, 6}, {371, 372, 11842}, {574, 576, 5038}, {574, 8586, 6}, {576, 5038, 6}, {1350, 10542, 3053}, {1670, 1671, 187}, {1689, 1690, 575}, {1691, 5028, 6}, {2023, 22712, 37637}, {2028, 8589, 1341}, {2029, 8589, 1340}, {2979, 20859, 1613}, {3053, 10542, 6}, {3060, 15302, 13410}, {3094, 8586, 32447}, {3094, 13330, 39}, {3098, 5028, 1691}, {3102, 3103, 11171}, {3104, 3105, 3}, {3917, 3981, 21001}, {5013, 11477, 6}, {5038, 8586, 576}, {5052, 13331, 6}, {5107, 37512, 575}, {5116, 15514, 6}, {7748, 34507, 11646}, {8041, 13410, 15302}, {12055, 37517, 6}, {13325, 13326, 39}, {22695, 22696, 22728}, {39229, 39230, 32}

X(44454) = STAMMLER-CIRCLE-POLE OF ORTHIC AXIS

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 24*a^4*b^2*c^2 + 10*a^2*b^4*c^2 + 16*b^6*c^2 + 10*a^2*b^2*c^4 - 30*b^4*c^4 + 2*a^2*c^6 + 16*b^2*c^6 - c^8) : :
X(44454) = 3 X[3] - 4 X[25], 7 X[3] - 8 X[6644], 5 X[3] - 8 X[7530], 13 X[3] - 16 X[12106], 5 X[3] - 4 X[21312], 7 X[25] - 6 X[6644], 5 X[25] - 6 X[7530], 13 X[25] - 12 X[12106], 2 X[25] - 3 X[18534], 5 X[25] - 3 X[21312], 3 X[381] - 2 X[1370], 8 X[1368] - 9 X[5055], 8 X[1596] - 7 X[3851], 7 X[3526] - 8 X[44233], 5 X[3843] - 4 X[18531], 5 X[6644] - 7 X[7530], 13 X[6644] - 14 X[12106], 4 X[6644] - 7 X[18534], 10 X[6644] - 7 X[21312], 16 X[6677] - 15 X[15694], 13 X[7530] - 10 X[12106], 4 X[7530] - 5 X[18534], 8 X[12106] - 13 X[18534], 20 X[12106] - 13 X[21312], 5 X[15693] - 6 X[26255], 7 X[15701] - 8 X[44212], 21 X[15703] - 20 X[31255], 7 X[15703] - 8 X[44275], 5 X[18534] - 2 X[21312], 5 X[19709] - 4 X[31152], 5 X[31255] - 6 X[44275]

X(44454) lies on these lines: {2, 3}, {51, 35237}, {159, 43621}, {1350, 16194}, {1384, 40237}, {1660, 9703}, {3531, 5644}, {3581, 35450}, {5621, 12295}, {6243, 12315}, {8193, 33697}, {8717, 10601}, {8780, 37477}, {10263, 12174}, {10625, 15811}, {12308, 14984}, {12902, 36201}, {13474, 37486}, {13598, 37493}, {14530, 37495}, {14855, 17810}, {14915, 33586}, {18435, 33878}, {18550, 43725}, {19005, 42226}, {19006, 42225}, {31670, 32621}, {35264, 43576}

X(44454) = reflection of X(i) in X(j) for these {i,j}: {3, 18534}, {1657, 18533}, {21312, 7530}, {35001, 37980}
X(44454) = Stammler-circle-inverse of X(468)
X(44454) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 33524, 7393}, {20, 7529, 3}, {25, 1370, 16419}, {378, 37945, 7387}, {381, 3534, 43957}, {382, 1657, 1885}, {382, 12083, 1597}, {382, 39568, 3}, {1597, 12083, 3}, {1597, 39568, 12083}, {1598, 1657, 3}, {3146, 37945, 378}, {3534, 5020, 3}, {3543, 12082, 9818}, {3845, 33532, 7484}, {9714, 12085, 3}, {15154, 15155, 468}, {15682, 37946, 22}, {15684, 37949, 3}, {17810, 33534, 14855}

X(44455) = STAMMLER-CIRCLE-POLE OF ANTI-ORTHIC AXIS

Barycentrics    a^2*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c + 8*a^2*b^2*c - 7*b^4*c - 2*a^3*c^2 + 8*a^2*b*c^2 - 14*a*b^2*c^2 + 8*b^3*c^2 + 2*a^2*c^3 + 8*b^2*c^3 + a*c^4 - 7*b*c^4 - c^5) : :
X(44455) = 3 X[3] - 4 X[55], 5 X[3] - 4 X[3428], 7 X[3] - 8 X[32613], 5 X[55] - 3 X[3428], 2 X[55] - 3 X[10679], 7 X[55] - 6 X[32613], 3 X[381] - 2 X[3434], 2 X[956] - 3 X[28444], 3 X[1482] - 2 X[25415], 8 X[2886] - 9 X[5055], 2 X[3428] - 5 X[10679], 7 X[3428] - 10 X[32613], 3 X[3830] - 2 X[18499], 5 X[3843] - 4 X[37820], 7 X[3851] - 8 X[7680], 16 X[6690] - 15 X[15694], 3 X[10247] - 4 X[37533], 7 X[10679] - 4 X[32613], 9 X[14269] - 8 X[18407], 21 X[15703] - 20 X[31245], 5 X[19709] - 4 X[31140], X[25415] - 3 X[37569]

X(44455) lies on these lines: {1, 3}, {8, 37234}, {30, 20075}, {42, 1480}, {355, 8168}, {381, 3434}, {390, 28459}, {519, 18519}, {528, 3830}, {956, 28444}, {1001, 3654}, {1012, 5844}, {1056, 28458}, {1376, 3656}, {1483, 37022}, {1537, 12331}, {1657, 37000}, {1824, 18535}, {2771, 41711}, {2886, 5055}, {3560, 12245}, {3621, 21669}, {3623, 37403}, {3632, 18761}, {3843, 37820}, {3851, 7680}, {3871, 6985}, {3913, 12699}, {3938, 7986}, {4301, 11499}, {5073, 5842}, {5080, 34629}, {5082, 6841}, {5274, 6882}, {5284, 5657}, {5434, 35249}, {5687, 22791}, {5905, 13278}, {6690, 15694}, {6765, 40263}, {6842, 8164}, {6890, 32214}, {6925, 32213}, {7580, 28212}, {8167, 26446}, {9708, 34718}, {9709, 18493}, {9812, 38665}, {10525, 11929}, {10528, 37406}, {10587, 44222}, {12607, 18542}, {12773, 25416}, {14269, 18407}, {15681, 34698}, {15703, 31245}, {16853, 25011}, {17784, 28452}, {18491, 31162}, {18524, 34647}, {18525, 32049}, {18543, 37356}, {19709, 31140}, {22758, 28234}, {25439, 28194}

X(44455) = reflection of X(i) in X(j) for these {i,j}: {3, 10679}, {1482, 37569}, {1657, 37000}, {6925, 32213}, {12702, 5119}
X(44455) = Stammler-circle-inverse of X(1155)
X(44455) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 40, 40296}, {1, 35448, 3}, {3, 1482, 12001}, {35, 35252, 3}, {40, 16202, 3}, {40, 37622, 16202}, {55, 25415, 999}, {56, 35251, 3}, {999, 10306, 35000}, {999, 35000, 3}, {1482, 10306, 3}, {1482, 12702, 65}, {1482, 35000, 999}, {3295, 12702, 3}, {3913, 12699, 18518}, {5537, 16200, 10269}, {6244, 10246, 3}, {7982, 11248, 10680}, {10222, 10310, 16203}, {10306, 22770, 40245}, {10310, 16203, 3}, {10680, 11248, 3}, {11248, 16207, 16203}, {11849, 22770, 3}, {35459, 37541, 3}, {37533, 37584, 11018}

X(44456) = STAMMLER-CIRCLE-POLE OF LEMOINE AXIS

Barycentrics    a^2*(a^4 - 8*a^2*b^2 + 7*b^4 - 8*a^2*c^2 - 2*b^2*c^2 + 7*c^4) : :
Trilinears    2 a - 3 R cot ω cos A : :
Trilinears    4 sin A - 3 cot ω cos A : :
X(44456) = 3 X[3] - 4 X[6], 7 X[3] - 8 X[182], 13 X[3] - 16 X[575], 5 X[3] - 8 X[576], 5 X[3] - 4 X[1350], 9 X[3] - 8 X[3098], 5 X[3] - 6 X[5050], 11 X[3] - 12 X[5085], 15 X[3] - 16 X[5092], 2 X[3] - 3 X[5093], 11 X[3] - 16 X[5097], 7 X[3] - 12 X[5102], 25 X[3] - 28 X[10541], X[3] - 4 X[11477], 7 X[3] - 10 X[11482], 9 X[3] - 10 X[12017], 17 X[3] - 16 X[14810], 25 X[3] - 32 X[15516], 17 X[3] - 24 X[15520], 23 X[3] - 24 X[17508], 29 X[3] - 32 X[20190], 31 X[3] - 40 X[22234], 23 X[3] - 32 X[22330], 13 X[3] - 12 X[31884], 3 X[3] - 2 X[33878], 3 X[3] - 8 X[37517], 19 X[3] - 24 X[39561], 3 X[4] - X[20080], 6 X[5] - 5 X[3620], 7 X[6] - 6 X[182], 13 X[6] - 12 X[575], 5 X[6] - 6 X[576], 5 X[6] - 3 X[1350], 2 X[6] - 3 X[1351], 3 X[6] - 2 X[3098], 10 X[6] - 9 X[5050], 11 X[6] - 9 X[5085], 5 X[6] - 4 X[5092], 8 X[6] - 9 X[5093], 11 X[6] - 12 X[5097], 7 X[6] - 9 X[5102], 25 X[6] - 21 X[10541], X[6] - 3 X[11477], 14 X[6] - 15 X[11482], 6 X[6] - 5 X[12017], 17 X[6] - 12 X[14810], 25 X[6] - 24 X[15516], 17 X[6] - 18 X[15520], 23 X[6] - 18 X[17508], 29 X[6] - 24 X[20190], 31 X[6] - 30 X[22234], 23 X[6] - 24 X[22330], 13 X[6] - 9 X[31884], 19 X[6] - 18 X[39561], 3 X[52] - 2 X[21851], 2 X[69] - 3 X[381], 3 X[69] - 4 X[18358], 2 X[74] - 3 X[39562], 8 X[141] - 9 X[5055], 2 X[141] - 3 X[20423], 13 X[182] - 14 X[575], 5 X[182] - 7 X[576], 10 X[182] - 7 X[1350], 4 X[182] - 7 X[1351], 9 X[182] - 7 X[3098], 20 X[182] - 21 X[5050], 22 X[182] - 21 X[5085], 15 X[182] - 14 X[5092], 16 X[182] - 21 X[5093], 11 X[182] - 14 X[5097], 2 X[182] - 3 X[5102], 50 X[182] - 49 X[10541], 2 X[182] - 7 X[11477], 4 X[182] - 5 X[11482], 36 X[182] - 35 X[12017], 17 X[182] - 14 X[14810], 25 X[182] - 28 X[15516], 17 X[182] - 21 X[15520], 23 X[182] - 21 X[17508], 29 X[182] - 28 X[20190], 31 X[182] - 35 X[22234], 23 X[182] - 28 X[22330], 26 X[182] - 21 X[31884], 12 X[182] - 7 X[33878], 3 X[182] - 7 X[37517], 19 X[182] - 21 X[39561], 3 X[193] - X[39874], 9 X[381] - 8 X[18358], 3 X[381] - 4 X[21850], 3 X[382] + 2 X[11008], 2 X[550] - 3 X[14912], 3 X[568] - 2 X[37511], 10 X[575] - 13 X[576], 20 X[575] - 13 X[1350], 8 X[575] - 13 X[1351], 18 X[575] - 13 X[3098], 40 X[575] - 39 X[5050], 44 X[575] - 39 X[5085], 15 X[575] - 13 X[5092], 32 X[575] - 39 X[5093], 11 X[575] - 13 X[5097], 28 X[575] - 39 X[5102], 100 X[575] - 91 X[10541], 4 X[575] - 13 X[11477], 56 X[575] - 65 X[11482], 72 X[575] - 65 X[12017], 17 X[575] - 13 X[14810], 25 X[575] - 26 X[15516], 34 X[575] - 39 X[15520], 46 X[575] - 39 X[17508], 29 X[575] - 26 X[20190], 62 X[575] - 65 X[22234], 23 X[575] - 26 X[22330], 4 X[575] - 3 X[31884], 24 X[575] - 13 X[33878], 6 X[575] - 13 X[37517], 38 X[575] - 39 X[39561], 4 X[576] - 5 X[1351], 9 X[576] - 5 X[3098], 4 X[576] - 3 X[5050], 22 X[576] - 15 X[5085], 3 X[576] - 2 X[5092], 16 X[576] - 15 X[5093], 11 X[576] - 10 X[5097], 14 X[576] - 15 X[5102], 10 X[576] - 7 X[10541], 2 X[576] - 5 X[11477], 28 X[576] - 25 X[11482], 36 X[576] - 25 X[12017], 17 X[576] - 10 X[14810], 5 X[576] - 4 X[15516], 17 X[576] - 15 X[15520], 23 X[576] - 15 X[17508], 29 X[576] - 20 X[20190], 31 X[576] - 25 X[22234], 23 X[576] - 20 X[22330], 26 X[576] - 15 X[31884], 12 X[576] - 5 X[33878], 3 X[576] - 5 X[37517], 19 X[576] - 15 X[39561], 8 X[597] - 7 X[15701], 3 X[599] - 4 X[19130], 4 X[599] - 5 X[19709], 2 X[1350] - 5 X[1351], 9 X[1350] - 10 X[3098], 2 X[1350] - 3 X[5050], 11 X[1350] - 15 X[5085], 3 X[1350] - 4 X[5092], 8 X[1350] - 15 X[5093], 11 X[1350] - 20 X[5097], 7 X[1350] - 15 X[5102], 5 X[1350] - 7 X[10541], X[1350] - 5 X[11477], 14 X[1350] - 25 X[11482], 18 X[1350] - 25 X[12017], 17 X[1350] - 20 X[14810], 5 X[1350] - 8 X[15516], 17 X[1350] - 30 X[15520], 23 X[1350] - 30 X[17508], 29 X[1350] - 40 X[20190], 31 X[1350] - 50 X[22234], 23 X[1350] - 40 X[22330], 13 X[1350] - 15 X[31884], 6 X[1350] - 5 X[33878], 3 X[1350] - 10 X[37517], 19 X[1350] - 30 X[39561], 9 X[1351] - 4 X[3098], 5 X[1351] - 3 X[5050], 11 X[1351] - 6 X[5085], 15 X[1351] - 8 X[5092], 4 X[1351] - 3 X[5093], 11 X[1351] - 8 X[5097], 7 X[1351] - 6 X[5102], 25 X[1351] - 14 X[10541], 7 X[1351] - 5 X[11482], 9 X[1351] - 5 X[12017], 17 X[1351] - 8 X[14810], 25 X[1351] - 16 X[15516], 17 X[1351] - 12 X[15520]

X(44456) lies on these lines: {3, 6}, {4, 11898}, {5, 3620}, {20, 1353}, {22, 11004}, {25, 323}, {30, 193}, {49, 10244}, {69, 381}, {74, 38263}, {141, 5055}, {159, 5899}, {206, 9703}, {382, 3564}, {383, 40901}, {394, 21969}, {399, 10752}, {517, 7996}, {518, 8148}, {524, 3830}, {542, 6144}, {550, 14912}, {597, 15701}, {599, 19130}, {895, 10620}, {1080, 40900}, {1154, 1597}, {1216, 3527}, {1352, 3630}, {1469, 7373}, {1482, 16496}, {1495, 3167}, {1503, 5073}, {1511, 19118}, {1598, 6403}, {1656, 3619}, {1657, 6776}, {1843, 18535}, {1974, 22115}, {1992, 3534}, {1993, 9909}, {1995, 16981}, {2104, 15155}, {2105, 15154}, {2781, 34777}, {2854, 12308}, {2979, 5644}, {2987, 5191}, {3056, 6767}, {3060, 5020}, {3426, 6391}, {3515, 38942}, {3517, 13421}, {3526, 10519}, {3528, 33748}, {3589, 14848}, {3618, 5054}, {3627, 5921}, {3629, 15681}, {3631, 3851}, {3751, 12702}, {3763, 5476}, {3818, 14269}, {3845, 11160}, {5032, 8703}, {5070, 14561}, {5072, 38136}, {5076, 39884}, {5095, 12121}, {5198, 15052}, {5422, 41462}, {5477, 38730}, {5544, 5650}, {5655, 32114}, {5847, 18525}, {5965, 36990}, {6033, 14645}, {6090, 10546}, {6329, 15707}, {6467, 35237}, {6515, 34609}, {6642, 14449}, {7484, 15018}, {7777, 40248}, {7788, 9993}, {8541, 35501}, {8584, 15695}, {8780, 37672}, {9306, 31860}, {9655, 39897}, {9668, 39873}, {9714, 19139}, {9924, 32063}, {10113, 32244}, {10246, 16491}, {10249, 39125}, {10601, 44107}, {10753, 13188}, {10754, 12188}, {10755, 12773}, {10756, 38574}, {10757, 38579}, {10758, 38572}, {10759, 12331}, {10760, 38589}, {10761, 38590}, {10762, 38591}, {10763, 38592}, {10764, 38573}, {10765, 38593}, {10766, 13115}, {10985, 40801}, {11002, 11284}, {11064, 21970}, {11174, 33706}, {11179, 15689}, {11180, 38335}, {11402, 15080}, {11412, 11479}, {11414, 15032}, {11456, 12160}, {11464, 16195}, {11470, 44091}, {11649, 37949}, {12083, 19459}, {12161, 41464}, {12164, 34382}, {12174, 12283}, {12220, 13391}, {12294, 18436}, {12295, 32272}, {12316, 39879}, {12601, 42283}, {12602, 42284}, {12699, 34379}, {12902, 34775}, {13093, 34788}, {13634, 37677}, {14531, 14914}, {14996, 19544}, {14997, 16434}, {15019, 21766}, {15533, 43150}, {15534, 15685}, {15696, 25406}, {15718, 38064}, {15720, 38110}, {15723, 38079}, {15988, 16418}, {17800, 29181}, {17811, 21849}, {17813, 35450}, {19140, 20987}, {19154, 34148}, {19277, 25898}, {20425, 42128}, {20426, 42125}, {24206, 42785}, {25321, 34153}, {28146, 39878}, {30771, 37643}, {31133, 37779}, {31152, 37644}, {32001, 44228}, {33533, 39522}, {33851, 38638}, {34207, 43704}, {37925, 41450}, {39893, 42263}, {39894, 42264}, {40107, 42786}, {40995, 44231}

X(44456) = reflection of X(i) in X(j) for these {i,j}: {3, 1351}, {6, 37517}, {20, 1353}, {69, 21850}, {399, 10752}, {1350, 576}, {1351, 11477}, {1657, 6776}, {3534, 1992}, {5921, 3627}, {6403, 10263}, {9821, 5052}, {9924, 34779}, {10620, 895}, {11160, 3845}, {11898, 4}, {12121, 5095}, {12188, 10754}, {12331, 10759}, {12702, 3751}, {12773, 10755}, {13115, 10766}, {13188, 10753}, {15154, 2105}, {15155, 2104}, {18436, 12294}, {18440, 31670}, {32244, 10113}, {32272, 12295}, {33878, 6}, {35002, 5107}, {35450, 17813}, {35456, 5111}, {35458, 15514}, {37484, 9967}, {38572, 10758}, {38573, 10764}, {38574, 10756}, {38579, 10757}, {38589, 10760}, {38590, 10761}, {38591, 10762}, {38592, 10763}, {38593, 10765}, {38730, 5477}, {39899, 193}, {40341, 3818}
X(44456) = Schoute-circle-inverse of X(5023)
X(44456) = Stammler-circle-inverse of X(187)
X(44456) = circle-{{X(371),X(372),PU(1),PU(39)}}-inverse of X(22331)
X(44456) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 5093}, {6, 1350, 5092}, {6, 3098, 12017}, {6, 5092, 5050}, {6, 11477, 37517}, {6, 33878, 3}, {6, 37517, 1351}, {15, 16, 5023}, {69, 21850, 381}, {182, 5102, 11482}, {371, 372, 22331}, {576, 1350, 5050}, {576, 5092, 6}, {1350, 5050, 3}, {1351, 5050, 576}, {1351, 11482, 5102}, {1351, 33878, 6}, {1384, 35002, 3}, {1993, 15107, 26864}, {2979, 9777, 16419}, {3098, 12017, 3}, {3167, 33586, 20850}, {3311, 3312, 5007}, {5017, 35458, 3}, {6199, 6395, 21309}, {6200, 6396, 5585}, {6221, 6398, 187}, {9605, 9821, 3}, {9732, 12314, 3}, {9733, 12313, 3}, {9777, 16419, 5644}, {9924, 34779, 32063}, {10519, 18583, 3526}, {10541, 15516, 5050}, {10625, 11432, 3}, {11426, 37486, 3}, {11485, 11486, 32}, {12017, 33878, 3098}, {15107, 26864, 9909}, {18440, 31670, 3830}, {22809, 22810, 382}, {35456, 40825, 3}, {37484, 37493, 3}, {38136, 40330, 5072}, {38596, 38597, 187}, {42115, 42116, 8588}

X(44457) = STAMMLER-CIRCLE-POLE OF DE LONGCHAMPS AXIS

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 14*a^4*b^2*c^2 + 8*a^2*b^4*c^2 + 8*b^6*c^2 + 8*a^2*b^2*c^4 - 14*b^4*c^4 + 2*a^2*c^6 + 8*b^2*c^6 - c^8) : :
X(44457) = 3 X[3] - 4 X[22], 5 X[3] - 4 X[378], 7 X[3] - 8 X[7502], 13 X[3] - 16 X[7555], X[3] - 4 X[12082], 9 X[3] - 8 X[18570], 5 X[22] - 3 X[378], 7 X[22] - 6 X[7502], 13 X[22] - 12 X[7555], X[22] - 3 X[12082], 2 X[22] - 3 X[12083], 3 X[22] - 2 X[18570], 7 X[378] - 10 X[7502], 13 X[378] - 20 X[7555], X[378] - 5 X[12082], 2 X[378] - 5 X[12083], 9 X[378] - 10 X[18570], 3 X[381] - 2 X[7391], 8 X[427] - 9 X[5055], 7 X[3526] - 8 X[25337], 3 X[3534] - 2 X[35481], 5 X[3843] - 4 X[31723], 7 X[3851] - 8 X[15760], 9 X[5054] - 8 X[44236], 16 X[6676] - 15 X[15694], 13 X[7502] - 14 X[7555], 2 X[7502] - 7 X[12082], 4 X[7502] - 7 X[12083], 9 X[7502] - 7 X[18570], 4 X[7555] - 13 X[12082], 8 X[7555] - 13 X[12083], 18 X[7555] - 13 X[18570], 9 X[12082] - 2 X[18570], 9 X[12083] - 4 X[18570], 9 X[14269] - 8 X[44288], 3 X[15684] - 4 X[35480], 9 X[15689] - 8 X[44249], 7 X[15701] - 8 X[44210], 21 X[15703] - 20 X[31236], 7 X[15703] - 8 X[44262], 9 X[15707] - 8 X[44218], 5 X[19709] - 4 X[31133], 5 X[31236] - 6 X[44262]

X(44457) lies on these lines: {2, 3}, {51, 8717}, {154, 37477}, {161, 2777}, {1350, 18435}, {1384, 19220}, {1498, 37484}, {1619, 9919}, {2781, 12308}, {2936, 38730}, {3098, 16194}, {3167, 37496}, {3581, 33534}, {4316, 9673}, {4324, 9658}, {5210, 40237}, {6000, 37494}, {6445, 13889}, {6446, 13943}, {8718, 12161}, {9609, 43618}, {9683, 42272}, {10540, 37483}, {11456, 13391}, {12367, 33878}, {12902, 37488}, {13340, 18451}, {13598, 36753}, {15177, 28168}, {17810, 40280}, {18439, 37486}, {26881, 43576}, {28208, 37546}, {33586, 35237}, {33697, 37557}, {33974, 34106}

X(44457) = reflection of X(i) in X(j) for these {i,j}: {3, 12083}, {12083, 12082}
X(44457) = Stammler-circle-inverse of X(858)
X(44457) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15684, 1597}, {3, 18535, 5055}, {3, 19709, 16419}, {3, 37949, 18534}, {4, 16661, 7516}, {20, 7517, 3}, {20, 37925, 6644}, {22, 7391, 7484}, {25, 3534, 3}, {376, 37945, 7530}, {381, 35243, 3}, {382, 1657, 12225}, {382, 11414, 3}, {382, 34864, 11403}, {550, 7506, 3}, {1593, 13564, 3}, {1656, 37198, 3}, {1657, 2070, 21312}, {1657, 7387, 3}, {2070, 21312, 3}, {2937, 12085, 3}, {3529, 12087, 26}, {3534, 37924, 25}, {5059, 12088, 12084}, {5899, 15681, 3}, {6636, 15682, 31861}, {6642, 15696, 3}, {6644, 37925, 7517}, {7387, 21312, 2070}, {7464, 37913, 18324}, {7492, 15640, 13596}, {13730, 16117, 3}, {14070, 18859, 3}, {15154, 15155, 858}, {18534, 39568, 37949}

X(44458) = STAMMLER-CIRCLES-RADICAL-CIRCLE-POLE OF DE LONGCHAMPS AXIS

Barycentrics    2*a^10 - 3*a^8*b^2 - 2*a^6*b^4 + 4*a^4*b^6 - b^10 - 3*a^8*c^2 + 18*a^6*b^2*c^2 - 12*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 12*a^4*b^2*c^4 + 12*a^2*b^4*c^4 - 2*b^6*c^4 + 4*a^4*c^6 - 6*a^2*b^2*c^6 - 2*b^4*c^6 + 3*b^2*c^8 - c^10 : :
X(44458) = 5 X[2] - 3 X[37077], 4 X[3] - X[18560], 5 X[4] - 8 X[9825], X[4] - 4 X[31829], 2 X[20] + X[6240], 3 X[376] - 2 X[7667], 4 X[548] - X[18563], 4 X[550] - X[12225], 5 X[631] - 2 X[1885], 7 X[3090] - 4 X[13488], X[3146] - 4 X[31833], 5 X[3522] - 2 X[12605], 9 X[3524] - 8 X[7734], 3 X[3524] - 2 X[34664], 7 X[3528] - 4 X[12362], X[3529] + 2 X[3575], 3 X[3839] - 4 X[10127], X[5059] + 2 X[7553], 15 X[5071] - 16 X[13361], X[5073] - 4 X[31830], 4 X[6756] - X[33703], 4 X[7540] - 5 X[7576], 6 X[7540] - 5 X[34603], 8 X[7540] - 5 X[34613], 2 X[7540] - 3 X[38320], 3 X[7540] - 5 X[38321], 7 X[7540] - 10 X[38322], 2 X[7540] - 5 X[38323], 3 X[7576] - 2 X[34603], 5 X[7576] - 6 X[38320], 3 X[7576] - 4 X[38321], 7 X[7576] - 8 X[38322], 4 X[7734] - 3 X[34664], 2 X[9825] - 5 X[31829], 8 X[10128] - 7 X[41106], 2 X[10575] + X[14516], X[10625] + 2 X[43577], 4 X[10691] - 5 X[19708], 2 X[11819] + X[17800], 2 X[12134] + X[12279], 3 X[14269] - 4 X[23410], 3 X[15045] - 2 X[16657], 3 X[15688] - X[18564], 5 X[15695] - X[18561], 5 X[15696] + X[18565], 7 X[15698] - 6 X[43957], 5 X[17538] + X[34797], 4 X[34603] - 3 X[34613], 5 X[34603] - 9 X[38320], 7 X[34603] - 12 X[38322], X[34603] - 3 X[38323], 5 X[34613] - 12 X[38320], 3 X[34613] - 8 X[38321], 7 X[34613] - 16 X[38322], X[34613] - 4 X[38323], 9 X[38320] - 10 X[38321], 21 X[38320] - 20 X[38322], 3 X[38320] - 5 X[38323], 7 X[38321] - 6 X[38322], 2 X[38321] - 3 X[38323], 4 X[38322] - 7 X[38323]

X(44458) lies on these lines: {2, 3}, {74, 343}, {541, 12825}, {542, 17854}, {599, 34778}, {1993, 4846}, {2777, 3917}, {5306, 41336}, {5434, 9627}, {8718, 34782}, {9306, 32111}, {10192, 15035}, {10575, 14516}, {10625, 43577}, {10706, 11744}, {11057, 14615}, {11454, 44201}, {11459, 15311}, {11645, 14913}, {12134, 12279}, {12827, 16111}, {14855, 17702}, {15045, 16657}, {22466, 43836}, {22802, 43652}, {28208, 34668}, {41587, 43601}

X(44458) = midpoint of X(11001) and X(18559)
X(44458) = reflection of X(i) in X(j) for these {i,j}: {382, 13490}, {7576, 38323}, {15682, 428}, {34603, 38321}, {34613, 7576}
X(44458) = 2nd-Droz-Farny-circle-inverse of X(7464)
X(44458) = Stammler-circles-radical-circle-inverse of X(858)
X(44458) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 20, 35491}, {3, 34350, 34005}, {20, 6636, 44249}, {20, 16661, 550}, {376, 7552, 37948}, {403, 35491, 378}, {550, 15760, 2071}, {2043, 2044, 11413}, {2071, 15760, 37118}, {3534, 34609, 21312}, {3547, 30552, 35477}, {6240, 35491, 18560}, {7512, 16661, 10323}, {7540, 38320, 7576}, {7552, 37948, 549}, {8703, 34477, 3}, {10154, 44241, 44268}, {10154, 44268, 186}, {18533, 35513, 12082}, {34603, 38321, 7576}, {34603, 38323, 38321}

X(44459) = CIRCUMCIRCLE-OF-INNER-NAPOLEON-TRIANGLE-POLE OF ORTHIC AXIS

Barycentrics    Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2 + b^2 + c^2) - 4*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*S : :
X(44459) = 5 X[631] - 6 X[11297], 7 X[3090] - 6 X[11298], 3 X[3545] - 2 X[11296], 4 X[3642] - 5 X[40330], 4 X[3643] - 3 X[10519], 2 X[10653] - 3 X[14853], X[39874] - 4 X[42117]

X(44459) lies on these lines: {2, 3}, {13, 36994}, {14, 41458}, {15, 36962}, {396, 41039}, {531, 11180}, {538, 36323}, {621, 32815}, {633, 32836}, {1503, 42154}, {2549, 5334}, {2794, 6770}, {3642, 40330}, {3643, 10519}, {5335, 7737}, {5478, 33388}, {5479, 18581}, {5480, 42155}, {5617, 23698}, {5868, 42164}, {5869, 42147}, {6108, 9752}, {6775, 43404}, {6776, 10654}, {7739, 42999}, {9735, 22797}, {10614, 36995}, {10653, 14853}, {14981, 35696}, {16242, 41037}, {22491, 41044}, {22513, 42134}, {23004, 43452}, {23235, 35691}, {32515, 40898}, {39874, 42117}, {41021, 41108}, {41022, 42085}, {41025, 42529}, {41038, 42940}, {42133, 43619}

X(44459) = reflection of X(i) in X(j) for these {i,j}: {376, 11295}, {6770, 6772}, {6773, 22512}, {6776, 10654}, {42155, 5480}, {44463, 4}
X(44459) = circumcircle-of-inner-Napoleon-triangle-inverse of X(468)
X(44459) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 376, 383}, {2043, 2044, 37173}, {2549, 22512, 5334}, {3830, 41016, 4}

X(44460) = CIRCUMCIRCLE-OF-INNER-NAPOLEON-TRIANGLE-POLE OF LEMOINE AXIS

Barycentrics    (a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2)*(2*a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4) - 2*Sqrt[3]*a^2*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*S : :
X(44460) = 3 X[2] - 4 X[33478], 2 X[2] + X[36323], 4 X[2] - X[36345], 5 X[2] - 2 X[36364], X[2] + 2 X[36384], X[4] + 2 X[3104], X[6194] - 4 X[33463], 4 X[22715] + 3 X[36323], 8 X[22715] - 3 X[36345], 5 X[22715] - 3 X[36364], X[22715] + 3 X[36384], 8 X[33478] + 3 X[36323], 16 X[33478] - 3 X[36345], 10 X[33478] - 3 X[36364], 2 X[33478] + 3 X[36384], 2 X[36323] + X[36345], 5 X[36323] + 4 X[36364], X[36323] - 4 X[36384], 5 X[36345] - 8 X[36364], X[36345] + 8 X[36384], X[36364] + 5 X[36384]

X(44460) lies on these lines: {2, 51}, {4, 3104}, {15, 33389}, {16, 10788}, {39, 42999}, {61, 33388}, {76, 43953}, {194, 22114}, {298, 20426}, {618, 36780}, {621, 37242}, {627, 3095}, {3094, 16940}, {3105, 42149}, {3106, 6773}, {3107, 37641}, {5334, 22707}, {5335, 31701}, {6782, 32465}, {7684, 22696}, {7737, 22708}, {9993, 41071}, {14538, 35925}, {14651, 43454}, {14881, 33413}, {18581, 43539}, {18582, 22701}, {22688, 40693}, {22691, 37640}, {32447, 37785}, {35917, 39656}, {41070, 43461}

X(44460) = midpoint of X(3104) and X(22693)
X(44460) = reflection of X(i) in X(j) for these {i,j}: {4, 22693}, {6194, 22714}, {7709, 3106}, {22686, 33479}, {22714, 33463}, {22715, 33478}, {36780, 618}, {44464, 262}
X(44460) = anticomplement of X(22715)
X(44460) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36323, 36345}, {2, 36384, 36323}, {11261, 22714, 2}, {22715, 33478, 2}

X(44461) = CIRCUMCIRCLE-OF-INNER-NAPOLEON-TRIANGLE-POLE OF DE LONGCHAMPS AXIS

Barycentrics    Sqrt[3]*a^2*(a^2 - b^2 - c^2)*(a^2 + b^2 + c^2) - 2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*S : :
X(44461) = 2 X[5] - 3 X[11298], 4 X[140] - 3 X[11297], 2 X[3098] + X[42086], 3 X[5085] - X[42154], 4 X[5092] - X[42085], 5 X[12017] - 2 X[42117], X[33878] + 2 X[42118]

X(44461) lies on these lines: {2, 3}, {13, 14539}, {15, 2549}, {16, 7737}, {61, 7739}, {182, 6775}, {397, 5865}, {511, 10653}, {531, 11179}, {538, 36364}, {616, 36995}, {617, 2782}, {621, 6773}, {627, 22531}, {1350, 42155}, {1352, 3642}, {2794, 5617}, {3098, 22513}, {3180, 32515}, {3734, 5613}, {5085, 42154}, {5092, 42085}, {5238, 22843}, {5334, 13102}, {5335, 20425}, {5344, 16629}, {5611, 37640}, {5864, 42148}, {5873, 32836}, {5978, 9744}, {5980, 14907}, {5981, 11185}, {6771, 6772}, {6774, 18581}, {7694, 9750}, {9988, 36998}, {10645, 21156}, {10646, 43618}, {10992, 35696}, {11092, 18911}, {11485, 15048}, {11486, 18907}, {12017, 42117}, {14538, 36968}, {14540, 42158}, {14541, 16965}, {16002, 41113}, {16242, 21159}, {18582, 36756}, {20416, 41120}, {20426, 37641}, {21157, 37835}, {21158, 42529}, {21163, 31702}, {21467, 40280}, {22687, 41022}, {22891, 31703}, {33878, 42118}, {36755, 42091}, {36759, 43455}

X(44461) = midpoint of X(1350) and X(42155)
X(44461) = reflection of X(i) in X(j) for these {i,j}: {1352, 3642}, {6772, 6771}, {10654, 182}, {11295, 549}, {22512, 6774}, {44465, 3}
X(44461) = circumcircle-of-inner-Napoleon-triangle-inverse of X(858)
X(44461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 37178, 5}, {11303, 35917, 2}, {15765, 18585, 11306}

X(44462) = CIRCUMCIRCLE-OF-INNER-NAPOLEON-TRIANGLE-POLE OF HATZIPOLAKIS AXIS

Barycentrics    Sqrt[3]*a^2*(a^4 - b^4 + b^2*c^2 - c^4) - 2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*S : :
X(44462) = 3 X[2] - 4 X[32460], X[5189] - 4 X[37975], 4 X[32461] - 5 X[37760]

X(44462) lies on these lines: {2, 3}, {14, 14169}, {62, 8015}, {299, 2453}, {476, 16770}, {523, 3180}, {531, 9143}, {621, 35315}, {691, 34376}, {3448, 11092}, {5474, 11130}, {5479, 8836}, {5612, 8173}, {5617, 14187}, {6773, 16771}, {6774, 41473}, {6800, 42154}, {7712, 42085}, {10653, 11002}, {10654, 11003}, {11549, 37641}, {14170, 36967}, {16529, 22738}, {19106, 30468}, {21466, 30466}, {22492, 34316}, {30485, 36993}, {36210, 40694}, {36962, 40710}, {40855, 41022}

X(44462) = reflection of X(i) in X(j) for these {i,j}: {3448, 11092}, {5189, 36186}, {36185, 32460}, {36186, 37975}, {44466, 23}
X(44462) = anticomplement of X(36185)
X(44462) = circumcircle-inverse of X(11145)
X(44462) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(383)
X(44462) = circumcircle-ofinner-Napoleon-triangle-inverse of X(5)
X(44462) = circumcircle-of-outer-Napoleon-triangle-inverse of X(44223)
X(44462) = psi-transform of X(6774)
X(44462) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36181, 44466}, {1113, 1114, 11145}, {1316, 36186, 2}, {32460, 36185, 2}

X(44463) = CIRCUMCIRCLE-OF-OUTER-NAPOLEON-TRIANGLE-POLE OF ORTHIC AXIS

Barycentrics    Sqrt[3]*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2+b^2+c^2)+4*(2*a^4-a^2*b^2-b^4-a^2*c^2+2*b^2*c^2-c^4)*S : :
X(44463) = 5 X[631] - 6 X[11298], 7 X[3090] - 6 X[11297], 3 X[3545] - 2 X[11295], 4 X[3642] - 3 X[10519], 4 X[3643] - 5 X[40330], 2 X[10654] - 3 X[14853], X[39874] - 4 X[42118]

X(44463) lies on these lines: {2, 3}, {13, 36761}, {14, 36992}, {16, 36961}, {395, 41038}, {530, 11180}, {538, 36322}, {622, 32815}, {634, 32836}, {1503, 42155}, {2549, 5335}, {2794, 6773}, {3642, 10519}, {3643, 40330}, {5334, 7737}, {5478, 18582}, {5479, 33389}, {5480, 42154}, {5613, 23698}, {5868, 42148}, {5869, 42165}, {6109, 9752}, {6772, 43403}, {6776, 10653}, {7739, 42998}, {9736, 22796}, {10613, 36993}, {10654, 14853}, {14981, 35692}, {16241, 41036}, {22492, 36775}, {22512, 42133}, {23005, 43451}, {23235, 35695}, {32515, 40899}, {39874, 42118}, {41020, 41107}, {41023, 42086}, {41024, 42528}, {41039, 42941}, {42134, 43619}

X(44463) = reflection of X(i) in X(j) for these {i,j}: {376, 11296}, {6770, 22513}, {6773, 6775}, {6776, 10653}, {42154, 5480}, {44459, 4}
X(44463) = circumcircle-of-outer-Napoleon-triangle-inverse of X(468)
X(44463) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 376, 1080}, {2043, 2044, 37172}, {2549, 22513, 5335}, {3830, 41017, 4}

X(44464) = CIRCUMCIRCLE-OF-OUTER-NAPOLEON-TRIANGLE-POLE OF LEMOINE AXIS

Barycentrics    (a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2)*(2*a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4) + 2*Sqrt[3]*a^2*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*S : :
X(44464) = 3 X[2] - 4 X[33479], 2 X[2] + X[36322], 4 X[2] - X[36347], 5 X[2] - 2 X[36365], X[2] + 2 X[36385], X[4] + 2 X[3105], X[6194] - 4 X[33462], 4 X[22714] + 3 X[36322], 8 X[22714] - 3 X[36347], 5 X[22714] - 3 X[36365], X[22714] + 3 X[36385], 8 X[33479] + 3 X[36322], 16 X[33479] - 3 X[36347], 10 X[33479] - 3 X[36365], 2 X[33479] + 3 X[36385], 2 X[36322] + X[36347], 5 X[36322] + 4 X[36365], X[36322] - 4 X[36385], 5 X[36347] - 8 X[36365], X[36347] + 8 X[36385], X[36365] + 5 X[36385]

X(44464) lies on these lines: {2, 51}, {4, 3105}, {15, 10788}, {16, 33388}, {39, 42998}, {62, 33389}, {76, 43954}, {194, 22113}, {299, 20425}, {622, 37242}, {628, 3095}, {3094, 16941}, {3104, 42152}, {3106, 37640}, {3107, 6770}, {3643, 36780}, {5334, 31702}, {5335, 22708}, {6783, 32466}, {7685, 22695}, {7737, 22707}, {9993, 41070}, {14539, 35925}, {14651, 43455}, {14881, 33412}, {18581, 22702}, {18582, 43538}, {22690, 40694}, {22692, 37641}, {32447, 37786}, {35918, 39656}, {41071, 43461}

X(44464) = midpoint of X(3105) and X(22694)
X(44464) = reflection of X(i) in X(j) for these {i,j}: {4, 22694}, {6194, 22715}, {7709, 3107}, {22684, 33478}, {22714, 33479}, {22715, 33462}, {44460, 262}
X(44464) = anticomplement of X(22714)
X(44464) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36322, 36347}, {2, 36385, 36322}, {11261, 22715, 2}, {22714, 33479, 2}

X(44465) = CIRCUMCIRCLE-OF-OUTER-NAPOLEON-TRIANGLE-POLE OF DE LONGCHAMPS AXIS

Barycentrics    Sqrt[3]*a^2*(a^2 - b^2 - c^2)*(a^2 + b^2 + c^2) + 2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*S : :
X(44465) = 2 X[5] - 3 X[11297], 4 X[140] - 3 X[11298], 2 X[3098] + X[42085], 3 X[5085] - X[42155], 4 X[5092] - X[42086], 5 X[12017] - 2 X[42118], X[33878] + 2 X[42117]

X(44465) lies on these lines: {2, 3}, {14, 14538}, {15, 7737}, {16, 2549}, {62, 7739}, {182, 6772}, {398, 5864}, {511, 10654}, {530, 11179}, {538, 36365}, {616, 2782}, {617, 36993}, {622, 6770}, {628, 22532}, {1350, 42154}, {1352, 3643}, {2794, 5613}, {3098, 22512}, {3181, 32515}, {3734, 5617}, {5085, 42155}, {5092, 42086}, {5237, 22890}, {5334, 20426}, {5335, 13103}, {5343, 16628}, {5615, 37641}, {5865, 42147}, {5872, 32836}, {5979, 9744}, {5980, 11185}, {5981, 14907}, {6771, 18582}, {6774, 6775}, {7694, 9749}, {9989, 36998}, {10645, 43618}, {10646, 21157}, {10992, 35692}, {11078, 18911}, {11485, 18907}, {11486, 15048}, {12017, 42118}, {14539, 36967}, {14540, 16964}, {14541, 42157}, {16001, 41112}, {16241, 21158}, {18581, 36755}, {20415, 41119}, {20425, 37640}, {21156, 37832}, {21159, 42528}, {21163, 31701}, {21466, 40280}, {22689, 41023}, {22846, 31704}, {33878, 42117}, {36756, 42090}, {36760, 43454}

X(44465) = midpoint of X(1350) and X(42154)
X(44465) = reflection of X(i) in X(j) for these {i,j}: {1352, 3643}, {6775, 6774}, {10653, 182}, {11296, 549}, {22513, 6771, {44461, 3}
X(44465) = circumcircle-of-outer-Napoleon-triangle-inverse of X(858)
X(44465) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3534, 44250}, {4, 37177, 5}, {11304, 35918, 2}, {15765, 18585, 11305}

X(44466) = CIRCUMCIRCLE-OF-OUTER-NAPOLEON-TRIANGLE-POLE OF HATZIPOLAKIS AXIS

Barycentrics    Sqrt[3]*a^2*(a^4 - b^4 + b^2*c^2 - c^4) + 2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*S : :
X(44466) = 3 X[2] - 4 X[32461], X[5189] - 4 X[37974], 4 X[32460] - 5 X[37760]

X(44466) lies on these lines: {2, 3}, {13, 14170}, {61, 8014}, {298, 2453}, {476, 16771}, {523, 3181}, {530, 9143}, {622, 35314}, {691, 34374}, {3448, 11078}, {5473, 11131}, {5478, 8838}, {5613, 14185}, {5616, 8172}, {6770, 16770}, {6771, 41472}, {6800, 42155}, {7712, 42086}, {10653, 11003}, {10654, 11002}, {11537, 37640}, {14169, 36968}, {16530, 22739}, {19107, 30465}, {21467, 30469}, {22491, 34315}, {30486, 36995}, {36211, 40693}, {36961, 40709}, {40854, 41023}

X(44466) = anticomplement of X(36186)
X(44466) = reflection of X(i) in X(j) for these {i,j}: {3448, 11078}, {5189, 36185}, {36185, 37974}, {36186, 32461}, {44462, 23}
X(44466) = circumcircle-inverse of X(11146)
X(44466) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(1080)
X(44466) = circumcircle-of-anticomplementary-triangle-inverse of X(10210)
X(44466) = circumcircle-of-outer-Napoleon-triangle-inverse of X(5)
X(44466) = psi-transform of X(6771)
X(44466) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36181, 44462}, {1113, 1114, 11146}, {1316, 36185, 2}, {14807, 14808, 10210}, {32461, 36186, 2}

X(44467) = MOSES-PARRY-CIRCLE-POLE OF EULER LINE

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4*b^2 - b^6 + a^4*c^2 - 4*a^2*b^2*c^2 + 2*b^4*c^2 + 2*b^2*c^4 - c^6) : :

X(44467) is the intersection of the diagonals of cyclic quadrilateral X(111)X(112)X(115)X(1560). (Randy Hutson, September 30, 2021)

X(44467) lies on these lines: {2, 339}, {6, 5505}, {25, 111}, {115, 427}, {186, 11580}, {187, 37969}, {230, 231}, {250, 15398}, {1112, 3124}, {1611, 2079}, {3162, 8770}, {5094, 8426}, {5523, 5913}, {6791, 12828}, {8744, 37962}, {8749, 9717}, {10301, 33842}, {10311, 15364}, {10317, 37980}, {10766, 15106}, {12824, 36828}, {13595, 36415}, {13854, 40347}, {19504, 39024}, {28662, 41618}, {32740, 41616}, {34809, 40126}, {39575, 39576}

X(44467) = Moses-Parry-circle-inverse of X(468)
X(44467) = polar conjugate of the isotomic conjugate of X(2854)
X(44467) = X(40119)-Ceva conjugate of X(25)
X(44467) = PU(4)-harmonic conjugate of X(2492)
X(44467) = radical center of {circumcircle, nine-point circle, Moses-Parry circle}
X(44467) = X(i)-isoconjugate of X(j) for these (i,j): {63, 2770}, {69, 36150}, {304, 32741}, {34055, 36824}
X(44467) = crossdifference of every pair of points on line {3, 14417}
X(44467) = barycentric product X(i)*X(j) for these {i,j}: {4, 2854}, {232, 37858}, {523, 7482}, {9177, 17983}, {31655, 40119}
X(44467) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 2770}, {1843, 36824}, {1973, 36150}, {1974, 32741}, {2854, 69}, {5140, 34171}, {7482, 99}, {9177, 6390}
X(44467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 41676, 34336}, {111, 112, 25}, {115, 1560, 427}, {2079, 8428, 21213}, {3018, 6103, 16318}, {3124, 35325, 1112}, {3291, 14580, 468}, {8105, 8106, 468}, {8426, 8427, 5094}, {16317, 16318, 468}

X(44468) = MOSES-PARRY-CIRCLE-POLE OF FERMAT LINE

Barycentrics    a^2*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 + 3*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 - 8*b^4*c^4 - a^2*c^6 + 3*b^2*c^6 + c^8) : :

X(44468) lies on these lines: {5, 39}, {6, 5663}, {30, 3003}, {111, 5024}, {112, 1593}, {187, 37950}, {230, 15122}, {232, 37984}, {246, 39024}, {543, 34990}, {566, 2549}, {690, 2492}, {1597, 8749}, {1989, 7739}, {2079, 15815}, {3053, 12084}, {3269, 16270}, {3291, 5159}, {3767, 18281}, {5094, 8426}, {5305, 6103}, {5309, 44287}, {5523, 37981}, {6593, 13233}, {6749, 18907}, {6772, 40695}, {6775, 40696}, {7514, 14910}, {8552, 14566}, {10766, 32251}, {13596, 18373}, {39832, 40121}

X(44468) = complement of isotomic conjugate of X(9139)
X(44468) = X(i)-complementary conjugate of X(j) for these (i,j): {923, 113}, {2159, 126}, {9139, 2887}, {36119, 34517}, {40352, 16597}
X(44468) = crosspoint of X(2) and X(9139)
X(44468) = crosssum of X(6) and X(5642)
X(44468) = crossdifference of every pair of points on line {2930, 9003}
X(44468) = {X(39),X(115)}-harmonic conjugate of X(2493)

leftri

Lozada-Lemoine circles: X(44469)-X(44514)

rightri

This preamble and centers X(44469)-X(44514), based on a construction by Anton Zakharov in Mathoverflow, were contributed by César Eliud Lozada, August 28, 2021.

In the three following constructions, let K be the symmedian point X(6)-of-ABC and T' = A'B'C' a triangle.

  1. Let Ab = B'C' ∩ AC and Ac = B'C' ∩ AB, and define Bc, Ca, Ba, Cb cyclically.

    1. The circle {{K, Ab, Ac}} cuts again AC and AB in A'b and A'c, respectively, and points B'c, C'a, B'a, C'b are defined similarly. For some triangles T' these last six points lie on a circle here named Lozada-Lemoine-circles-1A of T'.

      The appearance of (T', n) in the following list means that for triangle T' the corresponding circle has center X(n):

      (anti-Conway, 44469), (2nd anti-Conway, 44470), (anti-inner-Grebe, 44471), (anti-outer-Grebe, 44472), (anti-Honsberger, 6), (inner-Grebe, 44473), (outer-Grebe, 44474), (1st Kenmotu diagonals, 44475), (2nd Kenmotu diagonals, 44476), (inner tri-equilateral, 44477), (outer tri-equilateral, 44478) (1)

      (1): All listed triangles are perspective to ABC with perspector X(6), however, this is not a sufficient condition leading to the described circle.

    2. The circle {{K, Cb, Bc}} cuts again AC and AB in A'b and A'c, respectively, and points B'c, C'a, B'a, C'b are defined similarly. For some triangles T' these last six points lie on a circle here named Lozada-Lemoine-circles-1B of T'.

      The appearance of (T', n) in the following list means that for triangle T' the corresponding circle has center X(n):

      (anti-Conway, 44479), (2nd anti-Conway, 44480), (anti-inner-Grebe, 44481), (anti-outer-Grebe, 44482), (anticomplementary, 576), (Bevan antipodal, 576), (2nd Ehrmann, 575), (excentral, 576), (inner-Grebe, 44483), (outer-Grebe, 44484), (1st Kenmotu diagonals, 44485), (2nd Kenmotu diagonals, 44486), (Largest-circumscribed-equilateral, 576), (Moses-Soddy, 576), (Pelletier, 576), (Schroeter, 576), (Soddy, 576), (tangential, 576), (inner tri-equilateral, 44487), (outer tri-equilateral, 44488), (X-parabola-tangential, 576), (Yiu tangents, 576)

  2. Now, let Ab, Ac be the orthogonal projections of A' in AC and AB, respectively, and define Bc, Ca, Ba, Cb cyclically.

    1. For certain triangles T', points A'b, A'c, B'a, B'c, C'a, C'b defined similarly as in (1a), lie on a circle, here named Lozada-Lemoine-circles-2A of T'.

      The appearance of (T', n) in the following list means that for triangle T' the corresponding circle has center X(n):

      (ABC-X3 reflections, 576), (midheight, 44489), (orthic, 44470), (orthocentroidal, 44490), (reflection, 44491)

    2. Also, points A'b, A'c, B'a, B'c, C'a, C'b defined similarly as in (1b), lie on a circle for some triangles T'. These circles are named here Lozada-Lemoine-circles-2B of T'.

      The appearance of (T', n) in the following list means that for triangle T' the corresponding circle has center X(n):

      (midheight, 44492), (orthic, 44480), (orthocentroidal, 44493), (reflection, 44494)

  3. Finally, let Ab, Ac be the points at which the parallel line through A' to BC cuts AC and AB, respectively, and define Bc, Ca, Ba, Cb cyclically.

    1. Points built as in (1a) lie on a circle for some triangles T'. These circles are named here Lozada-Lemoine-circles-3A of T'.

      The appearance of (T', n) in the following list means that for triangle T' the corresponding circle has center X(n):

      (2nd anti-extouch, 44479), (1st Brocard-reflected, 5097)*, (1st excosine, 44495), (extouch, 576), (inner-Fermat, 44511), (outer-Fermat, 44512), (2nd Hatzipolakis, 576), (incentral, 576), (intouch, 576), (Lemoine, 576), (Macbeath, 576), (McCay, 44496), (medial, 576), (inner-Napoleon, 44497), (outer-Napoleon, 44498), (1st Neuberg, 44499), (2nd Neuberg, 44500), (orthic, 576), (Steiner, 576), (symmedial, 576), (inner-Vecten, 44501), (outer-Vecten, 44502), (Yff contact, 576)

      *This circle has squared radius (25*S^2+SW^2)*R^2/(16*SW^2).

    2. In the same way, points built as in (1b) lie on a circle for some triangles T'. These circles are named here Lozada-Lemoine-circles-3B of T'.

      The appearance of (T', n) in the following list means that for triangle T' the corresponding circle has center X(n):

      (1st anti-circumperp, 576), (2nd anti-extouch, 44469), (1st Brocard-reflected**, 5050), (1st Brocard, 6), (inner-Conway, 576), (1st excosine, 44503), (inner-Fermat, 44513), (outer-Fermat, 44514), (Gemini-017, 576), (Gemini-018, 576), (Gemini-029, 576), (Gemini-030, 576), (McCay, 44504), (inner-Napoleon, 44505), (outer-Napoleon, 44506), (1st Neuberg, 44507), (2nd Neuberg, 44508), (1st orthosymmedial, 6), (inner-Vecten, 44509), (outer-Vecten, 44510)

      **This circle has squared radius (4*S^2+SW^2)*R^2/(8*SW^2).

Notes:

X(44469) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF ANTI-CONWAY TRIANGLE

Barycentrics    a^2*(a^10-3*(b^2+c^2)*a^8+2*(b^2+c^2)^2*a^6+2*(b^2+c^2)*(b^4+c^4)*a^4-(3*b^8+2*b^4*c^4+3*c^8)*a^2+(b^4-c^4)*(b^2-c^2)^3) : :
X(44469) = 3*X(6)+X(37498) = 3*X(6)-X(44492) = X(68)-3*X(23327) = 3*X(5050)-X(37488) = X(11477)+3*X(37497) = 3*X(19139)-X(32139)

The squared-radius of this circle is ρ2 = (R^4*SW^2+(3*R^2-SW)^2*S^2)*R^2/((4*R^2-SW)^2*SW^2)

X(44469) lies on these lines: {3, 6}, {4, 22151}, {24, 15462}, {26, 9019}, {30, 34117}, {67, 15317}, {68, 23327}, {69, 37119}, {154, 37972}, {155, 542}, {156, 15581}, {184, 26283}, {382, 15140}, {394, 5094}, {399, 19379}, {524, 8548}, {613, 9630}, {858, 1899}, {895, 11458}, {1092, 8541}, {1147, 2393}, {1352, 1594}, {1498, 11645}, {1503, 18569}, {1992, 18916}, {1994, 16063}, {1995, 43811}, {2781, 12084}, {2854, 9925}, {3167, 15139}, {3564, 13371}, {3567, 14951}, {3618, 7558}, {3818, 7507}, {5422, 7495}, {5446, 19136}, {5476, 10982}, {5504, 13248}, {5622, 5889}, {6240, 31670}, {6593, 7530}, {6776, 37444}, {7387, 19153}, {7506, 9971}, {7517, 18374}, {7542, 16789}, {7568, 38110}, {7574, 18445}, {7592, 11179}, {8537, 43574}, {8550, 12161}, {8681, 15316}, {8705, 15582}, {9306, 43130}, {9932, 11255}, {9968, 14915}, {9976, 15106}, {9977, 32348}, {10168, 15805}, {10249, 12163}, {10250, 19458}, {11216, 15136}, {11416, 15073}, {11649, 34787}, {12085, 41725}, {12167, 41714}, {12293, 23049}, {13160, 14561}, {13564, 19151}, {14912, 41256}, {15135, 31152}, {15137, 15533}, {15577, 32171}, {16977, 41588}, {17814, 18553}, {18580, 44201}, {19140, 38791}, {19149, 22802}, {19150, 32341}, {19360, 32251}, {20423, 38323}, {21284, 33586}, {21970, 41674}, {23336, 34380}, {28695, 41255}, {31724, 36990}, {34155, 37196}, {34938, 41719}, {37118, 41614}

X(44469) = midpoint of X(i) and X(j) for these {i, j}: {155, 8549}, {576, 13346}, {5504, 13248}, {8548, 16266}, {37498, 44492}
X(44469) = reflection of X(i) in X(j) for these (i, j): (15581, 156), (34118, 13371), (44470, 575)
X(44469) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(44480)}} and {{A, B, C, X(67), X(8553)}}
X(44469) = Brocard circle-inverse of-X(44480)
X(44469) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44480), (3, 1351, 37473), (6, 36747, 576), (6, 36752, 44494), (6, 37483, 44493), (6, 37498, 44492), (6, 44503, 575), (182, 576, 389), (182, 44494, 36752), (578, 11511, 44479), (11416, 34148, 15073), (20806, 39588, 1352)

X(44470) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF 2nd ANTI-CONWAY TRIANGLE

Barycentrics    a^2*(a^10-2*(b^2+c^2)*a^8+2*b^2*c^2*a^6+2*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^4-(-4*b^2*c^2+(b^2-c^2)^2)*(b^4+c^4)*a^2-2*(b^4-c^4)*(b^2-c^2)*b^2*c^2) : :
X(44470) = 3*X(6)+X(17834) = X(155)-3*X(19153) = 2*X(156)-3*X(206) = X(156)-3*X(19154) = 3*X(182)-X(13346) = 3*X(5050)+X(37491) = 7*X(10541)-3*X(37497) = X(17834)-3*X(37488)

The squared-radius of this circle is ρ2 = R^2*((6*R^2-SW)^2*S^2+(2*R^2-SW)^2*SW^2)/(4*(4*R^2-SW)^2*SW^2)

X(44470) lies on these lines: {3, 6}, {5, 19136}, {20, 5622}, {24, 41614}, {25, 43130}, {26, 2393}, {54, 1992}, {68, 542}, {69, 3147}, {141, 16238}, {155, 19153}, {156, 206}, {184, 6515}, {193, 9545}, {235, 3818}, {343, 468}, {524, 1147}, {631, 43815}, {895, 7556}, {973, 9977}, {1092, 5095}, {1176, 14912}, {1209, 11178}, {1352, 1974}, {1503, 9927}, {1658, 9926}, {1660, 10154}, {2781, 7689}, {2854, 15582}, {2904, 20806}, {2937, 39562}, {3518, 11188}, {3574, 6816}, {4558, 37114}, {5181, 34116}, {5449, 34118}, {5476, 34664}, {5486, 40441}, {5562, 35603}, {5651, 43811}, {5663, 9968}, {5965, 10274}, {6776, 19121}, {7387, 8549}, {7488, 15073}, {7502, 15074}, {7506, 29959}, {8542, 12106}, {8550, 13292}, {8681, 9937}, {9027, 9925}, {9715, 10602}, {9827, 16776}, {9970, 14448}, {10192, 41619}, {10249, 12085}, {10539, 15069}, {10984, 11179}, {11411, 41719}, {11412, 22151}, {11424, 20423}, {11464, 41617}, {11649, 34788}, {11750, 32273}, {11799, 18474}, {13754, 34117}, {14070, 34787}, {14790, 23327}, {14791, 15118}, {14852, 41613}, {15132, 19138}, {15577, 34382}, {18475, 32284}, {19124, 31670}, {19137, 24206}, {19139, 41593}, {21659, 37201}, {25711, 41612}, {29012, 34786}, {30739, 37649}, {32263, 41674}, {32269, 44080}, {32275, 38851}, {34155, 41616}, {34751, 37928}, {39805, 41672}

X(44470) = midpoint of X(i) and X(j) for these {i, j}: {3, 44492}, {6, 37488}, {26, 8548}, {7387, 8549}
X(44470) = reflection of X(i) in X(j) for these (i, j): (206, 19154), (19139, 41593), (34118, 5449), (44469, 575)
X(44470) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(44479)}} and {{A, B, C, X(68), X(14961)}}
X(44470) = Brocard circle-inverse of-X(44479)
X(44470) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44479), (6, 52, 576), (6, 19131, 182), (182, 576, 578), (182, 13347, 20190), (182, 44489, 575), (343, 44077, 9306), (569, 17834, 13346), (575, 44490, 44489), (575, 44491, 182), (5050, 5157, 182), (7488, 37784, 15073), (15069, 18374, 10539), (44490, 44491, 575)

X(44471) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF ANTI-INNER-GREBE TRIANGLE

Barycentrics    a^2*((a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4)*S+(a^2+b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)) : :
X(44471) = 3*X(6)-X(1161) = 3*X(182)-2*X(9738) = 3*X(182)-4*X(44476) = 2*X(1161)-3*X(42858) = 3*X(3098)-4*X(43141) = 2*X(9733)-3*X(42859) = 5*X(22234)-4*X(44475)

The squared-radius of this circle is ρ2 = (4*SW^4+(9*S^2+5*SW^2)*S^2-(4*(3*S^2+SW^2))*S*SW)*R^2/(4*S^2*SW^2)

X(44471) lies on these lines: {3, 6}, {524, 5875}, {542, 5871}, {5591, 40107}, {6215, 34507}, {10514, 11178}, {15069, 26336}, {18509, 18553}, {29012, 39887}

X(44471) = midpoint of X(1160) and X(11477)
X(44471) = reflection of X(i) in X(j) for these (i, j): (9732, 575), (9738, 44476), (42858, 6), (44472, 576)
X(44471) = Brocard circle-inverse of-X(44483)
X(44471) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44483), (6, 11477, 11916), (6, 26341, 575), (182, 576, 44473), (576, 3098, 44485), (576, 44486, 44474), (1351, 44502, 576), (9738, 44476, 182)

X(44472) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF ANTI-OUTER-GREBE TRIANGLE

Barycentrics    a^2*(-(a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4)*S+(a^2+b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)) : :
X(44472) = 3*X(6)-X(1160) = 3*X(182)-2*X(9739) = 3*X(182)-4*X(44475) = 2*X(1160)-3*X(42859) = 3*X(3098)-4*X(43144) = 2*X(9732)-3*X(42858) = 5*X(22234)-4*X(44476)

The squared-radius of this circle is ρ2 = (4*SW^4+(9*S^2+5*SW^2)*S^2+(4*(3*S^2+SW^2))*S*SW)*R^2/(4*S^2*SW^2)

X(44472) lies on these lines: {3, 6}, {524, 5874}, {542, 5870}, {5590, 40107}, {6214, 34507}, {10515, 11178}, {15069, 26346}, {18511, 18553}, {29012, 39888}

X(44472) = midpoint of X(1161) and X(11477)
X(44472) = reflection of X(i) in X(j) for these (i, j): (9733, 575), (9739, 44475), (42859, 6), (44471, 576)
X(44472) = Brocard circle-inverse of-X(44484)
X(44472) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44484), (6, 11477, 11917), (6, 26348, 575), (182, 576, 44474), (576, 3098, 44486), (576, 44485, 44473), (1351, 44501, 576), (9739, 44475, 182)

X(44473) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF INNER-GREBE TRIANGLE

Barycentrics    a^2*(a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4+4*(a^2+b^2+c^2)*S) : :
X(44473) = 3*X(6)-X(3312) = 2*X(3312)-3*X(42832) = 5*X(11482)-X(11917)

The squared-radius of this circle is ρ2 = R^2*S^2*(9*S^2-24*S*SW+17*SW^2)/(4*SW^2*(2*SW-S)^2)

X(44473) lies on these lines: {3, 6}, {141, 13993}, {486, 11178}, {524, 19116}, {542, 1588}, {597, 642}, {3068, 25555}, {3069, 40107}, {5476, 7583}, {6460, 19924}, {6680, 35684}, {7581, 20423}, {7584, 34507}, {9540, 10168}, {13785, 18553}, {13886, 14561}, {13921, 38317}, {15069, 18510}, {19109, 32135}, {19111, 25556}, {19130, 31412}, {20301, 32253}, {29012, 39875}, {29317, 43407}

X(44473) = reflection of X(i) in X(j) for these (i, j): (42832, 6), (43118, 575)
X(44473) = Brocard circle-inverse of-X(44481)
X(44473) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44481), (6, 576, 44474), (6, 3311, 575), (6, 6417, 44482), (6, 9975, 44502), (6, 11477, 6418), (6, 44501, 576), (182, 576, 44471), (575, 9738, 182), (576, 39561, 44486), (576, 44485, 44472), (3102, 43125, 7690), (6417, 44482, 42833), (6500, 11482, 6), (9975, 44502, 576), (39561, 44499, 44474), (44501, 44502, 9975)

X(44474) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF OUTER-GREBE TRIANGLE

Barycentrics    a^2*(a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4-4*(a^2+b^2+c^2)*S) : :
X(44474) = 3*X(6)-X(3311) = 2*X(3311)-3*X(42833) = 5*X(11482)-X(11916)

The squared-radius of this circle is ρ2 = R^2*S^2*(9*S^2+24*S*SW+17*SW^2)/(4*SW^2*(2*SW+S)^2)

X(44474) lies on these lines: {3, 6}, {141, 13925}, {485, 11178}, {524, 19117}, {542, 1587}, {597, 641}, {3068, 40107}, {3069, 25555}, {5476, 7584}, {6459, 19924}, {6680, 35685}, {7582, 20423}, {7583, 34507}, {10168, 13935}, {13665, 18553}, {13880, 38317}, {13939, 14561}, {15069, 18512}, {19108, 32135}, {19110, 25556}, {19130, 42561}, {20301, 32252}, {29012, 39876}, {29317, 43408}

X(44474) = reflection of X(i) in X(j) for these (i, j): (42833, 6), (43119, 575)
X(44474) = Brocard circle-inverse of-X(44482)
X(44474) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44482), (6, 576, 44473), (6, 3312, 575), (6, 6418, 44481), (6, 9974, 44501), (6, 11477, 6417), (6, 44502, 576), (182, 576, 44472), (575, 9739, 182), (576, 39561, 44485), (576, 44486, 44471), (3103, 43124, 7692), (6418, 44481, 42832), (6501, 11482, 6), (9974, 44501, 576), (39561, 44499, 44473), (44501, 44502, 9974)

X(44475) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF 1st KENMOTU-DIAGONALS TRIANGLE

Barycentrics    a^2*(-2*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)) : :
X(44475) = 3*X(6)+X(9732) = 3*X(182)-X(9739) = 3*X(182)+X(44472) = X(1160)-9*X(5050) = 5*X(22234)-X(44471) = 3*X(39561)+X(42858)

The squared-radius of this circle is ρ2 = ((3*S^2+SW^2)^2-4*S^2*SW^2+2*S*SW*(3*S^2-SW^2))*R^2/(16*S^2*SW^2)

X(44475) lies on these lines: {3, 6}, {491, 34507}, {641, 40107}, {6251, 19130}, {6290, 18553}, {11645, 13749}, {14561, 32489}, {22525, 22727}, {22594, 35930}

X(44475) = midpoint of X(i) and X(j) for these {i, j}: {576, 9738}, {9739, 44472}
X(44475) = reflection of X(i) in X(j) for these (i, j): (43141, 20190), (44476, 575)
X(44475) = Brocard circle-inverse of-X(44486)
X(44475) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44486), (6, 3103, 44502), (6, 44509, 575), (182, 576, 372), (182, 44472, 9739), (575, 5092, 44484), (575, 5097, 44481), (44482, 44483, 575)

X(44476) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF 2nd KENMOTU-DIAGONALS TRIANGLE

Barycentrics    a^2*(2*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)) : :
X(44476) = 3*X(6)+X(9733) = 3*X(182)-X(9738) = 3*X(182)+X(44471) = X(1161)-9*X(5050) = 5*X(22234)-X(44472) = 3*X(39561)+X(42859)

The squared-radius of this circle is ρ2 = ((3*S^2+SW^2)^2-4*S^2*SW^2-2*S*SW*(3*S^2-SW^2))*R^2/(16*S^2*SW^2)

X(44476) lies on these lines: {3, 6}, {492, 34507}, {642, 40107}, {6250, 19130}, {6289, 18553}, {11645, 13748}, {14561, 32488}, {22525, 22726}, {22623, 35930}

X(44476) = midpoint of X(i) and X(j) for these {i, j}: {576, 9739}, {9738, 44471}
X(44476) = reflection of X(i) in X(j) for these (i, j): (43144, 20190), (44475, 575)
X(44476) = Brocard circle-inverse of-X(44485)
X(44476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 3102, 44501), (6, 44510, 575), (182, 576, 371), (182, 44471, 9738), (575, 5092, 44483), (575, 5097, 44482), (44481, 44484, 575)

X(44477) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF INNER TRI-EQUILATERAL TRIANGLE

Barycentrics    a^2*(-2*sqrt(3)*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)) : :
X(44477) = 3*X(182)-X(9736)

The squared-radius of this circle is ρ2 = R^2*(S^2*(27*S^2+4*SW^2)+2*sqrt(3)*SW*S*(3*S^2-SW^2)+SW^4)/(48*SW^2*S^2)

X(44477) lies on these lines: {3, 6}, {303, 34507}, {542, 33476}, {5476, 25164}, {5965, 22866}, {11645, 41039}, {12151, 25157}, {22525, 22715}, {22689, 32135}

X(44477) = midpoint of X(576) and X(9735)
X(44477) = reflection of X(44478) in X(575)
X(44477) = Brocard circle-inverse of-X(44488)
X(44477) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44488), (6, 5611, 576), (6, 44505, 575), (182, 576, 16)

X(44478) = CENTER OF LOZADA-LEMOINE-CIRCLE-1A OF OUTER TRI-EQUILATERAL TRIANGLE

Barycentrics    a^2*(2*sqrt(3)*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)) : :
X(44478) = 3*X(182)-X(9735)

The squared-radius of this circle is ρ2 = R^2*(S^2*(27*S^2+4*SW^2)-2*sqrt(3)*SW*S*(3*S^2-SW^2)+SW^4)/(48*SW^2*S^2)

X(44478) lies on these lines: {3, 6}, {302, 34507}, {542, 33477}, {5476, 25154}, {5965, 22911}, {11645, 41038}, {12151, 25167}, {22525, 22714}, {22687, 32135}

X(44478) = midpoint of X(576) and X(9736)
X(44478) = reflection of X(44477) in X(575)
X(44478) = Brocard circle-inverse of-X(44487)
X(44478) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44487), (6, 5615, 576), (6, 44506, 575), (182, 576, 15)

X(44479) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF ANTI-CONWAY TRIANGLE

Barycentrics    a^2*((b^2+c^2)*a^8+6*(b^2+c^2)*b^2*c^2*a^4-2*(b^4+3*b^2*c^2+c^4)*a^6+2*(b^4+c^4+(b^2-c^2)*b*c)*(b^4+c^4-(b^2-c^2)*b*c)*a^2+(b^8-c^8)*(-b^2+c^2)) : :
X(44479) = 3*X(2)+X(15073) = 3*X(6)-X(52) = X(52)+3*X(9967) = 3*X(69)-7*X(7999) = 3*X(182)-2*X(9729) = X(185)-3*X(11179) = 3*X(1351)+X(37484) = 3*X(3313)-X(37484) = 3*X(5050)+X(18438) = 3*X(5050)-X(19161) = 9*X(5050)-5*X(37481) = 3*X(5085)-X(37511) = X(6243)-5*X(11482) = 3*X(9730)-X(37473) = 3*X(11574)-X(15644) = 2*X(15074)+X(43130) = 2*X(16625)-5*X(22234) = 3*X(16836)-4*X(20190) = 3*X(18438)+5*X(37481) = 3*X(19161)-5*X(37481)

The squared-radius of this circle is: ρ2 = ((6*R^2-SW)^2*S^2+(2*R^2-SW)^2*SW^2)/(16*SW^2*R^2)

X(44479) lies on these lines: {2, 15073}, {3, 6}, {5, 2393}, {26, 19136}, {51, 7493}, {54, 22151}, {68, 5486}, {69, 7999}, {140, 12235}, {141, 5449}, {155, 32621}, {185, 11179}, {186, 43815}, {235, 19130}, {343, 3819}, {468, 5943}, {524, 1216}, {542, 5907}, {597, 5462}, {895, 7550}, {973, 14763}, {1177, 34155}, {1205, 9970}, {1209, 5181}, {1352, 6467}, {1353, 22829}, {1656, 29959}, {1843, 3542}, {1885, 29012}, {1992, 11412}, {2386, 37242}, {2781, 40647}, {2854, 10170}, {3090, 11188}, {3147, 3618}, {3564, 11264}, {3589, 6153}, {3818, 18383}, {3917, 6515}, {5446, 9019}, {5476, 10110}, {5480, 17710}, {5562, 40673}, {5622, 14118}, {5891, 15069}, {6329, 32191}, {6642, 34787}, {6688, 34751}, {6723, 15082}, {6776, 12111}, {7395, 10602}, {7509, 41614}, {7514, 8548}, {8537, 43651}, {8547, 15581}, {8549, 9818}, {8550, 13754}, {9027, 15067}, {9813, 34788}, {9822, 38317}, {9969, 10095}, {9972, 21660}, {9977, 32368}, {10575, 43273}, {10984, 11470}, {11180, 15056}, {11416, 13434}, {11444, 15531}, {11645, 11750}, {12061, 16776}, {12220, 14853}, {12272, 40330}, {13367, 15462}, {13394, 44084}, {13491, 34146}, {14912, 41716}, {14913, 20303}, {16789, 41587}, {18474, 18553}, {21849, 44210}, {22352, 37929}, {31670, 37201}, {34114, 41593}, {34864, 39562}, {37126, 37784}

X(44479) = midpoint of X(i) and X(j) for these {i, j}: {5, 15074}, {6, 9967}, {1205, 9970}, {1216, 32284}, {1351, 3313}, {1352, 6467}, {5480, 17710}, {9972, 21660}, {10625, 11477}, {18438, 19161}
X(44479) = reflection of X(i) in X(j) for these (i, j): (389, 575), (576, 44495), (1353, 22829), (9969, 18583), (14913, 24206), (32191, 6329), (34507, 11793), (41714, 9822), (43130, 5)
X(44479) = complement of the complement of X(15073)
X(44479) = Brocard circle-inverse of-X(44470)
X(44479) = X(69)-of-X(5)-Brocard triangle
X(44479) = center of Lozada-Lemoine-circle-3A of 2nd anti-extouch triangle
X(44479) = X(43130)-of-Johnson-triangle
X(44479) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44470), (3, 44503, 182), (6, 569, 575), (6, 11477, 37493), (52, 37476, 9729), (182, 576, 44480), (569, 8538, 6), (578, 11511, 44469), (5050, 18438, 19161), (38317, 41714, 9822)

X(44480) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF 2nd ANTI-CONWAY TRIANGLE

Barycentrics    a^2*(a^10-3*(b^2+c^2)*a^8+2*(b^4+c^4)*a^6+2*(b^2+c^2)*(b^4+c^4)*a^4-(3*b^8+3*c^8-2*(2*b^4+3*b^2*c^2+2*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3) : :
X(44480) = 3*X(6)-X(36747)

The squared-radius of this circle is: ρ2 = (R^4*SW^2+(3*R^2-SW)^2*S^2)*R^2/((2*R^2-SW)^2*SW^2)

X(44480) lies on these lines: {3, 6}, {5, 34117}, {26, 19127}, {51, 26283}, {67, 1656}, {69, 7558}, {141, 9820}, {155, 34507}, {159, 41714}, {394, 15135}, {524, 12161}, {542, 1181}, {597, 18281}, {611, 9630}, {631, 22151}, {858, 5422}, {1176, 6403}, {1199, 1992}, {1352, 11441}, {1594, 14561}, {1614, 11188}, {1993, 7495}, {2781, 7526}, {3618, 37119}, {3796, 11649}, {3818, 19149}, {5012, 15073}, {5020, 15139}, {5094, 10601}, {5462, 19136}, {5480, 18569}, {5622, 10574}, {5944, 15577}, {5965, 32341}, {6240, 39588}, {6593, 15132}, {6642, 19153}, {6723, 15106}, {6759, 9813}, {6776, 34799}, {7401, 41719}, {7506, 18374}, {7507, 19130}, {7517, 9971}, {7592, 41614}, {7770, 41255}, {8541, 10984}, {8548, 8550}, {8549, 9977}, {8681, 19458}, {10539, 29959}, {10766, 26216}, {11061, 14789}, {11178, 17814}, {11179, 19467}, {11180, 43605}, {12061, 35707}, {12173, 29012}, {12225, 31670}, {13371, 18583}, {13861, 16776}, {14853, 37444}, {14984, 32046}, {15045, 43815}, {15069, 18445}, {15141, 15805}, {15317, 19151}, {15462, 17928}, {16063, 34545}, {16789, 34002}, {17810, 37972}, {18451, 18553}, {25406, 35471}, {32233, 39562}, {32276, 41731}

X(44480) = midpoint of X(i) and X(j) for these {i, j}: {1351, 37485}, {11477, 37486}
X(44480) = reflection of X(i) in X(j) for these (i, j): (3, 44491), (578, 575)
X(44480) = Brocard circle-inverse of-X(44469)
X(44480) = center of Lozada-Lemoine-Circle-2b of orthic triangle
X(44480) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44469), (3, 11482, 10510), (6, 11477, 36749), (6, 36752, 575), (6, 37514, 44503), (6, 44492, 576), (182, 576, 44479), (575, 9729, 182), (576, 44493, 44492), (576, 44494, 6), (6759, 9813, 43130), (37514, 44503, 182), (44493, 44494, 576)

X(44481) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF ANTI-INNER-GREBE TRIANGLE

Barycentrics    (2*a^4+b^4-4*b^2*c^2+c^4-3*(b^2+c^2)*a^2+(4*a^2+4*c^2+4*b^2)*S)*a^2 : :
X(44481) = 3*X(6)+X(372) = 5*X(6)-X(35841) = 3*X(6)-X(44501) = 5*X(372)+3*X(35841) = 3*X(597)-X(640) = 5*X(22234)-X(44485) = 3*X(35841)-5*X(44501)

The squared-radius of this circle is: ρ2 = (9*S^2-24*SW*S+17*SW^2)*R^2*S^2/(16*(SW-S)^2*SW^2)

X(44481) lies on these lines: {3, 6}, {486, 18553}, {542, 7584}, {597, 640}, {599, 13961}, {1352, 13939}, {1587, 5476}, {3069, 34507}, {3071, 11645}, {3589, 13925}, {3818, 39875}, {7582, 11179}, {7583, 25555}, {7798, 22594}, {8550, 19116}, {8981, 10168}, {8992, 32149}, {9976, 19110}, {9977, 19095}, {11178, 13951}, {13966, 40107}, {13972, 24206}, {14561, 26469}, {19130, 22596}, {25561, 42262}, {29323, 42271}, {32252, 41731}, {43150, 43431}

X(44481) = midpoint of X(i) and X(j) for these {i, j}: {32, 44502}, {372, 44501}, {576, 43121}
X(44481) = reflection of X(44483) in X(575)
X(44481) = Brocard circle-inverse of-X(44473)
X(44481) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44473), (6, 372, 44501), (6, 575, 44482), (6, 1505, 44499), (6, 3312, 576), (6, 3594, 9975), (6, 5050, 42833), (6, 5062, 44500), (6, 6418, 44474), (6, 6420, 44502), (6, 6432, 9974), (182, 576, 9732), (575, 5097, 44475), (575, 44476, 44484), (6421, 43125, 43141), (39561, 44510, 575), (42832, 44474, 6418)

X(44482) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF ANTI-OUTER-GREBE TRIANGLE

Barycentrics    a^2*(2*a^4+b^4-4*b^2*c^2+c^4-3*(b^2+c^2)*a^2-(4*a^2+4*c^2+4*b^2)*S) : :
X(44482) = 3*X(6)+X(371) = 5*X(6)-X(35840) = 3*X(6)-X(44502) = 5*X(371)+3*X(35840) = 3*X(597)-X(639) = 5*X(22234)-X(44486) = 3*X(35840)-5*X(44502)

The squared-radius of this circle is: ρ2 = (9*S^2+24*SW*S+17*SW^2)*R^2*S^2/(16*(SW+S)^2*SW^2)

X(44482) lies on these lines: {3, 6}, {485, 18553}, {542, 7583}, {597, 639}, {599, 13903}, {1352, 13886}, {1588, 5476}, {3068, 34507}, {3070, 11645}, {3589, 13993}, {3818, 31412}, {7581, 11179}, {7584, 25555}, {7798, 22623}, {8550, 19117}, {8976, 11178}, {8981, 40107}, {9976, 19111}, {9977, 19096}, {10168, 13966}, {13910, 24206}, {13983, 32149}, {14561, 26468}, {19130, 22625}, {25561, 42265}, {29323, 42272}, {32253, 41731}, {43150, 43430}

X(44482) = midpoint of X(i) and X(j) for these {i, j}: {32, 44501}, {371, 44502}, {576, 43120}
X(44482) = reflection of X(44484) in X(575)
X(44482) = Brocard circle-inverse of-X(44474)
X(44482) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44474), (6, 371, 44502), (6, 575, 44481), (6, 3311, 576), (6, 3592, 9974), (6, 5050, 42832), (6, 5058, 44500), (6, 6417, 44473), (6, 6419, 44501), (6, 6431, 9975), (6, 44501, 22330), (182, 576, 9733), (575, 5097, 44476), (575, 44475, 44483), (6422, 43124, 43144), (39561, 44509, 575), (42833, 44473, 6417)

X(44483) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF INNER-GREBE TRIANGLE

Barycentrics    (-(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2))*a^2 : :
X(44483) = 3*X(6)+X(11824) = 3*X(182)-X(43121) = 3*X(182)+X(44485) = 3*X(5085)+X(35841)

The squared-radius of this circle is: ρ2 = (9*S^2+24*SW*S+17*SW^2)*R^2*S^2/(16*(SW+S)^2*SW^2)

X(44483) lies on these lines: {3, 6}, {542, 6215}, {640, 5875}, {3818, 39887}, {5476, 6202}, {5591, 34507}, {6277, 9977}, {7732, 9976}, {10514, 18553}, {10783, 11179}, {32280, 41731}

X(44483) = midpoint of X(i) and X(j) for these {i, j}: {3, 44501}, {640, 8550}, {43121, 44485}
X(44483) = reflection of X(44481) in X(575)
X(44483) = Brocard circle-inverse of-X(44471)
X(44483) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44471), (6, 1161, 576), (182, 575, 44484), (182, 576, 43118), (182, 44485, 43121), (182, 44509, 575), (575, 5092, 44476), (575, 44475, 44482), (5092, 44507, 44484), (11824, 26341, 43121)

X(44484) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF OUTER-GREBE TRIANGLE

Barycentrics    a^2*((2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)) : :
X(44484) = 3*X(6)+X(11825) = 3*X(182)-X(43120) = 3*X(182)+X(44486) = 3*X(5085)+X(35840)

The squared-radius of this circle is: ρ2 = ((9*S^2+5*SW^2)*S^2+4*(3*S^2+SW^2)*SW*S+4*SW^4)*R^2/(16*(SW+S)^2*SW^2)

X(44484) lies on these lines: {3, 6}, {542, 6214}, {639, 5874}, {3818, 39888}, {5476, 6201}, {5590, 34507}, {6276, 9977}, {7733, 9976}, {10515, 18553}, {10784, 11179}, {32281, 41731}

X(44484) = midpoint of X(i) and X(j) for these {i, j}: {3, 44502}, {639, 8550}, {43120, 44486}
X(44484) = reflection of X(44482) in X(575)
X(44484) = Brocard circle-inverse of-X(44472)
X(44484) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44472), (6, 1160, 576), (182, 575, 44483), (182, 576, 43119), (182, 43121, 20190), (182, 44486, 43120), (182, 44510, 575), (575, 5092, 44475), (575, 44476, 44481), (5092, 44507, 44483), (11825, 26348, 43120)

X(44485) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF 1st KENMOTU DIAGONALS TRIANGLE

Barycentrics    a^2*(-2*(a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)) : :
X(44485) = 3*X(182)-2*X(43121) = 3*X(182)-4*X(44483) = X(8982)-3*X(11179) = X(11824)+3*X(35841) = 5*X(22234)-4*X(44481)

The squared-radius of this circle is: ρ2 = ((3*S^2+SW^2)^2-4*S^2*SW^2-2*S*SW*(3*S^2-SW^2))*R^2/(4*(SW-S)^2*SW^2)

X(44485) lies on these lines: {3, 6}, {492, 40107}, {640, 34507}, {1352, 32488}, {6036, 13758}, {6118, 38317}, {6289, 11178}, {8982, 11179}

X(44485) = reflection of X(i) in X(j) for these (i, j): (372, 575), (576, 44501), (34507, 640), (43121, 44483)
X(44485) = Brocard circle-inverse of-X(44476)
X(44485) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44476), (6, 43119, 44510), (182, 576, 44486), (575, 43120, 182), (576, 3098, 44471), (576, 39561, 44474), (35424, 44499, 44486), (43119, 44510, 182), (43121, 44483, 182), (44472, 44473, 576)

X(44486) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF 2nd KENMOTU DIAGONALS TRIANGLE

Barycentrics    a^2*(2*(a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)) : :
X(44486) = 3*X(182)-2*X(43120) = 3*X(182)-4*X(44484) = 3*X(11179)-X(26441) = X(11825)+3*X(35840) = 5*X(22234)-4*X(44482)

The squared-radius of this circle is: ρ2 = ((3*S^2+SW^2)^2-4*S^2*SW^2+2*S*SW*(3*S^2-SW^2))*R^2/(4*(SW+S)^2*SW^2)

X(44486) lies on these lines: {3, 6}, {491, 40107}, {639, 34507}, {1352, 32489}, {6036, 13638}, {6119, 38317}, {6290, 11178}, {11179, 26441}

X(44486) = reflection of X(i) in X(j) for these (i, j): (371, 575), (576, 44502), (34507, 639), (43120, 44484)
X(44486) = Brocard circle-inverse of-X(44475)
X(44486) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44475), (3, 44510, 182), (6, 43118, 44509), (182, 576, 44485), (575, 43121, 182), (576, 3098, 44472), (576, 39561, 44473), (35424, 44499, 44485), (43118, 44509, 182), (43120, 44484, 182), (44471, 44474, 576)

X(44487) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF INNER TRI-EQUILATERAL TRIANGLE

Barycentrics    a^2*(-2*sqrt(3)*(a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)) : :
X(44487) = 3*X(6)-X(5615) = 3*X(182)-2*X(13349) = 3*X(5476)-2*X(7685) = 4*X(8590)-3*X(39554) = 3*X(11179)-X(36995) = 4*X(15516)-3*X(36758) = 4*X(20190)-3*X(21159)

The squared-radius of this circle is: ρ2 = (S^2*(27*S^2+4*SW^2)+SW^4-2*S*sqrt(3)*SW*(3*S^2-SW^2))*R^2/(4*(SW-S*sqrt(3))^2*SW^2)

X(44487) lies on these lines: {3, 6}, {302, 40107}, {383, 25559}, {542, 20429}, {624, 34507}, {5459, 5476}, {5979, 25560}, {5980, 22684}, {6774, 37785}, {11179, 36995}, {11645, 36994}

X(44487) = reflection of X(i) in X(j) for these (i, j): (16, 575), (576, 44497), (34507, 624)
X(44487) = Brocard circle-inverse of-X(44478)
X(44487) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44478), (3, 44505, 182), (182, 576, 44488), (575, 13350, 182)

X(44488) = CENTER OF LOZADA-LEMOINE-CIRCLE-1B OF OUTER TRI-EQUILATERAL TRIANGLE

Barycentrics    a^2*(2*sqrt(3)*(a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)) : :
X(44488) = 3*X(6)-X(5611) = 3*X(182)-2*X(13350) = 3*X(5476)-2*X(7684) = 4*X(8590)-3*X(39555) = 3*X(11179)-X(36993) = 4*X(15516)-3*X(36757) = 4*X(20190)-3*X(21158)

The squared-radius of this circle is: ρ2 = (S^2*(27*S^2+4*SW^2)+SW^4+2*sqrt(3)*SW*S*(3*S^2-SW^2))*R^2/(4*(SW+sqrt(3)*S)^2*SW^2)

X(44488) lies on these lines: {3, 6}, {303, 40107}, {542, 20428}, {623, 34507}, {1080, 25560}, {5460, 5476}, {5978, 25559}, {5981, 22686}, {6771, 37786}, {11179, 36993}, {11645, 36992}

X(44488) = reflection of X(i) in X(j) for these (i, j): (15, 575), (576, 44498), (34507, 623)
X(44488) = Brocard circle-inverse of-X(44477)
X(44488) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44477), (3, 44506, 182), (182, 576, 44487), (575, 13349, 182)

X(44489) = CENTER OF LOZADA-LEMOINE-CIRCLE-2A OF MIDHEIGHT TRIANGLE

Barycentrics    a^2*(a^10-2*(b^2+c^2)*a^8+10*b^2*c^2*a^6+2*(b^2+c^2)*(b^4-9*b^2*c^2+c^4)*a^4-(b^2-c^2)^2*(b^4-8*b^2*c^2+c^4)*a^2-2*(b^4-c^4)*(b^2-c^2)*b^2*c^2) : :
X(44489) = 3*X(6)+X(9786)

X(44489) lies on these lines: {3, 6}, {4, 43812}, {24, 40673}, {184, 4232}, {206, 12007}, {542, 39571}, {1092, 1992}, {1614, 1974}, {3564, 19137}, {3567, 8541}, {5032, 34148}, {5462, 8548}, {5476, 12233}, {5480, 22802}, {5622, 10990}, {5890, 11470}, {6642, 8681}, {6644, 32284}, {6759, 8550}, {6776, 26883}, {7592, 44102}, {8549, 10110}, {9306, 11225}, {9925, 43586}, {9976, 11746}, {10169, 15311}, {10282, 32621}, {11179, 34621}, {11255, 16881}, {11431, 15462}, {11579, 38791}, {13567, 34507}, {15033, 35483}, {15043, 37784}, {15577, 22829}, {16187, 37643}, {16270, 41618}, {18583, 22660}, {19121, 33748}, {19124, 32601}, {20423, 43810}, {32046, 33591}

X(44489) = midpoint of X(8550) and X(15873)
X(44489) = reflection of X(44503) in X(575)
X(44489) = Brocard circle-inverse of-X(44495)
X(44489) = The squared-radius of this circle is: ρ2 = ((12*R^2-SW)^2*S^2+(4*R^2-SW)^2*SW^2)*R^2/(4*((8*R^2-SW)^2*SW^2))
X(44489) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44495), (6, 389, 576), (182, 576, 13346), (575, 44470, 182), (575, 44490, 44470), (1992, 43815, 1092), (5050, 19126, 182), (5462, 8548, 9813), (8550, 19136, 6759)

X(44490) = CENTER OF LOZADA-LEMOINE-CIRCLE-2A OF ORTHOCENTROIDAL TRIANGLE

Barycentrics    a^2*(a^10-2*(b^2+c^2)*a^8+6*b^2*c^2*a^6+2*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)*a^4-(b^8+c^8-2*(4*b^4-5*b^2*c^2+4*c^4)*b^2*c^2)*a^2-2*(b^4-c^4)*(b^2-c^2)*b^2*c^2) : :
X(44490) = 3*X(6)+X(37489) = 3*X(182)-X(37480) = X(11511)-3*X(39561)

The squared-radius of this circle is: ρ2 = ((9*R^2-SW)^2*S^2+(3*R^2-SW)^2*SW^2)*R^2/(4*(6*R^2-SW)^2*SW^2)

X(44490) lies on these lines: {3, 6}, {4, 11579}, {20, 43810}, {26, 8547}, {110, 37644}, {184, 7426}, {542, 19136}, {1147, 19138}, {1986, 11470}, {1992, 15462}, {2777, 18431}, {2854, 12106}, {3580, 5651}, {5462, 12039}, {5622, 20423}, {6759, 41613}, {8550, 16619}, {8584, 18579}, {9027, 43586}, {9971, 39562}, {9976, 34417}, {11225, 44077}, {11459, 32599}, {11645, 18396}, {12007, 19154}, {14389, 22112}, {14852, 18553}, {15534, 22115}, {16187, 37638}, {19137, 43150}, {20301, 23325}, {21852, 39125}, {25328, 34514}, {33851, 37814}, {41618, 44274}

X(44490) = midpoint of X(576) and X(11438)
X(44490) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 568, 576), (182, 576, 13352), (567, 37489, 37480), (575, 44470, 44491), (44470, 44489, 575)

X(44491) = CENTER OF LOZADA-LEMOINE-CIRCLE-2A OF REFLECTION TRIANGLE

Barycentrics    a^2*(a^10-2*(b^2+c^2)*a^8-2*b^2*c^2*a^6+2*(b^2+c^2)*(b^4+c^4)*a^4-(b^4+c^4+2*(b^2+c^2)*b*c)*(b^4+c^4-2*(b^2+c^2)*b*c)*a^2-2*(b^4-c^4)*(b^2-c^2)*b^2*c^2) : :
X(44491) = 3*X(6)+X(37486) = 3*X(182)-X(578) = X(578)+3*X(19126) = 3*X(5050)+X(37485) = 7*X(10541)-3*X(37506)

The squared-radius of this circle is: ρ2 = ((3*R^2-SW)^2*S^2+(R^2-SW)^2*SW^2)*R^2/(4*(2*R^2-SW)^2*SW^2)

X(44491) lies on these lines: {2, 43811}, {3, 6}, {5, 19127}, {49, 599}, {66, 32344}, {70, 1176}, {141, 7568}, {184, 7495}, {206, 24206}, {524, 32046}, {631, 11061}, {858, 43650}, {1147, 40107}, {1594, 1974}, {1656, 18374}, {2888, 6776}, {2918, 9813}, {2937, 9971}, {3519, 19151}, {3589, 13371}, {3818, 13160}, {4550, 9968}, {5012, 43653}, {5622, 19467}, {5943, 26283}, {6152, 8541}, {6240, 19124}, {6639, 38851}, {6759, 18553}, {7393, 19153}, {7514, 34117}, {7525, 9019}, {8550, 32358}, {10168, 18281}, {10539, 11178}, {10984, 34224}, {11179, 43812}, {12106, 32154}, {12173, 29323}, {13434, 20423}, {14561, 19121}, {14791, 19136}, {15133, 20301}, {16776, 37440}, {18569, 19130}, {19128, 37119}, {19150, 41590}, {19468, 32251}, {38064, 43815}

X(44491) = midpoint of X(i) and X(j) for these {i, j}: {3, 44480}, {182, 19126}
X(44491) = intersection, other than A,B,C, of conics {{A, B, C, X(39), X(70)}} and {{A, B, C, X(67), X(13351)}}
X(44491) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 37473, 3098), (6, 6243, 576), (182, 576, 569), (182, 37515, 20190), (182, 44470, 575), (575, 44470, 44490), (5085, 19129, 182), (5157, 19131, 182), (13353, 37486, 578), (17704, 20190, 5092)

X(44492) = CENTER OF LOZADA-LEMOINE-CIRCLE-2B OF MIDHEIGHT TRIANGLE

Barycentrics    (a^10-3*(b^2+c^2)*a^8+2*(b^2+c^2)^2*a^6+2*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)*a^4-(3*b^8+3*c^8-2*(6*b^4-b^2*c^2+6*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3)*a^2 : :
X(44492) = 3*X(6)-X(37498) = 3*X(6)-2*X(44469) = 2*X(1147)-3*X(19153) = 3*X(19149)-2*X(32139)

The squared-radius of this circle is: ρ2 = (4*R^4*SW^2+(6*R^2-SW)^2*S^2)*R^2*S^4/(SA^2*SB^2*SC^2*SW^2)

X(44492) lies on these lines: {3, 6}, {4, 41614}, {20, 37784}, {22, 15073}, {26, 1177}, {30, 8548}, {69, 3542}, {154, 41615}, {155, 524}, {156, 9925}, {159, 32048}, {235, 1352}, {394, 468}, {542, 1498}, {597, 15805}, {895, 12082}, {1092, 44102}, {1147, 19153}, {1503, 12293}, {1598, 43130}, {1657, 39562}, {1885, 31670}, {1992, 7592}, {1993, 7493}, {2063, 38282}, {2393, 7387}, {2781, 12163}, {2854, 15581}, {3147, 20806}, {3564, 19149}, {5486, 12161}, {5562, 11470}, {5622, 11413}, {5965, 17824}, {6193, 41719}, {6391, 39879}, {6642, 19136}, {6759, 8681}, {6776, 37201}, {6816, 14853}, {7529, 29959}, {7716, 41714}, {8263, 21841}, {9813, 10110}, {9972, 11576}, {9976, 33534}, {10154, 34966}, {10249, 12084}, {10519, 26206}, {10594, 11188}, {10601, 30739}, {10602, 11414}, {10982, 20423}, {10984, 40673}, {11255, 13391}, {11456, 41617}, {11649, 37928}, {11799, 15069}, {13383, 19139}, {14852, 34118}, {15462, 35602}, {16266, 34351}, {17811, 40107}, {17814, 34507}, {17825, 25555}, {18569, 23049}, {19154, 23041}, {19924, 34622}, {21850, 31815}, {22151, 35486}, {23327, 23335}, {31725, 36990}, {32138, 34778}, {32284, 32621}

X(44492) = midpoint of X(i) and X(j) for these {i, j}: {1351, 37491}, {6391, 39879}, {11477, 17834}
X(44492) = reflection of X(i) in X(j) for these (i, j): (3, 44470), (155, 34117), (8549, 8548), (9925, 156), (13346, 575), (34787, 26), (37498, 44469)
X(44492) = Brocard circle-inverse of-X(44503)
X(44492) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44503), (6, 11477, 36747), (6, 37498, 44469), (6, 37514, 575), (182, 576, 44495), (575, 17704, 182), (576, 44480, 6), (576, 44493, 44480), (1351, 6243, 11477), (11482, 36753, 6)

X(44493) = CENTER OF LOZADA-LEMOINE-CIRCLE-2B OF ORTHOCENTROIDAL TRIANGLE

Barycentrics    (a^10-3*(b^2+c^2)*a^8+2*(b^4+b^2*c^2+c^4)*a^6+2*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^4-(3*b^8+3*c^8-2*(4*b^4+b^2*c^2+4*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3)*a^2 : :
X(44493) = 3*X(182)-2*X(11430) = 2*X(5092)-3*X(19131) = X(11456)+3*X(41614) = 4*X(20190)-3*X(39242)

The squared-radius of this circle is: ρ2 = (9*R^4*SW^2+(9*R^2-2*SW)^2*S^2)*R^2/(4*(3*R^2-SW)^2*SW^2)

X(44493) lies on these lines: {3, 6}, {22, 11649}, {69, 7552}, {399, 15069}, {524, 44262}, {542, 11456}, {1352, 15052}, {1658, 40929}, {3619, 14940}, {5972, 15066}, {8548, 9976}, {8549, 35237}, {9970, 11459}, {10601, 32216}, {11179, 37784}, {11216, 35243}, {11579, 15072}, {11663, 12088}, {12061, 17714}, {12106, 32217}, {13198, 15073}, {13406, 18358}, {14984, 19127}, {15032, 41617}, {15068, 16534}, {15087, 15534}, {15106, 37638}, {18396, 32251}, {29317, 39588}, {39562, 43273}

X(44493) = midpoint of X(11477) and X(37494)
X(44493) = reflection of X(13352) in X(575)
X(44493) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 37483, 44469), (575, 16836, 182), (576, 44480, 44494), (15068, 34117, 19140), (19140, 34507, 15068), (44480, 44492, 576)

X(44494) = CENTER OF LOZADA-LEMOINE-CIRCLE-2B OF REFLECTION TRIANGLE

Barycentrics    (a^10-3*(b^2+c^2)*a^8+2*(b^4-b^2*c^2+c^4)*a^6+2*(b^2+c^2)*(b^4+3*b^2*c^2+c^4)*a^4-(b^4-3*c^4)*(3*b^4-c^4)*a^2+(b^4-c^4)*(b^2-c^2)^3)*a^2 : :
X(44494) = 3*X(6)-X(36749) = 5*X(22234)-2*X(37505)

The squared-radius of this circle is: ρ2 = (R^4*SW^2+(3*R^2-2*SW)^2*S^2)*R^2/(4*(R^2-SW)^2*SW^2)

X(44494) lies on these lines: {3, 6}, {51, 26284}, {143, 19127}, {155, 11178}, {156, 16776}, {195, 599}, {539, 8548}, {542, 7592}, {597, 12359}, {1199, 14789}, {1899, 5169}, {1993, 40107}, {3818, 32139}, {5422, 21243}, {5449, 19139}, {5476, 18381}, {6689, 19150}, {7566, 19130}, {9972, 15531}, {10168, 32348}, {11188, 11423}, {12161, 12585}, {14561, 18912}, {14763, 19360}, {15024, 43811}, {15043, 15462}, {15069, 15087}, {15074, 36153}, {15118, 34155}, {18383, 19149}, {18445, 18553}, {19140, 36253}, {20301, 25335}, {20303, 26926}, {23300, 33332}, {32251, 41731}

X(44494) = reflection of X(569) in X(575)
X(44494) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 11477, 14627), (6, 36752, 44469), (6, 36753, 575), (6, 44480, 576), (389, 575, 182), (576, 44480, 44493), (36752, 44469, 182)

X(44495) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF 1st EXCOSINE TRIANGLE

Barycentrics    a^2*((b^2+c^2)*a^8+18*(b^2+c^2)*b^2*c^2*a^4-2*(b^4+5*b^2*c^2+c^4)*a^6+2*(b^4-3*b^2*c^2+c^4)*(b^2-c^2)^2*a^2+(b^8-c^8)*(-b^2+c^2)) : :
X(44495) = 3*X(6)-X(389) = 5*X(6)-X(19161) = 7*X(6)-X(21851) = 9*X(6)-X(37473) = X(52)-5*X(11482) = 3*X(182)-2*X(17704) = 5*X(389)-3*X(19161) = 7*X(389)-3*X(21851) = 3*X(389)-X(37473) = 3*X(1351)+X(10625) = X(3313)+3*X(5102) = 9*X(5093)-X(6243) = 3*X(5093)+X(9967) = X(6243)+3*X(9967) = X(10625)-3*X(11574) = 2*X(15012)-5*X(22234) = X(16625)-4*X(22330) = 7*X(19161)-5*X(21851) = 9*X(19161)-5*X(37473) = 9*X(21851)-7*X(37473)

The squared-radius of this circle is: ρ2 = ((12*R^2-SW)^2*S^2+(4*R^2-SW)^2*SW^2)/(64*SW^2*R^2)

X(44495) lies on these lines: {3, 6}, {4, 40673}, {5, 8681}, {51, 4232}, {54, 44102}, {143, 33591}, {193, 11444}, {524, 11793}, {542, 12241}, {597, 11695}, {1199, 1205}, {1353, 5876}, {1503, 22829}, {1843, 9781}, {1974, 9707}, {1992, 5562}, {2393, 10110}, {2781, 13382}, {2854, 15465}, {3091, 15531}, {3819, 11433}, {5032, 5889}, {5446, 15074}, {5462, 14984}, {5476, 43130}, {5480, 32366}, {5890, 35483}, {5943, 11427}, {6000, 8550}, {6241, 12294}, {6467, 14853}, {6688, 23292}, {6759, 32621}, {6776, 11381}, {7592, 11470}, {9820, 9822}, {9969, 12061}, {9977, 22830}, {10282, 19136}, {10602, 10982}, {11487, 34507}, {11645, 13403}, {11649, 37897}, {12007, 34146}, {12242, 32246}, {13434, 37784}, {13567, 40107}, {13568, 19924}, {13570, 18388}, {13598, 20423}, {14561, 14913}, {14865, 43812}, {15082, 37643}, {18390, 18553}, {19596, 43829}, {32142, 34380}, {34565, 37977}, {34854, 42873}

X(44495) = midpoint of X(i) and X(j) for these {i, j}: {5, 32284}, {576, 44479}, {1351, 11574}, {5446, 15074}, {5480, 32366}, {11477, 15644}
X(44495) = reflection of X(i) in X(j) for these (i, j): (9729, 575), (9822, 18583)
X(44495) = Brocard circle-inverse of-X(44489)
X(44495) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44489), (6, 578, 575), (6, 11477, 11432), (182, 576, 44492), (389, 11425, 17704)

X(44496) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF MCCAY TRIANGLE

Barycentrics    a^2*(4*a^4-7*(b^2+c^2)*a^2+7*b^4-4*b^2*c^2+7*c^4) : :
X(44496) = 3*X(6)-X(187) = X(6)-3*X(1570) = 7*X(6)-3*X(1691) = 5*X(6)-3*X(1692) = 11*X(6)-3*X(2076) = 5*X(6)-X(5104) = X(6)+3*X(5111) = 3*X(6)+X(8586) = 5*X(6)+3*X(15514) = 17*X(6)-9*X(35006) = 5*X(6)-2*X(38010) = X(187)-9*X(1570) = 7*X(187)-9*X(1691) = 5*X(187)-9*X(1692) = 2*X(187)-3*X(2030) = 11*X(187)-9*X(2076) = 5*X(187)-3*X(5104) = X(187)+3*X(5107) = X(187)+9*X(5111) = 5*X(187)+9*X(15514) = 5*X(187)-6*X(38010)

The squared-radius of this circle is: ρ2 = (27*S^2*(3*S^2-SW^2)+4*SW^4)*R^2*S^2/(4*(3*S^2-SW^2)^2*SW^2)

X(44496) lies on these lines: {2, 42011}, {3, 6}, {30, 41672}, {111, 3292}, {316, 1992}, {352, 39024}, {353, 44109}, {394, 21448}, {524, 625}, {597, 7619}, {599, 31275}, {842, 8779}, {895, 10630}, {1383, 3060}, {1495, 13192}, {2386, 39848}, {3054, 40107}, {3055, 25555}, {3630, 5031}, {3849, 8584}, {5032, 14712}, {5095, 5523}, {5140, 8541}, {5148, 8540}, {5194, 16785}, {5476, 31415}, {5477, 11645}, {5650, 7708}, {5969, 15301}, {6791, 40112}, {6792, 13857}, {7813, 41146}, {8681, 9132}, {8787, 32479}, {9486, 36212}, {10765, 13509}, {10766, 21639}, {11580, 23061}, {13449, 43448}, {15066, 22111}, {15534, 31173}, {18424, 18553}, {20976, 32237}, {20977, 39689}, {34507, 43620}, {34565, 39389}

X(44496) = midpoint of X(i) and X(j) for these {i, j}: {6, 5107}, {187, 8586}, {1570, 5111}, {1692, 15514}, {11477, 18860}, {15534, 31173}, {44497, 44498}
X(44496) = reflection of X(i) in X(j) for these (i, j): (2030, 6), (5104, 38010)
X(44496) = isogonal conjugate of X(10153)
X(44496) = barycentric product X(6)*X(41133)
X(44496) = trilinear product X(31)*X(41133)
X(44496) = intersection, other than A,B,C, of conics {{A, B, C, X(6), X(41133)}} and {{A, B, C, X(249), X(15655)}}
X(44496) = circumcircle-inverse of-X(15655)
X(44496) = 2nd Lemoine circle (cosine circle)-inverse of-X(5085)
X(44496) = Moses circle-inverse of-X(8589)
X(44496) = crossdifference of every pair of points on line {X(523), X(15534)}
X(44496) = crosssum of X(2) and X(8859)
X(44496) = X(923)-complementary conjugate of-X(15850)
X(44496) = X(6)-Daleth conjugate of-X(8589)
X(44496) = X(6)-Hirst inverse of-X(15655)
X(44496) = X(512)-vertex conjugate of-X(15655)
X(44496) = radical trace of Brocard circle and Ehrmann circle
X(44496) = radical trace of Brocard circle and circle described in Hyacinthos #20367 (11/15/2011, Quang Tuan Bui)
X(44496) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 574, 575), (6, 5104, 1692), (6, 5111, 5107), (6, 8586, 187), (6, 11477, 1384), (6, 13330, 5008), (6, 15514, 5104), (6, 37517, 41413), (187, 5107, 8586), (576, 44499, 44500), (1379, 1380, 15655), (1570, 5107, 6), (1666, 1667, 5085), (1692, 5104, 38010), (1692, 38010, 2030), (2028, 2029, 8589), (5038, 10631, 8590), (8589, 10485, 20190), (9974, 9975, 11477), (15520, 42852, 6), (21309, 35002, 187), (22242, 22243, 5024), (44501, 44502, 575)

X(44497) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF INNER-NAPOLEON TRIANGLE

Barycentrics    a^2*(2*sqrt(3)*(a^2+b^2+c^2)*S+3*a^4-9*(b^2+c^2)*a^2+6*b^4-6*b^2*c^2+6*c^4) : :
X(44497) = 3*X(6)-X(16) = 5*X(6)-3*X(36758) = 5*X(16)-9*X(36758) = 3*X(597)-2*X(6672) = 3*X(599)-5*X(40335) = X(622)+3*X(1992) = X(5104)-3*X(36757) = X(5615)-5*X(11482) = 2*X(21402)-5*X(22234)

The squared-radius of this circle is: ρ2 = (27*S^2-12*sqrt(3)*S*SW+7*SW^2)*R^2*S^2/(4*(SW-sqrt(3)*S)^2*SW^2)

X(44497) lies on these lines: {3, 6}, {30, 41621}, {51, 37776}, {193, 42983}, {524, 624}, {530, 8584}, {542, 5321}, {597, 6672}, {599, 40335}, {622, 1992}, {625, 34508}, {1352, 42139}, {1353, 42923}, {1503, 42136}, {3180, 16940}, {3292, 37775}, {3589, 43103}, {3618, 43463}, {3818, 42103}, {5334, 20429}, {5335, 20423}, {5353, 8540}, {5357, 19369}, {5476, 18582}, {5480, 42138}, {5965, 31706}, {6108, 43228}, {6776, 43466}, {7685, 11542}, {8550, 42117}, {8681, 10662}, {10632, 44102}, {10678, 32302}, {11178, 42095}, {11179, 42119}, {11645, 19107}, {11646, 22856}, {11649, 36980}, {14848, 42817}, {15069, 42125}, {15073, 21648}, {15534, 42975}, {16809, 18553}, {18581, 34507}, {18583, 42627}, {19130, 42110}, {19924, 42088}, {22496, 31173}, {23302, 25555}, {23303, 40107}, {25561, 42918}, {29012, 42108}, {29181, 42584}, {31670, 42141}, {33749, 42147}, {36994, 42126}, {41037, 42128}, {42130, 43273}

X(44497) = midpoint of X(i) and X(j) for these {i, j}: {15, 8586}, {576, 44487}, {11477, 14539}
X(44497) = reflection of X(i) in X(j) for these (i, j): (13349, 575), (44498, 44496)
X(44497) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 15, 575), (6, 576, 44498), (6, 11477, 11486)

X(44498) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF OUTER-NAPOLEON TRIANGLE

Barycentrics    a^2*(-2*sqrt(3)*(a^2+b^2+c^2)*S+3*a^4-9*(b^2+c^2)*a^2+6*b^4-6*b^2*c^2+6*c^4) : :
X(44498) = 3*X(6)-X(15) = 5*X(6)-3*X(36757) = 5*X(15)-9*X(36757) = 3*X(597)-2*X(6671) = 3*X(599)-5*X(40334) = X(621)+3*X(1992) = X(5104)-3*X(36758) = X(5611)-5*X(11482) = 2*X(21401)-5*X(22234)

The squared-radius of this circle is: ρ2 = (27*S^2+12*sqrt(3)*SW*S+7*SW^2)*R^2*S^2/(4*(SW+sqrt(3)*S)^2*SW^2)

X(44498) lies on these lines: {3, 6}, {30, 41620}, {51, 37775}, {193, 42982}, {524, 623}, {531, 8584}, {542, 5318}, {597, 6671}, {599, 40334}, {621, 1992}, {625, 34509}, {1352, 42142}, {1353, 42922}, {1503, 42137}, {3181, 16941}, {3292, 37776}, {3589, 43102}, {3618, 43464}, {3818, 42106}, {5334, 20423}, {5335, 20428}, {5353, 19369}, {5357, 8540}, {5476, 18581}, {5480, 42135}, {5965, 31705}, {6109, 43229}, {6776, 43465}, {7684, 11543}, {8550, 42118}, {8681, 10661}, {10633, 44102}, {10677, 32301}, {11178, 42098}, {11179, 42120}, {11645, 19106}, {11646, 22900}, {11649, 36978}, {14848, 42818}, {15069, 42128}, {15073, 21647}, {15534, 42974}, {16808, 18553}, {18582, 34507}, {18583, 42628}, {19130, 42107}, {19924, 42087}, {22495, 31173}, {23302, 40107}, {23303, 25555}, {25561, 42919}, {29012, 42109}, {29181, 42585}, {31670, 42140}, {33749, 42148}, {36992, 42127}, {41036, 42125}, {42131, 43273}

X(44498) = midpoint of X(i) and X(j) for these {i, j}: {16, 8586}, {576, 44488}, {11477, 14538}
X(44498) = reflection of X(i) in X(j) for these (i, j): (13350, 575), (44497, 44496)
X(44498) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 16, 575), (6, 576, 44497), (6, 11477, 11485)

X(44499) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF 1st NEUBERG TRIANGLE

Barycentrics    a^2*(2*a^4-(b^2+c^2)*a^2+3*b^4+3*c^4) : :
X(44499) = 3*X(6)-X(32) = 5*X(6)-X(5017) = 4*X(6)-X(41413) = 5*X(32)-3*X(5017) = X(32)+3*X(5028) = 4*X(32)-3*X(41413) = X(315)+3*X(1992) = 3*X(597)-2*X(6680) = 3*X(599)-5*X(7867) = X(5017)+5*X(5028) = 4*X(5017)-5*X(41413) = 4*X(5028)+X(41413) = 3*X(5050)-X(35387) = 3*X(5093)-X(35389) = 3*X(15520)-X(35431) = X(35424)-3*X(39561)

The squared-radius of this circle is: ρ2 = R^2*(9*S^4-11*S^2*SW^2+4*SW^4)*S^2/(4*((SW^2+S^2)^2-4*S^2*SW^2)*SW^2)

X(44499) lies on these lines: {3, 6}, {51, 34945}, {69, 7828}, {115, 18553}, {141, 7886}, {185, 10766}, {193, 7797}, {230, 40107}, {251, 21969}, {315, 1992}, {323, 40130}, {373, 39024}, {384, 10754}, {394, 40126}, {524, 626}, {542, 5254}, {597, 6680}, {599, 7867}, {754, 8584}, {760, 4663}, {1180, 13366}, {1194, 34986}, {1196, 9225}, {2548, 5476}, {2794, 8550}, {3292, 9465}, {3329, 36849}, {3618, 7769}, {3767, 34507}, {3815, 6721}, {3819, 42295}, {3852, 39125}, {3981, 40350}, {5032, 20065}, {5182, 7783}, {5280, 19369}, {5299, 8540}, {5354, 23061}, {5477, 7765}, {5969, 7816}, {6034, 25561}, {6467, 34137}, {7738, 11179}, {7748, 11645}, {7755, 15993}, {7760, 39099}, {7779, 10336}, {7787, 22486}, {7792, 32458}, {7818, 15534}, {7839, 10350}, {8574, 8675}, {8681, 23128}, {8743, 11470}, {8779, 15073}, {9607, 33749}, {9753, 37665}, {11178, 13881}, {12294, 41363}, {13754, 39524}, {14561, 31404}, {14567, 20859}, {14700, 32127}, {14994, 17129}, {15819, 39095}, {16984, 36859}, {32237, 44116}, {39575, 44102}

X(44499) = midpoint of X(i) and X(j) for these {i, j}: {6, 5028}, {1351, 13355}, {2458, 15514}, {5162, 8586}, {7818, 15534}, {11477, 30270}, {13330, 32452}, {44501, 44502}
X(44499) = reflection of X(i) in X(j) for these (i, j): (13335, 575), (39750, 15516)
X(44499) = crosssum of X(2) and X(7806)
X(44499) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 39, 575), (6, 576, 44500), (6, 1351, 5039), (6, 1504, 44482), (6, 1505, 44481), (6, 1570, 5097), (6, 3094, 1692), (6, 5034, 15516), (6, 5111, 5052), (6, 8586, 5008), (6, 10542, 3), (6, 11477, 30435), (6, 13330, 5007), (6, 15514, 12212), (1351, 40268, 11477), (1692, 3094, 5092), (1692, 37512, 39560), (3094, 39560, 37512), (5007, 5107, 13330), (7772, 43183, 13357), (9974, 9975, 5102), (37512, 39560, 5092), (44473, 44474, 39561), (44485, 44486, 35424), (44496, 44500, 576)

X(44500) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF 2nd NEUBERG TRIANGLE

Barycentrics    a^2*(5*(b^2+c^2)*a^2-b^4+4*b^2*c^2-c^4) : :
X(44500) = 3*X(6)-X(39) = 5*X(6)-X(3094) = 3*X(6)+X(13330) = 7*X(6)-3*X(13331) = 5*X(39)-3*X(3094) = X(39)+3*X(5052) = 7*X(39)-9*X(13331) = X(76)+3*X(1992) = 3*X(193)+5*X(31276) = 3*X(1351)+X(9821) = X(3094)+5*X(5052) = 3*X(3094)+5*X(13330) = 7*X(3094)-15*X(13331) = X(3095)-5*X(11482) = 3*X(5052)-X(13330) = 7*X(5052)+3*X(13331) = 3*X(5093)-X(35439) = X(9821)-3*X(13354) = 7*X(13330)+9*X(13331) = 3*X(14994)-5*X(31276)

The squared-radius of this circle is: ρ2 = (9*S^2+4*SW^2)*R^2*S^2/(4*(S^2+SW^2)*SW^2)

X(44500) lies on these lines: {3, 6}, {51, 9465}, {69, 7858}, {76, 1992}, {83, 39099}, {193, 14994}, {194, 5032}, {230, 25555}, {251, 13366}, {262, 5304}, {263, 14252}, {373, 9463}, {524, 3934}, {538, 8584}, {542, 7745}, {597, 6683}, {599, 7903}, {732, 32455}, {1180, 21969}, {1194, 20977}, {1506, 15993}, {1613, 6688}, {2023, 35021}, {2393, 27375}, {2548, 34507}, {2782, 41672}, {3051, 3291}, {3068, 22723}, {3069, 22722}, {3202, 19136}, {3629, 24256}, {3767, 5476}, {3815, 40107}, {3819, 20965}, {3917, 15302}, {4663, 14839}, {5280, 8540}, {5286, 20423}, {5299, 19369}, {5305, 11623}, {5354, 15019}, {5359, 15004}, {5475, 18553}, {5640, 40130}, {5643, 11580}, {5969, 20583}, {6194, 14930}, {6329, 10007}, {7736, 15819}, {7747, 11645}, {7839, 10754}, {8541, 8743}, {8550, 18907}, {9466, 15534}, {10219, 21001}, {10312, 44102}, {11646, 39590}, {11649, 16308}, {14928, 19687}, {15069, 15484}, {18906, 41622}, {19063, 26456}, {19064, 26463}, {20081, 32451}, {21760, 39543}, {22712, 37665}, {39024, 44107}, {40332, 40341}

X(44500) = midpoint of X(i) and X(j) for these {i, j}: {6, 5052}, {39, 13330}, {193, 14994}, {1351, 13354}, {3629, 24256}, {5028, 35432}, {5188, 11477}, {9466, 15534}, {18906, 41622}
X(44500) = reflection of X(i) in X(j) for these (i, j): (10007, 6329), (13334, 575)
X(44500) = intersection, other than A,B,C, of conics {{A, B, C, X(4), X(8722)}} and {{A, B, C, X(32), X(18842)}}
X(44500) = 2nd Brocard circle-inverse of-X(5024)
X(44500) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 32, 575), (6, 576, 44499), (6, 1692, 15516), (6, 5017, 5034), (6, 5058, 44482), (6, 5062, 44481), (6, 11173, 42852), (6, 11477, 9605), (6, 12212, 1692), (6, 13330, 39), (6, 40825, 39561), (32, 575, 2030), (39, 5052, 13330), (187, 5038, 20190), (371, 372, 8722), (576, 44499, 44496), (1670, 1671, 5024), (1689, 1690, 11477), (3051, 13410, 3291), (3291, 13410, 5943), (5017, 5034, 5092), (11482, 43136, 6), (35007, 39560, 38010), (44501, 44502, 5097)

X(44501) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF INNER-VECTEN TRIANGLE

Barycentrics    a^2*(2*(a^2+b^2+c^2)*(2*a^4-5*(b^2+c^2)*a^2+3*b^4-4*b^2*c^2+3*c^4)*S+4*S^2*(5*(b^2+c^2)*a^2-b^4+4*b^2*c^2-c^4)) : :
X(44501) = 3*X(6)-X(372) = 3*X(6)-2*X(44481) = X(372)+3*X(35841) = X(638)+3*X(1992) = 9*X(5032)-X(43133) = 3*X(35841)+2*X(44481)

The squared-radius of this circle is: ρ2 = (9*S^2-12*S*SW+5*SW^2)*R^2*S^2/(4*(S^2-2*S*SW+SW^2)*SW^2)

X(44501) lies on these lines: {3, 6}, {69, 13939}, {141, 6119}, {485, 5476}, {486, 34507}, {524, 640}, {542, 3071}, {590, 25555}, {597, 8981}, {599, 13951}, {615, 40107}, {638, 1992}, {641, 14645}, {1132, 11180}, {1352, 42561}, {1587, 20423}, {2393, 30427}, {3299, 19369}, {3301, 8540}, {3317, 21356}, {3788, 35684}, {3818, 42268}, {5032, 43133}, {6459, 11179}, {6565, 18553}, {8550, 42215}, {8584, 32421}, {8681, 10666}, {8996, 32621}, {10880, 44102}, {11178, 42262}, {11314, 42060}, {11645, 35821}, {12971, 32292}, {13032, 13038}, {13785, 15069}, {13925, 18583}, {15073, 21641}, {19130, 42273}, {19924, 42259}, {24206, 42583}, {29012, 42271}, {31670, 39875}

X(44501) = midpoint of X(i) and X(j) for these {i, j}: {6, 35841}, {576, 44485}, {11477, 11824}
X(44501) = reflection of X(i) in X(j) for these (i, j): (3, 44483), (32, 44482), (372, 44481), (43121, 575), (44502, 44499)
X(44501) = Brocard-circle-inverse of X(44657)
X(44501) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44657), (6, 371, 575), (6, 372, 44481), (6, 576, 44502), (6, 3102, 44476), (6, 6419, 44482), (6, 9974, 44474), (6, 9975, 576), (6, 11477, 3312), (6, 13330, 5062), (6, 19145, 39561), (371, 1505, 43121), (575, 43144, 182), (575, 44496, 44502), (576, 44472, 1351), (576, 44473, 6), (576, 44474, 9974), (3102, 5058, 43120), (3364, 3389, 5058), (5097, 44500, 44502), (6417, 11482, 6), (9974, 44474, 44502), (9975, 44473, 44502), (15520, 42833, 6), (22330, 44482, 6)

X(44502) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF OUTER-VECTEN TRIANGLE

Barycentrics    a^2*(a^4+2*b^4-2*b^2*c^2+2*c^4-3*(b^2+c^2)*a^2-(2*a^2+2*c^2+2*b^2)*S) : :
X(44502) = 3*X(6)-X(371) = 3*X(6)-2*X(44482) = X(371)+3*X(35840) = X(637)+3*X(1992) = 9*X(5032)-X(43134) = 3*X(35840)+2*X(44482)

The squared-radius of this circle is ρ2 = (9*S^2+12*SW*S+5*SW^2)*R^2*S^2/(4*(S^2+2*SW*S+SW^2)*SW^2)

X(44502) lies on these lines: {3, 6}, {69, 13886}, {141, 6118}, {485, 34507}, {486, 5476}, {524, 639}, {542, 3070}, {590, 40107}, {597, 13966}, {599, 8976}, {615, 25555}, {637, 1992}, {642, 14645}, {1131, 11180}, {1352, 31412}, {1588, 20423}, {2393, 30428}, {3299, 8540}, {3301, 19369}, {3316, 21356}, {3788, 35685}, {3818, 42269}, {5032, 43134}, {6460, 11179}, {6564, 18553}, {8550, 42216}, {8584, 32419}, {8681, 10665}, {10881, 44102}, {11178, 42265}, {11313, 42009}, {11645, 35820}, {12965, 32291}, {13030, 13037}, {13665, 15069}, {13993, 18583}, {15073, 21640}, {19130, 42270}, {19924, 42258}, {24206, 42582}, {29012, 42272}, {31670, 39876}

X(44502) = midpoint of X(i) and X(j) for these {i, j}: {6, 35840}, {576, 44486}, {11477, 11825}
X(44502) = reflection of X(i) in X(j) for these (i, j): (3, 44484), (32, 44481), (371, 44482), (43120, 575), (44501, 44499)
X(44502) = Brocard-circle-inverse of X(44656)
X(44502) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44656), (6, 371, 44482), (6, 372, 575), (6, 576, 44501), (6, 3103, 44475), (6, 6420, 44481), (6, 9974, 576), (6, 9975, 44473), (6, 11477, 3311), (6, 13330, 5058), (6, 19146, 39561), (372, 1504, 43120), (575, 43141, 182), (575, 44496, 44501), (576, 44471, 1351), (576, 44473, 9975), (576, 44474, 6), (3103, 5062, 43121), (3365, 3390, 5062), (5097, 44500, 44501), (6418, 11482, 6), (9974, 44474, 44501), (9975, 44473, 44501), (15520, 42832, 6)

X(44503) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF 1st EXCOSINE TRIANGLE

Barycentrics    a^2*(a^10-3*(b^2+c^2)*a^8+2*(b^4+6*b^2*c^2+c^4)*a^6+2*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)*a^4-(3*b^8+3*c^8-2*(2*b^4-9*b^2*c^2+2*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3) : :
X(44503) = 3*X(597)-X(15873)

The squared-radius of this circle is: ρ2 = (4*R^4*SW^2+(6*R^2-SW)^2*S^2)*R^2/((8*R^2-SW)^2*SW^2)

X(44503) lies on these lines: {3, 6}, {5, 8549}, {24, 43815}, {69, 26879}, {140, 5486}, {155, 8550}, {235, 14561}, {394, 11245}, {468, 10601}, {524, 18951}, {542, 17814}, {597, 15873}, {631, 41614}, {1092, 40673}, {1147, 32621}, {1181, 11179}, {2393, 6642}, {3523, 37784}, {3526, 5181}, {3542, 3618}, {3564, 18952}, {5020, 43130}, {5422, 7493}, {5622, 7503}, {5892, 11216}, {5944, 23041}, {6644, 15074}, {6723, 9976}, {6776, 6816}, {6803, 18919}, {7387, 19136}, {7393, 19458}, {7526, 10249}, {7592, 22151}, {8537, 15045}, {8547, 15582}, {9813, 11695}, {9826, 13248}, {10168, 19361}, {10519, 40318}, {10605, 43814}, {10984, 44102}, {11255, 12006}, {11416, 15043}, {11459, 43812}, {11645, 15811}, {11649, 37933}, {11793, 17836}, {14853, 37201}, {14912, 20806}, {15069, 25738}, {15073, 17928}, {15121, 31255}, {15311, 34117}, {15462, 19357}, {16238, 38110}, {17809, 41615}, {17811, 34507}, {26221, 39141}, {35259, 43811}

X(44503) = reflection of X(44489) in X(575)
X(44503) = Brocard circle-inverse of-X(44492)
X(44503) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44492), (6, 37498, 576), (6, 37514, 44480), (182, 576, 9729), (182, 44479, 3), (182, 44480, 37514), (575, 44469, 6), (6644, 15074, 34787)

X(44504) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF MCCAY TRIANGLE

Barycentrics    a^2*(7*a^8-20*(b^2+c^2)*a^6+2*(13*b^4+4*b^2*c^2+13*c^4)*a^4-4*(b^2+c^2)*(2*b^2+b*c-2*c^2)*(2*b^2-b*c-2*c^2)*a^2+3*b^8-2*(10*b^4-13*b^2*c^2+10*c^4)*b^2*c^2+3*c^8) : :

The squared-radius of this circle is: ρ2 = (9*S^4*(9*S^2-SW^2)-SW^4*(5*S^2-SW^2))*R^2/(4*SW^2*(6*S^2-SW^2)^2)

X(44504) lies on these lines: {3, 6}, {183, 22525}, {5921, 32963}, {6036, 11184}, {6776, 33006}, {8352, 11179}, {8753, 21460}, {21501, 37527}, {32998, 40330}

X(44504) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (575, 44507, 44508), (44505, 44506, 6), (44509, 44510, 3)

X(44505) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF INNER-NAPOLEON TRIANGLE

Barycentrics    a^2*(-2*sqrt(3)*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)) : :

The squared-radius of this circle is: ρ2 = (SW^4+(27*S^2+4*SW^2)*S^2-2*sqrt(3)*(3*S^2+SW^2)*S*SW)*R^2/(4*(SW-2*sqrt(3)*S)^2*SW^2)

X(44505) lies on these lines: {3, 6}, {6774, 9763}

X(44505) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 44504, 44506), (182, 575, 44506), (182, 576, 13349), (182, 44487, 3), (575, 44477, 6)

X(44506) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF OUTER-NAPOLEON TRIANGLE

Barycentrics    a^2*(2*sqrt(3)*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)) : :

The squared-radius of this circle is: ρ2 = (SW^4+(27*S^2+4*SW^2)*S^2+2*sqrt(3)*(3*S^2+SW^2)*S*SW)*R^2/(4*(SW+2*sqrt(3)*S)^2*SW^2)

X(44506) lies on these lines: {3, 6}, {6771, 9761}

X(44506) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 44504, 44505), (182, 575, 44505), (182, 576, 13350), (182, 44488, 3), (575, 44478, 6)

X(44507) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF 1ST NEUBERG TRIANGLE

Barycentrics    a^2*(3*a^8-6*(b^2+c^2)*a^6+8*(b^4+c^4)*a^4-2*(b^2+c^2)*(3*b^4-4*b^2*c^2+3*c^4)*a^2+b^8-2*(4*b^4-3*b^2*c^2+4*c^4)*b^2*c^2+c^8) : :
X(44507) = 3*X(5050)-X(40825)

The squared-radius of this circle is: ρ2 = (S^4*(9*S^2-5*SW^2)-SW^4*(S^2-SW^2))*R^2/(4*(2*S^2-SW^2)^2*SW^2)

X(44507) lies on these lines: {3, 6}, {325, 9755}, {542, 11318}, {1352, 7887}, {3618, 37446}, {5025, 6776}, {5182, 11257}, {5622, 38523}, {5967, 41238}, {6036, 7778}, {7841, 11179}, {9752, 16989}, {10349, 12177}, {14912, 32823}, {18583, 40279}

X(44507) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (182, 575, 44508), (182, 576, 13335), (2025, 39764, 6), (44483, 44484, 5092), (44504, 44508, 575), (44509, 44510, 6)

X(44508) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF 2nd NEUBERG TRIANGLE

Barycentrics    a^2*(a^8-8*(b^2+c^2)*a^6+2*(5*b^4+4*b^2*c^2+5*c^4)*a^4-4*(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^2+b^8-2*(2*b^4-7*b^2*c^2+2*c^4)*b^2*c^2+c^8) : :
X(44508) = 9*X(5050)-X(10983)

The squared-radius of this circle is: ρ2 = (S^4*(9*S^2+7*SW^2)+SW^4*(3*S^2+SW^2))*R^2/(4*(2*S^2+SW^2)^2*SW^2)

X(44508) lies on these lines: {3, 6}, {631, 39099}, {1352, 32992}, {1975, 31958}, {5921, 33261}, {6776, 16924}, {7770, 12177}, {7786, 10753}, {7851, 14561}, {7864, 14853}, {8177, 12007}, {8370, 11179}, {10982, 14133}, {13111, 14848}, {15271, 34507}, {22525, 39093}

X(44508) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 5050, 5038), (182, 575, 44507), (182, 576, 13334), (182, 35424, 5085), (575, 44507, 44504), (35431, 39561, 6), (44509, 44510, 5050)

X(44509) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF INNER-VECTEN TRIANGLE

Barycentrics    a^2*(-2*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)) : :
X(44509) = 3*X(6)+X(12306) = 3*X(182)-X(12975) = 9*X(5050)-X(12314) = 3*X(5050)-X(19146) = X(12314)-3*X(19146)

The squared-radius of this circle is: ρ2 = (S^2*(9*S^2+2*SW^2)-2*S*SW*(3*S^2+SW^2)+SW^4)*R^2/(4*(SW-2*S)^2*SW^2)

X(44509) lies on these lines: {3, 6}, {524, 13087}, {542, 6290}, {1503, 22596}, {2782, 22594}, {6776, 26469}, {8550, 23312}, {12299, 44102}, {13749, 22820}

X(44509) = midpoint of X(i) and X(j) for these {i, j}: {3, 9975}, {576, 7692}, {8550, 23312}
X(44509) = Brocard-circle-inverse of X(44655)
X(44509) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44655), (3, 44504, 44510), (6, 9732, 576), (6, 43118, 44486), (6, 44507, 44510), (182, 575, 44510), (182, 576, 43121), (182, 12974, 20190), (182, 44486, 43118), (575, 44475, 6), (575, 44482, 39561), (575, 44483, 182), (5050, 44508, 44510), (12306, 43118, 12975)

X(44510) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF OUTER-VECTEN TRIANGLE

Barycentrics    a^2*(2*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S+(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)) : :
X(44510) = 3*X(6)+X(12305) = 3*X(182)-X(12974) = 9*X(5050)-X(12313) = 3*X(5050)-X(19145) = X(12313)-3*X(19145)

The squared-radius of this circle is: ρ2 = (S^2*(9*S^2+2*SW^2)+2*S*SW*(3*S^2+SW^2)+SW^4)*R^2/(4*(SW+2*S)^2*SW^2)

X(44510) lies on these lines: {3, 6}, {524, 13088}, {542, 6289}, {1503, 22625}, {2782, 22623}, {6776, 26468}, {8550, 23311}, {12298, 44102}, {13748, 22819}

X(44510) = midpoint of X(i) and X(j) for these {i, j}: {3, 9974}, {576, 7690}, {8550, 23311}
X(44510) = Brocard-circle-inverse of X(44654)
X(44510) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 44654), (3, 44504, 44509), (6, 9733, 576), (6, 43119, 44485), (6, 44507, 44509), (182, 575, 44509), (182, 576, 43120), (182, 12975, 20190), (182, 44485, 43119), (182, 44486, 3), (575, 44476, 6), (575, 44481, 39561), (575, 44484, 182), (5050, 44508, 44509), (9974, 19145, 12962), (12305, 43119, 12974)

X(44511) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF INNER-FERMAT TRIANGLE

Barycentrics    a^2*(2*sqrt(3)*(a^2+b^2+c^2)*S+a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4) : :
X(44511) = 3*X(6)-X(62) = 3*X(597)-2*X(6695) = X(634)+3*X(1992)

The squared-radius of this circle is: ρ2 = (9*S^2-12*sqrt(3)*S*SW+13*SW^2)*R^2*S^2/(4*(sqrt(3)*SW-S)^2*SW^2)

X(44511) lies on these lines: {3, 6}, {14, 18553}, {395, 40107}, {396, 14137}, {398, 542}, {524, 636}, {532, 8584}, {597, 6695}, {599, 42989}, {630, 3589}, {634, 1992}, {2393, 30390}, {3818, 42159}, {5254, 16002}, {5476, 40693}, {7745, 16001}, {7797, 22114}, {7817, 34508}, {8550, 41023}, {10168, 16772}, {11178, 42153}, {11303, 22579}, {11645, 16964}, {15069, 42975}, {19130, 42166}, {19924, 42148}, {20423, 42998}, {24206, 42599}, {29012, 42164}, {34507, 40694}, {34573, 42591}, {37825, 42999}, {43228, 44219}

X(44511) = midpoint of X(11477) and X(14541)
X(44511) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 61, 575), (6, 576, 44512), (6, 3364, 44482), (6, 3365, 44481), (6, 36757, 15516), (6, 44497, 44498), (575, 44499, 44512), (576, 44512, 44498), (22330, 44500, 44512), (44497, 44512, 576), (44501, 44502, 44497)

X(44512) = CENTER OF LOZADA-LEMOINE-CIRCLE-3A OF OUTER-FERMAT TRIANGLE

Barycentrics    a^2*(-2*sqrt(3)*(a^2+b^2+c^2)*S+a^4-3*(b^2+c^2)*a^2+2*b^4-2*b^2*c^2+2*c^4) : :
X(44512) = 3*X(6)-X(61) = 3*X(597)-2*X(6694) = X(633)+3*X(1992)

The squared-radius of this circle is: ρ2 = (9*S^2-12*sqrt(3)*S*SW+13*SW^2)*R^2*S^2/(4*(sqrt(3)*SW-S)^2*SW^2)

X(44512) lies on these lines: {3, 6}, {13, 18553}, {395, 14136}, {396, 40107}, {397, 542}, {524, 635}, {533, 8584}, {597, 6694}, {599, 42988}, {629, 3589}, {633, 1992}, {2393, 30391}, {3818, 42162}, {5254, 16001}, {5476, 40694}, {7745, 16002}, {7797, 22113}, {7817, 34509}, {8550, 41022}, {10168, 16773}, {11178, 42156}, {11304, 22580}, {11645, 16965}, {15069, 42974}, {19130, 42163}, {19924, 42147}, {20423, 42999}, {24206, 42598}, {29012, 42165}, {34507, 40693}, {34573, 42590}, {37824, 42998}

X(44512) = midpoint of X(11477) and X(14540)
X(44512) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 62, 575), (6, 576, 44511), (6, 3389, 44482), (6, 3390, 44481), (6, 36758, 15516), (6, 44498, 44497), (575, 44499, 44511), (576, 44511, 44497), (22330, 44500, 44511), (44498, 44511, 576), (44501, 44502, 44498)

X(44513) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF INNER-FERMAT TRIANGLE

Barycentrics    a^2*(sqrt(3)*(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)-2*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S) : :

The squared-radius of this circle is: ρ2 = ((9*S^2+4*SW^2)*S^2-2*sqrt(3)*(3*S^2+SW^2)*SW*S+3*SW^4)*R^2/(4*(sqrt(3)*SW-2*S)^2*SW^2)

X(44513) lies on these lines: {3, 6}, {542, 11306}, {5873, 8550}, {6774, 34507}, {11179, 11304}, {25555, 41041}

X(44513) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 44507, 44514), (6, 5865, 576), (182, 575, 44514), (182, 44505, 44506), (575, 44514, 44506), (10541, 44504, 44514), (44505, 44514, 575), (44509, 44510, 44505)

X(44514) = CENTER OF LOZADA-LEMOINE-CIRCLE-3B OF OUTER-FERMAT TRIANGLE

Barycentrics    a^2*(sqrt(3)*(a^2+b^2+c^2)*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)+2*(2*a^4-3*(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4)*S) : :

The squared-radius of this circle is: ρ2 = ((9*S^2+4*SW^2)*S^2+2*sqrt(3)*(3*S^2+SW^2)*SW*S+3*SW^4)*R^2/(4*(sqrt(3)*SW+2*S)^2*SW^2)

X(44514) lies on these lines: {3, 6}, {542, 11305}, {5872, 8550}, {6771, 34507}, {11179, 11303}, {25555, 41040}

X(44514) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 44507, 44513), (6, 5864, 576), (182, 575, 44513), (182, 44506, 44505), (575, 44513, 44505), (10541, 44504, 44513), (44506, 44513, 575), (44509, 44510, 44506)

X(44515) = X(3)X(161)∩X(26)X(195)

Barycentrics    (a^14-3*(b^2+c^2)*a^12+(b^2+c^2)^2*a^10+(b^2+c^2)*(5*b^4+2*b^2*c^2+5*c^4)*a^8-(5*b^8+5*c^8+3*(2*b^4+b^2*c^2+2*c^4)*b^2*c^2)*a^6-(b^2+c^2)*(b^8+c^8-(2*b^2-c^2)*(b^2-2*c^2)*b^2*c^2)*a^4+(3*b^8+3*c^8+2*(b^4+b^2*c^2+c^4)*b^2*c^2)*(b^2-c^2)^2*a^2-(b^8-c^8)*(b^2-c^2)^3)*a^2 : :
Barycentrics    (SB+SC)*(2*(3*R^2-SA-SW)*S^2+(11*R^4+2*(2*SA-7*SW)*R^2-2*(SA^2-SB*SC-2*SW^2))*SA) : :

See Antreas Hatzipolakis and César Lozada, euclid 2116.

X(44515) lies on these lines: {3, 161}, {22, 12307}, {23, 20424}, {26, 195}, {54, 143}, {156, 32338}, {399, 41726}, {567, 11808}, {1147, 15137}, {1154, 1614}, {1658, 12254}, {2888, 7502}, {2918, 3519}, {3518, 8254}, {3574, 18378}, {5663, 7691}, {5899, 15800}, {6242, 37932}, {6639, 32346}, {6746, 15037}, {7488, 32423}, {7512, 21230}, {7517, 32333}, {7555, 25714}, {7730, 32046}, {10282, 11597}, {10610, 13363}, {11804, 18282}, {12107, 36966}, {12325, 38435}, {12380, 13368}, {12899, 41596}, {15647, 22815}, {22051, 37936}, {32349, 40276}, {37922, 43573}

X(44515) = reflection of X(i) in X(j) for these (i, j): (54, 5944), (15800, 43831)
X(44515) = {X(10610), X(13365)}-harmonic conjugate of X(43651)

X(44516) = X(2)X(1614)∩X(3)X(1568)

Barycentrics    (-a^2+b^2+c^2)*(2*a^8-4*(b^2+c^2)*a^6+(b^4-4*b^2*c^2+c^4)*a^4+2*(b^4-c^4)*(b^2-c^2)*a^2-(b^2-c^2)^4) : :
X(44516) = 3*X(2)+X(1614), 5*X(631)-X(11440), 3*X(7552)+X(34148)

See Antreas Hatzipolakis and César Lozada, euclid 2116.

X(44516) lies on these lines: {2, 1614}, {3, 1568}, {4, 39242}, {5, 5944}, {49, 539}, {110, 1209}, {113, 14118}, {125, 18128}, {140, 5663}, {143, 12242}, {156, 21243}, {184, 5449}, {185, 20191}, {195, 41586}, {265, 10619}, {343, 41597}, {389, 10020}, {468, 5462}, {542, 34826}, {549, 43604}, {569, 7505}, {578, 10201}, {631, 11440}, {858, 17712}, {1147, 3549}, {1154, 15806}, {1216, 6676}, {1495, 5576}, {1594, 44407}, {1656, 35259}, {1658, 18388}, {2070, 3574}, {2888, 9705}, {2918, 37972}, {3357, 18580}, {3515, 7706}, {3523, 4846}, {3589, 43130}, {5012, 14940}, {5446, 13383}, {5447, 11064}, {5892, 16238}, {5943, 44232}, {6146, 36253}, {6640, 10984}, {7392, 15436}, {7399, 43586}, {7542, 13754}, {7550, 38795}, {7552, 34148}, {7568, 11793}, {7569, 35264}, {7577, 11750}, {7728, 18364}, {8254, 10095}, {9707, 18474}, {9729, 44452}, {9730, 10018}, {9927, 19357}, {10024, 13367}, {10125, 13630}, {10182, 37814}, {10254, 21659}, {10575, 37118}, {10615, 30482}, {11003, 26917}, {11225, 32136}, {11430, 12897}, {11536, 44322}, {11585, 13394}, {11591, 32348}, {11702, 34149}, {11800, 40632}, {12006, 44234}, {12010, 43575}, {12038, 15760}, {12233, 34351}, {12900, 37513}, {13289, 32364}, {13403, 13406}, {13419, 39504}, {13431, 37779}, {13434, 37943}, {13474, 44236}, {13491, 25563}, {13909, 19356}, {13970, 19355}, {14157, 18488}, {14643, 34864}, {14677, 43585}, {15074, 16776}, {15644, 25337}, {20299, 40276}, {22352, 37452}, {32046, 43573}, {32068, 36153}, {32142, 34004}, {36752, 37453}, {37760, 38848}

X(44516) = midpoint of X(i) and X(j) for these {i, j}: {3, 43831}, {5, 5944}, {10024, 13367}, {15806, 34577}
X(44516) = reflection of X(6746) in X(5462)
X(44516) = complement of the complement of X(1614)
X(44516) = barycentric product X(343)*X(36842)

X(44517) = X(1)X(6)∩X(3)X(115)

Barycentrics    a*(a^6 - a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - a*b^5 - a^5*c - a^4*b*c + a^2*b^3*c + a*b^4*c - 2*b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a^3*c^3 + a^2*b*c^3 + 4*b^3*c^3 + a^2*c^4 + a*b*c^4 - a*c^5 - 2*b*c^5) : :

X(44517) lies on these lines: {1, 6}, {3, 115}, {21, 230}, {32, 7489}, {187, 13743}, {404, 3054}, {1006, 5254}, {1012, 5023}, {1030, 9840}, {1213, 25906}, {3053, 3560}, {3055, 17536}, {3815, 5047}, {5013, 6883}, {5124, 13732}, {5306, 16858}, {5428, 43291}, {6920, 7745}, {7735, 16865}, {7736, 16859}, {8553, 13730}, {9300, 16861}, {11108, 31489}, {11342, 19720}, {17544, 37665}

X(44517) = crossdifference of every pair of points on line {513, 6132}

X(44518) = X(3)X(115)∩X(4)X(6)

Barycentrics    a^4 - a^2*b^2 - 2*b^4 - a^2*c^2 + 4*b^2*c^2 - 2*c^4 : :
X(44518) = 2 X[3788] - 3 X[11318], X[3926] - 3 X[16041], 3 X[7776] - 2 X[7916], 3 X[7825] - X[7916], 4 X[7886] - 3 X[11288]

X(44518) lies on these lines: {2, 15815}, {3, 115}, {4, 6}, {5, 2549}, {11, 9597}, {12, 9598}, {20, 230}, {30, 3053}, {32, 382}, {39, 381}, {69, 2996}, {76, 338}, {99, 7887}, {112, 35490}, {140, 43620}, {141, 32974}, {148, 1975}, {154, 460}, {172, 12943}, {183, 6655}, {187, 1657}, {194, 7773}, {232, 37197}, {290, 30496}, {297, 26958}, {315, 33229}, {316, 6144}, {325, 14063}, {384, 7851}, {385, 33019}, {485, 18939}, {486, 18940}, {524, 6392}, {538, 7776}, {543, 3788}, {546, 2548}, {548, 21843}, {550, 5210}, {574, 1656}, {577, 8990}, {578, 9604}, {625, 7781}, {940, 23903}, {999, 9651}, {1003, 7828}, {1007, 32980}, {1015, 9669}, {1078, 33234}, {1150, 23942}, {1184, 7391}, {1194, 5064}, {1196, 34609}, {1368, 8770}, {1370, 1611}, {1384, 5073}, {1479, 16781}, {1500, 9654}, {1504, 13665}, {1505, 13785}, {1506, 3851}, {1569, 38743}, {1570, 39899}, {1571, 9956}, {1572, 22793}, {1597, 27371}, {1609, 39568}, {1613, 14957}, {1698, 31443}, {1853, 3981}, {1879, 11479}, {1914, 12953}, {1968, 44438}, {1971, 17845}, {2023, 11257}, {2088, 15538}, {2165, 12362}, {2241, 9668}, {2242, 9655}, {2275, 10896}, {2276, 10895}, {2393, 40325}, {2475, 5275}, {2886, 31490}, {3054, 3523}, {3055, 5056}, {3091, 3815}, {3094, 6248}, {3146, 7735}, {3291, 31152}, {3295, 9664}, {3329, 33018}, {3436, 21956}, {3522, 5585}, {3526, 37512}, {3534, 5206}, {3543, 5306}, {3545, 31400}, {3583, 16502}, {3589, 32971}, {3614, 31497}, {3618, 32979}, {3627, 5305}, {3734, 7861}, {3763, 6656}, {3785, 33238}, {3830, 5309}, {3832, 7736}, {3839, 9300}, {3843, 5475}, {3845, 7739}, {3850, 31406}, {3853, 5319}, {3855, 9606}, {3856, 31417}, {3926, 16041}, {3934, 7872}, {5007, 5076}, {5022, 36654}, {5028, 18440}, {5038, 10358}, {5054, 15515}, {5055, 31455}, {5059, 37689}, {5072, 7603}, {5077, 7830}, {5079, 31652}, {5111, 13449}, {5116, 7770}, {5124, 37415}, {5134, 14974}, {5280, 18513}, {5283, 17532}, {5299, 18514}, {5304, 17578}, {5346, 21309}, {5355, 43136}, {5395, 41895}, {5461, 34504}, {5737, 23897}, {6034, 9880}, {6103, 8778}, {6337, 32972}, {6409, 21737}, {6421, 6565}, {6422, 6564}, {6423, 35820}, {6424, 35821}, {6531, 18848}, {6658, 7806}, {6772, 11305}, {6775, 11306}, {6781, 17800}, {6823, 9722}, {6871, 37661}, {7388, 8252}, {7389, 8253}, {7395, 18353}, {7396, 40326}, {7406, 37646}, {7503, 9609}, {7509, 15109}, {7571, 38862}, {7610, 7833}, {7615, 8359}, {7620, 21358}, {7750, 8667}, {7751, 7842}, {7752, 31859}, {7753, 14269}, {7759, 22253}, {7762, 8352}, {7763, 8716}, {7772, 15484}, {7774, 32996}, {7775, 32450}, {7777, 32993}, {7782, 14061}, {7783, 32966}, {7785, 14062}, {7786, 15031}, {7787, 14042}, {7788, 7885}, {7789, 14064}, {7791, 15271}, {7792, 14035}, {7793, 33256}, {7795, 33184}, {7797, 11361}, {7798, 7843}, {7800, 8357}, {7802, 14568}, {7803, 8370}, {7804, 7902}, {7810, 40727}, {7816, 7844}, {7817, 11159}, {7823, 14614}, {7827, 11317}, {7832, 33219}, {7834, 11286}, {7835, 33218}, {7839, 14044}, {7840, 20105}, {7847, 11285}, {7852, 33237}, {7853, 17130}, {7857, 33235}, {7864, 11174}, {7867, 33241}, {7868, 7933}, {7873, 17131}, {7874, 33240}, {7881, 7934}, {7886, 11288}, {7891, 20094}, {7893, 19570}, {7898, 17129}, {7903, 31173}, {7912, 14045}, {7919, 33217}, {7920, 14066}, {7924, 31276}, {7935, 9466}, {7942, 33220}, {7945, 14046}, {7947, 33289}, {7951, 31448}, {7989, 9574}, {8356, 32832}, {8553, 11414}, {8556, 32828}, {8589, 15720}, {8719, 39663}, {8754, 10602}, {9289, 35142}, {9465, 31133}, {9540, 9601}, {9593, 18492}, {9600, 10576}, {9603, 10539}, {9608, 10594}, {9619, 9955}, {9620, 18480}, {9699, 18378}, {9745, 31857}, {9924, 41762}, {10097, 23105}, {10311, 12173}, {10312, 35480}, {10329, 41231}, {10583, 14034}, {10722, 12829}, {11063, 12082}, {11184, 33006}, {11231, 31422}, {11235, 17448}, {11236, 20691}, {11289, 43029}, {11290, 43028}, {11303, 16644}, {11304, 16645}, {11331, 41254}, {11585, 15075}, {11646, 15069}, {12188, 43183}, {12203, 39560}, {12293, 23128}, {12601, 35841}, {12602, 35840}, {12902, 14901}, {12963, 42263}, {12968, 42264}, {13108, 32452}, {13161, 16777}, {13468, 33272}, {13567, 37174}, {13711, 42260}, {13834, 42261}, {13850, 41491}, {13932, 41490}, {14001, 32826}, {14068, 16989}, {14537, 38335}, {14880, 22515}, {14907, 19695}, {15491, 32987}, {15513, 15696}, {15668, 23905}, {16055, 31125}, {16589, 17528}, {16986, 19690}, {16992, 33824}, {17004, 33260}, {17005, 33011}, {17006, 33022}, {17008, 32997}, {18403, 22120}, {18404, 23115}, {18841, 32532}, {19758, 37049}, {19780, 42097}, {19781, 42096}, {20065, 33279}, {20181, 26558}, {20998, 41238}, {21001, 37190}, {21043, 23899}, {21965, 24248}, {22110, 32831}, {22329, 33192}, {25639, 31449}, {29012, 40825}, {29323, 41412}, {30771, 34481}, {31430, 31441}, {31451, 31479}, {31456, 31493}, {31461, 31476}, {31463, 42273}, {31468, 31488}, {31644, 40879}, {31709, 42154}, {31710, 42155}, {32151, 43449}, {32459, 32970}, {32817, 33292}, {32820, 33290}, {32822, 33285}, {32829, 32984}, {32834, 33210}, {32838, 33215}, {32872, 42850}, {32963, 37647}, {32965, 37688}, {32989, 44381}, {33013, 42849}, {33023, 34229}, {33278, 37671}, {33802, 37902}, {34511, 37350}, {35287, 44401}, {35488, 39575}, {35955, 43459}, {36251, 42156}, {36252, 42153}, {37638, 39691}, {41406, 42431}, {41407, 42432}

X(44518) = midpoint of X(i) and X(j) for these {i,j}: {6392, 32006}, {42645, 42646}
X(44518) = reflection of X(i) in X(j) for these {i,j}: {3053, 3767}, {7776, 7825}
X(44518) = isotomic conjugate of the isogonal conjugate of X(34481)
X(44518) = polar conjugate of the isotomic conjugate of X(30771)
X(44518) = crosspoint of X(4) and X(2996)
X(44518) = crosssum of X(i) and X(j) for these (i,j): {3, 3053}, {6, 8780}, {577, 41619}
X(44518) = crossdifference of every pair of points on line {520, 6132}
X(44518) = areal center of cevian triangles of PU(4)
X(44518) = barycentric product X(i)*X(j) for these {i,j}: {4, 30771}, {76, 34481}
X(44518) = barycentric quotient X(i)/X(j) for these {i,j}: {30771, 69}, {34481, 6}
X(44518) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 115, 13881}, {3, 13881, 37637}, {4, 5254, 6}, {4, 5286, 7745}, {4, 5523, 2207}, {4, 43448, 5254}, {5, 2549, 5013}, {5, 5013, 31489}, {12, 9598, 31477}, {20, 230, 5023}, {76, 7784, 599}, {76, 7841, 7784}, {76, 7911, 7879}, {115, 7748, 3}, {115, 7756, 7746}, {148, 5025, 1975}, {194, 7773, 9766}, {194, 14041, 7773}, {546, 15048, 2548}, {574, 39565, 1656}, {671, 7841, 34505}, {1506, 3851, 18584}, {1506, 18424, 3851}, {1975, 5025, 7778}, {2996, 32982, 69}, {3070, 3071, 6776}, {3091, 7738, 3815}, {3627, 5305, 7737}, {3734, 7861, 7866}, {3815, 7738, 22332}, {3830, 30435, 7747}, {3843, 9605, 5475}, {3850, 31406, 31415}, {3851, 5024, 1506}, {3934, 7872, 11287}, {5013, 31489, 31492}, {5024, 18424, 18584}, {5072, 31467, 7603}, {5210, 43619, 11742}, {5254, 7745, 5286}, {5286, 7745, 6}, {5309, 7747, 30435}, {5475, 7765, 9605}, {6337, 32972, 44377}, {7746, 7748, 7756}, {7746, 7756, 3}, {7772, 39590, 15484}, {7782, 14061, 33233}, {7784, 34505, 76}, {7816, 7844, 32954}, {7841, 7879, 7911}, {7841, 34505, 599}, {7842, 32457, 7751}, {7864, 16044, 11174}, {7872, 18546, 3934}, {7879, 7911, 7784}, {7885, 20081, 7788}, {7933, 17128, 7868}, {11648, 39563, 381}, {14064, 32815, 7789}, {23251, 23261, 36990}, {35830, 35831, 3}, {43291, 43619, 5210}

X(44519) = X(3)X(115)∩X(6)X(20)

Barycentrics    5*a^4 - 5*a^2*b^2 - 2*b^4 - 5*a^2*c^2 + 4*b^2*c^2 - 2*c^4 : :
X(44519) = 2 X[2548] - 3 X[5013], 5 X[2548] - 6 X[31406], 5 X[5013] - 4 X[31406], X[32826] - 3 X[33215]

X(44519) lies on these lines: {3, 115}, {4, 8719}, {5, 43619}, {6, 20}, {30, 2548}, {32, 3534}, {39, 1657}, {99, 7784}, {141, 33023}, {148, 33275}, {183, 33260}, {187, 15696}, {194, 6144}, {230, 3522}, {315, 8353}, {325, 32997}, {376, 5023}, {381, 37512}, {382, 574}, {548, 3767}, {550, 2549}, {566, 37196}, {599, 1975}, {626, 5077}, {1003, 7846}, {1078, 34505}, {1384, 7765}, {1506, 3830}, {1571, 28160}, {1656, 15515}, {2207, 35481}, {2996, 13468}, {3054, 15717}, {3055, 3832}, {3068, 9601}, {3146, 3815}, {3526, 8589}, {3528, 5585}, {3529, 7745}, {3530, 43620}, {3552, 7923}, {3589, 32981}, {3627, 31401}, {3763, 7791}, {3843, 18584}, {3853, 31415}, {3926, 33247}, {4296, 9594}, {4302, 16781}, {4324, 16502}, {5024, 7747}, {5054, 39565}, {5059, 7736}, {5063, 34622}, {5070, 18424}, {5073, 5475}, {5275, 37256}, {5286, 17538}, {5309, 15689}, {5691, 31443}, {5925, 32445}, {6337, 33272}, {6409, 26516}, {6410, 26521}, {6421, 42266}, {6422, 42267}, {6655, 7778}, {6658, 11174}, {6704, 11286}, {6781, 30435}, {7354, 31477}, {7503, 15109}, {7737, 15704}, {7739, 15686}, {7750, 33253}, {7753, 15685}, {7763, 19695}, {7773, 33256}, {7774, 33209}, {7777, 19691}, {7781, 7882}, {7782, 7841}, {7783, 7900}, {7787, 9855}, {7789, 32986}, {7790, 33235}, {7792, 33244}, {7797, 33268}, {7800, 8354}, {7802, 7905}, {7803, 33250}, {7808, 11159}, {7816, 7914}, {7839, 32480}, {7851, 13586}, {7861, 11288}, {7864, 33265}, {7872, 32456}, {7896, 15301}, {7898, 32821}, {7904, 20094}, {7913, 33242}, {7918, 33220}, {8252, 11294}, {8253, 11293}, {8553, 37198}, {8667, 33207}, {8725, 9605}, {8770, 10691}, {9300, 15683}, {9597, 15338}, {9598, 15326}, {9600, 35820}, {9604, 13346}, {9608, 12082}, {9609, 11413}, {9619, 28146}, {9655, 31451}, {9674, 13665}, {9722, 12976}, {10483, 31448}, {10992, 11646}, {11184, 33192}, {11257, 32469}, {11318, 22247}, {11648, 15513}, {12103, 15048}, {14064, 32459}, {15069, 32152}, {15075, 44249}, {15271, 32819}, {15491, 32979}, {15534, 20065}, {15682, 31404}, {15693, 39563}, {15700, 18362}, {16306, 16386}, {16310, 36748}, {16989, 33214}, {18480, 31422}, {19102, 42261}, {19105, 42260}, {21843, 33923}, {28168, 31430}, {28172, 31396}, {31295, 37661}, {31400, 33703}, {31403, 42414}, {31411, 42226}, {31457, 43457}, {31463, 42272}, {31829, 36751}, {32815, 33226}, {32826, 33215}, {32982, 44377}, {32996, 37647}, {34506, 41147}, {34873, 35930}, {42787, 43449}

X(44519) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7748, 13881}, {4, 15815, 31489}, {99, 7910, 7881}, {99, 33234, 7784}, {376, 5254, 5023}, {382, 31467, 39590}, {548, 3767, 5210}, {550, 2549, 3053}, {574, 39590, 31467}, {3843, 31455, 18584}, {5024, 17800, 7747}, {6459, 6460, 33748}, {7872, 32456, 32954}, {7881, 7910, 7784}, {7881, 33234, 7910}, {32819, 32965, 15271}, {42258, 42259, 25406}

X(44520) = X(3)X(115)∩X(6)X(21)

Barycentrics    a*(2*a^6 - 2*a^5*b - 4*a^4*b^2 + 4*a^3*b^3 + 2*a^2*b^4 - 2*a*b^5 - 2*a^5*c + a^4*b*c - a^2*b^3*c + 2*a*b^4*c - 2*b^5*c - 4*a^4*c^2 + 4*a^2*b^2*c^2 + 4*a^3*c^3 - a^2*b*c^3 + 4*b^3*c^3 + 2*a^2*c^4 + 2*a*b*c^4 - 2*a*c^5 - 2*b*c^5) : :

X(44520) lies on these lines: {3, 115}, {6, 21}, {230, 4189}, {405, 31489}, {1006, 15815}, {2549, 5428}, {3053, 6914}, {3054, 4188}, {3055, 16859}, {3767, 7508}, {3815, 16865}, {5023, 6906}, {5254, 6875}, {5585, 37403}, {7737, 31649}, {7739, 28463}, {9604, 13323}, {11742, 37426}, {12104, 15048}

X(44520) = crossdifference of every pair of points on line {6132, 8672}

X(44521) = X(3)X(115)∩X(6)X(22)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 + 2*b^6*c^2 + 3*a^2*b^2*c^4 - 2*b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8) : :

X(44521) lies on these lines: {2, 13585}, {3, 115}, {6, 22}, {23, 3815}, {24, 15815}, {25, 31489}, {26, 5013}, {32, 13564}, {39, 2937}, {230, 6636}, {511, 9604}, {566, 10311}, {574, 2070}, {1194, 2965}, {1506, 18378}, {2548, 17714}, {2549, 7502}, {3054, 15246}, {3055, 13595}, {3767, 7525}, {5023, 10323}, {5024, 9699}, {5063, 37928}, {5116, 37123}, {5254, 7512}, {5309, 34006}, {5475, 5899}, {7492, 7735}, {7545, 7603}, {7555, 15048}, {7736, 37913}, {7738, 38435}, {7745, 12088}, {9590, 31443}, {9608, 22332}, {9712, 31490}, {9714, 31492}, {10314, 14806}, {11742, 21312}, {13621, 31455}, {15515, 43809}, {15574, 40341}, {15818, 36748}, {18472, 19220}, {18570, 43619}, {19165, 44453}, {31401, 37440}, {44180, 44377}

X(44521) = crossdifference of every pair of points on line {826, 6132}
X(44521) = {X(22),X(9609)}-harmonic conjugate of X(6)

X(44522) = X(3)X(115)∩X(6)X(23)

Barycentrics    a^2*(2*a^8 - 4*a^6*b^2 + 4*a^2*b^6 - 2*b^8 - 4*a^6*c^2 + a^4*b^2*c^2 + 3*a^2*b^4*c^2 + 6*b^6*c^2 + 3*a^2*b^2*c^4 - 8*b^4*c^4 + 4*a^2*c^6 + 6*b^2*c^6 - 2*c^8) : :

X(44522) lies on these lines: {3, 115}, {6, 23}, {22, 11063}, {25, 30537}, {230, 7492}, {576, 9604}, {1995, 9609}, {2549, 7575}, {3518, 22332}, {3767, 7555}, {3815, 14002}, {5013, 12106}, {5254, 7556}, {5306, 37913}, {7506, 31492}, {7737, 37967}, {7739, 37936}, {9699, 37923}, {10311, 41335}, {10985, 13351}, {12088, 22331}, {12105, 15048}, {15109, 40916}, {37950, 43619}

X(44522) = crossdifference of every pair of points on line {3906, 6132}

X(44523) = X(3)X(115)∩X(6)X(24)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 - a^2*b^2*c^4 - 2*b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8) : :

X(44523) lies on these lines: {3, 115}, {6, 24}, {22, 1611}, {26, 3053}, {32, 2070}, {186, 5254}, {187, 2937}, {230, 7488}, {338, 1078}, {389, 9604}, {574, 43809}, {631, 15109}, {1609, 16195}, {1658, 3767}, {2548, 12106}, {2549, 37814}, {2931, 23128}, {3054, 37126}, {3518, 7745}, {5013, 6644}, {5206, 13564}, {5305, 7575}, {5306, 37940}, {5309, 37922}, {5475, 13621}, {6642, 31489}, {7525, 21843}, {7545, 39590}, {7556, 11063}, {7737, 37440}, {7747, 18378}, {8553, 9715}, {8770, 15818}, {9609, 15815}, {9697, 15087}, {9699, 30435}, {11648, 37955}, {18472, 38463}, {21844, 43448}

X(44523) = crossdifference of every pair of points on line {6132, 6368}
X(44523) = {X(9609),X(17928)}-harmonic conjugate of X(15815)

X(44524) = X(3)X(115)∩X(6)X(25)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 2*a^4*b^2*c^2 + 4*b^6*c^2 - 6*b^4*c^4 + 2*a^2*c^6 + 4*b^2*c^6 - c^8) : :

X(44524) lies on these lines: {2, 9609}, {3, 115}, {6, 25}, {22, 230}, {23, 7735}, {24, 5254}, {26, 3767}, {32, 7517}, {39, 7506}, {50, 26283}, {172, 9658}, {183, 338}, {186, 43448}, {187, 12083}, {570, 10314}, {571, 1196}, {577, 34481}, {1184, 2965}, {1384, 5899}, {1609, 9909}, {1914, 9673}, {1995, 3815}, {2165, 15818}, {2548, 13861}, {2549, 6644}, {3053, 7387}, {3054, 7485}, {3518, 5286}, {3563, 15073}, {5013, 6642}, {5020, 31489}, {5023, 11414}, {5063, 40350}, {5210, 35243}, {5305, 37440}, {5309, 9699}, {6423, 35776}, {6424, 35777}, {6676, 9722}, {6781, 44457}, {7484, 15109}, {7502, 43291}, {7514, 43620}, {7530, 7737}, {7545, 15484}, {7736, 13595}, {7745, 10594}, {8573, 20850}, {8667, 15574}, {8770, 36748}, {9465, 26284}, {9605, 13621}, {9723, 44377}, {10046, 16781}, {12106, 15048}, {14002, 37665}, {14579, 21448}, {18378, 30435}, {20998, 40805}, {21397, 35481}, {33272, 34883}, {37689, 37913}, {38872, 44467}, {40801, 44439}

X(44524) = crossdifference of every pair of points on line {525, 6132}
X(44524) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {22, 230, 8553}, {1971, 3981, 6}, {3518, 5286, 9608}, {7746, 9700, 3}, {9909, 34809, 1609}

X(44525) = X(3)X(115)∩X(6)X(26)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 + 2*b^6*c^2 + a^2*b^2*c^4 - 2*b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8) : :

X(44525) lies on these lines: {3, 115}, {6, 26}, {22, 1184}, {23, 7745}, {24, 5013}, {32, 2937}, {39, 2070}, {52, 9604}, {140, 15109}, {187, 13564}, {195, 9697}, {230, 7512}, {1506, 13621}, {1658, 2549}, {1691, 2916}, {1971, 2917}, {2548, 37440}, {3518, 3815}, {3767, 7502}, {5210, 10323}, {5254, 7488}, {5286, 7556}, {5475, 18378}, {5899, 7747}, {6644, 15815}, {7506, 31489}, {7529, 18584}, {7555, 11063}, {7603, 18369}, {7735, 38435}, {7737, 17714}, {7753, 37956}, {9300, 37939}, {9603, 10282}, {9605, 9699}, {10117, 32445}, {10312, 37932}, {11250, 43619}, {12106, 31401}, {12107, 15048}, {19165, 38525}, {22159, 39537}, {33717, 42535}, {34864, 39565}, {37512, 43809}

X(44525) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7748, 34866}, {24, 9609, 5013}

X(44526) = X(3)X(115)∩X(6)X(30)

Barycentrics    3*a^4 - 3*a^2*b^2 - 2*b^4 - 3*a^2*c^2 + 4*b^2*c^2 - 2*c^4 : :
X(44526) = 3 X[6] - 2 X[7737], 5 X[6] - 6 X[7739], 3 X[6] - 4 X[15048], 5 X[6] - 4 X[18907], 5 X[6] - 2 X[43618], X[6] + 2 X[43619], X[69] - 3 X[33272], 2 X[141] - 3 X[32986], 3 X[599] - 4 X[7761], 3 X[2549] - X[7737], 5 X[2549] - 3 X[7739], 3 X[2549] - 2 X[15048], 5 X[2549] - 2 X[18907], 5 X[2549] - X[43618], 4 X[3589] - 3 X[14033], 4 X[3631] - 3 X[32836], 4 X[3734] - 5 X[3763], 2 X[3734] - 3 X[11287], 5 X[3763] - 6 X[11287], 4 X[4045] - 3 X[11286], 3 X[5077] - 2 X[7761], 5 X[7737] - 9 X[7739], 5 X[7737] - 6 X[18907], 5 X[7737] - 3 X[43618], X[7737] + 3 X[43619], 9 X[7739] - 10 X[15048], 3 X[7739] - 2 X[18907], 3 X[7739] - X[43618], 3 X[7739] + 5 X[43619], 4 X[7798] - 3 X[15534], 4 X[7804] - 3 X[11159], 3 X[10516] - 4 X[37242], 4 X[14929] - 3 X[15533], 5 X[15048] - 3 X[18907], 10 X[15048] - 3 X[43618], 2 X[15048] + 3 X[43619], 2 X[18907] + 5 X[43619], X[32815] - 3 X[32986], X[43618] + 5 X[43619]

Let KA be the symmedian point of the A-anti-altimedial triangle, and define KB, KC cyclically. X(44526) = X(6)-of-KAKBKC. X(44526) is also X(69) of the reflection triangle of X(6). (Randy Hutson, September 30, 2021)

X(44526) lies on these lines: {2, 11147}, {3, 115}, {4, 3815}, {5, 15815}, {6, 30}, {20, 3053}, {32, 1657}, {39, 382}, {69, 33272}, {76, 33234}, {99, 7778}, {141, 32815}, {148, 183}, {187, 3534}, {194, 33256}, {230, 376}, {232, 44438}, {315, 19695}, {316, 9766}, {325, 8716}, {378, 9609}, {381, 574}, {385, 33264}, {538, 40341}, {543, 599}, {546, 31401}, {549, 43620}, {550, 3767}, {570, 18494}, {620, 11318}, {671, 7610}, {754, 6144}, {999, 9664}, {1003, 7790}, {1015, 9668}, {1285, 3529}, {1350, 15993}, {1384, 5309}, {1478, 31477}, {1500, 9655}, {1506, 3843}, {1513, 8719}, {1569, 38744}, {1571, 18480}, {1572, 28146}, {1611, 7667}, {1648, 15538}, {1656, 37512}, {1870, 9594}, {1975, 3314}, {2023, 10723}, {2207, 18560}, {2275, 12953}, {2276, 12943}, {2548, 3627}, {2782, 15069}, {3054, 3524}, {3055, 3545}, {3070, 12257}, {3071, 12256}, {3094, 36990}, {3146, 7738}, {3172, 40234}, {3258, 35901}, {3269, 18396}, {3295, 9651}, {3526, 15515}, {3543, 7736}, {3552, 7851}, {3585, 31448}, {3589, 14033}, {3631, 32836}, {3734, 3763}, {3785, 33247}, {3788, 35022}, {3830, 5024}, {3845, 31415}, {3849, 7798}, {3851, 31455}, {3853, 31406}, {3861, 31450}, {3926, 33238}, {4045, 11286}, {5017, 14532}, {5054, 8589}, {5055, 18424}, {5073, 7747}, {5076, 39590}, {5116, 35930}, {5206, 15696}, {5275, 17579}, {5304, 15683}, {5305, 15704}, {5306, 11001}, {5318, 44463}, {5321, 44459}, {5339, 22512}, {5340, 22513}, {5355, 15685}, {5459, 6772}, {5460, 6775}, {5523, 35481}, {5569, 36523}, {5585, 8703}, {5587, 31443}, {5895, 32445}, {5899, 9699}, {5913, 16063}, {6032, 31133}, {6284, 9597}, {6337, 32982}, {6421, 35821}, {6422, 35820}, {6423, 42267}, {6424, 42266}, {6564, 9600}, {6658, 7864}, {6759, 9603}, {6800, 36181}, {7354, 9598}, {7386, 8770}, {7514, 15109}, {7618, 37350}, {7620, 11168}, {7750, 32997}, {7753, 15684}, {7754, 7802}, {7763, 33229}, {7765, 17800}, {7770, 7847}, {7773, 7783}, {7774, 33192}, {7776, 7781}, {7782, 7887}, {7787, 19696}, {7788, 7898}, {7789, 32974}, {7791, 32819}, {7792, 33007}, {7793, 33267}, {7795, 8357}, {7797, 33257}, {7803, 19687}, {7804, 11159}, {7806, 33265}, {7816, 7866}, {7823, 19691}, {7828, 33235}, {7835, 33219}, {7844, 11288}, {7852, 33242}, {7861, 32954}, {7868, 7924}, {7874, 33241}, {7875, 19686}, {7879, 7910}, {7881, 7911}, {7885, 32821}, {7908, 15301}, {7913, 33237}, {7918, 33217}, {7919, 33220}, {8288, 37638}, {8352, 11184}, {8353, 8667}, {8354, 8556}, {8356, 11185}, {8553, 35243}, {8588, 15688}, {8597, 11163}, {8860, 41135}, {8976, 9674}, {8981, 9601}, {9112, 16965}, {9113, 16964}, {9220, 9818}, {9300, 15682}, {9541, 9602}, {9604, 13352}, {9606, 17578}, {9607, 14482}, {9619, 22793}, {9620, 28160}, {9650, 31461}, {9654, 31451}, {9745, 10989}, {9862, 39646}, {9880, 40248}, {9956, 31422}, {10311, 37196}, {10317, 19220}, {10418, 32216}, {10516, 37242}, {10722, 11257}, {11063, 33532}, {11165, 31173}, {11173, 19924}, {11174, 11361}, {11297, 43028}, {11298, 43029}, {11317, 42849}, {11359, 24275}, {11480, 44461}, {11481, 44465}, {12017, 22862}, {12605, 15075}, {14269, 43457}, {14614, 14712}, {14929, 15533}, {15491, 32983}, {15655, 15689}, {15693, 18362}, {15820, 34609}, {16041, 44377}, {16043, 32826}, {16989, 33193}, {16990, 33263}, {17008, 33207}, {18492, 31421}, {18561, 22121}, {18562, 22120}, {18563, 23115}, {18573, 44468}, {20065, 33271}, {30771, 40349}, {31152, 39602}, {31441, 38140}, {31463, 42284}, {31467, 31652}, {32828, 33226}, {33006, 37647}, {33008, 37688}, {33216, 44381}, {33418, 42491}, {33419, 42490}, {35490, 39575}, {35606, 36194}

X(44526) = midpoint of X(2549) and X(43619)
X(44526) = reflection of X(i) in X(j) for these {i,j}: {6, 2549}, {599, 5077}, {6144, 22253}, {7737, 15048}, {32815, 141}, {43618, 18907}
X(44526) = crossdifference of every pair of points on line {6132, 8675}
X(44526) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 115, 37637}, {20, 5254, 3053}, {99, 7841, 7778}, {115, 37637, 13881}, {148, 183, 34505}, {148, 7833, 183}, {230, 376, 5210}, {316, 31859, 9766}, {376, 43448, 230}, {381, 574, 31489}, {381, 31489, 18584}, {550, 3767, 5023}, {671, 35955, 7610}, {1384, 15681, 6781}, {1975, 6655, 7784}, {2549, 7737, 15048}, {2549, 43618, 7739}, {3146, 7738, 7745}, {3314, 20094, 1975}, {3734, 11287, 3763}, {3830, 5024, 5475}, {5073, 9605, 7747}, {5309, 6781, 1384}, {6284, 9597, 16781}, {6655, 20094, 3314}, {6772, 11296, 16644}, {6775, 11295, 16645}, {7737, 15048, 6}, {7739, 18907, 6}, {7739, 43618, 18907}, {7748, 7756, 3}, {7781, 7842, 7776}, {7783, 33019, 7773}, {7816, 7872, 7866}, {7844, 32456, 11288}, {8356, 11185, 15271}, {8597, 32480, 11163}, {8703, 21843, 5585}, {8703, 43291, 21843}, {15515, 39565, 3526}, {22862, 22906, 12017}, {32815, 32986, 141}, {42154, 42155, 43273}

X(44527) = X(3)X(115)∩X(6)X(49)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 4*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + 4*b^6*c^2 - 2*a^2*b^2*c^4 - 6*b^4*c^4 + 2*a^2*c^6 + 4*b^2*c^6 - c^8) : :

X(44527) lies on these lines: {3, 115}, {6, 49}, {24, 3767}, {25, 32}, {26, 230}, {39, 6642}, {140, 9609}, {159, 1692}, {161, 19627}, {187, 7387}, {233, 31455}, {1384, 18378}, {1504, 8276}, {1505, 8277}, {1506, 5020}, {1598, 7747}, {1609, 9714}, {1658, 43291}, {1995, 2548}, {2241, 10046}, {2242, 10037}, {2549, 17928}, {2937, 8553}, {3053, 7517}, {3054, 7516}, {3124, 14585}, {3291, 26283}, {3517, 7755}, {3518, 7735}, {3964, 7888}, {5023, 12083}, {5058, 8908}, {5206, 11414}, {5254, 6644}, {5305, 9608}, {5475, 7529}, {6781, 39568}, {7503, 43620}, {7542, 9722}, {7737, 10594}, {7745, 13861}, {7780, 15574}, {8588, 37198}, {9604, 36753}, {9697, 11402}, {9818, 39565}, {10323, 21843}, {12963, 35777}, {12968, 35776}, {13621, 30435}, {15484, 18369}, {15513, 35243}, {18560, 21397}, {19459, 39764}, {20987, 40825}, {22467, 43448}, {32048, 32661}, {32977, 44180}, {33238, 34883}, {37951, 41361}

X(44527) = X(1969)-isoconjugate of X(44405)
X(44527) = crosssum of X(69) and X(6515)
X(44527) = crossdifference of every pair of points on line {3265, 6132}
X(44527) = barycentric product X(25)*X(3548)
X(44527) = barycentric quotient X(i)/X(j) for these {i,j}: {3548, 305}, {14575, 44405}
X(44527) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5305, 12106, 9608}, {7749, 9700, 3}

X(44528) = X(3)X(115)∩X(6)X(64)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 6*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - 4*b^6*c^2 - 4*a^2*b^2*c^4 + 10*b^4*c^4 + 2*a^2*c^6 - 4*b^2*c^6 - c^8) : :

X(44528) lies on these lines: {3, 115}, {4, 9608}, {6, 64}, {20, 8553}, {230, 11413}, {338, 1975}, {378, 5254}, {2548, 31861}, {2549, 7526}, {3053, 12085}, {3520, 21397}, {3767, 12084}, {5013, 9818}, {5023, 21312}, {5286, 14865}, {5866, 32972}, {7395, 15815}, {7527, 7738}, {7735, 12086}, {7745, 35502}, {9603, 18451}, {9604, 11425}, {9609, 14118}, {9722, 31829}, {11325, 20987}, {11479, 31489}

X(44528) = crossdifference of every pair of points on line {6132, 8057}

X(44529) = X(3)X(115)∩X(6)X(67)

Barycentrics    a^10 - 2*a^8*b^2 + a^6*b^4 + a^4*b^6 - 2*a^2*b^8 + b^10 - 2*a^8*c^2 + 3*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 2*a^2*b^6*c^2 - 3*b^8*c^2 + a^6*c^4 - 2*a^4*b^2*c^4 + 2*b^6*c^4 + a^4*c^6 + 2*a^2*b^2*c^6 + 2*b^4*c^6 - 2*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(44529) lies on these lines: {2, 94}, {3, 115}, {6, 67}, {50, 230}, {111, 930}, {112, 1594}, {187, 7574}, {265, 32761}, {427, 38872}, {1368, 14910}, {1995, 9220}, {2088, 15061}, {2165, 40347}, {2549, 18580}, {3016, 14643}, {3018, 31489}, {3767, 18281}, {3815, 30789}, {5159, 16310}, {5254, 37118}, {5286, 37119}, {5475, 7579}, {5477, 32306}, {7778, 18375}, {8553, 26283}, {8889, 39176}, {9604, 17974}, {10254, 19220}, {10510, 15993}, {11646, 32233}, {15122, 43291}, {15133, 32661}, {16308, 19656}, {34844, 36751}

X(44529) = crossdifference of every pair of points on line {6132, 9517}
X(44529) = {X(230),X(858)}-harmonic conjugate of X(50)

X(44530) = X(3)X(115)∩X(6)X(76)

Barycentrics    a^8 + a^2*b^6 - a^4*b^2*c^2 - 4*a^2*b^4*c^2 + 2*b^6*c^2 - 4*a^2*b^2*c^4 - 4*b^4*c^4 + a^2*c^6 + 2*b^2*c^6 : :

X(44530) lies on these lines: {3, 115}, {4, 2076}, {6, 76}, {32, 7697}, {230, 384}, {458, 21001}, {1613, 41231}, {1691, 6248}, {2549, 34873}, {3053, 10104}, {3054, 7824}, {3406, 39560}, {3734, 32189}, {3788, 31489}, {3815, 7836}, {3934, 11356}, {5013, 40108}, {5017, 10516}, {5023, 9756}, {5116, 5254}, {5162, 39565}, {6287, 7747}, {6655, 9478}, {7737, 32151}, {7745, 15993}, {7919, 11285}, {10358, 13330}, {12251, 15514}, {14061, 34885}, {17128, 39095}, {37334, 39663}, {37446, 38654}, {43291, 44224}

X(44530) = crossdifference of every pair of points on line {688, 6132}
X(44530) = {X(35830),X(35831)}-harmonic conjugate of X(38732)

X(44531) = X(3)X(115)∩X(6)X(98)

Barycentrics    a^8 - 2*a^6*b^2 + 2*a^4*b^4 - 3*a^2*b^6 - 2*a^6*c^2 + a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 2*b^6*c^2 + 2*a^4*c^4 + 2*a^2*b^2*c^4 + 4*b^4*c^4 - 3*a^2*c^6 - 2*b^2*c^6 : :

X(44531) lies on these lines: {2, 4048}, {3, 115}, {5, 43449}, {6, 98}, {32, 13111}, {39, 12188}, {99, 11285}, {114, 10516}, {140, 34873}, {147, 3815}, {148, 7824}, {183, 1916}, {230, 2076}, {385, 15514}, {574, 7697}, {599, 32458}, {1003, 9166}, {1506, 6287}, {1569, 5024}, {2782, 5013}, {3027, 31477}, {3053, 12042}, {3054, 37455}, {3934, 8178}, {4027, 11174}, {5017, 6034}, {5023, 34473}, {5149, 6722}, {5152, 7770}, {5254, 14651}, {5461, 11286}, {5475, 38744}, {5880, 5988}, {5939, 10352}, {5969, 8556}, {5976, 15271}, {5984, 7736}, {6421, 35824}, {6422, 35825}, {6721, 42786}, {6784, 17970}, {7745, 9862}, {7752, 35701}, {7844, 11356}, {7887, 38907}, {8288, 30789}, {8667, 36849}, {9300, 11177}, {9600, 35878}, {10053, 16781}, {10488, 42849}, {11184, 33683}, {11676, 39663}, {12215, 44377}, {13174, 31443}, {13586, 44401}, {14532, 38747}, {14614, 36864}, {14981, 31492}, {15597, 33273}, {16921, 32528}, {22332, 38664}, {35006, 39095}, {39839, 43843}

X(44531) = crossdifference of every pair of points on line {5113, 6132}
X(44531) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 2023, 6}, {115, 7748, 38732}, {115, 38224, 13881}, {230, 5999, 2076}, {5152, 14061, 7770}, {5984, 7736, 12830}, {13873, 13926, 38224}, {14651, 37334, 38654}

X(44532) = X(3)X(115)∩X(6)X(99)

Barycentrics    3*a^8 - 6*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - 6*a^6*c^2 + 3*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + 2*b^6*c^2 + 6*a^4*c^4 - 2*a^2*b^2*c^4 - 4*b^4*c^4 - a^2*c^6 + 2*b^2*c^6 : :

X(44532) lies on these lines: {3, 115}, {6, 99}, {32, 13188}, {39, 19910}, {98, 5023}, {148, 230}, {187, 12188}, {384, 3815}, {550, 43449}, {620, 11286}, {1285, 35951}, {1503, 2076}, {1569, 30435}, {1975, 39652}, {2023, 15815}, {2782, 3053}, {3054, 33273}, {3231, 35933}, {3552, 5989}, {4226, 20998}, {5013, 33813}, {5116, 35925}, {5149, 35022}, {5152, 33235}, {5210, 12042}, {5254, 13172}, {5306, 8591}, {6423, 35878}, {6424, 35879}, {7747, 38743}, {7816, 34870}, {8178, 32456}, {8290, 37665}, {8553, 39832}, {8719, 38642}, {9478, 32965}, {10089, 16781}, {11646, 38749}, {12176, 39560}, {12829, 22331}, {15452, 31477}, {21001, 35941}, {32528, 33257}, {34873, 44224}, {35369, 37689}

X(44532) = crossdifference of every pair of points on line {888, 6132}
X(44532) = {X(2023),X(21166)}-harmonic conjugate of X(15815)

X(44533) = X(3)X(115)∩X(6)X(110)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 5*a^4*b^2*c^2 - 3*a^2*b^4*c^2 + 6*b^6*c^2 - 3*a^2*b^2*c^4 - 10*b^4*c^4 + 2*a^2*c^6 + 6*b^2*c^6 - c^8) : :

X(44533) lies on these lines: {2, 13582}, {3, 115}, {6, 110}, {23, 230}, {25, 1989}, {32, 7545}, {50, 3291}, {112, 10594}, {187, 37924}, {231, 37972}, {265, 15538}, {399, 15544}, {575, 9604}, {686, 39232}, {1611, 38872}, {1634, 5020}, {1990, 37777}, {2965, 10985}, {3003, 40350}, {3018, 34809}, {3053, 7530}, {3054, 7496}, {3511, 21513}, {3518, 27376}, {3767, 12106}, {3815, 16042}, {5007, 18369}, {5013, 44468}, {5023, 12082}, {5158, 34481}, {5159, 34988}, {5210, 33532}, {5306, 13595}, {5477, 32254}, {5585, 41463}, {5621, 7418}, {5941, 11646}, {7575, 43291}, {7735, 14002}, {7753, 21308}, {7755, 13621}, {8428, 15959}, {8749, 36616}, {8770, 14910}, {9166, 35936}, {9209, 15470}, {9609, 40916}, {9696, 15039}, {9698, 22462}, {10317, 38463}, {10413, 38724}, {10418, 11284}, {18859, 39563}, {35296, 44401}, {38997, 39078}

X(44533) = polar conjugate of the isotomic conjugate of X(39562)
X(44533) = crossdifference of every pair of points on line {690, 6132}
X(44533) = barycentric product X(4)*X(39562)
X(44533) = barycentric quotient X(39562)/X(69)
X(44533) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 230, 11063}, {115, 2079, 34866}, {1995, 33900, 2930}, {11141, 11142, 7669}

X(44534) = X(3)X(115)∩X(6)X(114)

Barycentrics    a^8 - 2*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 + b^8 - 2*a^6*c^2 - a^4*b^2*c^2 - 2*b^6*c^2 + 3*a^4*c^4 + 2*b^4*c^4 - a^2*c^6 - 2*b^2*c^6 + c^8 : :

X(44534) lies on these lines: {2, 694}, {3, 115}, {5, 34870}, {6, 114}, {32, 6033}, {39, 15561}, {98, 230}, {99, 5254}, {147, 7735}, {148, 16925}, {172, 12184}, {187, 38741}, {325, 5111}, {542, 40825}, {543, 11288}, {574, 38750}, {620, 5013}, {671, 35297}, {1384, 38744}, {1569, 5309}, {1609, 9861}, {1648, 30789}, {1914, 12185}, {2021, 11632}, {2493, 38652}, {2549, 33813}, {2679, 17970}, {2782, 3767}, {2794, 3053}, {3054, 37450}, {4027, 7806}, {5023, 38749}, {5025, 39652}, {5038, 7792}, {5149, 6680}, {5152, 7857}, {5206, 38742}, {5210, 38747}, {5306, 6054}, {5461, 11287}, {5465, 14605}, {5984, 37689}, {6393, 8781}, {6656, 14061}, {6721, 31489}, {6722, 7866}, {7737, 22505}, {7738, 7932}, {7763, 35700}, {7778, 32458}, {7779, 36859}, {8290, 16984}, {8295, 37455}, {8356, 9166}, {8363, 31268}, {9300, 23234}, {9478, 37688}, {9598, 15452}, {9604, 39805}, {9753, 13330}, {11060, 34365}, {12042, 43449}, {12176, 37446}, {13172, 43448}, {13862, 42535}, {14651, 38642}, {14901, 15545}, {15815, 38748}, {22332, 38751}, {23053, 33008}, {24975, 32740}, {30435, 38743}, {34212, 40347}, {37242, 43620}, {37243, 39565}, {37459, 43291}

X(44534) = complement of X(46236)
X(44534) = crosspoint of X(98) and X(8781)
X(44534) = crosssum of X(511) and X(1692)
X(44534) = crossdifference of every pair of points on line {5027, 6132}
X(44534) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {115, 7746, 38224}, {147, 7735, 12829}, {230, 1513, 1691}, {2023, 5976, 3094}, {13873, 13926, 3}

X(44535) = X(3)X(115)∩X(6)X(140)

Barycentrics    5*a^4 - 5*a^2*b^2 + 2*b^4 - 5*a^2*c^2 - 4*b^2*c^2 + 2*c^4 : :

X(44535) lies on these lines: {2, 3053}, {3, 115}, {4, 3054}, {5, 5023}, {6, 140}, {32, 3526}, {39, 5054}, {76, 7610}, {141, 32970}, {183, 7836}, {187, 1656}, {230, 631}, {325, 33000}, {381, 5206}, {382, 15513}, {487, 615}, {488, 590}, {524, 32829}, {549, 3767}, {550, 5585}, {574, 15720}, {599, 3788}, {618, 16644}, {619, 16645}, {632, 2548}, {639, 8252}, {640, 8253}, {1030, 19547}, {1078, 7778}, {1153, 6683}, {1384, 1506}, {1560, 8778}, {1588, 9602}, {1611, 7499}, {1657, 8588}, {1691, 3763}, {1968, 37453}, {1970, 26958}, {1971, 40686}, {1975, 17004}, {2076, 14693}, {2207, 10018}, {2549, 3530}, {3055, 3533}, {3523, 5254}, {3525, 3815}, {3546, 36748}, {3552, 17006}, {3589, 32978}, {3628, 7737}, {3630, 32825}, {3785, 32977}, {3843, 6781}, {3850, 43618}, {3851, 15655}, {3926, 13468}, {3934, 11288}, {5007, 31467}, {5017, 6680}, {5024, 7755}, {5055, 7747}, {5070, 5475}, {5073, 12815}, {5079, 39590}, {5215, 31239}, {5304, 9606}, {5305, 14869}, {5306, 15702}, {5309, 15701}, {5326, 9596}, {5355, 31457}, {5368, 9605}, {5433, 16781}, {5569, 7830}, {6144, 7764}, {6392, 23055}, {6642, 8553}, {7294, 9599}, {7494, 8770}, {7622, 32450}, {7735, 10303}, {7739, 11812}, {7762, 11184}, {7763, 8667}, {7769, 7877}, {7771, 7887}, {7774, 33204}, {7780, 7916}, {7789, 32989}, {7792, 33001}, {7793, 7941}, {7795, 8556}, {7807, 15271}, {7824, 7932}, {7831, 33218}, {7841, 43459}, {7851, 33004}, {7854, 31274}, {7857, 7859}, {7868, 33245}, {7881, 12829}, {7886, 11287}, {7935, 33240}, {8376, 8960}, {8591, 8860}, {9300, 15709}, {9604, 13336}, {9675, 13951}, {9698, 43136}, {9770, 32871}, {9771, 32884}, {10104, 12177}, {10299, 43448}, {10356, 37071}, {10516, 37466}, {11173, 25555}, {11174, 33015}, {11648, 15700}, {11793, 15575}, {12108, 15048}, {13846, 41490}, {13847, 41491}, {14033, 32867}, {14061, 33234}, {14064, 44381}, {14067, 43450}, {14093, 39563}, {14907, 33249}, {15484, 35007}, {15515, 15693}, {15597, 32838}, {15688, 18362}, {15694, 30435}, {15712, 43291}, {16239, 18907}, {16925, 37688}, {16989, 33188}, {16990, 33262}, {17008, 33206}, {19780, 43029}, {19781, 43028}, {20065, 37647}, {22831, 42093}, {22832, 42094}, {23053, 35287}, {27376, 35486}, {32828, 33216}, {32832, 35297}, {32883, 32983}, {33190, 41139}, {33215, 44401}, {33217, 42535}, {33272, 39143}, {33923, 43619}, {41406, 42936}, {41407, 42937}

X(44535) = midpoint of X(41975) and X(41976)
X(44535) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7749, 37637}, {3, 37637, 13881}, {5, 21843, 5023}, {32, 3526, 31489}, {230, 631, 5013}, {549, 3767, 15815}, {1078, 7940, 7879}, {1078, 33233, 7778}, {3785, 32977, 44377}, {7815, 32954, 3763}, {7879, 7940, 7778}, {7879, 33233, 7940}, {8588, 39565, 1657}, {8860, 33274, 34505}, {15694, 30435, 31455}, {17004, 33259, 1975}, {32989, 34229, 7789}

X(44536) = X(3)X(115)∩X(6)X(147)

Barycentrics    a^8 - 2*a^6*b^2 + 4*a^4*b^4 + a^2*b^6 + 2*b^8 - 2*a^6*c^2 - 3*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - 2*b^6*c^2 + 4*a^4*c^4 - 2*a^2*b^2*c^4 + a^2*c^6 - 2*b^2*c^6 + 2*c^8 : :

X(44536) lies on these lines: {2, 39091}, {3, 115}, {6, 147}, {45, 5988}, {98, 14458}, {99, 7943}, {114, 6034}, {148, 7851}, {230, 40236}, {671, 33220}, {1916, 7778}, {2023, 31489}, {3053, 43449}, {3124, 30789}, {3763, 5976}, {5306, 5984}, {7806, 11606}, {7868, 8782}, {7923, 20094}, {8178, 32954}, {9478, 15271}, {9862, 22331}, {11164, 33246}, {15561, 31492}, {32819, 33225}, {35006, 43460}, {36849, 40341}

X(44536) = {X(13873),X(13926)}-harmonic conjugate of X(38739)

X(44537) = X(3)X(115)∩X(6)X(156)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 + 6*b^6*c^2 - a^2*b^2*c^4 - 10*b^4*c^4 + 2*a^2*c^6 + 6*b^2*c^6 - c^8) : :

X(44537) lies on these lines: {3, 115}, {6, 156}, {230, 12088}, {1180, 1995}, {2207, 10312}, {3518, 5523}, {3767, 37440}, {5007, 7545}, {5306, 34484}, {5309, 13621}, {7530, 22331}, {7755, 18378}, {7772, 18369}, {10316, 38463}, {11063, 17714}, {11648, 43809}, {18362, 34864}

X(44538) = X(3)X(115)∩X(6)X(186)

Barycentrics    a^2*(2*a^8 - 4*a^6*b^2 + 4*a^2*b^6 - 2*b^8 - 4*a^6*c^2 + 7*a^4*b^2*c^2 - 3*a^2*b^4*c^2 + 2*b^6*c^2 - 3*a^2*b^2*c^4 + 4*a^2*c^6 + 2*b^2*c^6 - 2*c^8) : :

X(44538) lies on these lines: {3, 115}, {6, 186}, {25, 18429}, {230, 10298}, {338, 7771}, {1658, 3053}, {2549, 15646}, {3767, 15331}, {5013, 37814}, {5023, 7488}, {5210, 7502}, {5254, 21844}, {5585, 6636}, {5913, 7492}, {6644, 31489}, {7575, 7737}, {9604, 11438}, {9608, 35479}, {9609, 15078}, {9699, 37922}, {15048, 18571}, {15815, 22467}, {34152, 43619}, {37936, 43618}

X(44538) = {X(3),X(2079)}-harmonic conjugate of X(37637)

X(44539) = X(3)X(115)∩X(6)X(194)

Barycentrics    2*a^8 - 3*a^6*b^2 + 3*a^4*b^4 - 3*a^6*c^2 + a^4*b^2*c^2 - 3*a^2*b^4*c^2 + 2*b^6*c^2 + 3*a^4*c^4 - 3*a^2*b^2*c^4 - 4*b^4*c^4 + 2*b^2*c^6 : :

X(44539) lies on these lines: {3, 115}, {6, 194}, {32, 13108}, {230, 3552}, {382, 5162}, {401, 21001}, {1003, 14568}, {2076, 9873}, {2549, 44224}, {3054, 33004}, {3734, 34870}, {3815, 7891}, {5017, 15069}, {5023, 11676}, {5254, 35925}, {7769, 7770}, {7841, 34885}, {9863, 15993}, {11257, 39560}, {18440, 35374}

X(44539) = crossdifference of every pair of points on line {3221, 6132}

X(44540) = X(3)X(115)∩X(6)X(315)

Barycentrics    a^8 + 3*a^6*b^2 - a^4*b^4 - a^2*b^6 + 2*b^8 + 3*a^6*c^2 - 8*a^4*b^2*c^2 - 5*a^2*b^4*c^2 - 4*b^6*c^2 - a^4*c^4 - 5*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 4*b^2*c^6 + 2*c^8 : :

X(44540) lies on these lines: {3, 115}, {6, 315}, {230, 7791}, {1656, 2021}, {1691, 10358}, {3053, 20576}, {3054, 16925}, {5286, 15993}, {6683, 7862}, {7735, 7904}, {7745, 20194}, {7817, 11287}, {7913, 13357}, {7933, 39095}, {15815, 37450}, {25555, 40825}

X(44541) = X(3)X(115)∩X(6)X(376)

Barycentrics    9*a^4 - 9*a^2*b^2 - 2*b^4 - 9*a^2*c^2 + 4*b^2*c^2 - 2*c^4 : :
X(44541) = 5 X[11742] + 4 X[31415], 4 X[31415] - 5 X[31489]

X(44541) lies on these lines: {3, 115}, {6, 376}, {20, 3815}, {30, 11742}, {39, 15696}, {99, 599}, {148, 7610}, {183, 20094}, {187, 15688}, {230, 5585}, {325, 33207}, {378, 15109}, {381, 8589}, {382, 7603}, {548, 3053}, {549, 43619}, {550, 5013}, {574, 3534}, {590, 26618}, {615, 26617}, {620, 5077}, {1384, 15695}, {1506, 17800}, {1587, 9601}, {1657, 37512}, {1975, 33275}, {2548, 12103}, {2549, 5210}, {3054, 15692}, {3055, 3543}, {3314, 33260}, {3522, 5023}, {3526, 39601}, {3528, 5254}, {3589, 35927}, {3763, 8356}, {3767, 33923}, {3830, 18584}, {5024, 6781}, {5054, 11614}, {5073, 31455}, {5275, 36004}, {5309, 15655}, {5475, 15681}, {6144, 31859}, {6409, 35944}, {6410, 35945}, {7738, 22331}, {7745, 17538}, {7761, 35022}, {7771, 34505}, {7773, 33267}, {7778, 7833}, {7782, 7784}, {7789, 33226}, {7792, 33208}, {7845, 11165}, {7851, 33276}, {7934, 33234}, {8252, 35949}, {8253, 35948}, {8556, 32815}, {8588, 14093}, {8716, 14907}, {8719, 36990}, {9112, 36968}, {9113, 36967}, {9300, 15697}, {9604, 37480}, {9766, 14976}, {9855, 42849}, {11063, 41463}, {11159, 14762}, {11174, 33265}, {11287, 32456}, {11299, 43028}, {11300, 43029}, {11480, 44250}, {12007, 41400}, {12100, 43620}, {15271, 33008}, {15326, 31477}, {15684, 43457}, {15686, 43618}, {15690, 18907}, {15694, 18424}, {15704, 31401}, {15706, 39563}, {15716, 18362}, {15993, 31884}, {16644, 35932}, {16645, 35931}, {16984, 33014}, {19103, 42261}, {19104, 42260}, {19708, 43448}, {21843, 34200}, {22332, 37665}, {26958, 35937}, {28168, 31441}, {32459, 32986}, {33192, 37647}, {33272, 44377}, {33751, 40825}, {36751, 44241}, {38749, 43273}, {39809, 40248}

X(44541) = midpoint of X(11742) and X(31489)
X(44541) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7756, 13881}, {230, 10304, 5585}, {2549, 8703, 5210}, {5024, 15689, 6781}, {8716, 14907, 40341}

X(44542) = X(3)X(115)∩X(6)X(474)

Barycentrics    a*(a^6 - a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - a*b^5 - a^5*c + 5*a^4*b*c - 5*a^2*b^3*c + a*b^4*c + 2*b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a^3*c^3 - 5*a^2*b*c^3 - 4*b^3*c^3 + a^2*c^4 + a*b*c^4 - a*c^5 + 2*b*c^5) : :

X(44542) lies on these lines: {3, 115}, {6, 474}, {21, 3054}, {187, 37251}, {230, 404}, {3053, 6911}, {3055, 17535}, {3149, 5023}, {3815, 17531}, {5124, 19514}, {5210, 6985}, {5254, 6940}, {5306, 36006}, {5585, 37426}, {6946, 7745}, {7735, 17572}, {8553, 37034}, {8588, 16117}, {11063, 16427}, {16408, 31489}, {25946, 37646}

X(44542) = crossdifference of every pair of points on line {4132, 6132}

X(44543) = EULER LINE INTERCEPT OF X(183)X(754)

Barycentrics    -a^4 - 3 a^2 b^2 + 2 b^4 - 3 a^2 c^2 - 6 b^2 c^2 + 2 c^4 : :

See Kadir Altintas and Francisco Javier García Capitán, euclid 2127.

X(44543) lies on these lines: {2,3}, {6,14568}, {39,18546}, {76,9766}, {83,13881}, {115,11174}, {148,5024}, {183,754}, {316,15271}, {385,15484}, {538,11163}, {598,7610}, {599,7809}, {625,7868}, {671,2023}, {1506,1975}, {2548,7754}, {3734,7603}, {3763,7934}, {3814,20172}, {3815,11185}, {3934,7773}, {4045,18424}, {5031,21358}, {5050,14651}, {5182,7884}, {5640,12525}, {6179,12156}, {7615,7739}, {7622,11164}, {7745,13468}, {7752,7881}, {7753,14614}, {7775,7788}, {7778,18584}, {7786,15031}, {7799,11184}, {7808,7851}, {7811,8556}, {7812,8667}, {7817,18362}, {7875,14535}, {9745,23297}, {14561,22525}

X(44544) = X(5)X(6697)∩X(68)X(5663)

Barycentrics    a^2*((b^2+c^2)*a^12-2*(2*b^4+b^2*c^2+2*c^4)*a^10+(b^2+c^2)*(5*b^4-7*b^2*c^2+5*c^4)*a^8+2*(3*b^4-4*b^2*c^2+3*c^4)*b^2*c^2*a^6-(b^4-c^4)*(b^2-c^2)*(5*b^4+6*b^2*c^2+5*c^4)*a^4+4*(b^2-c^2)^2*(b^8+c^8+(b^4+3*b^2*c^2+c^4)*b^2*c^2)*a^2-(b^4-c^4)*(b^2-c^2)^3*(b^4+b^2*c^2+c^4)) : :
Barycentrics    (SB+SC)*((8*R^2-SB-SC)*S^2+(SA^2-SB*SC+2*SW^2-2*(4*R^2-2*SA+7*SW)*R^2)*SA) : :
X(44544) = X(3)-3*X(41715), 2*X(140)-3*X(41580), 3*X(154)-2*X(10627), 3*X(568)-X(12324), 3*X(1853)-4*X(10095), 3*X(2979)-5*X(14530), 3*X(3060)-X(34780), 3*X(5656)-X(18436), 3*X(5890)-X(13093), 3*X(5946)-2*X(6247), 5*X(10574)-3*X(35450), 3*X(11206)-X(37484), X(11412)-3*X(32063), 6*X(13363)-5*X(40686), 5*X(15026)-4*X(20299), 3*X(15067)-4*X(16252), 4*X(16982)-3*X(34751)

See Antreas Hatzipolakis and César Lozada, euclid 2143.

X(44544) lies on these lines: {3, 41715}, {5, 6697}, {64, 13630}, {68, 5663}, {140, 41580}, {143, 14216}, {154, 10627}, {185, 13488}, {468, 43896}, {568, 12324}, {1112, 11457}, {1154, 1498}, {1503, 10263}, {1619, 16266}, {1853, 10095}, {2781, 5609}, {2883, 5876}, {2979, 14530}, {3060, 34780}, {3357, 41589}, {3527, 5890}, {3627, 5446}, {5656, 18436}, {5889, 12315}, {5946, 6247}, {6225, 34783}, {6241, 44438}, {6243, 34781}, {7516, 34778}, {9833, 13391}, {9919, 32338}, {10574, 35450}, {11206, 37484}, {11412, 32063}, {13363, 40686}, {13491, 15311}, {15026, 20299}, {15067, 16252}, {16982, 34751}, {18952, 34944}, {22802, 22804}, {25738, 41736}

X(44544) = midpoint of X(i) and X(j) for these {i, j}: {5878, 6293}, {5889, 12315}, {6225, 34783}, {6243, 34781}
X(44544) = reflection of X(i) in X(j) for these (i, j): (64, 13630), (3357, 41589), (5876, 2883), (6101, 6759), (13491, 41725), (14216, 143)

X(44545) = X(5)X(10)∩X(6)X(19)

Barycentrics    a^3*b^2*(a+b)*c^2*(a+c)*(b+c)*(a^5*b+a^4*b^2-a*b^5-b^6+a^5*c+2*a^3*b^2*c-3*a*b^4*c+a^4*c^2+2*a^3*b*c^2+4*a*b^3*c^2+b^4*c^2+4*a*b^2*c^3-3*a*b*c^4+b^2*c^4-a*c^5-c^6) : :
X(44545) = 3*X(51)-X(1858), 3*X(5902)-X(18732)

See Antreas Hatzipolakis and Ercole Suppa, euclid 2138.

X(44545) lies on these lines: {1,197}, {4,17869}, {5,10}, {6,19}, {8,15435}, {30,14453}, {51,1858}, {56,20276}, {72,10869}, {389,6001}, {518,14913}, {612,3057}, {912,12235}, {1325,1798}, {1385,39582}, {1610,17016}, {1824,1837}, {1828,1836}, {1854,17810}, {1953,28266}, {2183,2292}, {2339,19860}, {2771,12236}, {2778,7687}, {2933,37539}, {3185,3931}, {3556,7713}, {3666,23361}, {3753,19784}, {3812,6703}, {3868,9004}, {3869,14555}, {5902,18732}, {8231,30556}, {9957,30142}, {10327,14923}, {12709,14557}, {13323,34339}, {13750,18180}, {23846,37548}, {31811,39523}

X(44545) = midpoint of X(65) and X(1829)
X(44545) = reflection of X(37613) in X(3812)
X(44545) = complement of X(41600)
X(44545) = complement of the isogonal conjugate of X(40454)
X(44545) = complementary conjugate of the complement of X(40454)
X(44545) = crosssum of X(3) and X(960)
X(44545) = crosspoint of X(4) and X(961)
X(44545) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (960,5836,5835), (2362,16232,478)

X(44546) = X(5)X(916)∩X(6)X(31)

Barycentrics    a^2*(a+b)*(a+c)*(b+c)*(a^2-b^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6*b^3-a^5*b^4-2*a^4*b^5+2*a^3*b^6+a^2*b^7-a*b^8+a^6*b^2*c-3*a^4*b^4*c+3*a^2*b^6*c-b^8*c+a^6*b*c^2-2*a^3*b^4*c^2-a^2*b^5*c^2+2*a*b^6*c^2+a^6*c^3-3*a^2*b^4*c^3+2*b^6*c^3-a^5*c^4-3*a^4*b*c^4-2*a^3*b^2*c^4-3*a^2*b^3*c^4-2*a*b^4*c^4-b^5*c^4-2*a^4*c^5-a^2*b^2*c^5-b^4*c^5+2*a^3*c^6+3*a^2*b*c^6+2*a*b^2*c^6+2*b^3*c^6+a^2*c^7-a*c^8-b*c^8) : :
X(44546) = 3*X(51)-X(1839), 3*X(3060)+X(20291)

See Antreas Hatzipolakis and Ercole Suppa, euclid 2138.

X(44546) lies on these lines: {4,15320}, {5,916}, {6,31}, {51,1839}, {389,516}, {2772,7687}, {3060,20291}, {9028,14913}

X(44546) = midpoint of X(71) and X(14053)
X(44546) = crosssum of X(3) and X(34830)

X(44547) = X(1)X(6)∩X(4)X(65)

Barycentrics    a^3*b^2*(a+b)*c^2*(a+c)*(b+c)*(a^2-b^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^5*b-a^4*b^2-2*a^3*b^3+2*a^2*b^4+a*b^5-b^6+a^5*c-2*a^3*b^2*c+a*b^4*c-a^4*c^2-2*a^3*b*c^2-4*a^2*b^2*c^2-2*a*b^3*c^2+b^4*c^2-2*a^3*c^3-2*a*b^2*c^3+2*a^2*c^4+a*b*c^4+b^2*c^4+a*c^5-c^6) : :
X(44547) = 3*X(51)-X(1829),3*X(11245)+X(12135)

See Antreas Hatzipolakis and Ercole Suppa, euclid 2138.

X(44547) lies on these lines: {1,6}, {3,1708}, {4,65}, {5,226}, {7,6835}, {8,11433}, {10,13567}, {11,12691}, {20,10394}, {25,40660}, {28,2182}, {33,1712}, {34,34032}, {40,9786}, {42,774}, {46,7580}, {51,1829}, {55,12710}, {56,12675}, {57,1071}, {63,11344}, {78,16465}, {165,1192}, {181,39591}, {184,11363}, {185,1902}, {201,14547}, {210,3085}, {224,37282}, {225,5721}, {227,37699}, {241,4303}, {255,4641}, {329,938}, {354,3086}, {355,39571}, {386,17102}, {387,7952}, {388,14872}, {389,517}, {440,10974}, {442,1737}, {443,5784}, {452,3869}, {497,5758}, {498,3740}, {499,3742}, {511,37613}, {515,12241}, {516,12432}, {569,24301}, {578,1385}, {581,1214}, {631,17603}, {758,6738}, {908,39772}, {910,2939}, {920,4640}, {943,11428}, {946,5173}, {962,5809}, {971,4292}, {974,2778}, {997,37244}, {1006,2646}, {1038,36746}, {1040,36745}, {1058,17642}, {1060,36742}, {1062,36754}, {1125,16193}, {1155,3651}, {1158,37541}, {1159,40266}, {1175,2074}, {1181,40658}, {1260,3811}, {1319,19365}, {1329,14454}, {1425,1876}, {1427,1745}, {1445,10884}, {1454,11502}, {1465,37732}, {1466,18238}, {1482,11432}, {1496,32912}, {1497,3744}, {1593,12262}, {1620,16192}, {1698,26958}, {1750,3339}, {1751,9895}, {1770,15726}, {1785,1834}, {1788,6908}, {1838,6354}, {1844,1901}, {1854,17822}, {1899,5090}, {1903,5746}, {2183,18673}, {2194,30733}, {2262,5802}, {2285,5776}, {2594,8758}, {2771,7687}, {2800,13601}, {2801,4298}, {2836,32246}, {2900,5687}, {3057,3488}, {3333,17625}, {3340,12672}, {3419,5836}, {3485,6846}, {3486,6987}, {3574,32331}, {3576,11425}, {3579,11438}, {3586,5903}, {3600,40269}, {3616,11427}, {3660,12005}, {3671,30329}, {3678,12564}, {3682,25091}, {3697,31434}, {3754,12446}, {3779,26939}, {3827,9969}, {3873,14986}, {3874,11019}, {3876,5703}, {3911,9940}, {3947,15064}, {4259,37179}, {4293,12680}, {4294,5759}, {4304,31793}, {4662,10039}, {4848,31788}, {5044,6675}, {5045,12242}, {5087,5570}, {5396,37565}, {5428,17010}, {5435,6962}, {5439,25525}, {5440,37308}, {5665,38271}, {5693,11529}, {5704,6933}, {5707,37696}, {5715,9581}, {5719,31835}, {5722,5812}, {5766,7671}, {5799,39579}, {5884,6260}, {5887,6913}, {5902,5927}, {6642,9928}, {6765,17658}, {6776,7718}, {6829,17606}, {6834,37566}, {6861,11374}, {6863,10202}, {6886,8232}, {6889,24914}, {6896,11023}, {6907,34339}, {6986,37787}, {6990,17605}, {7367,8886}, {7713,17810}, {8069,11517}, {8226,12047}, {8257,16410}, {9578,18908}, {9777,11396}, {9780,37643}, {9848,30305}, {9856,10392}, {9955,18388}, {10167,15803}, {10246,11426}, {10445,32118}, {10591,17604}, {10914,12625}, {10958,18838}, {11245,12135}, {11399,37538}, {11430,13624}, {11496,30223}, {11500,37550}, {11570,13257}, {11699,12227}, {12514,13615}, {12689,24248}, {13369,37582}, {13373,15325}, {13403,28160}, {14913,29957}, {15178,37505}, {15435,24476}, {15823,37306}, {16200,17622}, {16845,25917}, {17556,24473}, {18165,25516}, {18240,33709}, {18390,18480}, {18398,37692}, {18447,36750}, {18455,37509}, {18732,34371}, {18839,37722}, {20423,34643}, {20612,24982}, {22766,37249}, {24929,31837}, {31397,34790}, {31937,39542}, {33597,37583}, {35242,37487}, {36279,37411}, {37415,39598}, {37709,39779}

X(44547) = midpoint of X(i) and X(j) for these {i,j}: {65,1858}, {72,14054}, {185,1902}, {950,15556}
X(44547) = reflection of X(4292) in X(37544)
X(44547) = X(i)-complementary conjugate of X(j) for these (i,j): (943,34823), (1175,34851), (2982,18589)
X(44547) = X(513)-he conjugate of X(1054)
X(44547) = crossdifference of every pair of points on line X(513)-X(36054)
X(44547) = crosssum of X(i) and X(j) for these {i,j}: {1,3074}, {3,942}, {6,23207}
X(44547) = crosspoint of X(4)and X(943)
X(44547) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,1728,405), (1,10398,10396), (1,10399,5728), (1,18397,72), (65,1837,7686), (65,1864,4), (65,1898,1836), (65,12688,4295), (72,405,960), (72,3555,11523), (72,5728,1), (201,14547,37528), (226,10395,5), (405,5729,1728), (920,11507,4640), (942,5777,226), (954,5728,5572), (1071,3149,9942), (1210,18389,942), (1708,10393,3), (1737,13750,3812), (3487,6832,11375), (3678,12564,13405), (3876,11020,5703), (5044,11018,13411), (5693,11529,12709), (7957,14100,4294), (10122,13411,11018), (10398,18412,5728), (10399,18397,1), (30329,31803,3671), (31789,37730,950)

X(44548) = X(6)X(41)∩X(389)X(515)

Barycentrics    a^2*(a+b)*(a+c)*(b+c)*(a^2-b^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^8*b^3+a^7*b^4-3*a^6*b^5-3*a^5*b^6+3*a^4*b^7+3*a^3*b^8-a^2*b^9-a*b^10+a^8*b^2*c-2*a^6*b^4*c+2*a^2*b^8*c-b^10*c+a^8*b*c^2+a^5*b^4*c^2-3*a^4*b^5*c^2-2*a^3*b^6*c^2+2*a^2*b^7*c^2+a*b^8*c^2+a^8*c^3-4*a^2*b^6*c^3+3*b^8*c^3+a^7*c^4-2*a^6*b*c^4+a^5*b^2*c^4-2*a^3*b^4*c^4+a^2*b^5*c^4+b^7*c^4-3*a^6*c^5-3*a^4*b^2*c^5+a^2*b^4*c^5-3*b^6*c^5-3*a^5*c^6-2*a^3*b^2*c^6-4*a^2*b^3*c^6-3*b^5*c^6+3*a^4*c^7+2*a^2*b^2*c^7+b^4*c^7+3*a^3*c^8+2*a^2*b*c^8+a*b^2*c^8+3*b^3*c^8-a^2*c^9-a*c^10-b*c^10) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 2138.

X(44548) lies on these lines: {4,12930}, {5,34831}, {6,41}, {389,515}, {2779,7687}, {9786,15622}

X(44548) = midpoint of X(73) and X(14055)
X(44548) = crosssum of X(3)and X(34831)
X(44548) = {X(73),X(13738)}-harmonic conjugate of X(37836)

X(44549) = X(6)X(36894)∩X(187)X(441)

Barycentrics    (2*a^8 - a^6*b^2 - 2*a^4*b^4 - a^2*b^6 + 2*b^8 - 3*a^6*c^2 + 5*a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 - 7*a^2*b^2*c^4 - b^4*c^4 + 3*a^2*c^6 + 3*b^2*c^6 - c^8)*(2*a^8 - 3*a^6*b^2 - a^4*b^4 + 3*a^2*b^6 - b^8 - a^6*c^2 + 5*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 3*b^6*c^2 - 2*a^4*c^4 + 5*a^2*b^2*c^4 - b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + 2*c^8) : :

See Antreas Hatzipolakis and Peter Moses, euclid 2144.

X(44549) lies on these lines: {6, 36894}, {187, 441}, {512, 11746}, {1503, 10151}

leftri

Centers and perspectors of ellipses [SCE, line] [SIE, line]: X(44550)-X(44555)

rightri

This preamble is contributed by Peter Moses, August 24-30, 2021.

Abbreviations: SCE = Steiner circumellipse; SIE = Steiner inellipse.

Suppose that L is a line given by u x + v y + w z = 0 (barycentrics). The SCE-inverse of L, denoted by [SCE, L], is given by

u (x^2 - y z) + v (y^2 - z x) + w (z^2 - x y) = 0,

and the SIE-inverse of L, denoted by [SIE, L], is given by

(2u + v + w) (x^2 - y z) + (u + 2v + w) (y^2 - z x) + (u + v + 2w) (z^2 - x y) = 0.

The center of [SCE, L] is -u + 2v + 2w : : = reflection of u : v : w in X(2).

The center of [SIE, L] is 2u + 5v + 5w : : = complement of midpoint of u : v : w and X(2).

The perspector of [SCE, L] is (2 v^2 + u w) (u v + 2 w^2) : : .

The perspector of [SIE, L] is (4 u^2 + 9 v^2 + 4 w^2 + 11 v w + 9 w u + 11 u v)*(4 u^2 + 4 v^2 + 9 w^2 + 11 v w + 11 w u + 9 u v) : :

The appearance of (L, k) in the following list means that X(k) is the center of the ellipse [SCE, L]:

(Brocard axis, 36900), (orthic axis, 1992), (anti-orthic axis, 4664), (Lemoine axis, 7757), (de Longchamps axis, 599), (Gergonne line, 3241), (Fermat line, 9979), (X(1)X(6), 31150), (Koiller line, 31169), (X(1)X(3), 44550), (Soddy line, 44551), (van Aubel line, 44552), (X(1)X(5), 44553), (Napoleon axis, 44554), (Hatzipolakis axis, 44555)

The appearance of (L, k) in the following list means that X(k) is the perspector of the ellipse [SCE, L]:

(orthic axis, 44556), (Lemoine aixs, 44557), (de Longchamps axis, 44558), (Gergonne line, 44559)

The appearance of (L, k) in the following list means that X(k) is the center of the ellipse [SIE, L]:

(orthic axis, 597), (anti-orthic axis, 4755), (de Logchamps axis, 20582), (Gergonne line, 551), (brocard axis, 44560), (X(1)X(3), 44561), (Lemoinne axis, 44562), (Soddy line, 44563), (Fermat line, 44564), (van Aubel line, 44565), (X(1)X(5), 44566), (X(1)X(6), 44567), (Napoleon axis, 44568), (Hatzipolakis axis, 44569), (Koiller line, 44570)

The appearance of (L, k) in the following list means that X(k) is the perspector of the ellipse [SIE, L]:

(orthic axis, 44571), (Gergonne line, 44572)

X(44550) = CENTER OF ELLIPSE [SCE, X(1)X(3)]

Barycentrics    (b - c)*(-2*a^3 + 2*a*b^2 - a*b*c + b^2*c + 2*a*c^2 + b*c^2) : :
X(44550) = 2 X[650] + X[21222], X[693] - 4 X[3960], 4 X[905] - X[4391], 2 X[905] + X[17496], 2 X[3669] + X[4560], 4 X[3669] - X[4801], 2 X[3762] - 5 X[31209], X[3904] + 2 X[4025], X[4391] + 2 X[17496], X[4462] - 4 X[14838], X[4474] - 4 X[25380], 2 X[4560] + X[4801], 2 X[17069] + X[30725], 2 X[31149] - 3 X[44429]

X(44550) lies on these lines: {2, 905}, {514, 1635}, {519, 1734}, {522, 14413}, {525, 1636}, {551, 8714}, {650, 21222}, {693, 3960}, {824, 30656}, {918, 14411}, {1946, 17549}, {2787, 31149}, {3227, 18821}, {3241, 3900}, {3669, 4560}, {3762, 31209}, {3904, 4025}, {3910, 14412}, {4462, 14838}, {4474, 25380}, {4664, 28898}, {4750, 28468}, {4776, 29148}, {4980, 23685}, {6002, 31147}, {13587, 22091}, {14415, 23880}, {16370, 22160}, {17069, 30725}, {20979, 28840}, {29126, 44435}, {29236, 36848}

X(44550) = midpoint of X(2) and X(17496)
X(44550) = reflection of X(i) in X(j) for these {i,j}: {2, 905}, {4391, 2}
X(44550) = anticomplement of X(45664)
X(44550) = crossdifference of every pair of points on line {2177, 34417}
X(44550) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {905, 17496, 4391}, {3669, 4560, 4801}

X(44551) = CENTER OF ELLIPSE [SCE, SODDY LINE]

Barycentrics    (b - c)*(-5*a^2 + 2*a*b + 3*b^2 + 2*a*c - 2*b*c + 3*c^2) : :
X(44551) = 5 X[2] - X[25259], X[3239] + 2 X[4025], X[3239] - 4 X[7658], 5 X[3239] - 2 X[25259], 2 X[3676] + X[4765], X[3676] + 2 X[17069], X[3798] + 2 X[21212], X[4025] + 2 X[7658], 5 X[4025] + X[25259], 3 X[4453] + X[31150], 3 X[4750] + X[31147], X[4765] - 4 X[17069], 10 X[7658] - X[25259], X[16892] + 2 X[43061]

X(44551) lies on these lines: {2, 2400}, {514, 1635}, {522, 1638}, {525, 14345}, {599, 9031}, {652, 3928}, {658, 32040}, {2482, 35112}, {2786, 44432}, {3667, 4750}, {3676, 4762}, {3798, 4785}, {3828, 29212}, {4379, 28161}, {4728, 4962}, {4786, 44435}, {16892, 43061}, {20521, 23878}, {21183, 27486}

X(44551) = midpoint of X(i) and X(j) for these {i,j}: {2, 4025}, {4786, 44435}, {21183, 27486}
X(44551) = reflection of X(i) in X(j) for these {i,j}: {2, 7658}, {3239, 2}
X(44551) = anticomplement of X(45334)
X(44551) = crossdifference of every pair of points on line {2177, 41424}
X(44551) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3676, 17069, 4765}, {4025, 7658, 3239}

X(44552) = CENTER OF ELLIPSE [SCE, VAN AUBEL LINE]

Barycentrics    (b^2 - c^2)*(-5*a^4 + 2*a^2*b^2 + 3*b^4 + 2*a^2*c^2 - 2*b^2*c^2 + 3*c^4) : :
X(44552) = 3 X[1637] - X[31174], X[2525] - 4 X[14341], X[3265] - 4 X[6587], X[3265] + 2 X[33294], 2 X[6587] + X[33294], 3 X[9979] + X[36900], 3 X[14420] + X[31176]

X(44552) lies on these lines: {2, 2419}, {351, 523}, {525, 1637}, {648, 31510}, {671, 42738}, {1992, 9007}, {2501, 23878}, {2525, 14341}, {2799, 9209}, {3566, 14420}, {14568, 41357}

X(44552) = midpoint of X(2) and X(33294)
X(44552) = reflection of X(i) in X(j) for these {i,j}: {2, 6587}, {3265, 2}
X(44552) = crossdifference of every pair of points on line {574, 26864}
X(44552) = {X(6587),X(33294)}-harmonic conjugate of X(3265)

X(44553) = CENTER OF ELLIPSE [SCE, LINE X(1)X(5)]

Barycentrics    (b - c)*(a^3 - 3*a^2*b - a*b^2 + 3*b^3 - 3*a^2*c + 5*a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2 + 3*c^3) : :
X(44553) = 4 X[676] - 3 X[38314], X[3904] - 4 X[10015]

X(44553) lies on these lines: {2, 3904}, {514, 1635}, {525, 14391}, {664, 32040}, {676, 38314}, {903, 918}, {1638, 41802}, {3241, 6366}, {3679, 23887}, {3910, 14394}, {4391, 36038}, {4707, 21141}, {4762, 43052}, {9521, 34632}, {19293, 23184}, {21129, 28890}, {23884, 30565}, {28468, 31147}

X(44553) = reflection of X(i) in X(j) for these {i,j}: {2, 10015}, {3904, 2}
X(44553) = anticomplement of X(45341)
X(44553) = crossdifference of every pair of points on line {2177, 44109}

X(44554) = CENTER OF ELLIPSE [SCE, NAPOLEON AXIS]

Barycentrics    (b^2 - c^2)*(a^4 - 4*a^2*b^2 + 3*b^4 - 4*a^2*c^2 - 5*b^2*c^2 + 3*c^4) : :
X(44554) = 3 X[3268] - 4 X[31174], 3 X[9979] - 2 X[36900], 4 X[12077] - X[41298]

X(44554) lies on these lines: {2, 12077}, {351, 523}, {3268, 31174}, {14446, 23872}, {14447, 23873}

X(44554) = reflection of X(i) in X(j) for these {i,j}: {2, 12077}, {41298, 2}

X(44555) = CENTER OF ELLIPSE [SCE, HATZIPOLAKIS AXIS]

Barycentrics    a^6 - 4*a^4*b^2 + 5*a^2*b^4 - 2*b^6 - 4*a^4*c^2 - 3*a^2*b^2*c^2 + 2*b^4*c^2 + 5*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(44555) = 5 X[2] - 4 X[11064], X[23] - 4 X[41586], X[23] + 2 X[41724], 2 X[110] - 3 X[37907], 3 X[186] - 4 X[15361], X[323] - 4 X[3580], 5 X[323] - 8 X[11064], X[323] + 2 X[37779], 3 X[323] - 4 X[40112], 4 X[597] - 3 X[22151], 2 X[1992] - 3 X[37784], 5 X[3580] - 2 X[11064], 2 X[3580] + X[37779], 3 X[3580] - X[40112], 4 X[7426] - 3 X[35265], 3 X[8859] - 2 X[14999], 2 X[9143] - 3 X[35265], 4 X[11064] + 5 X[37779], 6 X[11064] - 5 X[40112], 4 X[13857] - 5 X[30745], X[14683] - 4 X[32269], X[14683] - 3 X[37909], 2 X[23061] - 5 X[30745], 2 X[23236] - 5 X[37953], 4 X[30714] - 7 X[37957], 4 X[32225] - 3 X[37907], 4 X[32269] - 3 X[37909], 4 X[35266] - 5 X[37760], 3 X[37779] + 2 X[40112], 2 X[41586] + X[41724]

X(44555) lies on these lines: {2, 6}, {23, 542}, {30, 3448}, {51, 25561}, {52, 7565}, {94, 671}, {110, 32225}, {186, 15361}, {381, 11002}, {399, 44266}, {511, 9140}, {525, 14391}, {530, 11092}, {531, 11078}, {539, 32263}, {547, 7605}, {576, 38397}, {1216, 43836}, {1503, 37901}, {2482, 35296}, {3410, 41588}, {3564, 7426}, {5169, 20423}, {5459, 33529}, {5460, 33530}, {5463, 11146}, {5464, 11145}, {5640, 11178}, {5642, 5965}, {5648, 8262}, {7464, 20126}, {7492, 43273}, {7570, 15019}, {7693, 18358}, {7703, 37517}, {7712, 39899}, {8288, 8586}, {8596, 40853}, {8724, 35298}, {9213, 36255}, {10020, 11271}, {10294, 15362}, {10296, 11564}, {10545, 43150}, {10706, 13754}, {11477, 31857}, {11645, 15107}, {11646, 13192}, {12383, 44265}, {12828, 37962}, {13857, 23061}, {14002, 15069}, {14683, 32269}, {14830, 37183}, {14918, 37765}, {15032, 44262}, {15052, 44275}, {16042, 34507}, {18387, 40909}, {18947, 37943}, {23236, 37953}, {24981, 32267}, {26869, 33884}, {30714, 37957}, {32515, 36194}, {35266, 37760}, {37126, 43573}

X(44555) = midpoint of X(i) and X(j) for these {i,j}: {2, 37779}, {15360, 41724}
X(44555) = reflection of X(i) in X(j) for these {i,j}: {2, 3580}, {23, 15360}, {110, 32225}, {323, 2}, {399, 44266}, {5648, 8262}, {7464, 20126}, {9143, 7426}, {9213, 36255}, {10989, 9140}, {12383, 44265}, {15360, 41586}, {23061, 13857}, {24981, 32267}
X(44555) = anticomplement of X(40112)
X(44555) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {9060, 7192}, {34802, 4329}
X(44555) = crossdifference of every pair of points on line {512, 44109}
X(44555) = barycentric product X(3260)*X(39239)
X(44555) = barycentric quotient X(i)/X(j) for these {i,j}: {10294, 10295}, {15362, 381}, {39239, 74}
X(44555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 32225, 37907}, {323, 34545, 22151}, {323, 37784, 1994}, {3580, 6515, 37784}, {3580, 37779, 323}, {6792, 15993, 11580}, {7426, 9143, 35265}, {8115, 8116, 11004}, {37785, 37786, 41626}, {39107, 39108, 18122}, {41586, 41724, 23}

X(44556) = PERSPECTOR OF ELLIPSE [SCE, ORTHIC AXIS]

Barycentrics    (a^4 - 4*a^2*b^2 + 3*b^4 + 6*a^2*c^2 - 4*b^2*c^2 + c^4)*(a^4 + 6*a^2*b^2 + b^4 - 4*a^2*c^2 - 4*b^2*c^2 + 3*c^4) : :

X(44556) lies on these lines: {4, 13479}, {30, 1351}, {125, 36889}, {523, 37643}, {1007, 3260}, {1990, 4232}, {2847, 35906}, {9308, 34285}, {16303, 35260}, {16326, 26869}, {34417, 39453}

X(44556) = isogonal conjugate of X(6090)
X(44556) = isotomic conjugate of X(32817)
X(44556) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6090}, {31, 32817}, {15144, 35200}
X(44556) = trilinear pole of line {1499, 1514}
X(44556) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 32817}, {6, 6090}, {1990, 15144}

X(44557) = PERSPECTOR OF ELLIPSE [SCE, LEMOINE AXIS]

Barycentrics    a^2*(b^4 + 2*a^2*c^2)*(2*a^2*b^2 + c^4) : :

X(44557) lies on these lines: {110, 9515}, {187, 353}, {385, 30495}, {512, 9465}, {524, 3094}, {598, 3124}, {694, 3972}, {695, 6179}, {729, 34811}, {5640, 43950}, {7031, 40935}, {7937, 41259}, {11057, 20859}, {11654, 18872}, {30229, 35146}, {34154, 39024}

X(44557) = isogonal conjugate of X(3734)
X(44557) = isogonal conjugate of the anticomplement of X(4045)
X(44557) = isogonal conjugate of the complement of X(2549)
X(44557) = X(1)-isoconjugate of X(3734)
X(44557) = trilinear pole of line {351, 9009}
X(44557) = barycentric quotient X(6)/X(3734)

X(44558) = PERSPECTOR OF ELLIPSE [SCE, DE LONGCHAMPS AXIS]

Barycentrics    (2*b^4 + a^2*c^2)*(a^2*b^2 + 2*c^4) : :

X(44558) lies on these lines: {67, 7761}, {183, 9465}, {538, 599}, {625, 18575}, {626, 18375}, {2854, 34227}, {3001, 5094}, {3124, 9462}, {3314, 9464}, {3778, 4361}, {6322, 6325}, {7934, 18023}, {13377, 31173}

X(44558) = isotomic conjugate of X(3972)
X(44558) = isotomic conjugate of the anticomplement of X(7853)
X(44558) = isotomic conjugate of the complement of X(7898)
X(44558) = isotomic conjugate of the isogonal conjugate of X(30495)
X(44558) = X(7853)-cross conjugate of X(2)
X(44558) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3972}, {163, 4108}
X(44558) = cevapoint of X(2) and X(7898)
X(44558) = trilinear pole of line {3906, 9148}
X(44558) = barycentric product X(76)*X(30495)
X(44558) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3972}, {523, 4108}, {30495, 6}

X(44559) = PERSPECTOR OF ELLIPSE [SCE, GERGONNE LINE]

Barycentrics    (a^2 - 4*a*b + 3*b^2 + 6*a*c - 4*b*c + c^2)*(a^2 + 6*a*b + b^2 - 4*a*c - 4*b*c + 3*c^2) : :

X(44559) lies on these lines: {390, 527}, {1323, 5222}, {5328, 29627}, {26007, 36887}, {31189, 31190}

X(44559) = trilinear pole of line {1638, 6006}

X(44560) = CENTER OF ELLIPSE [SIE, BROCARD AXIS]

Barycentrics    (b^2 - c^2)*(5*a^4 - 5*a^2*b^2 - 5*a^2*c^2 + 2*b^2*c^2) : :
X(44560) = 5 X[2] - X[850], 13 X[2] - 5 X[31072], 7 X[2] - 5 X[31277], 7 X[2] + X[31296], 3 X[2] + X[36900], 4 X[2] + X[41300], 3 X[351] + X[31176], 5 X[647] + X[850], 2 X[647] + X[30476], 13 X[647] + 5 X[31072], 3 X[647] + X[31174], 7 X[647] + 5 X[31277], 7 X[647] - X[31296], 3 X[647] - X[36900], 4 X[647] - X[41300], 2 X[850] - 5 X[30476], 13 X[850] - 25 X[31072], 3 X[850] - 5 X[31174], 7 X[850] - 25 X[31277], 7 X[850] + 5 X[31296], 3 X[850] + 5 X[36900], 4 X[850] + 5 X[41300], X[19912] + 3 X[32232], 13 X[30476] - 10 X[31072], 3 X[30476] - 2 X[31174], 7 X[30476] - 10 X[31277], 7 X[30476] + 2 X[31296], 3 X[30476] + 2 X[36900], 2 X[30476] + X[41300], 15 X[31072] - 13 X[31174], 7 X[31072] - 13 X[31277], 35 X[31072] + 13 X[31296], 15 X[31072] + 13 X[36900], 20 X[31072] + 13 X[41300], 7 X[31174] - 15 X[31277], 7 X[31174] + 3 X[31296], 4 X[31174] + 3 X[41300], 5 X[31277] + X[31296], 15 X[31277] + 7 X[36900], 20 X[31277] + 7 X[41300], 3 X[31296] - 7 X[36900], 4 X[31296] - 7 X[41300], 4 X[36900] - 3 X[41300]

X(44560) lies on these lines: {2, 647}, {351, 31176}, {512, 11176}, {523, 44401}, {525, 14345}, {542, 22264}, {549, 30209}, {597, 8675}, {2799, 9209}, {4139, 4763}, {5996, 8644}, {6041, 11163}, {8651, 25423}, {8704, 9189}, {9030, 20582}, {9404, 19722}, {11633, 34290}, {11645, 42654}, {19912, 32232}

X(44560) = midpoint of X(i) and X(j) for these {i,j}: {2, 647}, {5996, 8644}, {31174, 36900}
X(44560) = reflection of X(30476) in X(2)
X(44560) = complement of X(31174)
X(44560) = crossdifference of every pair of points on line {237, 5210}
X(44560) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36900, 31174}, {647, 30476, 41300}, {647, 31174, 36900}, {647, 31277, 31296}

X(44561) = CENTER OF ELLIPSE [SIE, LINE X(1)X(3)]

Barycentrics    (b - c)*(5*a^3 - 5*a*b^2 - 2*a*b*c + 2*b^2*c - 5*a*c^2 + 2*b*c^2) : :
X(44561) = 5 X[2] - X[4391], 7 X[2] + X[17496], 5 X[905] + X[4391], 7 X[905] - X[17496], X[1734] + 3 X[25055], X[3960] + 2 X[31287], 7 X[4391] + 5 X[17496], 3 X[14419] + X[31149]

X(44561) lies on these lines: {2, 905}, {514, 14425}, {525, 14345}, {551, 3900}, {1734, 25055}, {1946, 16371}, {3960, 31287}, {4755, 28898}, {4762, 14838}, {5325, 20318}, {14419, 28475}, {16370, 22091}, {16417, 22160}, {29126, 44432}, {30234, 44429}

X(44561) = midpoint of X(i) and X(j) for these {i,j}: {2, 905}, {30234, 44429}
X(44561) = complement of X(45664)

X(44562) = CENTER OF ELLIPSE [SIE, LEMOINE AXIS]

Barycentrics    5*a^2*b^2 + 5*a^2*c^2 + 2*b^2*c^2 : :
X(44562) = 5 X[2] - X[76], 7 X[2] + X[194], 3 X[2] + X[7757], X[2] - 5 X[7786], 11 X[2] + X[11055], 7 X[2] - X[14711], 17 X[2] - X[20081], 31 X[2] + X[20105], 7 X[2] - 5 X[31239], 13 X[2] - 5 X[31276], 4 X[2] + X[32450], 7 X[5] + 5 X[32523], 5 X[39] + X[76], 7 X[39] - X[194], 2 X[39] + X[3934], X[39] + 2 X[6683], 3 X[39] - X[7757], X[39] + 5 X[7786], 3 X[39] + X[9466], 11 X[39] - X[11055], 7 X[39] + X[14711], 17 X[39] + X[20081], 31 X[39] - X[20105], 7 X[39] + 5 X[31239], 13 X[39] + 5 X[31276], 4 X[39] - X[32450], 7 X[76] + 5 X[194], 2 X[76] - 5 X[3934], X[76] - 10 X[6683], 3 X[76] + 5 X[7757], X[76] - 25 X[7786], 3 X[76] - 5 X[9466], 11 X[76] + 5 X[11055], 7 X[76] - 5 X[14711], 17 X[76] - 5 X[20081], 31 X[76] + 5 X[20105], 7 X[76] - 25 X[31239], 13 X[76] - 25 X[31276], 4 X[76] + 5 X[32450], 2 X[194] + 7 X[3934], X[194] + 14 X[6683], 3 X[194] - 7 X[7757], X[194] + 35 X[7786], 3 X[194] + 7 X[9466], 11 X[194] - 7 X[11055], 17 X[194] + 7 X[20081], 31 X[194] - 7 X[20105], X[194] + 5 X[31239], 13 X[194] + 35 X[31276], 4 X[194] - 7 X[32450], 3 X[262] + X[376], X[376] - 3 X[21163], X[381] + 3 X[11171], X[549] - 3 X[40108], 3 X[598] + X[33264], X[599] + 3 X[13331], 5 X[631] - X[33706]

X(44562) lies on these lines: {2, 39}, {3, 44422}, {5, 32523}, {6, 15482}, {30, 11272}, {37, 40479}, {83, 13586}, {140, 7829}, {183, 41748}, {187, 3329}, {262, 376}, {381, 11171}, {384, 31652}, {511, 549}, {524, 10007}, {543, 2023}, {547, 2782}, {551, 14839}, {574, 1003}, {598, 33264}, {599, 13331}, {620, 3589}, {625, 3815}, {626, 31406}, {631, 33706}, {726, 4755}, {730, 3828}, {732, 20582}, {736, 22110}, {754, 8359}, {1078, 5041}, {1506, 7861}, {1569, 14971}, {1656, 7902}, {1916, 41134}, {2021, 3849}, {2482, 6661}, {2548, 7842}, {2549, 32983}, {3055, 6722}, {3094, 7622}, {3095, 5054}, {3106, 11302}, {3107, 11301}, {3228, 39968}, {3524, 5188}, {3543, 22682}, {3545, 11257}, {3618, 22486}, {3734, 5024}, {3763, 7908}, {3819, 10191}, {3839, 32522}, {3972, 8589}, {5007, 7824}, {5008, 7771}, {5013, 7808}, {5052, 5569}, {5055, 6248}, {5066, 32516}, {5071, 7709}, {5149, 9888}, {5306, 34506}, {5319, 32978}, {5355, 37688}, {5475, 33017}, {5943, 44215}, {5971, 39389}, {5976, 9167}, {6179, 41940}, {6194, 15721}, {6292, 7895}, {6656, 9698}, {6704, 7789}, {7603, 7790}, {7618, 14039}, {7697, 15703}, {7736, 7761}, {7745, 8354}, {7747, 8353}, {7748, 33016}, {7751, 8556}, {7758, 32960}, {7759, 16043}, {7764, 7849}, {7765, 32992}, {7772, 7780}, {7774, 7848}, {7775, 11287}, {7777, 7853}, {7781, 22332}, {7787, 15513}, {7791, 7843}, {7798, 15271}, {7800, 7882}, {7805, 7815}, {7810, 41624}, {7811, 15810}, {7818, 11163}, {7821, 7876}, {7830, 8358}, {7831, 7845}, {7833, 14537}, {7840, 31168}, {7844, 31489}, {7847, 39590}, {7856, 33015}, {7858, 7873}, {7862, 31467}, {7864, 39565}, {7865, 9766}, {7878, 33004}, {7909, 16897}, {7919, 17005}, {7924, 31173}, {8176, 16041}, {8178, 12055}, {8703, 14881}, {9166, 11152}, {9771, 10150}, {9821, 15693}, {10124, 32515}, {11361, 32479}, {12040, 24256}, {12251, 15709}, {12263, 19883}, {12782, 25055}, {13354, 38064}, {14001, 31450}, {14033, 34504}, {14046, 39266}, {14093, 22728}, {14994, 21358}, {15048, 15491}, {15246, 37875}, {15692, 37809}, {15694, 15819}, {15699, 32448}, {15702, 22712}, {15713, 32521}, {16925, 31457}, {21356, 32451}, {22691, 37351}, {22692, 37352}, {22707, 37170}, {22708, 37171}, {25555, 37459}, {31407, 33025}, {31417, 32982}, {31492, 32954}, {32994, 39601}, {33013, 39563}, {33213, 44377}

X(44562) = midpoint of X(i) and X(j) for these {i,j}: {2, 39}, {3, 44422}, {194, 14711}, {262, 21163}, {5066, 32516}, {7745, 8354}, {7747, 8353}, {7753, 8356}, {7757, 9466}, {7810, 41624}, {7811, 41750}, {7833, 14537}, {8359, 9300}, {8703, 14881}, {15819, 32447}
X(44562) = reflection of X(i) in X(j) for these {i,j}: {2, 6683}, {3934, 2}, {7830, 8358}, {40344, 8359}
X(44562) = complement of X(9466)
X(44562) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7757, 9466}, {39, 3934, 32450}, {39, 6683, 3934}, {39, 7786, 6683}, {39, 9466, 7757}, {39, 31239, 194}, {574, 7804, 32456}, {574, 11174, 7804}, {3329, 33273, 12150}, {3815, 4045, 625}, {5013, 7808, 7816}, {7764, 8362, 7849}, {7772, 11285, 7780}, {7803, 31455, 7886}, {7815, 9605, 7805}, {7858, 33021, 7873}, {7878, 33004, 35007}, {7919, 17005, 31275}, {8362, 9606, 7764}, {12150, 33273, 187}, {15810, 41750, 7811}

X(44563) = CENTER OF ELLIPSE [SIE, SODDY LINE]

Barycentrics    (b - c)*(-17*a^2 + 14*a*b + 3*b^2 + 14*a*c - 14*b*c + 3*c^2) : :
X(44563) = 5 X[2] - X[3239], 7 X[2] + X[4025], 17 X[2] - X[25259], 7 X[3239] + 5 X[4025], X[3239] + 5 X[7658], 17 X[3239] - 5 X[25259], X[4025] - 7 X[7658], 17 X[4025] + 7 X[25259], 17 X[7658] + X[25259]

X(44563) lies on these lines: {2, 2400}, {514, 14425}, {3667, 26275}, {9031, 20582}

X(44563) = midpoint of X(2) and X(7658)
X(44563) = complement of X(45334)

X(44564) = CENTER OF ELLIPSE [SIE, FERMAT LINE]

Barycentrics    (b^2 - c^2)*(-4*a^4 + 3*a^2*b^2 + b^4 + 3*a^2*c^2 - 4*b^2*c^2 + c^4) : :
Barycentrics    (cot B - cot C) (cot^2 A - 2 (cot A) (cot B + cot C) + 3 cot B cot C) : :
X(44564) = 5 X[2] - X[3268], 3 X[2] + X[9979], X[351] + 3 X[8371], X[351] - 3 X[9189], 5 X[1637] + X[3268], 3 X[1637] - X[9979], 3 X[1637] + X[14417], 3 X[3268] + 5 X[9979], 3 X[3268] - 5 X[14417], 3 X[5466] + X[9131], X[6587] + 2 X[14341], 2 X[6587] + X[30476], 3 X[8371] - X[9134], 3 X[9125] - X[9131], X[9134] + 3 X[9189], 3 X[10278] + X[14610], 3 X[11176] - X[14610], X[12075] + 2 X[44451], 4 X[14341] - X[30476], 5 X[31277] + X[33294]

X(44564) lies on these lines: {2, 1637}, {3, 9529}, {25, 25644}, {125, 14697}, {351, 2793}, {381, 44202}, {402, 5972}, {523, 44401}, {525, 3239}, {542, 42736}, {549, 44204}, {597, 9003}, {690, 5461}, {804, 10189}, {1196, 2507}, {1995, 42659}, {2492, 6719}, {2848, 35282}, {4763, 6089}, {5466, 9125}, {5943, 39469}, {9209, 23878}, {10278, 11176}, {12075, 44451}, {14273, 14977}, {14401, 15595}, {14582, 18883}, {23301, 32478}, {31277, 33294}, {33752, 42665}

X(44564) = midpoint of X(i) and X(j) for these {i,j}: {2, 1637}, {3, 44203}, {125, 14697}, {351, 9134}, {381, 44202}, {549, 44204}, {2492, 18310}, {5466, 9125}, {8371, 9189}, {9979, 14417}, {10278, 11176}, {14273, 14977}
X(44564) = complement of X(14417)
X(44564) = center of circle {{X(2),X(107),X(111),X(125)}}
X(44564) = X(i)-complementary conjugate of X(j) for these (i,j): {19, 5099}, {111, 34846}, {112, 16597}, {162, 126}, {691, 18589}, {823, 34517}, {897, 127}, {923, 15526}, {1973, 23992}, {8753, 8287}, {14908, 16595}, {17983, 21253}, {24019, 5181}, {32676, 2482}, {32729, 1214}, {32740, 16573}, {36045, 16051}, {36060, 122}, {36085, 1368}, {36115, 30739}, {36128, 125}, {36142, 3}
X(44564) = crossdifference of every pair of points on line {154, 5191}
X(44564) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9979, 14417}, {351, 8371, 9134}, {1637, 14417, 9979}, {6587, 14341, 30476}, {9134, 9189, 351}

X(44565) = CENTER OF ELLIPSE [SIE, VAN AUBEL LINE]

Barycentrics    (b^2 - c^2)*(-17*a^4 + 14*a^2*b^2 + 3*b^4 + 14*a^2*c^2 - 14*b^2*c^2 + 3*c^4) : :
X(44565) = 5 X[2] - X[3265], 7 X[2] + X[33294], X[3265] + 5 X[6587], 7 X[3265] + 5 X[33294], 7 X[6587] - X[33294], 3 X[9209] + X[31174]

X(44565) lies on these lines: {2, 2419}, {523, 44401}, {597, 9007}, {9209, 31174}, {14341, 23878}, {30442, 37672}

X(44565) = midpoint of X(2) and X(6587)
X(44565) = crossdifference of every pair of points on line {5210, 42671}

X(44566) = CENTER OF ELLIPSE [SIE, LINE X(1)X(5)]

Barycentrics    (b - c)*(-2*a^3 - 3*a^2*b + 2*a*b^2 + 3*b^3 - 3*a^2*c + 8*a*b*c - 5*b^2*c + 2*a*c^2 - 5*b*c^2 + 3*c^3) : :
X(44566) = 5 X[2] - X[3904], X[3904] + 5 X[10015], X[24473] - 3 X[30691]

X(44566) lies on these lines: {2, 3904}, {514, 14425}, {519, 676}, {525, 1637}, {551, 6366}, {918, 21198}, {3828, 23887}, {4049, 6084}, {4528, 4745}, {4904, 21950}, {11125, 39472}, {24473, 30691}, {26275, 28294}, {28481, 31149}

X(44566) = midpoint of X(2) and X(10015)
X(44566) = reflection of X(4528) in X(4745)
X(44566) = complement of X(45341)

X(44567) = CENTER OF ELLIPSE [SIE, LINE X(1)X(6)]

Barycentrics    (b - c)*(5*a^2 - 5*a*b - 5*a*c + 2*b*c) : :
X(44567) = 5 X[2] - X[693], 7 X[2] + X[17494], 11 X[2] + 5 X[26777], 17 X[2] - X[26824], 13 X[2] - 5 X[26985], X[2] + 7 X[27115], 3 X[2] + X[31150], X[2] - 5 X[31209], 7 X[2] - 5 X[31250], 5 X[650] + X[693], 2 X[650] + X[4885], 7 X[650] - X[17494], 11 X[650] - 5 X[26777], 17 X[650] + X[26824], 13 X[650] + 5 X[26985], X[650] - 7 X[27115], 3 X[650] - X[31150], X[650] + 5 X[31209], 7 X[650] + 5 X[31250], X[650] + 2 X[31287], 2 X[693] - 5 X[4885], 7 X[693] + 5 X[17494], 11 X[693] + 25 X[26777], 17 X[693] - 5 X[26824], 13 X[693] - 25 X[26985], X[693] + 35 X[27115], 3 X[693] + 5 X[31150], X[693] - 25 X[31209], 7 X[693] - 25 X[31250], X[693] - 10 X[31287], 3 X[1635] + X[31147], 2 X[2516] + X[3835], 2 X[4394] + X[4940], X[4394] + 2 X[25666], 2 X[4521] + X[17069], 7 X[4885] + 2 X[17494], 11 X[4885] + 10 X[26777], 17 X[4885] - 2 X[26824], 13 X[4885] - 10 X[26985], X[4885] + 14 X[27115], 3 X[4885] + 2 X[31150], X[4885] - 10 X[31209], 7 X[4885] - 10 X[31250], X[4885] - 4 X[31287], 3 X[4893] + X[31148], X[4940] - 4 X[25666], 2 X[14838] + X[20317], 11 X[17494] - 35 X[26777], 17 X[17494] + 7 X[26824], 13 X[17494] + 35 X[26985], X[17494] - 49 X[27115], 3 X[17494] - 7 X[31150], X[17494] + 35 X[31209], X[17494] + 5 X[31250], X[17494] + 14 X[31287], 85 X[26777] + 11 X[26824], 13 X[26777] + 11 X[26985], 5 X[26777] - 77 X[27115], 15 X[26777] - 11 X[31150], X[26777] + 11 X[31209], 7 X[26777] + 11 X[31250], 5 X[26777] + 22 X[31287], 13 X[26824] - 85 X[26985], X[26824] + 119 X[27115], 3 X[26824] + 17 X[31150], X[26824] - 85 X[31209], 7 X[26824] - 85 X[31250], X[26824] - 34 X[31287], 5 X[26985] + 91 X[27115], 15 X[26985] + 13 X[31150], X[26985] - 13 X[31209], 7 X[26985] - 13 X[31250], 5 X[26985] - 26 X[31287], 21 X[27115] - X[31150], 7 X[27115] + 5 X[31209], 49 X[27115] + 5 X[31250], 7 X[27115] + 2 X[31287], X[31150] + 15 X[31209], 7 X[31150] + 15 X[31250], X[31150] + 6 X[31287], 7 X[31207] - X[43067], 7 X[31209] - X[31250], 5 X[31209] - 2 X[31287], 5 X[31250] - 14 X[31287]

X(44567) lies on these lines: {2, 650}, {30, 8142}, {513, 4763}, {514, 14425}, {523, 44401}, {528, 10006}, {549, 8760}, {551, 14077}, {597, 9001}, {1635, 6008}, {1639, 28898}, {2516, 3835}, {3035, 40540}, {3742, 9443}, {3828, 29066}, {3829, 15283}, {4394, 4785}, {4421, 8641}, {4521, 17069}, {4755, 4777}, {4893, 31148}, {4944, 27486}, {4948, 7662}, {4995, 11934}, {6084, 44432}, {9015, 20582}, {10196, 30520}, {10199, 35100}, {14727, 30610}, {14838, 20317}, {28840, 31286}, {31207, 43067}

X(44567) = midpoint of X(i) and X(j) for these {i,j}: {2, 650}, {4944, 27486}, {4948, 7662}
X(44567) = reflection of X(i) in X(j) for these {i,j}: {2, 31287}, {4885, 2}
X(44567) = complement of X(45320)
X(44567) = crossdifference of every pair of points on line {2223, 5210}
X(44567) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 31209, 31287}, {650, 31250, 17494}, {650, 31287, 4885}, {4394, 25666, 4940}, {27115, 31209, 650}

X(44568) = CENTER OF ELLIPSE [SIE, NAPOLEON LINE]

Barycentrics    (b^2 - c^2)*(-2*a^4 - a^2*b^2 + 3*b^4 - a^2*c^2 - 8*b^2*c^2 + 3*c^4) : :
X(44568) = 5 X[2] - X[41298], 3 X[1637] - X[36900], 3 X[9134] - X[31176], 5 X[12077] + X[41298], 3 X[30474] - 5 X[31174]

X(44568) lies on these lines: {2, 12077}, {523, 44401}, {1637, 36900}, {2501, 23878}, {2799, 30474}, {9134, 31176}

X(44568) = midpoint of X(2) and X(12077)

X(44569) = CENTER OF ELLIPSE [SIE, HATZIPOLAKIS AXIS]

Barycentrics    2*a^6 + a^4*b^2 - 8*a^2*b^4 + 5*b^6 + a^4*c^2 + 12*a^2*b^2*c^2 - 5*b^4*c^2 - 8*a^2*c^4 - 5*b^2*c^4 + 5*c^6 : :
X(44569) = 5 X[2] - X[323], 7 X[2] + X[37779], 2 X[125] + X[32269], X[323] + 5 X[3580], 2 X[323] - 5 X[11064], 7 X[323] + 5 X[37779], 3 X[323] - 5 X[40112], 3 X[403] - X[10706], X[3292] - 4 X[37911], X[3448] + 2 X[15448], X[3448] + 3 X[37907], 2 X[3580] + X[11064], 7 X[3580] - X[37779], 3 X[3580] + X[40112], 2 X[5159] + X[41586], 7 X[11064] + 2 X[37779], 3 X[11064] - 2 X[40112], X[11160] + 3 X[37784], X[11799] - 3 X[15362], 3 X[15362] + X[20126], 2 X[15448] - 3 X[37907], X[16619] + 2 X[20379], 3 X[21356] + X[41617], 3 X[37779] + 7 X[40112]

X(44569) lies on these lines: {2, 6}, {23, 5621}, {30, 125}, {265, 44265}, {297, 671}, {373, 547}, {381, 20192}, {403, 10706}, {468, 542}, {511, 12099}, {525, 1637}, {541, 1514}, {549, 39242}, {858, 15360}, {1503, 7426}, {2482, 39021}, {3066, 3545}, {3292, 37911}, {3448, 15448}, {3543, 10606}, {3564, 5642}, {3830, 21970}, {3845, 34417}, {5094, 20423}, {5159, 13857}, {5943, 25565}, {6146, 34351}, {6791, 43291}, {7493, 43273}, {7542, 43573}, {7552, 26879}, {7565, 11745}, {8352, 41254}, {10264, 44266}, {10293, 11799}, {10989, 29181}, {11178, 35283}, {11179, 13394}, {11180, 35259}, {11284, 32599}, {11539, 22112}, {11579, 40114}, {11645, 32223}, {12310, 37955}, {13169, 32220}, {13754, 16227}, {14856, 16183}, {15471, 41720}, {16619, 20379}, {16657, 44218}, {18281, 41587}, {18390, 44285}, {21243, 25561}, {23294, 34613}, {23332, 31133}, {23410, 34826}, {35018, 44300}, {35303, 40710}, {35304, 40709}, {40920, 44456}

X(44569) = midpoint of X(i) and X(j) for these {i,j}: {2, 3580}, {125, 32225}, {265, 44265}, {858, 15360}, {7426, 9140}, {10264, 44266}, {11799, 20126}, {13169, 32220}, {13857, 41586}
X(44569) = reflection of X(i) in X(j) for these {i,j}: {11064, 2}, {13857, 5159}, {32269, 32225}, {35266, 468}, {37904, 32223}, {41720, 15471}
X(44569) = complement of X(40112)
X(44569) = isotomic conjugate of the polar conjugate of X(37984)
X(44569) = X(i)-complementary conjugate of X(j) for these (i,j): {9060, 4369}, {34802, 18589}
X(44569) = crosssum of X(32) and X(40114)
X(44569) = crossdifference of every pair of points on line {512, 26864}
X(44569) = barycentric product X(69)*X(37984)
X(44569) = barycentric quotient X(37984)/X(4)
X(44569) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15362, 20126, 11799}, {37638, 37643, 37648}

X(44570) = CENTER OF ELLIPSE [SIE, KOILLER LINE]

Barycentrics    5*a^3*b - 10*a^2*b^2 + 5*a*b^3 + 5*a^3*c - 2*a^2*b*c - 5*a*b^2*c + 2*b^3*c - 10*a^2*c^2 - 5*a*b*c^2 - 4*b^2*c^2 + 5*a*c^3 + 2*b*c^3 : :
X(44570) = 5 X[2] - X[85], 7 X[2] + X[3177], 17 X[2] - X[20089], 3 X[2] + X[31169], X[2] - 5 X[31269], X[85] + 5 X[1212], 7 X[85] + 5 X[3177], 2 X[85] - 5 X[6706], 17 X[85] - 5 X[20089], 3 X[85] + 5 X[31169], X[85] - 25 X[31269], 7 X[1212] - X[3177], 2 X[1212] + X[6706], 17 X[1212] + X[20089], 3 X[1212] - X[31169], X[1212] + 5 X[31269], 2 X[3177] + 7 X[6706], 17 X[3177] + 7 X[20089], 3 X[3177] - 7 X[31169], X[3177] + 35 X[31269], 17 X[6706] - 2 X[20089], 3 X[6706] + 2 X[31169], X[6706] - 10 X[31269], 3 X[20089] + 17 X[31169], X[20089] - 85 X[31269], X[31169] + 15 X[31269]

X(44570) lies on these lines: {2, 85}, {518, 551}, {527, 10012}, {3739, 24036}, {3828, 28850}, {6666, 17044}, {16814, 24203}, {34625, 41313}

X(44570) = midpoint of X(2) and X(1212)
X(44570) = reflection of X(6706) in X(2)

X(44571) = PERSPECTOR OF ELLIPSE [SIE, KOILLER LINE]

Barycentrics    (2*a^4 + 5*a^2*b^2 + 2*b^4 + a^2*c^2 + b^2*c^2 + c^4)*(2*a^4 + a^2*b^2 + b^4 + 5*a^2*c^2 + b^2*c^2 + 2*c^4) : :

X(44571) lies on these lines: {597, 754}, {3329, 31124}, {7792, 26235}

X(44571) = trilinear pole of line {12073, 14420}

X(44572) = PERSPECTOR OF ELLIPSE [SIE, GERGONNE LINE]

Barycentrics    (2*a^2 + 5*a*b + 2*b^2 + a*c + b*c + c^2)*(2*a^2 + a*b + b^2 + 5*a*c + b*c + 2*c^2) : :

X(44572) lies on these lines: {524, 551}, {4031, 7181}, {6629, 26860}, {14210, 17023}, {16826, 27081}

X(44572) = trilinear pole of line {4750, 28209}

X(44573) = X(3)X(74)∩X(20)X(1986)

Barycentrics    a^2*(a^12*(b^2+c^2)-4*a^10*(b^4-b^2*c^2+c^4)-(b^2-c^2)^4*(b^6+4*b^4*c^2+4*b^2*c^4+c^6)+a^8*(5*b^6-8*b^4*c^2-8*b^2*c^4+5*c^6)-2*a^6*(5*b^6*c^2-18*b^4*c^4+5*b^2*c^6)+2*a^2*(b^2-c^2)^2*(2*b^8-b^6*c^2-8*b^4*c^4-b^2*c^6+2*c^8)-a^4*(5*b^10-23*b^8*c^2+22*b^6*c^4+22*b^4*c^6-23*b^2*c^8+5*c^10)) : :
Barycentrics    c^2*SA*(108 R^4 - 12 R^2 SA + SB SC + (-34 R^2 + 3 SA) SW + 2 SW^2) : :
X(44573) = 3*X(3)-X(7723),3*X(3)-2*X(13416),5*X(3)-X(22584),3*X(74)+X(15102),X(110)+3*X(15072),3*X(376)+X(7722),X(382)-3*X(16222),2*X(550)+X(13148),3*X(974)-2*X(11806),5*X(3522)-X(12219),3*X(5642)+X(17856),X(6241)+3*X(15035),2*X(6723)-3*X(16836),2*X(7723)-3*X(12358),5*X(7723)-3*X(22584),3*X(9730)-2*X(11746),3*X(9730)-X(12295),2*X(10113)-3*X(12099),5*X(10574)-X(10733),X(10721)-3*X(12824),X(11381)-3*X(36518),3*X(11459)-7*X(15036),X(11562)+3*X(14855),X(11806)-3*X(40647),3*X(12041)-X(15101),X(12111)-5*X(15051),X(12162)-3*X(38793),X(12270)+3*X(15055),3*X(12358)-4*X(13416),5*X(12358)-2*X(22584),X(12825)-3*X(15035),X(13202)-3*X(16223),10*X(13416)-3*X(22584),2*X(14641)+X(16105),3*X(14855)-X(16111),5*X(15021)-X(15100),5*X(15059)-9*X(20791),3*X(15072)-X(17854),3*X(17853)+X(24981),X(18439)-5*X(38794),X(21650)-3*X(38727),X(34783)+3*X(38723)

See Antreas Hatzipolakis and Ercole Suppa, euclid 2147.

X(44573) lies on these lines: {2,12292}, {3,74}, {4,9826}, {5,12133}, {20,1986}, {30,1112}, {113,2883}, {125,15760}, {143,18565}, {146,6643}, {185,16163}, {265,15740}, {376,7722}, {382,16222}, {542,17855}, {550,13148}, {974,6146}, {1038,7727}, {1040,19470}, {1060,3024}, {1062,3028}, {1181,5504}, {1204,22109}, {1514,10297}, {1539,18404}, {2072,32111}, {2777,12605}, {2781,9967}, {2854,37511}, {3522,12219}, {3548,5656}, {3549,15061}, {5642,17856}, {5972,6000}, {6639,34128}, {6699,7542}, {6723,16836}, {6759,20771}, {6776,12121}, {6823,10264}, {7553,15473}, {7687,9729}, {7728,13203}, {9730,11746}, {10024,20304}, {10111,18914}, {10113,12099}, {10254,15088}, {10255,32137}, {10272,16196}, {10574,10733}, {10628,12363}, {10721,12824}, {10984,32607}, {10996,12317}, {11381,36518}, {11413,15463}, {11513,35826}, {11514,35827}, {11557,14641}, {11561,18563}, {11598,34116}, {11709,24301}, {12022,12236}, {12084,12228}, {12085,15472}, {12140,31833}, {12162,23328}, {12227,13346}, {12302,13198}, {12893,16165}, {13202,16223}, {13445,27866}, {13623,18125}, {13754,38726}, {15059,20791}, {15151,16003}, {15462,19149}, {17853,24981}, {18439,38794}, {18947,35513}, {19126,32305}, {19504,21312}, {20417,34002}, {20773,37814}, {21650,38727}, {27082,34783}, {31829,32423}

X(44573) = midpoint of X(i) and X(j) for these {i,j}: {20,1986}, {110,17854}, {113,10575}, {185,16163}, {1511,13491}, {6241,12825}, {11557,14641}, {11562,16111}
X(44573) = reflection of X(i) in X(j) for these (i,j): (4,9826), (265,16270), (974,40647), (1112,14708), (7553,15473), (7687,9729), (7723,13416), (10111,18914), (12133,5), (12140,31833), (12236,13630), (12295,11746), (12358,3), (15738,6699), (16003,15151), (16105,11557)
X(44573) = circumperp conjugate of X(12412)
X(44573) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,7723,13416), (110,15072,17854), (6241,15035,12825), (7723,13416,12358), (9730,12295,11746), (11456,15072,13491), (11562,14855,16111)

X(44574) = X(2)X(10354)∩X(111)X(7610)

Barycentrics    4*a^12 - 17*a^10*b^2 - 16*a^8*b^4 + 24*a^6*b^6 + 10*a^4*b^8 - 7*a^2*b^10 + 2*b^12 - 17*a^10*c^2 + 106*a^8*b^2*c^2 - 15*a^6*b^4*c^2 - 86*a^4*b^6*c^2 + 40*a^2*b^8*c^2 - 12*b^10*c^2 - 16*a^8*c^4 - 15*a^6*b^2*c^4 + 42*a^4*b^4*c^4 - 25*a^2*b^6*c^4 + 6*b^8*c^4 + 24*a^6*c^6 - 86*a^4*b^2*c^6 - 25*a^2*b^4*c^6 + 40*b^6*c^6 + 10*a^4*c^8 + 40*a^2*b^2*c^8 + 6*b^4*c^8 - 7*a^2*c^10 - 12*b^2*c^10 + 2*c^12 : :
X(44574) = X[111] - 3 X[9829], 3 X[6031] + X[14360], 2 X[6719] - 3 X[10163], X[34792] - 3 X[38716]

See Antreas Hatzipolakis and Peter Moses, euclid 2152.

X(44574) lies on these lines: {2, 10354}, {111, 7610}, {126, 3849}, {376, 6031}, {1296, 12505}, {2854, 32311}, {5512, 31606}, {6719, 10163}, {7664, 9123}, {10355, 40727}, {12506, 40556}, {23699, 31729}, {31744, 33962}, {34792, 38716}

X(44574) = midpoint of X(1296) and X(12505)
X(44574) = reflection of X(i) in X(j) for these {i,j}: {5512, 31606}, {12506, 40556}

leftri

E-inverses of points on the Euler line, where E is a permutation ellipse: X(44575)-X(44580) and X(44549)-X(44653)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, September 1, 2021.

Three specific permutation ellipses are described in the preamble just before X(41133), as follows:

(1) The trisector ellipse passes through the points 0:1:2, 0:2:1, 1:0:2, 2:0:1, 1:2:0, 2:1:0. These six points trisect the sides of ABC. The ellipse is given by 2(x^2 + y^2 + z^2) - 5(y z + z x + x y) = 0.

(2) The unique self-dual permutation ellipse is given by x^2 + y^2 + z^2 - 4 (y z + z x + x y) = 0.

(3) The Steiner midway ellipse (SME), is, loosely speaking, the ellipse midway between the Steiner inellipse (SIE) and the Steiner circumellipse (SCE). That is, for each P on SCE, let P' be the intersection of the ray GP with SIE, and let P'' be the midpoint of PP'. Then SME is the set of all such midpoints. SME is given by 7(x^2 + y^2 + z^2) - 34(y z + z x + x y) = 0.

In general, the inverse of a point P = p : q : r in an ellipse j (x^2 + y^2 + z^2) - k (y z + z x + x y) = 0 is the point k*p^2 - j*p*q + j*q^2 - j*p*r - k*q*r + j*r^2 : : .

The center of every permutation ellipse E is X(2), so that the E-inverse of each point P on the Euler line is also on the Euler line. If P = X(2) + t*X(3) and E is give by h*(x^2 + y^2 + z^2) - k (y z + z x + x y) = 0, then

(E-inverse of P) = (4 (h - k) S^4 + 3 t ((2 h - k) S^4 - (2 h + k) SA SB SC SW)) X(2) - 4 (h - k) (1 + t) S^4 X(3).

The appearance of {i,j} in the following list means that X(j) = trisector-ellipse-inverse of X(i):

{3,44575}, {4,44576}, {5,44577}, {297,3545}, {376,44578}, {381,44579}, {401,5054}, {441,10304}, {448,15671}, {3524,40884}, {3839,44216}, {5055,40885}, {15699,40853}, {37907,40856}

The appearance of {i,j} in the following list means that X(j) = Steiner-midway-ellipse-inverse of X(i):

{297,3860}, {401,44580}, {441,15690}, {12101,44216}, {15685,44335}, {15759,40884}, {19710,44346}, {33699,44334}

The appearance of {i,j} in the following list means that X(j) = self-dual-ellipse-inverse of X(i):

{3,40884}, {4,44216}, {5,40885}, {20,44346}, {23, 44649}, {25, 44650}, {140, 44651}, {237, 44652}, {297,381}, {376,441}, {401,549}, {402, 44653}, {448,15670}, {547,40853}, {2454,2479}, {2455,2480}, {3534,44578}, {3543,44334}, {3830,44576}, {3845,44579}, {5066,44577}, {6660,6661}, {7426,40856}, {7924,21536}, {8703,44575}, {10684,44215}, {15013,44210}, {15014,44212}, {15158,44348}, {15159,44349}, {15677,44336}, {15683,44335}, {19686,44347}, {37901,44338}, {44211,44328}, {44213,44329}

The appearance of {i,j} in the following list means that X(j) = Steiner-circumellipse-inverse of X(i):

{3,401}, {4,297}, {5,40853}, {20,441}, {21,448}, {22,15013}, {23,40856}, {24,44328}, {25,15014}, {26,44329}, {27,447}, {28,44330}, {29,44331}, {237,10684}, {376,40884}, {381,40885}, {384,6660}, {427,40889}, {449,452}, {458,35474}, {468,40890}, {472,11093}, {473,11094}, {858,35923}, {1113,44332}, {1114,44333}, {2479,2479}, {2480,2480}, {3146,44334}, {3534,44575}, {3543,44216}, {3830,44579}, {3845,44577}, {4235,7473}, {4618,11355}, {5059,44335}, {6655,21536}, {6658,44347}, {7500,44340}, {8613,15781}, {11001,44578}, {14953,37045}, {15680,44336}, {15682,44576}, {15683,44346}, {20062,44337}, {20063,44338}, {31292,44342}, {31293,44343}, {31294,44344}, {31304,44339}, {31305,44341}, {37174,44228}, {37188,44252}

The appearance of {i,j} in the following list means that X(j) = Steiner-incircle-ellipse-inverse of X(i):

{3,441}, {4,44334}, {5,297}, {20,44335}, {21,44336}, {22,44337}, {23,44338}, {24,44339}, {25,44340}, {26,44341}, {27,44342}, {28,44343}, {29,44344}, {140,401}, {237,44345}, {376,44346}, {381,44216}, {384,44347}, {447,6678}, {448,6675}, {449,11108}, {468,40856}, {547,40885}, {549,40884}, {1113,44348}, {1114,44349}, {1375,37045}, {2454,2454}, {2455,2455}, {3628,40853}, {3845,44576}, {5066,44579}, {5159,35923}, {6656,21536}, {6660,7819}, {6676,15013}, {6677,15014}, {8703,44578}, {10020,44329}, {10109,44577}, {12100,44575}, {16238,44328}, {37911,40890}

X(44575) = TRISECTOR-ELLIPSE-INVERSE OF X(3)

Barycentrics    5*a^8 - 8*a^6*b^2 + 3*a^4*b^4 - 2*a^2*b^6 + 2*b^8 - 8*a^6*c^2 + 5*a^4*b^2*c^2 + 2*a^2*b^4*c^2 + b^6*c^2 + 3*a^4*c^4 + 2*a^2*b^2*c^4 - 6*b^4*c^4 - 2*a^2*c^6 + b^2*c^6 + 2*c^8 : :

X(44575) lies on these lines: {2, 3}, {385, 23967}, {1494, 3284}, {2966, 7840}, {5641, 7925}, {9410, 44436}, {14919, 31621}, {22110, 39359}

X(44576) = TRISECTOR-ELLIPSE-INVERSE OF X(4)

Barycentrics    4*a^8 - a^6*b^2 - 3*a^4*b^4 - 7*a^2*b^6 + 7*b^8 - a^6*c^2 + 4*a^4*b^2*c^2 + 7*a^2*b^4*c^2 - 10*b^6*c^2 - 3*a^4*c^4 + 7*a^2*b^2*c^4 + 6*b^4*c^4 - 7*a^2*c^6 - 10*b^2*c^6 + 7*c^8 : :

X(44576) lies on these lines: {2, 3}, {230, 5641}, {393, 36889}, {1494, 1990}, {2966, 44401}, {3284, 40477}, {7809, 11064}, {7884, 37648}, {14568, 44569}, {16080, 31621}, {22329, 35088}, {39358, 40996}

X(44577) = TRISECTOR-ELLIPSE-INVERSE OF X(5)

Barycentrics    a^8 - 7*a^6*b^2 + 6*a^4*b^4 + 5*a^2*b^6 - 5*b^8 - 7*a^6*c^2 + a^4*b^2*c^2 - 5*a^2*b^4*c^2 + 11*b^6*c^2 + 6*a^4*c^4 - 5*a^2*b^2*c^4 - 12*b^4*c^4 + 5*a^2*c^6 + 11*b^2*c^6 - 5*c^8 : :

X(44577) lies on these lines: {2, 3}, {340, 18487}, {5641, 7779}, {9410, 14918}, {36435, 37766}, {36889, 40896}, {39359, 44367}

X(44578) = TRISECTOR-ELLIPSE-INVERSE OF X(376)

Barycentrics    8*a^8 - 11*a^6*b^2 + 3*a^4*b^4 - 5*a^2*b^6 + 5*b^8 - 11*a^6*c^2 + 8*a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 2*b^6*c^2 + 3*a^4*c^4 + 5*a^2*b^2*c^4 - 6*b^4*c^4 - 5*a^2*c^6 - 2*b^2*c^6 + 5*c^8 : :

X(44578) lies on these lines: {2, 3}, {69, 36427}, {325, 23967}, {2966, 22110}, {5641, 44377}, {7799, 11064}, {9308, 36889}, {18487, 40477}

X(44579) = TRISECTOR-ELLIPSE-INVERSE OF X(381)

Barycentrics    a^8 + 2*a^6*b^2 - 3*a^4*b^4 - 4*a^2*b^6 + 4*b^8 + 2*a^6*c^2 + a^4*b^2*c^2 + 4*a^2*b^4*c^2 - 7*b^6*c^2 - 3*a^4*c^4 + 4*a^2*b^2*c^4 + 6*b^4*c^4 - 4*a^2*c^6 - 7*b^2*c^6 + 4*c^8 : :

X(44579) lies on these lines: {2, 3}, {264, 36430}, {340, 3163}, {385, 5641}, {1494, 18487}, {1990, 39358}, {3580, 19570}, {7840, 35088}, {9410, 16080}, {11078, 41995}, {11092, 41996}, {14920, 36435}, {22329, 39359}, {39563, 41254}, {40506, 43768}

X(44580) = STEINER-MIDWAY-ELLIPSE-INVERSE OF X(401)

Barycentrics    34*a^4 - 41*a^2*b^2 + 7*b^4 - 41*a^2*c^2 - 14*b^2*c^2 + 7*c^4 : :
X(44580) = 7*X[2] + 9*X[3]

X(44580) lies on these lines: {2, 3}, {15, 42419}, {16, 42420}, {298, 33609}, {299, 33608}, {511, 41153}, {517, 41150}, {590, 42524}, {615, 42525}, {2782, 41151}, {3564, 41152}, {4745, 13624}, {4995, 37602}, {5351, 43107}, {5352, 43100}, {9541, 42640}, {10645, 43108}, {10646, 43109}, {11542, 42792}, {11543, 42791}, {11694, 38727}, {14711, 32516}, {15520, 21167}, {18487, 36422}, {23698, 41148}, {32787, 41962}, {32788, 41961}, {33614, 33618}, {33615, 33619}, {34380, 41149}, {41100, 42496}, {41101, 42497}, {41112, 42627}, {41113, 42628}, {41121, 42123}, {41122, 42122}, {41977, 42504}, {41978, 42505}, {42085, 43247}, {42086, 43246}, {42090, 43644}, {42091, 43649}, {42121, 42511}, {42124, 42510}, {42415, 43001}, {42416, 43000}, {42506, 43775}, {42507, 43776}, {42532, 42945}, {42533, 42944}, {42631, 43416}, {42632, 43417}, {42888, 43101}, {42889, 43104}, {42952, 42955}, {42953, 42954}, {43002, 43404}, {43003, 43403}, {43016, 43310}, {43017, 43311}, {43542, 43640}, {43543, 43639}

X(44581) = X(2)X(32638)∩X(4)X(195)

Barycentrics    -2 a^22+17 a^20 b^2-64 a^18 b^4+141 a^16 b^6-204 a^14 b^8+210 a^12 b^10-168 a^10 b^12+114 a^8 b^14-66 a^6 b^16+29 a^4 b^18-8 a^2 b^20+b^22+17 a^20 c^2-102 a^18 b^2 c^2+252 a^16 b^4 c^2-323 a^14 b^6 c^2+207 a^12 b^8 c^2-3 a^10 b^10 c^2-143 a^8 b^12 c^2+183 a^6 b^14 c^2-132 a^4 b^16 c^2+53 a^2 b^18 c^2-9 b^20 c^2-64 a^18 c^4+252 a^16 b^2 c^4-368 a^14 b^4 c^4+234 a^12 b^6 c^4-60 a^10 b^8 c^4+59 a^8 b^10 c^4-172 a^6 b^12 c^4+228 a^4 b^14 c^4-144 a^2 b^16 c^4+35 b^18 c^4+141 a^16 c^6-323 a^14 b^2 c^6+234 a^12 b^4 c^6-60 a^10 b^6 c^6-3 a^8 b^8 c^6+64 a^6 b^10 c^6-182 a^4 b^12 c^6+204 a^2 b^14 c^6-75 b^16 c^6-204 a^14 c^8+207 a^12 b^2 c^8-60 a^10 b^4 c^8-3 a^8 b^6 c^8-18 a^6 b^8 c^8+57 a^4 b^10 c^8-168 a^2 b^12 c^8+90 b^14 c^8+210 a^12 c^10-3 a^10 b^2 c^10+59 a^8 b^4 c^10+64 a^6 b^6 c^10+57 a^4 b^8 c^10+126 a^2 b^10 c^10-42 b^12 c^10-168 a^10 c^12-143 a^8 b^2 c^12-172 a^6 b^4 c^12-182 a^4 b^6 c^12-168 a^2 b^8 c^12-42 b^10 c^12+114 a^8 c^14+183 a^6 b^2 c^14+228 a^4 b^4 c^14+204 a^2 b^6 c^14+90 b^8 c^14-66 a^6 c^16-132 a^4 b^2 c^16-144 a^2 b^4 c^16-75 b^6 c^16+29 a^4 c^18+53 a^2 b^2 c^18+35 b^4 c^18-8 a^2 c^20-9 b^2 c^20+c^22 : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 2168.

X(44581) lies on these lines: {2,32638}, {4,195}, {184,31675}, {578,12026}, {2937,6343}, {6243,13505}, {8494,13512}

leftri

Kenmotu-centers triangles: X(44582)-X(44648)

rightri

This preamble and centers X(44582)-X(44648) were contributed by César Eliud Lozada, September 1, 2021.

Let A', B', C' be the centers of the inner-Kenmotu squares, as showed in MathWorld's Kenmotu Point. Triangle A'B'C' is named here the 1st Kenmotu-centers triangle of ABC. As there exists an outer version of these squares with centers A", B", C", the triangle A"B"C" is refered here as the 2nd Kenmotu-centers triangle of ABC.

Barycentric coordinates of A' and A" are:

A' = a^2+2*S : b^2 : c^2

A" = a^2-2*S : b^2 : c^2

Both triangles are homothetic to ABC with homothetic center X(6). A'B'C' is the pedal triangle of X(371)-of-ABC with respect to the 1st Kenmotu-diagonals triangle and A"B"C" is the pedal triangle of X(372)-of-ABC with respect to the 2nd Kenmotu-diagonals triangle.

In the following list, (T, i, j) means that pairs of triangles (T, A'B'C'), (T, A"B"C") are perspective with perspectors X(i) and X(j), respectively:

(*ABC, 6, 6), (*ABC-X3 reflections, 1151, 1152), (*anti-Aquila, 7968, 7969), (*anti-Ara, 5412, 5413), (*anti-1st Auriga, 44582, 44583), (*anti-2nd Auriga, 44584, 44585), (*5th anti-Brocard, 44586, 44587), (*2nd anti-circumperp-tangential, 2067, 6502), (anti-Conway, 6, 6), (2nd anti-Conway, 6, 6), (*anti-Ehrmann-mid, 13665, 13785), (*anti-Euler, 1587, 1588), (2nd anti-extouch, 44588, 44589), (*anti-inner-Grebe, 6, 6), (*anti-outer-Grebe, 6, 6), (anti-Honsberger, 6, 6), (*anti-1st Kenmotu-free-vertices, 5062, 39), (*anti-2nd Kenmotu-free-vertices, 39, 5058), (*anti-Mandart-incircle, 44590, 44591), (anti-orthocentroidal, 44592, 44593), (*anti-3rd tri-squares-central, 44594, 44595), (*anti-4th tri-squares-central, 44596, 44597), (*anti-X3-ABC reflections, 372, 371), (*anti-inner-Yff, 19050, 19049), (*anti-outer-Yff, 19048, 19047), (*anticomplementary, 3068, 3069), (*Aquila, 18991, 18992), (*Ara, 44598, 44599), (*1st Auriga, 44600, 44601), (*2nd Auriga, 44602, 44603), (2nd Brocard, 6, 6), (*5th Brocard, 44604, 44605), (*2nd circumperp tangential, 44606, 44607), (circumsymmedial, 6, 6), (*Ehrmann-mid, 6564, 6565), (2nd Ehrmann, 6, 6), (*Euler, 3071, 3070), (1st excosine, 44608, 44609), (9th Fermat-Dao, 6, 6), (10th Fermat-Dao, 6, 6), (13th Fermat-Dao, 6, 6), (14th Fermat-Dao, 6, 6), (*outer-Garcia, 13911, 13973), (*Gemini 107, 13846, 13847), (*Gemini 109, 8253, 8252), (*Gemini 110, 615, 590), (*Gemini 111, 7585, 7586), (*Gossard, 44610, 44611), (*inner-Grebe, 6, 6), (*outer-Grebe, 6, 6), (Hatzipolakis-Moses, 44612, 44613), (3rd Hatzipolakis, 44614, 44615), (2nd Hyacinth, 44616, 44617), (*infinite-altitude, 3070, 3071), (*Johnson, 485, 486), (*inner-Johnson, 44618, 44619), (*outer-Johnson, 44620, 44621), (*1st Johnson-Yff, 31472, 44622), (*2nd Johnson-Yff, 44623, 44624), (*1st Kenmotu-centers, --, 6), (*2nd Kenmotu-centers, 6, --), (1st Kenmotu diagonals, 6, 6), (2nd Kenmotu diagonals, 6, 6), (*1st Kenmotu-free-vertices, 371, 6420), (*2nd Kenmotu-free-vertices, 6419, 372), (Lucas antipodal tangential, 44625, npt), (Lucas(-1) antipodal tangential, npt, 44626), (*Lucas homothetic, 44627, 44628), (*Lucas(-1) homothetic, 44629, 44630), (Mandart-excircles, 44631, 44632), (*Mandart-incircle, 2066, 5414), (*medial, 590, 615), (midheight, 44633, 44634), (*5th mixtilinear, 44635, 44636), (orthic, 44637, 44638), (orthocentroidal, 44639, 44640), (2nd orthosymmedial, 6, 6), (reflection, 44641, 44642), (symmedial, 6, 6), (tangential, 6, 6), (inner tri-equilateral, 6, 6), (outer tri-equilateral, 6, 6), (*3rd tri-squares-central, 590, 32787), (*4th tri-squares-central, 32788, 615), (Walsmith, 6, 6), (*X3-ABC reflections, 3311, 3312), (*inner-Yff, 1335, 1124), (*outer-Yff, 1124, 1335), (*inner-Yff tangents, 44643, 44644), (*outer-Yff tangents, 44645, 44646)

where an asterisk * is used for homothetic triangles and "npt" stands for "not perspective triangles". Also, in the above list, infinite-altitude triangle is inversely homothetic to both Kenmotu-centers triangles and these are inversely similar to the orthocentroidal and anti-orthocentroidal triangles.

X(44582) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-1ST AURIGA AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*((-2*(a^3-(b+c)*a^2-a*(b^2+c^2)+(b^2-c^2)*(b-c))*S-(a+b-c)*(a-b+c)*(-a+b+c)*(a^2-b^2-4*b*c-c^2))*D+2*b*c*(2*a*(a^3-(b+c)*a^2-a*(b^2+c^2)+(b^2-c^2)*(b-c))*S+4*S^2*(2*a^2-3*a*(b+c)+(b-c)^2))) : : , where D=4*S*sqrt(R*(4*R+r))

X(44582) lies on these lines: {1, 44584}, {6, 5597}, {55, 44585}, {372, 26398}, {485, 26386}, {590, 26359}, {1151, 26290}, {1587, 26381}, {2066, 26351}, {2067, 26380}, {3068, 26394}, {3071, 26326}, {5412, 26371}, {7968, 26365}, {13665, 18496}, {13911, 26382}, {18991, 26296}, {19048, 26400}, {19050, 26399}, {26302, 44598}, {26310, 44604}, {26319, 44606}, {26379, 44586}, {26383, 44610}, {26387, 44623}, {26388, 31472}, {26389, 44620}, {26390, 44618}, {26393, 44590}, {26395, 44635}, {26396, 44594}, {26397, 44596}, {26401, 44645}, {26402, 44643}

X(44582) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5597, 44583), (5597, 26385, 6)

X(44583) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-1ST AURIGA AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*((2*(a^3-(b+c)*a^2-a*(b^2+c^2)+(b^2-c^2)*(b-c))*S-(a+b-c)*(a-b+c)*(-a+b+c)*(a^2-b^2-4*b*c-c^2))*D+2*b*c*(-2*a*(a^3-(b+c)*a^2-a*(b^2+c^2)+(b^2-c^2)*(b-c))*S+4*S^2*(2*a^2-3*a*(b+c)+(b-c)^2))) : : , where D=4*S*sqrt(R*(4*R+r))

X(44583) lies on these lines: {1, 44585}, {6, 5597}, {55, 44584}, {371, 26398}, {486, 26386}, {615, 26359}, {1152, 26290}, {1588, 26381}, {3069, 26394}, {3070, 26326}, {5413, 26371}, {5414, 26351}, {6502, 26380}, {7969, 26365}, {13785, 18496}, {13973, 26382}, {18992, 26296}, {19047, 26400}, {19049, 26399}, {26302, 44599}, {26310, 44605}, {26319, 44607}, {26379, 44587}, {26383, 44611}, {26387, 44624}, {26388, 44622}, {26389, 44621}, {26390, 44619}, {26393, 44591}, {26395, 44636}, {26396, 44595}, {26397, 44597}, {26401, 44646}, {26402, 44644}

X(44583) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5597, 44582), (5597, 26384, 6)

X(44584) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-2ND AURIGA AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*(-(-2*(a^3-(b+c)*a^2-a*(b^2+c^2)+(b^2-c^2)*(b-c))*S-(a+b-c)*(a-b+c)*(-a+b+c)*(a^2-b^2-4*b*c-c^2))*D+2*b*c*(2*a*(a^3-(b+c)*a^2-a*(b^2+c^2)+(b^2-c^2)*(b-c))*S+4*S^2*(2*a^2-3*a*(b+c)+(b-c)^2))) : : , where D=4*S*sqrt(R*(4*R+r))

X(44584) lies on these lines: {1, 44582}, {6, 5598}, {55, 44583}, {372, 26422}, {485, 26410}, {590, 26360}, {1151, 26291}, {1587, 26405}, {2066, 26352}, {2067, 26404}, {3068, 26418}, {3071, 26327}, {5412, 26372}, {7968, 26366}, {13665, 18498}, {13911, 26406}, {18991, 26297}, {19048, 26424}, {19050, 26423}, {26303, 44598}, {26311, 44604}, {26320, 44606}, {26403, 44586}, {26407, 44610}, {26411, 44623}, {26412, 31472}, {26413, 44620}, {26414, 44618}, {26417, 44590}, {26419, 44635}, {26420, 44594}, {26421, 44596}, {26425, 44645}, {26426, 44643}

X(44584) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5598, 44585), (5598, 26409, 6)

X(44585) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-2ND AURIGA AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(-(2*(a^3-(b+c)*a^2-a*(b^2+c^2)+(b^2-c^2)*(b-c))*S-(a+b-c)*(a-b+c)*(-a+b+c)*(a^2-b^2-4*b*c-c^2))*D+2*b*c*(-2*a*(a^3-(b+c)*a^2-a*(b^2+c^2)+(b^2-c^2)*(b-c))*S+4*S^2*(2*a^2-3*a*(b+c)+(b-c)^2))) : : , where D=4*S*sqrt(R*(4*R+r))

X(44585) lies on these lines: {1, 44583}, {6, 5598}, {55, 44582}, {371, 26422}, {486, 26410}, {615, 26360}, {1152, 26291}, {1588, 26405}, {3069, 26418}, {3070, 26327}, {5413, 26372}, {5414, 26352}, {6502, 26404}, {7969, 26366}, {13785, 18498}, {13973, 26406}, {18992, 26297}, {19047, 26424}, {19049, 26423}, {26303, 44599}, {26311, 44605}, {26320, 44607}, {26403, 44587}, {26407, 44611}, {26411, 44624}, {26412, 44622}, {26413, 44621}, {26414, 44619}, {26417, 44591}, {26419, 44636}, {26420, 44595}, {26421, 44597}, {26425, 44646}, {26426, 44644}

X(44585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5598, 44584), (5598, 26408, 6)

X(44586) = HOMOTHETIC CENTER OF THESE TRIANGLES: 5th ANTI-BROCARD AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*(a^6-(b^2+c^2)*a^4+(2*b^4+b^2*c^2+2*c^4)*a^2+(b^2+c^2)*b^2*c^2-2*S*(a^4-b^2*c^2)) : :

X(44586) lies on these lines: {3, 6}, {83, 590}, {98, 3071}, {485, 10796}, {486, 10104}, {615, 1078}, {1124, 10802}, {1335, 10801}, {1587, 10788}, {1971, 30427}, {2066, 10799}, {2067, 12835}, {3068, 7787}, {3069, 7793}, {3070, 12110}, {3224, 26461}, {3972, 19090}, {3981, 8576}, {5412, 11380}, {6179, 19089}, {6229, 13934}, {6561, 14880}, {6564, 18502}, {6813, 42535}, {7583, 32134}, {7780, 13983}, {7804, 8992}, {7808, 8253}, {7815, 8252}, {7968, 11364}, {7969, 12194}, {9540, 10359}, {10358, 42265}, {10789, 18991}, {10790, 44598}, {10791, 13911}, {10794, 44618}, {10795, 44620}, {10797, 31472}, {10798, 44623}, {10800, 44635}, {10803, 44643}, {10804, 44645}, {11294, 26430}, {11490, 44590}, {11837, 44600}, {11838, 44602}, {11839, 44610}, {11840, 44627}, {11841, 44629}, {12150, 32787}, {12203, 42258}, {13665, 18501}, {13938, 32788}, {19048, 26432}, {19050, 26431}, {22520, 44606}, {26379, 44582}, {26403, 44584}, {26429, 44594}

X(44586) = intersection, other than A,B,C, of conics {{A, B, C, X(83), X(5058)}} and {{A, B, C, X(98), X(43121)}}
X(44586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 32, 44587), (32, 5034, 43124), (32, 18994, 6), (371, 35766, 3398), (1207, 2965, 44587), (1342, 1343, 5058), (1687, 1688, 43121), (1691, 34870, 44587), (6421, 6424, 3311)

X(44587) = HOMOTHETIC CENTER OF THESE TRIANGLES: 5th ANTI-BROCARD AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(a^6-(b^2+c^2)*a^4+(2*b^4+b^2*c^2+2*c^4)*a^2+(b^2+c^2)*b^2*c^2+2*S*(a^4-b^2*c^2)) : :

X(44587) lies on these lines: {3, 6}, {83, 615}, {98, 3070}, {485, 10104}, {486, 10796}, {590, 1078}, {1124, 10801}, {1335, 10802}, {1588, 10788}, {1971, 30428}, {3068, 7793}, {3069, 7787}, {3071, 12110}, {3224, 26454}, {3972, 19089}, {3981, 8577}, {5413, 11380}, {5414, 10799}, {6179, 19090}, {6228, 13882}, {6502, 12835}, {6560, 14880}, {6565, 18502}, {6811, 42535}, {7584, 32134}, {7780, 8992}, {7804, 13983}, {7808, 8252}, {7815, 8253}, {7968, 12194}, {7969, 11364}, {10358, 42262}, {10359, 13935}, {10789, 18992}, {10790, 44599}, {10791, 13973}, {10794, 44619}, {10795, 44621}, {10797, 44622}, {10798, 44624}, {10800, 44636}, {10803, 44644}, {10804, 44646}, {11293, 26429}, {11490, 44591}, {11837, 44601}, {11838, 44603}, {11839, 44611}, {11840, 44628}, {11841, 44630}, {12150, 32788}, {12203, 42259}, {13785, 18501}, {13885, 32787}, {19047, 26432}, {19049, 26431}, {22520, 44607}, {26379, 44583}, {26403, 44585}, {26430, 44597}, {31463, 39387}

X(44587) = intersection, other than A,B,C, of conics {{A, B, C, X(83), X(5062)}} and {{A, B, C, X(98), X(43120)}}
X(44587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 32, 44586), (32, 5034, 43125), (32, 18993, 6), (83, 13938, 615), (372, 35767, 3398), (1207, 2965, 44586), (1342, 1343, 5062), (1687, 1688, 43120), (1691, 34870, 44586), (6422, 6423, 3312)

X(44588) = PERSPECTOR OF THESE TRIANGLES: 2ND ANTI-EXTOUCH AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*(-a^2+b^2+c^2)*(8*(a^4+(b^2-c^2+2)*(b^2-c^2-2)+4)*S*b^2*c^2-(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6-3*(b^2+c^2)*a^4+3*(b^2+c^2)^2*a^2-(b^4-c^4)*(b^2-c^2))) : :

X(44588) lies on these lines: {3, 26945}, {25, 44633}, {125, 8943}, {184, 8939}, {371, 1181}, {372, 19360}, {1583, 10962}, {1593, 3070}, {1599, 18924}, {1899, 44589}, {3311, 19362}, {3312, 19361}, {3964, 11091}, {5406, 11514}, {6398, 19348}, {8573, 18998}, {44598, 44637}

X(44589) = PERSPECTOR OF THESE TRIANGLES: 2ND ANTI-EXTOUCH AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(-a^2+b^2+c^2)*(8*(a^4+(b^2-c^2+2)*(b^2-c^2-2)+4)*S*b^2*c^2+(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6-3*(b^2+c^2)*a^4+3*(b^2+c^2)^2*a^2-(b^4-c^4)*(b^2-c^2))) : :

X(44589) lies on these lines: {3, 26873}, {25, 44634}, {125, 8939}, {184, 8943}, {371, 19360}, {372, 1181}, {1584, 10960}, {1593, 3071}, {1600, 18923}, {1899, 44588}, {3311, 19361}, {3312, 19362}, {3964, 11090}, {5407, 11513}, {6221, 19348}, {8573, 18997}, {44599, 44638}

X(44590) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*(a^5-(b+c)*a^4-2*(b^2-b*c+c^2)*a^3+2*(b+c)*(b^2+c^2)*a^2+(b^4+c^4+2*(b^2-b*c+c^2)*b*c)*a-(2*a^3-2*(b+c)*a^2+2*(b-c)^2*a-2*(b+c)*(b^2+c^2))*S-(b^2-c^2)^2*(b+c)) : :

X(44590) lies on these lines: {1, 8943}, {3, 7969}, {6, 31}, {21, 19065}, {35, 18991}, {56, 44635}, {100, 3068}, {197, 44598}, {371, 11248}, {372, 10267}, {404, 13902}, {405, 13973}, {485, 11499}, {590, 1376}, {615, 1001}, {1124, 11508}, {1151, 10310}, {1335, 11507}, {1486, 44599}, {1587, 11491}, {1621, 3069}, {1703, 10902}, {2067, 11509}, {2077, 9583}, {2178, 34121}, {2362, 37579}, {3070, 11500}, {3071, 11496}, {3295, 7968}, {3303, 19013}, {3311, 11849}, {3312, 37621}, {3746, 18992}, {3871, 19066}, {4413, 8253}, {4421, 32787}, {4423, 8252}, {4428, 13940}, {5217, 19014}, {5248, 13936}, {5259, 13947}, {5284, 32786}, {5412, 11383}, {5537, 9616}, {5687, 13911}, {6200, 35238}, {6221, 35000}, {6410, 8273}, {6419, 35773}, {6502, 11510}, {6564, 18491}, {7133, 8609}, {7583, 32141}, {8167, 32790}, {8715, 13883}, {8939, 8941}, {8983, 25440}, {10269, 35763}, {10534, 18621}, {10679, 35775}, {11249, 35641}, {11490, 44586}, {11492, 44600}, {11493, 44602}, {11494, 44604}, {11501, 31472}, {11502, 44623}, {11503, 44627}, {11504, 44629}, {11848, 44610}, {13665, 18524}, {13901, 19024}, {14882, 18996}, {19047, 35808}, {19049, 35809}, {26393, 44582}, {26417, 44584}, {26512, 44594}, {26513, 44596}, {35239, 35611}, {35642, 37622}, {35785, 35810}

X(44590) = crosspoint of X(1252) and X(6135)
X(44590) = crosssum of X(1086) and X(6364)
X(44590) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 7969, 44606), (6, 55, 44591), (42, 606, 6), (55, 19000, 6), (371, 35772, 11248), (902, 41421, 6), (1376, 13887, 590), (3303, 19013, 44636), (5414, 5415, 6)

X(44591) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(a^5-(b+c)*a^4-2*(b^2-b*c+c^2)*a^3+2*(b+c)*(b^2+c^2)*a^2+(b^4+c^4+2*(b^2-b*c+c^2)*b*c)*a+(2*a^3-2*(b+c)*a^2+2*(b-c)^2*a-2*(b+c)*(b^2+c^2))*S-(b^2-c^2)^2*(b+c)) : :

X(44591) lies on these lines: {1, 8939}, {3, 7968}, {6, 31}, {21, 19066}, {35, 18992}, {56, 44636}, {100, 3069}, {197, 44599}, {371, 10267}, {372, 11248}, {404, 13959}, {405, 13911}, {486, 11499}, {590, 1001}, {615, 1376}, {1124, 11507}, {1152, 10310}, {1335, 11508}, {1486, 44598}, {1588, 11491}, {1621, 3068}, {1702, 10902}, {2067, 11510}, {2178, 34125}, {3070, 11496}, {3071, 11500}, {3295, 7969}, {3303, 19014}, {3311, 37621}, {3312, 11849}, {3746, 18991}, {3871, 19065}, {4413, 8252}, {4421, 32788}, {4423, 8253}, {4428, 13887}, {5217, 19013}, {5248, 13883}, {5259, 13893}, {5284, 32785}, {5413, 11383}, {5687, 13973}, {6396, 35238}, {6398, 35000}, {6409, 8273}, {6420, 35772}, {6502, 11509}, {6565, 18491}, {7584, 32141}, {8167, 32789}, {8609, 42013}, {8715, 13936}, {8943, 8945}, {9583, 34486}, {9616, 15931}, {10269, 35762}, {10533, 18621}, {10679, 35774}, {11249, 35642}, {11490, 44587}, {11492, 44601}, {11493, 44603}, {11494, 44605}, {11501, 44622}, {11502, 44624}, {11503, 44628}, {11504, 44630}, {11848, 44611}, {13785, 18524}, {13958, 19023}, {13971, 25440}, {14882, 18995}, {16232, 37579}, {19048, 35809}, {19050, 35808}, {26393, 44583}, {26417, 44585}, {26512, 44595}, {26513, 44597}, {35239, 35610}, {35641, 37622}, {35784, 35811}

X(44591) = crosspoint of X(1252) and X(6136)
X(44591) = crosssum of X(1086) and X(6365)
X(44591) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 7968, 44607), (6, 55, 44590), (42, 605, 6), (55, 18999, 6), (372, 35773, 11248), (1376, 13940, 615), (2066, 5416, 6), (3303, 19014, 44635)

X(44592) = PERSPECTOR OF THESE TRIANGLES: ANTI-ORTHOCENTROIDAL AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*(-18*(b^2-c^2)^2*b^2*c^2*(-a^2+b^2+c^2)*S-a^12+3*(b^2+c^2)*a^10-18*b^2*c^2*a^8-(b^2+c^2)*(10*b^4-31*b^2*c^2+10*c^4)*a^6+3*(5*b^8+5*c^8-(b^4+11*b^2*c^2+c^4)*b^2*c^2)*a^4-9*(b^6-c^6)*(b^4-c^4)*a^2+(b^2-c^2)^4*(b^2+2*c^2)*(2*b^2+c^2)) : :

X(44592) lies on these lines: {74, 3070}, {125, 44593}, {371, 399}, {34417, 44639}

X(44593) = PERSPECTOR OF THESE TRIANGLES: ANTI-ORTHOCENTROIDAL AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(-18*(b^2-c^2)^2*b^2*c^2*(-a^2+b^2+c^2)*S+a^12-3*(b^2+c^2)*a^10+18*b^2*c^2*a^8+(b^2+c^2)*(10*b^4-31*b^2*c^2+10*c^4)*a^6-3*(5*b^8+5*c^8-(b^4+11*b^2*c^2+c^4)*b^2*c^2)*a^4+9*(b^6-c^6)*(b^4-c^4)*a^2-(b^2-c^2)^4*(b^2+2*c^2)*(2*b^2+c^2)) : :

X(44593) lies on these lines: {74, 3071}, {125, 44592}, {372, 399}, {34417, 44640}

X(44594) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-3RD TRI-SQUARES-CENTRAL AND 1ST KENMOTU-CENTERS

Barycentrics    a^4+12*S*a^2+4*(b^2+c^2)*a^2-(b^2-c^2)^2 : :

X(44594) lies on these lines: {2, 6}, {20, 12962}, {39, 19064}, {371, 12124}, {372, 26516}, {393, 19042}, {485, 26468}, {1151, 26294}, {1285, 8375}, {1504, 1587}, {1588, 5475}, {2066, 26355}, {2067, 26435}, {3071, 26330}, {3087, 8035}, {3311, 18907}, {3524, 8376}, {5062, 9540}, {5412, 26375}, {5477, 19056}, {6419, 39660}, {6420, 31400}, {6422, 7581}, {6428, 31406}, {6564, 13651}, {6781, 9541}, {7968, 26369}, {8960, 19102}, {12963, 42522}, {12969, 31465}, {13665, 18539}, {13911, 26444}, {18991, 26300}, {19048, 26518}, {19050, 26517}, {22726, 44500}, {24244, 26460}, {26306, 44598}, {26314, 44604}, {26324, 44606}, {26396, 44582}, {26420, 44584}, {26429, 44586}, {26449, 44610}, {26473, 44623}, {26479, 31472}, {26485, 44620}, {26490, 44618}, {26512, 44590}, {26514, 44635}, {26519, 44645}, {26520, 44643}, {31401, 31483}, {31414, 44518}, {35822, 43448}, {43257, 43618}

X(44594) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 230, 26456), (6, 3068, 44595), (6, 3815, 19053), (6, 7585, 44596), (6, 7736, 44597), (6, 31463, 7586), (6, 32787, 7735), (193, 7585, 3068), (230, 26456, 44595), (3068, 26361, 590), (3068, 26456, 230), (3068, 26462, 6), (8974, 13639, 44394), (31403, 44597, 7736)

X(44595) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-3RD TRI-SQUARES-CENTRAL AND 2ND KENMOTU-CENTERS

Barycentrics    3*a^4+4*S*a^2+(b^2-c^2)^2 : :

X(44595) lies on these lines: {2, 6}, {4, 6423}, {20, 12968}, {32, 1588}, {39, 13935}, {115, 23249}, {187, 9541}, {371, 19102}, {372, 5286}, {393, 5200}, {486, 26468}, {488, 33348}, {631, 6422}, {1152, 7738}, {1285, 23273}, {1384, 42215}, {1504, 9540}, {1505, 5319}, {1587, 3767}, {2165, 18819}, {2459, 35945}, {3053, 6459}, {3070, 26330}, {3087, 3127}, {3156, 8573}, {3312, 5305}, {3524, 9600}, {5023, 42638}, {5024, 35256}, {5218, 31459}, {5254, 6460}, {5280, 13963}, {5299, 13962}, {5411, 16318}, {5414, 26355}, {5420, 31400}, {6398, 15048}, {6424, 7582}, {6462, 32989}, {6502, 26435}, {6531, 24244}, {6560, 43448}, {6561, 41411}, {6564, 13834}, {6813, 39876}, {7584, 30435}, {7737, 23259}, {7745, 42561}, {7746, 31411}, {7747, 23263}, {7748, 43407}, {7969, 26369}, {8960, 19103}, {9575, 13971}, {9593, 13975}, {9605, 13966}, {10164, 31427}, {10577, 31404}, {10881, 41361}, {11293, 26429}, {11648, 43256}, {12969, 42523}, {13356, 13938}, {13357, 19089}, {13665, 43291}, {13711, 35822}, {13785, 18539}, {13881, 31412}, {13973, 26444}, {15484, 18762}, {18510, 21309}, {18992, 26300}, {19006, 34809}, {19047, 26518}, {19049, 26517}, {19105, 35770}, {26306, 44599}, {26314, 44605}, {26324, 44607}, {26396, 44583}, {26420, 44585}, {26449, 44611}, {26473, 44624}, {26479, 44622}, {26485, 44621}, {26490, 44619}, {26512, 44591}, {26514, 44636}, {26519, 44646}, {26520, 44644}, {30478, 31464}, {32497, 33364}

X(44595) = polar conjugate of the isotomic conjugate of X(12257)
X(44595) = barycentric product X(4)*X(12257)
X(44595) = trilinear product X(19)*X(12257)
X(44595) = intersection, other than A,B,C, of conics {{A, B, C, X(69), X(12257)}} and {{A, B, C, X(83), X(31403)}}
X(44595) = crosssum of X(6) and X(12305)
X(44595) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6, 31403), (2, 8975, 590), (6, 230, 3068), (6, 615, 7736), (6, 3068, 44594), (6, 7586, 44597), (6, 7735, 44596), (230, 26456, 44594), (3068, 3069, 492), (3068, 26456, 6), (3767, 5062, 1587), (5304, 7586, 6), (5413, 41515, 26375)

X(44596) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-4TH TRI-SQUARES-CENTRAL AND 1ST KENMOTU-CENTERS

Barycentrics    3*a^4-4*S*a^2+(b^2-c^2)^2 : :

X(44596) lies on these lines: {2, 6}, {4, 6424}, {20, 12963}, {32, 1587}, {39, 9540}, {115, 23259}, {172, 31408}, {371, 5286}, {372, 19105}, {393, 5412}, {485, 26469}, {487, 33349}, {631, 6421}, {1151, 7738}, {1285, 23267}, {1384, 42216}, {1504, 5319}, {1505, 13935}, {1588, 3767}, {2066, 26356}, {2067, 26436}, {2165, 18820}, {2460, 35944}, {2549, 9541}, {3053, 6460}, {3071, 26331}, {3087, 3128}, {3155, 8573}, {3311, 5305}, {4386, 31413}, {5007, 31411}, {5023, 42637}, {5024, 35255}, {5254, 6459}, {5280, 13905}, {5299, 13904}, {5410, 16318}, {5418, 31400}, {6221, 15048}, {6423, 7581}, {6463, 32989}, {6531, 24243}, {6560, 41410}, {6561, 43448}, {6565, 13711}, {6811, 39875}, {7583, 30435}, {7737, 23249}, {7745, 31412}, {7747, 23253}, {7748, 43408}, {7968, 26370}, {8981, 9605}, {8983, 9575}, {9593, 13912}, {9600, 43509}, {9646, 31402}, {10576, 31404}, {10880, 41361}, {11294, 26430}, {11648, 43257}, {12962, 42522}, {13356, 13885}, {13357, 19090}, {13665, 18907}, {13785, 43291}, {13834, 35823}, {13881, 42561}, {13911, 26445}, {15484, 18538}, {18512, 21309}, {18991, 26301}, {19005, 34809}, {19048, 26523}, {19050, 26522}, {19102, 35771}, {26307, 44598}, {26315, 44604}, {26325, 44606}, {26397, 44582}, {26421, 44584}, {26450, 44610}, {26474, 44623}, {26480, 31472}, {26486, 44620}, {26491, 44618}, {26513, 44590}, {26515, 44635}, {26524, 44645}, {26525, 44643}, {32494, 33365}

X(44596) = polar conjugate of the isotomic conjugate of X(12256)
X(44596) = barycentric product X(4)*X(12256)
X(44596) = trilinear product X(19)*X(12256)
X(44596) = intersection, other than A,B,C, of conics {{A, B, C, X(69), X(12256)}} and {{A, B, C, X(325), X(24243)}}
X(44596) = crosssum of X(6) and X(12306)
X(44596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 13949, 615), (6, 230, 3069), (6, 590, 7736), (6, 3068, 31403), (6, 3069, 44597), (6, 7585, 44594), (6, 7735, 44595), (6, 31463, 37665), (230, 26463, 44597), (2549, 9675, 9541), (3068, 3069, 491), (3069, 26463, 6), (3767, 5058, 1588), (5304, 7585, 6), (5412, 41516, 26376), (8972, 37665, 31463)

X(44597) = HOMOTHETIC CENTER OF THESE TRIANGLES: ANTI-4TH TRI-SQUARES-CENTRAL AND 2ND KENMOTU-CENTERS

Barycentrics    a^4-12*S*a^2+4*(b^2+c^2)*a^2-(b^2-c^2)^2 : :

X(44597) lies on these lines: {2, 6}, {20, 12969}, {39, 19063}, {371, 26521}, {372, 12123}, {393, 19041}, {486, 26469}, {1152, 26295}, {1285, 8376}, {1505, 1588}, {1587, 5475}, {3070, 26331}, {3087, 8036}, {3312, 18907}, {3524, 8375}, {5058, 13935}, {5413, 26376}, {5414, 26356}, {5477, 19055}, {6419, 31400}, {6420, 39661}, {6421, 7582}, {6427, 31406}, {6502, 26436}, {6565, 13770}, {7969, 26370}, {12968, 42523}, {13785, 26438}, {13973, 26445}, {18992, 26301}, {19047, 26523}, {19049, 26522}, {22727, 44500}, {24243, 26455}, {26307, 44599}, {26315, 44605}, {26325, 44607}, {26397, 44583}, {26421, 44585}, {26430, 44587}, {26450, 44611}, {26474, 44624}, {26480, 44622}, {26486, 44621}, {26491, 44619}, {26513, 44591}, {26515, 44636}, {26524, 44646}, {26525, 44644}, {35823, 43448}, {43256, 43618}

X(44597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 230, 26463), (6, 3069, 44596), (6, 3815, 19054), (6, 7586, 44595), (6, 7736, 44594), (6, 32788, 7735), (193, 7586, 3069), (230, 26463, 44596), (3069, 26362, 615), (3069, 26457, 6), (3069, 26463, 230), (7736, 44594, 31403), (13759, 13950, 44392)

X(44598) = HOMOTHETIC CENTER OF THESE TRIANGLES: ARA AND 1ST KENMOTU-CENTERS

Barycentrics    (2*a^2*b^2*c^2+(a^2+b^2-c^2)*(a^2-b^2+c^2)*S)*a^2 : :

X(44598) lies on these lines: {3, 485}, {6, 25}, {22, 3068}, {23, 7585}, {24, 1587}, {26, 7583}, {32, 8996}, {186, 23267}, {197, 44590}, {371, 7387}, {372, 6642}, {378, 23249}, {486, 7529}, {571, 26953}, {615, 5020}, {1124, 10046}, {1131, 14118}, {1151, 11414}, {1181, 12239}, {1335, 10037}, {1486, 44591}, {1588, 10594}, {1593, 23251}, {1597, 42284}, {1598, 3071}, {1600, 32806}, {1609, 3155}, {1995, 3069}, {2066, 10833}, {2067, 18954}, {2070, 18512}, {3103, 10960}, {3156, 31463}, {3311, 7517}, {3312, 7506}, {3518, 7581}, {3520, 23269}, {5062, 44527}, {5198, 23261}, {5899, 6199}, {6200, 35243}, {6221, 12083}, {6409, 37198}, {6417, 18378}, {6418, 13621}, {6419, 35777}, {6460, 17928}, {6561, 18534}, {6564, 9818}, {6636, 8972}, {6644, 42216}, {7393, 10576}, {7395, 42265}, {7484, 8253}, {7485, 32785}, {7503, 31412}, {7512, 13886}, {7514, 18538}, {7525, 13925}, {7530, 42215}, {7545, 18510}, {7582, 34484}, {7584, 13861}, {7586, 13595}, {7968, 11365}, {7969, 9798}, {8185, 18991}, {8190, 44600}, {8191, 44602}, {8192, 44635}, {8193, 13911}, {8194, 44627}, {8195, 44629}, {8252, 11284}, {8414, 19410}, {8573, 44193}, {8577, 26920}, {8854, 11513}, {8943, 44634}, {9540, 10323}, {9541, 12082}, {9658, 18996}, {9673, 19038}, {9694, 33524}, {9909, 32787}, {9937, 10665}, {10790, 44586}, {10828, 44604}, {10829, 44618}, {10830, 44620}, {10831, 31472}, {10832, 44623}, {10834, 44643}, {10835, 44645}, {11417, 26283}, {11427, 15187}, {11433, 15188}, {11479, 42273}, {11484, 42583}, {11853, 44610}, {12085, 35820}, {12087, 43512}, {13564, 13903}, {13567, 15200}, {13620, 43889}, {13884, 21213}, {13893, 37557}, {13943, 32788}, {14070, 35822}, {15199, 23292}, {15212, 26958}, {16064, 36549}, {16419, 32789}, {18535, 42283}, {18998, 19044}, {18999, 20988}, {19000, 20989}, {19048, 26309}, {19050, 26308}, {19117, 37440}, {21312, 42264}, {22654, 44606}, {23253, 35502}, {23275, 26863}, {26302, 44582}, {26303, 44584}, {26306, 44594}, {26307, 44596}, {31414, 38444}, {39568, 42258}, {42275, 44454}, {44588, 44637}

X(44598) = crosssum of X(371) and X(11514)
X(44598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 13889, 590), (6, 25, 44599), (25, 5595, 20987), (25, 19006, 6), (371, 35776, 7387), (3312, 7506, 8277), (6560, 9682, 3), (9694, 33524, 42638), (19459, 44524, 44599)

X(44599) = HOMOTHETIC CENTER OF THESE TRIANGLES: ARA AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(2*a^2*b^2*c^2-(a^2+b^2-c^2)*(a^2-b^2+c^2)*S) : :

X(44599) lies on these lines: {3, 486}, {6, 25}, {22, 3069}, {23, 7586}, {24, 1588}, {26, 7584}, {186, 23273}, {197, 44591}, {371, 6642}, {372, 7387}, {378, 23259}, {485, 7529}, {590, 5020}, {1124, 10037}, {1132, 14118}, {1152, 11414}, {1181, 12240}, {1335, 10046}, {1486, 44590}, {1505, 8996}, {1587, 10594}, {1593, 23261}, {1597, 42283}, {1598, 3070}, {1599, 32805}, {1609, 3156}, {1995, 3068}, {2070, 18510}, {3102, 10962}, {3311, 7506}, {3312, 7517}, {3518, 7582}, {3520, 23275}, {5058, 8908}, {5063, 26953}, {5198, 23251}, {5414, 10833}, {5892, 9687}, {5899, 6395}, {6396, 35243}, {6398, 12083}, {6410, 37198}, {6417, 13621}, {6418, 18378}, {6420, 35776}, {6459, 17928}, {6502, 18954}, {6560, 18534}, {6565, 9818}, {6636, 13941}, {6644, 42215}, {7393, 10577}, {7395, 42262}, {7484, 8252}, {7485, 32786}, {7503, 42561}, {7512, 13939}, {7514, 18762}, {7525, 13993}, {7530, 42216}, {7545, 18512}, {7581, 34484}, {7583, 13861}, {7585, 13595}, {7968, 9798}, {7969, 11365}, {8185, 18992}, {8190, 44601}, {8191, 44603}, {8192, 44636}, {8193, 13973}, {8194, 44628}, {8195, 44630}, {8253, 11284}, {8406, 19411}, {8573, 44192}, {8576, 8911}, {8855, 11514}, {8939, 44633}, {9658, 18995}, {9673, 19037}, {9909, 32788}, {9937, 10666}, {10323, 13935}, {10790, 44587}, {10828, 44605}, {10829, 44619}, {10830, 44621}, {10831, 44622}, {10832, 44624}, {10834, 44644}, {10835, 44646}, {11418, 26283}, {11427, 15188}, {11433, 15187}, {11479, 42270}, {11484, 42582}, {11853, 44611}, {12085, 35821}, {12087, 43511}, {13564, 13961}, {13567, 15199}, {13620, 43890}, {13889, 32787}, {13937, 21213}, {13947, 37557}, {14070, 35823}, {15200, 23292}, {15211, 26958}, {16064, 36550}, {16419, 32790}, {18535, 42284}, {18997, 19043}, {18999, 20989}, {19000, 20988}, {19047, 26309}, {19049, 26308}, {19116, 37440}, {21312, 42263}, {22654, 44607}, {23263, 35502}, {23269, 26863}, {26302, 44583}, {26303, 44585}, {26306, 44595}, {26307, 44597}, {33524, 42637}, {39568, 42259}, {42276, 44454}, {44589, 44638}

X(44599) = crosssum of X(372) and X(11513)
X(44599) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 13943, 615), (6, 25, 44598), (25, 5594, 20987), (25, 19005, 6), (372, 35777, 7387), (3311, 7506, 8276), (5420, 9683, 3), (19459, 44524, 44598)

X(44600) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1ST AURIGA AND 1ST KENMOTU-CENTERS

Barycentrics    a*(-2*(a^3-(b+c)^2*a+D)*S-a*D*(a+b+c)) : : , where D=4*S*sqrt(R*(4*R+r))

X(44600) lies on these lines: {1, 44603}, {6, 5597}, {55, 7969}, {371, 11252}, {485, 8200}, {590, 5599}, {1124, 11879}, {1151, 11822}, {1335, 11877}, {1587, 11843}, {2066, 11873}, {2067, 18955}, {3068, 5601}, {3070, 9834}, {3071, 8196}, {3311, 11875}, {5412, 11384}, {5598, 44635}, {6200, 35244}, {6419, 35781}, {6564, 18495}, {7583, 32146}, {7968, 11366}, {8186, 18991}, {8190, 44598}, {8197, 13911}, {8201, 44627}, {8202, 44629}, {11207, 32787}, {11253, 35641}, {11492, 44590}, {11493, 44606}, {11837, 44586}, {11861, 44604}, {11863, 44610}, {11865, 44618}, {11867, 44620}, {11869, 31472}, {11871, 44623}, {11881, 44643}, {11883, 44645}, {13944, 32788}, {19009, 44636}, {35245, 35611}, {35779, 35810}

X(44600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5597, 44601), (55, 7969, 44602), (371, 35778, 11252), (5597, 19008, 6), (5599, 13890, 590)

X(44601) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1ST AURIGA AND 2ND KENMOTU-CENTERS

Barycentrics    a*(2*(a^3-(b+c)^2*a+D)*S-a*D*(a+b+c)) : : , where D=4*S*sqrt(R*(4*R+r))

X(44601) lies on these lines: {1, 44602}, {6, 5597}, {55, 7968}, {372, 11252}, {486, 8200}, {615, 5599}, {1124, 11877}, {1152, 11822}, {1335, 11879}, {1588, 11843}, {3069, 5601}, {3070, 8196}, {3071, 9834}, {3312, 11875}, {5413, 11384}, {5414, 11873}, {5598, 44636}, {6396, 35244}, {6420, 35778}, {6502, 18955}, {6565, 18495}, {7584, 32146}, {7969, 11366}, {8186, 18992}, {8190, 44599}, {8197, 13973}, {8201, 44628}, {8202, 44630}, {11207, 32788}, {11253, 35642}, {11492, 44591}, {11493, 44607}, {11837, 44587}, {11861, 44605}, {11863, 44611}, {11865, 44619}, {11867, 44621}, {11869, 44622}, {11871, 44624}, {11881, 44644}, {11883, 44646}, {13890, 32787}, {19010, 44635}, {35245, 35610}, {35780, 35811}

X(44601) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5597, 44600), (55, 7968, 44603), (372, 35781, 11252), (5599, 13944, 615)

X(44602) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2ND AURIGA AND 1ST KENMOTU-CENTERS

Barycentrics    a*(-2*(a^3-(b+c)^2*a-D)*S+a*D*(a+b+c)) : : , where D=4*S*sqrt(R*(4*R+r))

X(44602) lies on these lines: {1, 44601}, {6, 5598}, {55, 7969}, {371, 11253}, {485, 8207}, {590, 5600}, {1124, 11880}, {1151, 11823}, {1335, 11878}, {1587, 11844}, {2066, 11874}, {2067, 18956}, {3068, 5602}, {3070, 9835}, {3071, 8203}, {3311, 11876}, {5412, 11385}, {5597, 44635}, {6200, 35245}, {6419, 35779}, {6564, 18497}, {7583, 32147}, {7968, 11367}, {8187, 18991}, {8191, 44598}, {8204, 13911}, {8208, 44627}, {8209, 44629}, {11208, 32787}, {11252, 35641}, {11492, 44606}, {11493, 44590}, {11838, 44586}, {11862, 44604}, {11864, 44610}, {11866, 44618}, {11868, 44620}, {11870, 31472}, {11872, 44623}, {11882, 44643}, {11884, 44645}, {13945, 32788}, {19007, 44636}, {35244, 35611}, {35781, 35810}

X(44602) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5598, 44603), (55, 7969, 44600), (371, 35780, 11253), (5598, 19010, 6), (5600, 13891, 590)

X(44603) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2ND AURIGA AND 2ND KENMOTU-CENTERS

Barycentrics    a*(2*(a^3-(b+c)^2*a-D)*S+a*D*(a+b+c)) : : , where D=4*S*sqrt(R*(4*R+r))

X(44603) lies on these lines: {1, 44600}, {6, 5598}, {55, 7968}, {372, 11253}, {486, 8207}, {615, 5600}, {1124, 11878}, {1152, 11823}, {1335, 11880}, {1588, 11844}, {3069, 5602}, {3070, 8203}, {3071, 9835}, {3312, 11876}, {5413, 11385}, {5414, 11874}, {5597, 44636}, {6396, 35245}, {6420, 35780}, {6502, 18956}, {6565, 18497}, {7584, 32147}, {7969, 11367}, {8187, 18992}, {8191, 44599}, {8204, 13973}, {8208, 44628}, {8209, 44630}, {11208, 32788}, {11252, 35642}, {11492, 44607}, {11493, 44591}, {11838, 44587}, {11862, 44605}, {11864, 44611}, {11866, 44619}, {11868, 44621}, {11870, 44622}, {11872, 44624}, {11882, 44644}, {11884, 44646}, {13891, 32787}, {19008, 44635}, {35244, 35610}, {35778, 35811}

X(44603) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5598, 44602), (55, 7968, 44601), (372, 35779, 11253), (5598, 19009, 6), (5600, 13945, 615)

X(44604) = HOMOTHETIC CENTER OF THESE TRIANGLES: 5th BROCARD AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*(4*(b^2+c^2)*a^4+(b^4+5*b^2*c^2+c^4)*a^2+(4*a^4+4*(b^2+c^2)*a^2+2*b^4+2*b^2*c^2+2*c^4)*S+(b^4+b^2*c^2+c^4)*(b^2+c^2)) : :

X(44604) lies on these lines: {3, 6}, {485, 9996}, {590, 3096}, {615, 7846}, {1124, 10047}, {1335, 10038}, {1587, 9862}, {2066, 10877}, {2067, 18957}, {2896, 3068}, {3069, 10583}, {3070, 9873}, {3071, 9993}, {3099, 18991}, {5412, 11386}, {6564, 18500}, {7583, 32151}, {7804, 13877}, {7811, 32787}, {7865, 13846}, {7914, 8253}, {7968, 11368}, {7969, 9941}, {9540, 10357}, {9857, 13911}, {9997, 44635}, {10356, 42265}, {10828, 44598}, {10871, 44618}, {10872, 44620}, {10873, 31472}, {10874, 44623}, {10875, 44627}, {10876, 44629}, {10878, 44643}, {10879, 44645}, {11494, 44590}, {11861, 44600}, {11862, 44602}, {11885, 44610}, {13665, 18503}, {13946, 32788}, {19048, 26318}, {19050, 26317}, {22744, 44606}, {26310, 44582}, {26311, 44584}, {26314, 44594}, {26315, 44596}, {35255, 42787}

X(44604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 32, 44605), (32, 9994, 2076), (32, 19012, 6), (371, 35782, 9821), (3096, 13892, 590)

X(44605) = HOMOTHETIC CENTER OF THESE TRIANGLES: 5th BROCARD AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(4*(b^2+c^2)*a^4+(b^4+5*b^2*c^2+c^4)*a^2-(4*a^4+4*(b^2+c^2)*a^2+2*b^4+2*b^2*c^2+2*c^4)*S+(b^4+b^2*c^2+c^4)*(b^2+c^2)) : :

X(44605) lies on these lines: {3, 6}, {486, 9996}, {590, 7846}, {615, 3096}, {1124, 10038}, {1335, 10047}, {1588, 9862}, {2896, 3069}, {3068, 10583}, {3070, 9993}, {3071, 9873}, {3099, 18992}, {5413, 11386}, {5414, 10877}, {6502, 18957}, {6565, 18500}, {7584, 32151}, {7804, 13930}, {7811, 32788}, {7865, 13847}, {7914, 8252}, {7968, 9941}, {7969, 11368}, {9857, 13973}, {9997, 44636}, {10356, 42262}, {10357, 13935}, {10828, 44599}, {10871, 44619}, {10872, 44621}, {10873, 44622}, {10874, 44624}, {10875, 44628}, {10876, 44630}, {10878, 44644}, {10879, 44646}, {11494, 44591}, {11861, 44601}, {11862, 44603}, {11885, 44611}, {13785, 18503}, {13892, 32787}, {19047, 26318}, {19049, 26317}, {22744, 44607}, {26310, 44583}, {26311, 44585}, {26314, 44595}, {26315, 44597}, {35256, 42787}

X(44605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 32, 44604), (32, 9995, 2076), (32, 19011, 6), (372, 35783, 9821), (3096, 13946, 615)

X(44606) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP TANGENTIAL AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*((2*a^4+8*b*c*a^2+4*(b+c)*b*c*a-2*(b^2+c^2)*(b-c)^2)*S-(a+b+c)*(a^5-(b+c)*a^4-2*(b^2-b*c+c^2)*a^3+2*(b^2-c^2)*(b-c)*a^2+(b^4+c^4-6*(b^2-b*c+c^2)*b*c)*a-(b^2-c^2)*(b-c)^3)) : :

X(44606) lies on these lines: {1, 8939}, {3, 7969}, {6, 41}, {21, 13902}, {36, 18991}, {55, 44635}, {104, 1587}, {371, 11249}, {372, 10269}, {404, 19065}, {474, 13973}, {485, 22758}, {590, 958}, {605, 1201}, {615, 25524}, {956, 13911}, {993, 8983}, {999, 7968}, {1124, 22767}, {1151, 3428}, {1335, 22766}, {1470, 2362}, {1703, 37561}, {2066, 10966}, {2975, 3068}, {3069, 5253}, {3070, 12114}, {3071, 22753}, {3304, 18999}, {3311, 22765}, {3312, 37535}, {3556, 10533}, {5204, 19000}, {5258, 13893}, {5260, 32785}, {5412, 22479}, {5414, 22768}, {5416, 44646}, {5563, 18992}, {5584, 6409}, {6200, 35239}, {6419, 35785}, {6564, 18761}, {7583, 32153}, {8666, 13883}, {9583, 11012}, {10267, 35763}, {10680, 35775}, {11194, 32787}, {11248, 35641}, {11492, 44602}, {11493, 44600}, {13665, 26321}, {16232, 26437}, {18965, 19026}, {19003, 37587}, {19047, 35769}, {19049, 35768}, {22520, 44586}, {22654, 44598}, {22744, 44604}, {22755, 44610}, {22759, 31472}, {22760, 44623}, {22761, 44627}, {22762, 44629}, {22764, 32788}, {26319, 44582}, {26320, 44584}, {26324, 44594}, {26325, 44596}, {35238, 35611}, {35773, 35810}

X(44606) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 7969, 44590), (6, 56, 44607), (56, 19014, 6), (371, 35784, 11249), (958, 22763, 590), (3304, 18999, 44636), (35773, 35810, 37622)

X(44607) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP TANGENTIAL AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(-(2*a^4+8*b*c*a^2+4*(b+c)*b*c*a-2*(b^2+c^2)*(b-c)^2)*S-(a+b+c)*(a^5-(b+c)*a^4-2*(b^2-b*c+c^2)*a^3+2*(b^2-c^2)*(b-c)*a^2+(b^4+c^4-6*(b^2-b*c+c^2)*b*c)*a-(b^2-c^2)*(b-c)^3)) : :

X(44607) lies on these lines: {1, 8943}, {3, 7968}, {6, 41}, {21, 13959}, {36, 18992}, {55, 44636}, {104, 1588}, {371, 10269}, {372, 11249}, {404, 19066}, {474, 13911}, {486, 22758}, {590, 25524}, {606, 1201}, {615, 958}, {956, 13973}, {993, 13971}, {999, 7969}, {1124, 22766}, {1152, 3428}, {1335, 22767}, {1470, 16232}, {1702, 37561}, {2066, 22768}, {2362, 26437}, {2975, 3069}, {3068, 5253}, {3070, 22753}, {3071, 12114}, {3304, 19000}, {3311, 37535}, {3312, 22765}, {3556, 10534}, {5204, 18999}, {5258, 13947}, {5260, 32786}, {5413, 22479}, {5414, 10966}, {5415, 44645}, {5563, 18991}, {5584, 6410}, {5706, 41479}, {6396, 35239}, {6420, 35784}, {6565, 18761}, {7584, 32153}, {8666, 13936}, {10267, 35762}, {10680, 35774}, {11194, 32788}, {11248, 35642}, {11492, 44603}, {11493, 44601}, {13785, 26321}, {18966, 19025}, {19004, 37587}, {19048, 35768}, {19050, 35769}, {22520, 44587}, {22654, 44599}, {22744, 44605}, {22755, 44611}, {22759, 44622}, {22760, 44624}, {22761, 44628}, {22762, 44630}, {22763, 32787}, {26319, 44583}, {26320, 44585}, {26324, 44595}, {26325, 44597}, {35238, 35610}, {35772, 35811}

X(44607) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 7968, 44591), (6, 56, 44606), (56, 19013, 6), (372, 35785, 11249), (958, 22764, 615), (35772, 35811, 37622)

X(44608) = PERSPECTOR OF THESE TRIANGLES: 1ST EXCOSINE AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*(a^12-2*(b^2+c^2)*a^10-(5*b^2-c^2)*(b^2-5*c^2)*a^8+4*(b^2+c^2)*(5*b^4-14*b^2*c^2+5*c^4)*a^6-16*(a^6+(b^2-c^2)^2*a^2-2*(b^4-c^4)*(b^2-c^2))*S*b^2*c^2-(b^2-c^2)^2*(5*b^2-2*b*c+5*c^2)*(5*b^2+2*b*c+5*c^2)*a^4+2*(b^2-c^2)^2*a^2*(b^2+c^2)*(7*b^4+10*b^2*c^2+7*c^4)-(b^2-c^2)^4*(3*b^2+c^2)*(b^2+3*c^2)) : :

X(44608) lies on these lines: {64, 3070}, {154, 8939}, {371, 1498}, {1162, 17816}, {1853, 44609}, {10962, 17820}, {17810, 44633}, {17822, 19087}

X(44609) = PERSPECTOR OF THESE TRIANGLES: 1ST EXCOSINE AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(a^12-2*(b^2+c^2)*a^10-(5*b^2-c^2)*(b^2-5*c^2)*a^8+4*(b^2+c^2)*(5*b^4-14*b^2*c^2+5*c^4)*a^6+16*(a^6+(b^2-c^2)^2*a^2-2*(b^4-c^4)*(b^2-c^2))*S*b^2*c^2-(b^2-c^2)^2*(5*b^2-2*b*c+5*c^2)*(5*b^2+2*b*c+5*c^2)*a^4+2*(b^2-c^2)^2*a^2*(b^2+c^2)*(7*b^4+10*b^2*c^2+7*c^4)-(b^2-c^2)^4*(3*b^2+c^2)*(b^2+3*c^2)) : :

X(44609) lies on these lines: {64, 3071}, {154, 8943}, {372, 1498}, {1163, 17815}, {1853, 44608}, {10960, 17819}, {17810, 44634}, {17822, 19088}

X(44610) = HOMOTHETIC CENTER OF THESE TRIANGLES: GOSSARD AND 1ST KENMOTU-CENTERS

Barycentrics    (2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*((a^4+(b^2-2*c^2)*a^2-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+(b^2-c^2)*(b^2+2*c^2))*a^2+(2*a^8-2*(b^2+c^2)*a^6-2*(2*b^2-c^2)*(b^2-2*c^2)*a^4+6*(b^4-c^4)*(b^2-c^2)*a^2-2*(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2)*S) : :

X(44610) lies on these lines: {6, 402}, {30, 485}, {371, 11251}, {372, 26451}, {590, 1650}, {615, 15183}, {1124, 11913}, {1335, 11912}, {1587, 11845}, {1651, 32787}, {2066, 11909}, {2067, 18958}, {3068, 4240}, {3070, 12113}, {3071, 11897}, {3311, 11911}, {5412, 11832}, {6200, 35241}, {6419, 35791}, {6564, 18507}, {7583, 32162}, {7968, 11831}, {7969, 12438}, {8253, 15184}, {8998, 9033}, {11839, 44586}, {11848, 44590}, {11852, 18991}, {11853, 44598}, {11863, 44600}, {11864, 44602}, {11885, 44604}, {11900, 13911}, {11903, 44618}, {11904, 44620}, {11905, 31472}, {11906, 44623}, {11907, 44627}, {11908, 44629}, {11910, 44635}, {11914, 44643}, {11915, 44645}, {13665, 18508}, {13948, 32788}, {16190, 42259}, {16212, 19066}, {19048, 26453}, {19050, 26452}, {22755, 44606}, {26383, 44582}, {26407, 44584}, {26449, 44594}, {26450, 44596}

X(44610) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 402, 44611), (371, 35790, 11251), (402, 19018, 6), (1650, 13894, 590)

X(44611) = HOMOTHETIC CENTER OF THESE TRIANGLES: GOSSARD AND 2ND KENMOTU-CENTERS

Barycentrics    (2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*((a^4+(b^2-2*c^2)*a^2-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+(b^2-c^2)*(b^2+2*c^2))*a^2-(2*a^8-2*(b^2+c^2)*a^6-2*(2*b^2-c^2)*(b^2-2*c^2)*a^4+6*(b^4-c^4)*(b^2-c^2)*a^2-2*(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2)*S) : :

X(44611) lies on these lines: {6, 402}, {30, 486}, {371, 26451}, {372, 11251}, {590, 15183}, {615, 1650}, {1124, 11912}, {1335, 11913}, {1588, 11845}, {1651, 32788}, {3069, 4240}, {3070, 11897}, {3071, 12113}, {3312, 11911}, {5413, 11832}, {5414, 11909}, {6396, 35241}, {6420, 35790}, {6502, 18958}, {6565, 18507}, {7584, 32162}, {7968, 12438}, {7969, 11831}, {8252, 15184}, {9033, 13990}, {11839, 44587}, {11848, 44591}, {11852, 18992}, {11853, 44599}, {11863, 44601}, {11864, 44603}, {11885, 44605}, {11900, 13973}, {11903, 44619}, {11904, 44621}, {11905, 44622}, {11906, 44624}, {11907, 44628}, {11908, 44630}, {11910, 44636}, {11914, 44644}, {11915, 44646}, {13785, 18508}, {13894, 32787}, {16190, 42258}, {16212, 19065}, {19047, 26453}, {19049, 26452}, {22755, 44607}, {26383, 44583}, {26407, 44585}, {26449, 44595}, {26450, 44597}

X(44611) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 402, 44610), (372, 35791, 11251), (402, 19017, 6), (1650, 13948, 615)

X(44612) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*(2*(2*a^10-5*(b^2+c^2)*a^8+2*(b^4+3*b^2*c^2+c^4)*a^6+(b^2+c^2)*(4*b^4-5*b^2*c^2+4*c^4)*a^4-4*(b^6-c^6)*(b^2-c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(b^4-3*b^2*c^2+c^4))*S+((b^2+c^2)*a^2-(b^2-c^2)^2)*(3*a^8-8*(b^2+c^2)*a^6+3*(2*b^4+3*b^2*c^2+2*c^4)*a^4-(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2)) : :

X(44612) lies on these lines: {371, 6102}, {3070, 13403}, {21640, 44637}

X(44613) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(-2*(2*a^10-5*(b^2+c^2)*a^8+2*(b^4+3*b^2*c^2+c^4)*a^6+(b^2+c^2)*(4*b^4-5*b^2*c^2+4*c^4)*a^4-4*(b^6-c^6)*(b^2-c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(b^4-3*b^2*c^2+c^4))*S+((b^2+c^2)*a^2-(b^2-c^2)^2)*(3*a^8-8*(b^2+c^2)*a^6+3*(2*b^4+3*b^2*c^2+2*c^4)*a^4-(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2)) : :

X(44613) lies on these lines: {372, 6102}, {3071, 13403}, {21641, 44638}

X(44614) = PERSPECTOR OF THESE TRIANGLES: 3RD HATZIPOLAKIS AND 1ST KENMOTU-CENTERS

Barycentrics    (3*(b^2+c^2)*a^10-(11*b^4+2*b^2*c^2+11*c^4)*a^8+(b^2+c^2)*(14*b^4-15*b^2*c^2+14*c^4)*a^6-(6*b^8+6*c^8+5*(-4*b^2*c^2+(b^2-c^2)^2)*b^2*c^2)*a^4-(b^4-c^4)*(b^2-c^2)*(b^4-5*b^2*c^2+c^4)*a^2+(4*a^10-10*(b^2+c^2)*a^8+4*(b^4+7*b^2*c^2+c^4)*a^6+2*(2*b-c)*(b+2*c)*(b-2*c)*(2*b+c)*(b^2+c^2)*a^4-8*(b^2-c^2)^2*(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(2*b^4-6*b^2*c^2+2*c^4))*S+(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^4)*a^2 : :

X(44614) lies on these lines: {54, 22961}, {371, 13630}

X(44615) = PERSPECTOR OF THESE TRIANGLES: 3RD HATZIPOLAKIS AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(3*(b^2+c^2)*a^10-(11*b^4+2*b^2*c^2+11*c^4)*a^8+(b^2+c^2)*(14*b^4-15*b^2*c^2+14*c^4)*a^6-(6*b^8+6*c^8+5*(-4*b^2*c^2+(b^2-c^2)^2)*b^2*c^2)*a^4-(b^4-c^4)*(b^2-c^2)*(b^4-5*b^2*c^2+c^4)*a^2-(4*a^10-10*(b^2+c^2)*a^8+4*(b^4+7*b^2*c^2+c^4)*a^6+2*(2*b-c)*(b+2*c)*(b-2*c)*(2*b+c)*(b^2+c^2)*a^4-8*(b^2-c^2)^2*(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(2*b^4-6*b^2*c^2+2*c^4))*S+(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^4) : :

X(44615) lies on these lines: {54, 22960}, {372, 13630}

X(44616) = PERSPECTOR OF THESE TRIANGLES: 2ND HYACINTH AND 1ST KENMOTU-CENTERS

Barycentrics    a^2*(-a^2+b^2+c^2)*(2*(a^8-(b^2+c^2)*a^6-(b^4-4*b^2*c^2+c^4)*a^4+(b^4-c^4)*(b^2-c^2)*a^2+2*(b^2-c^2)^2*b^2*c^2)*S-(-a^2+b^2+c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)) : :

X(44616) lies on these lines: {125, 10960}, {184, 10962}, {185, 371}, {216, 44617}, {1151, 17818}, {1885, 3070}, {1899, 6413}, {5412, 44633}, {6146, 10897}, {6414, 13198}, {6467, 11513}, {8939, 19355}, {10938, 18457}, {11417, 26441}, {15905, 19022}

X(44617) = PERSPECTOR OF THESE TRIANGLES: 2ND HYACINTH AND 2ND KENMOTU-CENTERS

Barycentrics    a^2*(-a^2+b^2+c^2)*(-2*(a^8-(b^2+c^2)*a^6-(b^4-4*b^2*c^2+c^4)*a^4+(b^4-c^4)*(b^2-c^2)*a^2+2*(b^2-c^2)^2*b^2*c^2)*S-(-a^2+b^2+c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)) : :

X(44617) lies on these lines: {125, 10962}, {184, 8963}, {185, 372}, {216, 44616}, {1152, 17818}, {1885, 3071}, {1899, 6414}, {5413, 44634}, {6146, 10898}, {6413, 13198}, {6467, 11514}, {8943, 19356}, {8982, 11418}, {10938, 18459}, {15905, 19021}

X(44618) = HOMOTHETIC CENTER OF THESE TRIANGLES: INNER-JOHNSON AND 1ST KENMOTU-CENTERS

Barycentrics    a^7-(b+c)*a^6+(b+c)^2*a^5-(b+c)*(b^2+c^2)*a^4-(b^2+c^2)*(3*b^2-8*b*c+3*c^2)*a^3+3*(b^4-c^4)*(b-c)*a^2+(b^2-c^2)^2*(b-c)^2*a+2*(a^5-(b+c)*a^4-2*(b^2-3*b*c+c^2)*a^3+2*(b^2-c^2)*(b-c)*a^2-(b^2+c^2)*(b-c)^2*a+(b^4-c^4)*(b-c))*S-(b^2-c^2)^3*(b-c) : :

X(44618) lies on these lines: {5, 19048}, {6, 11}, {12, 44643}, {355, 485}, {371, 10525}, {372, 26492}, {377, 13906}, {496, 19047}, {590, 1376}, {1124, 10948}, {1151, 11826}, {1335, 10523}, {1587, 10785}, {1588, 10598}, {2066, 10947}, {2067, 18961}, {3068, 3434}, {3069, 10584}, {3070, 12114}, {3071, 10893}, {3311, 11928}, {5412, 11390}, {6200, 35249}, {6419, 35797}, {6564, 18516}, {7583, 10943}, {7741, 26465}, {7968, 11373}, {8983, 17647}, {10794, 44586}, {10826, 18991}, {10829, 44598}, {10871, 44604}, {10914, 13911}, {10944, 31472}, {10945, 44627}, {10946, 44629}, {10949, 19028}, {11235, 32787}, {11865, 44600}, {11866, 44602}, {11903, 44610}, {13665, 18519}, {13846, 34612}, {13898, 19000}, {13952, 32788}, {13973, 17619}, {26390, 44582}, {26414, 44584}, {26459, 37720}, {26490, 44594}, {26491, 44596}, {31584, 31586}, {37722, 44644}

X(44618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 11, 44619), (11, 19024, 6), (371, 35796, 10525), (485, 7969, 44620), (1376, 13895, 590)

X(44619) = HOMOTHETIC CENTER OF THESE TRIANGLES: INNER-JOHNSON AND 2ND KENMOTU-CENTERS

Barycentrics    a^7-(b+c)*a^6+(b+c)^2*a^5-(b+c)*(b^2+c^2)*a^4-(b^2+c^2)*(3*b^2-8*b*c+3*c^2)*a^3+3*(b^4-c^4)*(b-c)*a^2+(b^2-c^2)^2*(b-c)^2*a-2*(a^5-(b+c)*a^4-2*(b^2-3*b*c+c^2)*a^3+2*(b^2-c^2)*(b-c)*a^2-(b^2+c^2)*(b-c)^2*a+(b^4-c^4)*(b-c))*S-(b^2-c^2)^3*(b-c) : :

X(44619) lies on these lines: {5, 19047}, {6, 11}, {12, 44644}, {355, 486}, {371, 26492}, {372, 10525}, {377, 13964}, {496, 19048}, {615, 1376}, {1124, 10523}, {1152, 11826}, {1335, 10948}, {1587, 10598}, {1588, 10785}, {3068, 10584}, {3069, 3434}, {3070, 10893}, {3071, 12114}, {3312, 11928}, {5413, 11390}, {5414, 10947}, {6396, 35249}, {6420, 35796}, {6502, 18961}, {6565, 18516}, {7584, 10943}, {7741, 26459}, {7969, 11373}, {10794, 44587}, {10826, 18992}, {10829, 44599}, {10871, 44605}, {10914, 13973}, {10944, 44622}, {10945, 44628}, {10946, 44630}, {10949, 19027}, {11235, 32788}, {11865, 44601}, {11866, 44603}, {11903, 44611}, {13785, 18519}, {13847, 34612}, {13895, 32787}, {13911, 17619}, {13955, 18999}, {13971, 17647}, {26390, 44583}, {26414, 44585}, {26465, 37720}, {26490, 44595}, {26491, 44597}, {31585, 31587}, {37722, 44643}

X(44619) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 11, 44618), (11, 19023, 6), (372, 35797, 10525), (486, 7968, 44621), (1376, 13952, 615)

X(44620) = HOMOTHETIC CENTER OF THESE TRIANGLES: OUTER-JOHNSON AND 1ST KENMOTU-CENTERS

Barycentrics    2*(a^6-(3*b^2+4*b*c+3*c^2)*a^4-2*(b+c)*b*c*a^3+(b^2-4*b*c+c^2)*(b+c)^2*a^2+(b^4-c^4)*(b^2-c^2))*S+(a+b+c)*(a^7-(b+c)*a^6+(b+c)^2*a^5-(b+c)*(b^2+4*b*c+c^2)*a^4-(3*b^4-2*b^2*c^2+3*c^4)*a^3+(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^2+(b^2-c^2)^2*(b-c)^2*a-(b^2-c^2)^3*(b-c)) : :

X(44620) lies on these lines: {5, 19050}, {6, 12}, {11, 44645}, {72, 13911}, {355, 485}, {371, 10526}, {372, 26487}, {495, 19049}, {590, 958}, {1124, 10523}, {1151, 11827}, {1335, 10954}, {1587, 10786}, {1588, 10599}, {2066, 10953}, {2067, 18962}, {2478, 13907}, {3068, 3436}, {3069, 10585}, {3070, 11500}, {3071, 10894}, {3311, 11929}, {5412, 11391}, {6200, 35250}, {6253, 23251}, {6419, 35799}, {6564, 18517}, {7583, 10942}, {7951, 26464}, {7968, 11374}, {8253, 24953}, {10795, 44586}, {10827, 18991}, {10830, 44598}, {10872, 44604}, {10950, 44623}, {10951, 44627}, {10952, 44629}, {10955, 19030}, {11236, 32787}, {11867, 44600}, {11868, 44602}, {11904, 44610}, {13665, 18518}, {13846, 34606}, {13883, 21077}, {13893, 41229}, {13897, 19014}, {13953, 32788}, {15888, 44646}, {26389, 44582}, {26413, 44584}, {26458, 37719}, {26485, 44594}, {26486, 44596}

X(44620) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 12, 44621), (12, 19026, 6), (371, 35798, 10526), (485, 7969, 44618), (958, 13896, 590)

X(44621) = HOMOTHETIC CENTER OF THESE TRIANGLES: OUTER-JOHNSON AND 2ND KENMOTU-CENTERS

Barycentrics    -2*(a^6-(3*b^2+4*b*c+3*c^2)*a^4-2*(b+c)*b*c*a^3+(b^2-4*b*c+c^2)*(b+c)^2*a^2+(b^4-c^4)*(b^2-c^2))*S+(a+b+c)*(a^7-(b+c)*a^6+(b+c)^2*a^5-(b+c)*(b^2+4*b*c+c^2)*a^4-(3*b^4-2*b^2*c^2+3*c^4)*a^3+(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^2+(b^2-c^2)^2*(b-c)^2*a-(b^2-c^2)^3*(b-c)) : :

X(44621) lies on these lines: {5, 19049}, {6, 12}, {11, 44646}, {72, 13973}, {355, 486}, {371, 26487}, {372, 10526}, {495, 19050}, {615, 958}, {1124, 10954}, {1152, 11827}, {1335, 10523}, {1587, 10599}, {1588, 10786}, {2478, 13965}, {3068, 10585}, {3069, 3436}, {3070, 10894}, {3071, 11500}, {3312, 11929}, {5413, 11391}, {5414, 10953}, {6253, 23261}, {6396, 35250}, {6420, 35798}, {6502, 18962}, {6565, 18517}, {7584, 10942}, {7951, 26458}, {7969, 11374}, {8252, 24953}, {10795, 44587}, {10827, 18992}, {10830, 44599}, {10872, 44605}, {10950, 44624}, {10951, 44628}, {10952, 44630}, {10955, 19029}, {11236, 32788}, {11867, 44601}, {11868, 44603}, {11904, 44611}, {13785, 18518}, {13847, 34606}, {13896, 32787}, {13936, 21077}, {13947, 41229}, {13954, 19013}, {15888, 44645}, {26389, 44583}, {26413, 44585}, {26464, 37719}, {26485, 44595}, {26486, 44597}

X(44621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 12, 44620), (12, 19025, 6), (372, 35799, 10526), (486, 7968, 44619), (958, 13953, 615)

X(44622) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1ST JOHNSON-YFF AND 2ND KENMOTU-CENTERS

Barycentrics    (2*(a^4-2*(b+c)^2*a^2-(b^2+c^2)*(b+c)^2)*S+(-a+b+c)*(a+b+c)*(a^4+2*(b^2+b*c+c^2)*a^2-(b^2-c^2)^2))*(a-b+c)*(a+b-c) : :

X(44622) lies on these lines: {1, 486}, {2, 2067}, {3, 9647}, {4, 5414}, {5, 1335}, {6, 12}, {10, 16232}, {11, 3298}, {35, 6561}, {36, 5420}, {55, 3071}, {56, 615}, {57, 13947}, {65, 13973}, {92, 1586}, {226, 2362}, {371, 498}, {372, 1478}, {388, 3069}, {390, 1132}, {442, 1377}, {485, 3301}, {492, 1909}, {495, 1124}, {496, 18762}, {497, 42561}, {499, 10577}, {590, 18996}, {908, 30557}, {999, 13951}, {1056, 13939}, {1151, 5432}, {1152, 7354}, {1378, 17757}, {1479, 6565}, {1504, 31476}, {1587, 10590}, {1588, 2066}, {1656, 9661}, {1702, 31434}, {1703, 9612}, {1773, 6203}, {2476, 31484}, {3068, 10588}, {3070, 10895}, {3102, 10063}, {3295, 13785}, {3297, 15888}, {3299, 31475}, {3304, 13955}, {3311, 9646}, {3312, 9654}, {3476, 13959}, {3485, 19065}, {3582, 42603}, {3583, 42268}, {3585, 6560}, {3592, 13901}, {3600, 13941}, {3614, 19030}, {4292, 13975}, {4293, 13935}, {4294, 23259}, {4299, 6396}, {4302, 35821}, {4317, 35813}, {4324, 42275}, {5010, 42260}, {5062, 9650}, {5083, 13976}, {5177, 31413}, {5217, 42258}, {5218, 6459}, {5219, 18991}, {5229, 6460}, {5252, 7968}, {5261, 7586}, {5413, 11392}, {5433, 8252}, {5434, 13847}, {5726, 19003}, {6221, 31499}, {6284, 23261}, {6347, 13388}, {6398, 9655}, {6410, 15326}, {6419, 13905}, {6420, 35800}, {6422, 31460}, {6429, 31500}, {6437, 9648}, {7288, 32786}, {7483, 9678}, {7582, 8164}, {7583, 10592}, {7741, 42274}, {7969, 11375}, {8253, 18965}, {8833, 26040}, {9578, 18992}, {10039, 35775}, {10055, 10666}, {10056, 35808}, {10106, 13971}, {10483, 42261}, {10573, 35789}, {10576, 13904}, {10797, 44587}, {10820, 18968}, {10831, 44599}, {10873, 44605}, {10896, 42270}, {10944, 44619}, {10956, 44644}, {10957, 44646}, {11237, 18995}, {11501, 44591}, {11869, 44601}, {11870, 44603}, {11905, 44611}, {11930, 44628}, {11931, 44630}, {12047, 35774}, {12647, 35642}, {12943, 42259}, {12953, 42283}, {13897, 32787}, {13898, 42582}, {13934, 18989}, {13962, 35769}, {13966, 18990}, {15338, 42263}, {15868, 35819}, {15950, 44635}, {18510, 31474}, {18513, 22644}, {19047, 26482}, {19049, 26481}, {22759, 44607}, {24987, 30556}, {25466, 31473}, {26388, 44583}, {26412, 44585}, {26479, 44595}, {26480, 44597}, {31464, 37661}, {31562, 42013}, {38235, 39542}

X(44622) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(1586)}} and {{A, B, C, X(92), X(486)}}
X(44622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 486, 44624), (5, 1335, 44623), (6, 12, 31472), (12, 19027, 6), (56, 13954, 615), (226, 13936, 2362), (372, 35801, 1478), (388, 3069, 6502), (495, 7584, 1124), (1478, 13963, 372), (1588, 3085, 2066), (3298, 42262, 11), (3301, 7951, 485), (3311, 31479, 9646), (3614, 19030, 42265), (5261, 7586, 31408), (6565, 35809, 1479), (7354, 13958, 1152), (10577, 35768, 499), (10895, 19037, 3070), (15888, 19029, 3297)

X(44623) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2ND JOHNSON-YFF AND 1ST KENMOTU-CENTERS

Barycentrics    (-a+b+c)*(2*(a^4-2*(b-c)^2*a^2-(b^2+c^2)*(b-c)^2)*S+(a-b+c)*(a+b-c)*(a^4+2*(b^2-b*c+c^2)*a^2-(b^2-c^2)^2)) : :

X(44623) lies on these lines: {1, 485}, {2, 5414}, {3, 9661}, {4, 2067}, {5, 1335}, {6, 11}, {12, 3298}, {35, 5418}, {36, 6560}, {55, 590}, {56, 3070}, {227, 38487}, {273, 1659}, {350, 491}, {371, 1479}, {372, 499}, {382, 9647}, {388, 31412}, {390, 8972}, {486, 3301}, {495, 18538}, {496, 1124}, {497, 2066}, {498, 10576}, {615, 19037}, {946, 16232}, {950, 8983}, {999, 13665}, {1058, 13886}, {1131, 3600}, {1151, 6284}, {1152, 5433}, {1210, 2362}, {1377, 4187}, {1378, 24390}, {1478, 6564}, {1500, 31481}, {1587, 3086}, {1588, 10591}, {1697, 13893}, {1702, 9614}, {1737, 35774}, {1837, 7969}, {2276, 31463}, {2478, 31453}, {2961, 6204}, {3057, 13911}, {3058, 13846}, {3069, 10589}, {3071, 10896}, {3103, 10079}, {3295, 8976}, {3297, 19028}, {3299, 37720}, {3303, 13897}, {3311, 9669}, {3486, 13902}, {3583, 6561}, {3584, 42602}, {3585, 42269}, {3586, 9583}, {3594, 18966}, {3816, 31473}, {4293, 23249}, {4294, 9540}, {4299, 35820}, {4302, 6200}, {4309, 35812}, {4316, 42276}, {4330, 9680}, {5058, 9665}, {5204, 42259}, {5218, 32785}, {5225, 6459}, {5274, 7585}, {5393, 7133}, {5412, 11393}, {5432, 8253}, {6221, 9660}, {6409, 15338}, {6419, 35803}, {6420, 13962}, {6429, 9662}, {6460, 7288}, {6734, 30557}, {7173, 19027}, {7280, 42261}, {7354, 23251}, {7584, 10593}, {7951, 42277}, {7968, 11376}, {8252, 13958}, {8909, 12428}, {8960, 13905}, {8981, 15171}, {8988, 15558}, {9580, 9616}, {9581, 18991}