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This is PART 24: Centers X(46001) - X(48000)

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)




leftri  Centers of Panchapakesan circles: X(46001) - X(46008)  rightri

This preamble and centers X(46001)-X(46008) were contributed by César Eliud Lozada, November 15, 2021.

Let ABC be a triangle and P, Q two isogonal conjugate points (Q also denoted as P-1). Let Pa, Pb, Pc the centers of circles {{P,B,C}}, {{P,C,A}} and {{P,A,B}}, respectively, and similarly, let Qa, Qb, Qc the centers of circles {{Q,B,C}}, {{Q,C,A}} and {{Q,A,B}}, respectively. Denote Ap = AP ∩ QQa and cyclically Bp and Cp. Finally, denote Aq=AQ ∩ PPa and cyclically Bq and Cq. Then eight points P, Q, Ap, Bp, Cp, Aq, Bq, Cq lie on a circle. (Sriram Panchapakesan, Euclid 3162, November 14, 2021.)

The above described circle is named here the Panchapakesan circle of P and Q. For P = x:y:z, its center O* is:

  O* = a^2*(a^2*y^2 + b^2*x^2 + (a^2 + b^2 - c^2)*x*y)*(a^2*z^2 + c^2*x^2 + (a^2 - b^2 + c^2)*x*z)*(z^2*b^2 - y^2*c^2) : :

Some properties of this circle are:

  1. O* lies in the infinity if P (or Q) lie in the infinity, or on the circumcircle or on McCay cubic K003. (César Lozada, Euclid 3174)
  2. If K(P, ABC) denotes the Panchapakesan circle of P and P-1, then the four circles K(P, ABC), K(A, BCP), K(B, CAP), K(C, ABP) are concurrent in a point R*(P). (Vu Thanh Tung, Euclid 3175)
  3. R*(P) is the circumcircle-inverse of P-1 . (César Lozada, Euclid 3181)
  4. The circumcircle-inverses of P and P-1 also lie on the Panchapakesan circle of P and P-1. (Elias M. Hagos , Euclid 3178)
  5. For any P, the circumcircle of ABC and the Panchapakesan circle of P and P-1 are orthogonal. (Sriram Panchapakesan, Euclid 3179)

In the following list, (i, j) means that the center of the Panchapakesan circle of X(i) and its isogonal conjugate is X(j):

(2, 46001), (3, 523), (4, 523), (5, 46002), (6, 46001), (7, 46003), (8, 46004), (9, 46006), (11, 46007), (13, 6137), (14, 6138), (15, 6137), (16, 6138), (20, 46005), (36, 1769), (54, 46002), (55, 46003), (56, 46004), (57, 46006), (59, 46007), (64, 46005), (80, 1769), (186, 46008), (265, 46008), (1157, 46002), (1263, 46002).
Note: only finite points X(i) were taken in this list.

underbar

X(46001) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(2) AND X(6)

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

X(46001) lies on these lines: {6, 11186}, {110, 9124}, {351, 523}, {512, 2030}, {526, 7625}, {597, 1499}, {598, 25423}, {669, 1383}, {691, 1576}, {882, 9009}, {3566, 14279}, {6088, 8644}, {8704, 11621}, {9044, 9208}, {9155, 9164}, {9182, 18829}, {11580, 17414}, {11622, 32217}, {14606, 18818}, {19127, 39518}, {23297, 23301}, {35364, 43697}

X(46001) = midpoint of X(i) and X(j) for these {i, j}: {6, 11186}, {669, 9178}, {8599, 23287}
X(46001) = reflection of X(32231) in X(11621)
X(46001) = isogonal conjugate of X(9146)
X(46001) = polar conjugate of the isotomic conjugate of X(30491)
X(46001) = barycentric product X(i)*X(j) for these {i, j}: {4, 30491}, {6, 8599}, {111, 23287}, {115, 11636}, {351, 18818}, {512, 598}
X(46001) = barycentric quotient X(i)/X(j) for these (i, j): (32, 9145), (213, 3908), (351, 39785), (512, 599), (523, 9464), (598, 670)
X(46001) = trilinear product X(i)*X(j) for these {i, j}: {19, 30491}, {31, 8599}, {598, 798}, {661, 1383}, {923, 23287}, {1924, 40826}
X(46001) = trilinear quotient X(i)/X(j) for these (i, j): (31, 9145), (42, 3908), (512, 36263), (598, 799), (661, 599), (798, 574)
X(46001) = trilinear pole of the line {3124, 9135}
X(46001) = perspector of the circumconic {{A, B, C, X(598), X(1383)}}
X(46001) = inverse of X(24976) in Kiepert parabola
X(46001) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(2030)}} and {{A, B, C, X(25), X(7426)}}
X(46001) = cevapoint of X(512) and X(8644)
X(46001) = crossdifference of every pair of points on line {X(574), X(599)}
X(46001) = crosspoint of X(i) and X(j) for these (i, j): {1296, 39389}, {1383, 11636}
X(46001) = crosssum of X(i) and X(j) for these (i, j): {523, 16509}, {597, 1499}, {599, 3906}
X(46001) = X(i)-Dao conjugate of-X(j) for these (i, j): (115, 9464), (206, 9145), (512, 17414), (1084, 599)
X(46001) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 9145}, {86, 3908}, {99, 36263}, {163, 9464}
X(46001) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (32, 9145), (213, 3908), (351, 39785), (512, 599)
X(46001) = center of circle {{X(2), X(6), X(23)}}
X(46001) = X(11621)-of-anti-McCay triangle
X(46001) = X(2492)-of-4th anti-Brocard triangle
X(46001) = X(1383)-vertex conjugate of-X(11580)


X(46002) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(5) AND X(54)

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

X(46002) lies on these lines: {137, 8901}, {523, 10096}, {526, 11702}, {1510, 42650}, {8254, 45147}, {8562, 11701}

X(46002) = isogonal conjugate of X(43965)
X(46002) = barycentric product X(526)*X(11538)
X(46002) = barycentric quotient X(i)/X(j) for these (i, j): (526, 15108), (2081, 21230)
X(46002) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(523)}} and {{A, B, C, X(137), X(933)}}
X(46002) = crossdifference of every pair of points on line {X(15109), X(34520)}
X(46002) = crosspoint of X(1291) and X(39390)
X(46002) = crosssum of X(523) and X(24385)
X(46002) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {5, 54, 1157}, {19651, 20424, 30481}
X(46002) = X(526)-reciprocal conjugate of-X(15108)


X(46003) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(7) AND X(55)

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

X(46003) lies on the line {6139, 43050}

X(46003) = isogonal conjugate of the anticomplement of X(43959)
X(46003) = center of circle {{X(7), X(55), X(1155)}}
X(46003) = barycentric quotient X(2488)/X(34522)


X(46004) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(8) AND X(56)

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

X(46004) lies on these lines: {900, 4397}, {3733, 7419}

X(46004) = center of circle {{X(8), X(56), X(1319)}}
X(46004) = crossdifference of every pair of points on line {X(34524), X(34543)}


X(46005) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(20) AND X(64)

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

X(46005) lies on these lines: {523, 14329}, {525, 5894}, {2489, 2881}, {9178, 41894}, {15292, 39201}

X(46005) = isogonal conjugate of the anticomplement of X(1562)
X(46005) = barycentric product X(i)*X(j) for these {i, j}: {523, 41894}, {647, 18848}
X(46005) = barycentric quotient X(i)/X(j) for these (i, j): (512, 26958), (647, 40995), (661, 18691)
X(46005) = trilinear product X(i)*X(j) for these {i, j}: {661, 41894}, {810, 18848}
X(46005) = trilinear quotient X(i)/X(j) for these (i, j): (523, 18691), (656, 40995), (661, 26958), (810, 1204)
X(46005) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(18778)}} and {{A, B, C, X(25), X(16386)}}
X(46005) = cevapoint of X(512) and X(42658)
X(46005) = crossdifference of every pair of points on line {X(26958), X(40995)}
X(46005) = crosssum of X(525) and X(5894)
X(46005) = X(i)-Dao conjugate of-X(j) for these (i, j): (125, 40995), (244, 18691), (1084, 26958)
X(46005) = X(i)-isoconjugate-of-X(j) for these {i, j}: {110, 18691}, {162, 40995}, {662, 26958}, {811, 1204}
X(46005) = center of circle {{X(20), X(64), X(2071)}}
X(46005) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (512, 26958), (647, 40995), (661, 18691)


X(46006) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(9) AND X(57)

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

X(46006) lies on these lines: {8257, 28292}, {9029, 21789}, {23351, 23865}

X(46006) = midpoint of X(23351) and X(23865)
X(46006) = isogonal conjugate of the anticomplement of X(43960)
X(46006) = barycentric product X(513)*X(34525)
X(46006) = trilinear product X(649)*X(34525)
X(46006) = trilinear quotient X(657)/X(34526)
X(46006) = center of circle {{X(9), X(57), X(2078)}}
X(46006) = X(658)-isoconjugate-of-X(34526)


X(46007) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(11) AND X(59)

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

X(46007) lies on the line {676, 15253}

X(46007) = center of circle {{X(11), X(59), X(14667)}}


X(46008) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(186) AND X(265)

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

X(46008) lies on these lines: {403, 523}, {526, 10113}, {5448, 9033}, {39235, 45147}

X(46008) = center of circle {{X(4), X(186), X(265)}}
X(46008) = crosssum of X(526) and X(6102)


X(46009) = X(1)X(37413)∩X(2)X(1804)

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

X(46009) lies on the cubic K1245 and these lines: {1, 37413}, {2, 1804}, {4, 11}, {6, 57}, {19, 43058}, {28, 1035}, {196, 6046}, {225, 37818}, {226, 7011}, {278, 6611}, {940, 7125}, {1014, 5932}, {1214, 1766}, {1410, 4185}, {1470, 37310}, {1617, 40960}, {3075, 11425}, {3911, 5120}, {5706, 7114}, {5909, 37582}, {6516, 30828}, {7053, 34050}, {7532, 19762}, {8748, 40837}, {8808, 13478}, {10400, 16580}, {13737, 15654}, {24030, 43160}, {37046, 37583}

X(46009) = {X(1410),X(4185)}-harmonic conjugate of X(41402)


X(46010) = X(2)X(1444)∩X(3)X(37)

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^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(46010) lies on the conic {{A,B,C,X(2),X(6)}}, the cubics K321 and K1245, and on these lines: {2, 1444}, {3, 37}, {6, 1437}, {19, 3435}, {25, 1333}, {28, 393}, {42, 48}, {56, 1880}, {284, 45129}, {478, 603}, {941, 2303}, {958, 19285}, {967, 5115}, {1036, 2214}, {1108, 3420}, {1427, 7053}, {1791, 14624}, {3433, 5322}, {4252, 14553}, {4254, 39974}, {4261, 37257}, {5069, 39951}, {5110, 39967}, {5120, 39798}, {5124, 39982}, {5301, 11365}, {10037, 22118}, {13478, 24005}, {15668, 16580}, {16606, 23086}, {40144, 45786}

X(46010) = isogonal conjugate of X(5739)
X(46010) = isogonal conjugate of the anticomplement of X(940)
X(46010) = X(i)-cross conjugate of X(j) for these (i,j): {2281, 2214}, {5019, 6}
X(46010) = cevapoint of X(3124) and X(8639)
X(46010) = trilinear pole of line {512, 22383}
X(46010) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5739}, {2, 12514}, {8, 45126}, {10, 27174}, {58, 42707}, {63, 406}, {75, 36744}, {304, 44086}, {345, 1452}, {612, 14258}
X(46010) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5739}, {25, 406}, {31, 12514}, {32, 36744}, {37, 42707}, {604, 45126}, {1333, 27174}, {1395, 1452}, {1974, 44086}, {2221, 14258}
X(46010) = {X(2303),X(11337)}-harmonic conjugate of X(36744)


X(46011) = X(3)X(281)∩X(4)X(6)

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

X(46011) lies on the cubic K1245 and these lines: {3, 281}, {4, 6}, {19, 1158}, {48, 515}, {57, 5307}, {92, 3101}, {278, 41007}, {412, 2322}, {572, 5136}, {860, 5816}, {961, 40836}, {966, 37414}, {1754, 1957}, {1766, 41013}, {1857, 37538}, {1880, 17102}, {5236, 24220}, {8755, 37530}

X(46011) = polar conjugate of the isotomic conjugate of X(24537)
X(46011) = barycentric product X(4)*X(24537)
X(46011) = barycentric quotient X(24537)/X(69)


X(46012) = X(3)X(9)∩X(19)X(18237)

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^3 - a^2*b - a*b^2 + b^3 - a^2*c - 3*b^2*c - a*c^2 - 3*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(46012) lies on the cubic K1245 and these lines: {3, 9}, {19, 18237}, {189, 1150}, {285, 11344}, {391, 411}, {572, 16293}, {940, 1422}, {961, 40836}, {3149, 5120}, {8808, 13478}, {12114, 40942}

X(46012) = barycentric product X(84)*X(19860)
X(46012) = barycentric quotient X(19860)/X(322)
X(46012) = {X(1436),X(1903)}-harmonic conjugate of X(268)


X(46013) = X(4)X(961)∩X(6)X(42467)

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

X(46013) lies on the cubic K1245 and these lines: {4, 961}, {6, 42467}, {572, 34279}, {13478, 24005}


X(46014) = X(4)X(960)∩X(57)X(573)

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

X(46014) lies on the cubic K1246 and these lines: {4, 960}, {57, 573}, {189, 5739}, {581, 937}, {3194, 37410}, {36100, 37419}

X(46014) = X(1436)-isoconjugate of X(19860)
X(46014) = barycentric quotient X(40)/X(19860)


X(46015) = X(6)X(104)∩X(57)X(2051)

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

X(46015) lies on the cubic K1246 and these lines: {6, 104}, {57, 2051}, {515, 2183}, {573, 38955}


X(46016) = X(1)X(25490)∩X(4)X(386)

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

X(46016) lies on the cubic K1246 and these lines: {1, 25490}, {4, 386}, {6, 859}, {9, 22350}, {42, 5727}, {57, 959}, {995, 37642}, {4312, 5313}


X(46017) = X(1)X(9786)∩X(4)X(65)

Barycentrics    a*(a + b - c)*(a - b + c)*(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(46017) lies on the cubic K1246 and these lines: {1, 9786}, {4, 65}, {6, 57}, {7, 11433}, {19, 34032}, {46, 37413}, {51, 1876}, {56, 37310}, {77, 11350}, {169, 34048}, {208, 5706}, {221, 7713}, {226, 6708}, {241, 44708}, {278, 2262}, {354, 11436}, {389, 942}, {573, 1214}, {578, 37582}, {950, 13568}, {1155, 11429}, {1192, 3601}, {1210, 12233}, {1425, 1829}, {1452, 19349}, {1767, 2285}, {1892, 1899}, {1901, 10379}, {2051, 8808}, {2183, 37755}, {2807, 5173}, {2982, 32677}, {3340, 10373}, {3911, 23292}, {4254, 7011}, {4292, 12241}, {5122, 11430}, {5219, 26958}, {5226, 37643}, {5435, 11427}, {5708, 11432}, {5746, 40837}, {5836, 6358}, {5930, 44662}, {5932, 36850}, {7053, 34052}, {7066, 45120}, {10391, 20122}, {10903, 10969}, {10974, 18641}, {11399, 40658}, {11425, 15803}, {11426, 37545}, {11438, 24929}, {17106, 34499}, {17441, 45963}, {19365, 32636}, {20617, 44548}, {23982, 40940}, {30282, 37487}, {43915, 44546}

X(46017) = X(i)-complementary conjugate of X(j) for these (i,j): {947, 6389}, {40396, 18589}
X(46017) = crossdifference of every pair of points on line {3900, 36054}
X(46017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65, 19366, 44547}, {1439, 14557, 223}, {1452, 19349, 40660}, {13437, 13459, 4295}


X(46018) = X(2)X(2245)∩X(6)X(859)

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

X(46018) lies on the conic {{A,B,C,X(2),X(6)}}, the cubic K1246, and these lines: {2, 2245}, {6, 859}, {9, 45095}, {32, 34079}, {37, 517}, {42, 2183}, {44, 16606}, {251, 4290}, {579, 39798}, {583, 39956}, {941, 4271}, {960, 19257}, {966, 14624}, {967, 40153}, {995, 28658}, {1169, 4275}, {1400, 1457}, {1875, 1880}, {2176, 14260}, {2278, 4216}, {2350, 5165}, {4253, 39981}, {4254, 45129}, {4266, 39974}, {4270, 28625}, {4285, 39961}, {5036, 39982}, {5043, 39960}

X(46018) = isogonal conjugate of X(1150)
X(46018) = isogonal conjugate of the anticomplement of X(5718)
X(46018) = isogonal conjugate of the complement of X(31034)
X(46018) = X(4274)-cross conjugate of X(6)
X(46018) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1150}, {2, 993}, {63, 5136}, {75, 2278}, {13136, 14299}
X(46018) = trilinear pole of line {512, 3310}
X(46018) = barycentric product X(i)*X(j) for these {i,j}: {1, 994}, {58, 45095}
X(46018) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 1150}, {25, 5136}, {31, 993}, {32, 2278}, {994, 75}, {45095, 313}


X(46019) = X(4)X(6)∩X(19)X(946)

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

X(46019) lies on the cubic K1246 and these lines: {4, 6}, {19, 946}, {20, 2326}, {33, 10445}, {57, 1848}, {281, 517}, {406, 573}, {608, 41344}, {959, 2358}, {1474, 37395}, {1712, 39579}, {1753, 5750}, {3213, 4292}, {10478, 37388}, {24220, 37382}, {24553, 37378}, {26118, 45786}


X(46020) = X(4)X(959)∩X(6)X(2050)

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

X(46020) lies on the cubic K1246 and these lines: {4, 959}, {6, 2050}, {573, 19608}, {10478, 40160}, {19607, 23512}


X(46021) = X(4)X(57)∩X(271)X(5739)

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

X(46021) lies on the cubic K1246 and these lines: {4, 57}, {271, 5739}, {282, 573}, {285, 411}, {581, 1433}


X(46022) = X(3)X(9)∩X(189)X(5739)

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

X(46022) lies on the cubic K1246 and these lines: {3, 9}, {189, 5739}, {959, 2358}, {2051, 8808}, {3427, 7003}, {5798, 37544}, {6001, 40942}, {6245, 9119}

X(46022) = barycentric product X(84)*X(24987)
X(46022) = barycentric quotient X(24987)/X(322)


X(46023) = ISOGONAL CONJUGATE OF X(1340)

Barycentrics    1/(a^4 - a^2*b^2 - a^2*c^2 - 2*b^2*c^2 - (-a^2 + b^2 + c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]) : :

X(46023) lies on the Keipert circumhyperbola, the cubics K055 and K281, and these lines: {2, 1380}, {3, 14633}, {4, 14631}, {5, 6177}, {6, 3414}, {30, 182}, {32, 6178}, {76, 3558}, {83, 2558}, {98, 31863}, {262, 1341}, {381, 3413}, {671, 31862}, {1340, 3972}, {1349, 5475}, {1379, 10788}, {2559, 12110}, {3399, 13326}, {3424, 35913}, {7787, 14630}

X(46023) = reflection of X(46024) in X(5476)
X(46023) = isogonal conjugate of X(1340)
X(46023) = X(i)-cross conjugate of X(j) for these (i,j): (1349,6178), (5475, 46024)
X(46023) = X(1)-isoconjugate of X(1340)
X(46023) = trilinear pole of line {523, 5638}
X(46023) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 1340}, {1341, 7998}, {45819, 46024}
X(46023) = {X(182),X(10796)}-harmonic conjugate of X (46024)


X(46024) = ISOGONAL CONJUGATE OF X(1341)

Barycentrics    1/(a^4 - a^2*b^2 - a^2*c^2 - 2*b^2*c^2 + (-a^2 + b^2 + c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]) : :

X(46024) lies on the Keipert circumhyperbola, the cubics K055 and K281, and these lines: {2, 1379}, {3, 14632}, {4, 14630}, {5, 6178}, {6, 3413}, {30, 182}, {32, 6177}, {76, 3557}, {83, 2559}, {98, 31862}, {262, 1340}, {381, 3414}, {671, 31863}, {1341, 3972}, {1348, 5475}, {1380, 10788}, {2558, 12110}, {3399, 13325}, {3424, 35914}, {7787, 14631}

X(46024) = reflection of X(46023) in X(5476)
X(46024) = isogonal conjugate of X(1341)
X(46024) = X(i)-cross conjugate of X(j) for these (i,j): (1348,6177), (5475, 46023)
X(46024) = X(1)-isoconjugate of X(1341)
X(46024) = trilinear pole of line {523, 5639}
X(46024) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 1341}, {1340, 7998}, {45819, 46023}
X(46024) = {X(182),X(10796)}-harmonic conjugate of X(46023)


X(46025) = X(3)X(54)∩X(5)X(53)

Barycentrics    a^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^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 4*a^6*c^2 + 3*a^4*b^2*c^2 + 4*a^2*b^4*c^2 - 3*b^6*c^2 + 6*a^4*c^4 + 4*a^2*b^2*c^4 + 4*b^4*c^4 - 4*a^2*c^6 - 3*b^2*c^6 + c^8) : :
X(46025) = 3 X[3] - X[31388], X[3] - 3 X[32078], 2 X[140] - 3 X[12012], 2 X[546] - 3 X[14635], 5 X[632] - 6 X[44914], 5 X[1656] - 3 X[11197], 4 X[3628] - 3 X[10184], X[31388] - 9 X[32078], X[31388] + 3 X[42441], 3 X[32078] + X[42441]

See Antreas Hatzipolakis and Peter Moses, euclid 3217.

X(46025) lies on these lines: {2, 14978}, {3, 54}, {5, 53}, {26, 26898}, {30, 35717}, {52, 26907}, {140, 12012}, {143, 418}, {155, 36751}, {156, 6641}, {546, 14635}, {549, 33549}, {568, 26876}, {632, 6509}, {852, 32205}, {1216, 45112}, {1578, 18940}, {1579, 18939}, {1656, 11197}, {2072, 34768}, {3060, 26896}, {3567, 26895}, {3628, 10184}, {5609, 41212}, {5647, 10539}, {5663, 26897}, {6243, 26874}, {6638, 15026}, {7393, 40681}, {7526, 23709}, {10263, 30258}, {11793, 34990}, {13371, 26905}, {13856, 37452}, {14790, 26870}, {15869, 21230}, {16239, 44436}, {19347, 44200}, {22804, 36245}, {26865, 37493}, {26880, 37440}

X(46025) = midpoint of X(i) and X(j) for these {i,j}: {3, 42441}, {30258, 42556}
X(46025) = reflection of X(35719) in X(5)
X(46025) = complement of X(14978)
X(46025) = complement of the isogonal conjugate of X(20574)
X(46025) = X(i)-complementary conjugate of X(j) for these (i,j): {288, 20305}, {20574, 10}, {39181, 21253}
X(46025) = X(35311)-Ceva conjugate of X(520)
X(46025) = X(2190)-isoconjugate of X(14938)
X(46025) = crossdifference of every pair of points on line {12077, 23286}
X(46025) = barycentric product X(343)*X(1199)
X(46025) = barycentric quotient X(i)/X(j) for these {i,j}: {216, 14938}, {1199, 275}
X(46025) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 195, 97}, {3, 13409, 10627}, {32078, 42441, 3}


X(46026) = X(4)X(83)∩X(141)X(427)

Barycentrics    (b^2+c^2)*(2*a^2+b^2+c^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
X(46026) = 3*X(1176)-5*X(3618), X(18440)+3*X(45034), 3*X(18488)+2*X(21850), 6*X(38136)-X(44866)

See Antreas Hatzipolakis and César Lozada, euclid 3218.

X(46026) lies on these lines: {2, 41464}, {4, 83}, {6, 5064}, {25, 2916}, {51, 23300}, {52, 1595}, {125, 9969}, {141, 427}, {155, 18440}, {159, 38396}, {185, 1907}, {193, 7378}, {264, 40035}, {378, 32600}, {428, 3589}, {511, 6152}, {542, 2914}, {858, 9822}, {1162, 3128}, {1163, 3127}, {1503, 3574}, {1568, 3818}, {1593, 35240}, {1594, 11817}, {1597, 40909}, {1829, 1861}, {2904, 39588}, {3564, 13431}, {5092, 7576}, {5094, 5646}, {5095, 32455}, {5133, 11574}, {5169, 12220}, {5895, 11403}, {5965, 13420}, {6030, 6995}, {6287, 22138}, {6292, 22078}, {6329, 44102}, {6697, 9971}, {7391, 19126}, {7394, 19137}, {8754, 39931}, {10294, 32250}, {10594, 38317}, {12167, 40341}, {14216, 14853}, {14865, 29317}, {15062, 15741}, {15583, 40673}, {15809, 37648}, {15812, 31099}, {16198, 36153}, {19125, 36990}, {20184, 38359}, {22970, 23047}, {26177, 28665}, {27366, 27371}, {31267, 44082}, {31390, 39691}, {32587, 45478}, {32588, 45479}, {38136, 44866}

X(46026) = midpoint of X(6) and X(15321)
X(46026) = complement of X(41464)
X(46026) = polar conjugate of X(40425)
X(46026) = crosspoint of X(i) and X(j) for these (i, j): {4, 427}, {428, 44142}
X(46026) = crosssum of X(3) and X(1176)
X(46026) = X(i)-Ceva conjugate of-X(j) for these (i, j): (4, 428), (427, 28666)
X(46026) = X(141)-Dao conjugate of-X(41435)
X(46026) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 40425}, {82, 41435}
X(46026) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 40425), (39, 41435), (427, 10159), (428, 83)
X(46026) = perspector of the circumconic {{A, B, C, X(41676), X(42396)}}
X(46026) = Jerabek-circumhyperbola-inverse of X(9969)
X(46026) = polar-circle-inverse of X(38946)
X(46026) = pole wrt polar circle of trilinear polar of X(40425) (line X(826)X(14318))
X(46026) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(28666)}} and {{A, B, C, X(6), X(14247)}}
X(46026) = Zosma transform of X(82)
X(46026) = barycentric product X(i)*X(j) for these {i, j}: {4, 6292}, {19, 20898}, {25, 42554}, {27, 21038}, {39, 44142}, {83, 28666}
X(46026) = barycentric quotient X(i)/X(j) for these (i, j): (4, 40425), (39, 41435), (427, 10159), (428, 83), (1843, 3108)
X(46026) = trilinear product X(i)*X(j) for these {i, j}: {4, 17457}, {19, 6292}, {25, 20898}, {27, 21817}, {28, 21038}, {38, 428}
X(46026) = trilinear quotient X(i)/X(j) for these (i, j): (38, 41435), (92, 40425), (428, 82)
X(46026)= {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (427, 3867, 1843), (428, 3589, 44091)


X(46027) = X(6)X(382)∩X(143)X(185)

Barycentrics    (2*a^4+(b^2+c^2)*a^2-3*(b^2-c^2)^2)*(2*a^6-3*(b^2+c^2)*a^4+2*b^2*c^2*a^2+(b^4-c^4)*(b^2-c^2)) : :
X(46027) = 3*X(4)-X(15062), 3*X(381)-X(18442), 2*X(382)+X(44866), X(3529)-3*X(6030), 2*X(3627)+X(34563), 5*X(3627)+X(44755), 5*X(5076)-X(33541), 2*X(15062)-3*X(18488), 5*X(17578)+X(43599), 5*X(34563)-2*X(44755)

See Antreas Hatzipolakis and César Lozada, euclid 3218.

X(46027) lies on these lines: {4, 5449}, {5, 35240}, {6, 382}, {30, 3574}, {113, 3575}, {143, 185}, {155, 12173}, {381, 18442}, {539, 13420}, {546, 44106}, {1112, 11560}, {1531, 31830}, {1568, 45971}, {1843, 12162}, {1986, 5446}, {2904, 35480}, {2914, 17702}, {3060, 16880}, {3146, 8718}, {3153, 43597}, {3529, 6030}, {3589, 12605}, {3830, 5895}, {3853, 10113}, {5076, 33541}, {5448, 18559}, {5663, 32340}, {5889, 15110}, {6152, 13754}, {6240, 12038}, {6756, 22970}, {7487, 15751}, {10110, 18323}, {10294, 30714}, {10539, 32605}, {11457, 17578}, {11559, 38447}, {13431, 44665}, {13474, 40949}, {16835, 32533}, {18128, 43612}, {18376, 37490}, {18377, 43817}, {23047, 32110}, {32478, 38359}, {34564, 43585}

X(46027) = midpoint of X(i) and X(j) for these {i, j}: {382, 3521}, {3146, 8718}
X(46027) = reflection of X(i) in X(j) for these (i, j): (11560, 1112), (18488, 4), (35240, 5), (44866, 3521)
X(46027) = crosspoint of X(4) and X(6240)
X(46027) = X(4)-Ceva conjugate of-X(546)
X(46027) = anti-excenters-incenter-reflections-to-orthic similarity image of X(18488)
X(46027) = Ehrmann-side-to-orthic similarity image of X(18442)
X(46027) = X(546)-reciprocal conjugate of-X(42410)
X(46027) = barycentric quotient X(546)/X(42410)


X(46028) = EULER LINE INTERCEPT OF X(11)X(16137)

Barycentrics    2*(b^2-b*c+c^2)*a^5-2*(b+c)*(b^2+c^2)*a^4-(4*b^4+4*c^4+(b^2+c^2)*b*c)*a^3+4*(b^3-c^3)*(b^2-c^2)*a^2+(2*b^2+3*b*c+2*c^2)*(b^2-c^2)^2*a-2*(b^2-c^2)^3*(b-c) : :
X(46028) = 3*X(4)+5*X(15674), 7*X(4)+9*X(31669), 3*X(5)-X(442), 5*X(5)-X(5499), 3*X(5)+X(16160), 7*X(5)-X(37401), 5*X(5)+X(37447), X(21)+3*X(381), X(21)-3*X(44257), X(382)+3*X(21161), 5*X(442)-3*X(5499), X(442)+3*X(6841), 7*X(442)-3*X(37401), 5*X(442)+3*X(37447), 2*X(546)+X(12104), 3*X(547)-X(11277), X(550)-3*X(28465), 5*X(632)-X(31651)

See Antreas Hatzipolakis and César Lozada, euclid 3218.

X(46028) lies on these lines: {2, 3}, {11, 16137}, {12, 15174}, {758, 9955}, {1699, 16139}, {3585, 5427}, {3649, 7741}, {3817, 33592}, {3899, 21677}, {5424, 5560}, {5426, 18492}, {7173, 11544}, {7988, 16132}, {8227, 33858}, {8261, 31937}, {10113, 16164}, {11263, 22798}, {12558, 40273}, {16118, 31231}, {16125, 22936}, {16126, 38021}, {16159, 19919}, {18253, 25639}, {18357, 44669}, {18480, 35016}, {18493, 34195}, {22938, 35204}, {33857, 37692}

X(46028) = midpoint of X(i) and X(j) for these {i, j}: {3, 44258}, {4, 5428}, {5, 6841}, {381, 44257}, {442, 16160}, {546, 10021}, {3627, 44238}, {3845, 15670}, {3861, 44254}, {5499, 37447}, {8261, 31937}, {10113, 16164}, {11263, 22798}, {15687, 44255}, {16125, 22936}, {16159, 19919}, {18480, 35016}, {21677, 22791}, {22938, 35204}, {31649, 37230}
X(46028) = reflection of X(i) in X(j) for these (i, j): (11276, 16239), (12104, 10021)
X(46028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 550, 6829), (5, 632, 6991), (5, 3845, 2476), (5, 3857, 6941), (5, 3858, 6980), (5, 6831, 3628), (5, 8226, 3850), (5, 16160, 442), (21, 5141, 442), (381, 6873, 5), (5154, 19709, 5)


X(46029) = EULER LINE INTERCEPT OF X(113)X(15060)

Barycentrics    (b^2+c^2)*a^8-2*(b^4-b^2*c^2+c^4)*a^6-3*(b^2+c^2)*b^2*c^2*a^4+(2*b^4+b^2*c^2+2*c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(46029) = 9*X(2)-X(35481), 3*X(3)+X(35480), 3*X(5)-X(427), 3*X(5)-2*X(13413), X(22)+3*X(381), X(22)-3*X(44262), X(378)-5*X(1656), 3*X(381)-X(44288), X(382)+3*X(44837), X(427)+3*X(15760), 2*X(427)-3*X(39504), 2*X(546)+X(7555), 3*X(547)-X(44236), 3*X(549)-X(44249)

See Antreas Hatzipolakis and César Lozada, euclid 3218.

X(46029) lies on these lines: {2, 3}, {113, 15060}, {182, 11801}, {184, 32423}, {185, 34826}, {265, 5012}, {399, 3410}, {569, 43575}, {578, 8254}, {1147, 15806}, {1154, 18388}, {1181, 18356}, {1209, 5876}, {1263, 15367}, {1352, 25336}, {1568, 15067}, {1614, 6288}, {2781, 24206}, {2979, 7699}, {3521, 11440}, {3574, 10263}, {3818, 19127}, {5448, 11591}, {5449, 13630}, {5663, 21243}, {6243, 20424}, {6689, 13403}, {7592, 32165}, {7731, 11805}, {9019, 19130}, {9306, 10272}, {9927, 32046}, {10112, 32136}, {10113, 16165}, {10193, 32743}, {10264, 12270}, {10540, 41171}, {10610, 21659}, {11204, 23315}, {11804, 12902}, {12281, 18435}, {13399, 13491}, {13470, 18383}, {13561, 40647}, {13565, 14076}, {13851, 37513}, {16000, 34224}, {16252, 40276}, {16789, 21850}, {16837, 22335}, {16881, 41587}, {18436, 21230}, {18475, 30522}, {20584, 26883}, {22660, 31834}, {26913, 40280}, {26958, 44754}, {32171, 44516}, {32210, 43577}, {32351, 34786}, {37470, 40685}, {43651, 43821}

X(46029) = midpoint of X(i) and X(j) for these {i, j}: {3, 44263}, {4, 7502}, {5, 15760}, {22, 44288}, {381, 44262}, {546, 25337}, {3627, 44239}, {3818, 19127}, {3845, 44210}, {10113, 16165}, {15687, 44261}, {16789, 21850}, {18572, 37969}
X(46029) = reflection of X(i) in X(j) for these (i, j): (427, 13413), (7555, 25337), (39504, 5)
X(46029) = complement of X(18570)
X(46029) = inverse of X(18572) in: MacBeath inconic, nine-point circle
X(46029) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 10254, 5), (3, 381, 3153), (3, 1656, 6143), (3, 34797, 550), (5, 235, 3850), (5, 549, 2072), (5, 550, 1594), (5, 3627, 5576), (5, 3845, 5133), (5, 7399, 3628), (5, 11563, 381), (5, 15761, 546), (22, 37353, 427), (140, 37968, 549), (381, 5899, 4), (403, 37347, 5), (1656, 16868, 5), (3628, 44912, 547), (5133, 11799, 3845), (6823, 13371, 548), (7577, 35480, 427), (10024, 13160, 5), (10024, 37347, 403), (34577, 45971, 1658), (44262, 44288, 22)


X(46030) = EULER LINE INTERCEPT OF X(51)X(113)

Barycentrics    (b^2+c^2)*a^8-2*(b^2-c^2)^2*a^6+2*(b^2+c^2)*b^2*c^2*a^4+2*(b^4-3*b^2*c^2+c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(46030) = 3*X(5)-X(1368), X(25)+3*X(381), X(25)-3*X(44275), 2*X(546)+X(12106), X(1368)+3*X(1596), X(1370)-9*X(3545)

See Antreas Hatzipolakis and César Lozada, euclid 3218.

X(46030) lies on these lines: {2, 3}, {51, 113}, {125, 16194}, {143, 15873}, {156, 12241}, {343, 15060}, {399, 45968}, {1353, 45016}, {1498, 18952}, {1531, 44106}, {1533, 14855}, {2393, 19130}, {2883, 13630}, {3580, 18435}, {3818, 19136}, {5448, 10110}, {5449, 44870}, {5480, 14984}, {5504, 10272}, {5654, 34966}, {5663, 13567}, {5876, 41587}, {6053, 11225}, {6247, 32137}, {8263, 9971}, {9220, 9722}, {9955, 44662}, {10095, 12233}, {10113, 20772}, {10169, 18583}, {10539, 12370}, {10540, 12022}, {11381, 43817}, {11439, 26917}, {11441, 32358}, {11455, 26913}, {11472, 26958}, {11579, 11801}, {12359, 45959}, {14389, 40114}, {15032, 45967}, {15807, 32171}, {16252, 32046}, {16261, 23293}, {16534, 34986}, {18439, 26879}, {20300, 36201}, {20304, 23332}, {31804, 43575}, {32139, 39571}, {34224, 43821}

X(46030) = midpoint of X(i) and X(j) for these {i, j}: {3, 44276}, {4, 6644}, {5, 1596}, {381, 44275}, {546, 44233}, {3627, 44241}, {3818, 19136}, {3845, 44212}, {7530, 18531}, {8263, 21850}, {10113, 20772}, {14791, 18534}, {15687, 44273}, {44260, 44288}, {44263, 44274}
X(46030) = reflection of X(i) in X(j) for these (i, j): (12106, 44233), (44920, 3850)
X(46030) = complement of the circumperp conjugate of X(11799)
X(46030) = nine-point-circle-inverse of X(47336)
X(46030) = 1st-Droz-Farny-circle-inverse X(7464)
X(46030) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 3845, 427), (5, 3858, 7403), (5, 6823, 3628), (5, 43893, 549), (25, 5133, 1368), (381, 403, 5), (381, 10254, 5133), (381, 11818, 546), (546, 31830, 4), (546, 44235, 5), (1906, 11585, 3627), (3091, 10024, 5), (3545, 37347, 5), (3832, 16868, 5576), (3850, 13406, 5), (3851, 13160, 5), (3861, 10224, 1595), (5072, 14788, 5), (5133, 10254, 5), (5576, 16868, 5), (7576, 18403, 3627), (9818, 10201, 140), (13490, 23323, 4), (18494, 18568, 3853), (18570, 44270, 468), (19709, 37990, 5), (34664, 37971, 7502)


X(46031) = EULER LINE INTERCEPT OF X(113)X(16227)

Barycentrics    2*(b^2+c^2)*a^8-2*(2*b^4-b^2*c^2+2*c^4)*a^6+(b^2+c^2)*b^2*c^2*a^4+(4*b^4-3*b^2*c^2+4*c^4)*(b^2-c^2)^2*a^2-2*(b^4-c^4)*(b^2-c^2)^3 : :
X(46031) = 3*X(2)+X(31726), 7*X(5)-X(858), 3*X(5)-X(2072), 3*X(5)+X(11563), 5*X(5)+X(11799), 5*X(5)-X(37938), 7*X(5)+X(43893), 2*X(5)+X(44961), X(23)+11*X(5072), 3*X(140)-2*X(16976), X(140)+2*X(37984), X(186)+3*X(381), X(186)-3*X(44282), 3*X(381)+2*X(44900), X(382)+3*X(37941), 7*X(403)+X(858), 3*X(403)+X(2072), 3*X(403)-X(11563), 5*X(403)-X(11799), 5*X(403)+X(37938), 7*X(403)-X(43893)

See Antreas Hatzipolakis and César Lozada, euclid 3218.

X(46031) lies on these lines: {2, 3}, {113, 16227}, {523, 39510}, {1514, 40685}, {1539, 21663}, {3564, 34155}, {6000, 20304}, {7687, 30522}, {7951, 10149}, {10095, 32411}, {10272, 44665}, {10540, 14644}, {11704, 18439}, {11745, 20193}, {11793, 13446}, {12241, 15806}, {12290, 45622}, {13367, 43865}, {13754, 41671}, {14643, 40111}, {16328, 36412}, {18504, 34783}, {26917, 45957}, {32137, 32767}

X(46031) = midpoint of X(i) and X(j) for these {i, j}: {3, 44283}, {4, 15646}, {5, 403}, {381, 44282}, {468, 23323}, {546, 44234}, {858, 43893}, {1539, 21663}, {2070, 18572}, {2071, 44267}, {2072, 11563}, {3153, 37936}, {3627, 44246}, {3845, 44214}, {7574, 37947}, {7575, 18403}, {10151, 44452}, {11793, 13446}, {11799, 37938}, {15687, 44280}, {31726, 34152}, {37984, 44911}, {44263, 44281}
X(46031) = reflection of X(i) in X(j) for these (i, j): (140, 44911), (186, 44900), (10096, 37942), (10257, 3628), (13473, 3861), (18571, 44234), (23323, 3850), (32411, 10095), (37931, 22249), (37968, 44452), (44452, 15350), (44961, 403)
X(46031) = complement of X(34152)
X(46031) = inverse of X(3627) in: MacBeath inconic, nine-point circle
X(46031) = inverse of X(21844) in polar circle
X(46031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 10024, 3628), (5, 11563, 2072), (5, 13406, 140), (5, 44235, 546), (235, 10224, 3853), (1312, 1313, 3627), (3628, 31829, 140), (3850, 31830, 546), (5066, 44233, 546), (10255, 44958, 3627), (18570, 34330, 140)


X(46032) = X(8)X(291)∩X(10)X(75)

Barycentrics    a*((b^3+c^3)*a-b*c*(b^2+3*b*c+c^2)) : :
X(46032) = 5*X(3617)-X(21219)

See Vu Thanh Tung and César Lozada, euclid 3221.

X(46032) lies on these lines: {1, 3795}, {8, 291}, {10, 75}, {38, 29593}, {238, 3501}, {244, 17230}, {312, 20340}, {518, 21868}, {536, 24456}, {594, 4446}, {728, 39954}, {982, 3661}, {1107, 3097}, {1278, 4941}, {1376, 3507}, {1574, 14839}, {1698, 21264}, {1706, 3751}, {1740, 4649}, {2321, 17065}, {2345, 24478}, {3061, 3864}, {3123, 4740}, {3293, 22327}, {3617, 21219}, {3679, 24464}, {3701, 20440}, {3912, 17063}, {3967, 25125}, {4041, 4444}, {4051, 22116}, {4078, 30063}, {4110, 42027}, {4438, 27321}, {4443, 4665}, {4445, 7241}, {4704, 22174}, {4904, 20255}, {5687, 8298}, {6382, 19567}, {11364, 25440}, {12263, 27091}, {13178, 38499}, {16476, 16549}, {17143, 32020}, {17889, 20486}, {20456, 29617}, {20917, 24165}, {24575, 42696}, {27255, 40328}, {27299, 33159}, {29659, 35101}, {32921, 41240}

X(46032) = midpoint of X(8) and X(330)
X(46032) = reflection of X(i) in X(j) for these (i, j): (1, 16604), (6376, 10)
X(46032) = X(8)-Beth conjugate of-X(6376)
X(46032) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10009)}} and {{A, B, C, X(291), X(6376)}}
X(46032) = {X(10), X(12782)}-harmonic conjugate of X(984)


X(46033) = X(4)X(14941)∩X(5)X(264)

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

See Vu Thanh Tung and César Lozada, euclid 3221.

X(46033) lies on these lines: {3, 38297}, {4, 14941}, {5, 264}, {127, 14059}, {35709, 40800}, {38974, 40804}


X(46034) = X(4)X(6)∩X(20)X(1078)

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

See Angel Montesdeoca, euclid 3223.

X(46034) lies on these lines: {4,6}, {20,1078}, {30,7620}, {147,32827}, {193,38664}, {316,5921}, {376,9756}, {381,7710}, {458,35260}, {542,23334}, {543,22664}, {671,2794}, {3091,7790}, {3146,14712}, {3524,8719}, {3545,15428}, {3839,7694}, {3926,39266}, {4232,41254}, {5024,40927}, {5188,32834}, {5309,9748}, {5999,32815}, {7739,22682}, {8370,25406}, {9752,14651}, {10516,33190}, {10991,43618}, {11257,31400}, {11623,37689}, {12203,32971}, {20079,32002}, {22575,41023}, {22576,41022}, {29181,34505}, {32064,39908}, {34473,35927}

X(46034) = midpoint of X(3424) and X(3543)
X(46034) = reflection of X(i) in X(j) for these {i,j}: {376,9756}, {7710,381}


X(46035) = X(3)X(2133)∩X(4)X(1138)

Barycentrics    (a^8+2*(b^2-2*c^2)*a^6-(6*b^4-b^2*c^2-6*c^4)*a^4+(b^2-c^2)*(2*b^4+3*b^2*c^2+4*c^4)*a^2+(b^2-c^2)^4)*(a^8-2*(2*b^2-c^2)*a^6+(6*b^4+b^2*c^2-6*c^4)*a^4-(b^2-c^2)*(4*b^4+3*b^2*c^2+2*c^4)*a^2+(b^2-c^2)^4)*(3*a^12-7*(b^2+c^2)*a^10-(b^4-21*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(7*b^4-16*b^2*c^2+7*c^4)*a^6-(b^2-c^2)^2*(11*b^4+24*b^2*c^2+11*c^4)*a^4+(b^4-c^4)*(b^2-c^2)*(b^4+10*b^2*c^2+c^4)*a^2+(b^6-c^6)*(b^2-c^2)^3) : :
Barycentrics    (S^2-3*(3*R^2-SB)*SB)*(S^2-3*(3*R^2-SC)*SC)*(5*S^2-24*R^2*(6*R^2+SA-3*SW)+6*SA^2-4*SB*SC-9*SW^2) : :

See Antreas Hatzipolakis and César Lozada, euclid 3224.

X(46035) lies on the cubic K005 and these lines: {3, 2133}, {4, 1138}, {5, 20123}, {3336, 38934}, {3463, 38935}, {15774, 15791}

X(46035) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(2132)}} and {{A, B, C, X(4), X(2133)}}


X(46036) = X(3)X(2132)∩X(4)X(2133)

Barycentrics    a^2*(a^12-(3*b^2-c^2)*a^10+(3*b^4+9*b^2*c^2-11*c^4)*a^8-2*(b^2-c^2)*(b^4+6*b^2*c^2+7*c^4)*a^6+(b^2-c^2)*(3*b^6+c^6-(7*b^2-19*c^2)*b^2*c^2)*a^4-(b^2-c^2)^3*(3*b^4-7*c^4)*a^2+(b^4+5*b^2*c^2+3*c^4)*(b^2-c^2)^4)*(a^12+(b^2-3*c^2)*a^10-(11*b^4-9*b^2*c^2-3*c^4)*a^8+2*(b^2-c^2)*(7*b^4+6*b^2*c^2+c^4)*a^6-(b^2-c^2)*(b^6+3*c^6+(19*b^2-7*c^2)*b^2*c^2)*a^4-(b^2-c^2)^3*(7*b^4-3*c^4)*a^2+(3*b^4+5*b^2*c^2+c^4)*(b^2-c^2)^4)*(a^8-4*(b^2+c^2)*a^6+(6*b^4+b^2*c^2+6*c^4)*a^4-(b^2+c^2)*(4*b^4-5*b^2*c^2+4*c^4)*a^2+(b^4+4*b^2*c^2+c^4)*(b^2-c^2)^2) : :
Barycentrics    (SB+SC)*(S^2-3*(3*R^2-SA)*SA)*(S^2-24*R^2*(6*R^2+SB-3*SW)+2*SB*(SB+2*SW)-9*SW^2)*(S^2-24*R^2*(6*R^2+SC-3*SW)+2*SC*(SC+2*SW)-9*SW^2) : :

See Antreas Hatzipolakis and César Lozada, euclid 3224.

X(46036) lies on the cubic K005 and these lines: {3, 2132}, {4, 2133}, {5, 20123}, {3462, 3471}, {8918, 8919}, {15773, 15790}


X(46037) = ISOGONAL CONJUGATE OF X(38934)

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

See Antreas Hatzipolakis and César Lozada, euclid 3224.

X(46037) lies on the cubic K005 and these lines: {1, 3470}, {3, 5677}, {4, 1768}, {5, 34299}, {195, 3469}, {3461, 38935}, {7344, 8929}, {7345, 8930}

X(46037) = isogonal conjugate of X(38934)
X(46037) = X(484)-isoconjugate-of-X(3466)
X(46037) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(3464)}} and {{A, B, C, X(4), X(3465)}}


X(46038) = X(2)X(914)∩(3)X(2164)

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

X(46038) lies on the cubic K1242 and these lines: {2, 914}, {3, 2164}, {6, 1069}, {90, 1172}

X(46038) = X(1068)-isoconjugate of X(45127)
X(46038) = barycentric product X(i)*X(j) for these {i,j}: {90, 377}, {1448, 36626}, {20570, 37538}
X(46038) = barycentric quotient X(i)/X(j) for these {i,j}: {377, 20930}, {36082, 13395}, {37538, 46}, {43214, 21077}


X(46039) = X(4)X(804)∩X(99)X(511)

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

See Antreas Hatzipolakis and César Lozada, euclid 3240.

X(46039) lies on the cubic K289 and these lines: {4, 804}, {99, 511}, {1976, 41173}, {7417, 44420}

X(46039) = antigonal conjugate of the isotomic conjugate of X(35364)
X(46039) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(99)}} and {{A, B, C, X(114), X(511)}}
X(46039) = barycentric quotient X(230)/X(2782)
X(46039) = trilinear product X(1733)*X(2698)
X(46039) = trilinear quotient X(1733)/X(2782)


X(46040) = X(4)X(804)∩X(98)X(512)

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

See Antreas Hatzipolakis and César Lozada, euclid 3240.

X(46040) lies on Kiepert circumhyperbola and these lines: {2, 3569}, {4, 804}, {76, 2799}, {83, 16069}, {98, 512}, {115, 43665}, {262, 690}, {523, 43532}, {525, 1916}, {671, 8430}, {878, 12176}, {3399, 9479}, {6321, 35098}, {9420, 37991}, {23870, 43539}, {23871, 43538}, {39295, 40866}

X(46040) = reflection of X(43665) in X(115)
X(46040) = antigonal conjugate of X(43665)
X(46040) = antipode of X(43665) in Kiepert circumhyperbola
X(46040) = intersection, other than A, B, C, of circumconics Kiepert hyperbola and {{A, B, C, X(99), X(15412)}}
X(46040) = trilinear pole of the line {523, 44114}
X(46040) = barycentric product X(850)*X(2698)
X(46040) = barycentric quotient X(i)/X(j) for these (i, j): (523, 2782), (882, 16068)
X(46040) = trilinear product X(1577)*X(2698)
X(46040) = trilinear quotient X(1577)/X(2782)


X(46041) = X(1)X(1769)∩X(4)X(900)

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

See Antreas Hatzipolakis and César Lozada, euclid 3240.

X(46041) lies on Feuerbach circumhyperbola and these lines: {1, 1769}, {4, 900}, {7, 4453}, {8, 2804}, {9, 14418}, {11, 43728}, {80, 522}, {84, 2827}, {104, 953}, {108, 35011}, {521, 1320}, {1000, 6366}, {1389, 8674}, {2826, 3427}, {3577, 3887}, {3900, 24297}, {4926, 23959}, {7004, 23838}, {8058, 12641}, {8677, 38513}, {10090, 21189}, {10698, 42757}, {10738, 35097}, {13143, 35057}, {30198, 34256}

X(46041) = reflection of X(i) in X(j) for these (i, j): (10698, 42757), (43728, 11)
X(46041) = antigonal conjugate of X(43728)
X(46041) = antipode of X(43728) in Feuerbach circumhyperbola
X(46041) = intersection, other than A, B, C, of circumconics Feuerbach hyperbola and {{A, B, C, X(11), X(108)}}
X(46041) = barycentric product X(953)*X(4391)
X(46041) = barycentric quotient X(i)/X(j) for these (i, j): (513, 43043), (650, 952), (663, 2265), (953, 651)
X(46041) = trilinear product X(i)*X(j) for these {i, j}: {104, 37629}, {522, 953}
X(46041) = trilinear quotient X(i)/X(j) for these (i, j): (514, 43043), (522, 952), (650, 2265), (953, 109)


X(46042) = X(4)X(926)∩X(103)X(514)

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

See Antreas Hatzipolakis and César Lozada, euclid 3240.

X(46042) lies on these lines: {4, 926}, {103, 514}, {1002, 30691}

X(46042) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(103)}} and {{A, B, C, X(116), X(514)}}
X(46042) = trilinear product X(1734)*X(2724)
X(46042) = trilinear quotient X(1734)/X(2808)


X(46043) = X(4)X(2457)∩X(519)X(1293)

Barycentrics    2*a^10-8*(b+c)*a^9+(9*b^2+34*b*c+9*c^2)*a^8+(b+c)*(5*b^2-54*b*c+5*c^2)*a^7-(49*b^4+49*c^4-(89*b^2+2*b*c+89*c^2)*b*c)*a^6+(b+c)*(17*b^4+17*c^4+6*(17*b^2-43*b*c+17*c^2)*b*c)*a^5+(53*b^6+53*c^6-(235*b^4+235*c^4-93*(b+c)^2*b*c)*b*c)*a^4-(b^2-c^2)*(b-c)*(25*b^4+25*c^4+22*b*c*(2*b^2-7*b*c+2*c^2))*a^3-(b^2-c^2)^2*(13*b^4+13*c^4-b*c*(107*b^2-130*b*c+107*c^2))*a^2+(b^2-c^2)^2*(b+c)*(11*b^4+11*c^4-6*b*c*(9*b^2-11*b*c+9*c^2))*a+(b^2-c^2)^2*(b+c)^2*(-2*b^4-2*c^4+3*(3*b^2-4*b*c+3*c^2)*b*c) : :

See Antreas Hatzipolakis and César Lozada, euclid 3240.

X(46043) lies on these lines: {4, 2457}, {519, 1293}


X(46044) = X(4)X(14266)∩X(100)X(517)

Barycentrics    a*((b^2+c^2)*a^10-(b+c)^3*a^9-(4*b^4+4*c^4-(7*b^2+6*b*c+7*c^2)*b*c)*a^8+4*(b^4-3*b^2*c^2+c^4)*(b+c)*a^7+2*(3*b^6+3*c^6-(10*b^4+10*c^4-3*(b^2+3*b*c+c^2)*b*c)*b*c)*a^6-2*(b^2-c^2)*(b-c)*(3*b^4-8*b^2*c^2+3*c^4)*a^5-2*(2*b^6+2*c^6-(5*b^4+5*c^4-2*(2*b^2+7*b*c+2*c^2)*b*c)*b*c)*(b-c)^2*a^4+4*(b^2-c^2)^2*(b+c)*(b^4+c^4-(4*b^2-7*b*c+4*c^2)*b*c)*a^3+(b^6+c^6-(4*b^4+4*c^4-(19*b^2-34*b*c+19*c^2)*b*c)*b*c)*(b^2-c^2)^2*a^2-(b^2-c^2)^4*(b-c)^2*b*c-(b^2-c^2)^3*(b-c)*(b^4+c^4-2*(2*b-c)*(b-2*c)*b*c)*a) : :
X(46044) = X(12248)-4*X(33647)

See Antreas Hatzipolakis and César Lozada, euclid 3240.

X(46044) lies on these lines: {4, 14266}, {100, 517}, {104, 14115}, {108, 18838}, {119, 34151}, {901, 12775}, {912, 15343}, {2818, 3259}, {2829, 3025}, {6941, 31847}, {6950, 34583}, {12248, 33647}, {12776, 14511}, {15313, 18341}

X(46044) = reflection of X(i) in X(j) for these (i, j): (104, 14115), (34151, 119)


X(46045) = X(4)X(523)∩X(30)X(110)

Barycentrics    2*a^16-4*(b^2+c^2)*a^14-3*((b^2-c^2)^2-4*b^2*c^2)*a^12+(b^2+c^2)*(7*b^4-18*b^2*c^2+7*c^4)*a^10+(10*b^8+10*c^8-3*(13*b^4-20*b^2*c^2+13*c^4)*b^2*c^2)*a^8-2*(b^4-c^4)*(b^2-c^2)*(11*b^4-16*b^2*c^2+11*c^4)*a^6+(9*b^8+9*c^8+2*(7*b^4-16*b^2*c^2+7*c^4)*b^2*c^2)*(b^2-c^2)^2*a^4+(b^4-c^4)*(b^2-c^2)^3*(3*b^4-14*b^2*c^2+3*c^4)*a^2-(b^2-c^2)^6*(2*b^4+3*b^2*c^2+2*c^4) : :
X(46045) = 4*X(125)-3*X(40630), 3*X(403)-2*X(11657), 3*X(3845)-2*X(21316), 4*X(3850)-3*X(21315), 4*X(12068)-3*X(38700), 2*X(12079)-3*X(14644), 5*X(14934)-2*X(21317), 3*X(15035)-4*X(31945), 2*X(22104)-3*X(36518), 3*X(31378)-2*X(38726), X(36193)-3*X(38789)

See Antreas Hatzipolakis and César Lozada, euclid 3240.

X(46045) lies on these lines: {4, 523}, {30, 110}, {74, 3154}, {107, 403}, {113, 7471}, {125, 32417}, {146, 17511}, {186, 1624}, {476, 36169}, {546, 34209}, {1539, 16168}, {1553, 38791}, {2777, 3258}, {3845, 21316}, {3850, 21315}, {3853, 21269}, {5663, 10689}, {6070, 7687}, {10295, 16319}, {10733, 14480}, {10745, 37985}, {12068, 38700}, {12079, 14644}, {14611, 17702}, {14731, 36172}, {14983, 16334}, {15035, 31945}, {16111, 31379}, {18560, 38936}, {18809, 43911}, {22104, 36518}, {31378, 38726}, {34584, 38610}, {36161, 43831}, {36193, 38789}, {44990, 44992}

X(46045) = midpoint of X(i) and X(j) for these {i, j}: {110, 44967}, {146, 17511}, {477, 10721}, {7728, 20957}, {10733, 14480}, {14731, 36172}
X(46045) = reflection of X(i) in X(j) for these (i, j): (74, 3154), (476, 36169), (1553, 38791), (6070, 7687), (7471, 113), (10295, 16319), (16111, 31379), (21269, 3853), (34150, 4), (34153, 33505), (34209, 546), (36164, 3258)
X(46045) = perspector of the circumconic {{A, B, C, X(16080), X(30528)}}


X(46046) = X(4)X(512)∩X(99)X(511)

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

See Antreas Hatzipolakis and César Lozada, euclid 3240.

X(46046) lies on these lines: {4, 512}, {98, 14113}, {99, 511}, {112, 1692}, {114, 12833}, {13860, 41330}, {31848, 37446}

X(46046) = reflection of X(i) in X(j) for these (i, j): (98, 14113), (12833, 114), (13137, 31850)


X(46047) = X(4)X(525)∩X(112)X(1503)

Barycentrics    (2*a^20-4*(b^2+c^2)*a^18+3*(b^2+c^2)^2*a^16-(b^2+c^2)*(7*b^4-10*b^2*c^2+7*c^4)*a^14+(17*b^8+17*c^8-(3*b^4+26*b^2*c^2+3*c^4)*b^2*c^2)*a^12-(b^4-c^4)*(b^2-c^2)*(27*b^4+32*b^2*c^2+27*c^4)*a^10+(b^2-c^2)^2*(31*b^8+31*c^8+(63*b^4+76*b^2*c^2+63*c^4)*b^2*c^2)*a^8-(b^4-c^4)*(b^2-c^2)*(21*b^8+21*c^8+2*(10*b^4+11*b^2*c^2+10*c^4)*b^2*c^2)*a^6+(b^2-c^2)^2*(9*b^12+9*c^12+(17*b^8+17*c^8+(5*b^4+2*b^2*c^2+5*c^4)*b^2*c^2)*b^2*c^2)*a^4-5*(b^4-c^4)^3*(b^2-c^2)*(b^4+c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2*(2*b^8+2*c^8+(b^2+c^2)^2*b^2*c^2))*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :

See Antreas Hatzipolakis and César Lozada, euclid 3240.

X(46047) lies on these lines: {4, 525}, {112, 1503}, {1289, 2710}


X(46048) = X(2)X(98)∩X(3081)X(8029)

Barycentrics    (2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)^3 : :
X(46048) = X[2] - 3 X[34761]

X(46048) lies on the cubic K656 and these lines: {2, 98}, {3081, 8029}, {8030, 23616}, {14583, 23968}

X(46048) = X(542)^3
X(46048) = X(542)-Ceva conjugate of X(23967)
X(46048) = crosspoint of X(542) and X(23967)
X(46048) = barycentric product X(542)*X(23967)
X(46048) = barycentric quotient X(23967)/X(5641)


X(46049) = X(2)X(690)∩X(524)X(10190)

Barycentrics    (b^2 - c^2)^3*(-2*a^2 + b^2 + c^2)^3 : :
X(46049) = 50X[2] - 3 X[34763], 7 X[2] - 3 X[45294], 3 X[1648] - X[8029], 3 X[1649] - X[8030], 2 X[8029] - 3 X[14423], 7 X[34763] - X[45294]

X(46049) lies on the cubic K656 and these lines: {2, 690}, {524, 10190}, {1641, 33906}, {1648, 8029}, {1649, 8030}, {5468, 37880}, {11123, 33921}, {14443, 14444}

X(46049) = midpoint of X(14443) and X(14444)
X(46049) = reflection of X(14423) in X(1648)
X(46049) = X(690)^3
X(46049) = X(i)-Ceva conjugate of X(j) for these (i,j): {690, 23992}, {33915, 14444}, {33919, 14443}, {34763, 41176}
X(46049) = X(34539)-isoconjugate of X(36085)
X(46049) = crosspoint of X(i) and X(j) for these (i,j): {690, 23992}, {1648, 1649}, {14443, 33919}, {14444, 33915}
X(46049) = crosssum of X(691) and X(34539)
X(46049) = crossdifference of every pair of points on line {249, 2502}
X(46049) = barycentric product X(i)*X(j) for these {i,j}: {115, 33915}, {523, 14444}, {524, 14443}, {690, 23992}, {1648, 1649}, {2482, 33919}, {8029, 8030}, {22260, 23106}, {34763, 41176}
X(46049) = barycentric quotient X(i)/X(j) for these {i,j}: {351, 34539}, {8030, 31614}, {14443, 671}, {14444, 99}, {21906, 34574}, {23992, 892}, {33915, 4590}, {39689, 45773}, {41176, 34760}


X(46050) = X(2)X(900)∩X(519)X(10196)

Barycentrics    (2*a - b - c)^3*(b - c)^3 : :
X(46050) = X[2] - 3 X[34764], 7 X[2] - 3 X[45295], 3 X[1647] - X[6545], 5 X[1647] + X[40472], 3 X[6544] - X[8028], 5 X[6545] + 3 X[40472], 7 X[34764] - X[45295]

X(46050) lies on the cubic K656 and these lines: {2, 900}, {519, 10196}, {764, 1647}, {1644, 33905}, {1960, 40172}, {3251, 4543}, {6546, 33920}

X(46050) = isotomic conjugate of the isogonal conjugate of X(14637)
X(46050) = X(i)-Ceva conjugate of X(j) for these (i,j): {900, 35092}, {6550, 14442}
X(46050) = X(i)-isoconjugate of X(j) for these (i,j): {679, 6551}, {765, 39414}, {4618, 9268}, {4638, 5376}
X(46050) = crosspoint of X(i) and X(j) for these (i,j): {900, 35092}, {1647, 6544}, {6550, 14442}
X(46050) = crosssum of X(4638) and X(9268)
X(46050) = crossdifference of every pair of points on line {1252, 2226}
X(46050) = barycentric product X(i)*X(j) for these {i,j}: {76, 14637}, {519, 14442}, {900, 35092}, {1086, 33922}, {1639, 14027}, {1647, 6544}, {3762, 42084}, {4370, 6550}, {4530, 39771}, {4542, 30725}, {6545, 8028}, {8661, 36791}
X(46050) = barycentric quotient X(i)/X(j) for these {i,j}: {1015, 39414}, {1017, 6551}, {2087, 4618}, {3251, 5376}, {4370, 6635}, {4542, 4582}, {8028, 6632}, {8661, 2226}, {14442, 903}, {14637, 6}, {14835, 1023}, {33922, 1016}, {35092, 4555}, {42084, 3257}
X(46050) = X(900)^3


X(46051) = X(2)X(812)∩X(4375)X(27855)

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

X(46051) lies on the cubic K656 and these lines: {2, 812}, {4375, 27855}, {6545, 8027}, {6654, 8632}, {8028, 8031}

X(46051) = X(812)^3
X(46051) = X(812)-Ceva conjugate of X(35119)
X(46051) = crosspoint of X(812) and X(35119)
X(46051) = barycentric product X(i)*X(j) for these {i,j}: {812, 35119}, {4375, 27918}, {6545, 6652}, {27846, 27855}
X(46051) = barycentric quotient X(i)/X(j) for these {i,j}: {6652, 6632}, {35119, 4562}


X(46052) = X(2)X(1637)∩X(2395)X(43673)

Barycentrics    (b^2 - c^2)^3*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4)^3 : :
X(46052) = X[2] - 3 X[34765]

X(46052) lies on the cubic K656 and these lines: {2, 1637}, {2395, 43673}, {3081, 8030}, {8029, 23616}, {14966, 40173}

X(46052) = X(2799)^3
X(46052) = X(2799)-Ceva conjugate of X(35088)
X(46052) = crosspoint of X(2799) and X(35088)
X(46052) = barycentric product X(2799)*X(35088)
X(46052) = barycentric quotient X(i)/X(j) for these {i,j}: {868, 41173}, {35088, 2966}


X(46053) = X(2)X(14)∩X(16)X(115)

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

See Kousik Sett and César Lozada, euclid 3249.

In the construction described at X(46054), if the first Fermat point F1 is replaced by the second Fermat point F2, then triangle LaLbLc is homothetic to the 2nd isodynamic-Dao triangle at X(46053). (Randy Hutson, November 30, 2021)

X(46053) lies on these lines: {2, 14}, {3, 23004}, {4, 33389}, {6, 22510}, {13, 41094}, {16, 115}, {17, 6783}, {18, 3104}, {61, 1506}, {62, 3767}, {182, 11646}, {230, 36760}, {542, 37832}, {622, 25235}, {624, 6782}, {671, 13084}, {2023, 3107}, {2782, 36766}, {5238, 16002}, {5321, 20253}, {5469, 6775}, {5470, 10653}, {5472, 25560}, {5475, 36759}, {5479, 19107}, {5613, 6777}, {6117, 16249}, {6321, 9736}, {6672, 35918}, {6773, 6778}, {6781, 30559}, {7835, 42675}, {9117, 32909}, {9873, 33420}, {10612, 22856}, {10646, 21157}, {11087, 40696}, {11480, 13102}, {11488, 16529}, {11542, 22893}, {11602, 33813}, {14137, 16961}, {16644, 22997}, {16808, 41023}, {16809, 22512}, {16962, 41746}, {16963, 43276}, {21843, 30560}, {22797, 42919}, {22846, 43620}, {22998, 33476}, {25164, 36967}, {31709, 36968}, {31710, 45880}, {32628, 36301}, {33416, 36772}

X(46053) = midpoint of X(14) and X(16241)
X(46053) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (14, 16967, 6114), (14, 22490, 37835), (16, 22891, 115), (115, 6774, 16), (5460, 6109, 14), (5469, 16242, 6775), (6114, 6670, 16967), (6773, 18582, 6778), (6777, 16966, 5613)


X(46054) = X(2)X(13)∩X(15)X(115)

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

See Kousik Sett and César Lozada, euclid 3249.

From a post by Tran Quang Hung (ADGEOM #5186, February 28, 2019): Let ABC be a triangle with the first Fermat point F1. Let La, Lb, Lc be centers of Lester circles of triangles F1BC, F1CA, F1AB respectively. Then LaLbLc is an equilateral triangle. X(46054) is the homothetic center of LaLbLc and the 1st isodynamic-Dao triangle. (Randy Hutson, November 30, 2021)

X(46054) lies on these lines: {2, 13}, {3, 23005}, {4, 33388}, {6, 22511}, {14, 41098}, {15, 115}, {17, 3105}, {18, 6782}, {61, 3767}, {62, 1506}, {182, 11646}, {230, 36759}, {542, 37835}, {621, 25236}, {623, 6783}, {671, 13083}, {2023, 3106}, {5237, 16001}, {5238, 36772}, {5318, 20252}, {5469, 10654}, {5470, 6772}, {5471, 25559}, {5475, 36760}, {5478, 19106}, {5617, 6778}, {6116, 16250}, {6321, 9735}, {6671, 35917}, {6770, 6777}, {6781, 30560}, {7835, 42674}, {9115, 32907}, {9873, 33421}, {10611, 22900}, {10645, 21156}, {11082, 40695}, {11481, 13103}, {11489, 16530}, {11543, 22847}, {11603, 33813}, {14136, 16960}, {16645, 22998}, {16808, 22513}, {16809, 41022}, {16962, 43277}, {16963, 41745}, {21843, 30559}, {22796, 42918}, {22891, 43620}, {22997, 33477}, {25154, 36968}, {31709, 45879}, {31710, 36967}, {32627, 36300}, {36765, 42914}, {36782, 42092}

X(46054) = midpoint of X(13) and X(16242)
X(46054) = {X(i), X(j)}-harmonic conjugate of X(k) for these (i, j, k): (13, 16966, 6115), (13, 22489, 37832), (15, 22846, 115), (115, 6771, 15), (5459, 6108, 13), (5470, 16241, 6772), (6115, 6669, 16966), (6770, 18581, 6777), (6778, 16967, 5617), (11646, 38224, 46053)


X(46055) = X(14)X(36248)∩X(15)X(302)

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

See Kousik Sett and César Lozada, euclid 3249.

X(46055) lies on these lines: {14, 36248}, {15, 302}, {3457, 11581}

X(46055) = intersection, other than A, B, C, of circumconics {{A, B, C, X(14), X(302)}} and {{A, B, C, X(15), X(618)}}
X(46055) = barycentric quotient X(396)/X(34509)


X(46056) = X(13)X(36249)∩X(16)X(303)

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

See Kousik Sett and César Lozada, euclid 3249.

X(46056) lies on these lines: {13, 36249}, {16, 303}, {3458, 11582}

X(46056) = intersection, other than A, B, C, of circumconics {{A, B, C, X(13), X(303)}} and {{A, B, C, X(16), X(619)}}
X(46056) = barycentric quotient X(395)/X(34508)


X(46057) = X(4)X(51)∩X(520)X(6587)

Barycentrics    a^2*((b^2+c^2)*a^14+(b^4-4*b^2*c^2+c^4)*a^12-19*(b^4-c^4)*(b^2-c^2)*a^10+(45*b^4+44*b^2*c^2+45*c^4)*(b^2-c^2)^2*a^8-3*(b^4-c^4)*(b^2-c^2)*(15*b^4+2*b^2*c^2+15*c^4)*a^6+(19*b^8+19*c^8+2*b^2*c^2*(23*b^4-17*b^2*c^2+23*c^4))*(b^2-c^2)^2*a^4-(b^4-c^4)*(b^2-c^2)^3*(b^4+30*b^2*c^2+c^4)*a^2-(b^2-c^2)^4*(b^8+c^8-2*b^2*c^2*(3*b^4+11*b^2*c^2+3*c^4))) : :
Barycentrics    (SB+SC)*(S^4+(4*R^2-SW)*(48*R^2+SA-8*SW)*S^2+2*(8*R^2*(2*R^2-SW)+SW^2)*(3*SA-SW)*SA) : :

See Antreas Hatzipolakis and César Lozada, euclid 3264.

X(46057) lies on these lines: {4, 51}, {6, 34147}, {520, 6587}, {1192, 11589}, {6760, 11426}, {9786, 34109}, {11425, 12096}

X(46057) = crossdifference of every pair of points on line {X(1498), X(32320)}
X(46057) = perspector of the circumconic {{A, B, C, X(3346), X(15352)}}
X(46057) = inverse of X(14361) in polar circle


X(46058) = X(13)X(2992)∩X(14)X(14372)

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

See César Lozada, euclid 3265.

X(46058) lies on the cubic K261a and these lines: {13, 2992}, {14, 14372}, {15, 5682}, {62, 8919}, {619, 39377}, {3438, 6104}, {6116, 16459}

X(46058) = X(13)-Dao conjugate of-X(621)
X(46058) = Miquel point of X(2992)


X(46059) = X(13)X(14373)∩X(14)X(2993)

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

See César Lozada, euclid 3265.

X(46059) lies on the cubic K261b and these lines: {13, 14373}, {14, 2993}, {16, 5681}, {61, 8918}, {618, 39378}, {3439, 6105}, {6117, 16460}

X(46059) = X(14)-Dao conjugate of-X(622)
X(46059) = Miquel point of X(2993)


X(46060) = X(14)X(19776)∩X(16)X(3440)

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

See César Lozada, euclid 3265.

X(46060) lies on the cubic K261b and these lines: {14, 19776}, {16, 3440}, {18, 32461}, {618, 6110}, {3170, 36209}

X(46060) = X(15)-Dao conjugate of-X(616)
X(46060) = Miquel point of X(19776)


X(46061) = X(13)X(19777)∩X(15)X(3441)

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

See César Lozada, euclid 3265.

X(46061) lies on the cubic K261a and these lines: {13, 19777}, {15, 3441}, {17, 32460}, {619, 6111}, {3171, 36208}

X(46061) = X(16)-Dao conjugate of-X(617)
X(46061) = Miquel point of X(19777)


X(46062) = X(30)X(511)∩X(9409)X(11587)

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

See Antreas Hatzipolakis and César Lozada, euclid 3272.

X(46062) lies on these lines: {30, 511}, {9409, 11587}

X(46062) = isogonal conjugate of the anticomplement of X(35592)
X(46062) = complementary conjugate of X(35592)
X(46062) = circumtangential-isogonal conjugate of the anticomplement of X(35592)
X(46062) = crossdifference of every pair of points on line {X(6), X(39019)}
X(46062) = crosspoint of X(933) and X(18401)
X(46062) = X(4)-Ceva conjugate of-X(35592)
X(46062) = X(1)-complementary conjugate of-X(35592)


X(46063) = X(30)X(511)∩X(1301)X(32713)

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

See Antreas Hatzipolakis and César Lozada, euclid 3272.

X(46063) lies on these lines: {30, 511}, {1301, 32713}

X(46063) = crossdifference of every pair of points on line {X(6), X(39020)}
X(46063) = crosspoint of X(1301) and X(5897)


X(46064) = X(30)X(3484)∩X(54)X(3575)

Barycentrics    (a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2)*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2)*(2*a^10-4*(b^2+c^2)*a^8+(b^4+4*b^2*c^2+c^4)*a^6+(b^4-c^4)*(b^2-c^2)*a^4+(b^4+c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
Barycentrics    (S^2+SA*SB)*(S^2+SA*SC)*(SW*S^4+(2*SA^2+3*SB*SC-2*SW^2)*SA*S^2+3*(SB+SC)^2*SA^3) : :

See Antreas Hatzipolakis and César Lozada, euclid 3275.

X(46064) lies on these lines: {30, 3484}, {54, 3575}, {97, 37636}, {275, 1971}, {323, 401}, {858, 15958}, {933, 1503}, {1540, 18400}, {1614, 36842}, {2167, 17043}, {4993, 33629}, {11064, 18315}, {25044, 34224}, {25739, 40631}

X(46064) = reflection of X(1540) in X(18402)
X(46064) = crossdifference of every pair of points on line {X(51), X(34983)}
X(46064) = X(340)-Ceva conjugate of-X(40631)
X(46064) = X(1953)-isoconjugate-of-X(18401)
X(46064) = X(54)-reciprocal conjugate of-X(18401)
X(46064) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(1540)}} and {{A, B, C, X(275), X(525)}}
X(46064) = barycentric product X(95)*X(18400)
X(46064) = barycentric quotient X(54)/X(18401)
X(46064) = trilinear product X(2167)*X(18400)
X(46064) = trilinear quotient X(2167)/X(18401)


X(46065) = X(2)X(1032)∩X(393)X(459)

Barycentrics    (a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))*(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*(2*a^10-(b^2+c^2)*a^8-8*(b^2-c^2)^2*a^6+10*(b^4-c^4)*(b^2-c^2)*a^4-2*(b^2-c^2)^2*(b^4+6*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
Barycentrics    (S^2-2*SA*SB)*(S^2-2*SA*SC)*((10*SA+SB+SC)*S^4+2*(SA^2-6*SB*SC-SW^2)*SA*S^2-6*(SB+SC)^2*SA^3) : :

See Antreas Hatzipolakis and César Lozada, euclid 3275.

X(46065) lies on these lines: {2, 1032}, {4, 28785}, {64, 3089}, {253, 37643}, {393, 459}, {525, 3239}, {1073, 13567}, {1301, 1503}, {2184, 18634}, {6247, 41085}, {6393, 44326}, {6696, 39268}, {12241, 14379}, {26937, 31942}

X(46065) = X(610)-isoconjugate-of-X(5897)
X(46065) = X(64)-reciprocal conjugate of-X(5897)
X(46065) = barycentric product X(253)*X(15311)
X(46065) = barycentric quotient X(64)/X(5897)
X(46065) = trilinear product X(2184)*X(15311)
X(46065) = trilinear quotient X(2184)/X(5897)


X(46066) = EULER LINE INTERCEPT OF X(1511)X(18800)

Barycentrics    10*a^10-23*(b^2+c^2)*a^8+2*(2*b^4+35*b^2*c^2+2*c^4)*a^6+(b^2+c^2)*(22*b^4-73*b^2*c^2+22*c^4)*a^4-(14*b^8+14*c^8-b^2*c^2*(25*b^4-6*b^2*c^2+25*c^4))*a^2+(b^4-c^4)*(b^2-c^2)*(b^4-4*b^2*c^2+c^4) : :

See Antreas Hatzipolakis and César Lozada, euclid 3278.

X(46066) lies on these lines: {2, 3}, {1511, 18800}, {2793, 9126}, {6055, 14650}, {6699, 19662}, {7622, 18122}, {9775, 14653}, {10264, 11161}

X(46066) = midpoint of X(3) and X(14694)


X(46067) = EULER LINE INTERCEPT OF X(113)X(18800)

Barycentrics    4*a^10-2*(b^2+c^2)*a^8-(11*b^4-10*b^2*c^2+11*c^4)*a^6+(b^2+c^2)*(7*b^4-4*b^2*c^2+7*c^4)*a^4+(7*b^8+7*c^8-b^2*c^2*(35*b^4-48*b^2*c^2+35*c^4))*a^2+(b^4-c^4)*(b^2-c^2)*(-5*b^4+11*b^2*c^2-5*c^4) : :

See Antreas Hatzipolakis and César Lozada, euclid 3278.

X(46067) lies on these lines: {2, 3}, {113, 18800}, {115, 45331}, {265, 11161}, {2793, 18309}, {5655, 8593}, {6054, 10748}, {7615, 40879}, {7687, 19662}, {10113, 40915}

X(46067) = reflection of X(14694) in X(5)
X(46067) = {X(31693), X(31694)}-harmonic conjugate of X(868)


X(46068) = EULER LINE INTERCEPT OF X(10272)X(18800)

Barycentrics    2*a^10-19*(b^2+c^2)*a^8+2*(13*b^4+25*b^2*c^2+13*c^4)*a^6+(b^2-8*c^2)*(8*b^2-c^2)*(b^2+c^2)*a^4-(28*b^8+28*c^8-b^2*c^2*(95*b^4-102*b^2*c^2+95*c^4))*a^2+(b^4-c^4)*(b^2-c^2)*(11*b^4-26*b^2*c^2+11*c^4) : :

See Antreas Hatzipolakis and César Lozada, euclid 3278.

X(46068) lies on these lines: {2, 3}, {10272, 18800}, {13162, 22110}, {19662, 20304}


X(46069) = EULER LINE INTERCEPT OF X(16163)X(18800)

Barycentrics    14*a^10-25*(b^2+c^2)*a^8-(7*b^4-80*b^2*c^2+7*c^4)*a^6+(b^2+c^2)*(29*b^4-77*b^2*c^2+29*c^4)*a^4-(7*b^8+7*c^8+2*b^2*c^2*(5*b^4-21*b^2*c^2+5*c^4))*a^2+(b^4-c^4)*(b^2-c^2)*(-4*b^4+7*b^2*c^2-4*c^4) : :
X(46069) = 5*X(20)+4*X(23720)

See Antreas Hatzipolakis and César Lozada, euclid 3278.

X(46069) lies on these lines: {2, 3}, {74, 11161}, {2793, 14977}, {11177, 14654}, {16111, 40915}, {16163, 18800}, {19662, 37853}

X(46069) = reflection of X(4) in X(14694)
X(46069) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 8598, 4235), (35931, 35932, 4226)


X(46070) = EULER LINE INTERCEPT OF X(16165)X(18800)

Barycentrics    10*a^12-13*(b^2+c^2)*a^10-(19*b^4-48*b^2*c^2+19*c^4)*a^8+13*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^6+4*(2*b^8+2*c^8-b^2*c^2*(10*b^4-9*b^2*c^2+10*c^4))*a^4-(b^6+c^6)*(13*b^4-30*b^2*c^2+13*c^4)*a^2+(b^4-4*b^2*c^2+c^4)*(b^4-c^4)^2 : :

See Antreas Hatzipolakis and César Lozada, euclid 3278.

X(46070) lies on these lines: {2, 3}, {16165, 18800}


X(46071) = X(13)-CEVA CONJUGATE OF X(39153)

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

X(46071) lies on the cubic K261a and these lines: {13, 37773}, {14, 79}, {15, 3464}, {16, 18593}, {36, 6104}, {62, 2306}, {2153, 5620}, {11076, 14158}, {36211, 39151}

X(46071) = X(13)-Ceva conjugate of X(39153)
X(46071) = X(14)-isoconjugate of X(7343)
X(46071) = barycentric product X(i)*X(j) for these {i,j}: {13, 40612}, {299, 11076}, {17484, 39153}
X(46071) = barycentric quotient X(i)/X(j) for these {i,j}: {2152, 7343}, {3457, 11075}, {11076, 14}, {26744, 44688}, {39153, 21739}, {40612, 298}


X(46072) = ISOGONAL CONJUGATE OF X(5616)

Barycentrics    1/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 3*a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 + 3*a^2*c^4 + b^2*c^4 - c^6)*(3*a^2 - 3*b^2 - 3*c^2 - 2*Sqrt[3]*S)) : :

X(46072) lies on the cubics K561a and K439 and on these lines: {13, 5612}, {14, 1117}, {15, 1263}, {62, 3471}, {231, 1989}, {300, 11133}, {532, 11118}, {619, 11119}, {1291, 39424}, {8737, 10633}, {10677, 11139}, {11600, 34308}

X(46072) = isogonal conjugate of X(5616)
X(46072) = X(16)-cross conjugate of X(13)
X(46072) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5616}, {15, 1749}, {2151, 37779}, {2154, 40604}, {19306, 33529}
X(46072) = cevapoint of X(6138) and X(30452)
X(46072) = barycentric product X(i)*X(j) for these {i,j}: {13, 13582}, {299, 11071}, {300, 14579}, {471, 15392}, {3471, 36308}
X(46072) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5616}, {13, 37779}, {16, 40604}, {1263, 33529}, {1291, 17402}, {2153, 1749}, {3457, 11063}, {3471, 41887}, {6138, 8562}, {8737, 37943}, {8740, 2914}, {11071, 14}, {11081, 5612}, {13582, 298}, {14579, 15}, {15392, 40710}, {20578, 45147}, {23871, 45790}, {30452, 10413}, {36299, 10272}, {43704, 44718}


X(46073) = ISOGONAL CONJUGATE OF X(39152)

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

X(46073) lies on the cubics K058 and K261a and on these lines: {1, 62}, {10, 36931}, {13, 226}, {14, 80}, {15, 3465}, {16, 559}, {35, 6104}, {37, 101}, {55, 42616}, {65, 42680}, {203, 2801}, {519, 5240}, {1126, 11073}, {1251, 3383}, {3678, 7005}, {3961, 7088}, {3969, 40714}, {5995, 15168}, {7150, 10638}, {36737, 39150}, {37772, 39787}

X(46073) = isogonal conjugate of X(39152)
X(46073) = X(80)-Ceva conjugate of X(39151)
X(46073) = X(5357)-cross conjugate of X(42677)
X(46073) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39152}, {14, 36}, {15, 79}, {298, 6186}, {320, 3458}, {2151, 30690}, {2154, 3218}, {3179, 42680}, {4707, 5994}, {5240, 33654}, {7051, 36932}, {8738, 22128}, {17923, 36297}, {20565, 34394}, {21828, 23896}, {33653, 37773}, {39150, 41225}
X(46073) = cevapoint of X(35) and X(5357)
X(46073) = trilinear product X(i)*X(j) for these {i,j}: {13, 35}, {16, 80}, {299, 6187}, {319, 3457}, {559, 19551}, {2152, 18359}, {2153, 3219}, {5357, 14358}, {5995, 7265}, {20566, 34395}
X(46073) = barycentric product X(i)*X(j) for these {i,j}: {13, 3219}, {16, 18359}, {299, 2161}, {300, 2174}, {319, 2153}, {471, 1807}, {559, 7026}, {2003, 44690}, {2006, 44689}, {2152, 20566}, {3457, 33939}, {6198, 40709}, {33655, 40714}, {39153, 41226}
X(46073) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39152}, {13, 30690}, {16, 3218}, {299, 20924}, {1807, 40710}, {2152, 36}, {2153, 79}, {2161, 14}, {2174, 15}, {3219, 298}, {3457, 2160}, {5995, 13486}, {6187, 2154}, {6198, 470}, {7126, 36932}, {8740, 1870}, {10638, 5240}, {11081, 39153}, {14975, 8739}, {18359, 301}, {21824, 30465}, {33655, 554}, {34395, 7113}, {35194, 33529}, {36296, 7100}, {36910, 44691}, {42624, 39150}, {44689, 32851}
X(46073) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11789, 202}, {1, 19551, 39151}, {37, 24929, 46077}


X(46074) = X(13)-CEVA CONJUGATE OF X(14)

Barycentrics    (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(2*(5*a^8 - 14*a^6*b^2 + 12*a^4*b^4 - 2*a^2*b^6 - b^8 - 14*a^6*c^2 + 17*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 4*b^6*c^2 + 12*a^4*c^4 - 7*a^2*b^2*c^4 - 6*b^4*c^4 - 2*a^2*c^6 + 4*b^2*c^6 - c^8) + 4*Sqrt[3]*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*S) : :
X(46074) = X[14] - 4 X[11549], X[14] + 2 X[15743], 2 X[11549] + X[15743]

X(46074) lies on the cubic K261a and these lines: {13, 14993}, {14, 16}, {15, 1138}, {17, 32460}, {62, 8015}, {186, 8738}, {231, 1989}, {476, 2381}, {523, 16529}, {532, 11092}, {533, 23896}, {3129, 14583}, {3411, 11556}, {5612, 18285}, {5627, 11601}, {5899, 11141}, {6116, 37943}, {6672, 11120}, {8918, 42157}, {11300, 43086}, {16962, 18776}, {21311, 37949}, {21360, 40710}, {22827, 36758}, {36209, 37496}

X(46074) = midpoint of X(15743) and X(36210)
X(46074) = reflection of X(i) in X(j) for these {i,j}: {14, 36210}, {36210, 11549}
X(46074) = X(13)-Ceva conjugate of X(14)
X(46074) = barycentric product X(8173)*X(8836)
X(46074) = barycentric quotient X(11088)/X(8456)
X(46074) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 45779, 36968}, {16, 11085, 14}, {395, 11582, 14}, {10218, 36970, 14}, {11549, 15743, 14}, {15442, 40579, 14}


X(46075) = X(13)X(79)∩X(14)X(37772)

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

X(46075) lies on the cubic K261b and these lines: {13, 79}, {14, 37772}, {15, 18593}, {16, 3464}, {36, 6105}, {61, 3336}, {2154, 5620}, {11076, 14158}, {36210, 39150}

X(46075) = X(14)-Ceva conjugate of X(39152)
X(46075) = X(13)-isoconjugate of X(7343)
X(46075) = barycentric product X(i)*X(j) for these {i,j}: {14, 40612}, {298, 11076}, {17484, 39152}
X(46075) = barycentric quotient X(i)/X(j) for these {i,j}: {2151, 7343}, {3458, 11075}, {11076, 13}, {26744, 44689}, {39152, 21739}, {40612, 299}


X(46076) = ISOGONAL CONJUGATE OF X(5612)

Barycentrics    1/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 3*a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 + 3*a^2*c^4 + b^2*c^4 - c^6)*(3*a^2 - 3*b^2 - 3*c^2 + 2*Sqrt[3]*S)) : :

X(46076) lies on the cubics K261b and K439 and on these lines: {13, 1117}, {14, 5616}, {16, 1263}, {61, 3471}, {231, 1989}, {301, 11132}, {533, 11117}, {618, 11120}, {1291, 39425}, {8738, 10632}, {10678, 11138}, {11601, 34308}

X(46076) = isogonal conjugate of X(5612)
X(46076) = X(15)-cross conjugate of X(14)
X(46076) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5612}, {16, 1749}, {2152, 37779}, {2153, 40604}, {19306, 33530}
X(46076) = cevapoint of X(6137) and X(30453)
X(46076) = barycentric product X(i)*X(j) for these {i,j}: {14, 13582}, {298, 11071}, {301, 14579}, {470, 15392}, {3471, 36311}
X(46076) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5612}, {14, 37779}, {15, 40604}, {1263, 33530}, {1291, 17403}, {2154, 1749}, {3458, 11063}, {3471, 41888}, {6137, 8562}, {8738, 37943}, {8739, 2914}, {11071, 13}, {11086, 5616}, {13582, 299}, {14579, 16}, {15392, 40709}, {20579, 45147}, {23870, 45790}, {30453, 10413}, {36298, 10272}, {43704, 44719}


X(46077) = X(13)-ISOCONJUGATE OF X(36)

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

X(46077) lies on the cubics K058 and K261b and on these lines: {1, 61}, {10, 36930}, {13, 80}, {14, 226}, {15, 1082}, {16, 3465}, {35, 6105}, {37, 101}, {65, 42677}, {202, 2801}, {519, 5239}, {1126, 11072}, {3295, 42624}, {3376, 33653}, {3678, 7006}, {3961, 7089}, {3969, 40713}, {5994, 15168}, {36738, 39151}, {37773, 39788}

X(46077) = isogonal conjugate of X(39153)
X(46077) = X(80)-Ceva conjugate of X(39150)
X(46077) = X(5353)-cross conjugate of X(42680)
X(46077) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39153}, {13, 36}, {16, 79}, {299, 6186}, {320, 3457}, {1081, 7127}, {1251, 37772}, {2152, 30690}, {2153, 3218}, {2306, 5239}, {3179, 39151}, {4707, 5995}, {8737, 22128}, {17923, 36296}, {19373, 36933}, {20565, 34395}, {21828, 23895}, {41225, 42677}
X(46077) = cevapoint of X(35) and X(5353)
X(46077) = trilinear product X(i)*X(j) for these {i,j}: {14, 35}, {15, 80}, {298, 6187}, {319, 3458}, {1082, 7126}, {2151, 18359}, {2154, 3219}, {2307, 7043}, {5353, 14359}, {5994, 7265}, {20566, 34394}
X(46077) = barycentric product X(i)*X(j) for these {i,j}: {14, 3219}, {15, 18359}, {298, 2161}, {301, 2174}, {319, 2154}, {470, 1807}, {1082, 7043}, {2003, 44691}, {2006, 44688}, {2151, 20566}, {3458, 33939}, {6198, 40710}, {7052, 40713}, {39152, 41226}
X(46077) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39153}, {14, 30690}, {15, 3218}, {298, 20924}, {1250, 5239}, {1807, 40709}, {2151, 36}, {2154, 79}, {2161, 13}, {2174, 16}, {2307, 37772}, {3219, 299}, {3458, 2160}, {5994, 13486}, {6187, 2153}, {6198, 471}, {7052, 1081}, {8739, 1870}, {11086, 39152}, {14975, 8740}, {18359, 300}, {19551, 36933}, {21824, 30468}, {34394, 7113}, {35194, 33530}, {36297, 7100}, {36910, 44690}, {42624, 42677}, {44688, 32851}
X(46077) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7126, 39150}, {1, 7150, 7052}, {1, 11752, 203}, {37, 24929, 46073}, {7052, 7126, 7150}, {7052, 7150, 39150}


X(46078) = X(14)-CEVA CONJUGATE OF X(13)

Barycentrics    (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(2*(5*a^8 - 14*a^6*b^2 + 12*a^4*b^4 - 2*a^2*b^6 - b^8 - 14*a^6*c^2 + 17*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 4*b^6*c^2 + 12*a^4*c^4 - 7*a^2*b^2*c^4 - 6*b^4*c^4 - 2*a^2*c^6 + 4*b^2*c^6 - c^8) - 4*Sqrt[3]*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*S) : :
X(46078) = X[13] - 4 X[11537], X[13] + 2 X[11586], 2 X[11537] + X[11586]

X(46078) lies on the cubic K261b and these lines: {13, 15}, {14, 14993}, {16, 1138}, {18, 32461}, {61, 8014}, {186, 8737}, {231, 1989}, {476, 2380}, {523, 16530}, {532, 23895}, {533, 11078}, {3130, 14583}, {3412, 11555}, {5616, 18285}, {5627, 11600}, {5899, 11142}, {6117, 37943}, {6671, 11119}, {8919, 42158}, {11299, 43085}, {16963, 18777}, {21310, 37949}, {21359, 40709}, {22826, 36757}, {36208, 37496}

X(46078) = midpoint of X(11586) and X(36211)
X(46078) = reflection of X(i) in X(j) for these {i,j}: {13, 36211}, {36211, 11537}
X(46078) = X(14)-Ceva conjugate of X(13)
X(46078) = barycentric product X(8172)*X(8838)
X(46078) = barycentric quotient X(11083)/X(8446)
X(46078) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 45778, 36967}, {15, 11080, 13}, {396, 11581, 13}, {10217, 36969, 13}, {11537, 11586, 13}, {15441, 40578, 13}


X(46079) = X(16)X(3815)∩X(381)X(396)

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

See Stanley Rabinowitz and César Lozada, euclid 3337.

X(46079) lies on these lines: {16, 3815}, {182, 46080}, {381, 396}, {597, 11543}, {624, 3849}, {3054, 36759}, {5306, 46054}, {5478, 42138}, {5480, 11542}, {6771, 18907}, {7684, 42117}, {9996, 42627}, {10613, 43457}, {11480, 44465}, {22846, 22856}, {22861, 23302}


X(46080) = X(15)X(3815)∩X(381)X(395)

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

See Elias M Hagos and César Lozada, euclid 3337.

X(46080) lies on these lines: {15, 3815}, {182, 46079}, {381, 395}, {597, 11542}, {623, 3849}, {3054, 36760}, {5306, 46053}, {5479, 42135}, {5480, 11543}, {6774, 18907}, {7685, 42118}, {9996, 42628}, {10614, 43457}, {11481, 44461}, {22891, 22900}, {22907, 23303}


X(46081) = ISOGONAL CONJUGATE OF X(15034)

Barycentrics    (2*a^8-(3*b^2+c^2)*a^6+(2*b^4+9*b^2*c^2-9*c^4)*a^4-(b^2-c^2)*(3*b^4-6*b^2*c^2+13*c^4)*a^2+(2*b^2+5*c^2)*(b^2-c^2)^3)*(2*a^8-(b^2+3*c^2)*a^6-(9*b^4-9*b^2*c^2-2*c^4)*a^4+(b^2-c^2)*(13*b^4-6*b^2*c^2+3*c^4)*a^2-(5*b^2+2*c^2)*(b^2-c^2)^3) : :
X(46081) = 3*X(125)-X(41522), X(477)-5*X(12079), 3*X(1138)-7*X(3154), 9*X(6070)-X(10990)

See Antreas Hatzipolakis and César Lozada, euclid 3303.

X(46081) lies on these lines: {5, 9214}, {30, 6070}, {125, 41522}, {140, 15454}, {477, 12079}, {1138, 3154}, {1990, 12003}, {3471, 35018}, {3850, 14254}, {17986, 32230}

X(46081) = isogonal conjugate of X(15034)
X(46081) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(9139)}} and {{A, B, C, X(4), X(30)}}


X(46082) = ISOGONAL CONJUGATE OF X(39229)

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

See Antreas Hatzipolakis and César Lozada, euclid 3303.

X(46082) lies on Kiepert circumhyperbola, cubics K043, K599, K811 and these lines: {5, 542}, {671, 39229}, {7608, 39230}

X(46082) = isogonal conjugate of X(39229)


X(46083) = ISOGONAL CONJUGATE OF X(39230)

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

See Antreas Hatzipolakis and César Lozada, euclid 3303.

X(46083) lies on Kiepert circumhyperbola, cubics K043, K599, K811 and these lines: {5, 542}, {671, 39230}, {7608, 39229}

X(46083) = isogonal conjugate of X(39230)


X(46084) = X(3)X(143)∩X(113)X(3850)

Barycentrics    a^2*(2*a^4-5*(b^2+c^2)*a^2+3*(b^2-c^2)^2)*(a^4+b^4-3*b^2*c^2+c^4-2*(b^2+c^2)*a^2) : :
X(46084) = X(3)+5*X(1173), X(3)-5*X(15047), 9*X(3)-5*X(33542), 9*X(1173)+X(33542), 5*X(2889)-17*X(3533), 4*X(3850)+5*X(34564), 4*X(10095)-X(11817), 9*X(15047)-X(33542)

See Antreas Hatzipolakis and César Lozada, euclid 3304.

X(46084) lies on these lines: {2, 34483}, {3, 143}, {5, 11225}, {110, 34567}, {113, 3850}, {141, 5097}, {206, 15580}, {547, 1209}, {578, 33556}, {960, 33179}, {1147, 15026}, {1199, 5609}, {1493, 5943}, {1511, 5462}, {2883, 3845}, {2889, 3533}, {3519, 7605}, {3628, 34565}, {3853, 44866}, {4550, 6102}, {5041, 11672}, {5067, 45794}, {5640, 9704}, {5876, 33537}, {6101, 15004}, {6644, 15748}, {8718, 14483}, {10095, 11817}, {10627, 15018}, {10960, 35771}, {10962, 35770}, {11597, 13365}, {12041, 35478}, {12834, 14627}, {13596, 13630}, {14449, 44107}, {16239, 41586}, {18583, 34826}, {22949, 33541}, {23409, 24981}, {32068, 33332}, {34199, 43817}

X(46084) = midpoint of X(1173) and X(15047)
X(46084) = complement of X(34483)
X(46084) = complementary conjugate of the complement of X(34484)
X(46084) = inverse of X(34567) in Stammler hyperbola
X(46084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1199, 18874, 5609), (10095, 34545, 36153), (12834, 14627, 32205)


X(46085) = X(3)X(125)∩X(68)X(110)

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))*((b^2+c^2)*a^6-(b^4+c^4)*a^4-(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^4)*(-a^2+b^2+c^2) : :
X(46085) = 3*X(154)-X(12419), X(155)-3*X(14643), X(265)-3*X(14852), X(2931)+3*X(14852), 2*X(5448)-3*X(36518), 2*X(12038)-3*X(38793), X(12118)-3*X(15035), X(12302)-3*X(15061), X(12310)+3*X(38724), X(12319)-5*X(15081), X(12429)+3*X(32609), X(15133)-3*X(38724), 4*X(20191)-3*X(38727), 3*X(23515)+X(32263), 3*X(23515)-2*X(33547), X(32263)+2*X(33547), 5*X(38795)-2*X(41597)

See Antreas Hatzipolakis and César Lozada, euclid 3304.

X(46085) lies on the bicevian conic of X(2) and X(110) and on these lines: {2, 5504}, {3, 125}, {5, 11746}, {6, 12900}, {26, 41674}, {30, 11598}, {52, 45177}, {68, 110}, {74, 44440}, {113, 403}, {140, 22966}, {141, 14984}, {154, 12419}, {155, 14643}, {184, 10111}, {206, 542}, {343, 12358}, {468, 20771}, {511, 15116}, {539, 5642}, {541, 11744}, {567, 43839}, {568, 5448}, {960, 12261}, {974, 15760}, {1112, 41587}, {1147, 5972}, {1209, 10170}, {1493, 9820}, {1511, 44452}, {2072, 45780}, {2777, 7689}, {2883, 5663}, {3549, 13198}, {3564, 6593}, {3581, 13202}, {4550, 7687}, {5181, 34382}, {5654, 37644}, {6723, 15115}, {7728, 12163}, {8542, 12596}, {9826, 13567}, {10018, 30714}, {10020, 32391}, {10055, 10091}, {10071, 10088}, {10113, 34826}, {10264, 15151}, {10539, 32539}, {10639, 10663}, {10640, 10664}, {10733, 23293}, {10960, 12891}, {10962, 12892}, {11585, 41673}, {11672, 39021}, {12022, 12038}, {12041, 44158}, {12118, 15035}, {12140, 18474}, {12295, 18560}, {12319, 15081}, {12429, 32609}, {13383, 15647}, {13561, 23328}, {14915, 41603}, {15051, 26913}, {15088, 16254}, {15114, 23315}, {16003, 17854}, {19061, 19111}, {19062, 19110}, {20299, 34350}, {32227, 37453}, {37197, 37489}, {38795, 41597}

X(46085) = midpoint of X(i) and X(j) for these {i, j}: {68, 110}, {265, 2931}, {7728, 12163}, {9927, 12893}, {12121, 12293}, {12310, 15133}
X(46085) = reflection of X(i) in X(j) for these (i, j): (26, 41674), (125, 5449), (1147, 5972), (12041, 44158), (12901, 6699), (15115, 6723), (15647, 13383), (19479, 7687), (23306, 20304), (23315, 15114)
X(46085) = complement of X(5504)
X(46085) = complementary conjugate of X(10257)
X(46085) = center of the circumconic {{A, B, C, X(68), X(110)}}
X(46085) = inverse of X(38534) in Stammler hyperbola
X(46085) = antipode of X(1147) in bicevian conic of X(2) and X(110)
X(46085) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(1986)}} and {{A, B, C, X(125), X(16221)}}
X(46085) = barycentric product X(2072)*X(3580)
X(46085) = barycentric quotient X(2072)/X(2986)
X(46085) = trilinear product X(1725)*X(2072)
X(46085) = trilinear quotient X(i)/X(j) for these (i, j): (1725, 38534), (2072, 36053)
X(46085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (113, 12828, 11557), (265, 37638, 6699), (403, 12825, 113), (2931, 14852, 265), (12310, 38724, 15133)


X(46086) = X(2)X(38861)∩X(468)X(14052)

Barycentrics    (a^4 b^2-2 a^2 b^4+b^6+a^4 c^2-2 a^2 c^4+c^6) (2 a^8-2 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^4-6 b^4 c^4+2 a^2 c^6+4 b^2 c^6-c^8) : :
Barycentrics   (S^2 (6 R^2-2 SA-SW)+SA^2 SW) (-SB SC SW^2+S^2 (6 R^2 SA+4 SB SC-10 R^2 SW-SA SW+2 SW^2)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3319.

X(46086) lies on these lines: {2,38861}, {468,14052}, {1656,34810}, {2072,36519}, {3447,16760}

X(46086) = complement of X(46087)
X(46086) = complement of the isogonal conjugate of X(1112)
X(46086) = complementary conjugate of X(13416)
X(46086) = X(i)-complementary conjugate of X(j) for these (i,j): (1,13416), (1112,10)


X(46087) = ISOGONAL CONJUGATE OF X(1112)

Barycentrics    (a^2-b^2-c^2) (a^6+b^6-2 a^4 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+b^4 c^2-2 b^2 c^4+c^6) : :
Barycentrics   SA (S^2 (6 R^2-2 SC-SW)+SC^2 SW) (2 S^2 (3 R^2+SA+SC-2 SW)+(SA-SW) (SC-SW) SW) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3319.

X(46087) lies on these lines: {2,38861}, {3,39193}, {50,230}, {186,30716}, {476,3447}, {523,14060}, {631,14385}, {2165,36163}, {3564,5622}, {4558,34978}, {6036,40118}, {34178,38701}

X(46087) = reflection of X(30717) in the Euler line
X(46087) = isogonal conjugate of X(1112)
X(46087) = anticomplement of X(46086)
X(46087) = anticomplement of the complementary conjugate of X(13416)
X(46087) = X(i)-isoconjugate of X(j) for these (i,j): (19,34990), (158,23217), (2333,16734)
X(46087) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {3,34990}, {6,1112}, {577,23217}, {1444,16734}
X(46087) = cevapoint of X(i)and X(j) for these {i,j}: {3,125}, {647,34982}
X(46087) = barycentric quotient X(i)/X(j) for these {i,j}: {3,34990}, {577,23217}, {1444,16734}
X(46087) = trilinear quotient X(i)/X(j) for these (i,j): (63,34990), (255,23217)


X(46088) = X(50)X(647)∩X(97)X(2525)

Barycentrics    a^4*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2)*(-a^2+b^2+c^2)^2*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2)*(b^2-c^2) : :
Trilinears    sin 2A sec(B - C) (tan B - tan C) : :

See Antreas Hatzipolakis and César Lozada, euclid 3343.

X(46088) lies on these lines: {50, 647}, {97, 2525}, {571, 16040}, {577, 17434}, {933, 23964}, {1637, 15422}, {5063, 14346}, {11077, 32663}, {14586, 32640}, {15412, 44427}, {30451, 39201}

X(46088) = isogonal conjugate of the polar conjugate of X(23286)
X(46088) = crossdifference of every pair of points on line {X(5), X(324)}
X(46088) = crosspoint of X(i) and X(j) for these (i, j): {54, 16813}, {97, 15958}
X(46088) = crosssum of X(i) and X(j) for these (i, j): {5, 17434}, {53, 23290}, {324, 18314}, {525, 40684}
X(46088) = X(933)-Ceva conjugate of-X(184)
X(46088) = X(i)-Dao conjugate of-X(j) for these (i, j): (125, 324), (130, 36412), (525, 15415), (1147, 14570)
X(46088) = X(i)-isoconjugate-of-X(j) for these {i, j}: {5, 823}, {53, 811}, {92, 35360}, {107, 14213}
X(46088) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (54, 6528), (97, 6331), (184, 35360), (520, 311)
X(46088) = perspector of the circumconic {{A, B, C, X(54), X(14533)}}
X(46088) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(44886)}} and {{A, B, C, X(50), X(577)}}
X(46088) = barycentric product X(i)*X(j) for these {i, j}: {3, 23286}, {32, 15414}, {54, 520}, {95, 39201}, {97, 647}, {125, 15958}
X(46088) = barycentric quotient X(i)/X(j) for these (i, j): (54, 6528), (97, 6331), (184, 35360), (520, 311), (577, 14570), (647, 324)
X(46088) = trilinear product X(i)*X(j) for these {i, j}: {48, 23286}, {54, 822}, {97, 810}, {255, 2623}, {520, 2148}, {560, 15414}
X(46088) = trilinear quotient X(i)/X(j) for these (i, j): (48, 35360), (54, 823), (97, 811), (255, 14570), (520, 14213), (577, 2617)
X(46088) = {X(2623), X(23286)}-harmonic conjugate of X(647)


X(46089) = X(54)X(186)∩X(125)X(252)

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

See Antreas Hatzipolakis and César Lozada, euclid 3343.

X(46089) lies on these lines: {3, 15958}, {50, 14533}, {54, 186}, {97, 1216}, {125, 252}, {184, 20574}, {185, 1157}, {933, 1614}, {1141, 21659}, {1594, 46064}, {2169, 22342}, {3459, 24862}, {3484, 3520}, {6146, 40631}, {14585, 14586}, {19210, 22115}

X(46089) = X(6)-Dao conjugate of-X(45793)
X(46089) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 1087}, {19, 45793}, {53, 14213}, {92, 36412}
X(46089) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 45793), (48, 1087), (54, 324), (97, 311)
X(46089) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(50)}} and {{A, B, C, X(4), X(389)}}
X(46089) = barycentric product X(i)*X(j) for these {i, j}: {54, 97}, {95, 14533}, {275, 19210}, {2167, 2169}
X(46089) = barycentric quotient X(i)/X(j) for these (i, j): (3, 45793), (48, 1087), (54, 324), (97, 311), (184, 36412), (217, 23607)
X(46089) = trilinear product X(i)*X(j) for these {i, j}: {54, 2169}, {97, 2148}, {2167, 14533}, {2190, 19210}
X(46089) = trilinear quotient X(i)/X(j) for these (i, j): (3, 1087), (48, 36412), (63, 45793), (97, 14213), (603, 41279), (2148, 53)


X(46090) = X(54)X(74)∩X(417)X(15958)

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

See Antreas Hatzipolakis and César Lozada, euclid 3343.

X(46090) lies on these lines: {54, 74}, {417, 15958}, {3043, 34980}, {8884, 10152}, {11815, 13489}, {14533, 14586}, {15781, 44715}, {19189, 32715}, {25044, 39174}, {40353, 43753}

X(46090) = X(1147)-Dao conjugate of-X(1568)
X(46090) = X(i)-isoconjugate-of-X(j) for these {i, j}: {5, 1784}, {53, 14206}, {158, 1568}, {324, 2173}
X(46090) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (74, 324), (97, 3260), (577, 1568)
X(46090) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(3520)}} and {{A, B, C, X(4), X(185)}}
X(46090) = barycentric product X(i)*X(j) for these {i, j}: {54, 14919}, {74, 97}, {95, 18877}, {1494, 14533}, {2167, 35200}, {2169, 2349}
X(46090) = barycentric quotient X(i)/X(j) for these (i, j): (74, 324), (97, 3260), (577, 1568), (2148, 1784), (2169, 14206)
X(46090) = trilinear product X(i)*X(j) for these {i, j}: {54, 35200}, {74, 2169}, {97, 2159}, {2148, 14919}, {2167, 18877}
X(46090) = trilinear quotient X(i)/X(j) for these (i, j): (54, 1784), (97, 14206), (255, 1568), (822, 14391), (2148, 1990), (2159, 53)


X(46091) = (name pending)

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

See Antreas Hatzipolakis and César Lozada, euclid 3343.

X(46091) lies on this line: {54, 3431}

X(46091) = X(97)-reciprocal conjugate of-X(44135)
X(46091) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(13139)}} and {{A, B, C, X(54), X(14533)}}
X(46091) = barycentric product X(97)*X(3431)
X(46091) = barycentric quotient X(97)/X(44135)
X(46091) = trilinear product X(2169)*X(3431)
X(46091) = trilinear quotient X(2169)/X(381)


X(46092) = (name pending)

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

See Antreas Hatzipolakis and César Lozada, euclid 3343.

X(46092) lies on this line: {54, 9786}

X(46092) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(32534)}} and {{A, B, C, X(54), X(14533)}}
X(46092) = barycentric product X(97)*X(14528)
X(46092) = trilinear product X(2169)*X(14528)
X(46092) = trilinear quotient X(2169)/X(3091)


X(46093) = X(3)X(6663)∩X(23195)X(39071)

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

See Antreas Hatzipolakis and César Lozada, euclid 3346.

X(46093) lies on these lines: {3, 6663}, {23195, 39071}, {37084, 38999}

X(46093) = X(2)-Ceva conjugate of-X(32320)
X(46093) = X(i)-complementary conjugate of-X(j) for these (i, j): (31, 32320), (810, 36412)
X(46093) = X(520)-Dao conjugate of-X(6662)
X(46093) = X(1614)-reciprocal conjugate of-X(34538)
X(46093) = center of the circumconic {{A, B, C, X(3), X(95)}}
X(46093) = barycentric quotient X(1614)/X(34538)
X(46093) = trilinear quotient X(1614)/X(24021)


X(46094) = X(125)X(23195)∩X(160)X(7710)

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

See Antreas Hatzipolakis and César Lozada, euclid 3348.

X(46094) lies on the Johnson circumconic of the medial triangle and on these lines: {2, 23181}, {3, 36952}, {125, 23195}, {160, 7710}, {418, 2972}, {684, 9420}, {5664, 42731}, {5866, 39100}, {13367, 17423}, {14713, 15577}, {19161, 36790}, {22089, 33813}

X(46094) = complement of X(35098)
X(46094) = X(2)-Ceva conjugate of-X(3289)
X(46094) = X(31)-complementary conjugate of-X(3289)
X(46094) = center of the circumconic {{A, B, C, X(3), X(99)}}


X(46095) = X(2972)X(22080)∩X(10167)X(22390)

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

See Antreas Hatzipolakis and César Lozada, euclid 3348 and euclid 3354.

X(46095) lies on these lines: {2972, 22080}, {10167, 22390}, {13367, 39006}

X(46095) = center of the circumconic {{A, B, C, X(3), X(101)}}


X(46096) = X(6)X(35088)∩X(325)X(44099)

Barycentrics    2*a^16 - 6*a^14*b^2 + 8*a^12*b^4 - 4*a^10*b^6 - 7*a^8*b^8 + 16*a^6*b^10 - 16*a^4*b^12 + 10*a^2*b^14 - 3*b^16 - 6*a^14*c^2 + 12*a^12*b^2*c^2 - 12*a^10*b^4*c^2 + 12*a^8*b^6*c^2 - 16*a^6*b^8*c^2 + 20*a^4*b^10*c^2 - 18*a^2*b^12*c^2 + 8*b^14*c^2 + 8*a^12*c^4 - 12*a^10*b^2*c^4 + 8*a^8*b^4*c^4 - 2*a^6*b^6*c^4 - 14*a^4*b^8*c^4 + 20*a^2*b^10*c^4 - 16*b^12*c^4 - 4*a^10*c^6 + 12*a^8*b^2*c^6 - 2*a^6*b^4*c^6 + 20*a^4*b^6*c^6 - 12*a^2*b^8*c^6 + 24*b^10*c^6 - 7*a^8*c^8 - 16*a^6*b^2*c^8 - 14*a^4*b^4*c^8 - 12*a^2*b^6*c^8 - 26*b^8*c^8 + 16*a^6*c^10 + 20*a^4*b^2*c^10 + 20*a^2*b^4*c^10 + 24*b^6*c^10 - 16*a^4*c^12 - 18*a^2*b^2*c^12 - 16*b^4*c^12 + 10*a^2*c^14 + 8*b^2*c^14 - 3*c^16 : :

X(46096) lies on the Vijay orthic-medial conic and these lines: {6, 35088}, {325, 44099}, {30717, 43705}


X(46097) = X(6)X(35088)∩X(297)X(8779)

Barycentrics    2*a^18 - 4*a^16*b^2 + 2*a^14*b^4 - 4*a^12*b^6 + 9*a^10*b^8 - 7*a^8*b^10 + 4*a^6*b^12 - 2*a^4*b^14 - a^2*b^16 + b^18 - 4*a^16*c^2 + 8*a^14*b^2*c^2 - 4*a^10*b^6*c^2 - 3*a^8*b^8*c^2 + 2*a^4*b^12*c^2 + 4*a^2*b^14*c^2 - 3*b^16*c^2 + 2*a^14*c^4 - 8*a^10*b^4*c^4 + 10*a^8*b^6*c^4 - 4*a^6*b^8*c^4 + 2*a^4*b^10*c^4 - 6*a^2*b^12*c^4 + 4*b^14*c^4 - 4*a^12*c^6 - 4*a^10*b^2*c^6 + 10*a^8*b^4*c^6 - 2*a^4*b^8*c^6 + 4*a^2*b^10*c^6 - 4*b^12*c^6 + 9*a^10*c^8 - 3*a^8*b^2*c^8 - 4*a^6*b^4*c^8 - 2*a^4*b^6*c^8 - 2*a^2*b^8*c^8 + 2*b^10*c^8 - 7*a^8*c^10 + 2*a^4*b^4*c^10 + 4*a^2*b^6*c^10 + 2*b^8*c^10 + 4*a^6*c^12 + 2*a^4*b^2*c^12 - 6*a^2*b^4*c^12 - 4*b^6*c^12 - 2*a^4*c^14 + 4*a^2*b^2*c^14 + 4*b^4*c^14 - a^2*c^16 - 3*b^2*c^16 + c^18 : :

X(46097) lies on the Vijay orthic-medial conic and these lines: {6, 35088}, {297, 8779}, {520, 23583}, {525, 6720}, {40550, 45327}

X(46097) = midpoint of X(297) and X(8779)
X(46097) = X(36092)-complementary conjugate of X(36471)


X(46098) = X(5)X(2794)∩X(6)X(39645)

Barycentrics    2*a^12 - 4*a^10*b^2 + 5*a^8*b^4 - 4*a^4*b^8 + 4*a^2*b^10 - 3*b^12 - 4*a^10*c^2 - 2*a^6*b^4*c^2 + 4*a^4*b^6*c^2 - 6*a^2*b^8*c^2 + 8*b^10*c^2 + 5*a^8*c^4 - 2*a^6*b^2*c^4 + 2*a^2*b^6*c^4 - 13*b^8*c^4 + 4*a^4*b^2*c^6 + 2*a^2*b^4*c^6 + 16*b^6*c^6 - 4*a^4*c^8 - 6*a^2*b^2*c^8 - 13*b^4*c^8 + 4*a^2*c^10 + 8*b^2*c^10 - 3*c^12 : :

X(46098) lies on the Vijay orthic-medial conic and these lines: {5, 2794}, {6, 39645}, {2871, 14913}, {36163, 43705}

X(46098) = crosssum of X(3) and X(39072)


X(46099) = X(6)X(39645)∩X(41369)X(44499)

Barycentrics    2*a^14 - 2*a^12*b^2 + 5*a^10*b^4 - 11*a^8*b^6 + 8*a^6*b^8 - 4*a^4*b^10 + a^2*b^12 + b^14 - 2*a^12*c^2 - 8*a^10*b^2*c^2 + 11*a^8*b^4*c^2 + 6*a^6*b^6*c^2 - 6*a^4*b^8*c^2 + 2*a^2*b^10*c^2 - 3*b^12*c^2 + 5*a^10*c^4 + 11*a^8*b^2*c^4 - 28*a^6*b^4*c^4 + 10*a^4*b^6*c^4 - a^2*b^8*c^4 + 3*b^10*c^4 - 11*a^8*c^6 + 6*a^6*b^2*c^6 + 10*a^4*b^4*c^6 - 4*a^2*b^6*c^6 - b^8*c^6 + 8*a^6*c^8 - 6*a^4*b^2*c^8 - a^2*b^4*c^8 - b^6*c^8 - 4*a^4*c^10 + 2*a^2*b^2*c^10 + 3*b^4*c^10 + a^2*c^12 - 3*b^2*c^12 + c^14 : :

X(46099) lies on the Vijay orthic-medial conic and these lines: {6, 39645}, {41369, 44499}


X(46100) = COMPLEMENT OF X(59)

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

X(46100) lies on these lines: {2, 59}, {9, 2957}, {10, 6073}, {11, 521}, {36, 856}, {123, 14115}, {124, 3259}, {125, 6075}, {513, 21252}, {518, 1737}, {1086, 21186}, {1618, 21293}, {2238, 2323}, {3041, 35967}, {3326, 24026}, {4086, 4092}, {6667, 33562}, {15635, 26933}, {19953, 38406}, {20335, 26013}

X(46100) = midpoint of X(1618) and X(21293)
X(46100) = reflection of X(i) in X(j) for these {i,j}: {59, 40531}, {33562, 6667}
X(46100) = anticomplement of X(40531)
X(46100) = complement of X(59)
X(46100) = complement of the isogonal conjugate of X(11)
X(46100) = complement of the isotomic conjugate of X(34387)
X(46100) = medial isogonal conjugate of X(3035)
X(46100) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 13006}, {44184, 522}
X(46100) = crosspoint of X(2) and X(34387)
X(46100) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 3035}, {2, 21232}, {6, 16578}, {8, 24003}, {9, 4422}, {11, 10}, {19, 36949}, {31, 13006}, {34, 15252}, {41, 23988}, {55, 24036}, {56, 24025}, {57, 17044}, {58, 34977}, {60, 16598}, {105, 24980}, {158, 3042}, {200, 3039}, {244, 1}, {261, 21254}, {270, 5972}, {312, 27076}, {341, 3038}, {479, 24009}, {513, 522}, {514, 4885}, {521, 20315}, {522, 513}, {604, 23585}, {644, 10196}, {649, 905}, {650, 514}, {661, 1577}, {663, 650}, {667, 6589}, {693, 17072}, {738, 23587}, {764, 3756}, {876, 25380}, {885, 3716}, {1015, 3752}, {1019, 17069}, {1022, 44902}, {1024, 918}, {1027, 676}, {1086, 142}, {1109, 34829}, {1111, 2886}, {1118, 24030}, {1146, 3452}, {1358, 11019}, {1422, 40555}, {1565, 34822}, {1647, 1145}, {2150, 34990}, {2170, 2}, {2185, 620}, {2189, 16599}, {2217, 6718}, {2254, 3126}, {2310, 9}, {2968, 34823}, {2969, 1210}, {3063, 6586}, {3119, 6554}, {3120, 442}, {3122, 2092}, {3123, 41886}, {3125, 17056}, {3239, 20317}, {3248, 17053}, {3271, 37}, {3669, 7658}, {3676, 3900}, {3700, 4129}, {3737, 523}, {3756, 12640}, {3900, 4521}, {3937, 17102}, {3942, 17073}, {4017, 656}, {4041, 661}, {4086, 31946}, {4124, 17793}, {4391, 3835}, {4435, 27929}, {4466, 18642}, {4516, 1213}, {4530, 16594}, {4560, 4369}, {4858, 141}, {4895, 6544}, {4939, 2885}, {6545, 4904}, {6591, 14837}, {7004, 3}, {7117, 1214}, {7129, 40535}, {7199, 17066}, {7252, 14838}, {7649, 521}, {8027, 16614}, {8034, 16613}, {8735, 226}, {9503, 40554}, {14430, 14434}, {14837, 20314}, {14935, 25066}, {14936, 1212}, {15635, 44675}, {16726, 3946}, {16727, 17050}, {16732, 17052}, {17197, 3739}, {17205, 3742}, {17435, 16593}, {17880, 1368}, {18101, 1215}, {18108, 4142}, {18155, 512}, {18191, 1125}, {18210, 18641}, {18344, 3239}, {21044, 1211}, {21132, 11}, {21138, 20528}, {23615, 5514}, {23838, 900}, {23893, 45326}, {23978, 21244}, {23989, 17046}, {24010, 5574}, {24026, 1329}, {26856, 21233}, {26932, 18589}, {27424, 40562}, {33676, 40538}, {34387, 2887}, {35015, 119}, {35348, 6366}, {35355, 4925}, {35519, 21260}, {36197, 38930}, {36800, 40548}, {38357, 6260}, {38362, 20264}, {40166, 116}, {40451, 5836}, {40528, 17355}, {42067, 20227}, {42069, 20262}, {42455, 124}, {42462, 26932}, {43923, 21172}, {43924, 6129}, {44426, 20316}
X(46100) = barycentric product X(13006)*X(34387)
X(46100) = barycentric quotient X(13006)/X(59)
X(46100) = {X(2),X(59)}-harmonic conjugate of X(40531)


X(46101) = COMPLEMENT OF X(4998)

Barycentrics    (a - b - c)*(b - c)^2*(2*a^3 - 2*a^2*b - a*b^2 + b^3 - 2*a^2*c + 4*a*b*c - b^2*c - a*c^2 - b*c^2 + c^3) : :
X(46101) = 3 X[2] + X[17036]

X(46101) lies on these lines: {2, 1252}, {6, 34530}, {11, 650}, {44, 40869}, {115, 35128}, {516, 9356}, {649, 3259}, {661, 6075}, {1015, 6506}, {1086, 7658}, {1146, 4521}, {1647, 17435}, {2238, 2323}, {3008, 6547}, {3035, 14589}, {3290, 5121}, {3452, 27942}, {3816, 5701}, {3825, 9367}, {4885, 35094}, {5375, 31272}, {5514, 5516}, {5548, 26074}, {9374, 10893}, {14298, 33646}, {21104, 40629}, {22102, 41405}, {27010, 28833}, {35113, 35509}

X(46101) = midpoint of X(4998) and X(17036)
X(46101) = reflection of X(9356) in the Gergonne line
X(46101) = isogonal conjugate of X(38809)
X(46101) = isotomic conjugate of X(31619)
X(46101) = complement of X(4998)
X(46101) = complement of the isogonal conjugate of X(3271)
X(46101) = complement of the isotomic conjugate of X(11)
X(46101) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 3035}, {3035, 11124}, {6630, 522}, {40520, 21132}
X(46101) = X(i)-isoconjugate of X(j) for these (i,j): {1, 38809}, {31, 31619}, {109, 31628}, {4564, 18771}
X(46101) = crosspoint of X(2) and X(11)
X(46101) = crosssum of X(6) and X(59)
X(46101) = X(11)-Ceva conjugate of Danneels point of X(11)
X(46101) = trilinear product X(i)*X(j) for these {i,j}: {11, 17439}, {514, 11124}, {650, 21105}, {2170, 3035}
X(46101) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 21232}, {9, 27076}, {11, 2887}, {31, 3035}, {32, 16578}, {41, 4422}, {55, 24003}, {60, 21254}, {200, 3038}, {244, 2886}, {513, 17072}, {522, 21260}, {560, 13006}, {604, 17044}, {649, 4885}, {650, 3835}, {657, 20317}, {663, 513}, {667, 522}, {764, 17059}, {798, 1577}, {875, 25380}, {884, 3716}, {1015, 142}, {1019, 17066}, {1027, 926}, {1086, 17046}, {1096, 3042}, {1111, 17047}, {1146, 21244}, {1253, 3039}, {1357, 11019}, {1395, 15252}, {1397, 24025}, {1919, 905}, {1946, 20315}, {1973, 36949}, {1977, 3752}, {1980, 6589}, {2150, 620}, {2170, 141}, {2175, 24036}, {2206, 34977}, {2310, 1329}, {2311, 40548}, {2319, 40562}, {2643, 34829}, {3063, 514}, {3121, 17056}, {3122, 442}, {3123, 20338}, {3125, 17052}, {3248, 1}, {3270, 34823}, {3271, 10}, {3709, 4129}, {3737, 512}, {3937, 34822}, {3942, 18639}, {4041, 31946}, {4124, 20542}, {4391, 21262}, {4435, 27854}, {4516, 3454}, {4560, 42327}, {4858, 626}, {6377, 20528}, {7004, 1368}, {7023, 24009}, {7117, 18589}, {7252, 4369}, {7337, 24030}, {7366, 23587}, {8027, 3756}, {8034, 8286}, {8641, 4521}, {8735, 20305}, {9447, 23988}, {14936, 3452}, {16726, 17050}, {17197, 21240}, {17435, 20540}, {18101, 21238}, {18155, 23301}, {18191, 3741}, {18344, 20316}, {21044, 21245}, {21132, 21252}, {21138, 20547}, {21143, 4904}, {22096, 17102}, {24012, 5574}, {34387, 21235}, {38365, 40607}, {38986, 41886}, {42067, 1210}, {43924, 3900}
X(46101) = barycentric product X(i)*X(j) for these {i,j}: {8, 43909}, {11, 3035}, {100, 42547}, {522, 21105}, {693, 11124}, {2170, 20881}, {4858, 17439}, {14589, 40166}, {17197, 21013}, {18645, 21044}, {20958, 34387}
X(46101) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 31619}, {6, 38809}, {650, 31628}, {3035, 4998}, {3271, 18771}, {11124, 100}, {14589, 31615}, {17439, 4564}, {18645, 4620}, {20958, 59}, {21105, 664}, {22055, 44717}, {42547, 693}, {43909, 7}
X(46101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17036, 4998}, {1647, 33573, 17435}


X(46102) = POLAR CONJUGATE OF X(11)

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

X(46102) lies on these lines: {2, 1262}, {4, 5377}, {34, 5378}, {59, 5080}, {108, 898}, {109, 17072}, {278, 5376}, {608, 5381}, {648, 35174}, {651, 4391}, {653, 3257}, {664, 6332}, {666, 1783}, {765, 1861}, {908, 4564}, {1016, 37790}, {1025, 1981}, {1275, 1944}, {2397, 2405}, {4551, 36797}, {4567, 4998}, {4585, 24035}, {7017, 34048}, {7045, 37774}, {21301, 32735}, {23984, 24032}, {37768, 43043}

X(46102) = isogonal conjugate of X(7117)
X(46102) = isotomic conjugate of X(26932)
X(46102) = polar conjugate of X(11)
X(46102) = isotomic conjugate of the anticomplement of X(36949)
X(46102) = isotomic conjugate of the complement of X(651)
X(46102) = isotomic conjugate of the isogonal conjugate of X(7115)
X(46102) = polar conjugate of the isotomic conjugate of X(4998)
X(46102) = polar conjugate of the isogonal conjugate of X(59)
X(46102) = pole wrt polar circle of trilinear polar of X(11) (line X(4530)X(14393))
X(46102) = perspector of ABC and orthoanticevian triangle of X(4998)
X(46102) = X(4998)-Ceva conjugate of X(44699)
X(46102) = X(i)-cross conjugate of X(j) for these (i,j): {2, 6335}, {4, 18026}, {8, 664}, {9, 36797}, {59, 4998}, {92, 648}, {219, 100}, {278, 653}, {281, 1897}, {321, 6648}, {329, 190}, {608, 108}, {3434, 4569}, {3436, 668}, {3681, 6606}, {3869, 99}, {4318, 927}, {5057, 35157}, {5080, 35174}, {5176, 4555}, {5279, 8707}, {5739, 32038}, {7078, 6516}, {11109, 811}, {14923, 6613}, {17913, 6331}, {20557, 18830}, {23541, 75}, {26668, 30610}, {26942, 4552}, {27382, 3699}, {27540, 646}, {28739, 4554}, {28950, 645}, {30807, 666}, {34040, 934}, {34048, 651}, {36949, 2}, {37279, 823}
X(46102) = cevapoint of X(i) and X(j) for these (i,j): {2, 651}, {4, 1783}, {9, 4551}, {12, 4559}, {59, 7115}, {100, 219}, {108, 608}, {190, 4417}, {278, 653}, {281, 1897}, {644, 7080}, {664, 33298}, {4552, 26942}
X(46102) = trilinear pole of line {100, 108}
X(46102) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7117}, {3, 2170}, {6, 7004}, {9, 3937}, {11, 48}, {19, 1364}, {31, 26932}, {32, 17880}, {34, 35072}, {41, 1565}, {55, 3942}, {56, 34591}, {57, 3270}, {60, 3708}, {63, 3271}, {71, 18191}, {77, 14936}, {78, 1015}, {125, 2150}, {184, 4858}, {212, 1086}, {213, 17219}, {219, 244}, {222, 2310}, {228, 17197}, {255, 8735}, {270, 3269}, {273, 39687}, {278, 2638}, {283, 3125}, {284, 18210}, {312, 22096}, {332, 3121}, {345, 3248}, {513, 652}, {514, 1946}, {521, 649}, {522, 22383}, {603, 1146}, {604, 2968}, {608, 24031}, {647, 3737}, {650, 1459}, {656, 7252}, {661, 23189}, {663, 905}, {665, 23696}, {667, 6332}, {764, 4587}, {810, 4560}, {906, 21132}, {909, 35014}, {1357, 3692}, {1358, 1802}, {1395, 23983}, {1437, 21044}, {1789, 20982}, {1790, 4516}, {1808, 39786}, {1812, 3122}, {1919, 35518}, {1977, 3718}, {2185, 20975}, {2189, 2632}, {2193, 3120}, {2194, 4466}, {2196, 4124}, {2204, 17216}, {2208, 16596}, {2289, 2969}, {2318, 16726}, {3022, 7177}, {3049, 18155}, {3063, 4025}, {3064, 23224}, {3119, 7053}, {3310, 37628}, {3719, 42067}, {3733, 8611}, {4017, 23090}, {4020, 18101}, {4041, 7254}, {4081, 7099}, {4091, 18344}, {4459, 7116}, {4530, 36058}, {4571, 21143}, {7125, 42069}, {7202, 8606}, {7289, 14935}, {7649, 36054}, {9247, 34387}, {14418, 23345}, {14578, 35015}, {15451, 39177}, {17435, 36057}, {22086, 23838}, {22386, 27424}, {24012, 30682}, {32656, 40166}, {32660, 42455}, {34434, 38344}, {36059, 42462}, {40527, 40958}
X(46102) = barycentric product X(i)*X(j) for these {i,j}: {4, 4998}, {7, 15742}, {12, 18020}, {34, 7035}, {59, 264}, {75, 7012}, {76, 7115}, {78, 24032}, {92, 4564}, {100, 18026}, {108, 668}, {190, 653}, {201, 23999}, {225, 4600}, {250, 34388}, {253, 44699}, {273, 765}, {278, 1016}, {281, 1275}, {312, 7128}, {318, 7045}, {319, 34922}, {331, 1252}, {345, 23984}, {608, 31625}, {644, 13149}, {646, 32714}, {648, 4552}, {651, 6335}, {664, 1897}, {811, 4551}, {908, 39294}, {1119, 4076}, {1262, 7017}, {1441, 5379}, {1783, 4554}, {1826, 4620}, {1861, 39293}, {1880, 4601}, {1969, 2149}, {1978, 32674}, {2052, 44717}, {3699, 36118}, {3718, 24033}, {4242, 35174}, {4559, 6331}, {4561, 36127}, {4566, 36797}, {4567, 40149}, {4572, 8750}, {4590, 8736}, {5376, 37790}, {6528, 23067}, {7140, 7340}, {8795, 44710}, {17924, 31615}, {23582, 26942}
X(46102) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 7004}, {2, 26932}, {3, 1364}, {4, 11}, {6, 7117}, {7, 1565}, {8, 2968}, {9, 34591}, {12, 125}, {19, 2170}, {25, 3271}, {27, 17197}, {28, 18191}, {33, 2310}, {34, 244}, {55, 3270}, {56, 3937}, {57, 3942}, {59, 3}, {65, 18210}, {75, 17880}, {78, 24031}, {86, 17219}, {92, 4858}, {100, 521}, {101, 652}, {108, 513}, {109, 1459}, {110, 23189}, {112, 7252}, {162, 3737}, {181, 20975}, {190, 6332}, {201, 2632}, {212, 2638}, {219, 35072}, {225, 3120}, {226, 4466}, {242, 4124}, {250, 60}, {264, 34387}, {273, 1111}, {278, 1086}, {281, 1146}, {307, 17216}, {318, 24026}, {329, 16596}, {331, 23989}, {345, 23983}, {388, 26933}, {393, 8735}, {517, 35014}, {572, 38344}, {607, 14936}, {608, 1015}, {645, 15411}, {646, 15416}, {648, 4560}, {651, 905}, {653, 514}, {664, 4025}, {668, 35518}, {692, 1946}, {765, 78}, {811, 18155}, {906, 36054}, {1016, 345}, {1018, 8611}, {1023, 14418}, {1110, 212}, {1118, 2969}, {1119, 1358}, {1252, 219}, {1262, 222}, {1275, 348}, {1309, 43728}, {1361, 35012}, {1395, 3248}, {1396, 16726}, {1397, 22096}, {1398, 1357}, {1415, 22383}, {1783, 650}, {1785, 35015}, {1804, 7215}, {1812, 16731}, {1813, 4091}, {1824, 4516}, {1825, 2611}, {1826, 21044}, {1846, 3259}, {1857, 42069}, {1875, 42753}, {1876, 3675}, {1877, 1647}, {1880, 3125}, {1897, 522}, {2149, 48}, {2171, 3708}, {2197, 3269}, {2594, 22094}, {2969, 7336}, {3064, 42462}, {3085, 26956}, {3436, 123}, {3695, 7068}, {3869, 34588}, {4076, 1265}, {4242, 3738}, {4417, 40626}, {4551, 656}, {4552, 525}, {4554, 15413}, {4559, 647}, {4564, 63}, {4565, 7254}, {4566, 17094}, {4567, 1812}, {4570, 283}, {4573, 15419}, {4600, 332}, {4619, 1813}, {4620, 17206}, {4998, 69}, {5089, 17435}, {5379, 21}, {5546, 23090}, {6065, 1260}, {6335, 4391}, {6356, 1367}, {6358, 20902}, {6516, 4131}, {6648, 15420}, {7009, 4459}, {7012, 1}, {7017, 23978}, {7035, 3718}, {7045, 77}, {7046, 4081}, {7066, 2972}, {7071, 3022}, {7079, 3119}, {7080, 7358}, {7115, 6}, {7128, 57}, {7140, 4092}, {7337, 42067}, {7339, 7053}, {7649, 21132}, {7719, 38375}, {7952, 38357}, {8736, 115}, {8750, 663}, {8756, 4530}, {11109, 34589}, {13149, 24002}, {14594, 23874}, {15385, 3435}, {15742, 8}, {17555, 124}, {17906, 21120}, {17916, 38358}, {17924, 40166}, {18020, 261}, {18026, 693}, {21664, 3326}, {23067, 520}, {23586, 30682}, {23706, 1769}, {23964, 2189}, {23981, 8677}, {23984, 278}, {23985, 608}, {24000, 270}, {24027, 603}, {24032, 273}, {24033, 34}, {26942, 15526}, {27382, 40616}, {31615, 1332}, {32085, 18101}, {32674, 649}, {32702, 2423}, {32714, 3669}, {33298, 40618}, {34388, 339}, {34922, 79}, {36037, 37628}, {36059, 23224}, {36086, 23696}, {36118, 3676}, {36127, 7649}, {36794, 27010}, {36797, 7253}, {37993, 41214}, {39293, 31637}, {39294, 34234}, {40149, 16732}, {40399, 40527}, {40446, 40451}, {42069, 5532}, {42070, 4542}, {43923, 764}, {44426, 42455}, {44699, 20}, {44710, 5562}, {44717, 394}, {44724, 44722}


X(46103) = POLAR CONJUGATE OF X(12)

Barycentrics    (a + b)^2*(a - b - c)*(a + c)^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) : :
Barycentrics    (sec A)/(1 + cos(B - C)) : :
Barycentrics    sec A sec^2(B/2 - C/2) : :

X(46103) lies on these lines: {2, 7054}, {4, 1798}, {21, 23207}, {27, 86}, {28, 37870}, {29, 270}, {33, 1808}, {81, 286}, {83, 39281}, {92, 648}, {110, 20242}, {162, 14004}, {163, 1746}, {261, 2189}, {275, 24624}, {314, 1172}, {331, 37543}, {422, 1824}, {448, 1214}, {469, 36794}, {593, 26856}, {940, 11341}, {1396, 1509}, {1826, 18812}, {1891, 41258}, {2193, 25515}, {5174, 19808}, {7518, 37666}, {10319, 37089}, {17907, 37181}, {18134, 40414}, {18139, 27418}, {31905, 32010}, {31909, 40415}, {39280, 39284}, {40574, 44129}

X(46103) = isogonal conjugate of X(2197)
X(46103) = isotomic conjugate of X(26942)
X(46103) = polar conjugate of X(12)
X(46103) = isotomic conjugate of the isogonal conjugate of X(2189)
X(46103) = polar conjugate of the isotomic conjugate of X(261)
X(46103) = polar conjugate of the isogonal conjugate of X(60)
X(46103) = X(i)-cross conjugate of X(j) for these (i,j): {60, 261}, {81, 2185}, {1172, 270}, {23542, 75}, {26932, 4560}
X(46103) = cevapoint of X(i) and X(j) for these (i,j): {11, 7252}, {27, 81}, {29, 1172}, {60, 2189}, {270, 2326}, {4560, 26932}, {18134, 32939}
X(46103) = trilinear pole of line {4560, 14024}
X(46103) = pole wrt polar circle of trilinear polar of X(12) (line X(2610)X(4024))
X(46103) = perspector of ABC and orthoanticevian triangle of X(261)
X(46103) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2197}, {3, 2171}, {6, 201}, {9, 1425}, {10, 1409}, {12, 48}, {19, 7066}, {31, 26942}, {37, 73}, {41, 6356}, {42, 1214}, {55, 37755}, {56, 3949}, {57, 3690}, {59, 3708}, {63, 181}, {65, 71}, {72, 1400}, {77, 1500}, {125, 2149}, {184, 6358}, {212, 6354}, {213, 307}, {219, 1254}, {222, 756}, {225, 3990}, {226, 228}, {227, 41087}, {255, 8736}, {281, 7138}, {306, 1402}, {348, 872}, {594, 603}, {604, 3695}, {647, 4551}, {656, 4559}, {661, 23067}, {810, 4552}, {1042, 3694}, {1231, 1918}, {1253, 20618}, {1260, 7147}, {1334, 1439}, {1410, 2321}, {1415, 4064}, {1427, 2318}, {1441, 2200}, {1459, 21859}, {1802, 6046}, {1813, 4705}, {1824, 40152}, {1826, 22341}, {1880, 3682}, {1946, 4605}, {2196, 7235}, {2198, 28786}, {2259, 41393}, {2632, 7115}, {2643, 44717}, {3215, 41508}, {3269, 7012}, {3692, 7143}, {4017, 4574}, {4024, 36059}, {4036, 32660}, {4055, 40149}, {4079, 6516}, {4564, 20975}, {6057, 7099}, {7064, 7177}, {7100, 21794}, {7109, 7182}, {7116, 7211}, {7125, 7140}, {8818, 22342}, {9247, 34388}, {23286, 35307}
X(46103) = barycentric product X(i)*X(j) for these {i,j}: {4, 261}, {11, 18020}, {21, 286}, {25, 18021}, {27, 333}, {28, 314}, {29, 86}, {33, 873}, {58, 44130}, {60, 264}, {75, 270}, {76, 2189}, {81, 31623}, {85, 2326}, {92, 2185}, {162, 18155}, {250, 34387}, {273, 1098}, {274, 1172}, {278, 7058}, {281, 1509}, {284, 44129}, {310, 2299}, {318, 757}, {331, 7054}, {332, 8747}, {345, 36419}, {348, 36421}, {552, 7046}, {593, 7017}, {645, 17925}, {648, 4560}, {811, 3737}, {1434, 2322}, {1444, 1896}, {1474, 28660}, {1969, 2150}, {2203, 40072}, {2204, 6385}, {2969, 6064}, {3064, 4610}, {4573, 17926}, {4590, 8735}, {4612, 17924}, {4623, 18344}, {4631, 6591}, {5931, 44698}, {6331, 7252}, {6336, 30606}, {6528, 23189}, {7004, 23999}, {7192, 36797}, {7340, 42069}, {8748, 17206}, {14006, 32010}, {14024, 18827}, {14616, 17515}, {17880, 24000}, {23582, 26932}, {31905, 36800}, {37870, 44734}
X(46103) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 201}, {2, 26942}, {3, 7066}, {4, 12}, {6, 2197}, {7, 6356}, {8, 3695}, {9, 3949}, {11, 125}, {19, 2171}, {21, 72}, {25, 181}, {27, 226}, {28, 65}, {29, 10}, {33, 756}, {34, 1254}, {55, 3690}, {56, 1425}, {57, 37755}, {58, 73}, {60, 3}, {81, 1214}, {86, 307}, {92, 6358}, {110, 23067}, {112, 4559}, {162, 4551}, {242, 7235}, {249, 44717}, {250, 59}, {261, 69}, {264, 34388}, {270, 1}, {272, 28786}, {274, 1231}, {278, 6354}, {279, 20618}, {281, 594}, {283, 3682}, {284, 71}, {286, 1441}, {314, 20336}, {318, 1089}, {333, 306}, {393, 8736}, {497, 21015}, {522, 4064}, {552, 7056}, {593, 222}, {603, 7138}, {607, 1500}, {648, 4552}, {653, 4605}, {757, 77}, {849, 603}, {873, 7182}, {942, 41393}, {950, 21671}, {1014, 1439}, {1021, 8611}, {1043, 3710}, {1098, 78}, {1119, 6046}, {1172, 37}, {1259, 4158}, {1333, 1409}, {1364, 2972}, {1396, 1427}, {1398, 7143}, {1408, 1410}, {1435, 7147}, {1437, 22341}, {1440, 6355}, {1474, 1400}, {1509, 348}, {1565, 1367}, {1783, 21859}, {1790, 40152}, {1812, 3998}, {1857, 7140}, {1896, 41013}, {2150, 48}, {2170, 3708}, {2185, 63}, {2189, 6}, {2193, 3990}, {2194, 228}, {2203, 1402}, {2204, 213}, {2212, 872}, {2287, 3694}, {2299, 42}, {2322, 2321}, {2326, 9}, {2328, 2318}, {2332, 1334}, {2905, 27691}, {2907, 3178}, {2968, 7068}, {2969, 1365}, {3064, 4024}, {3086, 26955}, {3194, 227}, {3271, 20975}, {3559, 21077}, {3737, 656}, {4183, 210}, {4211, 40961}, {4233, 41539}, {4248, 4848}, {4267, 22076}, {4556, 1813}, {4560, 525}, {4612, 1332}, {4636, 1331}, {4858, 20902}, {5317, 1880}, {5324, 17441}, {5546, 4574}, {6061, 1260}, {6727, 7591}, {7004, 2632}, {7009, 7211}, {7017, 28654}, {7046, 6057}, {7054, 219}, {7058, 345}, {7071, 7064}, {7117, 3269}, {7140, 6058}, {7192, 17094}, {7252, 647}, {7341, 7053}, {8735, 115}, {8747, 225}, {8748, 1826}, {11107, 3678}, {13739, 15556}, {14006, 1215}, {14024, 740}, {17104, 22342}, {17188, 21912}, {17197, 4466}, {17219, 17216}, {17515, 758}, {17519, 3753}, {17880, 17879}, {17925, 7178}, {17926, 3700}, {18020, 4998}, {18021, 305}, {18155, 14208}, {18191, 18210}, {18344, 4705}, {21044, 21046}, {21132, 21134}, {23189, 520}, {23964, 7115}, {24000, 7012}, {26856, 26932}, {26932, 15526}, {27958, 4019}, {28660, 40071}, {30606, 3977}, {30733, 41538}, {31623, 321}, {31900, 3649}, {31903, 3671}, {31905, 16609}, {31906, 5244}, {31909, 16603}, {31917, 16888}, {34387, 339}, {34856, 1874}, {36419, 278}, {36420, 608}, {36421, 281}, {36797, 3952}, {37168, 40663}, {37265, 8896}, {37390, 10408}, {37908, 20683}, {40950, 21674}, {41227, 15443}, {42069, 4092}, {43925, 7180}, {44129, 349}, {44130, 313}, {44426, 4036}, {44428, 6370}, {44698, 5930}, {44734, 31993}
X(46103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {27, 2905, 1848}, {33, 14006, 36797}, {1172, 44734, 31623}


X(46104) = POLAR CONJUGATE OF X(39)

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

X(46104) lies on these lines: {4, 18022}, {25, 183}, {51, 290}, {53, 16890}, {76, 33586}, {83, 458}, {251, 324}, {327, 43653}, {393, 37876}, {419, 44142}, {427, 6331}, {428, 17984}, {511, 34384}, {689, 3563}, {1176, 8795}, {1824, 40717}, {5640, 44176}, {6524, 17500}, {6995, 44144}, {6997, 40822}, {8753, 32581}, {10130, 40684}, {10550, 14593}, {10551, 39530}, {14486, 43976}, {17994, 17995}, {18384, 18817}, {23962, 37349}, {30505, 30506}, {38817, 39931}

X(46104) = isogonal conjugate of X(20775)
X(46104) = isotomic conjugate of X(3917)
X(46104) = polar conjugate of X(39)
X(46104) = isotomic conjugate of the anticomplement of X(5943)
X(46104) = isotomic conjugate of the complement of X(3060)
X(46104) = isotomic conjugate of the isogonal conjugate of X(32085)
X(46104) = polar conjugate of the isotomic conjugate of X(308)
X(46104) = polar conjugate of the isogonal conjugate of X(83)
X(46104) = X(i)-cross conjugate of X(j) for these (i,j): {4, 32085}, {83, 308}, {419, 16081}, {2501, 6331}, {5943, 2}, {10551, 251}, {17500, 83}, {17867, 75}, {44142, 264}
X(46104) = cevapoint of X(i) and X(j) for these (i,j): {2, 3060}, {4, 264}, {83, 32085}, {324, 30506}, {1843, 37125}
X(46104) = crosssum of X(3) and X(23174)
X(46104) = trilinear pole of line {2489, 4580}
X(46104) = pole wrt polar circle of trilinear polar of X(39) (line X(688)X(3005))
X(46104) = perspector of ABC and orthoanticevian triangle of X(308)
X(46104) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20775}, {3, 1964}, {6, 4020}, {31, 3917}, {38, 184}, {39, 48}, {63, 3051}, {69, 1923}, {141, 9247}, {212, 1401}, {222, 40972}, {228, 17187}, {255, 1843}, {304, 41331}, {326, 27369}, {560, 3933}, {577, 17442}, {603, 3688}, {688, 4592}, {810, 1634}, {822, 35325}, {906, 21123}, {1178, 22367}, {1437, 21035}, {1444, 41267}, {1790, 21814}, {1930, 14575}, {2084, 4558}, {2200, 16696}, {2236, 17970}, {2530, 32656}, {3005, 4575}, {3289, 3404}, {4100, 27376}, {8061, 32661}, {14585, 20883}, {23225, 35333}
X(46104) = barycentric product X(i)*X(j) for these {i,j}: {4, 308}, {19, 18833}, {25, 40016}, {53, 41488}, {76, 32085}, {82, 1969}, {83, 264}, {92, 3112}, {251, 18022}, {276, 17500}, {324, 39287}, {669, 42395}, {689, 2501}, {811, 18070}, {850, 42396}, {1176, 18027}, {1799, 2052}, {2489, 42371}, {4577, 14618}, {4580, 6528}, {4593, 24006}, {14970, 17984}, {16081, 20022}, {18082, 44129}, {18097, 44130}, {32581, 40826}, {39289, 40684}, {40425, 44142}, {42299, 44144}
X(46104) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4020}, {2, 3917}, {4, 39}, {6, 20775}, {19, 1964}, {25, 3051}, {27, 17187}, {33, 40972}, {76, 3933}, {82, 48}, {83, 3}, {92, 38}, {107, 35325}, {158, 17442}, {251, 184}, {264, 141}, {275, 16030}, {278, 1401}, {281, 3688}, {286, 16696}, {308, 69}, {318, 33299}, {331, 3665}, {393, 1843}, {419, 8623}, {427, 8041}, {428, 11205}, {458, 14096}, {648, 1634}, {689, 4563}, {733, 17970}, {827, 32661}, {850, 2525}, {1093, 27376}, {1176, 577}, {1235, 7794}, {1799, 394}, {1824, 21814}, {1826, 21035}, {1840, 40936}, {1969, 1930}, {1973, 1923}, {1974, 41331}, {2052, 427}, {2207, 27369}, {2295, 22367}, {2333, 41267}, {2489, 688}, {2501, 3005}, {2970, 39691}, {3112, 63}, {3199, 27374}, {3589, 22078}, {4577, 4558}, {4580, 520}, {4593, 4592}, {4599, 4575}, {4628, 32656}, {4972, 22077}, {6331, 4576}, {6335, 4553}, {6353, 3787}, {6528, 41676}, {6656, 22424}, {7017, 3703}, {7649, 21123}, {8024, 4175}, {8743, 23208}, {8753, 41272}, {8794, 19174}, {10312, 3203}, {10547, 14585}, {10548, 13367}, {10549, 23635}, {10550, 570}, {10566, 1459}, {13450, 27371}, {14618, 826}, {14970, 36214}, {16081, 20021}, {16889, 20727}, {16890, 20819}, {17500, 216}, {17907, 3313}, {17924, 2530}, {17984, 732}, {18022, 8024}, {18027, 1235}, {18070, 656}, {18082, 71}, {18083, 22069}, {18084, 22057}, {18085, 22394}, {18086, 22072}, {18087, 22053}, {18088, 22070}, {18089, 22060}, {18090, 22404}, {18091, 22065}, {18092, 22062}, {18093, 22409}, {18094, 22412}, {18095, 22064}, {18096, 22420}, {18097, 73}, {18098, 228}, {18099, 22061}, {18101, 7117}, {18102, 22066}, {18103, 20730}, {18105, 3049}, {18106, 22387}, {18107, 22090}, {18108, 22383}, {18109, 22067}, {18110, 22091}, {18111, 22093}, {18112, 22098}, {18700, 22399}, {18701, 22400}, {18704, 22402}, {18705, 22403}, {18833, 304}, {20022, 36212}, {20965, 23210}, {21447, 41584}, {21458, 8779}, {21459, 2393}, {24006, 8061}, {24243, 45594}, {24244, 26347}, {26224, 43652}, {27067, 22076}, {28724, 1092}, {32085, 6}, {32581, 574}, {34055, 255}, {34294, 20975}, {35360, 35319}, {36120, 3404}, {36794, 41328}, {37765, 9019}, {38817, 23174}, {38946, 22121}, {39182, 23286}, {39287, 97}, {39289, 31626}, {40016, 305}, {40425, 41435}, {41013, 3954}, {41488, 34386}, {41884, 22138}, {42037, 3796}, {42299, 43718}, {42395, 4609}, {42396, 110}, {44129, 16887}, {44142, 6292}, {44144, 14994}, {44146, 7813}
X(46104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {264, 32085, 308}, {428, 42394, 17984}


X(46105) = POLAR CONJUGATE OF X(23)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(a^4 - a^2*b^2 + b^4 - c^4)*(-a^4 + b^4 + a^2*c^2 - c^4) : :
Barycentrics    (tan A)/(2 sin 2A - 3 tan ω) : :

X(46105) lies on the Kiepert circumhyperbola and these lines: {2, 339}, {4, 67}, {83, 648}, {94, 297}, {98, 186}, {262, 7577}, {264, 598}, {275, 41254}, {328, 39295}, {458, 7578}, {468, 10511}, {671, 44146}, {1236, 22151}, {1289, 9076}, {2986, 17708}, {3406, 36820}, {3424, 18533}, {7550, 40448}, {7607, 14357}, {8744, 37778}, {10718, 18866}, {11606, 40889}, {13599, 14789}, {14223, 14618}, {14458, 18559}, {14830, 38552}, {35486, 43537}, {40393, 40684}, {40814, 43530}, {41079, 43673}, {43665, 44427}

X(46105) = isogonal conjugate of X(10317)
X(46105) = isotomic conjugate of X(22151)
X(46105) = polar conjugate of X(23)
X(46105) = isotomic conjugate of the isogonal conjugate of X(8791)
X(46105) = polar conjugate of the isotomic conjugate of X(18019)
X(46105) = polar conjugate of the isogonal conjugate of X(67)
X(46105) = X(i)-cross conjugate of X(j) for these (i,j): {67, 18019}, {468, 264}, {5523, 4}, {23557, 75}, {43291, 847}
X(46105) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10317}, {23, 48}, {31, 22151}, {63, 18374}, {163, 9517}, {184, 16568}, {255, 8744}, {316, 9247}, {560, 37804}, {662, 42659}, {2159, 16165}, {2492, 4575}, {6593, 36060}, {10547, 18715}, {14575, 20944}
X(46105) = cevapoint of X(i) and X(j) for these (i,j): {6, 21284}, {67, 8791}, {1235, 44146}, {1843, 14580}, {5523, 39269}
X(46105) = trilinear pole of line {427, 523} (the radical axis of the anticomplementary circle and tangential circle)
X(46105) = anticomplement of isotomic conjugate of polar conjugate of X(40949)
X(46105) = pole wrt polar circle of trilinear polar of X(23) (line X(2492)X(6593))
X(46105) = barycentric product X(i)*X(j) for these {i,j}: {4, 18019}, {67, 264}, {76, 8791}, {850, 935}, {1235, 9076}, {1969, 2157}, {2052, 34897}, {2373, 39269}, {3455, 18022}, {5094, 10512}, {10415, 44146}, {11605, 18018}, {14618, 17708}, {20883, 37221}
X(46105) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 22151}, {4, 23}, {6, 10317}, {25, 18374}, {30, 16165}, {67, 3}, {76, 37804}, {92, 16568}, {264, 316}, {331, 17088}, {393, 8744}, {403, 12824}, {427, 9019}, {468, 6593}, {512, 42659}, {523, 9517}, {935, 110}, {1969, 20944}, {2052, 37765}, {2157, 48}, {2501, 2492}, {3455, 184}, {5094, 10510}, {8744, 36415}, {8791, 6}, {9076, 1176}, {10415, 895}, {10511, 43697}, {11605, 22}, {14357, 3292}, {14618, 9979}, {16230, 33752}, {16318, 28343}, {17708, 4558}, {17983, 14246}, {18019, 69}, {18022, 40074}, {20883, 18715}, {34897, 394}, {37221, 34055}, {37981, 40949}, {39269, 858}, {43678, 37801}, {44146, 7664}


X(46106) = POLAR CONJUGATE OF X(74)

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) : :
Barycentrics    1 - 2 sec A cos B cos C : :

X(46106) lies on these lines: {2, 216}, {3, 13450}, {4, 4846}, {5, 44732}, {20, 1093}, {23, 107}, {30, 34334}, {53, 37648}, {92, 445}, {94, 16080}, {97, 8794}, {110, 450}, {111, 16081}, {125, 39569}, {133, 1533}, {186, 476}, {250, 36188}, {275, 34545}, {297, 525}, {311, 37638}, {317, 37644}, {323, 648}, {339, 44216}, {340, 37779}, {343, 1232}, {373, 39530}, {401, 23582}, {421, 19128}, {436, 5012}, {459, 5392}, {467, 13567}, {468, 2970}, {470, 8838}, {471, 8836}, {511, 35360}, {847, 3147}, {852, 32428}, {858, 6530}, {1075, 5889}, {1235, 11331}, {1249, 37645}, {1368, 14569}, {1370, 6524}, {1495, 4240}, {1629, 13595}, {1896, 2475}, {1947, 3219}, {1948, 3218}, {1990, 3260}, {1995, 33971}, {2207, 26212}, {2864, 20624}, {2986, 15262}, {3060, 3168}, {3146, 14249}, {3266, 6331}, {3284, 43752}, {3292, 35311}, {3628, 14978}, {4232, 43976}, {4993, 8795}, {5943, 30506}, {6330, 18019}, {6335, 32849}, {6515, 6820}, {6525, 7500}, {6528, 40885}, {6800, 37070}, {7017, 28605}, {8744, 41253}, {8796, 37874}, {8884, 44802}, {9308, 15066}, {9381, 18366}, {10002, 31099}, {11078, 11094}, {11092, 11093}, {11433, 37192}, {13409, 42453}, {14363, 45186}, {14919, 15459}, {14957, 34854}, {15018, 36794}, {15107, 35474}, {15351, 40853}, {16082, 21907}, {17484, 18026}, {17825, 41244}, {17928, 41365}, {18022, 39998}, {18027, 26166}, {18484, 23097}, {25987, 41013}, {26164, 27376}, {26235, 44144}, {31621, 44579}, {32205, 35719}, {34287, 35061}, {36192, 44096}, {37127, 43651}, {37174, 40814}, {37643, 41760}, {40506, 44578}, {40512, 44334}

X(46106) = isogonal conjugate of X(18877)
X(46106) = isotomic conjugate of X(14919)
X(46106) = anticomplement of X(44436)
X(46106) = polar conjugate of X(74)
X(46106) = isotomic conjugate of the isogonal conjugate of X(1990)
X(46106) = polar conjugate of the isotomic conjugate of X(3260)
X(46106) = polar conjugate of the isogonal conjugate of X(30)
X(46106) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 34549}, {1294, 4329}, {32646, 7253}, {36043, 850}
X(46106) = X(i)-Ceva conjugate of X(j) for these (i,j): {94, 324}, {264, 34334}, {18817, 14254}, {43752, 30}
X(46106) = X(i)-cross conjugate of X(j) for these (i,j): {30, 3260}, {1637, 4240}, {3163, 14254}, {5664, 648}, {34334, 264}
X(46106) = cevapoint of X(i) and X(j) for these (i,j): {6, 14703}, {30, 1990}, {186, 15262}, {1650, 14391}, {3003, 6000}
X(46106) = crosspoint of X(i) and X(j) for these (i,j): {687, 23582}, {18027, 18817}
X(46106) = crosssum of X(686) and X(3269)
X(46106) = trilinear pole of line {113, 133}
X(46106) = crossdifference of every pair of points on line {184, 39201}
X(46106) = pole wrt polar circle of trilinear polar of X(74) (line X(6)X(647))
X(46106) = perspector of ABC and orthoanticevian triangle of X(3260)
X(46106) = trilinear product X(i)*X(j) for these {i,j}: {2, 1784}, {4, 14206}, {19, 3260}, {30, 92}, {75, 1990}, {158, 11064}, {264, 2173}, {273, 7359}, {318, 6357}, {561, 14581}, {811, 1637}, {823, 9033}, {1099, 16080}, {1495, 1969}, {1577, 4240}, {2166, 14920}, {2631, 6528}, {6335, 11125}, {9406, 18022}, {14400, 18026}
X(46106) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18877}, {3, 2159}, {6, 35200}, {31, 14919}, {48, 74}, {63, 40352}, {163, 14380}, {184, 2349}, {255, 8749}, {326, 40354}, {520, 36131}, {577, 36119}, {603, 15627}, {647, 36034}, {656, 32640}, {810, 44769}, {822, 1304}, {1094, 39380}, {1095, 39381}, {1494, 9247}, {1953, 46090}, {2148, 44715}, {2151, 39377}, {2152, 39378}, {2315, 10419}, {2433, 4575}, {6149, 11079}, {9717, 36060}, {14575, 33805}, {15291, 19614}, {24018, 32715}
X(46106) = barycentric product X(i)*X(j) for these {i,j}: {4, 3260}, {5, 43752}, {30, 264}, {75, 1784}, {76, 1990}, {92, 14206}, {94, 14920}, {300, 6110}, {301, 6111}, {324, 43768}, {331, 7359}, {340, 14254}, {648, 41079}, {811, 36035}, {850, 4240}, {1494, 34334}, {1495, 18022}, {1502, 14581}, {1511, 18817}, {1568, 8795}, {1577, 24001}, {1637, 6331}, {1969, 2173}, {2052, 11064}, {2407, 14618}, {3284, 18027}, {6148, 6344}, {6357, 7017}, {6528, 9033}, {9214, 44146}, {9407, 44161}, {14391, 42405}, {15352, 41077}, {15454, 44138}, {16080, 36789}, {17924, 42716}, {20573, 39176}, {23347, 44173}, {35906, 44132}, {36891, 44145}
X(46106) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 35200}, {2, 14919}, {4, 74}, {5, 44715}, {6, 18877}, {13, 39377}, {14, 39378}, {19, 2159}, {25, 40352}, {30, 3}, {54, 46090}, {92, 2349}, {107, 1304}, {112, 32640}, {113, 13754}, {133, 6000}, {158, 36119}, {162, 36034}, {186, 14385}, {264, 1494}, {281, 15627}, {297, 35910}, {318, 44693}, {393, 8749}, {403, 14264}, {468, 9717}, {523, 14380}, {648, 44769}, {850, 34767}, {1249, 15291}, {1294, 15404}, {1300, 10419}, {1495, 184}, {1511, 22115}, {1514, 10605}, {1568, 5562}, {1636, 32320}, {1637, 647}, {1650, 2972}, {1784, 1}, {1969, 33805}, {1989, 11079}, {1990, 6}, {2052, 16080}, {2173, 48}, {2207, 40354}, {2407, 4558}, {2420, 32661}, {2501, 2433}, {2631, 822}, {2970, 12079}, {3163, 3284}, {3184, 12096}, {3258, 16186}, {3260, 69}, {3284, 577}, {3471, 43704}, {4240, 110}, {5642, 3292}, {5664, 8552}, {6000, 39174}, {6110, 15}, {6111, 16}, {6344, 5627}, {6357, 222}, {6528, 16077}, {6529, 32695}, {6530, 35908}, {6761, 38933}, {6793, 8779}, {7359, 219}, {7687, 34329}, {8749, 40353}, {9033, 520}, {9214, 895}, {9406, 9247}, {9407, 14575}, {9409, 39201}, {11064, 394}, {11080, 39380}, {11085, 39381}, {11125, 1459}, {11251, 5663}, {11589, 14379}, {13202, 21663}, {14206, 63}, {14249, 10152}, {14254, 265}, {14391, 17434}, {14395, 36054}, {14397, 30451}, {14398, 3049}, {14399, 22383}, {14400, 652}, {14401, 1636}, {14581, 32}, {14618, 2394}, {14920, 323}, {15144, 6090}, {15352, 15459}, {15454, 5504}, {15459, 34568}, {16080, 40384}, {16230, 32112}, {16240, 1495}, {16263, 22455}, {17983, 9139}, {18384, 40355}, {18486, 18477}, {18487, 5158}, {18507, 12041}, {18653, 1790}, {20772, 41615}, {23097, 16163}, {23347, 1576}, {24001, 662}, {24019, 36131}, {32713, 32715}, {34104, 34333}, {34170, 38937}, {34297, 8431}, {34334, 30}, {35201, 6149}, {35360, 36831}, {35906, 248}, {35912, 17974}, {36035, 656}, {36298, 36297}, {36299, 36296}, {36417, 40351}, {36789, 11064}, {36891, 43705}, {37943, 3470}, {38605, 6760}, {38956, 11589}, {39176, 50}, {39375, 12028}, {41079, 525}, {41392, 32662}, {41887, 44718}, {41888, 44719}, {42716, 1332}, {42750, 8677}, {43752, 95}, {43768, 97}, {44145, 36875}, {44146, 36890}, {44203, 30209}, {44721, 44727}
X(46106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 324, 40684}, {2, 2052, 324}, {2, 37766, 14165}, {2, 43988, 6509}, {297, 3580, 14918}, {450, 41204, 110}, {468, 2970, 44145}, {2052, 15466, 2}, {5943, 42400, 30506}, {6331, 44132, 3266}, {6820, 14361, 6515}, {14165, 37765, 37766}


X(46107) = POLAR CONJUGATE OF X(101)

Barycentrics    b^2*(b - c)*c^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) : :
Barycentrics    (csc 2A) (b - c) : :
Trilinears    A'-power of Stevanovic circle : :, where A'B'C' is the orthic triangle

X(46107) lies on these lines: {4, 20295}, {25, 26277}, {27, 649}, {92, 3064}, {273, 3676}, {297, 525}, {469, 3835}, {521, 23683}, {693, 17094}, {1577, 23595}, {3004, 39534}, {3261, 4025}, {3766, 18344}, {4106, 16228}, {4374, 43923}, {4467, 44428}, {6528, 35169}, {6994, 26853}, {7490, 27013}, {14208, 18076}, {17494, 17926}, {17496, 17925}, {17861, 21184}, {18026, 35174}, {21666, 23989}, {24032, 36118}, {25924, 26003}

X(46107) = isogonal conjugate of X(32656)
X(46107) = isotomic conjugate of X(1331)
X(46107) = polar conjugate of X(101)
X(46107) = isotomic conjugate of the isogonal conjugate of X(7649)
X(46107) = polar conjugate of the isotomic conjugate of X(3261)
X(46107) = polar conjugate of the isogonal conjugate of X(514)
X(46107) = pole wrt polar circle of trilinear polar of X(101) (line X(6)X(31))
X(46107) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1305, 4329}, {1751, 34188}
X(46107) = X(264)-Ceva conjugate of X(2973)
X(46107) = X(i)-cross conjugate of X(j) for these (i,j): {514, 3261}, {1111, 273}, {2973, 264}, {3120, 27}, {4077, 693}, {17877, 75}, {21102, 514}, {21108, 7649}, {21666, 2052}, {23752, 1577}, {24006, 17924}
X(46107) = cevapoint of X(i) and X(j) for these (i,j): {514, 7649}, {6586, 8676}, {14618, 24006}, {16732, 42455}, {17924, 44426}, {23595, 23752}
X(46107) = crosspoint of X(286) and X(18026)
X(46107) = crosssum of X(i) and X(j) for these (i,j): {3, 23093}, {228, 1946}
X(46107) = trilinear pole of line {116, 2973}
X(46107) = crossdifference of every pair of points on line {184, 2200}
X(46107) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32656}, {3, 692}, {6, 906}, {9, 32660}, {31, 1331}, {32, 1332}, {37, 32661}, {41, 1813}, {42, 4575}, {48, 101}, {55, 36059}, {59, 1946}, {63, 32739}, {71, 163}, {72, 1576}, {100, 184}, {108, 6056}, {109, 212}, {110, 228}, {112, 3990}, {162, 4055}, {190, 9247}, {213, 4558}, {219, 1415}, {255, 8750}, {560, 4561}, {577, 1783}, {603, 3939}, {604, 4587}, {652, 2149}, {662, 2200}, {668, 14575}, {810, 4570}, {901, 23202}, {905, 23990}, {919, 20752}, {1023, 32659}, {1110, 1459}, {1252, 22383}, {1333, 4574}, {1397, 4571}, {1409, 5546}, {1437, 4557}, {1461, 1802}, {1818, 32666}, {1918, 4592}, {2175, 6516}, {2193, 4559}, {2194, 23067}, {2205, 4563}, {2212, 6517}, {2253, 35182}, {2284, 32658}, {2289, 32674}, {2426, 36056}, {2427, 14578}, {2715, 42702}, {3049, 4567}, {3063, 44717}, {3682, 32676}, {3781, 34069}, {4020, 4628}, {4064, 23995}, {4553, 10547}, {5360, 43754}, {5377, 23225}, {5379, 39201}, {5380, 23200}, {5440, 32719}, {6335, 14585}, {6386, 40373}, {7078, 32652}, {7115, 36054}, {7193, 34067}, {8685, 20753}, {8687, 22074}, {8701, 23201}, {14574, 20336}, {14600, 42717}, {15439, 23207}, {15958, 21807}, {20818, 34080}, {22134, 32653}, {22345, 32736}, {22356, 32665}, {23344, 36058}
X(46107) = barycentric product X(i)*X(j) for these {i,j}: {4, 3261}, {19, 40495}, {27, 850}, {28, 20948}, {75, 17924}, {76, 7649}, {85, 44426}, {86, 14618}, {92, 693}, {158, 15413}, {190, 2973}, {264, 514}, {273, 4391}, {274, 24006}, {276, 21102}, {278, 35519}, {286, 1577}, {308, 21108}, {310, 2501}, {313, 17925}, {318, 24002}, {331, 522}, {513, 1969}, {523, 44129}, {561, 6591}, {648, 21207}, {649, 18022}, {653, 34387}, {658, 21666}, {811, 16732}, {1093, 30805}, {1111, 6335}, {1235, 10566}, {1459, 18027}, {1474, 44173}, {1847, 4397}, {1897, 23989}, {1919, 44161}, {1978, 2969}, {2052, 4025}, {2970, 4610}, {3064, 6063}, {3120, 6331}, {3267, 8747}, {3676, 7017}, {4077, 31623}, {4131, 6521}, {4444, 40717}, {4466, 6528}, {4572, 8735}, {4858, 18026}, {7178, 44130}, {7199, 41013}, {13149, 24026}, {15352, 17216}, {15742, 23100}, {16082, 36038}, {16747, 18070}, {18155, 40149}, {18344, 20567}, {21178, 43678}, {23595, 40422}, {23978, 36118}, {28659, 43923}
X(46107) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 906}, {2, 1331}, {4, 101}, {6, 32656}, {7, 1813}, {8, 4587}, {10, 4574}, {11, 652}, {19, 692}, {25, 32739}, {27, 110}, {28, 163}, {29, 5546}, {34, 1415}, {56, 32660}, {57, 36059}, {58, 32661}, {75, 1332}, {76, 4561}, {81, 4575}, {85, 6516}, {86, 4558}, {92, 100}, {108, 2149}, {158, 1783}, {225, 4559}, {226, 23067}, {244, 22383}, {264, 190}, {273, 651}, {274, 4592}, {278, 109}, {281, 3939}, {286, 662}, {310, 4563}, {312, 4571}, {318, 644}, {331, 664}, {338, 4064}, {348, 6517}, {393, 8750}, {423, 17943}, {512, 2200}, {513, 48}, {514, 3}, {521, 2289}, {522, 219}, {523, 71}, {525, 3682}, {647, 4055}, {648, 4570}, {649, 184}, {650, 212}, {652, 6056}, {653, 59}, {656, 3990}, {661, 228}, {664, 44717}, {667, 9247}, {693, 63}, {811, 4567}, {812, 7193}, {823, 5379}, {824, 3781}, {850, 306}, {876, 2196}, {900, 22356}, {905, 255}, {917, 35182}, {918, 1818}, {1019, 1437}, {1022, 36058}, {1027, 32658}, {1086, 1459}, {1111, 905}, {1118, 32674}, {1119, 1461}, {1235, 4568}, {1459, 577}, {1474, 1576}, {1565, 4091}, {1577, 72}, {1635, 23202}, {1647, 22086}, {1783, 1110}, {1785, 2427}, {1826, 4557}, {1839, 35327}, {1847, 934}, {1861, 2284}, {1870, 1983}, {1886, 2426}, {1897, 1252}, {1919, 14575}, {1969, 668}, {2052, 1897}, {2170, 1946}, {2254, 20752}, {2400, 1815}, {2401, 1795}, {2424, 32657}, {2489, 1918}, {2501, 42}, {2517, 5227}, {2530, 4020}, {2533, 22061}, {2786, 17976}, {2969, 649}, {2970, 4024}, {2973, 514}, {3004, 22097}, {3064, 55}, {3120, 647}, {3122, 3049}, {3125, 810}, {3239, 1260}, {3261, 69}, {3663, 23113}, {3667, 20818}, {3669, 603}, {3676, 222}, {3700, 2318}, {3737, 2193}, {3762, 5440}, {3766, 20769}, {3776, 3784}, {3798, 3167}, {3801, 20727}, {3835, 20760}, {3837, 20785}, {3900, 1802}, {3942, 23224}, {4017, 1409}, {4024, 3690}, {4025, 394}, {4036, 3949}, {4077, 1214}, {4086, 3694}, {4091, 1092}, {4131, 6507}, {4142, 23150}, {4369, 3955}, {4391, 78}, {4397, 3692}, {4425, 23139}, {4444, 295}, {4453, 22128}, {4458, 20741}, {4462, 4855}, {4466, 520}, {4560, 283}, {4581, 2359}, {4608, 1796}, {4750, 3292}, {4785, 23095}, {4791, 3940}, {4801, 4652}, {4815, 4047}, {4823, 3927}, {4858, 521}, {4962, 22147}, {4977, 22054}, {4978, 3916}, {4979, 23201}, {4988, 22080}, {5190, 8676}, {5236, 2283}, {5317, 32676}, {6006, 23073}, {6084, 20780}, {6331, 4600}, {6332, 1259}, {6335, 765}, {6336, 901}, {6544, 22371}, {6545, 3937}, {6548, 1797}, {6590, 7085}, {6591, 31}, {7004, 36054}, {7017, 3699}, {7101, 4578}, {7129, 32652}, {7141, 4103}, {7178, 73}, {7192, 1790}, {7199, 1444}, {7200, 22093}, {7202, 23226}, {7216, 1410}, {7253, 2327}, {7649, 6}, {7658, 22117}, {7661, 22124}, {8714, 22126}, {8735, 663}, {8747, 112}, {8750, 23990}, {8751, 32666}, {8752, 32719}, {8754, 4079}, {8756, 23344}, {10015, 22350}, {10566, 1176}, {11125, 3284}, {11263, 23084}, {13149, 7045}, {14208, 3998}, {14618, 10}, {14775, 2259}, {14837, 7078}, {15413, 326}, {16082, 36037}, {16732, 656}, {16892, 3917}, {17094, 40152}, {17167, 23181}, {17171, 1634}, {17197, 23189}, {17205, 7254}, {17420, 22074}, {17498, 1801}, {17761, 22160}, {17921, 38832}, {17922, 595}, {17924, 1}, {17925, 58}, {17926, 2328}, {17982, 2702}, {18022, 1978}, {18026, 4564}, {18155, 1812}, {18210, 822}, {18344, 41}, {20504, 20728}, {20505, 20730}, {20507, 20731}, {20508, 20732}, {20509, 20733}, {20510, 20734}, {20511, 20735}, {20512, 20736}, {20513, 20737}, {20515, 20738}, {20516, 20740}, {20517, 20739}, {20518, 20742}, {20519, 20743}, {20520, 20744}, {20521, 20745}, {20522, 20746}, {20525, 20747}, {20526, 20748}, {20883, 4553}, {20906, 22370}, {20948, 20336}, {20974, 22388}, {21102, 216}, {21103, 22052}, {21104, 22053}, {21105, 22055}, {21106, 22056}, {21107, 22057}, {21108, 39}, {21109, 14961}, {21110, 20819}, {21111, 22058}, {21112, 22059}, {21113, 22062}, {21114, 22064}, {21115, 22067}, {21116, 22068}, {21117, 22069}, {21118, 22070}, {21119, 22071}, {21120, 22072}, {21121, 22073}, {21122, 22075}, {21123, 20775}, {21124, 22076}, {21125, 22077}, {21126, 22078}, {21127, 22079}, {21128, 22081}, {21129, 22082}, {21130, 22083}, {21131, 20975}, {21132, 7117}, {21133, 22084}, {21134, 3269}, {21135, 22085}, {21136, 22087}, {21137, 22089}, {21138, 22090}, {21139, 22091}, {21140, 22092}, {21141, 22094}, {21142, 22095}, {21143, 22096}, {21144, 2524}, {21145, 22098}, {21146, 22099}, {21172, 15905}, {21173, 22118}, {21174, 22119}, {21175, 22120}, {21176, 22121}, {21178, 20806}, {21179, 22122}, {21180, 22123}, {21181, 22162}, {21182, 22125}, {21183, 22129}, {21184, 22130}, {21185, 22131}, {21186, 22132}, {21187, 22133}, {21188, 3157}, {21189, 22134}, {21190, 22135}, {21191, 20794}, {21192, 22136}, {21193, 22137}, {21194, 22138}, {21195, 20793}, {21196, 22139}, {21197, 22140}, {21198, 22141}, {21199, 22142}, {21200, 22143}, {21201, 22144}, {21202, 22145}, {21203, 22146}, {21204, 22148}, {21205, 22151}, {21206, 22152}, {21207, 525}, {21208, 22154}, {21209, 22156}, {21210, 22157}, {21211, 22158}, {21212, 22161}, {21665, 3234}, {21666, 3239}, {23100, 1565}, {23105, 21046}, {23224, 4100}, {23290, 21011}, {23345, 32659}, {23595, 942}, {23681, 35350}, {23726, 39796}, {23735, 22411}, {23748, 22440}, {23751, 23196}, {23752, 18591}, {23756, 20755}, {23772, 22443}, {23785, 23124}, {23799, 23131}, {23801, 23114}, {23803, 23160}, {23806, 23171}, {23824, 23092}, {23989, 4025}, {24002, 77}, {24006, 37}, {24220, 23161}, {24225, 23146}, {24237, 23187}, {24720, 22163}, {25381, 20797}, {26705, 15378}, {27918, 22384}, {28209, 22357}, {29013, 42463}, {30591, 3958}, {30805, 3964}, {31605, 23144}, {31623, 643}, {32085, 4628}, {32714, 24027}, {34387, 6332}, {34948, 563}, {35518, 3719}, {35519, 345}, {36118, 1262}, {36122, 36039}, {36123, 32641}, {36124, 919}, {36125, 32665}, {36127, 7115}, {36613, 29217}, {37203, 6099}, {37790, 23703}, {38357, 10397}, {38461, 23890}, {38462, 1023}, {39534, 2183}, {40149, 4551}, {40166, 7004}, {40445, 29163}, {40495, 304}, {40573, 15439}, {40627, 23212}, {40703, 42717}, {40717, 3570}, {40836, 36049}, {41013, 1018}, {42067, 1919}, {42069, 657}, {42455, 34591}, {42462, 3270}, {42754, 8677}, {43923, 604}, {43925, 2206}, {43931, 15373}, {43932, 7099}, {43933, 909}, {44129, 99}, {44130, 645}, {44143, 4115}, {44173, 40071}, {44312, 23093}, {44426, 9}, {44428, 2323}, {44721, 30720}, {45674, 23166}


X(46108) = POLAR CONJUGATE OF X(105)

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

X(46108) lies on these lines: {2, 17916}, {4, 8}, {19, 3729}, {27, 19835}, {29, 4968}, {37, 17913}, {75, 281}, {76, 331}, {107, 2754}, {112, 44330}, {225, 4044}, {239, 1783}, {240, 726}, {273, 1229}, {278, 312}, {297, 525}, {536, 14571}, {664, 45798}, {666, 8751}, {860, 3948}, {1013, 26227}, {1016, 37790}, {1089, 1838}, {1430, 17763}, {1435, 30567}, {1441, 26165}, {1748, 32933}, {1826, 20236}, {1861, 3717}, {1957, 4362}, {2223, 4238}, {2331, 3875}, {3006, 37371}, {3187, 8743}, {3263, 5089}, {3673, 17862}, {3701, 5125}, {3705, 37372}, {3757, 4183}, {3912, 5236}, {4054, 30687}, {4219, 7081}, {4358, 17923}, {4384, 7079}, {5307, 24630}, {6335, 37788}, {6656, 26153}, {7076, 32914}, {7172, 37104}, {7283, 41227}, {7414, 26243}, {7719, 33937}, {7770, 26203}, {7952, 20173}, {8756, 20881}, {13727, 23661}, {14954, 20045}, {16747, 31909}, {17442, 17760}, {17858, 20239}, {17859, 40942}, {17863, 17918}, {17903, 30699}, {17917, 18743}, {18026, 35158}, {18689, 26006}, {20336, 25252}, {20880, 37448}, {23581, 25935}, {24199, 25993}, {31130, 37102}, {31623, 31926}, {32714, 40862}, {32851, 37799}, {43675, 43678}

X(46108) = isogonal conjugate of X(32658)
X(46108) = isotomic conjugate of X(1814)
X(46108) = polar conjugate of X(105)
X(46108) = isotomic conjugate of the isogonal conjugate of X(5089)
X(46108) = polar conjugate of the isotomic conjugate of X(3263)
X(46108) = polar conjugate of the isogonal conjugate of X(518)
X(46108) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {26703, 4329}, {32688, 522}, {36093, 693}
X(46108) = X(264)-Ceva conjugate of X(34337)
X(46108) = X(i)-cross conjugate of X(j) for these (i,j): {518, 3263}, {24290, 4238}, {34337, 264}
X(46108) = cevapoint of X(i) and X(j) for these (i,j): {518, 5089}, {3290, 3827}
X(46108) = trilinear pole of line {120, 20621}
X(46108) = crossdifference of every pair of points on line {184, 22383}
X(46108) = pole wrt polar circle of trilinear polar of X(105) (line X(6)X(513))
X(46108) = perspector of the circumconic through the polar conjugates of PU(46) and PU(54)
X(46108) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32658}, {3, 1438}, {6, 36057}, {31, 1814}, {32, 31637}, {48, 105}, {163, 10099}, {184, 673}, {212, 1462}, {219, 1416}, {222, 2195}, {255, 8751}, {294, 603}, {577, 36124}, {652, 32735}, {884, 1813}, {885, 32660}, {905, 32666}, {906, 1027}, {919, 1459}, {1024, 36059}, {1331, 43929}, {1415, 23696}, {1437, 18785}, {1818, 41934}, {1946, 36146}, {2481, 9247}, {7099, 28071}, {14575, 18031}, {22383, 36086}
X(46108) = barycentric product X(i)*X(j) for these {i,j}: {4, 3263}, {75, 1861}, {76, 5089}, {92, 3912}, {241, 7017}, {264, 518}, {273, 3717}, {281, 40704}, {286, 3932}, {312, 5236}, {318, 9436}, {321, 15149}, {331, 3693}, {561, 2356}, {672, 1969}, {811, 4088}, {850, 4238}, {883, 44426}, {918, 6335}, {1826, 18157}, {1876, 3596}, {2052, 25083}, {2223, 18022}, {2481, 34337}, {3930, 44129}, {6331, 24290}, {9455, 44161}, {17924, 42720}, {18027, 20752}, {22116, 40717}, {30941, 41013}
X(46108) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36057}, {2, 1814}, {4, 105}, {6, 32658}, {19, 1438}, {33, 2195}, {34, 1416}, {75, 31637}, {92, 673}, {108, 32735}, {120, 34381}, {158, 36124}, {241, 222}, {264, 2481}, {278, 1462}, {281, 294}, {318, 14942}, {331, 34018}, {393, 8751}, {518, 3}, {522, 23696}, {523, 10099}, {653, 36146}, {665, 22383}, {672, 48}, {883, 6516}, {918, 905}, {926, 1946}, {1025, 1813}, {1026, 1331}, {1458, 603}, {1783, 919}, {1818, 255}, {1826, 18785}, {1861, 1}, {1876, 56}, {1897, 36086}, {1969, 18031}, {2223, 184}, {2254, 1459}, {2283, 36059}, {2284, 906}, {2340, 212}, {2356, 31}, {2969, 43921}, {3064, 1024}, {3252, 2196}, {3263, 69}, {3286, 1437}, {3675, 3937}, {3693, 219}, {3717, 78}, {3827, 34160}, {3912, 63}, {3930, 71}, {3932, 72}, {4088, 656}, {4238, 110}, {4437, 25083}, {4447, 3955}, {4684, 4652}, {4712, 1818}, {4899, 4855}, {4966, 3916}, {5089, 6}, {5236, 57}, {6184, 20752}, {6335, 666}, {6554, 23601}, {6591, 43929}, {7017, 36796}, {7046, 28071}, {7101, 6559}, {7649, 1027}, {8299, 7193}, {8750, 32666}, {8751, 41934}, {9436, 77}, {9454, 9247}, {9455, 14575}, {10029, 27832}, {14439, 22356}, {15149, 81}, {15344, 15382}, {15742, 5377}, {17435, 7117}, {17755, 20769}, {18026, 927}, {18157, 17206}, {18206, 1790}, {18344, 884}, {20621, 3827}, {20683, 228}, {20752, 577}, {22116, 295}, {23612, 20776}, {24290, 647}, {25083, 394}, {26706, 35185}, {30941, 1444}, {34230, 36058}, {34337, 518}, {34855, 7053}, {36819, 1795}, {37908, 2194}, {39258, 2200}, {40704, 348}, {41013, 13576}, {42071, 2223}, {42341, 22091}, {42720, 1332}, {42758, 8677}, {44426, 885}


X(46109) = POLAR CONJUGATE OF X(106)

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

X(46109) lies on these lines: {4, 21282}, {27, 19811}, {80, 5081}, {92, 264}, {107, 2760}, {242, 17987}, {281, 17740}, {297, 525}, {318, 6736}, {321, 41883}, {331, 40029}, {1145, 4723}, {1897, 32927}, {1904, 41013}, {2052, 4052}, {2997, 7003}, {3264, 3977}, {3995, 18677}, {4358, 37790}, {6335, 17923}, {6528, 35161}, {14206, 35516}, {17147, 18676}, {17495, 17906}, {17555, 37716}, {17861, 24177}, {21270, 32001}, {40013, 40149}

X(46109) = isogonal conjugate of X(32659)
X(46109) = isotomic conjugate of X(1797)
X(46109) = polar conjugate of X(106)
X(46109) = isotomic conjugate of the isogonal conjugate of X(8756)
X(46109) = polar conjugate of the isotomic conjugate of X(3264)
X(46109) = polar conjugate of the isogonal conjugate of X(519)
X(46109) = X(2370)-anticomplementary conjugate of X(4329)
X(46109) = X(519)-cross conjugate of X(3264)
X(46109) = pole wrt polar circle of trilinear polar of X(106) (line X(6)X(649))
X(46109) = cevapoint of X(i) and X(j) for these (i,j): {519, 8756}, {2390, 8610}
X(46109) = trilinear pole of line {121, 4768}
X(46109) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32659}, {3, 9456}, {6, 36058}, {31, 1797}, {48, 106}, {88, 184}, {219, 1417}, {255, 8752}, {577, 36125}, {603, 2316}, {810, 4591}, {901, 22383}, {903, 9247}, {905, 32719}, {906, 23345}, {1022, 32656}, {1459, 32665}, {2226, 23202}, {3049, 4622}, {5376, 22096}, {5440, 41935}, {14260, 14578}, {14575, 20568}, {23838, 32660}, {32658, 34230}
X(46109) = barycentric product X(i)*X(j) for these {i,j}: {4, 3264}, {44, 1969}, {75, 38462}, {76, 8756}, {92, 4358}, {264, 519}, {273, 4723}, {286, 3992}, {312, 37790}, {313, 37168}, {331, 2325}, {902, 18022}, {1877, 3596}, {2052, 3977}, {3762, 6335}, {3911, 7017}, {3943, 44129}, {4120, 6331}, {4768, 18026}, {6336, 36791}, {6528, 14429}, {9459, 44161}, {17924, 24004}, {18027, 22356}, {30939, 41013}, {40663, 44130}
X(46109) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36058}, {2, 1797}, {4, 106}, {6, 32659}, {19, 9456}, {34, 1417}, {44, 48}, {92, 88}, {158, 36125}, {264, 903}, {281, 2316}, {318, 1320}, {393, 8752}, {519, 3}, {648, 4591}, {678, 23202}, {811, 4622}, {900, 1459}, {902, 184}, {1023, 906}, {1145, 22350}, {1319, 603}, {1635, 22383}, {1639, 652}, {1647, 3937}, {1783, 32665}, {1785, 14260}, {1846, 1457}, {1861, 34230}, {1870, 16944}, {1877, 56}, {1878, 17109}, {1897, 901}, {1969, 20568}, {2052, 6336}, {2251, 9247}, {2325, 219}, {2969, 43922}, {2973, 6549}, {3264, 69}, {3689, 212}, {3762, 905}, {3911, 222}, {3943, 71}, {3977, 394}, {3992, 72}, {4120, 647}, {4169, 4574}, {4358, 63}, {4370, 22356}, {4432, 7193}, {4434, 3955}, {4439, 3781}, {4448, 22384}, {4487, 4855}, {4530, 7117}, {4723, 78}, {4730, 810}, {4738, 5440}, {4742, 4652}, {4759, 23095}, {4768, 521}, {4895, 1946}, {4922, 22093}, {4969, 22054}, {4975, 3916}, {5151, 1149}, {5440, 255}, {6331, 4615}, {6335, 3257}, {6336, 2226}, {6544, 22086}, {7017, 4997}, {7141, 4013}, {7649, 23345}, {8028, 22371}, {8750, 32719}, {8752, 41935}, {8756, 6}, {9459, 14575}, {14407, 3049}, {14418, 36054}, {14429, 520}, {14439, 20752}, {14618, 4049}, {15742, 9268}, {16704, 1790}, {17460, 23205}, {17780, 1331}, {17923, 40215}, {17924, 1022}, {20619, 2390}, {21805, 228}, {22356, 577}, {23344, 32656}, {23703, 36059}, {23757, 8677}, {24004, 1332}, {30731, 4587}, {30939, 1444}, {31011, 1796}, {32704, 35186}, {34587, 23169}, {36123, 10428}, {36791, 3977}, {36944, 1795}, {37168, 58}, {37790, 57}, {38462, 1}, {40101, 15383}, {40663, 73}, {40717, 27922}, {41013, 4674}, {42070, 902}, {44426, 23838}, {45144, 32657}


X(46110) = POLAR CONJUGATE OF X(109)

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

X(46110) lies on these lines: {4, 21302}, {29, 663}, {92, 514}, {107, 2769}, {158, 21185}, {286, 4406}, {297, 525}, {318, 44448}, {2804, 4397}, {3064, 6332}, {4040, 39585}, {5125, 17072}, {6335, 36804}, {17922, 37770}

X(46110) = isogonal conjugate of X(32660)
X(46110) = isotomic conjugate of X(1813)
X(46110) = polar conjugate of X(109)
X(46110) = isotomic conjugate of the isogonal conjugate of X(3064)
X(46110) = polar conjugate of the isotomic conjugate of X(35519)
X(46110) = polar conjugate of the isogonal conjugate of X(522)
X(46110) = X(41906)-anticomplementary conjugate of X(4329)
X(46110) = X(i)-Ceva conjugate of X(j) for these (i,j): {264, 21666}, {331, 34387}
X(46110) = X(i)-cross conjugate of X(j) for these (i,j): {522, 35519}, {1577, 4391}, {4858, 92}, {21044, 29}, {21666, 264}, {23104, 34387}
X(46110) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32660}, {3, 1415}, {6, 36059}, {31, 1813}, {32, 6516}, {48, 109}, {56, 906}, {57, 32656}, {59, 22383}, {65, 32661}, {73, 163}, {77, 32739}, {101, 603}, {108, 577}, {110, 1409}, {112, 22341}, {184, 651}, {212, 1461}, {222, 692}, {228, 4565}, {255, 32674}, {521, 23979}, {604, 1331}, {652, 24027}, {664, 9247}, {667, 44717}, {1106, 4587}, {1214, 1576}, {1231, 14574}, {1262, 1946}, {1332, 1397}, {1333, 23067}, {1400, 4575}, {1402, 4558}, {1408, 4574}, {1410, 5546}, {1414, 2200}, {1437, 4559}, {1459, 2149}, {1783, 7335}, {1802, 6614}, {1973, 6517}, {2283, 32658}, {2425, 36055}, {3939, 7099}, {4100, 36127}, {4554, 14575}, {6056, 32714}, {6510, 32728}, {7011, 32652}, {7114, 36049}, {7115, 23224}, {7125, 8750}, {8687, 22345}, {14578, 23981}, {14585, 18026}, {14597, 15439}, {20752, 32735}, {22096, 31615}, {22350, 32669}, {23207, 32651}, {23703, 32659}, {32676, 40152}, {40518, 44085}
X(46110) = cevapoint of X(i) and X(j) for these (i,j): {522, 3064}, {1577, 14618}
X(46110) = crosspoint of X(6335) and X(31623)
X(46110) = crosssum of X(1409) and X(22383)
X(46110) = trilinear pole of line {124, 20620}
X(46110) = crossdifference of every pair of points on line {184, 23197}
X(46110) = pole wrt polar circle of trilinear polar of X(109) (line X(6)X(41))
X(46110) = barycentric product X(i)*X(j) for these {i,j}: {4, 35519}, {29, 850}, {33, 40495}, {75, 44426}, {76, 3064}, {92, 4391}, {158, 35518}, {264, 522}, {273, 4397}, {281, 3261}, {286, 4086}, {312, 17924}, {314, 24006}, {318, 693}, {331, 3239}, {333, 14618}, {349, 17926}, {514, 7017}, {523, 44130}, {561, 18344}, {650, 1969}, {652, 18027}, {653, 23978}, {663, 18022}, {664, 21666}, {1172, 20948}, {1577, 31623}, {1896, 14208}, {1897, 34387}, {1978, 8735}, {2052, 6332}, {2299, 44173}, {2501, 28660}, {2973, 3699}, {3267, 8748}, {3596, 7649}, {3700, 44129}, {4572, 42069}, {4858, 6335}, {6331, 21044}, {6591, 28659}, {7020, 17896}, {7101, 24002}, {17925, 30713}, {18026, 24026}, {18155, 41013}, {20566, 44428}, {21207, 36797}
X(46110) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36059}, {2, 1813}, {4, 109}, {6, 32660}, {8, 1331}, {9, 906}, {10, 23067}, {11, 1459}, {19, 1415}, {21, 4575}, {27, 4565}, {29, 110}, {33, 692}, {55, 32656}, {69, 6517}, {75, 6516}, {92, 651}, {108, 24027}, {158, 108}, {190, 44717}, {264, 664}, {273, 934}, {278, 1461}, {281, 101}, {284, 32661}, {286, 1414}, {312, 1332}, {314, 4592}, {318, 100}, {331, 658}, {333, 4558}, {341, 4571}, {346, 4587}, {393, 32674}, {415, 17942}, {513, 603}, {514, 222}, {521, 255}, {522, 3}, {523, 73}, {525, 40152}, {607, 32739}, {650, 48}, {652, 577}, {653, 1262}, {656, 22341}, {661, 1409}, {663, 184}, {693, 77}, {850, 307}, {885, 36057}, {905, 7125}, {1021, 2193}, {1024, 32658}, {1093, 36127}, {1119, 6614}, {1146, 652}, {1172, 163}, {1459, 7335}, {1577, 1214}, {1639, 22356}, {1783, 2149}, {1785, 23981}, {1826, 4559}, {1839, 36075}, {1847, 4617}, {1855, 35326}, {1857, 8750}, {1861, 2283}, {1896, 162}, {1897, 59}, {1969, 4554}, {2052, 653}, {2170, 22383}, {2299, 1576}, {2310, 1946}, {2321, 4574}, {2322, 5546}, {2501, 1400}, {2517, 1038}, {2785, 17975}, {2804, 22350}, {2969, 43924}, {2973, 3676}, {3063, 9247}, {3064, 6}, {3239, 219}, {3261, 348}, {3452, 23113}, {3596, 4561}, {3669, 7099}, {3676, 7053}, {3700, 71}, {3709, 2200}, {3716, 7193}, {3737, 1437}, {3810, 3784}, {3900, 212}, {3904, 22128}, {3907, 3955}, {3910, 22097}, {4017, 1410}, {4024, 2197}, {4025, 1804}, {4036, 201}, {4041, 228}, {4064, 7066}, {4077, 1439}, {4086, 72}, {4124, 22384}, {4130, 1802}, {4140, 22061}, {4147, 20760}, {4163, 1260}, {4391, 63}, {4397, 78}, {4459, 22093}, {4468, 23144}, {4516, 810}, {4521, 20818}, {4522, 3781}, {4530, 22086}, {4543, 22371}, {4560, 1790}, {4768, 5440}, {4811, 4652}, {4858, 905}, {4895, 23202}, {4976, 22054}, {4985, 3916}, {5190, 43060}, {5514, 10397}, {6129, 7114}, {6331, 4620}, {6332, 394}, {6335, 4564}, {6362, 22053}, {6590, 2286}, {6591, 604}, {6608, 22079}, {6615, 22344}, {7003, 36049}, {7004, 23224}, {7008, 32652}, {7017, 190}, {7020, 13138}, {7040, 36082}, {7046, 3939}, {7101, 644}, {7253, 283}, {7649, 56}, {8058, 7078}, {8611, 3990}, {8735, 649}, {8748, 112}, {8755, 2425}, {9581, 35350}, {14331, 15905}, {14400, 3284}, {14432, 3292}, {14618, 226}, {14837, 7011}, {15313, 3215}, {15411, 6514}, {15413, 7183}, {15416, 3719}, {16082, 37136}, {16231, 34040}, {17197, 7254}, {17420, 22345}, {17880, 4131}, {17896, 7013}, {17899, 7364}, {17924, 57}, {17925, 1412}, {17926, 284}, {18022, 4572}, {18026, 7045}, {18155, 1444}, {18344, 31}, {20948, 1231}, {21044, 647}, {21102, 30493}, {21108, 1401}, {21119, 23154}, {21132, 3937}, {21207, 17094}, {21666, 522}, {23104, 2968}, {23615, 3270}, {23710, 23346}, {23752, 39791}, {23838, 36058}, {23978, 6332}, {24002, 7177}, {24006, 65}, {24026, 521}, {25128, 20794}, {26704, 15386}, {26932, 4091}, {28660, 4563}, {31623, 662}, {32674, 23979}, {32706, 35187}, {34387, 4025}, {34589, 23187}, {34591, 36054}, {35015, 8677}, {35196, 15958}, {35518, 326}, {35519, 69}, {36054, 4100}, {36118, 7339}, {36121, 36040}, {36123, 2720}, {36124, 32735}, {36797, 4570}, {37805, 23890}, {38462, 23703}, {39534, 1457}, {40149, 1020}, {40166, 3942}, {40495, 7182}, {40573, 32651}, {40836, 8059}, {41013, 4551}, {42069, 663}, {42337, 22072}, {42455, 7004}, {42462, 7117}, {43728, 1795}, {43923, 1106}, {43925, 16947}, {44129, 4573}, {44130, 99}, {44426, 1}, {44428, 36}, {44721, 43290}


X(46111) = POLAR CONJUGATE OF X(187)

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

X(46111) lies on these lines: {4, 41911}, {111, 16081}, {264, 2970}, {324, 42008}, {468, 8827}, {671, 2052}, {895, 8795}, {8753, 32581}, {8791, 18818}, {16089, 16092}

X(46111) = isogonal conjugate of X(23200)
X(46111) = isotomic conjugate of X(3292)
X(46111) = polar conjugate of X(187)
X(46111) = isotomic conjugate of the complement of X(41724)
X(46111) = isotomic conjugate of the isogonal conjugate of X(17983)
X(46111) = polar conjugate of the isotomic conjugate of X(18023)
X(46111) = polar conjugate of the isogonal conjugate of X(671)
X(46111) = pole wrt polar circle of trilinear polar of X(187) (line X(351)X(39689))
X(46111) = X(i)-cross conjugate of X(j) for these (i,j): {671, 18023}, {23679, 75}, {44146, 264}
X(46111) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23200}, {3, 922}, {31, 3292}, {48, 187}, {63, 14567}, {184, 896}, {255, 44102}, {351, 4575}, {524, 9247}, {560, 6390}, {810, 5467}, {2200, 16702}, {2642, 32661}, {3049, 23889}, {14210, 14575}, {14419, 32656}, {14908, 42081}, {36060, 39689}
X(46111) = cevapoint of X(i) and X(j) for these (i,j): {2, 41724}, {4, 37765}, {264, 44146}, {671, 17983}
X(46111) = trilinear pole of line {264, 8430}
X(46111) = barycentric product X(i)*X(j) for these {i,j}: {4, 18023}, {76, 17983}, {111, 18022}, {264, 671}, {561, 36128}, {892, 14618}, {895, 18027}, {897, 1969}, {1502, 8753}, {2052, 30786}, {5466, 6331}, {6528, 14977}, {9154, 44132}, {32740, 44161}
X(46111) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3292}, {4, 187}, {6, 23200}, {19, 922}, {25, 14567}, {76, 6390}, {92, 896}, {111, 184}, {264, 524}, {286, 16702}, {297, 9155}, {324, 41586}, {331, 7181}, {393, 44102}, {468, 39689}, {648, 5467}, {671, 3}, {691, 32661}, {811, 23889}, {850, 14417}, {892, 4558}, {895, 577}, {897, 48}, {923, 9247}, {1235, 7813}, {1969, 14210}, {2052, 468}, {2501, 351}, {2970, 1648}, {5380, 906}, {5466, 647}, {5968, 3289}, {6331, 5468}, {6528, 4235}, {7017, 3712}, {8430, 39469}, {8753, 32}, {8754, 21906}, {9139, 18877}, {9154, 248}, {9178, 3049}, {9214, 3284}, {10097, 39201}, {10561, 42659}, {10630, 14908}, {14246, 10317}, {14618, 690}, {14908, 14585}, {14977, 520}, {16080, 9717}, {16081, 5967}, {17924, 14419}, {17983, 6}, {17984, 5026}, {18022, 3266}, {18023, 69}, {18027, 44146}, {18312, 39474}, {18817, 43084}, {18818, 43697}, {19626, 40373}, {23894, 810}, {24006, 2642}, {30786, 394}, {31125, 3917}, {32740, 14575}, {34336, 8030}, {36085, 4575}, {36128, 31}, {36307, 36296}, {36310, 36297}, {37765, 6593}, {37778, 5095}, {40717, 4760}, {41013, 21839}, {44129, 6629}, {44145, 5477}, {44146, 2482}, {44173, 45807}, {44427, 44814}


X(46112) = BARYCENTRIC PRODUCT X(3)*X(15)

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

X(46112) lies on these lines: {3, 36297}, {6, 3132}, {15, 186}, {16, 5890}, {18, 252}, {50, 11136}, {61, 3567}, {62, 1199}, {184, 418}, {298, 17402}, {323, 40156}, {396, 32461}, {477, 5994}, {1568, 40682}, {3131, 11244}, {3166, 11464}, {3284, 36296}, {5063, 34395}, {5669, 35469}, {6137, 15470}, {8738, 42157}, {10640, 11453}, {11146, 40580}, {16645, 30542}, {21648, 22052}, {26882, 41089}, {34327, 40695}, {36760, 37641}

X(46112) = isogonal conjugate of the isotomic conjugate of X(44718)
X(46112) = isotomic conjugate of the polar conjugate of X(34394)
X(46112) = isogonal conjugate of the polar conjugate of X(15)
X(46112) = X(15)-Ceva conjugate of X(34394)
X(46112) = X(i)-isoconjugate of X(j) for these (i,j): {13, 92}, {19, 300}, {75, 8737}, {158, 40709}, {264, 2153}, {278, 44690}, {471, 2166}, {811, 20578}, {1577, 36306}, {1784, 36308}, {1969, 3457}, {2152, 18817}, {2184, 44702}, {23871, 36129}, {23895, 24006}
X(46112) = crosspoint of X(i) and X(j) for these (i,j): {15, 44718}, {32586, 36296}
X(46112) = crosssum of X(i) and X(j) for these (i,j): {13, 8737}, {470, 472}, {6111, 36299}
X(46112) = crossdifference of every pair of points on line {6116, 14618}
X(46112) = barycentric product X(i)*X(j) for these {i,j}: {3, 15}, {6, 44718}, {14, 22115}, {50, 40710}, {54, 44711}, {63, 2151}, {69, 34394}, {184, 298}, {323, 36297}, {394, 8739}, {470, 577}, {526, 38413}, {603, 44688}, {647, 17402}, {1511, 39378}, {4558, 6137}, {5616, 43704}, {5994, 8552}, {6117, 19210}, {6782, 42065}, {11086, 44719}, {11127, 32586}, {11131, 36296}, {11136, 40711}, {11137, 40712}, {11146, 32585}, {14379, 44700}, {14533, 33529}, {18877, 41887}, {23870, 32661}
X(46112) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 300}, {14, 18817}, {15, 264}, {32, 8737}, {50, 471}, {154, 44702}, {184, 13}, {212, 44690}, {298, 18022}, {418, 44713}, {470, 18027}, {577, 40709}, {1576, 36306}, {2151, 92}, {3049, 20578}, {3458, 6344}, {6137, 14618}, {8739, 2052}, {9247, 2153}, {11136, 472}, {11137, 473}, {14575, 3457}, {14585, 36296}, {14908, 36307}, {17402, 6331}, {18877, 36308}, {19627, 8740}, {22115, 299}, {32661, 23895}, {34394, 4}, {34980, 41997}, {36297, 94}, {38413, 35139}, {40710, 20573}, {44711, 311}, {44718, 76}
X(46112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 3165, 186}, {50, 11137, 11136}, {418, 577, 46113}, {11136, 11137, 34394}, {21648, 22052, 32586}


X(46113) = BARYCENTRIC PRODUCT X(3)*X(16)

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

X(46113) lies on these lines: {3, 36296}, {6, 3131}, {15, 5890}, {16, 186}, {17, 252}, {50, 11134}, {61, 1199}, {62, 3567}, {184, 418}, {299, 17403}, {323, 40157}, {395, 32460}, {477, 5995}, {1568, 40683}, {3132, 11243}, {3165, 11464}, {3284, 36297}, {5063, 34394}, {5668, 35470}, {6138, 15470}, {8737, 42158}, {10639, 11452}, {11145, 40581}, {16644, 30542}, {21647, 22052}, {26882, 41090}, {34328, 40696}, {36759, 37640}

X(46113) = isogonal conjugate of the isotomic conjugate of X(44719)
X(46113) = isotomic conjugate of the polar conjugate of X(34395)
X(46113) = isogonal conjugate of the polar conjugate of X(16)
X(46113) = X(16)-Ceva conjugate of X(34395)
X(46113) = X(i)-isoconjugate of X(j) for these (i,j): {14, 92}, {19, 301}, {75, 8738}, {158, 40710}, {264, 2154}, {278, 44691}, {470, 2166}, {811, 20579}, {1577, 36309}, {1784, 36311}, {1969, 3458}, {2151, 18817}, {2184, 44703}, {23870, 36129}, {23896, 24006}
X(46113) = crosspoint of X(i) and X(j) for these (i,j): {16, 44719}, {32585, 36297}
X(46113) = crosssum of X(i) and X(j) for these (i,j): {14, 8738}, {471, 473}, {6110, 36298}
X(46113) = crossdifference of every pair of points on line {6117, 14618}
X(46113) = barycentric product X(i)*X(j) for these {i,j}: {3, 16}, {6, 44719}, {13, 22115}, {50, 40709}, {54, 44712}, {63, 2152}, {69, 34395}, {184, 299}, {323, 36296}, {394, 8740}, {471, 577}, {526, 38414}, {603, 44689}, {647, 17403}, {1511, 39377}, {4558, 6138}, {5612, 43704}, {5995, 8552}, {6116, 19210}, {6783, 42065}, {11081, 44718}, {11126, 32585}, {11130, 36297}, {11134, 40711}, {11135, 40712}, {11145, 32586}, {14379, 44701}, {14533, 33530}, {18877, 41888}, {23871, 32661}
X(46113) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 301}, {13, 18817}, {16, 264}, {32, 8738}, {50, 470}, {154, 44703}, {184, 14}, {212, 44691}, {299, 18022}, {418, 44714}, {471, 18027}, {577, 40710}, {1576, 36309}, {2152, 92}, {3049, 20579}, {3457, 6344}, {6138, 14618}, {8740, 2052}, {9247, 2154}, {11134, 472}, {11135, 473}, {14575, 3458}, {14585, 36297}, {14908, 36310}, {17403, 6331}, {18877, 36311}, {19627, 8739}, {22115, 298}, {32661, 23896}, {34395, 4}, {34980, 41998}, {36296, 94}, {38414, 35139}, {40709, 20573}, {44712, 311}, {44719, 76}
X(46113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 3166, 186}, {50, 11134, 11135}, {418, 577, 46112}, {11134, 11135, 34395}, {21647, 22052, 32585}


X(46114) = X(30)X(113)∩X(140)X(389)

Barycentrics    (2*a^4 - 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) : :
X(46114) = {3 X[140] - 2 X[44673], X[323] + 2 X[40685], X[399] + 3 X[44450], 5 X[631] - X[32608], 5 X[632] + X[23061], X[10272] - 4 X[11064], X[11694] + 2 X[13857], 3 X[14156] - X[44673], 3 X[14643] - X[43893], 4 X[16239] - X[41586], 3 X[16532] - 5 X[38794], 3 X[22115] + X[25739], X[25739] - 3 X[37938], X[37496] + 3 X[37943]}

X(46114) lies on these lines: {2, 15038}, {3, 15806}, {5, 37495}, {30, 113}, {110, 43390}, {140, 389}, {323, 10821}, {343, 34331}, {399, 44450}, {511, 44234}, {546, 44686}, {548, 9820}, {631, 32608}, {632, 23061}, {858, 40111}, {1092, 10224}, {2072, 11801}, {3153, 34153}, {3628, 13142}, {5446, 20193}, {5447, 34004}, {5498, 5562}, {5972, 10096}, {6101, 10125}, {6143, 13420}, {6640, 45794}, {6677, 13451}, {9703, 31101}, {10124, 37649}, {10625, 18282}, {10627, 34577}, {11539, 14389}, {11563, 37477}, {11566, 37951}, {11585, 45970}, {13346, 44235}, {14449, 16238}, {14643, 43893}, {15137, 15426}, {15330, 37478}, {16239, 41586}, {16252, 32903}, {16266, 26958}, {16532, 38794}, {18281, 37669}, {18377, 35602}, {20424, 43809}, {22115, 25739}, {23336, 31834}, {32269, 44900}, {34148, 43575}, {37483, 44278}, {37496, 37943}

X(46114) = midpoint of X(i) and X(j) for these {i,j}: {5, 43574}, {858, 40111}, {3153, 34153}, {11563, 37477}, {22115, 37938}
X(46114) = reflection of X(i) in X(j) for these {i,j}: {140, 14156}, {10096, 5972}, {11801, 2072}, {32269, 44900}
X(46114) = X(2148)-complementary conjugate of X(40604)
X(46114) = X(2159)-isoconjugate of X(11538)
X(46114) = barycentric product X(i)*X(j) for these {i,j}: {30, 15108}, {3260, 15109}, {5664, 43965}, {6143, 11064}, {21230, 43768}
X(46114) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 11538}, {3471, 30526}, {6143, 16080}, {9697, 40352}, {15108, 1494}, {15109, 74}, {43965, 39290}
X(46114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 22051, 12006}, {10627, 43839, 34577}


X(46115) = X(2)X(40470)∩X(5)X(35912)

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

See Tran Quang Hung, Francisco Javier García Capitán and Peter Moses, euclid 3387.

X(46115) lies on these lines: {2, 40470}, {5, 35912}, {30, 39569}, {297, 43768}, {525, 23583}, {3800, 40542}, {11064, 44334}, {15526, 40512}

X(46115) = reflection of X(15526) in X(40512)
X(46115) = X(23616)-cross conjugate of X(648)
X(46115) = X(2159)-isoconjugate of X(45289)
X(46115) = cevapoint of X(i) and X(j) for these (i,j): {868, 9475}, {1650, 3163}, {2454, 2455}
X(46115) = trilinear pole of line {9033, 24981}
X(46115) = barycentric quotient X(30)/X(45289)






leftri  3rd-reflection axes: X(46116) - X(46122)  rightri

This preamble and centers X(46116)-X(46122) were contributed by César Eliud Lozada, November 30, 2021.

Let F0 be a geometric figure and L1, L2, L3 three distinct lines in an Euclidean plane. Let F1 be the reflection of F0 in L1, F2 the reflection of F1 in L2 and F3 the reflection of F2 in L3. Then F3 is a reflection of F0 if, and only if, L1, L2, L3 are concurrent.

The preceeding statement is known as the Three Reflections Theorem. Abundant information on this theorem can be found in the web. As a special reference, see Gunter Weiss, The Three Reflections Theorem Revisited, in this link, in which the theorem is extended to other geometries.

Centers X(46116)-X(46122) refer to tripoles of the final axis of reflection of F0 and F3, after succesive reflections of ABC in the indicated concurrent lines and in the order these lines are given.

underbar

X(46116) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(2), X(1)X(6), X(1)X(3)

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

X(46116) lies on these lines: {88, 1358}, {100, 30725}, {3257, 3676}, {3960, 46117}, {10015, 46122}, {43055, 43760}


X(46117) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(3), X(1)X(2), X(1)X(6)

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

X(46117) lies on these lines: {190, 43050}, {3669, 37143}, {3960, 46116}, {10015, 46121}

X(46117) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}} and {{A, B, C, X(109), X(3669)}}


X(46118) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(2), X(1)X(4), X(1)X(3)

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

X(46118) lies on these lines: {88, 3942}, {653, 30725}, {905, 3257}, {3960, 46119}, {34234, 43055}, {43050, 46122}

X(46118) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}} and {{A, B, C, X(106), X(1461)}}


X(46119) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(3), X(1)X(2), X(1)X(4)

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

X(46119) lies on these lines: {88, 16560}, {100, 1769}, {190, 10015}, {1086, 34234}, {3669, 37136}, {3960, 46118}, {33129, 37222}, {43050, 46120}

X(46119) = barycentric quotient X(i)/X(j) for these (i, j): (100, 6790), (1769, 45940)
X(46119) = trilinear quotient X(190)/X(6790)
X(46119) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}} and {{A, B, C, X(278), X(2397)}}
X(46119) = X(649)-isoconjugate-of-X(6790)
X(46119) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (100, 6790), (1769, 45940)


X(46120) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(2), X(1)X(4), X(1)X(6)

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

X(46120) lies on this line: {43050, 46119}


X(46121) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(2), X(1)X(6), X(1)X(4)

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

X(46121) lies on this line: {10015, 46117}


X(46122) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(4), X(1)X(2), X(1)X(6)

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

X(46122) lies on these lines: {10015, 46116}, {43050, 46118}


X(46123) = PERSPECTOR OF THIS ELLIPSE: X(2)-LINE CONJUGATE OF THE LINE AT IINFINITY

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

The center of this ellipse is X(597). The axes are parallel to the asymptotes of the Jerabek hyperbola, and it passes through X(i) for these i: 2, 6, 16482, 44889, 46124, 46125, 46126, 46127, 46128, 46129, 46130, 46131.

X(46123) lies on these lines: {597, 732}, {5008, 8623}


X(46124) = X(2)-LINE CONJUGATE OF X(511)

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

X(46124) lies on these lines: {2, 51}, {4, 38520}, {6, 523}, {182, 4226}, {468, 20977}, {597, 45662}, {868, 5480}, {1649, 44889}, {1976, 35278}, {2396, 18906}, {5108, 11284}, {5201, 37827}, {5468, 5651}, {5969, 9155}, {7417, 34417}, {7698, 23061}, {10753, 41254}, {11007, 21850}, {14223, 14932}, {14694, 20192}, {22735, 33876}, {31670, 36163}

X(46124) = crossdifference of every pair of points on line {511, 3288}
X(46124) = X(i)-line conjugate of X(j) for these (i,j): {2, 511}, {6, 3288}
X(46124) = {X(6),X(1316)}-harmonic conjugate of X(5967)


X(46125) = X(2)-LINE CONJUGATE OF X(514)

Barycentrics    a^2*(a^2*b^2 - 3*a*b^3 + 2*b^4 + a*b^2*c - b^3*c + a^2*c^2 + a*b*c^2 - 3*a*c^3 - b*c^3 + 2*c^4) : :
X(46125) = X[20974] + 2 X[23988]

X(46125) lies on these lines: {2, 514}, {6, 31}, {649, 24484}, {661, 5701}, {1635, 34583}, {2225, 9037}, {2810, 20974}, {31136, 34362}

X(46125) = crossdifference of every pair of points on line {514, 902}
X(46125) = X(i)-line conjugate of X(j) for these (i,j): {2, 514}, {6, 902}


X(46126) = X(2)-LINE CONJUGATE OF X(519)

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

X(46126) lies on these lines: {1, 2}, {6, 649}, {31, 16493}, {55, 16492}, {100, 8054}, {896, 16467}, {999, 17109}, {1100, 9360}, {1834, 3141}, {2177, 16501}, {2309, 16495}, {2810, 23644}, {3722, 17477}, {4360, 7035}, {4813, 24289}, {14752, 16576}, {17187, 34583}, {24696, 36872}

X(46126) = crosssum of X(1) and X(9458)
X(46126) = crossdifference of every pair of points on line {519, 649}
X(46126) = X(i)-line conjugate of X(j) for these (i,j): {1, 519} (and {X,519) for evey X on X(1)X(2)) , {6, 649}
X(46126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 43, 17780}, {1, 3216, 6789}, {16493, 23832, 31}


X(46127) = X(2)-LINE CONJUGATE OF X(523)

Barycentrics    a^2*(a^4*b^2 - 3*a^2*b^4 + 2*b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 3*a^2*c^4 - b^2*c^4 + 2*c^6) : :
X(46127) = X[3] + 2 X[18114], X[1634] + 2 X[20975], X[1634] - 4 X[34990], X[3001] + 2 X[3003], 2 X[3001] + X[5201], 4 X[3003] - X[5201], 2 X[7668] + X[14570], X[20975] + 2 X[34990]

X(46127) is the diagonal crosspoint of the cyclic quadrilateral X(2)X(15)X(16)X(9213). (Randy Hutson, January 11, 2022)

X(46127) lies on these lines: {2, 523}, {3, 6}, {110, 9142}, {114, 3014}, {237, 8705}, {373, 44114}, {524, 22087}, {549, 45331}, {597, 45662}, {599, 45330}, {868, 18122}, {895, 9145}, {1576, 14060}, {1624, 41670}, {1634, 2854}, {1645, 34811}, {1989, 38224}, {2421, 7998}, {2452, 40879}, {3018, 6036}, {3124, 40283}, {3163, 38737}, {3589, 15000}, {3733, 24500}, {5191, 6593}, {5502, 35259}, {5640, 15329}, {5650, 16186}, {5651, 9717}, {5972, 41359}, {5999, 32224}, {6128, 23698}, {6235, 13531}, {6771, 18776}, {6774, 18777}, {6787, 23099}, {7668, 14570}, {7820, 14357}, {9027, 36212}, {9171, 44814}, {9465, 14898}, {9513, 14380}, {11184, 32216}, {11216, 35302}, {11284, 14685}, {11416, 39231}, {14169, 35329}, {14170, 35330}, {14830, 34319}, {15921, 34235}, {16776, 23635}, {19663, 33237}, {23181, 45237}, {23347, 36176}, {32217, 37916}, {33962, 44468}, {34989, 41221}, {35268, 44127}

X(46127) = midpoint of X(9155) and X(20975)
X(46127) = reflection of X(i) in X(j) for these {i,j}: {1634, 9155}, {9155, 34990}
X(46127) = Brocard circle inverse of X(5467)
X(46127) = psi-transform of X(9138)
X(46127) = X(896)-isoconjugate of X(39450)
X(46127) = crosssum of X(523) and X(15359)
X(46127) = crossdifference of every pair of points on line {187, 523}
X(46127) = X(i)-line conjugate of X(j) for these (i,j): {2, 523}, {3, 187}
X(46127) = barycentric product X(249)*X(15359)
X(46127) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 39450}, {15359, 338}
X(46127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 5467}, {3, 1351, 15919}, {39, 21906, 6}, {3001, 3003, 5201}, {5191, 6593, 35357}, {5968, 33927, 34291}, {20975, 34990, 1634}


X(46128) = X(2)-LINE CONJUGATE OF X(525)

Barycentrics    a^2*(a^8*b^2 + a^6*b^4 - 3*a^4*b^6 - a^2*b^8 + 2*b^10 + a^8*c^2 - 6*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 + a^6*c^4 + 4*a^4*b^2*c^4 - 6*a^2*b^4*c^4 + b^6*c^4 - 3*a^4*c^6 + 4*a^2*b^2*c^6 + b^4*c^6 - a^2*c^8 - 3*b^2*c^8 + 2*c^10) : :
X(46128) = X[35325] + 2 X[38356]

X(46128) lies on these lines: {2, 525}, {6, 25}, {22, 2420}, {39, 44889}, {1196, 2088}, {1560, 1562}, {2781, 35325}, {3124, 12099}, {3269, 44467}, {5254, 35235}, {5890, 7418}, {6000, 14580}, {6792, 18950}, {32064, 35902}, {35906, 36178}, {37930, 44415}

X(46128) = crossdifference of every pair of points on line {525, 1495}
X(46128) = X(i)-line conjugate of X(j) for these (i,j): {2, 525}, {6, 1495}


X(46129) = X(2)-LINE CONJUGATE OF X(526)

Barycentrics    a^12*b^2 - 6*a^10*b^4 + 11*a^8*b^6 - 7*a^6*b^8 + a^2*b^12 + a^12*c^2 + 4*a^10*b^2*c^2 - 5*a^8*b^4*c^2 - 6*a^6*b^6*c^2 + 10*a^4*b^8*c^2 - 5*a^2*b^10*c^2 + b^12*c^2 - 6*a^10*c^4 - 5*a^8*b^2*c^4 + 18*a^6*b^4*c^4 - 9*a^4*b^6*c^4 + 7*a^2*b^8*c^4 - 3*b^10*c^4 + 11*a^8*c^6 - 6*a^6*b^2*c^6 - 9*a^4*b^4*c^6 - 6*a^2*b^6*c^6 + 2*b^8*c^6 - 7*a^6*c^8 + 10*a^4*b^2*c^8 + 7*a^2*b^4*c^8 + 2*b^6*c^8 - 5*a^2*b^2*c^10 - 3*b^4*c^10 + a^2*c^12 + b^2*c^12 : :

X(46129) lies on these lines: {2, 526}, {6, 13}, {524, 36189}, {804, 9144}, {1634, 5642}, {5648, 34383}, {7668, 9140}, {9143, 25051}, {20126, 41330}

X(46129) = midpoint of X(9143) and X(25051)
X(46129) = reflection of X(i) in X(j) for these {i,j}: {1634, 5642}, {9140, 7668}
X(46129) = crossdifference of every pair of points on line {526, 3016}
X(46129) = X(i)-line conjugate of X(j) for these (i,j): {2, 526}, {6, 3016}
X(46129) = {X(6),X(18332)}-harmonic conjugate of X(14559)


X(46130) = X(2)-LINE CONJUGATE OF X(542)

Barycentrics    a^2*(a^12*b^2 - 2*a^10*b^4 + 2*a^6*b^8 - a^4*b^10 + a^12*c^2 - 4*a^10*b^2*c^2 + 6*a^8*b^4*c^2 - 6*a^6*b^6*c^2 + 5*a^4*b^8*c^2 - 4*a^2*b^10*c^2 + 2*b^12*c^2 - 2*a^10*c^4 + 6*a^8*b^2*c^4 - 3*a^4*b^6*c^4 + 4*a^2*b^8*c^4 - 3*b^10*c^4 - 6*a^6*b^2*c^6 - 3*a^4*b^4*c^6 + b^8*c^6 + 2*a^6*c^8 + 5*a^4*b^2*c^8 + 4*a^2*b^4*c^8 + b^6*c^8 - a^4*c^10 - 4*a^2*b^2*c^10 - 3*b^4*c^10 + 2*b^2*c^12) : :
X(46130) =X[11061] - 3 X[25314], X[25051] - 3 X[25320]

X(46130) lies on these lines: {2, 98}, {3, 42743}, {6, 526}, {74, 37991}, {111, 34235}, {246, 2781}, {351, 44889}, {511, 7468}, {804, 1316}, {895, 9513}, {974, 38551}, {1503, 36189}, {1634, 2854}, {3124, 12099}, {5505, 43718}, {9129, 11284}, {11061, 25314}, {14984, 36790}, {20976, 35325}, {25051, 25320}

X(46130) = midpoint of X(3448) and X(25046)
X(46130) = reflection of X(i) in X(j) for these {i,j}: {110, 36213}, {20021, 125}
X(46130) = Brocard-circle inverse of X(5967)
X(46130) = psi-transform of X(7418)
X(46130) = crossdifference of every pair of points on line {542, 3569}
X(46130) = X(i)-line conjugate of X(j) for these (i,j): {2, 542}, {6, 3569}
X(46130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 5622, 1976}, {13414, 13415, 5967}


X(46131) = X(2)-LINE CONJUGATE OF X(690)

Barycentrics    a^2*(a^8*b^2 + 2*a^6*b^4 - 3*a^4*b^6 - 2*a^2*b^8 + 2*b^10 + a^8*c^2 - 12*a^6*b^2*c^2 + 9*a^4*b^4*c^2 + 10*a^2*b^6*c^2 - 6*b^8*c^2 + 2*a^6*c^4 + 9*a^4*b^2*c^4 - 24*a^2*b^4*c^4 + 5*b^6*c^4 - 3*a^4*c^6 + 10*a^2*b^2*c^6 + 5*b^4*c^6 - 2*a^2*c^8 - 6*b^2*c^8 + 2*c^10) : :
X(46131) = X[110] + 2 X[3124], X[4576] - 4 X[5972]

X(46131) lies on the cubic K793 and these lines: {2, 690}, {6, 110}, {23, 9181}, {2088, 9176}, {4576, 5972}, {7665, 25047}, {9140, 9169}, {9155, 40283}, {9775, 22265}, {10836, 13248}, {14999, 36168}, {15035, 37930}, {20975, 40282}, {31655, 38395}, {38523, 39576}

X(46131) = psi-transform of X(9178)
X(46131) = crossdifference of every pair of points on line {690, 2502}
X(46131) = X(i)-line conjugate of X(j) for these (i,j): {2, 690}, {6, 2502} X(46131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 9129, 110}, {2502, 6593, 110}


X(46132) = ISOTOMIC CONJUGATE OF X(788)

Barycentrics    (a - b)*b^3*(a^2 + a*b + b^2)*(a - c)*c^3*(a^2 + a*c + c^2) : :
X(46132) = 2 X[39347] - 3 X[43095]

X(46132) lies on the Steiner circumellipse and these lines: {2, 39347}, {75, 43096}, {99, 789}, {190, 6386}, {292, 18277}, {310, 18827}, {561, 31134}, {666, 5388}, {670, 3888}, {752, 30875}, {794, 4586}, {815, 9063}, {825, 9065}, {870, 3226}, {871, 903}, {985, 18824}, {1492, 4577}, {1502, 43099}, {1920, 7245}, {1978, 4562}, {2887, 14945}, {3225, 40747}, {3227, 43266}, {4645, 14603}, {6327, 40362}, {14621, 18825}, {18826, 40718}, {33514, 34069}

X(46132) = reflection of X(i) in X(j) for these {i,j}: {14945, 2887}, {43095, 2}
X(46132) = isogonal conjugate of X(8630)
X(46132) = isotomic conjugate of X(788)
X(46132) = isotomic conjugate of the isogonal conjugate of X(789)
X(46132) = complement of X(39347)
X(46132) = X(4586)-anticomplementary conjugate of X(39347)
X(46132) = X(i)-cross conjugate of X(j) for these (i,j): {788, 2}, {4441, 31625}, {30639, 334}, {30870, 561}, {30872, 40362}
X(46132) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8630}, {31, 788}, {32, 3250}, {513, 18900}, {560, 1491}, {649, 40728}, {667, 869}, {669, 3736}, {824, 1501}, {984, 1980}, {1919, 2276}, {1924, 40773}, {2205, 4481}, {4486, 18897}, {4522, 41280}, {7104, 45882}, {9006, 40415}, {9426, 30966}, {9454, 29956}, {9456, 14436}, {9468, 30654}, {14598, 30665}, {14599, 30671}, {17415, 38813}, {18894, 23596}, {20979, 40736}
X(46132) = cevapoint of X(i) and X(j) for these (i,j): {2, 788}, {513, 21264}, {561, 30870}, {824, 2887}, {4586, 43289}, {6327, 30872}, {20333, 30665}
X(46132) = trilinear pole of line {2, 561}
X(46132) = barycentric product X(i)*X(j) for these {i,j}: {75, 37133}, {76, 789}, {190, 871}, {561, 4586}, {693, 5388}, {825, 1928}, {870, 1978}, {1492, 1502}, {1921, 41072}, {3721, 9063}, {4602, 40718}, {4609, 40747}, {4613, 6385}, {6386, 14621}, {18891, 37207}, {30664, 44169}, {34069, 40362}
X(46132) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 788}, {6, 8630}, {75, 3250}, {76, 1491}, {100, 40728}, {101, 18900}, {190, 869}, {310, 4481}, {334, 30671}, {519, 14436}, {561, 824}, {646, 4517}, {668, 2276}, {670, 40773}, {752, 14402}, {789, 6}, {799, 3736}, {825, 560}, {870, 649}, {871, 514}, {874, 16514}, {932, 40736}, {985, 1919}, {1492, 32}, {1909, 45882}, {1920, 3805}, {1921, 30665}, {1966, 30654}, {1978, 984}, {2481, 29956}, {3261, 4475}, {3721, 17415}, {3888, 3117}, {3952, 3774}, {4554, 1469}, {4572, 7146}, {4583, 3862}, {4586, 31}, {4602, 30966}, {4613, 213}, {4817, 3248}, {5384, 32739}, {5388, 100}, {6386, 3661}, {9063, 38810}, {14603, 30639}, {14621, 667}, {16584, 9006}, {18891, 4486}, {27801, 4122}, {27853, 3783}, {28659, 4522}, {30664, 1922}, {30670, 7104}, {30874, 33904}, {31625, 3799}, {33946, 3116}, {34069, 1501}, {37133, 1}, {37207, 1911}, {40362, 30870}, {40718, 798}, {40746, 1980}, {40747, 669}, {41072, 292}, {43266, 8027}, {43289, 32664}, {44172, 23596}


X(46133) = ISOTOMIC CONJUGATE OF X(912)

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

X(46133) lies on the Steiner circumellipse and these lines: {69, 2973}, {92, 190}, {99, 286}, {264, 668}, {273, 664}, {290, 3657}, {317, 18026}, {340, 35156}, {648, 2990}, {913, 4586}, {2966, 32655}, {5081, 35174}

X(46133) = isotomic conjugate of X(912)
X(46133) = polar conjugate of X(8609)
X(46133) = isotomic conjugate of the isogonal conjugate of X(915)
X(46133) = polar conjugate of the isogonal conjugate of X(2990)
X(46133) = X(i)-cross conjugate of X(j) for these (i,j): {912, 2}, {3262, 264}, {4511, 31623}, {44428, 6335}
X(46133) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2252}, {31, 912}, {32, 914}, {48, 8609}, {184, 1737}, {212, 18838}, {810, 3658}
X(46133) = cevapoint of X(i) and X(j) for these (i,j): {2, 912}, {92, 5081}, {525, 3139}, {915, 2990}, {2969, 10015}
X(46133) = trilinear pole of line {2, 17924}
X(46133) = barycentric product X(i)*X(j) for these {i,j}: {75, 37203}, {76, 915}, {264, 2990}, {331, 45393}, {561, 913}, {1969, 36052}, {3261, 36106}, {3657, 6331}, {18022, 32655}, {32698, 40495}
X(46133) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2252}, {2, 912}, {4, 8609}, {75, 914}, {92, 1737}, {278, 18838}, {648, 3658}, {913, 31}, {915, 6}, {2990, 3}, {3657, 647}, {6099, 906}, {10015, 42769}, {15381, 14578}, {16082, 14266}, {17923, 11570}, {32655, 184}, {32698, 692}, {36052, 48}, {36106, 101}, {37203, 1}, {37790, 12832}, {37805, 12831}, {45393, 219}


X(46134) = ISOTOMIC CONJUGATE OF X(924)

Barycentrics    b^2*(-a + b)*(a + b)*(a - c)*c^2*(a + c)*(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(46134) = 9 X[2] - 8 X[40489], 3 X[39013] - 4 X[40489]

X(46134) lies on the Steiner circumellipse and these lines: {2, 39013}, {68, 290}, {76, 847}, {91, 18827}, {99, 925}, {316, 5962}, {648, 30450}, {671, 5392}, {850, 18878}, {1236, 5641}, {1494, 14615}, {2165, 3228}, {2966, 4611}, {4577, 32734}, {4586, 36145}, {6331, 18831}, {7763, 34853}, {8920, 43664}, {11185, 14593}, {14616, 20571}, {20573, 34385}

X(46134) = isogonal conjugate of X(34952)
X(46134) = isotomic conjugate of X(924)
X(46134) = anticomplement of X(39013)
X(46134) = polar conjugate of X(6753)
X(46134) = isotomic conjugate of the isogonal conjugate of X(925)
X(46134) = isotomic conjugate of the polar conjugate of X(30450)
X(46134) = X(2)-cross conjugate of polar conjugate of X(6754)
X(46134) = X(i)-cross conjugate of X(j) for these (i,j): {924, 2}, {925, 30450}, {4558, 6331}, {6334, 40832}, {11412, 249}, {14618, 76}, {25739, 39295}, {37444, 23582}, {44128, 18020}, {45780, 18879}, {45794, 4590}
X(46134) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34952}, {19, 30451}, {24, 810}, {31, 924}, {42, 34948}, {47, 512}, {48, 6753}, {560, 6563}, {563, 2501}, {571, 661}, {656, 44077}, {669, 44179}, {798, 1993}, {822, 8745}, {1748, 3049}, {1919, 42700}, {1924, 7763}, {2159, 14397}, {2180, 2623}, {4079, 18605}, {14574, 17881}, {36145, 39013}
X(46134) = cevapoint of X(i) and X(j) for these (i,j): {2, 924}, {69, 850}, {343, 523}, {512, 7746}, {525, 11585}, {847, 14618}
X(46134) = trilinear pole of line {2, 311}
X(46134) = barycentric product X(i)*X(j) for these {i,j}: {68, 6331}, {69, 30450}, {76, 925}, {91, 799}, {99, 5392}, {561, 36145}, {648, 20563}, {662, 20571}, {670, 2165}, {847, 4563}, {1502, 32734}, {14570, 34385}, {35139, 37802}
X(46134) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 924}, {3, 30451}, {4, 6753}, {6, 34952}, {30, 14397}, {68, 647}, {76, 6563}, {81, 34948}, {91, 661}, {94, 43088}, {96, 2623}, {99, 1993}, {107, 8745}, {110, 571}, {112, 44077}, {317, 15423}, {323, 44808}, {648, 24}, {662, 47}, {668, 42700}, {670, 7763}, {799, 44179}, {811, 1748}, {847, 2501}, {924, 39013}, {925, 6}, {1820, 810}, {2165, 512}, {2351, 3049}, {2617, 2180}, {4558, 1147}, {4563, 9723}, {4575, 563}, {5392, 523}, {6331, 317}, {6528, 11547}, {6753, 6754}, {14570, 52}, {14593, 2489}, {14618, 136}, {16391, 32320}, {18020, 41679}, {20563, 525}, {20571, 1577}, {20948, 17881}, {30450, 4}, {32734, 32}, {34385, 15412}, {35139, 18883}, {35360, 14576}, {36145, 31}, {37802, 526}, {38342, 14111}, {39289, 39184}, {39416, 39109}, {43187, 31635}, {44174, 32661}


X(46135) = ISOTOMIC CONJUGATE OF X(926)

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

X(46135) lies on the Steiner circumellipse and these lines: {2, 39014}, {76, 35158}, {85, 35167}, {99, 927}, {190, 3261}, {349, 35163}, {664, 4449}, {668, 40495}, {885, 14727}, {889, 43930}, {1121, 18031}, {1416, 18824}, {1441, 35152}, {1462, 18825}, {2481, 18033}, {3227, 34018}, {4554, 32041}, {4577, 32735}, {4586, 36146}, {6063, 18821}, {6606, 36802}, {18025, 35517}

X(46135) = isogonal conjugate of X(8638)
X(46135) = isotomic conjugate of X(926)
X(46135) = isotomic conjugate of the isogonal conjugate of X(927)
X(46135) = anticomplement of X(39014)
X(46135) = X(34085)-anticomplementary conjugate of X(14732)
X(46135) = X(i)-cross conjugate of X(j) for these (i,j): {883, 4554}, {926, 2}, {2398, 31624}, {3766, 85}, {20347, 1275}, {20556, 46102}, {43930, 34018}
X(46135) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8638}, {31, 926}, {33, 23225}, {41, 665}, {522, 9455}, {650, 9454}, {663, 2223}, {667, 2340}, {672, 3063}, {810, 37908}, {884, 42079}, {918, 9447}, {1024, 39686}, {1458, 8641}, {1919, 3693}, {1946, 2356}, {1980, 3717}, {2175, 2254}, {7252, 39258}, {15615, 36086}, {17435, 32739}, {36146, 39014}
X(46135) = cevapoint of X(i) and X(j) for these (i,j): {2, 926}, {518, 4885}, {522, 20335}, {693, 40704}, {883, 4554}, {918, 2886}, {3261, 35517}, {3900, 34852}, {34018, 43930}
X(46135) = trilinear pole of line {2, 4554}
X(46135) = barycentric product X(i)*X(j) for these {i,j}: {7, 36803}, {75, 34085}, {76, 927}, {561, 36146}, {664, 18031}, {666, 6063}, {668, 34018}, {673, 4572}, {919, 41283}, {1462, 6386}, {1502, 32735}, {2481, 4554}, {3261, 39293}, {4569, 36796}, {20567, 36086}, {31625, 43930}
X(46135) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 926}, {6, 8638}, {7, 665}, {85, 2254}, {105, 3063}, {109, 9454}, {190, 2340}, {222, 23225}, {294, 8641}, {349, 4088}, {528, 14411}, {648, 37908}, {651, 2223}, {653, 2356}, {658, 1458}, {664, 672}, {665, 15615}, {666, 55}, {668, 3693}, {673, 663}, {693, 17435}, {883, 6184}, {885, 14936}, {919, 2175}, {926, 39014}, {927, 6}, {1025, 42079}, {1275, 2283}, {1415, 9455}, {1416, 1919}, {1441, 24290}, {1462, 667}, {1814, 1946}, {1978, 3717}, {2283, 39686}, {2481, 650}, {4551, 39258}, {4552, 20683}, {4554, 518}, {4569, 241}, {4572, 3912}, {4573, 3286}, {4624, 14626}, {4625, 18206}, {4998, 2284}, {6063, 918}, {6185, 884}, {6516, 20752}, {6559, 4105}, {10015, 42771}, {13149, 1876}, {13576, 3709}, {14625, 8653}, {14942, 657}, {18026, 5089}, {18031, 522}, {24002, 3675}, {28132, 3022}, {31637, 652}, {32666, 9447}, {32735, 32}, {34018, 513}, {34085, 1}, {35333, 40972}, {36086, 41}, {36146, 31}, {36796, 3900}, {36802, 220}, {36803, 8}, {36838, 34855}, {39293, 101}, {40704, 3126}, {43042, 35505}, {43930, 1015}


X(46136) = ISOTOMIC CONJUGATE OF X(952)

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

X(4613) lies on the Steiner circumellipse and these lines: {69, 4555}, {75, 35174}, {99, 953}, {190, 908}, {320, 664}, {648, 16704}, {668, 3262}, {693, 18816}, {903, 4025}, {2481, 46041}, {2861, 35011}, {3663, 35169}, {4597, 5088}, {14616, 18155}, {35157, 42697}

X(46136) = isotomic conjugate of X(952)
X(46136) = isotomic conjugate of the isogonal conjugate of X(953)
X(46136) = X(952)-cross conjugate of X(2)
X(46136) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2265}, {31, 952}, {41, 43043}, {1110, 6075}
X(46136) = cevapoint of X(i) and X(j) for these (i,j): {2, 952}, {8, 30566}
X(46136) = trilinear pole of line {2, 3904}
X(46136) = barycentric product X(i)*X(j) for these {i,j}: {76, 953}, {4554, 46041}
X(46136) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2265}, {2, 952}, {7, 43043}, {953, 6}, {1086, 6075}, {10015, 35013}, {26611, 6073}, {35011, 32641}, {43043, 3319}, {46041, 650}


X(46137) = ISOTOMIC CONJUGATE OF X(971)

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

X(46137) lies on the Steiner circumellipse and these lines: {8, 18026}, {69, 4569}, {78, 664}, {85, 271}, {99, 972}, {190, 322}, {648, 2287}, {666, 40863}, {668, 1265}, {1809, 30806}, {3262, 35157}, {7358, 13149}

X(46137) = isotomic conjugate of X(971)
X(46137) = isotomic conjugate of the isogonal conjugate of X(972)
X(46137) = X(971)-cross conjugate of X(2)
X(46137) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2272}, {31, 971}, {41, 43044}
X(46137) = cevapoint of X(i) and X(j) for these (i,j): {2, 971}, {8, 30807}
X(46137) = trilinear pole of line {2, 17896}
X(46137) = barycentric product X(76)*X(972)
X(46137) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2272}, {2, 971}, {7, 43044}, {972, 6}, {10015, 42772}, {37780, 28344}


X(46138) = ISOTOMIC CONJUGATE OF X(1154)

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

X(46138) lies on the Steiner circumellipse and these lines: {94, 275}, {95, 99}, {264, 18831}, {265, 6528}, {300, 32036}, {301, 32037}, {338, 18315}, {664, 20565}, {670, 34384}, {1989, 42300}, {2966, 11077}, {4577, 39287}, {14859, 35139}, {16077, 43752}, {20573, 34385}, {33513, 39286}

X(46138) = isotomic conjugate of X(1154)
X(46138) = polar conjugate of X(11062)
X(46138) = isotomic conjugate of the isogonal conjugate of X(1141)
X(46138) = X(i)-cross conjugate of X(j) for these (i,j): {3, 40427}, {526, 18315}, {1154, 2}, {37779, 31617}, {41079, 42405}, {43768, 276}
X(46138) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2290}, {31, 1154}, {48, 11062}, {50, 1953}, {51, 6149}, {163, 2081}, {323, 2179}, {560, 1273}, {1625, 2624}, {2181, 22115}, {2617, 14270}, {9247, 14918}, {14213, 19627}, {34397, 44706}
X(46138) = cevapoint of X(i) and X(j) for these (i,j): {2, 1154}, {94, 265}, {264, 43752}, {338, 526}
X(46138) = trilinear pole of line {2, 2413}
X(46138) = barycentric product X(i)*X(j) for these {i,j}: {54, 20573}, {76, 1141}, {94, 95}, {97, 18817}, {265, 276}, {275, 328}, {1989, 34384}, {6344, 34386}, {7799, 14859}, {11077, 18022}, {14592, 18831}, {15412, 35139}, {18883, 34385}, {42405, 43083}
X(46138) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2290}, {2, 1154}, {4, 11062}, {54, 50}, {76, 1273}, {94, 5}, {95, 323}, {97, 22115}, {264, 14918}, {265, 216}, {275, 186}, {276, 340}, {300, 33530}, {301, 33529}, {328, 343}, {476, 1625}, {523, 2081}, {850, 41078}, {930, 2439}, {933, 14591}, {1141, 6}, {1989, 51}, {2166, 1953}, {2167, 6149}, {2413, 1510}, {2616, 2624}, {2623, 14270}, {4993, 3581}, {6344, 53}, {8795, 14165}, {8882, 34397}, {8901, 2088}, {10412, 12077}, {11060, 40981}, {11077, 184}, {14582, 15451}, {14592, 6368}, {14859, 1989}, {15412, 526}, {18359, 35194}, {18384, 3199}, {18817, 324}, {18831, 14590}, {18883, 52}, {20573, 311}, {30529, 143}, {32680, 2617}, {34384, 7799}, {34385, 37802}, {35139, 14570}, {39277, 40214}, {39290, 36831}, {40709, 44712}, {40710, 44711}, {43083, 17434}, {43084, 41586}, {43752, 14920}, {43768, 1511}


X(46139) = ISOTOMIC CONJUGATE OF X(1510)

Barycentrics    (a - b)*b^2*(a + b)*(a - c)*c^2*(a + c)*(a^4 - a^2*b^2 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(46139) = 9 X[2] - 8 X[40490], 3 X[39018] - 4 X[40490]

X(46139) lies on the Steiner circumellipse and these lines: {2, 39018}, {76, 25043}, {93, 1235}, {99, 930}, {252, 1078}, {290, 3519}, {311, 25148}, {316, 19552}, {648, 38342}, {671, 11140}, {2962, 18827}, {2963, 3228}, {4577, 32737}, {4586, 36148}, {7750, 35888}, {7769, 21975}, {10411, 18831}, {11117, 34390}, {11118, 34389}

X(46139) = isogonal conjugate of anticomplement of X(39512)
X(46139) = isogonal conjugate of circumcircle pole of Napoleon axis
X(46139) = isotomic conjugate of X(1510)
X(46139) = isotomic conjugate of the isogonal conjugate of X(930)
X(46139) = isotomic conjugate of the polar conjugate of X(38342)
X(46139) = anticomplement of X(39018)
X(46139) = X(i)-cross conjugate of X(j) for these (i,j): {930, 38342}, {1510, 2}, {6101, 249}, {18314, 76}
X(46139) = X(i)-isoconjugate of X(j) for these (i,j): {31, 1510}, {512, 2964}, {560, 41298}, {661, 2965}, {798, 1994}, {810, 3518}, {1096, 37084}, {1924, 7769}, {36148, 39018}
X(46139) = cevapoint of X(i) and X(j) for these (i,j): {2, 1510}, {523, 37636}, {525, 37452}, {635, 23873}, {636, 23872}, {850, 1232}, {1273, 45790}, {18314, 25043}
X(46139) = trilinear pole of line {2, 1225}
X(46139) = barycentric product X(i)*X(j) for these {i,j}: {69, 38342}, {76, 930}, {93, 4563}, {99, 11140}, {561, 36148}, {670, 2963}, {799, 2962}, {1502, 32737}, {3519, 6331}, {4558, 20572}, {32036, 34390}, {32037, 34389}
X(46139) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 1510}, {76, 41298}, {93, 2501}, {99, 1994}, {110, 2965}, {252, 2623}, {311, 20577}, {323, 44809}, {394, 37084}, {648, 3518}, {662, 2964}, {670, 7769}, {930, 6}, {1510, 39018}, {2962, 661}, {2963, 512}, {3519, 647}, {4558, 49}, {4563, 44180}, {6331, 32002}, {11140, 523}, {14111, 6753}, {14570, 143}, {18314, 137}, {18315, 25044}, {20572, 14618}, {25043, 12077}, {32036, 62}, {32037, 61}, {32737, 32}, {34389, 23873}, {34390, 23872}, {35139, 30529}, {35360, 14577}, {36148, 31}, {38342, 4}, {41677, 6152}


X(46140) = ISOTOMIC CONJUGATE OF X(2393)

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

X(46140) lies on the Steiner circumellipse and these lines: {4, 40421}, {22, 99}, {76, 648}, {190, 4456}, {315, 670}, {316, 11605}, {668, 4463}, {892, 1236}, {1177, 4577}, {2966, 11610}, {3267, 10718}, {6528, 11185}, {14615, 35179}, {16084, 18829}, {18831, 34384}, {33769, 35138}, {34360, 36793}

X(46140) = isotomic conjugate of X(2393)
X(46140) = polar conjugate of X(14580)
X(46140) = isotomic conjugate of the isogonal conjugate of X(2373)
X(46140) = X(i)-cross conjugate of X(j) for these (i,j): {23, 308}, {2393, 2}, {18019, 18023}, {44146, 76}
X(46140) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2393}, {32, 18669}, {48, 14580}, {560, 858}, {1236, 1917}, {1501, 20884}, {1973, 14961}, {2205, 17172}, {5523, 9247}, {32676, 42665}
X(46140) = cevapoint of X(i) and X(j) for these (i,j): {2, 2393}, {69, 3266}, {76, 316}, {35522, 36793}
X(46140) = trilinear pole of line {2, 2485}
X(46140) = barycentric product X(i)*X(j) for these {i,j}: {75, 37220}, {76, 2373}, {1177, 1502}, {18022, 18876}, {18024, 36823}
X(46140) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2393}, {4, 14580}, {69, 14961}, {75, 18669}, {76, 858}, {264, 5523}, {310, 17172}, {313, 21017}, {525, 42665}, {561, 20884}, {895, 34158}, {1177, 32}, {1502, 1236}, {2373, 6}, {3261, 21109}, {3266, 5181}, {9464, 19510}, {10422, 32740}, {18876, 184}, {36095, 32676}, {36823, 237}, {37220, 1}, {37765, 20410}, {41511, 14908}, {44146, 1560}, {46104, 21459}


X(46141) = ISOTOMIC CONJUGATE OF X(2771)

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

X(4613) lies on the Steiner circumellipse and these lines: {69, 35156}, {99, 2687}, {190, 14206}, {286, 16077}, {314, 35139}, {316, 39991}, {319, 35174}, {340, 18026}, {648, 37783}, {664, 17791}, {668, 3260}, {693, 1494}, {850, 18816}, {2481, 14224}

X(46141) = isotomic conjugate of X(2771)
X(46141) = isotomic conjugate of the isogonal conjugate of X(2687)
X(46141) = X(2771)-cross conjugate of X(2)
X(46141) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2771}, {810, 37966}
X(46141) = cevapoint of X(2) and X(2771)
X(46141) = barycentric product X(i)*X(j) for these {i,j}: {76, 2687}, {4554, 14224}
X(46141) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2771}, {648, 37966}, {2687, 6}, {14224, 650}, {39991, 8609}


X(46142) = ISOTOMIC CONJUGATE OF X(2782)

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

X(46142) lies on the Steiner circumellipse and these lines: {6, 2966}, {69, 18829}, {99, 511}, {183, 892}, {232, 385}, {290, 523}, {317, 39359}, {325, 670}, {671, 8430}, {1494, 32112}, {4019, 4562}, {4577, 39093}, {4580, 14970}, {5641, 23350}, {6528, 6530}, {10313, 39097}, {14356, 35139}, {16077, 35908}, {18831, 19189}, {20423, 30226}, {20975, 36897}, {38987, 43187}, {40801, 41074}

X(46142) = isotomic conjugate of X(2782)
X(46142) = isotomic conjugate of the isogonal conjugate of X(2698)
X(46142) = X(2782)-cross conjugate of X(2)
X(46142) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2782}, {1580, 16068}, {6071, 24041}
X(46142) = cevapoint of X(2) and X(2782)
X(46142) = trilinear pole of line {2, 3569}
X(46142) = Steiner-circumellipse-X(6)-antipode of X(2966)
X(46142) = barycentric product X(i)*X(j) for these {i,j}: {76, 2698}, {99, 46040}, {1916, 16069}, {8781, 46039}
X(46142) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2782}, {694, 16068}, {2698, 6}, {3124, 6071}, {16069, 385}, {36790, 6072}, {46039, 230}, {46040, 523}


X(46143) = ISOTOMIC CONJUGATE OF X(2789)

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

X(46143) lies on the Steiner circumellipse and these lines: {69, 35153}, {99, 2705}, {183, 35165}, {190, 14321}, {290, 3264}, {325, 903}, {668, 4404}, {671, 17132}, {3226, 39099}, {9487, 31144}, {14829, 35155}, {35150, 37668}

X(46143) = isotomic conjugate of X(2789)
X(46143) = isotomic conjugate of the isogonal conjugate of X(2705)
X(46143) = X(2789)-cross conjugate of X(2)
X(46143) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2789}, {667, 37764}, {798, 37792}, {4394, 17967}, {8643, 17958}
X(46143) = cevapoint of X(i) and X(j) for these (i,j): {2, 2789}, {8, 45661}
X(46143) = trilinear pole of line {2, 15903}
X(46143) = barycentric product X(i)*X(j) for these {i,j}: {76, 2705}, {99, 34899}
X(46143) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2789}, {99, 37792}, {190, 37764}, {1293, 17967}, {2705, 6}, {27834, 17958}, {34899, 523}


X(46144) = ISOTOMIC CONJUGATE OF X(2793)

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

X(46144) lies on the Steiner circumellipse and these lines: {2, 9487}, {69, 18823}, {99, 1499}, {183, 35146}, {290, 3266}, {325, 671}, {523, 35179}, {648, 9182}, {892, 2396}, {2418, 43674}, {2966, 5468}, {3228, 39099}, {4590, 35138}, {5641, 37668}, {6082, 9123}, {7840, 11162}, {17952, 22110}, {18829, 34203}, {33799, 42367}

X(46144) = reflection of X(i) in X(j) for these {i,j}: {9487, 2}, {17952, 22110}
X(46144) = isogonal conjugate of X(9135)
X(46144) = isotomic conjugate of X(2793)
X(46144) = isotomic conjugate of the isogonal conjugate of X(2709)
X(46144) = X(i)-cross conjugate of X(j) for these (i,j): {2793, 2}, {7840, 4590}, {34246, 5503}, {39905, 76}
X(46144) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9135}, {31, 2793}, {661, 2030}, {798, 22329}, {8644, 17959}, {17999, 36277}
X(46144) = cevapoint of X(i) and X(j) for these (i,j): {2, 2793}, {523, 22110}, {5503, 34246}
X(46144) = trilinear pole of line {2, 5503}
X(46144) = barycentric product X(i)*X(j) for these {i,j}: {76, 2709}, {99, 5503}, {4590, 34246}
X(46144) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2793}, {6, 9135}, {99, 22329}, {110, 2030}, {1296, 17968}, {2709, 6}, {4590, 34245}, {5468, 18800}, {5485, 18012}, {5503, 523}, {6082, 18775}, {11163, 14327}, {21448, 17999}, {34246, 115}, {35179, 17952}, {37216, 17959}


X(46145) = ISOTOMIC CONJUGATE OF X(2794)

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

X(46145) lies on the Steiner circumellipse and these lines: {4, 46096}, {69, 2966}, {99, 1503}, {290, 3267}, {325, 648}, {393, 35088}, {523, 35140}, {670, 30737}, {892, 37668}, {4577, 21458}, {6528, 44132}, {15526, 41932}, {16077, 32815}, {35139, 43089}, {40824, 41074}

X(46145) = isotomic conjugate of X(2794)
X(46145) = isotomic conjugate of the isogonal conjugate of X(2710)
X(46145) = X(2794)-cross conjugate of X(2)
X(46145) = X(31)-isoconjugate of X(2794)
X(46145) = cevapoint of X(2) and X(2794)
X(46145) = trilinear pole of line {2, 6333}
X(46145) = barycentric product X(76)*X(2710)
X(46145) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2794}, {287, 41175}, {2710, 6}


X(46146) = (name pending)

Barycentrics    a^16 - 2*a^14*b^2 - 2*a^12*b^4 + 2*a^10*b^6 + a^4*b^12 - 2*a^14*c^2 - 7*a^12*b^2*c^2 + 8*a^10*b^4*c^2 + 6*a^8*b^6*c^2 - 6*a^6*b^8*c^2 + 2*a^4*b^10*c^2 + b^14*c^2 - 2*a^12*c^4 + 8*a^10*b^2*c^4 + 11*a^8*b^4*c^4 - 14*a^6*b^6*c^4 - 4*a^4*b^8*c^4 - 4*a^2*b^10*c^4 - 2*b^12*c^4 + 2*a^10*c^6 + 6*a^8*b^2*c^6 - 14*a^6*b^4*c^6 + 5*a^4*b^6*c^6 + 8*a^2*b^8*c^6 - 6*a^6*b^2*c^8 - 4*a^4*b^4*c^8 + 8*a^2*b^6*c^8 + 2*b^8*c^8 + 2*a^4*b^2*c^10 - 4*a^2*b^4*c^10 + a^4*c^12 - 2*b^4*c^12 + b^2*c^14 : :

See Tran Quang Hung and Peter Moses, euclid 3426.

X(46146) lies on this line: {2, 3}


X(46147) = CROSSPOINT OF X(74) AND X(1494)

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

X(46147) lies on these lines: {2, 25045}, {3, 74}, {39, 35325}, {67, 9003}, {262, 5094}, {305, 670}, {660, 2349}, {694, 2433}, {858, 12079}, {1304, 21284}, {1634, 3917}, {2781, 44889}, {3933, 4576}, {7495, 16243}, {7574, 34150}, {8749, 39951}, {9515, 40351}, {10152, 12173}, {14424, 20021}, {16063, 36875}

X(46147) = complement of X(25045)
X(46147) = X(32640)-Ceva conjugate of X(14380)
X(46147) = X(i)-isoconjugate of X(j) for these (i,j): {30, 82}, {83, 2173}, {251, 14206}, {308, 9406}, {827, 36035}, {1176, 1784}, {1495, 3112}, {1637, 4599}, {1990, 34055}, {2420, 18070}, {2631, 42396}, {3405, 35906}, {4593, 14398}, {9407, 18833}, {18098, 18653}, {34072, 41079}
X(46147) = crosspoint of X(74) and X(1494)
X(46147) = crosssum of X(30) and X(1495)
X(46147) = barycentric product X(i)*X(j) for these {i,j}: {38, 2349}, {39, 1494}, {74, 141}, {427, 14919}, {826, 44769}, {1235, 18877}, {1304, 2525}, {1634, 2394}, {1930, 2159}, {1964, 33805}, {2433, 4576}, {3665, 15627}, {3917, 16080}, {3933, 8749}, {7813, 9139}, {8024, 40352}, {9717, 31125}, {14380, 41676}, {20021, 35910}, {20883, 35200}, {23285, 32640}, {34767, 35325}
X(46147) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 14206}, {39, 30}, {74, 83}, {141, 3260}, {427, 46106}, {688, 14398}, {826, 41079}, {1304, 42396}, {1401, 6357}, {1494, 308}, {1634, 2407}, {1843, 1990}, {1923, 9406}, {1964, 2173}, {2159, 82}, {2349, 3112}, {3005, 1637}, {3051, 1495}, {3688, 7359}, {3917, 11064}, {4553, 42716}, {8061, 36035}, {8749, 32085}, {14380, 4580}, {14919, 1799}, {16030, 43768}, {16080, 46104}, {17187, 18653}, {17442, 1784}, {18877, 1176}, {20775, 3284}, {21123, 11125}, {27369, 14581}, {32640, 827}, {33805, 18833}, {35200, 34055}, {35325, 4240}, {35910, 20022}, {36034, 4599}, {40352, 251}, {41331, 9407}, {44769, 4577}
X(46147) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 14919, 40352}, {14919, 40352, 9717}


X(46148) = CROSSPOINT OF X(101) AND X(190)

Barycentrics    a^2*(a - b)*(a - c)*(b^2 + c^2) : :
X(46148) = 2 X[20974] - 3 X[46125], 4 X[23988] - 3 X[46125]

X(46148) lies on these lines: {1, 38346}, {2, 25049}, {6, 8054}, {9, 30942}, {37, 18191}, {38, 17456}, {42, 694}, {67, 71}, {100, 649}, {101, 110}, {190, 670}, {513, 35310}, {518, 2225}, {672, 20785}, {896, 39258}, {1018, 4427}, {1755, 3930}, {2308, 28643}, {2350, 32913}, {2810, 20974}, {3219, 6651}, {3231, 21830}, {3404, 15523}, {3508, 17763}, {3588, 5279}, {3730, 17230}, {3835, 27134}, {3909, 7239}, {3937, 6184}, {3938, 20665}, {4020, 33299}, {4379, 4554}, {4553, 35309}, {4557, 35326}, {4568, 4576}, {4584, 4610}, {4600, 4603}, {4621, 35009}, {5364, 32912}, {6377, 46126}, {7075, 32925}, {8620, 21760}, {9026, 43046}, {15487, 20588}, {16550, 21382}, {17135, 21369}, {17187, 21814}, {17449, 20459}, {20295, 26795}, {20372, 29824}, {21362, 35341}, {25924, 26692}, {28743, 30835}

X(46148) = reflection of X(i) in X(j) for these {i,j}: {20974, 23988}, {25049, 44312}, {46158, 141}
X(46148) = isogonal conjugate of X(10566)
X(46148) = complement of X(25049)
X(46148) = anticomplement of X(44312)
X(46148) = isogonal conjugate of the isotomic conjugate of X(4568)
X(46148) = X(i)-Ceva conjugate of X(j) for these (i,j): {190, 4568}, {4600, 42}, {4603, 100}, {35334, 35309}
X(46148) = X(21123)-cross conjugate of X(39)
X(46148) = cevapoint of X(39) and X(21123)
X(46148) = crosspoint of X(101) and X(190)
X(46148) = crosssum of X(i) and X(j) for these (i,j): {514, 649}, {4375, 21832}
X(46148) = trilinear pole of line {39, 1964}
X(46148) = crossdifference of every pair of points on line {3120, 4107}
X(46148) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10566}, {2, 18108}, {10, 39179}, {28, 4580}, {58, 18070}, {82, 514}, {83, 513}, {87, 18107}, {251, 693}, {256, 18111}, {274, 18105}, {308, 667}, {649, 3112}, {651, 18101}, {689, 3121}, {733, 14296}, {827, 16732}, {905, 32085}, {1019, 18082}, {1111, 4628}, {1176, 17924}, {1799, 6591}, {1919, 18833}, {1980, 40016}, {3120, 4599}, {3122, 4593}, {3125, 4577}, {3737, 18097}, {4010, 39276}, {4107, 43763}, {4164, 14970}, {7192, 18098}, {7649, 34055}, {9309, 18110}, {16277, 16757}, {18113, 27834}, {18180, 39182}, {18210, 42396}, {21207, 34072}, {22383, 46104}, {27918, 36081}
X(46148) = barycentric product X(i)*X(j) for these {i,j}: {1, 4553}, {6, 4568}, {10, 1634}, {38, 100}, {39, 190}, {42, 4576}, {71, 41676}, {81, 35309}, {99, 21035}, {101, 141}, {109, 3703}, {110, 15523}, {306, 35325}, {427, 1331}, {518, 35333}, {651, 33299}, {662, 3954}, {664, 3688}, {668, 1964}, {670, 41267}, {692, 1930}, {765, 2530}, {799, 21814}, {826, 4570}, {906, 20883}, {1016, 21123}, {1018, 16696}, {1235, 32656}, {1252, 16892}, {1293, 4884}, {1332, 17442}, {1401, 3699}, {1843, 4561}, {1897, 3917}, {1923, 6386}, {1978, 3051}, {2084, 4601}, {2346, 35335}, {3005, 4600}, {3404, 42717}, {3665, 3939}, {3666, 35334}, {3933, 8750}, {3952, 17187}, {4020, 6335}, {4062, 36827}, {4093, 4589}, {4554, 40972}, {4557, 16887}, {4558, 21016}, {4567, 8061}, {4574, 17171}, {4594, 40936}, {4603, 16587}, {4628, 7794}, {7260, 21752}, {7953, 21038}, {8024, 32739}
X(46148) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 10566}, {31, 18108}, {37, 18070}, {38, 693}, {39, 514}, {71, 4580}, {100, 3112}, {101, 83}, {141, 3261}, {172, 18111}, {190, 308}, {427, 46107}, {663, 18101}, {668, 18833}, {688, 3122}, {692, 82}, {826, 21207}, {906, 34055}, {1331, 1799}, {1333, 39179}, {1401, 3676}, {1634, 86}, {1843, 7649}, {1897, 46104}, {1918, 18105}, {1923, 667}, {1930, 40495}, {1964, 513}, {1978, 40016}, {2084, 3125}, {2176, 18107}, {2236, 14296}, {2530, 1111}, {3005, 3120}, {3051, 649}, {3313, 21178}, {3688, 522}, {3703, 35519}, {3787, 3798}, {3917, 4025}, {3954, 1577}, {4020, 905}, {4079, 34294}, {4093, 4010}, {4553, 75}, {4557, 18082}, {4559, 18097}, {4567, 4593}, {4568, 76}, {4570, 4577}, {4576, 310}, {4600, 689}, {4601, 37204}, {8041, 16892}, {8061, 16732}, {8623, 4107}, {8643, 18113}, {8750, 32085}, {9019, 21205}, {9310, 18110}, {15523, 850}, {16696, 7199}, {16892, 23989}, {17187, 7192}, {17442, 17924}, {17456, 27712}, {20775, 1459}, {21016, 14618}, {21035, 523}, {21108, 2973}, {21123, 1086}, {21814, 661}, {23990, 4628}, {32656, 1176}, {32739, 251}, {33299, 4391}, {35309, 321}, {35319, 17167}, {35325, 27}, {35326, 18087}, {35333, 2481}, {35334, 30710}, {35335, 20880}, {40936, 2533}, {40972, 650}, {41267, 512}, {41331, 1919}, {41676, 44129}
X(46148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 25049, 44312}, {101, 1331, 32739}, {3909, 42723, 7239}, {20974, 23988, 46125}


X(46149) = CROSSPOINT OF X(105) AND X(2481)

Barycentrics    a*(a^2 + b^2 - a*c - b*c)*(b^2 + c^2)*(a^2 - a*b - b*c + c^2) : :
X(46149) = 5 X[3618] - 3 X[25316]

X(46149) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46149) lies on these lines: {1, 39957}, {2, 25050}, {6, 13476}, {38, 17456}, {65, 1462}, {67, 8674}, {69, 25048}, {81, 105}, {141, 3688}, {239, 335}, {291, 39979}, {314, 670}, {1086, 2876}, {1100, 1438}, {1279, 2195}, {1634, 16696}, {3056, 40505}, {3057, 28071}, {3271, 5845}, {3416, 4863}, {3589, 25323}, {3618, 25316}, {4437, 14839}, {4576, 16703}, {4974, 34378}, {5091, 20468}, {14942, 21334}, {20670, 38989}, {32658, 41332}, {36057, 40959}

X(46149) = midpoint of X(69) and X(25048)
X(46149) = reflection of X(i) in X(j) for these {i,j}: {4553, 141}, {25323, 3589}
X(46149) = complement of X(25050)
X(46149) = crosspoint of X(105) and X(2481)
X(46149) = crosssum of X(i) and X(j) for these (i,j): {238, 40910}, {518, 2223}
X(46149) = trilinear pole of line {39, 2530}
X(46149) = X(i)-isoconjugate of X(j) for these (i,j): {82, 518}, {83, 672}, {251, 3912}, {308, 9454}, {827, 4088}, {918, 4628}, {1026, 18108}, {1176, 1861}, {1799, 2356}, {1818, 32085}, {2223, 3112}, {2284, 10566}, {3286, 18082}, {4599, 24290}, {5089, 34055}, {9455, 18833}, {18098, 18206}
X(46149) = barycentric product X(i)*X(j) for these {i,j}: {38, 673}, {39, 2481}, {105, 141}, {294, 3665}, {427, 1814}, {514, 35333}, {666, 2530}, {1027, 4568}, {1235, 32658}, {1401, 36796}, {1438, 1930}, {1462, 3703}, {1964, 18031}, {3688, 34018}, {3933, 8751}, {10099, 41676}, {13576, 16696}, {16887, 18785}, {16892, 36086}, {17442, 31637}, {20883, 36057}
X(46149) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 3912}, {39, 518}, {105, 83}, {141, 3263}, {427, 46108}, {673, 3112}, {1027, 10566}, {1401, 241}, {1438, 82}, {1814, 1799}, {1843, 5089}, {1923, 9454}, {1964, 672}, {2481, 308}, {2530, 918}, {3005, 24290}, {3051, 2223}, {3665, 40704}, {3688, 3693}, {3917, 25083}, {3954, 3932}, {4020, 1818}, {4553, 42720}, {8061, 4088}, {8751, 32085}, {10099, 4580}, {16696, 30941}, {16887, 18157}, {17187, 18206}, {17442, 1861}, {18031, 18833}, {18785, 18082}, {20775, 20752}, {21035, 3930}, {21123, 2254}, {21814, 20683}, {32658, 1176}, {32666, 4628}, {33299, 3717}, {35325, 4238}, {35333, 190}, {36057, 34055}, {40972, 2340}, {41267, 39258}, {41331, 9455}, {43929, 18108}


X(46150) = CROSSPOINT OF X(106) AND X(903)

Barycentrics    a^2*(a + b - 2*c)*(a - 2*b + c)*(b^2 + c^2) : :
X(46150) = 2 X[23644] - 3 X[46126]

X(46150) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46150) lies on these lines: {8, 596}, {38, 4553}, {58, 106}, {88, 291}, {310, 670}, {320, 17449}, {901, 28485}, {902, 1623}, {1015, 23552}, {1320, 45989}, {1634, 17187}, {2810, 23644}, {3831, 4013}, {4080, 30942}, {4576, 16887}, {4615, 41209}

X(46150) = crosspoint of X(106) and X(903)
X(46150) = crosssum of X(519) and X(902)
X(46150) = trilinear pole of line {39, 21123}
X(46150) = X(i)-isoconjugate of X(j) for these (i,j): {44, 83}, {82, 519}, {251, 4358}, {308, 2251}, {902, 3112}, {1023, 10566}, {1176, 38462}, {3762, 4628}, {4120, 4599}, {4169, 39179}, {4448, 36081}, {4577, 4730}, {4593, 14407}, {5440, 32085}, {8756, 34055}, {9459, 18833}, {16704, 18098}, {17780, 18108}, {23202, 46104}
X(46150) = barycentric product X(i)*X(j) for these {i,j}: {38, 88}, {39, 903}, {106, 141}, {427, 1797}, {826, 4591}, {901, 16892}, {1022, 4553}, {1235, 32659}, {1401, 4997}, {1634, 4049}, {1930, 9456}, {1964, 20568}, {2084, 4634}, {2316, 3665}, {2530, 3257}, {3005, 4615}, {3917, 6336}, {3933, 8752}, {4080, 17187}, {4555, 21123}, {4568, 23345}, {4622, 8061}, {4674, 16696}, {20883, 36058}
X(46150) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 4358}, {39, 519}, {88, 3112}, {106, 83}, {141, 3264}, {427, 46109}, {688, 14407}, {903, 308}, {1401, 3911}, {1797, 1799}, {1843, 8756}, {1923, 2251}, {1964, 44}, {2084, 4730}, {2530, 3762}, {3005, 4120}, {3051, 902}, {3688, 2325}, {3917, 3977}, {3954, 3992}, {4020, 5440}, {4553, 24004}, {4591, 4577}, {4615, 689}, {4622, 4593}, {4634, 37204}, {6336, 46104}, {8752, 32085}, {9456, 82}, {16696, 30939}, {17187, 16704}, {17442, 38462}, {20568, 18833}, {20775, 22356}, {21035, 3943}, {21123, 900}, {21814, 21805}, {23345, 10566}, {32659, 1176}, {32719, 4628}, {33299, 4723}, {36058, 34055}, {40972, 3689}, {41331, 9459}


X(46151) = CROSSPOINT OF X(107) AND X(6528)

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

X(46151) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46151) lies on these lines: {4, 67}, {25, 9512}, {69, 41766}, {107, 110}, {112, 1289}, {132, 15526}, {141, 41375}, {393, 694}, {523, 37937}, {660, 823}, {670, 877}, {685, 16813}, {1075, 15258}, {1235, 27373}, {1576, 2409}, {1634, 41676}, {1843, 20021}, {2493, 6353}, {3168, 40138}, {4226, 41679}, {4230, 14570}, {6525, 14826}, {8057, 39192}, {8749, 11596}, {10002, 40330}, {11444, 14249}, {12358, 34334}, {15255, 39998}, {15435, 32000}, {16039, 44770}, {27376, 41585}, {34854, 37778}

X(46151) = reflection of X(46164) in X(141)
X(46151) = anticomplement of X(47413)
X(46151) = pole wrt polar circle of trilinear polar of X(4580) (line X(125)X(127))
X(46151) = polar conjugate of X(4580)
X(46151) = polar conjugate of the isotomic conjugate of X(41676)
X(46151) = polar conjugate of the isogonal conjugate of X(35325)
X(46151) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {15388, 6360}, {23582, 21288}, {23964, 21215}, {24000, 5596}, {44183, 4329}
X(46151) = X(23964)-Ceva conjugate of X(4)
X(46151) = X(i)-cross conjugate of X(j) for these (i,j): {826, 427}, {23881, 41375}, {35325, 41676}
X(46151) = cevapoint of X(i) and X(j) for these (i,j): {141, 23881}, {427, 826}, {523, 9969}, {6676, 8673}
X(46151) = crosspoint of X(107) and X(6528)
X(46151) = crosssum of X(520) and X(39201)
X(46151) = trilinear pole of line {39, 427}
X(46151) = X(i)-isoconjugate of X(j) for these (i,j): {48, 4580}, {82, 520}, {83, 822}, {251, 24018}, {326, 18105}, {577, 18070}, {647, 34055}, {656, 1176}, {661, 28724}, {810, 1799}, {827, 2632}, {3112, 39201}, {3269, 4599}, {3682, 18108}, {3990, 10566}, {4091, 18098}, {4630, 17879}, {10547, 14208}, {15526, 34072}, {18082, 23224}, {18097, 36054}, {37754, 42396}
X(46151) = barycentric product X(i)*X(j) for these {i,j}: {4, 41676}, {38, 823}, {39, 6528}, {99, 27376}, {107, 141}, {112, 1235}, {162, 20883}, {264, 35325}, {393, 4576}, {427, 648}, {811, 17442}, {826, 23582}, {1634, 2052}, {1783, 16747}, {1843, 6331}, {1897, 17171}, {1930, 24019}, {2525, 32230}, {3917, 15352}, {3933, 6529}, {4568, 8747}, {8024, 32713}, {8061, 23999}, {8795, 35319}, {14570, 19174}, {18831, 27371}, {23285, 23964}, {36827, 37778}, {41375, 44766}
X(46151) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 4580}, {38, 24018}, {39, 520}, {107, 83}, {110, 28724}, {112, 1176}, {141, 3265}, {158, 18070}, {162, 34055}, {427, 525}, {648, 1799}, {823, 3112}, {826, 15526}, {1235, 3267}, {1289, 40404}, {1634, 394}, {1843, 647}, {1964, 822}, {2207, 18105}, {3005, 3269}, {3051, 39201}, {3933, 4143}, {4553, 3998}, {4576, 3926}, {5317, 18108}, {6528, 308}, {6529, 32085}, {8061, 2632}, {8747, 10566}, {8884, 39182}, {15352, 46104}, {16696, 4131}, {16747, 15413}, {16813, 39287}, {16887, 30805}, {16892, 17216}, {17171, 4025}, {17187, 4091}, {17442, 656}, {19174, 15412}, {20775, 32320}, {20883, 14208}, {21016, 4064}, {21108, 4466}, {23285, 36793}, {23582, 4577}, {23964, 827}, {23977, 21458}, {23999, 4593}, {24000, 4599}, {24019, 82}, {27369, 3049}, {27371, 6368}, {27373, 2485}, {27374, 42293}, {27376, 523}, {32230, 42396}, {32713, 251}, {35319, 5562}, {35325, 3}, {36127, 18097}, {39691, 5489}, {40938, 8673}, {41375, 33294}, {41676, 69}, {41937, 4630}, {42405, 41488}
X(46151) = {X(107),X(648)}-harmonic conjugate of X(32713)


X(46152) = CROSSPOINT OF X(108) AND X(18026)

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

X(46152) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46152) lies on these lines: {65, 67}, {108, 110}, {427, 1401}, {513, 8750}, {653, 660}, {670, 18026}, {694, 1880}, {1463, 1876}, {1469, 1892}, {1897, 3888}, {4242, 4579}, {20621, 26932}

X(46152) = X(2530)-cross conjugate of X(427)
X(46152) = cevapoint of X(1401) and X(2530)
X(46152) = crosspoint of X(108) and X(18026)
X(46152) = crosssum of X(521) and X(1946)
X(46152) = trilinear pole of line {39, 17442}
X(46152) = X(i)-isoconjugate of X(j) for these (i,j): {78, 18108}, {82, 521}, {83, 652}, {219, 10566}, {251, 6332}, {284, 4580}, {332, 18105}, {522, 1176}, {650, 34055}, {663, 1799}, {1331, 18101}, {1946, 3112}, {2193, 18070}, {3064, 28724}, {3694, 39179}, {4628, 26932}, {10547, 35519}, {18082, 23189}, {18097, 23090}
X(46152) = barycentric product X(i)*X(j) for these {i,j}: {34, 4568}, {38, 653}, {39, 18026}, {65, 41676}, {108, 141}, {109, 20883}, {278, 4553}, {427, 651}, {664, 17442}, {1235, 1415}, {1401, 6335}, {1414, 21016}, {1441, 35325}, {1634, 40149}, {1783, 3665}, {1843, 4554}, {1880, 4576}, {1930, 32674}, {2530, 46102}, {3688, 13149}, {3703, 32714}, {4551, 17171}, {4559, 16747}, {4564, 21108}, {5236, 35333}, {6516, 27376}, {7012, 16892}, {33299, 36118}
X(46152) = barycentric quotient X(i)/X(j) for these {i,j}: {34, 10566}, {38, 6332}, {39, 521}, {65, 4580}, {108, 83}, {109, 34055}, {141, 35518}, {225, 18070}, {427, 4391}, {608, 18108}, {651, 1799}, {653, 3112}, {1401, 905}, {1415, 1176}, {1634, 1812}, {1843, 650}, {1964, 652}, {2530, 26932}, {3051, 1946}, {3665, 15413}, {3703, 15416}, {4553, 345}, {4568, 3718}, {6591, 18101}, {16892, 17880}, {17171, 18155}, {17442, 522}, {18026, 308}, {20775, 36054}, {20883, 35519}, {21016, 4086}, {21035, 8611}, {21108, 4858}, {21123, 7004}, {27369, 3063}, {27376, 44426}, {32674, 82}, {35309, 3710}, {35325, 21}, {36059, 28724}, {41676, 314}


X(46153) = CROSSPOINT OF X(109) AND X(664)

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

X(46153) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46153) lies on these lines: {1, 24237}, {6, 38991}, {65, 16726}, {67, 73}, {109, 110}, {292, 694}, {651, 660}, {663, 1633}, {664, 670}, {692, 1459}, {934, 29052}, {2875, 22084}, {3000, 45932}, {4014, 45937}, {4296, 39035}, {4551, 8050}, {4553, 35335}, {4620, 41209}, {17136, 35338}, {39046, 39047}

X(46153) = X(4620)-Ceva conjugate of X(1400)
X(46153) = X(2530)-cross conjugate of X(17187)
X(46153) = cevapoint of X(1964) and X(21123)
X(46153) = crosspoint of X(109) and X(664)
X(46153) = crosssum of X(522) and X(663)
X(46153) = trilinear pole of line {39, 1401}
X(46153) = crossdifference of every pair of points on line {18101, 21044}
X(46153) = X(i)-isoconjugate of X(j) for these (i,j): {8, 18108}, {9, 10566}, {82, 522}, {83, 650}, {100, 18101}, {251, 4391}, {284, 18070}, {308, 3063}, {314, 18105}, {521, 32085}, {663, 3112}, {1021, 18097}, {1172, 4580}, {1176, 44426}, {1799, 18344}, {1946, 46104}, {2319, 18107}, {2321, 39179}, {3064, 34055}, {3737, 18082}, {4124, 36081}, {4516, 4577}, {4560, 18098}, {4599, 21044}, {4612, 34294}, {4628, 4858}, {18113, 31343}
X(46153) = barycentric product X(i)*X(j) for these {i,j}: {38, 651}, {39, 664}, {56, 4568}, {57, 4553}, {59, 16892}, {73, 41676}, {101, 3665}, {109, 141}, {190, 1401}, {226, 1634}, {241, 35333}, {307, 35325}, {427, 1813}, {653, 3917}, {658, 3688}, {934, 33299}, {1014, 35309}, {1170, 35335}, {1235, 32660}, {1400, 4576}, {1414, 3954}, {1415, 1930}, {1461, 3703}, {1964, 4554}, {2530, 4564}, {3005, 4620}, {3051, 4572}, {3933, 32674}, {4020, 18026}, {4551, 16696}, {4552, 17187}, {4559, 16887}, {4565, 15523}, {4569, 40972}, {4573, 21035}, {4625, 21814}, {4628, 41285}, {4884, 38828}, {4998, 21123}, {6516, 17442}, {6517, 27376}, {16720, 29055}, {17171, 23067}, {20883, 36059}, {21108, 44717}, {24471, 35334}
X(46153) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 4391}, {39, 522}, {56, 10566}, {65, 18070}, {73, 4580}, {109, 83}, {141, 35519}, {427, 46110}, {604, 18108}, {649, 18101}, {651, 3112}, {653, 46104}, {664, 308}, {1401, 514}, {1403, 18107}, {1408, 39179}, {1415, 82}, {1634, 333}, {1813, 1799}, {1843, 3064}, {1923, 3063}, {1964, 650}, {2084, 4516}, {2530, 4858}, {3005, 21044}, {3051, 663}, {3665, 3261}, {3688, 3239}, {3917, 6332}, {3954, 4086}, {4020, 521}, {4553, 312}, {4554, 18833}, {4559, 18082}, {4568, 3596}, {4572, 40016}, {4576, 28660}, {4620, 689}, {9316, 18110}, {16696, 18155}, {16892, 34387}, {17187, 4560}, {17442, 44426}, {20775, 652}, {21035, 3700}, {21123, 11}, {21814, 4041}, {23845, 18086}, {32660, 1176}, {32674, 32085}, {33299, 4397}, {35309, 3701}, {35325, 29}, {35333, 36796}, {35335, 1229}, {36059, 34055}, {40936, 4140}, {40972, 3900}, {41267, 3709}, {41676, 44130}


X(46154) = CROSSPOINT OF X(111) AND X(671)

Barycentrics    a^2*(a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2)*(b^2 + c^2) : :
X(46154) = X[193] - 3 X[25315], 3 X[599] + X[25334], 3 X[599] - 2 X[36792], 2 X[6593] - 3 X[46131], 3 X[21358] - 2 X[45672], X[25334] + 2 X[36792]

X(46154) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46154) lies on these lines: {2, 17413}, {6, 110}, {39, 1634}, {67, 690}, {69, 6664}, {76, 338}, {115, 5181}, {141, 4576}, {193, 25315}, {524, 20977}, {660, 897}, {691, 755}, {694, 882}, {826, 36824}, {892, 14970}, {1648, 25328}, {1691, 12367}, {1843, 35325}, {1916, 23342}, {2353, 3053}, {2393, 3291}, {2916, 8869}, {3051, 30489}, {3094, 14609}, {3231, 8705}, {3589, 25325}, {3763, 30786}, {3954, 4553}, {5013, 15268}, {5017, 41443}, {5104, 17964}, {5106, 46127}, {5648, 6034}, {6698, 8288}, {6792, 32255}, {8050, 40085}, {8586, 9872}, {9019, 36827}, {9023, 17993}, {9225, 10510}, {9971, 13330}, {10418, 15118}, {10558, 45843}, {19596, 32729}, {19626, 30435}, {21358, 42008}, {27376, 41585}, {32241, 35902}, {32251, 35901}

X(46154) = midpoint of X(69) and X(25047)
X(46154) = reflection of X(i) in X(j) for these {i,j}: {6, 3124}, {4576, 141}, {25325, 3589}
X(46154) = complement of X(25052)
X(46154) = isotomic conjugate of the isogonal conjugate of X(41272)
X(46154) = isogonal conjugate of the isotomic conjugate of X(31125)
X(46154) = X(i)-Ceva conjugate of X(j) for these (i,j): {111, 41272}, {671, 31125}, {892, 9178}, {32729, 10097}
X(46154) = X(9019)-cross conjugate of X(6)
X(46154) = X(i)-isoconjugate of X(j) for these (i,j): {82, 524}, {83, 896}, {187, 3112}, {251, 14210}, {308, 922}, {351, 4593}, {468, 34055}, {662, 22105}, {690, 4599}, {2642, 4577}, {3405, 5967}, {5026, 43763}, {5467, 18070}, {6593, 37221}, {6629, 18098}, {14567, 18833}, {16702, 18082}, {18105, 24039}, {34072, 35522}
X(46154) = crosspoint of X(i) and X(j) for these (i,j): {111, 671}, {34539, 39413}
X(46154) = crosssum of X(187) and X(524)
X(46154) = trilinear pole of line {39, 3005}
X(46154) = crossdifference of every pair of points on line {690, 5026}
X(46154) = barycentric product X(i)*X(j) for these {i,j}: {6, 31125}, {38, 897}, {39, 671}, {76, 41272}, {111, 141}, {427, 895}, {523, 36827}, {691, 826}, {892, 3005}, {923, 1930}, {1235, 14908}, {1634, 5466}, {1843, 30786}, {2530, 5380}, {3051, 18023}, {3665, 5547}, {3703, 7316}, {3917, 17983}, {3933, 8753}, {4576, 9178}, {5968, 20021}, {7813, 10630}, {8024, 32740}, {8061, 36085}, {9019, 10415}, {10097, 41676}, {14424, 34574}, {14977, 35325}, {20775, 46111}, {20883, 36060}, {23285, 32729}, {23297, 42007}, {30489, 42008}
X(46154) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 14210}, {39, 524}, {111, 83}, {141, 3266}, {427, 44146}, {512, 22105}, {671, 308}, {688, 351}, {691, 4577}, {826, 35522}, {892, 689}, {895, 1799}, {897, 3112}, {923, 82}, {1401, 7181}, {1634, 5468}, {1843, 468}, {1923, 922}, {1964, 896}, {2084, 2642}, {2525, 45807}, {3005, 690}, {3051, 187}, {3688, 3712}, {3787, 32459}, {3917, 6390}, {3954, 42713}, {4553, 42721}, {5968, 20022}, {7813, 36792}, {8041, 7813}, {8623, 5026}, {8753, 32085}, {8877, 38946}, {9019, 7664}, {10097, 4580}, {14908, 1176}, {16696, 16741}, {17187, 6629}, {17983, 46104}, {18023, 40016}, {20775, 3292}, {21035, 4062}, {21123, 4750}, {21814, 21839}, {23894, 18070}, {27369, 44102}, {27376, 37778}, {31125, 76}, {32729, 827}, {32740, 251}, {35325, 4235}, {36060, 34055}, {36085, 4593}, {36142, 4599}, {36827, 99}, {38303, 31128}, {41272, 6}, {41331, 14567}, {42007, 10130}
X(46154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {111, 895, 32740}, {111, 42007, 6}, {895, 32740, 6}, {2502, 3124, 46131}, {32740, 42007, 895}


X(46155) = CROSSPOINT OF X(476) AND X(35139)

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

X(46155) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46155) lies on these lines: {67, 265}, {110, 476}, {231, 32223}, {660, 32680}, {670, 14221}, {694, 1989}, {826, 1634}, {2420, 23968}, {4576, 23285}, {9019, 20021}, {14254, 15067}, {14356, 24206}, {16776, 43084}, {29959, 36824}

X(46155) = reflection of X(265) in X(43087)
X(46155) = reflection of X(46157) in X(141)
X(46155) = crosspoint of X(476) and X(35139)
X(46155) = crosssum of X(526) and X(14270)
X(46155) = trilinear pole of line {39, 35319}
X(46155) = crossdifference of every pair of points on line {2088, 39495}
X(46155) = X(i)-isoconjugate of X(j) for these (i,j): {50, 18070}, {82, 526}, {83, 2624}, {251, 32679}, {2088, 4599}, {2290, 39182}, {3112, 14270}, {39495, 43763}
X(46155) = barycentric product X(i)*X(j) for these {i,j}: {38, 32680}, {39, 35139}, {94, 1634}, {141, 476}, {265, 41676}, {328, 35325}, {826, 39295}, {1235, 32662}, {1930, 32678}, {1989, 4576}, {8024, 14560}, {14559, 31125}, {20883, 36061}, {35319, 46138}, {36827, 43084}
X(46155) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 32679}, {39, 526}, {141, 3268}, {265, 4580}, {427, 44427}, {476, 83}, {1141, 39182}, {1634, 323}, {1964, 2624}, {2166, 18070}, {3005, 2088}, {3051, 14270}, {3917, 8552}, {3933, 45792}, {4553, 42701}, {4576, 7799}, {7813, 45808}, {8623, 39495}, {11060, 18105}, {14560, 251}, {15475, 34294}, {32662, 1176}, {32678, 82}, {32680, 3112}, {35139, 308}, {35319, 1154}, {35325, 186}, {36061, 34055}, {39295, 4577}, {41676, 340}


X(46156) = CROSSPOINT OF X(729) AND X(3228)

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

X(46156) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46156) lies on these lines: {2, 670}, {6, 38998}, {32, 110}, {39, 4576}, {67, 36255}, {351, 694}, {660, 37132}, {733, 9150}, {886, 40858}, {1634, 3051}, {3117, 14608}, {3231, 5201}, {4553, 21814}, {5468, 9468}, {8623, 36827}, {20021, 35366}, {20081, 42486}, {23584, 32973}, {27369, 35325}, {31125, 41178}

X(46156) = X(14406)-cross conjugate of X(4576)
X(46156) = crosspoint of X(729) and X(3228)
X(46156) = crosssum of X(538) and X(3231)
X(46156) = trilinear pole of line {39, 688} (the line through X(39) parallel to the trilinear polar of X(39))
X(46156) = crossdifference of every pair of points on line {887, 9148}
X(46156) = X(i)-isoconjugate of X(j) for these (i,j): {82, 538}, {83, 2234}, {887, 37204}, {888, 4593}, {3112, 3231}, {3405, 36822}, {4599, 9148}, {5118, 18070}, {18833, 33875}
X(46156) = barycentric product X(i)*X(j) for these {i,j}: {38, 37132}, {39, 3228}, {110, 35366}, {141, 729}, {688, 886}, {826, 32717}, {3005, 9150}, {3051, 34087}, {8061, 36133}, {31125, 41309}
X(46156) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 538}, {141, 30736}, {688, 888}, {729, 83}, {886, 42371}, {1634, 23342}, {1964, 2234}, {3005, 9148}, {3051, 3231}, {3228, 308}, {9150, 689}, {9494, 887}, {16696, 30938}, {32717, 4577}, {34087, 40016}, {35366, 850}, {36133, 4593}, {37132, 3112}, {41272, 14609}, {41331, 33875}


X(46157) = CROSSPOINT OF X(842) AND X(5641)

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

X(46157) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46157) lies on these lines: {23, 110}, {67, 523}, {670, 3260}, {694, 9210}, {826, 20021}, {1634, 9019}, {3917, 36827}, {6035, 41209}, {20859, 46128}, {32154, 46127}, {38939, 40107}, {38987, 44895}

X(46157) = reflection of X(46155) in X(141)
X(46157) = X(6035)-Ceva conjugate of X(14998)
X(46157) = crosspoint of X(842) and X(5641)
X(46157) = crosssum of X(542) and X(5191)
X(46157) = X(i)-isoconjugate of X(j) for these (i,j): {82, 542}, {83, 2247}, {1640, 4599}, {3112, 5191}, {3405, 34369}, {4593, 6041}, {6103, 34055}, {18312, 34072}
X(46157) = barycentric product X(i)*X(j) for these {i,j}: {39, 5641}, {141, 842}, {826, 5649}, {1634, 14223}, {3005, 6035}, {4576, 14998}, {35909, 41676}
X(46157) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 542}, {688, 6041}, {826, 18312}, {842, 83}, {1634, 14999}, {1843, 6103}, {1964, 2247}, {3005, 1640}, {3051, 5191}, {5641, 308}, {5649, 4577}, {6035, 689}, {35325, 7473}, {35909, 4580}


X(46158) = CROSSPOINT OF X(675) AND X(43093)

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

X(46158) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46158) lies on these lines: {6, 44312}, {67, 2774}, {69, 8050}, {86, 110}, {320, 334}, {670, 33297}, {1634, 16887}, {1930, 4553}, {2224, 41239}, {4675, 17750}, {17171, 35325}

X(46158) = midpoint of X(69) and X(25049)
X(46158) = reflection of X(6) in X(44312)
X(46158) = reflection of X(46148) in X(141)
X(46158) = crosspoint of X(675) and X(43093)
X(46158) = crosssum of X(674) and X(8618)
X(46158) = trilinear pole of line {39, 16892}
X(46158) = X(i)-isoconjugate of X(j) for these (i,j): {82, 674}, {83, 2225}, {3112, 8618}, {14964, 18098}
X(46158) = barycentric product X(i)*X(j) for these {i,j}: {38, 37130}, {39, 43093}, {141, 675}, {1930, 2224}
X(46158) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 674}, {141, 3006}, {675, 83}, {1401, 43039}, {1964, 2225}, {2224, 82}, {3051, 8618}, {4553, 42723}, {16892, 23887}, {17187, 14964}, {32682, 4628}, {35325, 4249}, {37130, 3112}, {43093, 308}


X(46159) = CROSSPOINT OF X(741) AND X(18827)

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

X(46159) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46159) lies on these lines: {31, 110}, {38, 4576}, {75, 670}, {291, 4651}, {660, 1757}, {694, 3572}, {745, 36066}, {1634, 1964}, {4553, 16696}, {17187, 21814}, {17208, 40017}, {41209, 43763}

X(46159) = X(4093)-cross conjugate of X(39)
X(46159) = cevapoint of X(39) and X(4093)
X(46159) = crosspoint of X(741) and X(18827)
X(46159) = crosssum of X(740) and X(3747)
X(46159) = trilinear pole of line {39, 2084}
X(46159) = X(i)-isoconjugate of X(j) for these (i,j): {82, 740}, {83, 2238}, {238, 18082}, {239, 18098}, {251, 3948}, {308, 41333}, {862, 1799}, {874, 18105}, {3112, 3747}, {3684, 18097}, {4154, 43763}, {4155, 4577}, {18099, 18786}, {35068, 39276}
X(46159) = barycentric product X(i)*X(j) for these {i,j}: {38, 37128}, {39, 18827}, {141, 741}, {291, 16696}, {292, 16887}, {295, 17171}, {335, 17187}, {1401, 36800}, {1634, 4444}, {1911, 16703}, {1930, 18268}, {1964, 40017}, {2196, 16747}, {2311, 3665}, {2530, 4584}, {3572, 4576}, {4589, 21123}, {8061, 36066}
X(46159) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 3948}, {39, 740}, {141, 35544}, {292, 18082}, {741, 83}, {876, 18070}, {1401, 16609}, {1634, 3570}, {1911, 18098}, {1923, 41333}, {1964, 2238}, {2084, 4155}, {3051, 3747}, {3688, 3985}, {4093, 35068}, {4576, 27853}, {8623, 4154}, {16696, 350}, {16703, 18891}, {16887, 1921}, {17171, 40717}, {17187, 239}, {18268, 82}, {18827, 308}, {21035, 4037}, {21123, 4010}, {36066, 4593}, {37128, 3112}, {40017, 18833}, {40972, 4433}


X(46160) = CROSSPOINT OF X(759) AND X(14616)

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

X(46160) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46160) lies on these lines: {1, 60}, {38, 1634}, {80, 8050}, {561, 670}, {660, 17763}, {1930, 4576}, {4553, 15523}, {17442, 35325}, {18165, 29683}, {18191, 22321}, {37536, 45926}

X(46160) = crosspoint of X(759) and X(14616)
X(46160) = crosssum of X(758) and X(3724)
X(46160) = trilinear pole of line {39, 8061}
X(46160) = X(i)-isoconjugate of X(j) for these (i,j): {36, 18082}, {82, 758}, {83, 2245}, {251, 3936}, {827, 6370}, {860, 1176}, {1799, 44113}, {1983, 18070}, {2323, 18097}, {2610, 4599}, {3112, 3724}, {3218, 18098}, {4577, 42666}, {4628, 4707}
X(46160) = barycentric product X(i)*X(j) for these {i,j}: {38, 24624}, {39, 14616}, {80, 16696}, {141, 759}, {826, 37140}, {1807, 17171}, {1930, 34079}, {2161, 16887}, {2341, 3665}, {6187, 16703}, {17187, 18359}, {23285, 32671}
X(46160) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 3936}, {39, 758}, {141, 35550}, {759, 83}, {1401, 18593}, {1411, 18097}, {1634, 4585}, {1964, 2245}, {2084, 42666}, {2161, 18082}, {2530, 4707}, {3005, 2610}, {3051, 3724}, {6187, 18098}, {8061, 6370}, {14616, 308}, {16696, 320}, {16703, 40075}, {16887, 20924}, {17187, 3218}, {17442, 860}, {21035, 4053}, {24624, 3112}, {32671, 827}, {34079, 82}, {35325, 4242}, {36069, 4599}, {37140, 4577}


X(46161) = CROSSPOINT OF X(805) AND X(18229)

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

X(46161) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46161) lies on these lines: {67, 3001}, {110, 669}, {511, 694}, {523, 670}, {660, 37134}, {688, 1634}, {732, 20021}, {3005, 4576}, {5201, 9468}, {14251, 38987}, {14607, 17415}, {18872, 46127}, {39292, 41209}

X(46161) = X(39292)-Ceva conjugate of X(694)
X(46161) = X(35319)-cross conjugate of X(39291)
X(46161) = crosspoint of X(805) and X(18829)
X(46161) = crosssum of X(804) and X(5027)
X(46161) = trilinear pole of line {39, 3118}
X(46161) = X(i)-isoconjugate of X(j) for these (i,j): {82, 804}, {659, 18099}, {1691, 18070}, {1966, 18105}, {2086, 4593}, {2238, 18111}, {3112, 5027}, {4039, 18108}, {4107, 18098}, {4164, 18082}
X(46161) = barycentric product X(i)*X(j) for these {i,j}: {38, 37134}, {39, 18829}, {141, 805}, {694, 4576}, {1634, 1916}, {3005, 39292}, {8024, 17938}, {8041, 41209}, {35325, 40708}, {36214, 41676}
X(46161) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 804}, {141, 14295}, {688, 2086}, {741, 18111}, {805, 83}, {813, 18099}, {882, 34294}, {1581, 18070}, {1634, 385}, {2531, 41178}, {3051, 5027}, {3917, 24284}, {4576, 3978}, {9468, 18105}, {16696, 14296}, {17187, 4107}, {17938, 251}, {18829, 308}, {18872, 22105}, {35325, 419}, {36214, 4580}, {37134, 3112}, {39292, 689}, {41676, 17984}


X(46162) = CROSSPOINT OF X(901) AND X(4555)

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

X(46162) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46162) lies on these lines: {67, 41327}, {106, 33844}, {110, 901}, {660, 876}, {670, 4555}, {1320, 32922}, {2530, 4553}, {3242, 34230}, {3699, 8050}, {4674, 18792}, {5289, 14260}, {21007, 25577}

X(46162) = crosspoint of X(901) and X(4555)
X(46162) = crosssum of X(900) and X(1960)
X(46162) = X(i)-isoconjugate of X(j) for these (i,j): {44, 10566}, {82, 900}, {83, 1635}, {251, 3762}, {519, 18108}, {1960, 3112}, {3285, 18070}, {3943, 39179}, {18101, 23703}, {18105, 30939}
X(46162) = barycentric product X(i)*X(j) for these {i,j}: {38, 3257}, {39, 4555}, {88, 4553}, {106, 4568}, {141, 901}, {1401, 4582}, {1634, 4080}, {1930, 32665}, {2530, 5376}, {3665, 5548}, {3954, 4622}, {4591, 15523}, {4615, 21035}, {4634, 21814}, {8024, 32719}, {9268, 16892}
X(46162) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 3762}, {39, 900}, {106, 10566}, {901, 83}, {1401, 30725}, {1634, 16704}, {1964, 1635}, {2441, 18113}, {3051, 1960}, {3257, 3112}, {3688, 1639}, {4553, 4358}, {4555, 308}, {4568, 3264}, {4674, 18070}, {9456, 18108}, {20775, 22086}, {21035, 4120}, {21123, 1647}, {21814, 4730}, {32665, 82}, {32719, 251}, {33299, 4768}, {35309, 3992}, {35325, 37168}, {40972, 4895}, {41267, 14407}


X(46163) = CROSSPOINT OF X(666) AND X(919)

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

X(46163) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46163) lies on these lines: {6, 38989}, {67, 17796}, {110, 919}, {645, 666}, {660, 2284}, {692, 21007}, {694, 21788}, {4553, 35333}, {4559, 32735}, {5452, 30825}, {28743, 28834}, {32666, 35327}

X(46163) = crosspoint of X(666) and X(919)
X(46163) = crosssum of X(665) and X(918)
X(46163) = trilinear pole of line {39, 20969}
X(46163) = X(i)-isoconjugate of X(j) for these (i,j): {82, 918}, {83, 2254}, {518, 10566}, {665, 3112}, {1025, 18101}, {3286, 18070}, {3912, 18108}, {3932, 39179}, {18098, 23829}, {18105, 18157}
X(46163) = barycentric product X(i)*X(j) for these {i,j}: {1, 35333}, {38, 36086}, {39, 666}, {105, 4553}, {141, 919}, {927, 3688}, {1401, 36802}, {1438, 4568}, {1634, 13576}, {1930, 32666}, {2530, 5377}, {3051, 36803}, {3703, 32735}, {33299, 36146}, {34085, 40972}
X(46163) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 918}, {666, 308}, {884, 18101}, {919, 83}, {1401, 43042}, {1438, 10566}, {1634, 30941}, {1964, 2254}, {3051, 665}, {4553, 3263}, {17187, 23829}, {18785, 18070}, {21035, 4088}, {21814, 24290}, {32666, 82}, {35325, 15149}, {35333, 75}, {36086, 3112}, {36803, 40016}


X(46164) = CROSSPOINT OF X(1297) AND X(35140)

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

X(46164) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46164) lies on these lines: {22, 110}, {67, 2435}, {141, 41375}, {511, 44894}, {670, 14615}, {694, 34212}, {1634, 3313}, {1853, 18018}, {3917, 35325}, {6330, 11331}, {34817, 43717}

X(46164) = reflection of X(46151) in X(141)
X(46164) = isogonal conjugate of X(21458)
X(46164) = crosspoint of X(1297) and X(35140)
X(46164) = crosssum of X(1503) and X(42671)
X(46164) = perspector of ABC and unary cofactor triangle of 1st orthosymmedial triangle
X(46164) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21458}, {82, 1503}, {83, 2312}, {3112, 42671}, {8766, 32085}, {16318, 34055}, {28343, 37221}
X(46164) = barycentric product X(i)*X(j) for these {i,j}: {39, 35140}, {141, 1297}, {1634, 43673}, {2419, 35325}, {2435, 41676}, {2525, 44770}, {3917, 6330}, {3933, 43717}, {4576, 34212}
X(46164) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 21458}, {39, 1503}, {141, 30737}, {1297, 83}, {1401, 43045}, {1634, 34211}, {1843, 16318}, {1964, 2312}, {2435, 4580}, {3051, 42671}, {3917, 441}, {4020, 8766}, {6330, 46104}, {20775, 8779}, {35140, 308}, {35325, 2409}, {43717, 32085}, {44770, 42396}


X(46165) = CROSSPOINT OF X(2373) AND X(46140)

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

X(46165) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46165) lies on these lines: {32, 14376}, {67, 9517}, {69, 110}, {141, 35325}, {315, 670}, {327, 44134}, {339, 32246}, {599, 36823}, {660, 37220}, {694, 9035}, {1235, 27373}, {1634, 3933}, {2892, 13219}, {3313, 4576}, {5201, 40996}, {39129, 41584}

X(46165) = midpoint of X(69) and X(25053)
X(46165) = reflection of X(35325) in X(141)
X(46165) = polar conjugate of X(21459)
X(46165) = X(37220)-anticomplementary conjugate of X(11061)
X(46165) = cevapoint of X(i) and X(j) for these (i,j): {141, 9019}, {3917, 7813}
X(46165) = crosspoint of X(2373) and X(46140)
X(46165) = trilinear pole of line {39, 2525}
X(46165) = X(i)-isoconjugate of X(j) for these (i,j): {48, 21459}, {82, 2393}, {251, 18669}, {14580, 34055}
X(46165) = barycentric product X(i)*X(j) for these {i,j}: {38, 37220}, {39, 46140}, {141, 2373}, {1177, 8024}, {1235, 18876}
X(46165) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 21459}, {38, 18669}, {39, 2393}, {141, 858}, {427, 5523}, {1177, 251}, {1843, 14580}, {1930, 20884}, {2373, 83}, {3917, 14961}, {7813, 5181}, {8024, 1236}, {15523, 21017}, {16887, 17172}, {16892, 21109}, {18876, 1176}, {37220, 3112}, {46140, 308}


X(46166) = CROSSPOINT OF X(1113) AND X(15164)

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*(a^2 - b^2 - c^2)*J) : :

X(46166) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46166) lies on these lines: {67, 2575}, {110, 1113}, {141, 427}, {468, 44126}, {511, 1312}, {524, 20405}, {660, 2580}, {670, 15164}, {694, 8106}, {1345, 1350}, {1346, 6403}, {1347, 7998}, {2781, 14500}, {13415, 15162}, {14808, 25408}

X(46166) = midpoint of X(14808) and X(25408)
X(46166) = reflection of X(46167) in X(141)
X(46166) = crosspoint of X(1113) and X(15164)
X(46166) = crosssum of X(2574) and X(42668)
X(46166) = X(i)-isoconjugate of X(j) for these (i,j): {82, 2574}, {83, 2578}, {251, 2582}, {1176, 2588}, {2577, 4580}, {2584, 32085}, {3112, 42668}, {8105, 34055}
X(46166) = barycentric product X(i)*X(j) for these {i,j}: {38, 2580}, {39, 15164}, {141, 1113}, {427, 8115}, {826, 39298}, {1634, 2593}, {1822, 20883}, {1930, 2576}, {2575, 41676}, {4576, 8106}, {8024, 44123}, {22340, 35325}
X(46166) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 2582}, {39, 2574}, {141, 22339}, {427, 2592}, {1113, 83}, {1634, 8116}, {1822, 34055}, {1843, 8105}, {1964, 2578}, {2575, 4580}, {2576, 82}, {2580, 3112}, {2589, 18070}, {3051, 42668}, {4020, 2584}, {8115, 1799}, {15164, 308}, {17442, 2588}, {35325, 1114}, {39298, 4577}, {41676, 15165}, {44123, 251}
X(46166) = {X(1113),X(8115)}-harmonic conjugate of X(44123)


X(46167) = CROSSPOINT OF X(1114) AND X(15165)

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*(a^2 - b^2 - c^2)*J) : :

X(46167) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46167) lies on these lines: {67, 2574}, {110, 1114}, {141, 427}, {468, 44125}, {511, 1313}, {524, 20406}, {660, 2581}, {670, 15165}, {694, 8105}, {1344, 1350}, {1346, 7998}, {1347, 6403}, {2781, 14499}, {13414, 15163}, {14807, 25407}

X(46167) = midpoint of X(14807) and X(25407)
X(46167) = reflection of X(46166) in X(141)
X(46167) = crosspoint of X(1114) and X(15165)
X(46167) = crosssum of X(2575) and X(42667)
X(46167) = X(i)-isoconjugate of X(j) for these (i,j): {82, 2575}, {83, 2579}, {251, 2583}, {1176, 2589}, {2576, 4580}, {2585, 32085}, {3112, 42667}, {8106, 34055}
X(46167) = barycentric product X(i)*X(j) for these {i,j}: {38, 2581}, {39, 15165}, {141, 1114}, {427, 8116}, {826, 39299}, {1634, 2592}, {1823, 20883}, {1930, 2577}, {2574, 41676}, {4576, 8105}, {8024, 44124}, {22339, 35325}
X(46167) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 2583}, {39, 2575}, {141, 22340}, {427, 2593}, {1114, 83}, {1634, 8115}, {1823, 34055}, {1843, 8106}, {1964, 2579}, {2574, 4580}, {2577, 82}, {2581, 3112}, {2588, 18070}, {3051, 42667}, {4020, 2585}, {8116, 1799}, {15165, 308}, {17442, 2589}, {35325, 1113}, {39299, 4577}, {41676, 15164}, {44124, 251}
X(46167) = {X(1114),X(8116)}-harmonic conjugate of X(44124)


X(46168) = (name pending)

Barycentrics    (4*a^8 - 13*a^6*b^2 + 18*a^4*b^4 - 13*a^2*b^6 + 4*b^8 - 11*a^6*c^2 + 11*a^4*b^2*c^2 + 11*a^2*b^4*c^2 - 11*b^6*c^2 + 9*a^4*c^4 + 3*a^2*b^2*c^4 + 9*b^4*c^4 - a^2*c^6 - b^2*c^6 - c^8)*(4*a^8 - 11*a^6*b^2 + 9*a^4*b^4 - a^2*b^6 - b^8 - 13*a^6*c^2 + 11*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - b^6*c^2 + 18*a^4*c^4 + 11*a^2*b^2*c^4 + 9*b^4*c^4 - 13*a^2*c^6 - 11*b^2*c^6 + 4*c^8) : :

See Antreas Hatzipolakis, Elias M. Hagos, Peter Moses and César Lozada euclid 3438 and euclid 3439.

X(46168) lies on this line: {12108, 32165}

X(46168) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(547)}} and {{A, B, C, X(3), X(550)}}


X(46169) = X(511)X(548)∩X(512)X(547)

Barycentrics    a^2*(2*(2*b^2-c^2)*(b^2-2*c^2)*a^8-3*(b^2+c^2)*(4*b^4-11*b^2*c^2+4*c^4)*a^6+2*(6*b^8+6*c^8-b^2*c^2*(13*b^4+b^2*c^2+13*c^4))*a^4-(b^2+c^2)*(4*b^8+4*c^8-5*b^2*c^2*(4*b^4-5*b^2*c^2+4*c^4))*a^2-(b^2-c^2)^2*b^2*c^2*(b^4+3*b^2*c^2+c^4)) : :
X(46169) = 5*X(140)-2*X(31848), 5*X(3111)-X(31848), 3*X(6785)-7*X(41330), X(12103)+2*X(31850), 4*X(16239)-X(18321)

See Antreas Hatzipolakis, Elias M. Hagos and César Lozada euclid 3439.

X(46169) lies on these lines: {30, 6785}, {140, 3111}, {511, 548}, {512, 547}, {3628, 6787}, {12103, 31850}, {16239, 18321}

X(46169) = reflection of X(i) in X(j) for these (i, j): (140, 3111), (6787, 3628)


X(46170) = X(525)X(548)∩X(547)X(1503)

Barycentrics    18*a^14-33*(b^2+c^2)*a^12+2*(10*b^4+19*b^2*c^2+10*c^4)*a^10-(b^2+c^2)*(29*b^4-43*b^2*c^2+29*c^4)*a^8+3*(b^2-c^2)^2*(10*b^4+17*b^2*c^2+10*c^4)*a^6+(b^4-c^4)*(b^2-c^2)*(b^4-9*b^2*c^2+c^4)*a^4-(b^2-c^2)^2*(4*b^8+4*c^8+3*b^2*c^2*(3*b^2+c^2)*(b^2+3*c^2))*a^2+(b^4-c^4)*(b^2-c^2)^3*(-3*b^4-8*b^2*c^2-3*c^4) : :
X(46170) = 5*X(140)-2*X(43389), 7*X(546)-4*X(43280), 5*X(3859)-2*X(43279), X(12103)+2*X(18338)

See Antreas Hatzipolakis, Elias M. Hagos and César Lozada euclid 3439.

X(46170) lies on these lines: {30, 6794}, {140, 43389}, {525, 548}, {546, 43280}, {547, 1503}, {3859, 43279}, {12103, 18338}


X(46171) = X(140)X(31847)∩X(517)X(548)

Barycentrics    a*(2*(2*b-c)*(b-2*c)*a^7+2*(b+c)*b*c*a^6-(12*b^4+12*c^4-(29*b^2-22*b*c+29*c^2)*b*c)*a^5-(b+c)*(5*b^2+4*b*c+5*c^2)*b*c*a^4+(12*b^6+12*c^6-(28*b^4+28*c^4-(25*b^2-4*b*c+25*c^2)*b*c)*b*c)*a^3+2*(b^2-c^2)*(b-c)*(b+2*c)*(2*b+c)*b*c*a^2-(b^2-c^2)^2*(4*b^4+4*c^4-3*(3*b^2-5*b*c+3*c^2)*b*c)*a-(b^2-c^2)^3*(b-c)*b*c) : :
X(46171) = 5*X(140)-2*X(31847), X(12103)+2*X(31849), X(31847)-5*X(34583)

See Antreas Hatzipolakis, Elias M. Hagos and César Lozada euclid 3439.

X(46171) lies on these lines: {140, 31847}, {517, 548}, {12103, 31849}

X(46171) = reflection of X(140) in X(34583)


X(46172) = X(32)X(143)∩X(98)X(5663)

Barycentrics    a^2*((b^2-c^2)^2*a^8-(b^2+c^2)*(3*b^4-7*b^2*c^2+3*c^4)*a^6+(3*b^8+3*c^8-2*(3*b^4-b^2*c^2+3*c^4)*b^2*c^2)*a^4-(b^2+c^2)*(b^8+c^8-3*b^2*c^2*(2*b^4-3*b^2*c^2+2*c^4))*a^2-(b^2-c^2)^2*b^2*c^2*(b^4-b^2*c^2+c^4)) : :
X(46172) = X(98)+3*X(41330), 3*X(3111)-X(33813), 3*X(6785)+X(38741), 5*X(14061)-X(18321), X(18322)+3*X(21445), X(31848)-3*X(34127)

See Antreas Hatzipolakis, Elias M. Hagos and César Lozada euclid 3439.

X(46172) lies on these lines: {32, 143}, {83, 32205}, {98, 5663}, {182, 12893}, {1078, 32142}, {2023, 14113}, {2080, 13391}, {2387, 14693}, {2698, 14734}, {2854, 32135}, {2882, 18583}, {3111, 33813}, {3398, 12006}, {5946, 11842}, {6101, 7793}, {6785, 38741}, {7787, 15026}, {8590, 11649}, {9517, 20304}, {10095, 32134}, {10104, 11591}, {10796, 13364}, {12042, 31850}, {14061, 18321}, {15074, 39560}, {18322, 21445}, {19155, 41277}, {21152, 39477}, {31848, 34127}, {32046, 32661}, {32515, 35060}

X(46172) = midpoint of X(12042) and X(31850)


X(46173) = X(30)X(44909)∩X(542)X(547)

Barycentrics    4*a^14-9*(b^2+c^2)*a^12+(7*b^4+10*b^2*c^2+7*c^4)*a^10-(b^2+c^2)*(6*b^4-7*b^2*c^2+6*c^4)*a^8+(b^2-c^2)^2*(2*b^2+3*c^2)*(3*b^2+2*c^2)*a^6-(b^4-c^4)*(b^2-c^2)*(b^4+3*b^2*c^2+c^4)*a^4-(b^2-c^2)^2*(b^8+c^8+b^2*c^2*(b^4+4*b^2*c^2+c^4))*a^2-2*(b^4-c^4)*(b^2-c^2)^3*b^2*c^2 : :

See Antreas Hatzipolakis, Elias M. Hagos and César Lozada euclid 3439.

X(46173) lies on these lines: {30, 44909}, {542, 547}, {17974, 32046}, {18338, 38608}

X(46173) = midpoint of X(18338) and X(38608)


X(46174) = X(5)X(3937)∩X(143)X(34753)

Barycentrics    a*((b-c)^2*a^7-(b^2+c^2)*(3*b^2-7*b*c+3*c^2)*a^5-(b+c)*(b^2+c^2)*b*c*a^4+(3*b^6+3*c^6-4*(2*b^4+2*c^4-b*c*(2*b^2-b*c+2*c^2))*b*c)*a^3+2*(b^3-c^3)*b*c*(b^2-c^2)*a^2-(b^2-c^2)^2*(b^4+c^4-b*c*(3*b^2-5*b*c+3*c^2))*a-(b^2-c^2)^3*(b-c)*b*c) : :
X(46174) = X(31847)-3*X(34126), X(33814)-3*X(34583)

See Antreas Hatzipolakis, Elias M. Hagos and César Lozada euclid 3439.

X(46174) lies on these lines: {5, 3937}, {143, 34753}, {1387, 14115}, {2841, 5901}, {2850, 20304}, {3025, 8068}, {5663, 13226}, {5844, 35059}, {6914, 36058}, {6971, 26914}, {6980, 26910}, {31847, 34126}, {31849, 38602}, {32046, 36059}, {33814, 34583}

X(46174) = midpoint of X(i) and X(j) for these {i, j}: {5, 3937}, {31849, 38602}


X(46175) = X(2)X(594)∩X(7)X(299)

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

See Er Jkh and Francisco Javier García Capitán euclid 3458.

X(46175) lies on these lines: {2,594}, {7,299}, {8,302}, {75, 303}, {298,319}, {300,34388}, {396,7227}, {1086,34541}, {4399,23303}, {4431,5243}, {4445,34540}, {4665,23302}, {7231,33458}, {9763,17118}, {11289,33941}, {17365,40901}, {34387,34390}

X(46175) = {X(2),X(42696)}-harmonic conjugate of X(46176)


X(46176) = X(2)X(594)∩X(7)X(298)

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

See Er Jkh and Francisco Javier García Capitán euclid 3458.

X(46176) lies on these lines: {2,594}, {7,298}, {8, 303|, {75, 302}, {299,319}, {301,34388}, {395,7227}, {1086,34540}, {4399,23302}, {4431,5242}, {4445,34541}, {4665,23303}, {7231,33459}, {9761,17118}, {11290,33941}, {17365,40900}, {34387,34389}

X(46176) = {X(2),X(42696)}-harmonic conjugate of X(46175)


X(46177) = CROSSPOINT OF X(101) AND X(664)

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

X(46177) lies on these lines: {1, 2140}, {42, 21725}, {55, 14714}, {100, 3903}, {101, 663}, {109, 43344}, {664, 4449}, {672, 3010}, {2340, 45932}, {2389, 43039}, {2398, 4551}, {3732, 4724}, {3900, 21859}, {5540, 38365}, {17072, 27135}, {17136, 35338}, {17439, 42079}, {21302, 26796}

X(46177) = X(39293)-Ceva conjugate of X(672)
X(46177) = crosspoint of X(i) and X(j) for these (i,j): {1, 9322}, {101, 664}
X(46177) = crosssum of X(i) and X(j) for these (i,j): {1, 9317}, {514, 663}, {17761, 21132}
X(46177) = trilinear pole of line {16588, 21746}
X(46177) = crossdifference of every pair of points on line {24237, 38991}
X(46177) = X(i)-isoconjugate of X(j) for these (i,j): {513, 40419}, {693, 3449}
X(46177) = barycentric product X(i)*X(j) for these {i,j}: {100, 17451}, {101, 2886}, {109, 40997}, {110, 21029}, {190, 21746}, {662, 21804}, {664, 16588}, {692, 20236}, {1018, 18165}, {1252, 21118}, {1897, 22070}, {4551, 16699}, {4572, 9449}, {4625, 21819}
X(46177) = barycentric quotient X(i)/X(j) for these {i,j}: {101, 40419}, {2886, 3261}, {9449, 663}, {16588, 522}, {16699, 18155}, {17451, 693}, {18165, 7199}, {20236, 40495}, {21029, 850}, {21118, 23989}, {21746, 514}, {21804, 1577}, {21819, 4041}, {22070, 4025}, {22368, 652}, {32739, 3449}, {40997, 35519}


X(46178) = CROSSPOINT OF X(105) AND X(1280)

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

X(46178) lies on these lines: {1, 39}, {55, 244}, {56, 20871}, {100, 3744}, {105, 910}, {612, 44304}, {1054, 3749}, {1086, 39047}, {1280, 3693}, {1282, 5332}, {2087, 10695}, {3242, 4712}, {3315, 3666}, {3722, 17017}, {3772, 26246}, {9507, 42819}, {10987, 35227}, {12740, 13277}, {14942, 27918}, {20999, 23847}, {33127, 36481}

X(46178) = X(39272)-Ceva conjugate of X(513)
X(46178) = crosspoint of X(i) and X(j) for these (i,j): {1, 9452}, {105, 1280}
X(46178) = crosssum of X(i) and X(j) for these (i,j): {1, 9451}, {518, 1279}
X(46178) = crossdifference of every pair of points on line {659, 3126}


X(46179) = X(30)X(511)∩X(39)X(226)

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

X(46179) lies on these lines: {30, 511}, {39, 226}, {48, 24263}, {63, 76}, {194, 5905}, {349, 4020}, {993, 12263}, {1478, 12782}, {3095, 37826}, {3934, 5745}, {7757, 31164}, {7786, 31266}, {11257, 18446}, {20078, 20081}, {20785, 44150}, {21165, 22712}, {21403, 22065}, {22001, 22036}


X(46180) = X(30)X(511)∩X(39)X(1212)

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

X(46180) lies on these lines: {1, 24333}, {7, 24247}, {9, 24249}, {10, 12933}, {30, 511}, {39, 1212}, {57, 24266}, {63, 194}, {76, 85}, {99, 5060}, {192, 10027}, {350, 33946}, {894, 24291}, {993, 22779}, {1055, 17136}, {1086, 21331}, {1111, 20335}, {1149, 24403}, {1334, 25237}, {1423, 25252}, {1475, 20247}, {1478, 9902}, {1575, 21138}, {1737, 24318}, {1916, 11608}, {2275, 24172}, {2321, 33936}, {2347, 20248}, {2549, 33869}, {3061, 3673}, {3212, 3501}, {3419, 24694}, {3509, 5088}, {3663, 3735}, {3665, 17046}, {3684, 3732}, {3693, 21232}, {3721, 24214}, {3726, 7200}, {3729, 24282}, {3741, 24255}, {3761, 21101}, {3831, 16720}, {3905, 7754}, {3930, 21139}, {3933, 4136}, {3934, 6706}, {4511, 9318}, {4566, 6168}, {4568, 6381}, {4694, 7208}, {4920, 5254}, {5074, 21090}, {5145, 30117}, {5289, 24352}, {5440, 24685}, {5905, 6542}, {7709, 21165}, {7751, 8669}, {7757, 31169}, {7781, 8720}, {7786, 31269}, {7805, 41656}, {8545, 40872}, {9311, 17158}, {9466, 41141}, {12053, 13110}, {12251, 18446}, {13108, 37826}, {16609, 25083}, {17050, 17451}, {17266, 31266}, {17310, 31164}, {17333, 27492}, {17355, 24254}, {17861, 20258}, {20016, 20078}, {20236, 30097}, {20432, 30055}, {20590, 23682}, {20893, 21443}, {21044, 33864}, {22034, 22036}, {24477, 42050}, {25254, 40886}, {25568, 42048}, {26563, 33299}, {29960, 33930}, {29968, 33943}, {29991, 33944}, {30030, 33933}, {30038, 33940}, {32453, 40859}, {32921, 37492}, {35957, 41773}, {44562, 44570}

X(46180) = crossdifference of every pair of points on line {6, 23655}
X(46180) = isotomic conjugate of trilinear pole of line X(2)X(663)
X(46180) = isotomic conjugate of Steiner-circumellipse-X(6)-antipode of X(664)
X(46180) = barycentric quotient X(13829)/X(13040)
X(46180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3212, 25242, 3501}, {3665, 40997, 17046}, {3693, 43037, 21232}, {3930, 21139, 30806}, {17451, 20880, 17050}


X(46181) = X(19)X(76)∩X(30)X(511)

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

X(46181) lies on these lines: {19, 76}, {30, 511}, {39, 18589}, {194, 4329}, {1486, 9917}, {3934, 40530}, {7757, 31158}, {7786, 31261}, {11257, 30265}, {20061, 20081}, {21160, 22712}


X(46182) = X(27)X(76)∩X(30)X(511)

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

X(46182) lies on these lines: {27, 76}, {30, 511}, {39, 440}, {194, 3151}, {3934, 6678}, {5188, 44243}, {6248, 15762}, {7757, 31153}, {7786, 31256}, {9917, 20834}, {11257, 30266}, {20081, 31292}, {21162, 22712}


X(46183) = X(30)X(511)∩X(38)X(76)

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

X(46193) lies on these lines: {30, 511}, {38, 76}, {39, 1215}, {194, 17165}, {1221, 17157}, {3934, 6682}, {4692, 12782}, {7757, 31161}, {7786, 31264}, {11257, 30272}, {20068, 20081}, {22024, 22036}

X(46183) = barycentric quotient X(23716)/X(19079)


X(46184) = X(2)X(2986)∩X(114)X(1576)

Barycentrics    2*a^8 - 4*a^6*b^2 + 3*a^4*b^4 - 2*a^2*b^6 + b^8 - 4*a^6*c^2 + 4*a^4*b^2*c^2 - 2*b^6*c^2 + 3*a^4*c^4 + 2*b^4*c^4 - 2*a^2*c^6 - 2*b^2*c^6 + c^8 : :
X(46184) = 3 X[2] + X[4558], X[2987] - 5 X[3618]

X(46184) lies on the Vijay orthic medial conic and these lines: {2, 2986}, {114, 1576}, {126, 8791}, {140, 12235}, {141, 40484}, {441, 44389}, {468, 44899}, {526, 5972}, {597, 6680}, {620, 2492}, {868, 22085}, {2987, 3618}, {3018, 14570}, {3284, 44388}, {6036, 7668}, {6593, 20399}, {6722, 34989}, {9034, 36949}, {9164, 44401}, {10112, 23702}, {15526, 40879}, {19136, 37466}, {23698, 34981}, {34843, 34844}, {38393, 38736}, {38394, 38734}, {40544, 40556}

X(46184) = complement of complement of X(4558)
X(46184) = X(i)-complementary conjugate of X(j) for these (i,j): {163, 136}, {925, 21253}, {32734, 8287}, {36145, 125}, {44174, 18589}
X(46184) = crossdifference of every pair of points on line {7669, 21731}
X(46184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {620, 23583, 34990}, {24975, 34990, 23583}


X(46185) = COMPLEMENT OF X(34980)

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

X(46185) lies on the Vijay orthic medial conic and these lines: {2, 34980}, {511, 44228}, {520, 23583}, {526, 5972}, {620, 34839}, {1576, 9306}, {2781, 5893}, {2871, 14913}, {2882, 3491}, {15595, 34383}

X(46185) = complement of X(34980)
X(46185) = X(i)-complementary conjugate of X(j) for these (i,j): {107, 16573}, {162, 35071}, {250, 828}, {648, 16595}, {811, 122}, {823, 15526}, {1093, 24040}, {1784, 42306}, {2617, 38976}, {6520, 23991}, {6528, 34846}, {6529, 16592}, {15352, 8287}, {23582, 1214}, {23590, 16583}, {23999, 3}, {24000, 216}, {24021, 6}, {24022, 1196}, {32230, 37}, {34538, 226}, {36126, 115}


X(46186) = X(2)X(112)∩X(2781)X(5893)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^14 - 2*a^12*b^2 - 7*a^10*b^4 + 7*a^8*b^6 + 8*a^6*b^8 - 8*a^4*b^10 - 3*a^2*b^12 + 3*b^14 - 2*a^12*c^2 + 16*a^10*b^2*c^2 - 7*a^8*b^4*c^2 - 38*a^6*b^6*c^2 + 18*a^4*b^8*c^2 + 22*a^2*b^10*c^2 - 9*b^12*c^2 - 7*a^10*c^4 - 7*a^8*b^2*c^4 + 60*a^6*b^4*c^4 - 10*a^4*b^6*c^4 - 45*a^2*b^8*c^4 + 9*b^10*c^4 + 7*a^8*c^6 - 38*a^6*b^2*c^6 - 10*a^4*b^4*c^6 + 52*a^2*b^6*c^6 - 3*b^8*c^6 + 8*a^6*c^8 + 18*a^4*b^2*c^8 - 45*a^2*b^4*c^8 - 3*b^6*c^8 - 8*a^4*c^10 + 22*a^2*b^2*c^10 + 9*b^4*c^10 - 3*a^2*c^12 - 9*b^2*c^12 + 3*c^14) : :
X(46186) = 3 X[127] - X[18876], 3 X[10718] + X[34163]

X(46186) lies on the Vijay orthic medial conic and these lines: {2, 112}, {2781, 5893}, {2794, 44241}, {10151, 12145}, {16976, 34841}, {41369, 44499}






leftri  Centers related to bicentric pair PU(197): X(46187) - X(46190)  rightri

Centers X(46187) - X(46190) were contributed by César Eliud Lozada, December 7, 2021.

Bicentric points P(197) and U(197) are the real foci of the De Longchamps ellipse. (See definition of this ellipse in Wolfram's Mathworld and coordinates of its real foci in PU(197)).

underbar

X(46187) = ISOGONAL CONJUGATE OF X(5253)

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

X(46187) lies on these lines: {35, 3293}, {60, 6043}, {88, 46188}, {319, 17751}, {519, 960}, {1183, 38882}, {1193, 1319}, {1825, 1829}, {2392, 13752}, {3450, 20986}, {3754, 43972}, {8679, 20617}, {20615, 24443}, {23638, 34434}

X(46187) = isogonal conjugate of X(5253)
X(46187) = barycentric quotient X(i)/X(j) for these (i, j): (10, 27792), (37, 17164)
X(46187) = trilinear quotient X(i)/X(j) for these (i, j): (10, 17164), (321, 27792)
X(46187) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(519)}} and {{A, B, C, X(2), X(35652)}}
X(46187) = cevapoint of X(42) and X(2347)
X(46187) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 17164), (37, 27792)
X(46187) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 17164}, {1333, 27792}
X(46187) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (10, 27792), (37, 17164)
X(46187) = cevapoint of PU(197)


X(46188) = X(583)X(992) ∩ X(942)X(3244)

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

X(46188) lies on these lines: {88, 46187}, {583, 992}, {942, 3244}, {3337, 31855}

X(46188) = crosspoint of PU(197)


X(46189) = X(6)X(101) ∩ X(39)X(1449)

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

X(46189) lies on these lines: {6, 101}, {37, 15828}, {39, 1449}, {1100, 1500}, {1475, 20228}, {1574, 5839}, {2087, 2171}, {2092, 16666}, {2220, 9341}, {2241, 5120}, {2275, 4263}, {3623, 39975}, {4253, 21785}, {4700, 28244}, {4860, 17071}, {4890, 22343}, {4969, 39798}, {5042, 16502}, {7757, 20168}, {8610, 16671}, {20090, 24625}, {20456, 23532}, {21746, 23524}

X(46189) = barycentric product X(1)*X(46190)
X(46189) = trilinear product X(6)*X(46190)
X(46189) = barycentric product of PU(197)
X(46189) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 1015, 21796), (2275, 16667, 4263)


X(46190) = X(1)X(88) ∩ X(12)X(1647)

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

X(46190) lies on these lines: {1, 88}, {12, 1647}, {31, 3333}, {37, 23649}, {38, 3616}, {42, 17609}, {56, 4332}, {145, 17063}, {354, 1201}, {495, 28096}, {518, 28352}, {551, 2292}, {595, 9340}, {596, 4975}, {756, 1125}, {902, 32636}, {942, 1149}, {960, 17449}, {978, 3889}, {982, 3622}, {986, 38314}, {999, 28082}, {1015, 21808}, {1056, 28074}, {1058, 33094}, {1193, 5045}, {1254, 1319}, {1388, 1393}, {1476, 2647}, {1616, 4860}, {1739, 3635}, {1962, 37592}, {2310, 11376}, {2975, 29820}, {2999, 30343}, {3086, 33127}, {3120, 37722}, {3123, 25557}, {3216, 3892}, {3241, 24174}, {3244, 4695}, {3290, 17474}, {3304, 3924}, {3337, 40091}, {3338, 3915}, {3555, 21805}, {3623, 9335}, {3636, 3670}, {3726, 39244}, {3742, 10459}, {3756, 15888}, {3873, 21214}, {3914, 21625}, {3930, 16604}, {3938, 25524}, {4075, 39697}, {4188, 17715}, {4666, 10448}, {4696, 4871}, {4714, 6532}, {4999, 29689}, {5221, 16486}, {5492, 5901}, {5542, 22172}, {6765, 9350}, {7191, 26261}, {7278, 21208}, {10586, 33144}, {11019, 21935}, {11037, 28016}, {11263, 23869}, {12005, 32486}, {17164, 42053}, {17448, 21921}, {17469, 37607}, {17480, 30947}, {21620, 28018}, {22167, 24325}, {24178, 33136}, {24216, 24987}, {24911, 25650}, {25055, 42039}, {25253, 42055}, {25591, 31161}, {26093, 32931}, {26111, 32937}, {27003, 37588}, {28257, 34790}, {28403, 38053}, {29818, 37539}, {31435, 36263}, {32856, 41012}, {32925, 34860}

X(46190) = barycentric product X(75)*X(46189)
X(46190) = trilinear product X(2)*X(46189)
X(46190) = crosspoint of X(1) and X(20615)
X(46190) = crosssum of X(1) and X(3871)
X(46190) = trilinear product of PU(197)
X(46190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 244, 4642), (1, 404, 3722), (354, 1201, 2650), (551, 3953, 2292), (2292, 3953, 42038), (3333, 28011, 31), (3555, 27627, 21805), (3616, 3976, 38), (3623, 9335, 24440), (11019, 23675, 21935)




leftri  Centers related to bicentric pairs PU(160) to PU(175): X(46191) - X(46263)  rightri

Contributed by César Eliud Lozada, December 7, 2021.

underbar

X(46191) = MIDPOINT OF PU(160)

Barycentrics    a*(a^5*b*c-(b+c)^3*a^4+(3*b+c)*(b+3*c)*(b+c)*a^2*b*c-(b^2-c^2)*(b-c)*b^2*c^2+(b^4+c^4)*a^3-(b^4+c^4-(5*b^2+13*b*c+5*c^2)*b*c)*a*b*c) : :

X(46191) lies on these lines: {1019, 6626}

X(46191) = midpoint of PU(160)


X(46192) = X(30)X(511) ∩ X(1019)X(6626)

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

X(46192) lies on these lines: {30, 511}, {1019, 6626}, {4444, 6625}

X(46192) = crossdifference of every pair of points on line {X(6), X(46195)}
X(46192) = ideal point of PU(160)


X(46193) = X(81)X(6651) ∩ X(757)X(4094)

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

X(46193) lies on these lines: {81, 6651}, {757, 4094}, {873, 18059}, {1961, 40439}, {2054, 17731}, {4594, 20090}, {6542, 37128}

X(46193) = isogonal conjugate of X(46195)
X(46193) = barycentric quotient X(i)/X(j) for these (i, j): (48, 20782), (1326, 20668), (1757, 20687)
X(46193) = trilinear quotient X(i)/X(j) for these (i, j): (3, 20782), (1931, 20668)
X(46193) = trilinear pole of the line {1019, 6626}
X(46193) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2054)}} and {{A, B, C, X(81), X(86)}}
X(46193) = cevapoint of X(i) and X(j) for these (i, j): {1, 17731}, {86, 740}
X(46193) = X(4)-isoconjugate-of-X(20782)
X(46193) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (48, 20782), (1326, 20668)
X(46193) = trilinear pole of PU(160)


X(46194) = X(58)X(291) ∩ X(99)X(1475)

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

X(46194) lies on these lines: {42, 40408}, {58, 291}, {81, 1500}, {83, 2350}, {86, 3294}, {99, 1475}, {213, 37128}, {274, 39252}, {662, 17745}, {757, 5280}, {1018, 32004}, {1334, 33770}, {1724, 24923}, {3842, 25526}, {4253, 17103}, {5525, 33953}, {16549, 17731}, {17754, 34016}, {18206, 36483}

X(46194) = crosssum of PU(160)


X(46195) = ISOGONAL CONJUGATE OF X(46193)

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

X(46195) lies on these lines: {1, 6626}, {37, 42}, {292, 3747}, {740, 20947}, {741, 36066}, {1149, 4128}, {1621, 1964}, {1914, 5147}, {1961, 4434}, {2643, 3290}, {3122, 20461}, {4079, 7234}, {8299, 38978}, {9277, 40433}, {9507, 20360}, {16784, 23648}, {21254, 33891}

X(46195) = isogonal conjugate of X(46193)
X(46195) = barycentric product X(92)*X(20782)
X(46195) = trilinear product X(4)*X(20782)
X(46195) = intersection, other than A, B, C, of circumconics {{A, B, C, X(37), X(9506)}} and {{A, B, C, X(292), X(20529)}}
X(46195) = crossdifference of every pair of points on line {X(1019), X(6626)}
X(46195) = crosspoint of X(i) and X(j) for these (i, j): {1, 2054}, {42, 741}
X(46195) = crosssum of X(i) and X(j) for these (i, j): {1, 17731}, {86, 740}
X(46195) = X(1)-line conjugate of-X(6626)
X(46195) = crossdifference of PU(160)


X(46196) = COMPLEMENT OF X(17169)

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

X(46196) lies on these lines: {1, 1573}, {2, 2350}, {6, 16842}, {9, 46}, {10, 1018}, {21, 35342}, {37, 762}, {45, 24429}, {58, 37675}, {101, 5260}, {169, 857}, {200, 4204}, {210, 3970}, {274, 29460}, {333, 29456}, {350, 29773}, {405, 4258}, {429, 7719}, {518, 25086}, {573, 3091}, {668, 29383}, {740, 24049}, {756, 16600}, {758, 21921}, {846, 46198}, {860, 7079}, {942, 17746}, {966, 4266}, {1019, 6626}, {1125, 3691}, {1211, 7308}, {1400, 3947}, {1475, 19862}, {1500, 31855}, {1577, 32008}, {1724, 5275}, {1764, 36662}, {1765, 37112}, {2092, 3731}, {2292, 16611}, {2294, 24048}, {2328, 28062}, {2503, 6537}, {3125, 21879}, {3216, 5283}, {3247, 4272}, {3496, 37049}, {3501, 19875}, {3624, 21384}, {3646, 41014}, {3678, 21808}, {3679, 4050}, {3684, 5259}, {3730, 9780}, {3739, 4721}, {3740, 16601}, {3760, 3948}, {3770, 25458}, {3882, 31144}, {3921, 4515}, {3930, 4015}, {3952, 22011}, {3983, 3991}, {3985, 4647}, {4002, 21872}, {4115, 17164}, {4199, 8580}, {4205, 17742}, {4251, 5047}, {4262, 16865}, {4424, 16605}, {4651, 21070}, {4754, 36812}, {5022, 16862}, {5030, 17531}, {5224, 17671}, {5257, 21061}, {5299, 17123}, {5506, 5540}, {5816, 6836}, {6707, 18164}, {7377, 21363}, {10176, 17451}, {10455, 26045}, {11108, 16783}, {15485, 41333}, {16503, 25542}, {16569, 21838}, {16572, 17056}, {16788, 34812}, {17129, 20138}, {17163, 24044}, {17185, 26044}, {17256, 21362}, {17260, 20372}, {17266, 31037}, {17277, 18046}, {17289, 20605}, {17292, 21383}, {17736, 41229}, {17744, 36478}, {18133, 29486}, {18230, 27039}, {20337, 36483}, {20367, 24603}, {21033, 25081}, {21372, 27065}, {21753, 26102}, {24045, 33108}, {24051, 27804}, {25088, 40967}, {25280, 29699}, {27033, 27091}, {29399, 29405}, {29440, 37686}, {29742, 30963}, {29812, 31238}, {32431, 37433}, {33557, 37508}

X(46196) = complement of X(17169)
X(46196) = barycentric product X(i)*X(j) for these {i, j}: {1, 17163}, {10, 5284}, {75, 4068}, {81, 24044}
X(46196) = trilinear product X(i)*X(j) for these {i, j}: {2, 4068}, {6, 17163}, {37, 5284}, {58, 24044}
X(46196) = perspector of the circumconic {{A, B, C, X(6742), X(46193)}}
X(46196) = crossdifference of every pair of points on line {X(2605), X(46195)}
X(46196) = X(i)-complementary conjugate of-X(j) for these (i, j): (1170, 17050), (1174, 3739), (1400, 45226)
X(46196) = X(i)-Zayin conjugate of-X(j) for these (i, j): (2, 3219), (514, 1019), (1255, 81)
X(46196) = bicentric sum of PU(160)
X(46196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 17499, 17175), (9, 1698, 16549), (37, 3697, 4006), (1125, 3691, 45751), (1213, 38930, 442), (2238, 16589, 1), (5283, 37673, 3216), (11108, 37658, 16783), (17277, 18140, 29433)


X(46197) = X(2)X(6) ∩ X(9)X(21783)

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

X(46197) lies on these lines: {2, 6}, {9, 21783}, {4068, 18755}

X(46197) = barycentric product X(1)*X(46198)
X(46197) = trilinear product X(6)*X(46198)
X(46197) = barycentric product of PU(160)


X(46198) = X(1)X(75) ∩ X(8)X(5539)

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

X(46198) lies on these lines: {1, 75}, {8, 5539}, {846, 46196}, {1574, 3571}, {2640, 17744}, {4418, 17499}, {21816, 24450}

X(46198) = barycentric product X(75)*X(46197)
X(46198) = trilinear product X(2)*X(46197)
X(46198) = trilinear product of PU(160)


X(46199) = ISOGONAL CONJUGATE OF X(10539)

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

X(46199) lies on these lines: {20, 6193}, {403, 14249}, {925, 44752}, {1249, 3003}, {2986, 46200}, {7871, 14615}, {9307, 26879}, {10152, 14264}, {11585, 40698}, {19185, 32534}

X(46199) = isogonal conjugate of X(10539)
X(46199) = trilinear quotient X(91)/X(46200)
X(46199) = trilinear pole of the line {686, 6587}
X(46199) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3147)}} and {{A, B, C, X(3), X(403)}}
X(46199) = cevapoint of X(3) and X(44752)
X(46199) = X(47)-isoconjugate-of-X(46200)
X(46199) = cevapoint of PU(161)


X(46200) = X(3)X(847) ∩ X(30)X(64)

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

X(46200) lies on these lines: {3, 847}, {5, 8906}, {26, 2351}, {30, 64}, {96, 14070}, {155, 34757}, {156, 32734}, {382, 5962}, {1899, 44209}, {1975, 46134}, {2165, 13383}, {2986, 46199}, {5392, 7387}, {6642, 40698}, {7529, 39116}, {12084, 16391}, {13292, 39111}, {16238, 32132}, {27367, 35930}

X(46200) = reflection of X(68) in the line X(523)X(20302)
X(46200) = trilinear product X(91)*X(10539)
X(46200) = trilinear quotient X(91)/X(46199)
X(46200) = X(925)-beth conjugate of-X(221)
X(46200) = X(47)-isoconjugate-of-X(46199)
X(46200) = crosspoint of PU(161)
X(46200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (847, 925, 3), (14593, 34853, 5)


X(46201) = X(4)X(15021) ∩ X(2986)X(44569)

Barycentrics    (5*a^6-(2*b^2+5*c^2)*a^4-(11*b^4-18*b^2*c^2+5*c^4)*a^2+(8*b^2+5*c^2)*(b^2-c^2)^2)*(5*a^6-(5*b^2+2*c^2)*a^4-(5*b^4-18*b^2*c^2+11*c^4)*a^2+(5*b^2+8*c^2)*(b^2-c^2)^2) : :

X(46201) lies on the Kiepert circumhyperbola and these lines: {4, 15021}, {2986, 44569}, {17503, 41254}, {40112, 44877}

X(46201) = isogonal conjugate of X(46203)
X(46201) = trilinear pole of the line {523, 3830}
X(46201) = cevapoint of X(6) and X(18571)
X(46201) = trilinear pole of PU(162)


X(46202) = X(110)X(20421) ∩ X(2930)X(3098)

Barycentrics    a^2*(7*a^8-(b^2+c^2)*a^6-(39*b^4-46*b^2*c^2+39*c^4)*a^4+(b^2+c^2)*(53*b^4-88*b^2*c^2+53*c^4)*a^2-10*(b^2-c^2)^2*(b^2+2*c^2)*(2*b^2+c^2)) : :

X(46202) lies on these lines: {110, 20421}, {389, 46221}, {2930, 3098}, {3357, 37496}, {4550, 15045}, {7689, 12112}, {10170, 37470}, {11438, 18369}, {11738, 15107}

X(46202) = crosssum of PU(162)


X(46203) = ISOGONAL CONJUGATE OF X(46201)

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

X(46203) lies on these lines: {3, 6}, {625, 45331}, {5306, 39602}, {6128, 43291}, {9142, 21639}, {13192, 23357}

X(46203) = isogonal conjugate of X(46201)
X(46203) = perspector of the circumconic {{A, B, C, X(110), X(20421)}}
X(46203) = crossdifference of every pair of points on line {X(523), X(3830)}
X(46203) = crosssum of X(6) and X(18571)
X(46203) = X(2)-Ceva conjugate of-X(39083)
X(46203) = X(31)-complementary conjugate of-X(39083)
X(46203) = crossdifference of PU(162)
X(46203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (50, 3003, 46222), (187, 40349, 5585), (3284, 34569, 50), (5024, 10317, 187), (15166, 15167, 18573)


X(46204) = X(6)X(1327) ∩ X(2165)X(18487)

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

X(46204) lies on these lines: {6, 1327}, {37, 46205}, {216, 46223}, {2165, 18487}, {3018, 15682}, {22165, 40802}

X(46204) = barycentric product X(i)*X(j) for these {i, j}: {1, 46205}, {1327, 1328}
X(46204) = barycentric quotient X(i)/X(j) for these (i, j): (25, 35472), (1327, 32809), (1328, 32808)
X(46204) = trilinear product X(6)*X(46205)
X(46204) = trilinear quotient X(19)/X(35472)
X(46204) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(3845)}}
X(46204) = X(63)-isoconjugate-of-X(35472)
X(46204) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 35472), (1327, 32809), (1328, 32808)
X(46204) = barycentric product of PU(162)


X(46205) = X(37)X(46204) ∩ X(91)X(18486)

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

X(46205) lies on these lines: {37, 46204}, {91, 18486}, {44706, 46224}

X(46205) = barycentric product X(75)*X(46204)
X(46205) = barycentric quotient X(19)/X(35472)
X(46205) = trilinear product X(i)*X(j) for these {i, j}: {2, 46204}, {1327, 1328}
X(46205) = trilinear quotient X(i)/X(j) for these (i, j): (4, 35472), (1328, 6200)
X(46205) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}} and {{A, B, C, X(318), X(33696)}}
X(46205) = X(3)-isoconjugate-of-X(35472)
X(46205) = X(19)-reciprocal conjugate of-X(35472)
X(46205) = trilinear product of PU(162)


X(46206) = ISOGONAL CONJUGATE OF X(34569)

Barycentrics    (5*a^6-(5*b^2+4*c^2)*a^4-(5*b^4-16*b^2*c^2+7*c^4)*a^2+(5*b^2+6*c^2)*(b^2-c^2)^2)*(5*a^6-(4*b^2+5*c^2)*a^4-(7*b^4-16*b^2*c^2+5*c^4)*a^2+(6*b^2+5*c^2)*(b^2-c^2)^2) : :

X(46206) lies on the Kiepert circumhyperbola and these lines: {4, 6723}, {98, 37911}, {648, 38253}, {38259, 41254}, {44569, 46210}

X(46206) = isogonal conjugate of X(34569)
X(46206) = isotomic conjugate of complement of X(47296)
X(46206) = polar conjugate of X(13473)
X(46206) = barycentric quotient X(4)/X(13473)
X(46206) = trilinear quotient X(92)/X(13473)
X(46206) = trilinear pole of the line {523, 3146}
X(46206) = intersection, other than A, B, C, of circumconics Kiepert hyperbola and {{A, B, C, X(287), X(6723)}}
X(46206) = cevapoint of X(6) and X(37941)
X(46206) = X(48)-isoconjugate-of-X(13473)
X(46206) = X(4)-reciprocal conjugate of-X(13473)
X(46206) = trilinear pole of PU(163)


X(46207) = X(110)X(3532) ∩ X(1498)X(2781)

Barycentrics    a^2*(7*a^8-36*(b^2+c^2)*a^6+2*(33*b^4-2*b^2*c^2+33*c^4)*a^4-4*(b^2+c^2)*(13*b^4-18*b^2*c^2+13*c^4)*a^2+5*(b^2-c^2)^2*(3*b^2+c^2)*(b^2+3*c^2)) : :

X(46207) lies on these lines: {6, 44870}, {110, 3532}, {389, 46215}, {1192, 10539}, {1498, 2781}, {1993, 22334}, {5907, 10541}, {12160, 15811}, {18369, 18451}, {27082, 41467}

X(46207) = crosssum of PU(163)
X(46207) = {X(110), X(3532)}-harmonic conjugate of X(15748)


X(46208) = ISOTOMIC CONJUGATE OF X(32841)

Barycentrics    (5*a^4-2*(b^2+c^2)*a^2-3*(b^2-c^2)^2)^2-64*(b^2-c^2)^2*S^2 : :

X(46208) lies on these lines: {6, 1131}, {37, 46209}, {216, 46217}, {18487, 46212}, {32840, 42407}, {33630, 45004}

X(46208) = isotomic conjugate of X(32841)
X(46208) = polar conjugate of the anticomplement of X(38292)
X(46208) = barycentric product X(i)*X(j) for these {i, j}: {1, 46209}, {4, 15749}, {1131, 1132}
X(46208) = barycentric quotient X(i)/X(j) for these (i, j): (25, 15750), (1131, 1271), (1132, 1270)
X(46208) = trilinear product X(i)*X(j) for these {i, j}: {6, 46209}, {19, 15749}
X(46208) = trilinear quotient X(19)/X(15750)
X(46208) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(3832)}}
X(46208) = X(63)-isoconjugate-of-X(15750)
X(46208) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 15750), (1131, 1271), (1132, 1270)
X(46208) = barycentric product of PU(163)
X(46208) = {X(1131), X(1132)}-harmonic conjugate of X(15749)


X(46209) = X(37)X(46208) ∩ X(65)X(15749)

Barycentrics    ((5*a^4-2*(b^2+c^2)*a^2-3*(b^2-c^2)^2)^2-64*(b^2-c^2)^2*S^2)/a : :

X(46209) lies on these lines: {37, 46208}, {65, 15749}, {18486, 46213}, {44706, 46218}

X(46209) = barycentric product X(i)*X(j) for these {i, j}: {75, 46208}, {92, 15749}
X(46209) = barycentric quotient X(i)/X(j) for these (i, j): (19, 15750), (75, 32841)
X(46209) = trilinear product X(i)*X(j) for these {i, j}: {2, 46208}, {4, 15749}, {1131, 1132}
X(46209) = trilinear quotient X(i)/X(j) for these (i, j): (4, 15750), (76, 32841), (1131, 1152), (1132, 1151)
X(46209) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}} and {{A, B, C, X(341), X(18815)}}
X(46209) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 15750}, {32, 32841}, {1151, 1152}
X(46209) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (19, 15750), (75, 32841)
X(46209) = trilinear product of PU(163)


X(46210) = TRILINEAR POLE OF LINE PU(164)

Barycentrics    (13*a^6-(16*b^2+13*c^2)*a^4-(7*b^4-36*b^2*c^2+13*c^4)*a^2+(10*b^2+13*c^2)*(b^2-c^2)^2)*(13*a^6-(13*b^2+16*c^2)*a^4-(13*b^4-36*b^2*c^2+7*c^4)*a^2+(13*b^2+10*c^2)*(b^2-c^2)^2) : :

X(46210) lies on the Kiepert circumhyperbola and these lines: {44569, 46206}

X(46210) = isogonal conjugate of X(46211)
X(46210) = trilinear pole of the line {523, 11001}
X(46210) = trilinear pole of PU(164)


X(46211) = ISOGONAL CONJUGATE OF X(46210)

Barycentrics    a^2*(10*a^6-7*(b^2+c^2)*a^4-4*(4*(b^2-c^2)^2-b^2*c^2)*a^2+13*(b^4-c^4)*(b^2-c^2)) : :

X(46211) lies on these lines: {3, 6}, {3163, 43291}

X(46211) = isogonal conjugate of X(46210)
X(46211) = crossdifference of every pair of points on line {X(523), X(11001)}
X(46211) = crossdifference of PU(164)
X(46211) = {X(187), X(5024)}-harmonic conjugate of X(40349)


X(46212) = X(6)X(14226) ∩ X(18487)X(46208)

Barycentrics    (13*a^4-8*(b^2+c^2)*a^2-5*(b^2-c^2)^2)^2-576*S^2*(b^2-c^2)^2 : :

X(46212) lies on these lines: {6, 14226}, {37, 46213}, {18487, 46208}

X(46212) = barycentric product X(1)*X(46213)
X(46212) = trilinear product X(6)*X(46213)
X(46212) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(41106)}}
X(46212) = barycentric product of PU(164)


X(46213) = X(37)X(46212) ∩ X(18486)X(46209)

Barycentrics    ((13*a^4-8*(b^2+c^2)*a^2-5*(b^2-c^2)^2)^2-576*S^2*(b^2-c^2)^2)/a : :

X(46213) lies on these lines: {37, 46212}, {18486, 46209}

X(46213) = barycentric product X(75)*X(46212)
X(46213) = trilinear product X(2)*X(46212)
X(46213) = trilinear product of PU(164)


X(46214) = TRILINEAR POLE OF LINE PU(165)

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

X(46214) lies on the Kiepert circumhyperbola and these lines: {}

X(46214) = isogonal conjugate of X(46216)
X(46214) = trilinear pole of the line {523, 3525}
X(46214) = trilinear pole of line PU(165)


X(46215) = X(389)X(46207) ∩ X(399)X(7529)

Barycentrics    a^2*(7*a^8-6*(b^2+c^2)*a^6-4*(6*b^4+b^2*c^2+6*c^4)*a^4+2*(b^2+c^2)*(19*b^4-54*b^2*c^2+19*c^4)*a^2-5*(b^2-c^2)^2*(b^2-3*c^2)*(3*b^2-c^2)) : :

X(46215) lies on these lines: {3, 6688}, {389, 46207}, {399, 7529}, {1598, 15045}, {3066, 10984}, {3531, 17928}, {5020, 10263}, {10170, 11484}, {12160, 43614}, {15606, 17810}, {20417, 38790}

X(46215) = crosssum of PU(165)


X(46216) = ISOGONAL CONJUGATE OF X(46214)

Barycentrics    a^2*(6*a^6-17*(b^2+c^2)*a^4+4*(4*(b^2+c^2)^2-9*b^2*c^2)*a^2-5*(b^4-c^4)*(b^2-c^2)) : :

X(46216) is the Brocard axis intercept of the line through the X(3311)-Ceva conjugate of X(3312) and the X(3312)-Ceva conjugate of X(3311). (Randy Hutson, January 11, 2022)

X(46216) lies on these lines: {3, 6}, {230, 37910}

X(46216) = isogonal conjugate of X(46214)
X(46216) = crossdifference of every pair of points on line {X(523), X(3525)}
X(46216) = crossdifference of PU(165)
X(46216) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (50, 3003, 34569), (50, 46222, 187), (3003, 18365, 40135)


X(46217) = ISOTOMIC CONJUGATE OF X(32839)

Barycentrics    (5*a^4-8*(b^2+c^2)*a^2+3*(b^2-c^2)^2)^2-64*S^2*(b^2-c^2)^2 : :

X(46217) lies on these lines: {6, 3316}, {37, 46218}, {216, 46208}, {308, 32867}, {8882, 12815}, {32829, 42332}, {32838, 42407}

X(46217) = isotomic conjugate of X(32839)
X(46217) = barycentric product X(1)*X(46218)
X(46217) = trilinear product X(6)*X(46218)
X(46217) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(5067)}}
X(46217) = barycentric product of PU(165)


X(46218) = X(37)X(46217) ∩ X(44706)X(46209)

Barycentrics    ((5*a^4-8*(b^2+c^2)*a^2+3*(b^2-c^2)^2)^2-64*S^2*(b^2-c^2)^2)/a : :

X(46218) lies on these lines: {37, 46217}, {44706, 46209}

X(46218) = barycentric product X(75)*X(46217)
X(46218) = barycentric quotient X(75)/X(32839)
X(46218) = trilinear product X(2)*X(46217)
X(46218) = trilinear quotient X(76)/X(32839)
X(46218) = X(32)-isoconjugate-of-X(32839)
X(46218) = X(75)-reciprocal conjugate of-X(32839)
X(46218) = trilinear product of PU(165)


X(46219) = EULER LINE INTERCEPT OF X(6)X(11614)

Barycentrics    5*a^4-9*(b^2+c^2)*a^2+4*(b^2-c^2)^2 : :
Barycentrics    cot B cot C - 9 : :
Trilinears    9 cos A + 8 cos B cos C : :
X(46219) = 9*X(3)+4*X(4)
X(46219) = 12*X(2)+X(3) = 15*X(2)-2*X(5) = 9*X(2)+4*X(140) = 14*X(2)-X(381) = 17*X(2)-4*X(547) = 11*X(2)+2*X(549) = 3*X(2)+10*X(632) = 18*X(2)-5*X(1656) = 15*X(2)+11*X(3525) = 6*X(2)+7*X(3526) = 9*X(2)+17*X(3533) = 10*X(2)+3*X(5054) = 16*X(2)-3*X(5055) = 9*X(2)-X(5068) = 6*X(2)-X(5079) = 5*X(2)+8*X(10124) = 9*X(2)+X(10299) = 3*X(2)+X(10303) = 7*X(2)+6*X(11539) = 8*X(2)+5*X(15694) = 19*X(2)-6*X(15699) = 19*X(2)+7*X(15702) = 20*X(2)-7*X(15703) = 17*X(2)+9*X(15709) = 2*X(2)+11*X(15723) = 3*X(2)-16*X(16239) = 15*X(2)+X(21734)

X(46219) lies on these lines: {2, 3}, {6, 11614}, {10, 37624}, {13, 42491}, {14, 42490}, {17, 10188}, {18, 10187}, {49, 43650}, {54, 14841}, {61, 42978}, {62, 42979}, {69, 32884}, {76, 10185}, {143, 7998}, {154, 14864}, {182, 9704}, {183, 7871}, {195, 15066}, {230, 31467}, {265, 38638}, {371, 42557}, {372, 42558}, {373, 5447}, {395, 42594}, {396, 42595}, {397, 42089}, {398, 42092}, {399, 34128}, {485, 41950}, {486, 41949}, {498, 7294}, {499, 5326}, {517, 34595}, {568, 11695}, {575, 21358}, {590, 6418}, {615, 6417}, {952, 19877}, {1001, 20107}, {1073, 22268}, {1125, 10247}, {1147, 22112}, {1154, 15028}, {1159, 24914}, {1351, 25555}, {1384, 1506}, {1385, 37712}, {1482, 3624}, {1649, 10279}, {1698, 10246}, {1853, 45185}, {1993, 15047}, {2055, 37877}, {2888, 20585}, {2979, 13421}, {3035, 31493}, {3054, 31401}, {3055, 21309}, {3060, 32205}, {3068, 6501}, {3069, 6500}, {3070, 6446}, {3071, 6445}, {3167, 43839}, {3311, 8252}, {3312, 8253}, {3519, 6689}, {3527, 26861}, {3567, 32142}, {3576, 30315}, {3589, 5093}, {3590, 43564}, {3591, 43565}, {3619, 11898}, {3622, 38112}, {3634, 5790}, {3655, 31399}, {3763, 5050}, {3815, 43136}, {3819, 6243}, {3828, 37727}, {3933, 32839}, {4413, 37621}, {4423, 11849}, {5023, 7603}, {5024, 7746}, {5085, 18553}, {5219, 37545}, {5309, 31492}, {5334, 42951}, {5335, 42950}, {5339, 16967}, {5340, 16966}, {5343, 42143}, {5344, 42146}, {5349, 42111}, {5350, 42114}, {5351, 43646}, {5352, 43645}, {5365, 42122}, {5366, 42123}, {5418, 6199}, {5420, 6395}, {5433, 31479}, {5462, 5650}, {5550, 5690}, {5640, 10627}, {5644, 42021}, {5646, 37494}, {5655, 38729}, {5708, 31231}, {5734, 38022}, {5886, 19878}, {5891, 13382}, {5892, 18436}, {5895, 10193}, {5907, 40280}, {5943, 37484}, {5946, 7999}, {6033, 38634}, {6101, 13321}, {6221, 10577}, {6321, 38635}, {6337, 32883}, {6390, 32838}, {6398, 10576}, {6407, 13785}, {6408, 13665}, {6427, 13847}, {6428, 13846}, {6447, 35823}, {6448, 35822}, {6449, 42262}, {6450, 42265}, {6451, 23261}, {6452, 23251}, {6455, 6565}, {6456, 6564}, {6472, 43377}, {6473, 43376}, {6474, 43509}, {6475, 43510}, {6496, 35821}, {6497, 35820}, {6667, 10993}, {6683, 32447}, {6684, 18493}, {6688, 10625}, {6721, 10991}, {6722, 10992}, {6723, 30714}, {7308, 37612}, {7607, 7940}, {7608, 43527}, {7610, 7764}, {7619, 34505}, {7728, 38633}, {7739, 31470}, {7749, 30435}, {7754, 17006}, {7755, 9605}, {7760, 8860}, {7767, 34803}, {7769, 32821}, {7776, 37647}, {7780, 11184}, {7781, 40727}, {7815, 11842}, {7869, 15271}, {7888, 8556}, {7988, 31663}, {7989, 17502}, {8148, 13464}, {8371, 32204}, {8550, 34573}, {8724, 38740}, {8972, 43505}, {8981, 32786}, {9140, 15039}, {9167, 20398}, {9306, 37471}, {9342, 32141}, {9540, 18510}, {9690, 18762}, {9691, 42215}, {9703, 13353}, {9755, 16988}, {9780, 12645}, {9956, 19872}, {10072, 31480}, {10156, 40263}, {10165, 18525}, {10168, 15069}, {10170, 34783}, {10172, 18481}, {10192, 34780}, {10198, 12001}, {10200, 12000}, {10219, 15644}, {10222, 38066}, {10263, 11451}, {10539, 13339}, {10540, 37515}, {10541, 11178}, {10574, 14128}, {10601, 14627}, {10605, 33540}, {10738, 38636}, {10742, 38637}, {10749, 38639}, {10982, 37496}, {10990, 12900}, {11017, 11455}, {11171, 31239}, {11230, 11522}, {11412, 13363}, {11426, 26958}, {11432, 12242}, {11444, 12006}, {11480, 42959}, {11481, 42958}, {11482, 40107}, {11488, 43102}, {11489, 43103}, {11591, 15045}, {11623, 15561}, {11632, 38751}, {11793, 37481}, {12017, 24206}, {12041, 15046}, {12174, 43608}, {12308, 15061}, {12315, 14862}, {12331, 34126}, {12815, 13881}, {12902, 38793}, {13108, 40108}, {13188, 34127}, {13336, 18350}, {13348, 14845}, {13432, 21230}, {13571, 17004}, {13935, 18512}, {13941, 43506}, {13966, 32785}, {14449, 33884}, {14530, 20299}, {14643, 20417}, {14861, 43719}, {14978, 44914}, {15034, 20396}, {15037, 15805}, {15040, 20304}, {15043, 15067}, {15051, 15088}, {15059, 32609}, {15178, 19875}, {15533, 22234}, {16241, 42153}, {16242, 42156}, {16772, 42975}, {16773, 42974}, {16836, 18439}, {16960, 42954}, {16961, 42955}, {16962, 43427}, {16963, 43426}, {17606, 37606}, {17811, 36753}, {17821, 32767}, {17825, 36749}, {17851, 23267}, {18526, 38042}, {18538, 42570}, {18581, 42945}, {18582, 42944}, {19854, 31235}, {19883, 34718}, {20104, 25524}, {20126, 38795}, {20400, 38069}, {20418, 38752}, {20791, 45959}, {21001, 43843}, {21154, 38756}, {22235, 42492}, {22236, 42489}, {22237, 42493}, {22238, 42488}, {22246, 30122}, {23236, 45311}, {23294, 26864}, {23302, 42149}, {23303, 42152}, {24926, 43731}, {25542, 26285}, {25563, 35450}, {28198, 31425}, {31162, 31447}, {31188, 34753}, {31274, 38224}, {31275, 38225}, {31276, 32519}, {31454, 43254}, {31487, 32788}, {32063, 40686}, {32149, 44453}, {32817, 32897}, {32818, 32898}, {32820, 32832}, {32824, 32867}, {32825, 34229}, {33520, 38774}, {33521, 38767}, {33537, 33887}, {33878, 38317}, {34565, 44749}, {35814, 43379}, {35815, 43378}, {36750, 37679}, {36754, 37682}, {36836, 37835}, {36843, 37832}, {36990, 42786}, {37509, 37674}, {37714, 38083}, {38727, 38790}, {38733, 38748}, {38737, 38744}, {38848, 41462}, {41943, 42593}, {41944, 42592}, {41967, 43323}, {41968, 43322}, {42095, 42157}, {42098, 42158}, {42117, 42495}, {42118, 42494}, {42121, 42817}, {42124, 42818}, {42125, 42150}, {42126, 42692}, {42127, 42693}, {42128, 42151}, {42135, 43770}, {42138, 43769}, {42144, 42473}, {42145, 42472}, {42147, 42910}, {42148, 42911}, {42154, 42580}, {42155, 42581}, {42160, 43101}, {42161, 43104}, {42163, 42500}, {42166, 42501}, {42431, 42915}, {42432, 42914}, {42474, 42528}, {42475, 42529}, {42476, 42895}, {42477, 42894}, {42522, 43374}, {42523, 43375}, {42572, 42602}, {42573, 42603}, {42627, 43447}, {42628, 43446}, {42688, 42798}, {42689, 42797}, {42779, 43467}, {42780, 43468}, {42795, 42890}, {42796, 42891}, {42815, 42924}, {42816, 42925}, {42896, 43370}, {42897, 43371}, {42982, 43445}, {42983, 43444}, {43006, 43024}, {43007, 43025}

X(46219) = midpoint of X(i) and X(j) for these {i, j}: {2045, 2046}, {3534, 35402}, {5067, 10303}, {5068, 10299}, {14893, 35421}, {15693, 35382}, {17800, 35406}
X(46219) = reflection of X(i) in X(j) for these (i, j): (5079, 5067), (11818, 7505), (18494, 13620)
X(46219) = complement of X(5067)
X(46219) = perspector of the circumconic {{A, B, C, X(648), X(46220)}}
X(46219) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5), X(14841)}} and {{A, B, C, X(20), X(22268)}}
X(46219) = crossdifference of every pair of points on line {X(647), X(46222)}
X(46219) = midpoint of PU(166)
X(46219) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 3526, 3), (4, 15720, 3), (5, 5054, 3), (20, 15693, 3), (140, 1656, 3), (381, 631, 3), (382, 549, 3), (548, 15700, 3), (549, 41984, 2), (632, 16239, 2), (1506, 44535, 1384), (1657, 3523, 3), (2070, 7516, 3), (2937, 7485, 3), (3524, 15696, 3), (3528, 15706, 3), (3530, 3534, 3), (3624, 11231, 1482), (3843, 15701, 3), (5070, 15694, 3), (5072, 14869, 3), (5079, 10303, 3), (6883, 45976, 3), (7484, 7506, 3), (7509, 45735, 3), (7514, 43809, 3), (7542, 30771, 3), (7998, 11465, 143), (13846, 35813, 6428), (13847, 35812, 6427), (14093, 44682, 3), (15688, 15717, 3), (15707, 17800, 3), (15723, 16239, 3), (17928, 34864, 3), (42936, 42937, 6), (43028, 43238, 18), (43029, 43239, 17)


X(46220) = TRILINEAR POLE OF LINE PU(166)

Barycentrics    (5*a^6-(18*b^2+5*c^2)*a^4+(21*b^4+2*b^2*c^2-5*c^4)*a^2-(8*b^2-5*c^2)*(b^2-c^2)^2)*(5*a^6-(5*b^2+18*c^2)*a^4-(5*b^4-2*b^2*c^2-21*c^4)*a^2+(5*b^2-8*c^2)*(b^2-c^2)^2) : :

X(46220) lies on the Kiepert circumhyperbola and these lines: {}

X(46220) = isogonal conjugate of X(46222)
X(46220) = trilinear pole of the line {523, 46219}
X(46220) = trilinear pole of line PU(166)


X(46221) = X(3)X(21849) ∩ X(389)X(46202)

Barycentrics    a^2*(7*a^8-41*(b^2+c^2)*a^6+(81*b^4+46*b^2*c^2+81*c^4)*a^4-(b^2+c^2)*(67*b^4-152*b^2*c^2+67*c^4)*a^2+10*(b^2-c^2)^2*(2*b^2-c^2)*(b^2-2*c^2)) : :

X(46221) lies on these lines: {3, 21849}, {389, 46202}, {10984, 13451}

X(46221) = crosssum of PU(166)


X(46222) = ISOGONAL CONJUGATE OF X(46220)

Barycentrics    a^2*(8*a^6-21*(b^2+c^2)*a^4+2*(9*b^4-b^2*c^2+9*c^4)*a^2-5*(b^4-c^4)*(b^2-c^2)) : :

X(46222) lies on these lines: {3, 6}

X(46222) = isogonal conjugate of X(46220)
X(46222) = crossdifference of every pair of points on line {X(523), X(46219)}
X(46222) = crossdifference of PU(166)
X(46222) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (50, 3003, 46203), (187, 46216, 50)


X(46223) = X(6)X(10194) ∩ X(216)X(46204)

Barycentrics    (5*a^4-9*(b^2+c^2)*a^2+4*(b^2-c^2)^2)^2-36*S^2*(b^2-c^2)^2 : :

X(46223) lies on these lines: {6, 10194}, {37, 46224}, {216, 46204}, {32832, 42332}

X(46223) = barycentric product X(1)*X(46224)
X(46223) = trilinear product X(6)*X(46224)
X(46223) = barycentric product of PU(166)


X(46224) = X(37)X(46223) ∩ X(44706)X(46205)

Barycentrics    ((5*a^4-9*(b^2+c^2)*a^2+4*(b^2-c^2)^2)^2-36*S^2*(b^2-c^2)^2)/a : :

X(46224) lies on these lines: {37, 46223}, {44706, 46205}

X(46224) = barycentric product X(75)*X(46223)
X(46224) = trilinear product X(2)*X(46223)
X(46224) = trilinear product of PU(166)


X(46225) = ISOTOMIC CONJUGATE OF X(40000)

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

X(46225) lies on these lines: {2, 14370}, {6, 2896}, {141, 28677}, {755, 7832}, {3589, 46227}, {6656, 14970}, {7859, 40850}, {17949, 46226}

X(46225) = isogonal conjugate of X(46227)
X(46225) = isotomic conjugate of X(40000)
X(46225) = barycentric product X(6)*X(40043)
X(46225) = barycentric quotient X(141)/X(46226)
X(46225) = trilinear product X(31)*X(40043)
X(46225) = trilinear quotient X(1930)/X(46226)
X(46225) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(17192)}} and {{A, B, C, X(2), X(2896)}}
X(46225) = X(39)-Dao conjugate of-X(46226)
X(46225) = X(141)-reciprocal conjugate of-X(46226)
X(46225) = cevapoint of PU(167)


X(46226) = X(2)X(39) ∩ X(3)X(16986)

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

X(46226) lies on these lines: {2, 39}, {3, 16986}, {4, 7938}, {5, 7931}, {6, 16895}, {20, 3818}, {30, 7928}, {32, 19689}, {69, 7787}, {83, 7779}, {99, 6292}, {115, 7944}, {140, 12188}, {141, 384}, {148, 6656}, {183, 7892}, {230, 14043}, {316, 7849}, {385, 7819}, {420, 12143}, {599, 7893}, {621, 635}, {622, 636}, {625, 33024}, {626, 16044}, {631, 14880}, {733, 35567}, {754, 32027}, {1003, 7904}, {1078, 7820}, {1352, 35422}, {1506, 7909}, {1930, 17280}, {1975, 3763}, {2548, 7897}, {3053, 14036}, {3096, 3734}, {3314, 7770}, {3329, 3933}, {3407, 7793}, {3552, 7800}, {3589, 7839}, {3619, 7791}, {3620, 20065}, {3785, 14037}, {3815, 7947}, {3972, 7854}, {4195, 17232}, {5025, 7868}, {5189, 31124}, {5224, 33827}, {5254, 7948}, {5475, 7922}, {5989, 7789}, {6658, 7761}, {6661, 7767}, {6704, 7813}, {7737, 7929}, {7745, 7939}, {7747, 7883}, {7748, 7937}, {7751, 7846}, {7752, 7869}, {7753, 7917}, {7754, 7875}, {7760, 7889}, {7768, 7804}, {7774, 16045}, {7777, 7881}, {7778, 16921}, {7783, 8362}, {7784, 11361}, {7788, 7921}, {7790, 7914}, {7792, 17129}, {7796, 7808}, {7802, 7865}, {7806, 33217}, {7812, 7896}, {7815, 7835}, {7816, 7831}, {7823, 7879}, {7826, 12150}, {7830, 31168}, {7833, 11164}, {7847, 20094}, {7855, 7878}, {7856, 17131}, {7858, 7895}, {7885, 8370}, {7891, 11285}, {7898, 14035}, {7901, 46236}, {7906, 11174}, {7907, 15271}, {7910, 19691}, {7912, 16924}, {7923, 8364}, {7924, 32819}, {7925, 32992}, {7933, 11185}, {7934, 32993}, {7936, 19693}, {8591, 20582}, {8724, 9302}, {9301, 44237}, {9862, 44224}, {9873, 11178}, {9939, 21356}, {10007, 32476}, {10304, 14458}, {10328, 35214}, {11293, 43407}, {11294, 43408}, {12110, 40107}, {13881, 14065}, {14069, 17008}, {14376, 37186}, {16897, 34573}, {16922, 44377}, {16984, 33185}, {17000, 17540}, {17004, 32954}, {17234, 17688}, {17238, 17691}, {17279, 33943}, {17300, 33953}, {17302, 39722}, {17358, 25242}, {17383, 19784}, {17681, 31090}, {17949, 46225}, {18358, 44251}, {20335, 30175}, {24206, 37336}, {24249, 30177}, {30174, 30949}, {32816, 33269}, {32999, 37690}, {33245, 37688}, {40000, 46227}

X(46226) = isogonal conjugate of X(46287)
X(46226) = anticomplement of X(7859)
X(46226) = crosssum of PU(183)
X(46226) = barycentric product X(141)*X(40000)
X(46226) = barycentric quotient X(141)/X(46225)
X(46226) = trilinear quotient X(40000)/X(82)
X(46226) = trilinear product X(38)*X(40000)
X(46226) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(14370)}} and {{A, B, C, X(76), X(1031)}}
X(46226) = X(39)-Dao conjugate of-X(46225)
X(46226) = X(141)-reciprocal conjugate of-X(46225)
X(46226) = crosspoint of PU(167)
X(46226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 76, 7797), (2, 7795, 7836), (2, 20081, 7803), (2, 31078, 19577), (69, 16898, 7787), (76, 7797, 19570), (76, 7822, 2), (76, 7943, 5309), (83, 7794, 7779), (99, 6292, 33021), (141, 384, 2896), (141, 24273, 5207), (384, 2896, 14712), (385, 7819, 10583), (1078, 7820, 33225), (1975, 3763, 7876), (3096, 3734, 6655), (3314, 7770, 7785), (3329, 3933, 13571), (3934, 7832, 2), (6656, 17128, 148), (7746, 7930, 2), (7769, 31239, 2), (7828, 7915, 2), (7839, 16896, 3589), (7879, 11286, 7823), (7880, 31239, 7769), (7914, 17130, 7790), (7915, 9466, 7828), (14001, 16990, 7793), (14001, 18840, 16990), (17129, 19694, 7792), (17280, 39724, 1930)


X(46227) = ISOGONAL CONJUGATE OF X(46225)

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

X(46227) lies on these lines: {2, 32}, {3, 41295}, {6, 14370}, {39, 46228}, {112, 28666}, {148, 8856}, {384, 28677}, {827, 5007}, {1176, 13331}, {3589, 46225}, {4577, 7839}, {5149, 28674}, {7765, 38946}, {7772, 14247}, {16896, 40425}, {18907, 28664}, {40000, 46226}

X(46227) = isogonal conjugate of X(46225)
X(46227) = isotomic conjugate of X(40043)
X(46227) = barycentric product X(i)*X(j) for these {i, j}: {6, 40000}, {251, 46226}
X(46227) = trilinear product X(31)*X(40000)
X(46227) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(14370)}} and {{A, B, C, X(6), X(2896)}}
X(46227) = crosssum of PU(167)
X(46227) = {X(251), X(9481)}-harmonic conjugate of X(32)


X(46228) = ISOGONAL CONJUGATE OF X(17949)

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

X(46228) lies on the cubics K222, K789 and these lines: {2, 1031}, {3, 9481}, {6, 22}, {32, 14247}, {39, 46227}, {83, 4045}, {115, 38946}, {187, 827}, {385, 4577}, {543, 38888}, {689, 35524}, {699, 783}, {733, 1691}, {1627, 8265}, {2076, 24973}, {3005, 18105}, {4628, 17735}, {7779, 40850}, {7794, 40003}, {8623, 9480}, {8928, 40236}, {9076, 16102}, {10130, 16986}, {13236, 34214}, {14712, 16095}, {14970, 39089}

X(46228) = isogonal conjugate of X(17949)
X(46228) = barycentric product X(i)*X(j) for these {i, j}: {1, 34054}, {6, 40850}, {82, 17799}, {83, 2076}, {99, 17997}, {110, 18010}
X(46228) = barycentric quotient X(i)/X(j) for these (i, j): (31, 17957), (251, 11606), (420, 1235), (733, 9477)
X(46228) = trilinear product X(i)*X(j) for these {i, j}: {6, 34054}, {31, 40850}, {82, 2076}, {163, 18010}, {251, 17799}, {662, 17997}
X(46228) = trilinear quotient X(i)/X(j) for these (i, j): (6, 17957), (82, 11606), (420, 20883)
X(46228) = trilinear pole of the line {5113, 17997}
X(46228) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(10329)}} and {{A, B, C, X(6), X(1031)}}
X(46228) = cevapoint of X(6) and X(9480)
X(46228) = crossdifference of every pair of points on line {X(826), X(6292)}
X(46228) = X(733)-Ceva conjugate of-X(251)
X(46228) = X(385)-Dao conjugate of-X(35540)
X(46228) = X(i)-Hirst inverse of-X(j) for these (i, j): {6, 251}, {32, 14885}, {251, 6}
X(46228) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 17957}, {38, 11606}
X(46228) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 17957), (251, 11606), (420, 1235), (733, 9477)
X(46228) = X(251)-vertex conjugate of-X(3005)
X(46228) = crossdifference of PU(167)
X(46228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 41295, 251), (32, 14247, 14885)


X(46229) = ISOGONAL CONJUGATE OF X(32681)

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

X(46229) lies on these lines: {30, 511}, {684, 42733}, {1637, 5664}, {1651, 9155}, {2394, 2986}, {8552, 14566}, {11007, 42736}, {32836, 45792}, {44564, 45681}

X(46229) = isogonal conjugate of X(32681)
X(46229) = barycentric product X(i)*X(j) for these {i, j}: {30, 30474}, {850, 10564}, {1637, 32833}
X(46229) = barycentric quotient X(i)/X(j) for these (i, j): (1, 36083), (30, 1302), (378, 1304), (1495, 32738), (1637, 34288)
X(46229) = trilinear product X(1577)*X(10564)
X(46229) = trilinear quotient X(i)/X(j) for these (i, j): (2, 36083), (30, 36149), (378, 36131)
X(46229) = crossdifference of every pair of points on line {X(6), X(32738)}
X(46229) = X(9)-Dao conjugate of-X(36083)
X(46229) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 36083}, {74, 36149}, {1302, 2159}
X(46229) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 36083), (30, 1302), (378, 1304)
X(46229) = ideal point of line PU(168)


X(46230) = TRILINEAR POLE OF LINE PU(168)

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

X(46230) lies on these lines: {3003, 40423}, {3580, 30474}, {16237, 44134}

X(46230) = isogonal conjugate of X(46233)
X(46230) = barycentric quotient X(30)/X(6795)
X(46230) = trilinear pole of the line {113, 46229}
X(46230) = X(30)-reciprocal conjugate of-X(6795)
X(46230) = trilinear pole of line PU(168)


X(46231) = X(113)X(40832) ∩ X(146)X(3260)

Barycentrics    1/a^2*(a^12-(b^2+c^2)*a^10-(3*b^4-11*b^2*c^2+3*c^4)*a^8+(b^2+c^2)*(5*b^4-14*b^2*c^2+5*c^4)*a^6-2*(b^8+c^8+2*b^2*c^2*(b^4-4*b^2*c^2+c^4))*a^4+2*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2+(b^2-c^2)^4*b^2*c^2) : :

X(46231) lies on these lines: {113, 40832}, {146, 3260}, {148, 41760}, {1975, 46247}

X(46231) = crosspoint of PU(168)


X(46232) = X(6)X(34178) ∩ X(10419)X(32681)

Barycentrics    a^2*(a^12-(b^2+c^2)*a^10-(3*b^4-11*b^2*c^2+3*c^4)*a^8+(b^2+c^2)*(5*b^4-14*b^2*c^2+5*c^4)*a^6-2*(b^8+c^8+2*(b^4-4*b^2*c^2+c^4)*b^2*c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2+(b^2-c^2)^4*b^2*c^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)) : :

X(46232) lies on these lines: {6, 34178}, {30, 46233}, {10419, 32681}

X(46232) = crosssum of PU(168)


X(46233) = ISOGONAL CONJUGATE OF X(46230)

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

X(46233) lies on these lines: {6, 32738}, {30, 46232}, {526, 686}

X(46233) = isogonal conjugate of X(46230)
X(46233) = barycentric product X(74)*X(6795)
X(46233) = perspector of the circumconic {{A, B, C, X(10419), X(32681)}}
X(46233) = crossdifference of every pair of points on line {X(113), X(46229)}
X(46233) = X(6)-Hirst inverse of-X(40352)
X(46233) = crossdifference of PU(168)


X(46234) = ISOTOMIC CONJUGATE OF X(2159)

Barycentrics    1/a^3*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2) : :

X(46234) lies on these lines: {75, 1725}, {76, 43682}, {92, 304}, {799, 36102}, {824, 1577}, {14210, 23994}

X(46234) = isotomic conjugate of X(2159)
X(46234) = barycentric product X(i)*X(j) for these {i, j}: {30, 561}, {75, 3260}, {76, 14206}, {304, 46106}, {305, 1784}, {670, 36035}
X(46234) = barycentric quotient X(i)/X(j) for these (i, j): (1, 40352), (19, 40354), (30, 31), (63, 18877), (69, 35200), (75, 74)
X(46234) = trilinear product X(i)*X(j) for these {i, j}: {2, 3260}, {30, 76}, {69, 46106}, {75, 14206}, {94, 6148}, {99, 41079}
X(46234) = trilinear quotient X(i)/X(j) for these (i, j): (2, 40352), (4, 40354), (25, 40351), (30, 32), (69, 18877), (76, 74)
X(46234) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(824)}} and {{A, B, C, X(92), X(1577)}}
X(46234) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 40352), (30, 9406), (133, 1973), (1511, 9247)
X(46234) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 40354}, {6, 40352}, {25, 18877}, {32, 74}
X(46234) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 40352), (19, 40354), (30, 31), (63, 18877)
X(46234) = trilinear product of PU(168)


X(46235) = X(114)X(39931) ∩ X(147)X(385)

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

X(46235) lies on the cubic K776 and these lines: {114, 39931}, {147, 385}, {287, 44534}, {297, 19599}

X(46235) = isogonal conjugate of X(46237)
X(46235) = barycentric quotient X(325)/X(46236)
X(46235) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(147)}} and {{A, B, C, X(69), X(46236)}}
X(46235) = X(69)-cross conjugate of-X(297)
X(46235) = X(325)-reciprocal conjugate of-X(46236)
X(46235) = cevapoint of PU(169)


X(46236) = X(4)X(99) ∩ X(69)X(98)

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

X(46236) lies on the cubic K780 and these lines: {2, 694}, {4, 99}, {69, 98}, {76, 14651}, {115, 7795}, {141, 44531}, {147, 325}, {148, 1975}, {193, 12829}, {297, 19599}, {305, 46247}, {315, 5152}, {384, 3815}, {543, 16041}, {620, 7808}, {626, 8178}, {631, 12176}, {671, 33285}, {1078, 10357}, {1281, 7179}, {1569, 34511}, {1987, 43714}, {2482, 14033}, {2548, 5149}, {2782, 3926}, {2794, 32006}, {3407, 10353}, {3705, 7061}, {3785, 12042}, {3933, 12188}, {4027, 7774}, {5490, 13873}, {5491, 13926}, {5939, 5984}, {5985, 45962}, {5986, 40123}, {6033, 32816}, {6036, 34229}, {6321, 32815}, {6330, 6340}, {6390, 13188}, {6394, 34841}, {7735, 36849}, {7736, 10352}, {7777, 8290}, {7788, 11177}, {7799, 39266}, {7868, 9478}, {7901, 46226}, {7912, 32528}, {8591, 14041}, {8724, 32837}, {9723, 39803}, {9766, 12830}, {9888, 32986}, {11164, 11184}, {11606, 43529}, {11632, 32836}, {12243, 32833}, {13137, 15631}, {14036, 42849}, {14039, 41134}, {14046, 41135}, {14061, 32951}, {14063, 20094}, {15561, 19910}, {16089, 44132}, {16925, 39652}, {22103, 34238}, {22505, 32827}, {22515, 32826}, {32828, 38224}, {32838, 34127}, {33290, 35369}

X(46236) = reflection of X(148) in X(44518)
X(46236) = anticomplement of X(44534)
X(46236) = barycentric quotient X(325)/X(46235)
X(46236) = X(297)-Ceva conjugate of-X(69)
X(46236) = X(325)-reciprocal conjugate of-X(46235)
X(46236) = crosspoint of PU(169)
X(46236) = X(3767)-of-1st anti-Brocard triangle
X(46236) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (98, 32458, 69), (99, 8781, 114), (114, 8781, 1007), (315, 5152, 9862), (325, 5989, 147), (325, 5999, 5207), (626, 8178, 43449), (1916, 5976, 18906), (1916, 34999, 8782), (33340, 33341, 4)


X(46237) = ISOGONAL CONJUGATE OF X(46235)

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

X(46237) lies on the cubic K782 and these lines: {6, 34130}, {98, 2458}, {232, 1692}, {237, 694}, {248, 511}, {287, 5207}, {2456, 17974}, {5034, 14355}, {5999, 41932}, {11610, 35388}

X(46237) = isogonal conjugate of X(46235)
X(46237) = barycentric product X(1976)*X(46236)
X(46237) = X(25)-Ceva conjugate of-X(248)
X(46237) = crosssum of PU(169)
X(46237) = {X(2065), X(2715)}-harmonic conjugate of X(1692)


X(46238) = ISOTOMIC CONJUGATE OF X(1910)

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

X(46238) lies on the cubic K1023 and these lines: {1, 75}, {19, 1102}, {38, 20627}, {63, 20641}, {76, 20236}, {190, 20643}, {240, 23996}, {325, 42703}, {518, 35551}, {561, 14213}, {668, 35150}, {726, 20629}, {746, 8624}, {799, 14206}, {824, 1577}, {1109, 20904}, {1284, 5977}, {1920, 6358}, {1921, 4858}, {1928, 1969}, {3926, 25252}, {4137, 16891}, {6382, 20237}, {10030, 20924}, {11683, 17206}, {16703, 20896}, {16706, 24786}, {16887, 21421}, {17289, 30103}, {17787, 33939}, {17871, 18056}, {17874, 18059}, {17884, 18064}, {17890, 18068}, {17897, 18075}, {18275, 18895}, {18837, 21406}, {20437, 40017}, {20879, 33764}, {20887, 35543}, {20911, 21442}, {24037, 46254}, {27801, 40564}, {30886, 30892}

X(46238) = isotomic conjugate of X(1910)
X(46238) = barycentric product X(i)*X(j) for these {i, j}: {63, 44132}, {69, 40703}, {75, 325}, {76, 1959}, {86, 42703}, {92, 6393}
X(46238) = barycentric quotient X(i)/X(j) for these (i, j): (1, 1976), (31, 14601), (48, 14600), (63, 248), (69, 293), (75, 98)
X(46238) = trilinear product X(i)*X(j) for these {i, j}: {2, 325}, {3, 44132}, {4, 6393}, {63, 40703}, {69, 297}, {75, 1959}
X(46238) = trilinear quotient X(i)/X(j) for these (i, j): (2, 1976), (3, 14600), (6, 14601), (69, 248), (76, 98), (99, 2715)
X(46238) = perspector of the circumconic {{A, B, C, X(561), X(799)}}
X(46238) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(240)}} and {{A, B, C, X(75), X(20948)}}
X(46238) = crosspoint of X(75) and X(1934)
X(46238) = crosssum of X(31) and X(1933)
X(46238) = X(i)-daleth conjugate of-X(j) for these (i, j): (75, 1930), (304, 18695)
X(46238) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 1976), (39, 3404), (132, 1973), (230, 8772)
X(46238) = X(i)-Hirst inverse of-X(j) for these (i, j): {75, 304}, {304, 75}
X(46238) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 14601}, {4, 14600}, {6, 1976}, {25, 248}
X(46238) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 1976), (31, 14601), (48, 14600), (63, 248)
X(46238) = trilinear product of PU(169)
X(46238) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (75, 304, 3403), (75, 1966, 1733), (75, 18156, 4008), (799, 20944, 14206), (1733, 14210, 1966)


X(46239) = ISOTOMIC CONJUGATE OF X(15013)

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

X(46239) lies on these lines: {2, 46151}, {69, 41676}, {127, 264}, {232, 2373}, {287, 2393}, {648, 1799}, {1289, 1843}, {3186, 41769}, {15526, 18018}, {46240, 46241}

X(46239) = reflection of X(i) in X(j) for these (i, j): (648, 40938), (18018, 15526)
X(46239) = isogonal conjugate of X(46243)
X(46239) = isotomic conjugate of X(15013)
X(46239) = trilinear pole of the line {427, 525}
X(46239) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}} and {{A, B, C, X(22), X(46240)}}
X(46239) = cevapoint of X(2) and X(40889)
X(46239) = trilinear pole of line PU(170)


X(46240) = X(194)X(7391) ∩ X(8788)X(28408)

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

X(46240) lies on these lines: {194, 7391}, {8788, 28408}, {46239, 46241}

X(46240) = isogonal conjugate of X(46242)
X(46240) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7391)}} and {{A, B, C, X(4), X(28412)}}
X(46240) = cevapoint of PU(170)


X(46241) = X(22)X(16097) ∩ X(25)X(40421)

Barycentrics    1/a^2*(a^8-(b^4+b^2*c^2+c^4)*a^4+(b^2+c^2)^2*b^2*c^2)*(a^4-b^4+c^4)*(a^2-b^2+c^2)*(a^4+b^4-c^4)*(a^2+b^2-c^2) : :

X(46241) lies on these lines: {22, 16097}, {25, 40421}, {2998, 13854}, {7391, 18018}, {46239, 46240}

X(46241) = crosspoint of PU(170)


X(46242) = ISOGONAL CONJUGATE OF X(46240)

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

X(46242) lies on these lines: {6, 34436}, {66, 46243}, {112, 1176}, {1691, 1968}, {5157, 17409}, {5596, 22075}, {7737, 24270}, {8778, 19125}, {19126, 36879}

X(46242) = isogonal conjugate of X(46240)
X(46242) = barycentric product X(206)*X(46241)
X(46242) = crosssum of PU(170)


X(46243) = ISOGONAL CONJUGATE OF X(46239)

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

X(46243) lies on these lines: {2, 22075}, {6, 25}, {23, 34137}, {66, 46242}, {125, 1691}, {287, 2373}, {647, 8673}, {1501, 1899}, {1799, 40404}, {2548, 14585}, {3269, 8627}, {5523, 15388}, {6638, 22391}, {10766, 15107}, {11064, 32661}, {13198, 14567}, {15139, 35325}

X(46243) = isogonal conjugate of X(46239)
X(46243) = barycentric product X(i)*X(j) for these {i, j}: {6, 15013}, {206, 16097}
X(46243) = trilinear product X(31)*X(15013)
X(46243) = perspector of the circumconic {{A, B, C, X(112), X(1176)}}
X(46243) = inverse of X(184) in MacBeath circumconic
X(46243) = intersection, other than A, B, C, of circumconics {{A, B, C, X(25), X(15013)}} and {{A, B, C, X(184), X(15388)}}
X(46243) = crossdifference of every pair of points on line {X(427), X(525)}
X(46243) = crosssum of X(2) and X(40889)
X(46243) = X(2)-Ceva conjugate of-X(39086)
X(46243) = X(6)-daleth conjugate of-X(21637)
X(46243) = X(i)-Hirst inverse of-X(j) for these (i, j): {6, 206}, {206, 6}
X(46243) = X(206)-vertex conjugate of-X(647)
X(46243) = crossdifference of PU(170)
X(46243) = {X(23), X(34137)}-harmonic conjugate of X(38356)


X(46244) = ISOGONAL CONJUGATE OF X(17453)

Barycentrics    1/a^3*(a^4-b^4+c^4)*(a^4+b^4-c^4) : :

X(46244) lies on these lines: {19, 37220}, {66, 21280}, {75, 17870}, {92, 39733}, {304, 18669}, {336, 44179}, {561, 1760}, {18018, 20336}, {18051, 18716}, {20884, 40364}, {21017, 40071}

X(46244) = isogonal conjugate of X(17453)
X(46244) = isotomic conjugate of X(2172)
X(46244) = barycentric product X(i)*X(j) for these {i, j}: {1, 40421}, {66, 561}, {75, 18018}, {304, 43678}, {1502, 2156}
X(46244) = barycentric quotient X(i)/X(j) for these (i, j): (1, 206), (9, 4548), (19, 17409), (31, 20968), (37, 21034), (38, 23208)
X(46244) = trilinear product X(i)*X(j) for these {i, j}: {2, 18018}, {6, 40421}, {66, 76}, {69, 43678}, {264, 14376}, {276, 41168}
X(46244) = trilinear quotient X(i)/X(j) for these (i, j): (2, 206), (3, 22075), (4, 17409), (6, 20968), (7, 7251), (8, 4548)
X(46244) = trilinear pole of the line {14208, 17901}
X(46244) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1760)}} and {{A, B, C, X(19), X(1577)}}
X(46244) = cevapoint of X(i) and X(j) for these (i, j): {1, 2156}, {2, 17492}, {75, 20915}
X(46244) = X(1)-cross conjugate of-X(561)
X(46244) = X(i)-Dao conjugate of-X(j) for these (i, j): (1, 4548), (9, 206), (10, 21034), (223, 7251)
X(46244) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 20968}, {3, 17409}, {4, 22075}, {6, 206}
X(46244) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 206), (9, 4548), (19, 17409), (31, 20968)
X(46244) = trilinear product of PU(170)


X(46245) = ISOTOMIC CONJUGATE OF X(40866)

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

X(46245) lies on these lines: {2, 879}, {297, 523}, {325, 525}, {327, 18312}, {512, 40077}, {647, 2966}, {850, 35088}, {4580, 20022}, {5641, 23878}, {9141, 36900}, {13485, 31296}, {15421, 35923}, {46246, 46247}

X(46245) = midpoint of X(31296) and X(39359)
X(46245) = reflection of X(i) in X(j) for these (i, j): (850, 35088), (2966, 647)
X(46245) = isogonal conjugate of X(46249)
X(46245) = isotomic conjugate of X(40866)
X(46245) = barycentric product X(850)*X(9513)
X(46245) = barycentric quotient X(i)/X(j) for these (i, j): (98, 43113), (512, 44127), (523, 1316), (850, 44155), (868, 31953)
X(46245) = trilinear product X(1577)*X(9513)
X(46245) = trilinear quotient X(i)/X(j) for these (i, j): (661, 44127), (1577, 1316)
X(46245) = Gibert-Simson transform of X(9513)
X(46245) = trilinear pole of the line {125, 2799}
X(46245) = inverse of X(9513) in Steiner circumellipse
X(46245) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(297)}} and {{A, B, C, X(110), X(23962)}}
X(46245) = X(i)-Dao conjugate of-X(j) for these (i, j): (115, 1316), (1084, 44127)
X(46245) = X(2)-Hirst inverse of-X(9513)
X(46245) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 1316}, {662, 44127}
X(46245) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (98, 43113), (512, 44127), (523, 1316), (850, 44155)
X(46245) = trilinear pole of line PU(171)


X(46246) = ISOTOMIC CONJUGATE OF X(9514)

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

X(46246) lies on these lines: {3448, 14721}, {40866, 45215}, {46245, 46247}

X(46246) = isogonal conjugate of X(46248)
X(46246) = isotomic conjugate of X(9514)
X(46246) = barycentric quotient X(i)/X(j) for these (i, j): (523, 9512), (850, 46247)
X(46246) = trilinear quotient X(1577)/X(9512)
X(46246) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3448)}} and {{A, B, C, X(110), X(23962)}}
X(46246) = X(115)-Dao conjugate of-X(9512)
X(46246) = X(163)-isoconjugate-of-X(9512)
X(46246) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (523, 9512), (850, 46247)
X(46246) = cevapoint of PU(171)


X(46247) = X(2)X(11794) ∩ X(99)X(23217)

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

X(46247) lies on these lines: {2, 11794}, {99, 23217}, {110, 23962}, {125, 290}, {184, 18022}, {305, 46236}, {311, 11056}, {850, 3448}, {1495, 17984}, {1975, 46231}, {3292, 44137}, {3978, 39266}, {5651, 40822}, {23292, 42394}, {31074, 44176}, {35319, 39355}, {46245, 46246}

X(46247) = isotomic conjugate of X(46603)
X(46247) = anticomplement of X(45215)
X(46247) = isotomic conjugate of the isogonal conjugate of X(9512)
X(46247) = barycentric product X(i)*X(j) for these {i, j}: {76, 9512}, {311, 39843}, {850, 9514}
X(46247) = barycentric quotient X(850)/X(46246)
X(46247) = trilinear product X(i)*X(j) for these {i, j}: {75, 9512}, {1577, 9514}
X(46247) = X(850)-reciprocal conjugate of-X(46246)
X(46247) = crosspoint of PU(171)
X(46247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (110, 23962, 44155), (290, 6331, 125)


X(46248) = ISOGONAL CONJUGATE OF X(46246)

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

X(46248) lies on these lines: {6, 3447}, {250, 2715}, {523, 23963}, {1576, 3050}, {3288, 38861}, {20975, 46252}

X(46248) = reflection of X(46249) in X(23963)
X(46248) = isogonal conjugate of X(46246)
X(46248) = barycentric product X(i)*X(j) for these {i, j}: {6, 9514}, {110, 9512}, {1576, 46247}, {1625, 39843}
X(46248) = trilinear product X(i)*X(j) for these {i, j}: {31, 9514}, {163, 9512}
X(46248) = crosssum of PU(171)
X(46248) = {X(250), X(2715)}-harmonic conjugate of X(3049)


X(46249) = ISOGONAL CONJUGATE OF X(46245)

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

X(46249) lies on these lines: {6, 157}, {110, 112}, {246, 17847}, {250, 2451}, {523, 23963}, {1640, 35278}, {2485, 34947}, {2502, 9408}, {2715, 3288}, {3049, 38861}, {3269, 13198}, {5027, 14574}, {9157, 46128}

X(46249) = reflection of X(46248) in X(23963)
X(46249) = isogonal conjugate of X(46245)
X(46249) = barycentric product X(i)*X(j) for these {i, j}: {6, 40866}, {99, 44127}, {110, 1316}, {511, 43113}, {1576, 44155}
X(46249) = barycentric quotient X(i)/X(j) for these (i, j): (1316, 850), (1576, 9513)
X(46249) = trilinear product X(i)*X(j) for these {i, j}: {31, 40866}, {163, 1316}, {662, 44127}
X(46249) = trilinear quotient X(i)/X(j) for these (i, j): (163, 9513), (1316, 1577)
X(46249) = perspector of the circumconic {{A, B, C, X(250), X(2715)}}
X(46249) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(1316)}} and {{A, B, C, X(99), X(38947)}}
X(46249) = crossdifference of every pair of points on line {X(125), X(2799)}
X(46249) = X(6)-Hirst inverse of-X(1576)
X(46249) = X(1316)-reciprocal conjugate of-X(850)
X(46249) = crossdifference of PU(171)
X(46249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (110, 112, 3569), (5191, 9475, 8429)


X(46250) = TRILINEAR POLE OF LINE PU(172)

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

X(46250) lies on these lines: {850, 39359}, {18020, 35088}

X(46250) = reflection of X(18020) in X(35088)
X(46250) = isogonal conjugate of X(46253)
X(46250) = isotomic conjugate of the anticomplement of X(40866)
X(46250) = trilinear pole of the line {2799, 5972}
X(46250) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(297)}} and {{A, B, C, X(30), X(18823)}}
X(46250) = trilinear pole of line PU(172)


X(46251) = CROSSPOINT OF PU(172)

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

X(46251) lies on these lines: {110, 685}

X(46251) = crosspoint of PU(172)


X(46252) = X(6)X(523) ∩ X(20975)X(46248)

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

X(46252) lies on these lines: {6, 523}, {250, 46253}, {20975, 46248}

X(46252) = crosssum of PU(172)


X(46253) = ISOGONAL CONJUGATE OF X(46250)

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

X(46253) lies on these lines: {6, 157}, {74, 2502}, {110, 3269}, {112, 3124}, {250, 46252}, {1648, 9862}, {2079, 3569}, {3050, 30715}, {5027, 39857}

X(46253) = isogonal conjugate of X(46250)
X(46253) = crossdifference of every pair of points on line {X(2799), X(5972)}
X(46253) = X(6)-Hirst inverse of-X(20975)
X(46253) = crossdifference of PU(172)


X(46254) = ISOTOMIC CONJUGATE OF X(3708)

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

X(46254) lies on these lines: {75, 1101}, {422, 4601}, {662, 20948}, {811, 24006}, {1275, 7058}, {20944, 23999}, {20953, 36142}, {24001, 24039}, {24037, 46238}

X(46254) = isotomic conjugate of X(3708)
X(46254) = polar conjugate of X(2643)
X(46254) = barycentric product X(i)*X(j) for these {i, j}: {4, 24037}, {19, 34537}, {27, 4601}, {69, 23999}, {75, 18020}, {92, 4590}
X(46254) = barycentric quotient X(i)/X(j) for these (i, j): (1, 20975), (4, 2643), (19, 3124), (27, 3125), (28, 3122), (29, 4516)
X(46254) = trilinear product X(i)*X(j) for these {i, j}: {2, 18020}, {4, 4590}, {19, 24037}, {25, 34537}, {27, 4600}, {28, 4601}
X(46254) = trilinear quotient X(i)/X(j) for these (i, j): (2, 20975), (4, 3124), (25, 1084), (27, 3122), (28, 3121), (32, 23216)
X(46254) = trilinear pole of the line {162, 799} (the tangent to conic {A,B,C,X(811),X(823)} at X(811))
X(46254) = intersection, other than A, B, C, of circumconics {{A, B, C, X(27), X(422)}} and {{A, B, C, X(28), X(15147)}}
X(46254) = cevapoint of X(i) and X(j) for these (i, j): {4, 17914}, {75, 662}, {92, 811}, {99, 7058}
X(46254) = X(i)-cross conjugate of-X(j) for these (i, j): (92, 811), (304, 799), (561, 4593)
X(46254) = X(9)-Dao conjugate of-X(20975)
X(46254) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 3124}, {6, 20975}, {25, 3269}, {32, 125}
X(46254) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 20975), (4, 2643), (19, 3124), (27, 3125)
X(46254) = trilinear product of PU(172)


X(46255) = ISOGONAL CONJUGATE OF X(11454)

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

X(46255) lies on these lines: {30, 10192}, {16080, 46256}

X(46255) = isogonal conjugate of X(11454)
X(46255) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(35480)}} and {{A, B, C, X(4), X(30)}}
X(46255) = cevapoint of PU(174)


X(46256) = X(3830)X(23324) ∩ X(16080)X(46255)

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

X(46256) lies on these lines: {3830, 23324}, {16080, 46255}

X(46256) = crosspoint of PU(174)


X(46257) = X(6)X(14269) ∩ X(115)X(393)

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

X(46257) lies on these lines: {6, 14269}, {115, 393}, {574, 44218}, {1285, 40136}, {5158, 9220}, {5206, 46262}, {18362, 18487}

X(46257) = barycentric product X(1)*X(46258)
X(46257) = trilinear product X(6)*X(46258)
X(46257) = barycentric product of PU(174)


X(46258) = X(158)X(1109) ∩ X(9219)X(18477)

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

X(46258) lies on these lines: {158, 1109}, {9219, 18477}

X(46258) = barycentric product X(75)*X(46257)
X(46258) = trilinear product X(2)*X(46257)
X(46258) = trilinear product of PU(174)


X(46259) = X(376)X(2979) ∩ X(3003)X(35486)

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

X(46259) lies on these lines: {376, 2979}, {2986, 46260}, {3003, 35486}, {7796, 44133}

X(46259) = isogonal conjugate of X(46261)
X(46259) = trilinear pole of the line {686, 9209}
X(46259) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(35486)}} and {{A, B, C, X(3), X(403)}}
X(46259) = cevapoint of PU(175)


X(46260) = X(30)X(1853) ∩ X(2453)X(15068)

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

X(46260) lies on these lines: {30, 1853}, {2453, 15068}, {2986, 46259}, {13881, 16618}

X(46260) = crosspoint of PU(175)


X(46261) = ISOGONAL CONJUGATE OF X(46259)

Barycentrics    a^2*(a^8-3*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4-(b^2+c^2)*(b^4+c^4)*a^2+4*(b^2-c^2)^2*b^2*c^2) : :
X(46261) = X(3)-3*X(35259) = 3*X(25)-X(37489) = 3*X(381)-X(18396) = 3*X(6090)-X(37483) = 3*X(9306)-X(37480) = 3*X(18451)+X(37489) = 3*X(19136)-2*X(44490) = 3*X(35259)-2*X(43586)

X(46261) lies on these lines: {2, 14157}, {3, 1495}, {4, 110}, {5, 182}, {20, 43598}, {22, 5891}, {23, 11459}, {24, 7689}, {25, 13754}, {26, 5907}, {30, 9306}, {32, 3016}, {49, 3843}, {51, 18445}, {52, 10594}, {54, 3832}, {64, 43604}, {68, 3089}, {140, 16187}, {141, 16618}, {146, 43578}, {154, 9818}, {155, 1351}, {156, 546}, {184, 381}, {185, 7506}, {186, 11454}, {235, 9927}, {343, 37971}, {378, 16194}, {382, 1092}, {389, 13861}, {394, 18534}, {399, 568}, {403, 18474}, {511, 7530}, {542, 19136}, {569, 1614}, {571, 45938}, {576, 2854}, {590, 9687}, {631, 43614}, {632, 13347}, {692, 18491}, {858, 16658}, {1181, 3066}, {1204, 10620}, {1216, 1350}, {1344, 32550}, {1345, 32549}, {1437, 37234}, {1498, 6642}, {1568, 31723}, {1593, 12038}, {1595, 9820}, {1596, 41619}, {1597, 8780}, {1625, 10311}, {1656, 10984}, {1657, 43652}, {1658, 45959}, {1660, 18400}, {1968, 2420}, {1974, 14852}, {1995, 9730}, {2070, 18435}, {2071, 11455}, {2072, 11550}, {2080, 5167}, {2883, 31833}, {2979, 37925}, {3090, 13336}, {3098, 15067}, {3146, 43576}, {3147, 20191}, {3167, 18535}, {3199, 23128}, {3357, 12041}, {3517, 12163}, {3518, 12111}, {3520, 11439}, {3523, 8718}, {3527, 38263}, {3541, 43839}, {3542, 5449}, {3543, 43574}, {3545, 5012}, {3547, 40330}, {3567, 43605}, {3627, 13346}, {3628, 37515}, {3830, 22115}, {3839, 9544}, {3850, 32046}, {3855, 13434}, {3917, 12083}, {4846, 5656}, {5020, 5892}, {5055, 43650}, {5068, 43651}, {5072, 13353}, {5076, 37495}, {5079, 37471}, {5097, 10110}, {5198, 36747}, {5320, 45923}, {5422, 14845}, {5447, 11414}, {5544, 11484}, {5562, 7517}, {5640, 15032}, {5663, 11438}, {5876, 37440}, {5878, 43577}, {5889, 34484}, {5890, 13595}, {5899, 23039}, {5972, 18281}, {6000, 6644}, {6090, 37483}, {6153, 17824}, {6241, 44802}, {6247, 16238}, {6643, 14927}, {6689, 7404}, {6699, 9934}, {6723, 20299}, {6756, 22660}, {6776, 43573}, {6785, 33803}, {6800, 37513}, {7487, 22750}, {7488, 15058}, {7502, 15060}, {7512, 15056}, {7525, 14128}, {7526, 10282}, {7527, 11464}, {7547, 15432}, {7550, 15080}, {7555, 33533}, {7565, 7699}, {8541, 45016}, {8542, 44493}, {8547, 15581}, {9703, 14269}, {10116, 39571}, {10154, 44201}, {10182, 18580}, {10201, 21243}, {10254, 44078}, {10274, 22804}, {10323, 21766}, {10535, 37697}, {10546, 12112}, {10575, 17928}, {10665, 35765}, {10666, 35764}, {10982, 44863}, {11064, 16654}, {11178, 44262}, {11202, 18570}, {11204, 15646}, {11206, 18537}, {11232, 39899}, {11250, 20773}, {11430, 31861}, {11440, 44879}, {11444, 12088}, {11449, 14865}, {11457, 43817}, {11479, 14530}, {11579, 36253}, {11585, 16655}, {11591, 17714}, {11692, 34751}, {11793, 14810}, {11801, 44235}, {11818, 18388}, {11935, 37472}, {12039, 44480}, {12082, 15066}, {12084, 13474}, {12085, 15811}, {12133, 12901}, {12272, 12364}, {12290, 22467}, {12308, 13621}, {12359, 21841}, {13292, 15873}, {13340, 37924}, {13419, 18569}, {13509, 15355}, {13567, 44233}, {13598, 16266}, {14002, 14094}, {14118, 26882}, {14156, 44441}, {14529, 31937}, {14560, 39170}, {14791, 29012}, {14831, 44106}, {15004, 15087}, {15062, 21844}, {15063, 32235}, {15132, 38791}, {15448, 34351}, {15687, 40111}, {16619, 34507}, {16621, 23335}, {17811, 35243}, {18358, 19126}, {18369, 37481}, {18376, 18418}, {18378, 18436}, {18390, 46030}, {18488, 37119}, {18531, 31383}, {19347, 21637}, {20725, 44240}, {20772, 44274}, {21451, 26917}, {23293, 37943}, {23329, 44452}, {23332, 44911}, {26864, 37506}, {26881, 35921}, {26885, 37584}, {26888, 37696}, {32111, 38323}, {32217, 44470}, {34117, 43130}, {34986, 39522}, {35266, 44218}, {36749, 43844}, {36987, 44457}, {37625, 43609}, {37897, 44683}, {42426, 43389}

X(46261) = midpoint of X(i) and X(j) for these {i, j}: {25, 18451}, {394, 18534}, {7530, 15068}, {18531, 31383}
X(46261) = reflection of X(i) in X(j) for these (i, j): (3, 43586), (11438, 12106), (13567, 44233), (18390, 46030)
X(46261) = isogonal conjugate of X(46259)
X(46261) = crossdifference of every pair of points on line {X(686), X(9209)}
X(46261) = crosssum of PU(175)
X(46261) = center of circle {{X(394), X(18534), X(36192)}}
X(46261) = X(18396)-of-Ehrmann-mid triangle
X(46261) = X(43586)-of-X3-ABC reflections triangle
X(46261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 15030, 4550), (3, 35259, 43586), (4, 110, 13352), (4, 10539, 1147), (4, 12118, 12897), (5, 34514, 23325), (23, 11459, 37478), (23, 15052, 11459), (24, 12162, 7689), (49, 3843, 11424), (52, 11441, 15083), (110, 13352, 1147), (113, 12140, 19479), (154, 9818, 18475), (155, 1598, 5446), (156, 546, 578), (235, 12134, 9927), (381, 10540, 184), (382, 18350, 1092), (399, 7545, 568), (568, 7545, 34417), (1181, 7529, 5462), (1495, 15030, 3), (1498, 6642, 40647), (1614, 3091, 569), (7387, 17814, 1216), (10282, 44870, 7526), (10539, 13352, 110), (10984, 22112, 13339), (11464, 16261, 7527), (13861, 32139, 389), (18439, 45735, 1204)


X(46262) = X(2)X(6) ∩ X(4)X(50)

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

X(46262) lies on these lines: {2, 6}, {3, 16310}, {4, 50}, {53, 18533}, {115, 577}, {186, 393}, {231, 3767}, {338, 37188}, {376, 1989}, {562, 2963}, {566, 631}, {571, 7737}, {647, 15328}, {1285, 2965}, {1609, 6644}, {1990, 35486}, {2072, 9722}, {2493, 7493}, {3018, 21843}, {3087, 7577}, {3147, 11062}, {3284, 7746}, {3525, 41335}, {5023, 37460}, {5054, 14836}, {5158, 7749}, {5206, 46257}, {5286, 7550}, {6036, 11511}, {6587, 38401}, {7514, 15048}, {7612, 18919}, {7755, 33871}, {9862, 41761}, {15484, 37347}, {15655, 44265}, {16051, 44529}, {16303, 44214}, {18324, 42459}, {35952, 44532}, {36748, 44526}, {38872, 44440}

X(46262) = barycentric product X(1)*X(46263)
X(46262) = trilinear product X(6)*X(46263)
X(46262) = inverse of X(37638) in Evans conic
X(46262) = crosssum of X(6) and X(37489)
X(46262) = barycentric product of PU(175)
X(46262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (231, 5063, 3767), (590, 615, 37638), (3068, 3069, 37644)


X(46263) = X(1)X(75) ∩ X(91)X(255)

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

X(46263) lies on these lines: {1, 75}, {91, 255}, {92, 6149}, {1895, 36063}

X(46263) = barycentric product X(75)*X(46262)
X(46263) = trilinear product X(2)*X(46262)
X(46263) = trilinear product of PU(175)


X(46264) = REFLECTION OF X(4) IN X(182)

Barycentrics    3*a^6 - a^4*b^2 - a^2*b^4 - b^6 - a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 + b^2*c^4 - c^6 : :
X(46264) = 3 X[2] - 4 X[5092], 5 X[2] - 4 X[25561], 15 X[2] - 14 X[42786], 3 X[3] - 2 X[141], 3 X[3] - X[18440], 7 X[3] - 6 X[21167], 3 X[4] - 5 X[3618], 2 X[4] - 3 X[14561], 3 X[4] - 4 X[19130], X[4] - 3 X[25406], 5 X[4] - 8 X[25555], 2 X[5] - 3 X[5085], 2 X[6] - 3 X[11179], 4 X[6] - 3 X[20423], 3 X[6] - 2 X[21850], X[6] - 3 X[43273], 4 X[6] - X[43621], 3 X[20] + X[193], X[69] - 3 X[376], 2 X[113] - 3 X[15462], 4 X[140] - 3 X[10516], 4 X[141] - 3 X[1352], 7 X[141] - 9 X[21167], X[141] - 3 X[44882], 3 X[165] - X[39885], 6 X[182] - 5 X[3618], 4 X[182] - 3 X[14561], 2 X[182] + X[14927], 3 X[182] - 2 X[19130], 2 X[182] - 3 X[25406], 5 X[182] - 4 X[25555], X[193] - 3 X[6776], 2 X[355] - 3 X[38116], 3 X[376] - 2 X[3098], 3 X[376] + X[39874], 3 X[381] - 4 X[3589], 3 X[381] - 5 X[12017], 2 X[381] - 3 X[38064], X[382] - 3 X[5050], 3 X[382] - 8 X[6329], 4 X[546] - 7 X[10541], 2 X[546] - 3 X[38110], 4 X[548] - X[15069], 4 X[548] - 3 X[31884], 6 X[549] - 5 X[3763], 3 X[549] - 2 X[18358], 6 X[550] - X[40341], 4 X[575] - X[3146], 4 X[575] - 3 X[14853], 2 X[576] + X[3529], 2 X[576] - 3 X[14912], 5 X[631] - 6 X[17508], 5 X[631] - 4 X[24206], 2 X[946] - 3 X[38029], 3 X[1350] - X[40341], 3 X[1351] - 4 X[32455], 3 X[1352] - 2 X[18440]
2

X(46264) lies on the cubic K1249 and these lines: {2, 1495}, {3, 66}, {4, 83}, {5, 5085}, {6, 30}, {20, 185}, {22, 1899}, {23, 18911}, {25, 37648}, {26, 35217}, {35, 12588}, {36, 12589}, {51, 7500}, {67, 12041}, {68, 34436}, {69, 74}, {98, 17008}, {110, 16063}, {113, 206}, {114, 7710}, {115, 5033}, {125, 7493}, {140, 10516}, {146, 19140}, {147, 7897}, {154, 1368}, {165, 39885}, {184, 1370}, {315, 7470}, {317, 35474}, {355, 38116}, {381, 3589}, {382, 5050}, {389, 31305}, {394, 7667}, {427, 3796}, {428, 10601}, {458, 16264}, {516, 24257}, {518, 18481}, {524, 3534}, {546, 10541}, {548, 15069}, {549, 3763}, {550, 1350}, {572, 36474}, {575, 3146}, {576, 3529}, {578, 34938}, {597, 3830}, {599, 8703}, {611, 7354}, {613, 6284}, {623, 33381}, {624, 33380}, {631, 17508}, {732, 8725}, {858, 6800}, {946, 38029}, {1147, 17712}, {1351, 1657}, {1353, 11477}, {1386, 12699}, {1428, 1479}, {1469, 4299}, {1478, 2330}, {1498, 12362}, {1511, 14982}, {1568, 28708}, {1595, 37476}, {1691, 3767}, {1692, 7748}, {1843, 18533}, {1853, 6676}, {1885, 44503}, {1975, 44251}, {1992, 11001}, {2030, 43448}, {2072, 31267}, {2393, 14855}, {2697, 2715}, {2777, 9970}, {2781, 17710}, {2792, 24728}, {2794, 12177}, {2854, 12121}, {2892, 13293}, {2916, 2931}, {2930, 34153}, {2937, 22550}, {3054, 40248}, {3056, 4302}, {3060, 20062}, {3066, 10301}, {3070, 19145}, {3071, 19146}, {3091, 20190}, {3242, 34773}, {3313, 13754}, {3416, 3579}, {3424, 15819}, {3431, 45835}, {3448, 7492}, {3522, 5921}, {3523, 18553}, {3524, 3619}, {3528, 33751}, {3543, 5476}, {3545, 7919}, {3546, 10282}, {3547, 18381}, {3587, 5227}, {3620, 10304}, {3627, 18583}, {3629, 15681}, {3630, 15689}, {3631, 15688}, {3785, 14994}, {3819, 14826}, {3853, 38136}, {3867, 18494}, {3923, 29040}, {4232, 32237}, {4260, 6869}, {4265, 5820}, {4549, 5663}, {5002, 32619}, {5003, 32618}, {5012, 7391}, {5026, 6033}, {5028, 7756}, {5034, 7747}, {5054, 34573}, {5059, 5097}, {5064, 37649}, {5093, 12007}, {5094, 13394}, {5116, 31401}, {5138, 5800}, {5157, 18420}, {5181, 38726}, {5182, 10722}, {5189, 11003}, {5204, 39892}, {5207, 7763}, {5217, 39891}, {5224, 13634}, {5241, 19544}, {5254, 40825}, {5422, 34603}, {5486, 8547}, {5596, 6000}, {5622, 10733}, {5640, 7519}, {5652, 32472}, {5654, 14791}, {5731, 39898}, {5805, 38115}, {5816, 36477}, {5846, 12702}, {5847, 31730}, {5848, 38761}, {5870, 21737}, {5871, 33347}, {5878, 12605}, {5890, 44831}, {5907, 34781}, {5943, 6995}, {5965, 12254}, {5967, 36163}, {5969, 38730}, {5972, 16051}, {5984, 6194}, {5999, 7777}, {6030, 23293}, {6034, 22515}, {6101, 9936}, {6144, 15686}, {6146, 11414}, {6193, 15644}, {6240, 39588}, {6241, 41716}, {6403, 11663}, {6459, 39875}, {6460, 39876}, {6593, 7728}, {6636, 11442}, {6643, 6759}, {6644, 20987}, {6655, 39141}, {6688, 7398}, {6698, 38728}, {6756, 9815}, {6803, 13347}, {6804, 44862}, {6816, 26883}, {6985, 36741}, {6997, 43650}, {7171, 7289}, {7386, 9306}, {7387, 39571}, {7395, 16655}, {7401, 13419}, {7467, 15652}, {7487, 9729}, {7488, 26937}, {7494, 21243}, {7509, 16659}, {7512, 11457}, {7525, 32140}, {7528, 13336}, {7553, 36752}, {7581, 42833}, {7582, 42832}, {7612, 35021}, {7694, 15980}, {7714, 18928}, {7716, 37458}, {7735, 41412}, {7791, 9873}, {7813, 30270}, {8177, 12188}, {8182, 9830}, {8229, 31229}, {8546, 35001}, {8584, 15685}, {8588, 19905}, {8717, 11579}, {8722, 10991}, {9053, 18526}, {9730, 9969}, {9738, 12257}, {9739, 12256}, {9753, 39750}, {9756, 37451}, {9822, 16836}, {9909, 13567}, {9924, 44241}, {9967, 10575}, {9993, 16989}, {10024, 20300}, {10065, 32243}, {10081, 32297}, {10154, 26958}, {10192, 21968}, {10201, 20304}, {10249, 15760}, {10323, 34224}, {10356, 32956}, {10565, 23291}, {10574, 31304}, {10605, 26926}, {10691, 17811}, {10721, 32271}, {10748, 14688}, {10783, 42858}, {10784, 42859}, {11002, 20063}, {11061, 12244}, {11064, 26864}, {11160, 15697}, {11245, 33586}, {11427, 44442}, {11433, 34608}, {11456, 20806}, {11464, 28408}, {11479, 16621}, {11541, 22234}, {11585, 23041}, {11646, 12042}, {11649, 13619}, {11676, 35424}, {11750, 19131}, {11898, 15696}, {12022, 12082}, {12054, 42534}, {12088, 18912}, {12100, 21358}, {12103, 34380}, {12167, 37196}, {12225, 44469}, {12241, 39568}, {12294, 44479}, {12295, 15118}, {12902, 25328}, {12918, 28343}, {13329, 36674}, {13331, 14881}, {13346, 18925}, {13354, 31958}, {13369, 24476}, {13403, 43810}, {13470, 19154}, {13564, 25738}, {13608, 31731}, {13635, 17234}, {13665, 13910}, {13748, 18539}, {13749, 26438}, {13785, 13972}, {14227, 36703}, {14242, 36701}, {14389, 31133}, {14538, 41021}, {14539, 41020}, {14683, 33884}, {14708, 40949}, {14848, 15684}, {14852, 16618}, {14893, 38079}, {15035, 41737}, {15041, 32306}, {15061, 32274}, {15074, 34350}, {15078, 26156}, {15107, 37644}, {15160, 41519}, {15161, 41518}, {15311, 34774}, {15326, 39873}, {15338, 39897}, {15516, 33748}, {15520, 33749}, {15533, 15690}, {15534, 19710}, {15595, 37188}, {15687, 38072}, {15693, 20582}, {15695, 22165}, {15988, 17579}, {16010, 32423}, {16165, 32227}, {16190, 39886}, {16196, 17821}, {16237, 18880}, {16370, 26543}, {16475, 41869}, {16491, 31162}, {16661, 34799}, {16776, 40280}, {16964, 36758}, {16965, 36757}, {17714, 18952}, {17810, 45298}, {17834, 18914}, {17845, 31829}, {18128, 18951}, {18325, 32217}, {18382, 19127}, {18400, 19126}, {18475, 44441}, {18480, 38047}, {18482, 38186}, {18483, 38049}, {18510, 36718}, {18512, 36734}, {18536, 32063}, {18537, 19137}, {18563, 34117}, {18564, 38790}, {18580, 34513}, {18917, 37478}, {18935, 35513}, {19118, 44438}, {19161, 40647}, {19459, 21312}, {19708, 21356}, {19925, 38118}, {20021, 37184}, {20477, 44252}, {20771, 38794}, {20791, 43129}, {21659, 37201}, {21732, 22260}, {21736, 43120}, {22338, 28662}, {22486, 33193}, {22683, 44667}, {22685, 44666}, {22687, 41022}, {22689, 41023}, {22791, 38315}, {22793, 38035}, {22796, 37170}, {22797, 37171}, {23292, 34609}, {24248, 29097}, {24309, 29046}, {24695, 29301}, {25320, 32273}, {25562, 41134}, {25565, 41106}, {25898, 37038}, {26118, 37527}, {26341, 36712}, {26348, 36711}, {26361, 45554}, {26362, 45555}, {26869, 32269}, {30739, 35259}, {31804, 37498}, {32191, 37481}, {32216, 35266}, {32218, 37958}, {32223, 37643}, {32250, 38727}, {32599, 33532}, {33703, 39561}, {33851, 38723}, {34511, 35002}, {34778, 44249}, {34787, 44240}, {35243, 37485}, {35422, 35925}, {35423, 35930}, {35840, 42267}, {35841, 42266}, {35934, 41328}, {36181, 46124}, {36213, 37190}, {36696, 44987}, {36709, 43119}, {36714, 43118}, {36883, 38623}, {37342, 45552}, {37343, 45553}, {37466, 40278}, {37638, 44210}, {37665, 44422}, {37689, 38010}, {37931, 41584}, {38040, 40273}, {39560, 40279}, {41005, 44248}, {41424, 44212}, {41482, 41714}, {41614, 44458}, {43407, 44502}, {43408, 44501}

X(46264) = midpoint of X(i) and X(j) for these {i,j}: {4, 14927}, {20, 6776}, {69, 39874}, {1351, 1657}, {1353, 15704}, {1992, 11001}, {6241, 41716}, {9967, 10575}, {11061, 12244}, {33878, 39899}
X(46264) = reflection of X(i) in X(j) for these {i,j}: {3, 44882}, {4, 182}, {66, 44883}, {67, 12041}, {69, 3098}, {146, 19140}, {194, 32429}, {382, 5480}, {599, 8703}, {1350, 550}, {1351, 8550}, {1352, 3}, {2892, 13293}, {2930, 34153}, {3242, 34773}, {3416, 3579}, {3448, 32305}, {3543, 5476}, {3627, 18583}, {3818, 5092}, {3830, 597}, {5181, 38726}, {5486, 8547}, {5596, 34776}, {5878, 19149}, {5921, 34507}, {6033, 5026}, {7728, 6593}, {9833, 36989}, {10721, 32271}, {10748, 14688}, {11179, 43273}, {11477, 1353}, {11646, 12042}, {11663, 6403}, {12294, 44479}, {12295, 15118}, {12699, 1386}, {12902, 25328}, {12918, 28343}, {14561, 25406}, {14982, 1511}, {18325, 32217}, {18438, 17710}, {18440, 141}, {19161, 40647}, {20423, 11179}, {22338, 28662}, {24476, 13369}, {31670, 6}, {34118, 15578}, {34507, 14810}, {34775, 23300}, {36883, 38623}, {36990, 5}, {39879, 34782}, {39884, 140}, {40107, 33751}, {40949, 14708}, {41735, 6759}, {43621, 31670}, {44439, 15074}, {44456, 3629}
X(46264) = anticomplement of X(3818)
X(46264) = crossdifference of every pair of points on line {2451, 2485}
X(46264) = X(182)-of-anti-Euler-triangle
X(46264) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 18437, 6389}, {3, 18440, 141}, {4, 182, 14561}, {4, 3618, 19130}, {4, 25406, 182}, {6, 31670, 20423}, {69, 376, 3098}, {125, 35268, 7493}, {140, 39884, 10516}, {141, 18440, 1352}, {182, 7790, 43456}, {182, 19130, 3618}, {376, 9862, 14907}, {376, 39874, 69}, {381, 12017, 3589}, {382, 5050, 5480}, {549, 18358, 3763}, {616, 617, 32833}, {3522, 5921, 10519}, {3522, 10519, 14810}, {3534, 39899, 33878}, {3589, 12017, 38064}, {3618, 19130, 14561}, {3620, 11180, 43150}, {3818, 5092, 2}, {3818, 42786, 25561}, {4299, 39900, 1469}, {4302, 39901, 3056}, {5085, 36990, 5}, {5921, 10519, 34507}, {6560, 6561, 2549}, {6636, 11442, 43653}, {6756, 37514, 9815}, {7386, 11206, 9306}, {7494, 32064, 21243}, {8982, 26441, 11257}, {10249, 34775, 23300}, {10653, 10654, 7739}, {10984, 19124, 182}, {11179, 31670, 6}, {11550, 22352, 2}, {13419, 37515, 7401}, {14810, 34507, 10519}, {14927, 25406, 4}, {16051, 35260, 5972}, {17508, 24206, 631}, {20423, 43621, 31670}, {26864, 31152, 11064}, {33750, 40330, 3523}, {41979, 41980, 15048}, {42085, 42086, 43619}


X(46265) = X(2)X(18376)∩X(5)X(32903)

Barycentrics    8*a^10-19*(b^2+c^2)*a^8+7*(b^4+4*b^2*c^2+c^4)*a^6+13*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(11*b^4+12*b^2*c^2+11*c^4)*a^2+2*(b^4-c^4)*(b^2-c^2)^3 : :
X(46265) = 5*X(2)-X(18376), 2*X(5)+X(32903), 4*X(140)-X(32767), X(154)+7*X(15701), 3*X(549)+X(10192), 3*X(549)-X(10193), 5*X(549)-X(23328), 5*X(631)+X(10282), 15*X(631)+X(11206), 5*X(631)-X(23329), 3*X(10182)-X(10192), 3*X(10182)+X(10193), 5*X(10182)+X(23328), 5*X(10192)+3*X(23328), 5*X(10193)-3*X(23328), 3*X(10282)-X(11206), 5*X(10282)+X(14216), 5*X(11206)+3*X(14216), X(11206)+3*X(23329), X(14216)-5*X(23329)

See Antreas Hatzipolakis and César Lozada, euclid 3484.

X(46265) lies on these lines: {2, 18376}, {5, 32903}, {140, 13470}, {154, 15701}, {511, 34477}, {549, 6000}, {631, 10282}, {632, 23324}, {1503, 11812}, {1853, 5054}, {2777, 12100}, {3523, 12250}, {3525, 34785}, {3526, 18383}, {3530, 15311}, {3819, 10628}, {5892, 44325}, {5943, 44214}, {6759, 15720}, {7568, 32415}, {10168, 10169}, {10303, 18381}, {10606, 15707}, {11204, 15693}, {11245, 44673}, {12108, 25563}, {13289, 15246}, {13367, 43808}, {14864, 17821}, {14869, 20299}, {15694, 23325}, {15713, 23332}, {15717, 22802}, {15722, 35450}, {34786, 46219}

X(46265) = midpoint of X(i) and X(j) for these {i, j}: {549, 10182}, {10192, 10193}, {10282, 23329}
X(46265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (549, 10192, 10193), (10182, 10193, 10192)


X(46266) = X(2)X(38710)∩X(3090)X(32536)

Barycentrics    2*a^16-16*(b^2+c^2)*a^14+12*(5*b^4+7*b^2*c^2+5*c^4)*a^12-3*(b^2+c^2)*(43*b^4+10*b^2*c^2+43*c^4)*a^10+11*(15*b^8+15*c^8+8*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^8-(b^4-c^4)*(b^2-c^2)*(122*b^4+29*b^2*c^2+122*c^4)*a^6+(46*b^8+46*c^8-(49*b^4+68*b^2*c^2+49*c^4)*b^2*c^2)*(b^2-c^2)^2*a^4-(b^4-c^4)*(b^2-c^2)^3*(5*b^4-39*b^2*c^2+5*c^4)*a^2-(b^4+9*b^2*c^2+c^4)*(b^2-c^2)^6 : :
Barycentrics    19*S^4+(R^2*(116*R^2-5*SA-84*SW)+2*SA^2-5*SB*SC+13*SW^2)*S^2+(R^2*(36*R^2-31*SW)+7*SW^2)*SB*SC : :
X(46266) = 7*X(3090)-X(32536), 4*X(3628)-X(34598), 11*X(5070)+X(30484), 2*X(16239)+X(32904)

See Antreas Hatzipolakis and César Lozada, euclid 3484.

X(46266) lies on these lines: {2, 38710}, {3090, 32536}, {3628, 34598}, {5070, 30484}, {10124, 18400}, {16239, 32904}, {25150, 34479}, {35728, 41992}


X(46267) = X(2)X(575)∩X(182)X(381)

Barycentrics    8*a^6-11*(b^2+c^2)*a^4+(b^4-24*b^2*c^2+c^4)*a^2+2*(b^4-c^4)*(b^2-c^2) : :
X(46267) = 5*X(2)-X(34507), 3*X(6)+5*X(15694), 2*X(140)+X(22330), 3*X(182)+X(381), 11*X(182)+X(36990), 5*X(182)-X(43273), X(376)+15*X(3618), X(376)-3*X(5092), X(376)+3*X(5476), 5*X(376)+3*X(31670), X(376)-9*X(38064), 11*X(381)-3*X(36990), 5*X(381)+3*X(43273), 5*X(575)+X(34507), 5*X(3618)+X(5092), 5*X(3618)-X(5476), 5*X(3618)+3*X(38064), 5*X(5092)+X(31670), X(5092)-3*X(38064), X(20190)+2*X(25555), 5*X(36990)+11*X(43273)

See Antreas Hatzipolakis and César Lozada, euclid 3484.

X(46267) lies on these lines: {2, 575}, {6, 15694}, {30, 20190}, {140, 22330}, {182, 381}, {376, 3618}, {511, 549}, {524, 10124}, {542, 547}, {576, 5054}, {599, 15723}, {632, 22165}, {1003, 39498}, {1350, 15718}, {1503, 11737}, {2030, 7753}, {3055, 41672}, {3098, 14848}, {3526, 15534}, {3543, 14561}, {3628, 33749}, {3830, 10541}, {3849, 8590}, {5050, 11178}, {5055, 18553}, {5071, 11179}, {5085, 15681}, {5097, 15702}, {5480, 15686}, {5643, 37907}, {5943, 7426}, {5965, 20582}, {7603, 10485}, {7708, 30516}, {8550, 15699}, {8584, 11539}, {8787, 34127}, {9466, 32149}, {9729, 44218}, {10169, 10182}, {11477, 15701}, {11649, 13363}, {11812, 41153}, {11842, 15810}, {12017, 15684}, {13334, 37461}, {13846, 44657}, {13847, 44656}, {14093, 17508}, {14537, 39560}, {14762, 32135}, {14810, 15692}, {14893, 29012}, {15018, 32225}, {15082, 40112}, {15687, 19130}, {15691, 29317}, {15714, 21850}, {16241, 44497}, {16242, 44498}, {16962, 44511}, {16963, 44512}, {18583, 19924}, {20301, 37347}, {21401, 35303}, {21402, 35304}, {22352, 37901}, {22486, 43147}, {31152, 44491}, {32787, 44481}, {32788, 44482}, {32907, 37351}, {32909, 37352}, {35404, 44882}, {44214, 44479}

X(46267) = midpoint of X(i) and X(j) for these {i, j}: {2, 575}, {597, 10168}, {5092, 5476}, {8584, 40107}, {10169, 10182}, {11179, 25561}, {14810, 20423}, {22486, 43147}
X(46267) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (597, 38110, 10168), (3618, 38064, 5476), (5476, 38064, 5092), (8584, 11539, 40107), (11179, 38317, 25561)


X(46268) = (name pending)

Barycentrics    a*(a*x^2-(b+2*c)*x*y-(2*b+c)*x*z-2*(b+c)*y*z) : :, where x:y:z=cos(A/2):cos(B/2):cos(C/2)

See Stanley Rabinowitz, Ivan Pavlov and César Lozada, euclid 3111 and euclid 3489.

X(46268) lies on this line: {37, 259}


X(46269) = (name pending)

Barycentrics    a*(2*x^2*y^2+5*x^2*y*z+2*x^2*z^2+6*x*y^2*z+6*x*y*z^2+4*y^2*z^2) : :, where x:y:z=cos(A/2):cos(B/2):cos(C/2)

See Stanley Rabinowitz and César Lozada, euclid 3072 and euclid 3489.

X(46269) lies on these lines: { }




leftri  Centers related to bicentric pairs PU(176) to PU(196): X(46270) - X(46328)  rightri

Centers X(46270)-X(46328) were contributed by César Eliud Lozada, December 8, 2021.

underbar

X(46270) = ISOGONAL CONJUGATE OF X(9412)

Barycentrics    (a^8-(7*b^2-5*c^2)*a^6+(6*b^4+7*b^2*c^2-12*c^4)*a^4+(b^2-c^2)*(5*b^4-12*b^2*c^2-5*c^4)*a^2-(5*b^4+5*b^2*c^2-c^4)*(b^2-c^2)^2)*(a^8+(5*b^2-7*c^2)*a^6-(12*b^4-7*b^2*c^2-6*c^4)*a^4+(b^2-c^2)*(5*b^4+12*b^2*c^2-5*c^4)*a^2+(b^4-5*b^2*c^2-5*c^4)*(b^2-c^2)^2) : :
X(46270) = 9*X(23582)-10*X(36435)

X(46270) lies on the cubic K860 and these lines: {2, 9410}, {30, 39358}, {10304, 35912}, {11064, 44575}, {23582, 36435}, {31621, 39008}, {44577, 46106}

X(46270) = reflection of X(31621) in X(39008)
X(46270) = anticomplement of X(9410)
X(46270) = isogonal conjugate of X(9412)
X(46270) = isotomic conjugate of X(39358)
X(46270) = barycentric quotient X(i)/X(j) for these (i, j): (30, 34582), (1494, 9410)
X(46270) = trilinear pole of the line {9033, 11049}
X(46270) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(30)}} and {{A, B, C, X(3), X(44577)}}
X(46270) = cevapoint of X(525) and X(39008)
X(46270) = X(1494)-cross conjugate of-X(2)
X(46270) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (30, 34582), (1494, 9410)
X(46270) = cevapoint of PU(176)


X(46271) = ISOTOMIC CONJUGATE OF X(39355)

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

X(46271) lies on the cubic K355 and these lines: {2, 39058}, {182, 32545}, {385, 41204}, {401, 12215}, {511, 39355}

X(46271) = anticomplement of X(39058)
X(46271) = isogonal conjugate of X(46272)
X(46271) = isotomic conjugate of X(39355)
X(46271) = cyclocevian conjugate of the anticomplement of X(40601)
X(46271) = barycentric quotient X(i)/X(j) for these (i, j): (1, 39342), (290, 39058)
X(46271) = trilinear quotient X(2)/X(39342)
X(46271) = trilinear pole of the line {6130, 24284}
X(46271) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(182)}} and {{A, B, C, X(4), X(401)}}
X(46271) = cevapoint of X(525) and X(38974)
X(46271) = X(290)-cross conjugate of-X(2)
X(46271) = X(9)-Dao conjugate of-X(39342)
X(46271) = X(6)-isoconjugate-of-X(39342)
X(46271) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 39342), (290, 39058)
X(46271) = cevapoint of PU(177)


X(46272) = ISOGONAL CONJUGATE OF X(46271)

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

X(46272) lies on these lines: {3, 1625}, {6, 98}, {25, 694}, {217, 37334}, {1691, 9418}, {1979, 2352}, {2076, 13236}, {2421, 5989}, {3053, 9431}, {3289, 5999}, {3331, 11676}, {5116, 5621}, {9259, 23383}, {9862, 45910}, {13330, 33983}

X(46272) = isogonal conjugate of X(46271)
X(46272) = barycentric product X(i)*X(j) for these {i, j}: {1, 39342}, {6, 39355}, {237, 39058}
X(46272) = trilinear product X(i)*X(j) for these {i, j}: {6, 39342}, {31, 39355}
X(46272) = intersection, other than A, B, C, of circumconics {{A, B, C, X(25), X(32542)}} and {{A, B, C, X(98), X(39683)}}
X(46272) = crossdifference of every pair of points on line {X(6130), X(24284)}
X(46272) = crosssum of X(525) and X(38974)
X(46272) = crosspoint of PU(89)
X(46272) = X(237)-Ceva conjugate of-X(6)
X(46272) = X(290)-Dao conjugate of-X(18024)
X(46272) = X(6)-Hirst inverse of-X(9419)
X(46272) = crosssum of PU(177)
X(46272) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (98, 9419, 6), (98, 26714, 9419)


X(46273) = ISOGONAL CONJUGATE OF X(9417)

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

X(46273) lies on the cubics K865, K1023 and these lines: {1, 336}, {63, 561}, {72, 290}, {75, 23996}, {98, 789}, {293, 1966}, {304, 1928}, {306, 1978}, {850, 30995}, {1214, 1920}, {1910, 4593}, {1926, 46238}, {1956, 40703}, {22456, 26702}, {40017, 43665}

X(46273) = isogonal conjugate of X(9417)
X(46273) = isotomic conjugate of X(1755)
X(46273) = polar conjugate of the isogonal conjugate of X(336)
X(46273) = barycentric product X(i)*X(j) for these {i, j}: {1, 18024}, {75, 290}, {76, 1821}, {98, 561}, {264, 336}, {287, 1969}
X(46273) = barycentric quotient X(i)/X(j) for these (i, j): (1, 237), (10, 5360), (19, 2211), (31, 9418), (63, 3289), (75, 511)
X(46273) = trilinear product X(i)*X(j) for these {i, j}: {2, 290}, {6, 18024}, {69, 16081}, {75, 1821}, {76, 98}, {92, 336}
X(46273) = trilinear quotient X(i)/X(j) for these (i, j): (2, 237), (4, 2211), (6, 9418), (69, 3289), (76, 511), (95, 41270)
X(46273) = trilinear pole of the line {75, 656}
X(46273) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(63)}} and {{A, B, C, X(75), X(3403)}}
X(46273) = cevapoint of X(i) and X(j) for these (i, j): {1, 16564}, {75, 1959}, {312, 35544}, {336, 1821}
X(46273) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 237), (37, 5360), (244, 2491), (290, 39342)
X(46273) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 9418}, {3, 2211}, {6, 237}, {25, 3289}
X(46273) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 237), (10, 5360), (19, 2211), (31, 9418)
X(46273) = trilinear product of PU(177)


X(46274) = ISOGONAL CONJUGATE OF X(9431)

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

X(46274) lies on these lines: {2, 9428}, {512, 25054}, {3231, 40858}, {38294, 44371}, {39010, 44168}

X(46274) = reflection of X(44168) in X(39010)
X(46274) = anticomplement of X(9428)
X(46274) = isogonal conjugate of X(9431)
X(46274) = isotomic conjugate of X(25054)
X(46274) = cyclocevian conjugate of the anticomplement of X(38996)
X(46274) = antigonal conjugate of the isogonal conjugate of X(9430)
X(46274) = barycentric quotient X(i)/X(j) for these (i, j): (1, 39337), (3, 23180), (512, 38237), (670, 9428)
X(46274) = trilinear quotient X(i)/X(j) for these (i, j): (2, 39337), (63, 23180), (661, 38237)
X(46274) = trilinear pole of the line {888, 36950}
X(46274) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1655)}} and {{A, B, C, X(2), X(512)}}
X(46274) = cevapoint of X(538) and X(39010)
X(46274) = X(670)-cross conjugate of-X(2)
X(46274) = X(i)-Dao conjugate of-X(j) for these (i, j): (6, 23180), (9, 39337), (1084, 38237)
X(46274) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 39337}, {19, 23180}, {662, 38237}
X(46274) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 39337), (3, 23180), (512, 38237), (670, 9428)
X(46274) = cevapoint of PU(178)


X(46275) = ISOTOMIC CONJUGATE OF X(8591)

Barycentrics    (a^4+(5*b^2-7*c^2)*a^2-5*b^4+5*b^2*c^2+c^4)*(a^4-(7*b^2-5*c^2)*a^2+b^4+5*b^2*c^2-5*c^4) : :
X(46275) = X(148)-4*X(18823) = X(8591)+2*X(39356)

X(46275) lies on the curve Q124 and these lines: {2, 39061}, {148, 18823}, {468, 8859}, {523, 41135}, {524, 8591}, {543, 35511}, {3266, 41136}, {5032, 5967}, {5486, 32480}, {34763, 44010}

X(46275) = anticomplement of X(39061)
X(46275) = isogonal conjugate of X(46276)
X(46275) = isotomic conjugate of X(8591)
X(46275) = cyclocevian conjugate of X(67)
X(46275) = barycentric quotient X(i)/X(j) for these (i, j): (1, 39339), (111, 41404), (524, 38239), (671, 39061)
X(46275) = trilinear quotient X(i)/X(j) for these (i, j): (2, 39339), (897, 41404)
X(46275) = trilinear pole of the line {690, 5461}
X(46275) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(468)}} and {{A, B, C, X(4), X(9855)}}
X(46275) = cevapoint of X(i) and X(j) for these (i, j): {2, 8596}, {523, 23992}
X(46275) = X(671)-cross conjugate of-X(2)
X(46275) = X(9)-Dao conjugate of-X(39339)
X(46275) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 39339}, {896, 41404}, {922, 39061}, {923, 38239}
X(46275) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 39339), (111, 41404), (524, 38239), (671, 39061)
X(46275) = cevapoint of PU(180)


X(46276) = ISOGONAL CONJUGATE OF X(46275)

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

X(46276) lies on these lines: {2, 8786}, {3, 40251}, {6, 110}, {25, 41911}, {31, 5168}, {48, 10987}, {154, 5191}, {184, 8585}, {187, 9225}, {351, 39232}, {352, 2076}, {353, 5116}, {524, 7665}, {574, 2936}, {599, 7664}, {843, 9217}, {1384, 1613}, {1495, 5104}, {1511, 45723}, {1641, 14360}, {1648, 9143}, {1915, 5008}, {1979, 5163}, {2030, 3506}, {2434, 10355}, {3053, 9486}, {3292, 8586}, {3569, 9412}, {3763, 40915}, {5026, 35279}, {5029, 21781}, {5108, 31128}, {5642, 11646}, {6437, 7598}, {6438, 7599}, {6439, 7601}, {6440, 7602}, {6719, 18800}, {8566, 37457}, {8591, 38239}, {9830, 30786}, {9872, 18374}, {9966, 15871}, {10540, 40115}, {10552, 15534}, {11061, 44915}, {11580, 14567}, {13192, 15514}, {14729, 45769}, {15504, 41424}, {15993, 35266}, {20481, 39560}, {37477, 40237}, {38623, 45722}, {40350, 44496}

X(46276) = midpoint of X(7665) and X(10553)
X(46276) = isogonal conjugate of X(46275)
X(46276) = barycentric product X(i)*X(j) for these {i, j}: {1, 39339}, {6, 8591}, {111, 38239}, {187, 39061}, {524, 41404}
X(46276) = trilinear product X(i)*X(j) for these {i, j}: {6, 39339}, {31, 8591}, {896, 41404}, {922, 39061}, {923, 38239}
X(46276) = perspector of the circumconic {{A, B, C, X(691), X(41404)}}
X(46276) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(38239)}} and {{A, B, C, X(111), X(8591)}}
X(46276) = crossdifference of every pair of points on line {X(690), X(5461)}
X(46276) = crosspoint of X(110) and X(34539)
X(46276) = crosspoint of PU(107)
X(46276) = crosssum of X(i) and X(j) for these (i, j): {2, 8596}, {523, 23992}
X(46276) = X(187)-Ceva conjugate of-X(6)
X(46276) = X(671)-Dao conjugate of-X(18023)
X(46276) = X(i)-Hirst inverse of-X(j) for these (i, j): {6, 39689}, {187, 41449}
X(46276) = X(351)-vertex conjugate of-X(39689)
X(46276) = crosssum of PU(180)
X(46276) = X(20998)-of-circumsymmedial triangle
X(46276) = X(41911)-of-Ara triangle
X(46276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 2502, 20998), (110, 111, 39689), (110, 2502, 6), (111, 39689, 6), (184, 8585, 10485), (2502, 39689, 111), (6593, 42007, 6)


X(46277) = ISOGONAL CONJUGATE OF X(922)

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

X(46277) lies on these lines: {75, 799}, {92, 811}, {111, 789}, {313, 1978}, {321, 668}, {523, 30992}, {561, 4602}, {892, 14616}, {923, 3112}, {1441, 4554}, {1821, 14206}, {1966, 17955}, {2157, 16568}, {4583, 31125}, {5466, 40017}, {14210, 18075}

X(46277) = isogonal conjugate of X(922)
X(46277) = isotomic conjugate of X(896)
X(46277) = complement of anticomplementary conjugate of X(21298)
X(46277) = anticomplement of complementary conjugate of X(21256)
X(46277) = trilinear pole of the line {75, 1577}
X(46277) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2157)}} and {{A, B, C, X(2), X(29615)}}
X(46277) = cevapoint of X(i) and X(j) for these (i, j): {1, 16568}, {2, 17491}, {6, 23862}, {10, 22047}
X(46277) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 187), (37, 21839), (115, 2642), (244, 351)
X(46277) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 14567}, {3, 44102}, {4, 23200}, {6, 187}
X(46277) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 187), (10, 21839), (19, 44102), (31, 14567)
X(46277) = trilinear product of PU(180)
X(46277) = barycentric product X(i)*X(j) for these {i, j}: {1, 18023}, {63, 46111}, {75, 671}, {76, 897}, {92, 30786}, {111, 561}
X(46277) = barycentric quotient X(i)/X(j) for these (i, j): (1, 187), (10, 21839), (19, 44102), (31, 14567), (48, 23200), (63, 3292)
X(46277) = trilinear product X(i)*X(j) for these {i, j}: {2, 671}, {3, 46111}, {4, 30786}, {6, 18023}, {69, 17983}, {75, 897}
X(46277) = trilinear quotient X(i)/X(j) for these (i, j): (2, 187), (3, 23200), (4, 44102), (6, 14567), (69, 3292), (76, 524)
X(46277) = {X(1109), X(20939)}-harmonic conjugate of X(799)


X(46278) = ISOGONAL CONJUGATE OF X(39087)

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

X(46278) lies on these lines: {385, 706}, {736, 3978}, {3114, 35078}, {20026, 40858}, {46279, 46282}

X(46278) = reflection of X(3114) in X(35078)
X(46278) = isogonal conjugate of X(39087)
X(46278) = trilinear pole of the line {804, 24256}
X(46278) = trilinear pole of line PU(181)


X(46279) = X(3114)X(18906) ∩ X(24256)X(41073)

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

X(46279) lies on these lines: {3114, 18906}, {24256, 41073}, {46278, 46282}

X(46279) = crosspoint of PU(181)


X(46280) = X(6)X(17970) ∩ X(1915)X(23209)

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

X(46280) lies on these lines: {6, 17970}, {1915, 23209}, {3407, 39087}

X(46280) = isogonal conjugate of X(46282)
X(46280) = crosssum of PU(181)


X(46281) = ISOTOMIC CONJUGATE OF X(3116)

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

X(46281) lies on the cubic K1031 and these lines: {1, 1925}, {31, 561}, {42, 7033}, {75, 1967}, {213, 3114}, {304, 46309}, {741, 9063}, {870, 23493}, {871, 1402}, {875, 4374}, {1969, 1973}, {3402, 3403}, {18833, 46289}

X(46281) = isotomic conjugate of X(3116)
X(46281) = barycentric product X(i)*X(j) for these {i, j}: {75, 3114}, {76, 3113}, {561, 3407}, {661, 9063}, {871, 17743}
X(46281) = barycentric quotient X(i)/X(j) for these (i, j): (1, 3117), (31, 18899), (75, 3094), (82, 43977), (561, 3314), (661, 17415)
X(46281) = trilinear product X(i)*X(j) for these {i, j}: {2, 3114}, {75, 3113}, {76, 3407}, {290, 8840}, {308, 14617}, {512, 9063}
X(46281) = trilinear quotient X(i)/X(j) for these (i, j): (2, 3117), (6, 18899), (76, 3094), (83, 43977), (512, 9006), (523, 17415)
X(46281) = trilinear pole of the line {798, 20948}
X(46281) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31)}} and {{A, B, C, X(75), X(1926)}}
X(46281) = cevapoint of X(1) and X(3403)
X(46281) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 3117), (244, 17415)
X(46281) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 18899}, {6, 3117}, {32, 3094}, {39, 43977}
X(46281) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 3117), (31, 18899), (75, 3094), (82, 43977)
X(46281) = trilinear product of PU(181)


X(46282) = ISOGONAL CONJUGATE OF X(46280)

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

X(46282) lies on these lines: {46278, 46279}

X(46282) = isogonal conjugate of X(46280)
X(46282) = cevapoint of PU(181)


X(46283) = X(3)X(6) ∩ X(76)X(148)

Barycentrics    a^2*((b^2+c^2)*a^4-(b^4+c^4)*a^2-(b^4+b^2*c^2+c^4)*(b^2+c^2)) : :
X(46283) = 3*X(39)-2*X(46305) = 3*X(7811)-X(9983) = 4*X(46305)-3*X(46313)

X(46283) lies on these lines: {3, 6}, {76, 148}, {141, 15821}, {194, 14023}, {262, 31455}, {315, 8149}, {384, 10347}, {524, 41756}, {538, 7811}, {626, 5976}, {698, 7767}, {732, 7826}, {736, 7750}, {1078, 1916}, {1506, 14881}, {1569, 38749}, {2023, 7749}, {2549, 12251}, {2782, 7756}, {2979, 3117}, {3060, 8570}, {3096, 3934}, {3097, 31422}, {3099, 12782}, {3229, 3917}, {3399, 12110}, {3767, 6194}, {3785, 31981}, {3972, 10346}, {5077, 14711}, {5149, 10350}, {5254, 32521}, {5309, 33706}, {5346, 10336}, {5969, 7810}, {6248, 9996}, {6292, 24256}, {6309, 7855}, {6636, 14602}, {6656, 18806}, {6683, 7846}, {7603, 9993}, {7746, 10357}, {7760, 32476}, {7768, 9865}, {7786, 10583}, {7800, 18906}, {7801, 9890}, {7804, 10345}, {7816, 10000}, {7827, 22564}, {7841, 7865}, {7842, 39266}, {7887, 7914}, {7889, 10007}, {7890, 41651}, {7893, 10335}, {7998, 9998}, {8623, 20859}, {9482, 10332}, {9651, 10063}, {9664, 10079}, {9862, 11257}, {9873, 22678}, {9941, 14839}, {9984, 38520}, {12503, 38529}, {12837, 31451}, {13108, 44526}, {13210, 38523}, {13235, 38521}, {13236, 38525}, {14537, 34733}, {27375, 39684}, {31400, 44434}, {32450, 33275}, {33274, 44562}, {34885, 39652}, {35700, 37004}, {39590, 40279}

X(46283) = midpoint of X(9821) and X(40252)
X(46283) = reflection of X(i) in X(j) for these (i, j): (7890, 41651), (46313, 39)
X(46283) = perspector of the circumconic {{A, B, C, X(110), X(46284)}}
X(46283) = inverse of X(2076) in 2nd Brocard circle
X(46283) = Moses-circle-inverse of Gallatly-circle-inverse of X(3)
X(46283) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(11606)}} and {{A, B, C, X(54), X(44423)}}
X(46283) = crossdifference of every pair of points on line {X(523), X(39089)}
X(46283) = midpoint of PU(182)
X(46283) = X(39)-of-5th Brocard triangle
X(46283) = X(24256)-of-6th Brocard triangle
X(46283) = X(46283)-of-circumsymmedial triangle
X(46283) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 32452, 39), (3, 44453, 32452), (32, 3094, 39), (32, 35248, 15513), (39, 5052, 5041), (39, 5188, 187), (39, 8589, 13334), (39, 15513, 2021), (39, 35007, 13357), (39, 46321, 5007), (76, 7854, 44772), (574, 3095, 39), (1078, 1916, 32189), (1670, 1671, 2076), (2896, 8782, 76), (3094, 9821, 32), (3095, 9821, 9301), (3098, 9821, 5188), (13325, 13326, 6)


X(46284) = ISOGONAL CONJUGATE OF X(39089)

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

X(46284) lies on these lines: {251, 38880}, {3229, 46314}, {18898, 36213}

X(46284) = isogonal conjugate of X(39089)
X(46284) = trilinear pole of the line {512, 46283}
X(46284) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(39), X(737)}}
X(46284) = trilinear pole of line PU(182)


X(46285) = X(3)X(16986) ∩ X(76)X(10997)

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

X(46285) lies on these lines: {3, 16986}, {76, 10997}, {99, 39090}, {194, 5989}, {3552, 11606}, {3818, 10998}

X(46285) = crosssum of PU(182)


X(46286) = ISOGONAL CONJUGATE OF X(7779)

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

X(46286) lies on the cubics K252, K1001 and these lines: {2, 4048}, {6, 3506}, {37, 19557}, {42, 19561}, {110, 3108}, {111, 8627}, {237, 46306}, {251, 3124}, {308, 338}, {694, 2076}, {1976, 35006}, {2502, 39389}, {2987, 15514}, {2998, 8177}, {3589, 39938}, {3750, 9281}, {5027, 17997}, {9178, 14428}, {16606, 40597}, {21513, 36213}, {23868, 34249}, {34572, 39024}, {40802, 44453}, {46227, 46287}

X(46286) = isogonal conjugate of X(7779)
X(46286) = barycentric product X(i)*X(j) for these {i, j}: {6, 11606}, {82, 17957}, {251, 17949}
X(46286) = barycentric quotient X(i)/X(j) for these (i, j): (25, 420), (31, 17799), (32, 2076), (251, 40850), (512, 9479), (669, 5113)
X(46286) = trilinear product X(i)*X(j) for these {i, j}: {31, 11606}, {251, 17957}
X(46286) = trilinear quotient X(i)/X(j) for these (i, j): (6, 17799), (19, 420), (31, 2076), (82, 40850), (251, 34054), (661, 9479)
X(46286) = trilinear pole of the line {512, 5007}
X(46286) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(3), X(36615)}}
X(46286) = crossdifference of every pair of points on line {X(5113), X(9479)}
X(46286) = crosssum of X(732) and X(15573)
X(46286) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 2076), (1084, 9479)
X(46286) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 17799}, {38, 40850}, {63, 420}, {75, 2076}
X(46286) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 420), (31, 17799), (32, 2076), (251, 40850)
X(46286) = X(694)-vertex conjugate of-X(694)
X(46286) = trilinear pole of line PU(183)


X(46287) = ISOGONAL CONJUGATE OF X(46226)

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

X(46287) lies on these lines: {6, 2896}, {32, 10329}, {213, 21880}, {1974, 11386}, {3224, 5359}, {14885, 46288}, {24273, 40043}, {26454, 44605}, {26461, 44604}, {46227, 46286}

X(46287) = isogonal conjugate of X(46226)
X(46287) = barycentric product X(251)*X(46225)
X(46287) = barycentric quotient X(251)/X(40000)
X(46287) = trilinear quotient X(82)/X(40000)
X(46287) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(21512)}} and {{A, B, C, X(6), X(32)}}
X(46287) = X(38)-isoconjugate-of-X(40000)
X(46287) = X(251)-reciprocal conjugate of-X(40000)
X(46287) = cevapoint of PU(183)


X(46288) = ISOGONAL CONJUGATE OF X(8024)

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

X(46288) lies on the cubic K486 and these lines: {6, 22}, {32, 206}, {53, 6531}, {69, 9516}, {82, 40747}, {83, 316}, {110, 39449}, {141, 1799}, {182, 10014}, {213, 14599}, {308, 3114}, {427, 46242}, {524, 40405}, {571, 40799}, {597, 42037}, {694, 18903}, {729, 827}, {1184, 8793}, {1333, 45785}, {1485, 41382}, {1576, 9468}, {1918, 18892}, {1974, 17409}, {2373, 40404}, {2422, 18105}, {2965, 32654}, {2980, 3767}, {3053, 28724}, {3224, 38834}, {3225, 4577}, {3629, 41909}, {3763, 10130}, {4630, 32740}, {5116, 46227}, {6664, 38826}, {7735, 21458}, {9418, 46308}, {9969, 10551}, {10328, 42554}, {12212, 39674}, {14575, 46319}, {14600, 42288}, {14601, 40981}, {14885, 46287}, {15321, 39691}, {16519, 34055}, {18268, 34072}, {18374, 18902}, {19125, 22075}, {19137, 41412}, {19156, 40825}, {22331, 40322}, {26926, 46243}, {32661, 41413}, {33739, 44166}

X(46288) = isogonal conjugate of X(8024)
X(46288) = polar conjugate of the isotomic conjugate of X(10547)
X(46288) = barycentric product X(i)*X(j) for these {i, j}: {1, 46289}, {4, 10547}, {6, 251}, {25, 1176}, {31, 82}, {32, 83}
X(46288) = barycentric quotient X(i)/X(j) for these (i, j): (25, 1235), (31, 1930), (32, 141), (82, 561), (83, 1502), (184, 3933)
X(46288) = trilinear product X(i)*X(j) for these {i, j}: {6, 46289}, {19, 10547}, {31, 251}, {32, 82}, {83, 560}, {163, 18105}
X(46288) = trilinear quotient X(i)/X(j) for these (i, j): (6, 1930), (19, 1235), (25, 20883), (31, 141), (32, 38), (41, 3703)
X(46288) = trilinear pole of the line {669, 14602}
X(46288) = perspector of the circumconic {{A, B, C, X(827), X(4630)}}
X(46288) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1180)}} and {{A, B, C, X(4), X(20960)}}
X(46288) = cevapoint of X(i) and X(j) for these (i, j): {32, 1501}, {251, 38834}
X(46288) = crossdifference of every pair of points on line {X(826), X(23285)}
X(46288) = crosspoint of X(83) and X(16277)
X(46288) = crosssum of X(i) and X(j) for these (i, j): {2, 1369}, {39, 3313}, {75, 20933}, {76, 40035}
X(46288) = X(251)-Ceva conjugate of-X(10547)
X(46288) = X(32)-cross conjugate of-X(251)
X(46288) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 141), (512, 39691), (626, 16893), (1084, 23285)
X(46288) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 1930}, {10, 16703}, {38, 76}, {39, 561}
X(46288) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 1235), (31, 1930), (32, 141), (82, 561)
X(46288) = X(308)-vertex conjugate of-X(40416)
X(46288) = barycentric product of PU(183)
X(46288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 2916, 23642), (32, 206, 16285), (251, 1176, 6), (251, 33632, 1176), (8627, 23642, 2916)


X(46289) = ISOGONAL CONJUGATE OF X(1930)

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

Let A'B'C' be the 1st orthosymmedial triangle. Let A" be the trilinear product B'*C', and define B" and C" cyclically. The lines AA", BB", CC" concur in X(46289). (Randy Hutson, January 11, 2022)

X(46289) lies on the cubic K1030 and these lines: {1, 82}, {6, 20969}, {10, 26270}, {31, 1917}, {38, 40398}, {42, 251}, {83, 16889}, {163, 1923}, {213, 14599}, {741, 827}, {923, 34072}, {1176, 1203}, {1402, 10547}, {1580, 3112}, {1582, 1930}, {1799, 32783}, {2206, 40148}, {2964, 36051}, {3402, 9247}, {4577, 18826}, {4599, 37132}, {5299, 7122}, {9417, 46309}, {17192, 24707}, {17442, 32676}, {18693, 37220}, {18833, 46281}, {23493, 38834}

X(46289) = isogonal conjugate of X(1930)
X(46289) = complement of anticomplementary conjugate of X(17489)
X(46289) = trilinear pole of the line {798, 1933}
X(46289) = perspector of the circumconic {{A, B, C, X(4599), X(4628)}}
X(46289) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31)}} and {{A, B, C, X(4), X(33720)}}
X(46289) = cevapoint of X(31) and X(560)
X(46289) = crossdifference of every pair of points on line {X(16892), X(23885)}
X(46289) = crosssum of X(i) and X(j) for these (i, j): {1, 21378}, {2, 21289}, {10, 22025}, {37, 22303}
X(46289) = X(i)-cross conjugate of-X(j) for these (i, j): (31, 82), (661, 32676)
X(46289) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 8024), (206, 38), (244, 23285), (251, 21598)
X(46289) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1930}, {2, 141}, {3, 1235}, {4, 3933}, {6, 8024}
X(46289) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 8024), (19, 1235), (25, 20883), (31, 141)
X(46289) = trilinear product of PU(183)
X(46289) = barycentric product X(i)*X(j) for these {i, j}: {1, 251}, {6, 82}, {25, 34055}, {31, 83}, {32, 3112}, {48, 32085}
X(46289) = barycentric quotient X(i)/X(j) for these (i, j): (1, 8024), (19, 1235), (25, 20883), (31, 141), (32, 38), (41, 3703)
X(46289) = trilinear product X(i)*X(j) for these {i, j}: {2, 46288}, {4, 10547}, {6, 251}, {25, 1176}, {31, 82}, {32, 83}
X(46289) = trilinear quotient X(i)/X(j) for these (i, j): (2, 8024), (3, 3933), (4, 1235), (6, 141), (19, 20883), (25, 427)
X(46289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 21378, 21336), (6, 20994, 20969), (82, 34055, 1), (1923, 1932, 163), (2244, 21336, 21378)


X(46290) = X(524)X(2076) ∩ X(9293)X(17997)

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

X(46290) lies on these lines: {385, 46291}, {524, 2076}, {8290, 46293}, {9293, 17997}, {15014, 39927}

X(46290) = isogonal conjugate of X(46292)
X(46290) = barycentric product X(i)*X(j) for these {i, j}: {385, 35511}, {804, 37880}
X(46290) = barycentric quotient X(i)/X(j) for these (i, j): (385, 148), (804, 10278), (1580, 2640)
X(46290) = trilinear product X(i)*X(j) for these {i, j}: {385, 9395}, {1580, 35511}
X(46290) = trilinear quotient X(385)/X(2640)
X(46290) = X(i)-isoconjugate-of-X(j) for these {i, j}: {148, 1967}, {694, 2640}, {882, 2644}
X(46290) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (385, 148), (804, 10278)
X(46290) = cevapoint of PU(185)


X(46291) = X(99)X(112) ∩ X(385)X(46290)

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

X(46291) lies on these lines: {99, 112}, {385, 46290}, {804, 17941}, {4027, 46293}, {4577, 17997}, {9218, 31998}

X(46291) = barycentric product X(i)*X(j) for these {i, j}: {148, 17941}, {385, 31998}, {804, 31632}, {880, 20998}
X(46291) = barycentric quotient X(i)/X(j) for these (i, j): (385, 9293), (1580, 9396)
X(46291) = trilinear product X(i)*X(j) for these {i, j}: {385, 2644}, {1580, 31998}
X(46291) = trilinear quotient X(385)/X(9396)
X(46291) = perspector of the circumconic {{A, B, C, X(18020), X(31632)}}
X(46291) = intersection, other than A, B, C, of circumconics {{A, B, C, X(112), X(9218)}} and {{A, B, C, X(148), X(41676)}}
X(46291) = crossdifference of every pair of points on line {X(19610), X(20975)}
X(46291) = X(385)-Ceva conjugate of-X(17941)
X(46291) = X(99)-Dao conjugate of-X(1916)
X(46291) = X(804)-Hirst inverse of-X(17941)
X(46291) = X(i)-isoconjugate-of-X(j) for these {i, j}: {694, 9396}, {882, 9395}
X(46291) = X(385)-reciprocal conjugate of-X(9293)
X(46291) = crosspoint of PU(185)


X(46292) = ISOGONAL CONJUGATE OF X(46290)

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

X(46292) lies on these lines: {111, 694}, {232, 16068}, {732, 1916}, {882, 10097}, {1967, 9506}

X(46292) = isogonal conjugate of X(46290)
X(46292) = barycentric product X(i)*X(j) for these {i, j}: {148, 694}, {805, 10278}, {882, 31998}, {1581, 2640}
X(46292) = barycentric quotient X(i)/X(j) for these (i, j): (148, 3978), (694, 35511), (805, 37880), (882, 9293)
X(46292) = trilinear product X(i)*X(j) for these {i, j}: {148, 1967}, {694, 2640}, {882, 2644}, {1581, 20998}
X(46292) = trilinear quotient X(i)/X(j) for these (i, j): (148, 1966), (694, 9395), (882, 9396)
X(46292) = X(882)-Ceva conjugate of-X(694)
X(46292) = X(99)-Dao conjugate of-X(880)
X(46292) = X(385)-isoconjugate-of-X(9395)
X(46292) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (148, 3978), (694, 35511), (805, 37880), (882, 9293)
X(46292) = crosssum of PU(185)


X(46293) = X(99)X(25054) ∩ X(543)X(5034)

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

X(46293) lies on these lines: {99, 25054}, {543, 5034}, {804, 4107}, {4027, 46291}, {8290, 46290}

X(46293) = X(45914)-of-6th anti-Brocard triangle
X(46293) = bicentric sum of PU(185)


X(46294) = X(99)X(249) ∩ X(110)X(18829)

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

X(46294) lies on these lines: {99, 249}, {110, 18829}, {325, 19576}, {385, 14602}, {523, 4577}, {1576, 4590}, {4027, 35078}, {11183, 14959}

X(46294) = barycentric product X(i)*X(j) for these {i, j}: {1, 46295}, {99, 4027}, {385, 17941}, {880, 1691}
X(46294) = barycentric quotient X(i)/X(j) for these (i, j): (110, 41517), (880, 18896), (1691, 882)
X(46294) = trilinear product X(i)*X(j) for these {i, j}: {6, 46295}, {662, 4027}, {880, 1933}
X(46294) = trilinear quotient X(i)/X(j) for these (i, j): (662, 41517), (880, 1934)
X(46294) = X(i)-Dao conjugate of-X(j) for these (i, j): (732, 2528), (804, 8029)
X(46294) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 41517}, {881, 1934}, {882, 1581}
X(46294) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (110, 41517), (880, 18896)
X(46294) = barycentric product of PU(185)


X(46295) = X(163)X(24037) ∩ X(799)X(4575)

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

X(46295) lies on these lines: {163, 24037}, {799, 4575}, {1577, 4593}, {1933, 1966}, {19572, 46238}

X(46295) = barycentric product X(i)*X(j) for these {i, j}: {75, 46294}, {799, 4027}, {880, 1580}, {1966, 17941}
X(46295) = barycentric quotient X(i)/X(j) for these (i, j): (662, 41517), (880, 1934), (1580, 882), (1933, 881)
X(46295) = trilinear product X(i)*X(j) for these {i, j}: {2, 46294}, {99, 4027}, {385, 17941}, {880, 1691}
X(46295) = trilinear quotient X(i)/X(j) for these (i, j): (99, 41517), (385, 882), (880, 1916), (1691, 881)
X(46295) = X(i)-isoconjugate-of-X(j) for these {i, j}: {512, 41517}, {694, 882}, {881, 1916}
X(46295) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (662, 41517), (880, 1934), (1580, 882)
X(46295) = trilinear product of PU(185)


X(46296) = TRILINEAR POLE OF LINE PU(186)

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

X(46296) lies on these lines: {}

X(46296) = isogonal conjugate of X(46298)
X(46296) = trilinear pole of the line {690, 7753}
X(46296) = trilinear pole of line PU(186)


X(46297) = X(3)X(5640) ∩ X(2076)X(32154)

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

X(46297) lies on these lines: {3, 5640}, {2076, 32154}, {5012, 38661}, {5116, 32740}, {10168, 13586}, {12215, 16511}

X(46297) = crosssum of PU(186)


X(46298) = ISOGONAL CONJUGATE OF X(46296)

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

X(46298) lies on these lines: {6, 110}, {183, 9140}, {323, 34383}, {385, 542}, {399, 32595}, {526, 3005}, {1384, 38661}, {2871, 15107}, {3329, 5642}, {5008, 13193}, {5092, 12192}, {5663, 9301}, {6784, 15018}, {7766, 9143}, {7998, 9145}, {9142, 15080}, {9976, 15920}, {13210, 14901}, {33878, 38653}

X(46298) = isogonal conjugate of X(46296)
X(46298) = crossdifference of every pair of points on line {X(690), X(7753)}
X(46298) = X(385)-of-anti-orthocentroidal triangle
X(46298) = crossdifference of PU(186)


X(46299) = X(6)X(30) ∩ X(385)X(1383)

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

X(46299) lies on these lines: {6, 30}, {385, 1383}, {3124, 45819}, {7766, 20099}

X(46299) = barycentric product X(1)*X(46300)
X(46299) = trilinear product X(6)*X(46300)
X(46299) = barycentric product of PU(186)


X(46300) = TRILINEAR PRODUCT OF PU(186)

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

X(46300) lies on these lines: {1, 14206}

X(46300) = barycentric product X(75)*X(46299)
X(46300) = trilinear product X(2)*X(46299)
X(46300) = trilinear product of PU(186)


X(46301) = X(6)X(13) ∩ X(32)X(110)

Barycentrics    a^2*(2*(b^2+c^2)*a^6-4*(b^4+c^4)*a^4+2*(b^6+c^6)*a^2-(b^2-c^2)^2*b^2*c^2) : :
X(46301) = X(74)-3*X(15920) = 3*X(110)-X(13210)

X(46301) lies on the Moses circle, cubic K291 and these lines: {6, 13}, {32, 110}, {39, 5663}, {74, 574}, {112, 3043}, {125, 217}, {146, 2549}, {187, 1511}, {216, 12358}, {230, 10272}, {232, 1986}, {323, 754}, {690, 1569}, {1015, 3028}, {1112, 3199}, {1495, 2387}, {1500, 3024}, {1561, 12112}, {1571, 9904}, {1572, 2948}, {1692, 6593}, {1968, 15463}, {2021, 38650}, {2207, 19504}, {2211, 5095}, {2241, 10088}, {2242, 10091}, {2275, 19470}, {2276, 7727}, {2421, 2482}, {2493, 15544}, {2548, 3448}, {2777, 7756}, {2854, 5052}, {2914, 8744}, {2931, 9699}, {3031, 9561}, {3047, 9697}, {3053, 32609}, {3055, 40685}, {3231, 5642}, {3289, 6781}, {3331, 13202}, {3569, 9408}, {3815, 10264}, {5007, 5609}, {5013, 10620}, {5017, 12584}, {5023, 15040}, {5028, 9970}, {5033, 15462}, {5034, 11579}, {5206, 15035}, {5585, 15042}, {5972, 7749}, {6126, 16784}, {7343, 16785}, {7603, 20304}, {7722, 39575}, {7728, 7748}, {7735, 20125}, {7736, 12317}, {7737, 12383}, {7745, 32423}, {7746, 14643}, {7747, 17702}, {7755, 16534}, {7765, 15063}, {7772, 14094}, {7810, 15066}, {7812, 11004}, {8588, 15051}, {9560, 34453}, {9605, 12308}, {9619, 33535}, {9635, 10118}, {9636, 12888}, {9650, 12903}, {9651, 12373}, {9664, 12374}, {9665, 12904}, {9675, 10819}, {9684, 10817}, {9698, 16003}, {9700, 10117}, {10065, 31451}, {10113, 39590}, {10294, 41358}, {10706, 11648}, {10721, 41367}, {12041, 37512}, {12133, 33843}, {12165, 45141}, {12219, 22240}, {15039, 22331}, {15041, 15815}, {15055, 15515}, {15061, 31455}, {15081, 31415}, {22401, 44573}, {23357, 32730}, {23515, 41334}, {32452, 38520}, {38632, 41940}, {38789, 44518}, {38790, 44526}

X(46301) = perspector of the circumconic {{A, B, C, X(476), X(32717)}}
X(46301) = touchpoint of the line {526, 46301} and Moses circle
X(46301) = intersection, other than A, B, C, of circumconics {{A, B, C, X(115), X(32730)}} and {{A, B, C, X(323), X(14901)}}
X(46301) = crossdifference of every pair of points on line {X(526), X(9140)}
X(46301) = midpoint of PU(187)
X(46301) = X(39)-of-anti-orthocentroidal triangle
X(46301) = reflection of X(39) in the line X(526)X(2491)
X(46301) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 399, 14901), (6, 1625, 3016), (6, 3016, 115), (12375, 12376, 19140), (36208, 36209, 25556)


X(46302) = X(98)X(17938) ∩ X(237)X(804)

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

X(46302) lies on these lines: {98, 17938}, {237, 804}, {511, 11052}, {523, 5106}, {524, 36213}, {1691, 5967}, {3231, 11176}, {3266, 5976}, {4230, 17984}, {5201, 23342}

X(46302) = midpoint of X(5201) and X(23342)
X(46302) = isogonal conjugate of X(46303)
X(46302) = trilinear pole of the line {690, 1569}
X(46302) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(468)}} and {{A, B, C, X(4), X(44215)}}
X(46302) = cevapoint of X(i) and X(j) for these (i, j): {237, 3231}, {385, 13586}, {887, 2086}
X(46302) = trilinear pole of line PU(187)


X(46303) = ISOGONAL CONJUGATE OF X(46302)

Barycentrics    ((b^4-b^2*c^2+c^4)*a^4-(b^6+c^6)*a^2-b^2*c^2*(b^4-3*b^2*c^2+c^4))*a^2 : :
X(46303) = X(805)-4*X(15630) = 3*X(6784)-X(6786) = 2*X(13137)+X(14510) = X(13188)-4*X(46172) = 4*X(14113)-X(14509) = 2*X(31850)+X(38664)

X(46303) lies on these lines: {2, 6784}, {6, 110}, {98, 385}, {99, 3111}, {115, 6787}, {141, 13518}, {183, 7998}, {290, 879}, {373, 3329}, {512, 671}, {524, 33873}, {526, 9140}, {542, 6785}, {694, 2086}, {888, 3228}, {2387, 14568}, {2782, 41330}, {2871, 3060}, {2979, 8667}, {3225, 14970}, {3511, 9155}, {4609, 33769}, {5201, 9142}, {5663, 12188}, {5969, 9828}, {6772, 25173}, {6775, 25178}, {7766, 11002}, {9027, 39099}, {9218, 14908}, {9418, 35265}, {9855, 32442}, {11163, 13240}, {11174, 12093}, {11673, 22329}, {13188, 46172}, {14113, 14509}, {15072, 39646}, {15271, 33879}, {23004, 31707}, {23005, 31708}, {31850, 38664}, {32547, 44518}, {38650, 44468}, {43664, 46142}

X(46303) = midpoint of X(385) and X(13207)
X(46303) = reflection of X(i) in X(j) for these (i, j): (2, 6784), (99, 3111), (6787, 115), (9855, 32442), (11673, 22329)
X(46303) = anticomplement of X(6786)
X(46303) = isogonal conjugate of X(46302)
X(46303) = perspector of the circumconic {{A, B, C, X(691), X(39291)}}
X(46303) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(35146)}} and {{A, B, C, X(111), X(36897)}}
X(46303) = crossdifference of every pair of points on line {X(690), X(1569)}
X(46303) = crosspoint of X(i) and X(j) for these (i, j): {290, 3228}, {886, 39292}
X(46303) = crosssum of X(i) and X(j) for these (i, j): {237, 3231}, {385, 13586}, {887, 2086}
X(46303) = crossdifference of PU(187)
X(46303) = X(385)-of-orthocentroidal triangle
X(46303) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (98, 512, 11632), (110, 2780, 9144), (111, 2780, 11632)
X(46303) = {X(6), X(9149)}-harmonic conjugate of X(110)


X(46304) = BARYCENTRIC PRODUCT OF PU(187)

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

X(46304) lies on these lines: {3, 6}

X(46304) = barycentric product of PU(187)


X(46305) = X(3)X(6) ∩ X(51)X(3117)

Barycentrics    a^2*((b^2+c^2)*a^4+2*(b^4+3*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)) : :
Trilinears    cos(A + 2ω) (cos(A + 2ω) sin A + cos(B + 2ω) sin B + cos(C + 2ω) sin C) + (sin^2 A + sin^2 B + sin^2 C) sin A : :
X(46305) = 3*X(39)-X(46283) = X(46283)+3*X(46313)

X(46305) lies on these lines: {3, 6}, {51, 3117}, {76, 2548}, {83, 39101}, {115, 38383}, {194, 14035}, {230, 11272}, {262, 3767}, {325, 1506}, {538, 7753}, {698, 41651}, {726, 41662}, {736, 7838}, {1569, 19687}, {1572, 12782}, {1916, 7839}, {1992, 13085}, {2023, 5305}, {2782, 7745}, {3229, 5943}, {3399, 39095}, {3933, 24256}, {5254, 14881}, {5309, 44422}, {5475, 6248}, {6033, 39590}, {6194, 31400}, {6309, 18906}, {6660, 14153}, {6683, 7749}, {7736, 12251}, {7737, 11257}, {7757, 33007}, {7764, 18806}, {7778, 31239}, {7785, 39266}, {7786, 16989}, {7804, 10349}, {7805, 32189}, {7819, 44380}, {7837, 9983}, {7855, 14994}, {8992, 31481}, {9225, 21513}, {9419, 42442}, {9466, 9766}, {9596, 10063}, {9599, 10079}, {9865, 13571}, {12837, 16502}, {13108, 15484}, {13366, 14602}, {13410, 37338}, {15819, 31455}, {18907, 32448}, {19090, 31411}, {22486, 34511}, {22712, 31401}, {31276, 31404}, {31406, 32521}, {31981, 32451}

X(46305) = midpoint of X(39) and X(46313)
X(46305) = perspector of the circumconic {{A, B, C, X(110), X(46306)}}
X(46305) = crossdifference of every pair of points on line {X(523), X(39093)}
X(46305) = midpoint of PU(188)
X(46305) = X(46305)-of-circumsymmedial triangle
X(46305) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 13330, 46321), (6, 3095, 39), (32, 39, 2021), (39, 187, 13334), (39, 5007, 13357), (39, 5052, 32), (39, 5188, 574), (39, 46321, 3), (576, 13356, 43183), (3094, 9605, 39), (7772, 32452, 39), (13357, 44500, 5007)


X(46306) = ISOGONAL CONJUGATE OF X(39093)

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

X(46306) lies on these lines: {237, 46286}, {420, 16081}, {2395, 5113}, {20027, 39292}, {30535, 36213}

X(46306) = isogonal conjugate of X(39093)
X(46306) = trilinear pole of the line {512, 46305}
X(46306) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(98), X(34214)}}
X(46306) = trilinear pole of line PU(188)


X(46307) = X(99)X(39094) ∩ X(1975)X(5116)

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

X(46307) lies on these lines: {99, 39094}, {1975, 5116}, {3399, 39093}, {5989, 14651}, {7750, 37334}, {7824, 46236}, {12215, 46226}

X(46307) = crosssum of PU(188)


X(46308) = X(69)X(3114) ∩ X(83)X(511)

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

X(46308) lies on these lines: {6, 20885}, {69, 3114}, {83, 511}, {213, 46309}, {688, 2422}, {729, 41413}, {1843, 6531}, {1974, 18899}, {3224, 5017}, {3225, 33755}, {5028, 10014}, {9418, 46288}, {9468, 40981}, {14601, 41331}, {39099, 40405}

X(46308) = barycentric product X(i)*X(j) for these {i, j}: {1, 46309}, {32, 3399}
X(46308) = barycentric quotient X(1501)/X(3398)
X(46308) = trilinear product X(i)*X(j) for these {i, j}: {6, 46309}, {560, 3399}
X(46308) = trilinear quotient X(560)/X(3398)
X(46308) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(32)}} and {{A, B, C, X(25), X(20885)}}
X(46308) = X(561)-isoconjugate-of-X(3398)
X(46308) = barycentric product of PU(188)


X(46309) = X(1)X(3400) ∩ X(213)X(46308)

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

X(46309) lies on these lines: {1, 3400}, {213, 46308}, {304, 46281}, {1959, 3112}, {1967, 2179}, {3399, 7594}, {9417, 46289}, {17442, 36120}

X(46309) = barycentric product X(i)*X(j) for these {i, j}: {31, 3399}, {75, 46308}, {694, 3400}
X(46309) = barycentric quotient X(560)/X(3398)
X(46309) = trilinear product X(i)*X(j) for these {i, j}: {2, 46308}, {32, 3399}
X(46309) = trilinear quotient X(i)/X(j) for these (i, j): (32, 3398), (694, 20027)
X(46309) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31)}} and {{A, B, C, X(304), X(9247)}}
X(46309) = X(i)-isoconjugate-of-X(j) for these {i, j}: {76, 3398}, {385, 20027}
X(46309) = X(560)-reciprocal conjugate of-X(3398)
X(46309) = trilinear product of PU(188)


X(46310) = ISOGONAL CONJUGATE OF X(39095)

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

X(46310) lies on these lines: {25, 36213}, {263, 3095}, {287, 8842}, {393, 39931}, {694, 36212}, {1976, 2456}, {2395, 24284}, {3978, 16081}

X(46310) = isogonal conjugate of X(39095)
X(46310) = barycentric quotient X(511)/X(38383)
X(46310) = trilinear pole of the line {512, 5188}
X(46310) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(76), X(182)}}
X(46310) = X(511)-reciprocal conjugate of-X(38383)
X(46310) = trilinear pole of line PU(189)


X(46311) = X(99)X(39096) ∩ X(384)X(1503)

Barycentrics    a^12+(8*b^4+13*b^2*c^2+8*c^4)*a^8-2*(b^2+c^2)*(3*b^4-b^2*c^2+3*c^4)*a^6-(b^8-10*b^4*c^4+c^8)*a^4-2*(b^4-c^4)*(b^2-c^2)*(b^4+5*b^2*c^2+c^4)*a^2-(b^2-c^2)^2*(b^4+6*b^2*c^2+c^4)*b^2*c^2 : :

X(46311) lies on these lines: {99, 39096}, {384, 1503}, {574, 11257}, {1975, 5999}, {3424, 3552}, {7710, 7770}, {7738, 13860}, {7824, 9756}, {11381, 17970}, {33198, 35423}

X(46311) = crosssum of PU(189)


X(46312) = X(2)X(6) ∩ X(3511)X(15905)

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

X(46312) lies on these lines: {2, 6}, {3511, 15905}, {40799, 41331}

X(46312) = barycentric product of PU(189)


X(46313) = X(3)X(6) ∩ X(51)X(3229)

Barycentrics    a^2*((b^2+c^2)*a^4+(b^4+4*b^2*c^2+c^4)*a^2-b^6-c^6) : :
Trilinears    sin A - sin 3ω cos(A + ω) : :
X(46313) = 3*X(3095)-X(40252) = X(46283)-4*X(46305)

X(46313) lies on these lines: {3, 6}, {51, 3229}, {69, 31982}, {76, 5475}, {115, 14881}, {193, 31981}, {194, 6658}, {262, 7746}, {325, 18806}, {385, 32189}, {538, 7812}, {698, 41756}, {732, 7890}, {736, 7762}, {881, 8711}, {1569, 10992}, {1916, 7760}, {1994, 14602}, {2023, 7755}, {2241, 12837}, {2242, 12836}, {2548, 12251}, {2782, 7747}, {3060, 3117}, {3180, 6581}, {3181, 6294}, {3202, 19558}, {3314, 3934}, {3734, 18548}, {3815, 32521}, {5286, 44434}, {5969, 41651}, {5976, 7764}, {6194, 31401}, {6248, 39590}, {6660, 45843}, {6683, 7857}, {7745, 32515}, {7749, 11272}, {7757, 33265}, {7758, 18906}, {7774, 8149}, {7775, 7788}, {7794, 24256}, {7801, 22486}, {7843, 39266}, {7862, 7868}, {7877, 9983}, {7905, 9865}, {8782, 13571}, {9650, 10063}, {9665, 10079}, {14251, 27375}, {18501, 44539}, {22712, 31455}, {22728, 44518}, {31276, 31415}, {32450, 33257}

X(46313) = midpoint of X(7877) and X(9983)
X(46313) = reflection of X(i) in X(j) for these (i, j): (39, 46305), (46283, 39)
X(46313) = perspector of the circumconic {{A, B, C, X(110), X(46314)}}
X(46313) = inverse of X(5116) in 2nd Brocard circle
X(46313) = crossdifference of every pair of points on line {X(523), X(39097)}
X(46313) = crosssum of X(2) and X(8177)
X(46313) = circle-{{X(4),X(194),X(3557),X(3558)}}-inverse of X(3094)
X(46313) = midpoint of PU(190)
X(46313) = X(46313)-of-circumsymmedial triangle
X(46313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 32452, 39), (32, 3095, 39), (39, 5008, 13357), (39, 5052, 5007), (39, 5188, 37512), (39, 15513, 13334), (39, 35007, 2021), (39, 46321, 187), (576, 3095, 35437), (576, 13330, 5052), (1670, 1671, 5116), (3094, 7772, 39), (3095, 13330, 32), (3102, 3103, 44423), (3557, 3558, 3094), (5052, 35439, 1570)


X(46314) = ISOGONAL CONJUGATE OF X(39097)

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

X(46314) lies on these lines: {3229, 46284}

X(46314) = isogonal conjugate of X(39097)
X(46314) = trilinear pole of the line {512, 46313}
X(46314) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(98), X(41517)}}
X(46314) = trilinear pole of line PU(190)


X(46315) = X(3)X(148) ∩ X(99)X(39098)

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

X(46315) lies on these lines: {3, 148}, {99, 39098}, {9737, 10998}, {32189, 34885}

X(46315) = crosssum of PU(190)


X(46316) = ISOGONAL CONJUGATE OF X(39099)

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

X(46316) lies on the cubic K756 and these lines: {2, 2782}, {6, 6784}, {25, 34096}, {110, 30535}, {111, 237}, {263, 3124}, {308, 37688}, {351, 2395}, {468, 16081}, {694, 3291}, {1383, 5191}, {1976, 14567}, {2433, 9208}, {2491, 9178}, {2502, 11166}, {2987, 14510}, {2998, 17008}, {3228, 22329}, {5106, 21448}, {7610, 9462}, {8644, 14606}, {8770, 20885}, {8842, 39292}, {8901, 42300}, {11284, 36213}, {14998, 17414}, {16092, 18818}, {27809, 37764}, {37439, 37876}, {46317, 46320}

X(46316) = isogonal conjugate of X(39099)
X(46316) = barycentric product X(6)*X(43532)
X(46316) = barycentric quotient X(32)/X(2080)
X(46316) = trilinear product X(31)*X(43532)
X(46316) = trilinear quotient X(i)/X(j) for these (i, j): (31, 2080), (923, 21460)
X(46316) = trilinear pole of the line {512, 5052}
X(46316) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(32), X(7607)}}
X(46316) = X(206)-Dao conjugate of-X(2080)
X(46316) = X(75)-isoconjugate-of-X(2080)
X(46316) = X(32)-reciprocal conjugate of-X(2080)
X(46316) = X(25)-vertex conjugate of-X(694)
X(46316) = trilinear pole of line PU(191)


X(46317) = X(262)X(5028) ∩ X(263)X(3148)

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

X(46317) lies on these lines: {262, 5028}, {263, 3148}, {5034, 14252}, {5052, 26714}, {46316, 46320}

X(46317) = barycentric product X(263)*X(46318)
X(46317) = crosspoint of PU(191)


X(46318) = X(2)X(12215) ∩ X(3)X(32815)

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

X(46318) lies on these lines: {2, 12215}, {3, 32815}, {69, 13860}, {76, 9737}, {98, 13354}, {99, 15819}, {141, 44531}, {183, 1350}, {230, 384}, {262, 39099}, {385, 13330}, {1003, 23055}, {1007, 40330}, {1078, 7470}, {1975, 7824}, {2076, 13468}, {4048, 37637}, {5017, 37667}, {5152, 6055}, {5976, 14931}, {5989, 37455}, {6337, 11285}, {7610, 11164}, {7612, 35925}, {8290, 17006}, {8591, 11168}, {9466, 9888}, {9752, 35930}, {11185, 11676}, {11286, 16509}, {11356, 43291}, {32832, 38907}, {35021, 35422}

X(46318) = isogonal conjugate of X(46320)
X(46318) = crosssum of PU(191)
X(46318) = {X(5989), X(37688)}-harmonic conjugate of X(37455)


X(46319) = ISOGONAL CONJUGATE OF X(20023)

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

X(46319) lies on the cubic K1057 and these lines: {3, 83}, {6, 160}, {25, 6531}, {32, 3202}, {39, 10014}, {183, 327}, {213, 3402}, {385, 37465}, {669, 2422}, {729, 1384}, {1501, 14601}, {1974, 41331}, {2186, 21010}, {2207, 27369}, {3053, 3224}, {3225, 3511}, {3329, 37184}, {5201, 9516}, {6037, 36822}, {9468, 41278}, {11159, 38889}, {14252, 30435}, {14575, 46288}, {15271, 37338}, {22331, 36615}, {23210, 39951}, {32740, 34416}, {33875, 39238}, {37344, 42313}, {39646, 39682}

X(46319) = isogonal conjugate of X(20023)
X(46319) = barycentric product X(i)*X(j) for these {i, j}: {1, 3402}, {6, 263}, {25, 43718}, {31, 2186}, {32, 262}, {39, 42288}
X(46319) = barycentric quotient X(i)/X(j) for these (i, j): (25, 44144), (31, 3403), (32, 183), (213, 42711), (262, 1502), (263, 76)
X(46319) = trilinear product X(i)*X(j) for these {i, j}: {6, 3402}, {31, 263}, {32, 2186}, {262, 560}, {327, 1917}, {798, 26714}
X(46319) = trilinear quotient X(i)/X(j) for these (i, j): (6, 3403), (19, 44144), (31, 183), (42, 42711), (262, 561), (263, 75)
X(46319) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(14575)}} and {{A, B, C, X(6), X(32)}}
X(46319) = X(206)-Dao conjugate of-X(183)
X(46319) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 3403}, {63, 44144}, {75, 183}, {86, 42711}
X(46319) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 44144), (31, 3403), (32, 183), (213, 42711)
X(46319) = barycentric product of PU(191)


X(46320) = ISOGONAL CONJUGATE OF X(46318)

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

X(46320) lies on these lines: {6194, 7774}, {46316, 46317}

X(46320) = isogonal conjugate of X(46318)
X(46320) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(5017)}} and {{A, B, C, X(182), X(46316)}}
X(46320) = cevapoint of PU(191)


X(46321) = X(3)X(6) ∩ X(51)X(8623)

Barycentrics    a^2*(3*(b^2+c^2)*a^4+4*b^2*c^2*a^2-(b^2+c^2)*(b^4+c^4)) : :
X(46321) = 3*X(32)-2*X(13357) = 3*X(32)-X(32452) = 3*X(39)-4*X(13357) = 3*X(39)-2*X(32452) = 4*X(626)-5*X(31239) = 3*X(9466)-4*X(18806) = 4*X(13335)-3*X(21163) = 3*X(14711)-2*X(37004)

X(46321) lies on these lines: {3, 6}, {51, 8623}, {76, 7737}, {193, 6309}, {194, 33244}, {230, 14881}, {315, 3934}, {538, 33007}, {626, 7603}, {736, 19687}, {754, 8370}, {1506, 15819}, {2056, 20854}, {2548, 22712}, {3229, 3787}, {3399, 22521}, {3629, 41651}, {5477, 41756}, {5976, 7762}, {6248, 7747}, {6683, 33001}, {7746, 9753}, {7749, 20576}, {7757, 33208}, {7767, 24256}, {7786, 21843}, {7804, 10350}, {7805, 36849}, {7823, 39266}, {7826, 14994}, {11159, 14711}, {12829, 23718}, {14153, 21512}, {15993, 44230}, {18502, 44530}, {18907, 32521}, {22564, 34604}, {22682, 39565}, {31415, 33261}, {32450, 33254}, {36212, 41278}

X(46321) = midpoint of X(76) and X(20065)
X(46321) = reflection of X(i) in X(j) for these (i, j): (39, 32), (315, 3934), (5052, 35432), (5188, 35430), (32452, 13357), (35439, 35431)
X(46321) = perspector of the circumconic {{A, B, C, X(110), X(46322)}}
X(46321) = inverse of X(2024) in: Brocard inellipse, Moses circle
X(46321) = crossdifference of every pair of points on line {X(523), X(39101)}
X(46321) = X(6)-daleth conjugate of-X(2024)
X(46321) = midpoint of PU(192)
X(46321) = Brocard axis intercept, other than X(182), of circle {{X(182),PU(39)}}
X(46321) = center of circle {{X(76), X(20065), X(38527)}}
X(46321) = X(46321)-of-circumsymmedial triangle
X(46321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 13330, 46305), (3, 46305, 39), (32, 5162, 13335), (32, 32452, 13357), (32, 43183, 5007), (39, 15513, 21163), (187, 46313, 39), (2021, 3095, 39), (2028, 2029, 2024), (3053, 3095, 2021), (5007, 46283, 39), (5052, 5188, 39), (5162, 13335, 15513), (13357, 32452, 39), (35430, 35432, 32)


X(46322) = ISOGONAL CONJUGATE OF X(39101)

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

X(46322) lies on these lines: {}

X(46322) = isogonal conjugate of X(39101)
X(46322) = trilinear pole of the line {512, 46321}
X(46322) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(232), X(36213)}}
X(46322) = trilinear pole of line PU(192)


X(46323) = X(99)X(39102) ∩ X(148)X(7470)

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

X(46323) lies on these lines: {99, 39102}, {148, 7470}, {194, 37334}, {6337, 7824}

X(46323) = crosssum of PU(192)


X(46324) = ISOGONAL CONJUGATE OF X(40461)

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

X(46324) lies on these lines: {}

X(46324) = isogonal conjugate of X(40461)
X(46324) = trilinear pole of the line {39541, 40458}
X(46324) = trilinear pole of line PU(195)


X(46325) = MIDPOINT OF PU(196)

Barycentrics    ((b^4-29*b^2*c^2+c^4)*a^4-(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^2*b^2*c^2)/a^2 : :

X(46325) lies on these lines: {2, 647}, {327, 46326}

X(46325) = midpoint of PU(196)


X(46326) = ISOTOMIC CONJUGATE OF X(16187)

Barycentrics    ((b^2-10*c^2)*a^2-b^4+b^2*c^2)*((10*b^2-c^2)*a^2-b^2*c^2+c^4)/a^2 : :

X(46326) lies on these lines: {297, 15265}, {327, 46325}, {18020, 22112}

X(46326) = isogonal conjugate of X(46327)
X(46326) = isotomic conjugate of X(16187)
X(46326) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(297)}} and {{A, B, C, X(125), X(22112)}}
X(46326) = cevapoint of PU(196)


X(46327) = ISOGONAL CONJUGATE OF X(46326)

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

X(46327) lies on these lines: {6, 157}, {237, 33871}, {5640, 22143}, {14930, 44089}, {20968, 41940}, {23200, 33872}

X(46327) = isogonal conjugate of X(46326)
X(46327) = barycentric product X(6)*X(16187)
X(46327) = trilinear product X(31)*X(16187)
X(46327) = crosssum of PU(196)


X(46328) = X(2)X(6331) ∩ X(125)X(327)

Barycentrics    (9*a^4-(-b^2+c^2)^2)/a^4 : :

X(46328) lies on these lines: {2, 6331}, {76, 37648}, {125, 327}, {264, 30739}, {1502, 11059}, {7386, 46104}, {11284, 17984}, {11433, 34384}, {16187, 44155}, {22112, 46247}

X(46328) = barycentric product X(1285)*X(1502)
X(46328) = barycentric quotient X(1285)/X(32)
X(46328) = trilinear product X(561)*X(1285)
X(46328) = trilinear quotient X(1285)/X(560)
X(46328) = X(1285)-reciprocal conjugate of-X(32)
X(46328) = barycentric product of PU(196)


X(46329) = (name pending)

Barycentrics a*( -16*(b+c)*a*b*c*x*y*z-4*b*c*(a^2+(2*b+c)*a+b^2-c^2)*x*y-4*b*c*(a^2+(b+2*c)*a-b^2+c^2)*x*z-4*a*b*c*(2*a+b+c)*y*z-4*a*b*c*(c*y+b*z)+a^4+2*(b+c)*a^3+5*b*c*a^2-(b+c)*(2*b^2-3*b*c+2*c^2)*a-(b^2-c^2)^2) : : , where x=cos(A/2), y=cos(B/2), z=cos(C/2)

Antreas Hatzipolakis and César Lozada, euclid 3494.

X(46329) lies on these lines: { }


X(46330) = X(6)X(57)∩X(85)X(189)

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

See Antreas Hatzipolakis and Peter Moses, euclid 3502.

X(46330) lies on these lines: {6, 57}, {77, 6611}, {85, 189}, {142, 6708}, {241, 28274}, {515, 942}, {940, 1435}, {1119, 40149}, {1456, 4224}, {1876, 10391}, {2182, 34035}, {3666, 37755}, {4340, 34231}, {4349, 11018}, {4359, 4566}, {5745, 20201}, {7248, 37566}, {8808, 21239}, {9940, 40657}, {20197, 41867}, {37523, 40933}, {43058, 44708}

X(46330) = barycentric product X(3668)*X(10461)
X(46330) = barycentric quotient X(10461)/X(1043)
X(46330) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 223, 15509}, {942, 40644, 9942}


X(46331) = X(38)X(65)∩X(141)X(226)

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

See Antreas Hatzipolakis and Peter Moses, euclid 3502..

X(46331) lies on these lines: {38, 65}, {57, 16696}, {85, 16703}, {141, 226}, {1407, 20617}, {7341, 17074}, {10473, 46149}

X(46331) = X(i)-isoconjugate of X(j) for these (i,j): {8, 4264}, {219, 37390}, {284, 26115}, {7054, 10408}
X(46331) = trilinear pole of line {2530, 4017}
X(46331) = barycentric quotient X(i)/X(j) for these {i,j}: {34, 37390}, {65, 26115}, {604, 4264}, {1254, 10408}


X(46332) = EULER LINE INTERCEPT OF X(5318)X(42952)

Barycentrics    58*a^4-53*(b^2+c^2)*a^2-5*(b^2-c^2)^2 : :
X(46332) = X(2)+3*X(548), 13*X(2)+3*X(1657), 9*X(2)+7*X(3534), 11*X(2)-3*X(3627), 15*X(2)-7*X(3845), 5*X(2)-3*X(3850), 13*X(2)-7*X(3860), 11*X(2)-7*X(5066), X(2)+7*X(8703), 9*X(2)-7*X(10109), 6*X(2)-7*X(11540), 5*X(2)-7*X(11812), 3*X(2)-7*X(12100), 19*X(2)-7*X(12101), 2*X(2)-3*X(12108), 19*X(2)-15*X(12812), X(2)+15*X(14093), 7*X(2)-9*X(14890), X(2)-3*X(14891), 13*X(2)-9*X(14892), 7*X(2)-3*X(14893), 19*X(2)-3*X(15684), 5*X(2)+3*X(15686), 7*X(2)+9*X(15689), 5*X(2)+7*X(15690), 7*X(2)-15*X(15712), X(2)-7*X(15759), 17*X(2)+15*X(17538), 17*X(2)+7*X(19710), 17*X(2)-9*X(23046), 5*X(2)-9*X(41983), 4*X(2)-7*X(44580), 11*X(2)-9*X(45757), 8*X(2)-9*X(45758), X(2)-9*X(45759), 13*X(2)-15*X(45760)

As a point on the Euler line, X(46332) has Shinagawa coefficients [-53, 63].

See Antreas Hatzipolakis and César Lozada, Euclid 3503 .

X(46332) lies on these lines: {2, 3}, {5318, 42952}, {5321, 42953}, {6484, 41946}, {6485, 41945}, {9300, 15602}, {9681, 10142}, {28212, 31662}, {34754, 42791}, {34755, 42792}, {35770, 42524}, {35771, 42525}, {41943, 42891}, {41944, 42890}, {42087, 43200}, {42088, 43199}, {42508, 43635}, {42509, 43634}, {42528, 43109}, {42529, 43108}, {42532, 42924}, {42533, 42925}, {42631, 42912}, {42632, 42913}, {42906, 43247}, {42907, 43246}, {42942, 42977}, {42943, 42976}

X(46332) = midpoint of X(i) and X(j) for these {i, j}: {376, 3530}, {548, 14891}, {549, 44245}, {550, 10124}, {3534, 10109}, {3628, 15691}, {3850, 15686}, {8703, 15759}, {11737, 12103}, {11812, 15690}, {12102, 15681}, {14890, 15689}, {33923, 34200}
X(46332) = reflection of X(i) in X(j) for these (i, j): (3856, 10124), (11540, 12100), (12108, 14891), (35018, 549), (41988, 35018)
X(46332) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 8703, 548), (3, 15688, 3543), (140, 3855, 3628), (376, 15706, 3627), (548, 12812, 550), (549, 35400, 547), (3545, 41992, 547), (3832, 11539, 547), (3850, 11812, 2), (5066, 15711, 3530), (8703, 15711, 376), (8703, 45759, 2), (11001, 19711, 547), (11539, 15686, 3627), (11541, 15702, 3545), (11812, 15759, 3), (12100, 15701, 3530), (14093, 45759, 548), (14891, 45757, 3530), (15684, 15693, 2), (15686, 45759, 3), (15688, 15714, 140), (15688, 17800, 376), (15697, 15716, 5), (15698, 17538, 2), (15698, 19710, 140), (15718, 23046, 140), (33923, 44245, 3528), (34200, 41982, 3), (44245, 45760, 1657)


X(46333) = EULER LINE INTERCEPT OF X(397)X(42586)

Barycentrics    31*a^4-20*(b^2+c^2)*a^2-11*(b^2-c^2)^2 : :
X(46333) = 11*X(2)-14*X(3), 10*X(2)-7*X(4), X(2)-7*X(20), 4*X(2)-7*X(376), 17*X(2)-14*X(381), 5*X(2)-8*X(548), X(2)+2*X(1657), 19*X(2)-7*X(3146), 6*X(2)-7*X(3524), 8*X(2)+7*X(3529), 5*X(2)-14*X(3534), 13*X(2)-7*X(3543), 8*X(2)-7*X(3545), 7*X(2)-4*X(3627), 9*X(2)-7*X(3839), 13*X(2)-10*X(3843), 19*X(2)-16*X(3850), 13*X(2)-14*X(5054), 15*X(2)-14*X(5055), 17*X(2)+7*X(5059), 5*X(2)-7*X(10304), 2*X(2)+7*X(11001), 7*X(2)-10*X(14093), 19*X(2)-14*X(14269), 15*X(2)-16*X(14890), 13*X(2)-16*X(14891), 9*X(2)-8*X(14892), 11*X(2)-8*X(14893), X(2)+14*X(15681), 16*X(2)-7*X(15682), 5*X(2)+7*X(15683), 5*X(2)-2*X(15684), 13*X(2)+14*X(15685), X(2)-4*X(15686), 9*X(2)-14*X(15688), 5*X(2)-6*X(15706), 17*X(2)-20*X(15712), 2*X(2)-5*X(17538), 8*X(2)-11*X(21735), 5*X(2)-4*X(23046), 4*X(2)-X(33703), 7*X(2)-11*X(35418), 7*X(2)-8*X(41983), 17*X(2)-16*X(45757), 3*X(2)-4*X(45759)

As a point on the Euler line, X(46333) has Shinagawa coefficients [-10, 21].

See Antreas Hatzipolakis and César Lozada, Euclid 3503 .

X(46333) lies on these lines: {2, 3}, {397, 42586}, {398, 42587}, {485, 43521}, {486, 43522}, {3068, 43342}, {3069, 43343}, {3592, 43785}, {3594, 43786}, {3625, 34638}, {3633, 6361}, {3653, 28154}, {4324, 10385}, {4668, 31730}, {5731, 28202}, {6435, 43336}, {6436, 43337}, {6449, 43340}, {6450, 43341}, {6451, 43507}, {6452, 43508}, {6470, 43384}, {6471, 43385}, {6486, 42570}, {6487, 42571}, {7739, 14075}, {7750, 32877}, {7811, 32822}, {7850, 32817}, {7967, 28198}, {8591, 14692}, {9778, 28208}, {10653, 43300}, {10654, 43301}, {11488, 42929}, {11489, 42928}, {13702, 42520}, {14226, 35821}, {14241, 35820}, {14912, 19924}, {16962, 42090}, {16963, 42091}, {18481, 34631}, {19053, 42266}, {19054, 42267}, {19106, 43201}, {19107, 43202}, {19875, 28172}, {20053, 34632}, {28146, 38314}, {28158, 38021}, {28164, 38074}, {28190, 38066}, {31412, 43568}, {32455, 43273}, {32787, 43339}, {32788, 43338}, {32878, 37671}, {33606, 42149}, {33607, 42152}, {33750, 38072}, {35822, 42414}, {35823, 42413}, {36969, 42795}, {36970, 42796}, {37640, 42100}, {37641, 42099}, {38742, 41135}, {41100, 42934}, {41101, 42935}, {41107, 42435}, {41108, 42436}, {41112, 42434}, {41113, 42433}, {41121, 43550}, {41122, 43551}, {41945, 43407}, {41946, 43408}, {42093, 43100}, {42094, 43107}, {42096, 42685}, {42097, 42684}, {42108, 43299}, {42109, 43298}, {42112, 42528}, {42113, 42529}, {42119, 43481}, {42120, 43482}, {42140, 42430}, {42141, 42429}, {42258, 43256}, {42259, 43257}, {42271, 43381}, {42272, 43380}, {42275, 43510}, {42276, 43509}, {42472, 43467}, {42473, 43468}, {42480, 42966}, {42481, 42967}, {42514, 43002}, {42515, 43003}, {42521, 43486}, {42561, 43569}, {42588, 43633}, {42589, 43632}, {42631, 43492}, {42632, 43491}, {42637, 43431}, {42638, 43430}, {42686, 42940}, {42687, 42941}, {43463, 43544}, {43464, 43545}

X(46333) = midpoint of X(i) and X(j) for these {i, j}: {1657, 15689}, {3529, 3545}, {5054, 15685}, {10304, 15683}
X(46333) = reflection of X(i) in X(j) for these (i, j): (2, 15689), (4, 10304), (382, 15699), (3146, 14269), (3543, 5054), (3545, 376), (3627, 41983), (3830, 17504), (3839, 15688), (5054, 550), (10304, 3534), (14269, 8703), (15682, 3545), (15684, 23046), (15689, 15686), (15699, 15690), (17504, 15691), (23046, 548), (37907, 44246), (38335, 45759), (41135, 38742)
X(46333) = anticomplement of X(38335)
X(46333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 15684, 4), (2, 17538, 376), (3, 14893, 2), (4, 3534, 376), (20, 11001, 376), (20, 15704, 4), (376, 33703, 2), (376, 41099, 3), (381, 15712, 2), (382, 15022, 4), (548, 15684, 2), (549, 5072, 2), (549, 15640, 4), (550, 19708, 376), (1657, 15686, 2), (3146, 3526, 4), (3528, 15697, 376), (3534, 15683, 4), (3543, 5066, 4), (3627, 14093, 2), (3843, 14891, 2), (3845, 41989, 381), (3850, 15718, 2), (5055, 14890, 2), (5059, 15697, 381), (15681, 19710, 20), (15691, 15702, 376), (15693, 41990, 2), (15706, 23046, 2), (38335, 45759, 2)


X(46334) = REFLECTION OF X(41108) IN X(41100)

Barycentrics    -19*a^4 + 11*a^2*b^2 + 8*b^4 + 11*a^2*c^2 - 16*b^2*c^2 + 8*c^4 - 6*Sqrt[3]*a^2*S : :
X(46334) = 11 X[62] - 8 X[398], 7 X[62] - 4 X[16964], 3 X[62] - 4 X[41100], 3 X[62] - 2 X[41108], 5 X[62] - 8 X[42148], X[62] - 4 X[42158], 17 X[62] - 8 X[42164], 5 X[62] - 2 X[42432], 21 X[62] - 20 X[42521], 13 X[62] - 16 X[42924], 9 X[62] - 16 X[43109], 9 X[62] - 8 X[43229], X[62] + 2 X[43633], 14 X[398] - 11 X[16964], 6 X[398] - 11 X[41100], 12 X[398] - 11 X[41108], 5 X[398] - 11 X[42148], 2 X[398] - 11 X[42158], 17 X[398] - 11 X[42164], 20 X[398] - 11 X[42432], 42 X[398] - 55 X[42521], 13 X[398] - 22 X[42924], 9 X[398] - 22 X[43109], 9 X[398] - 11 X[43229], 4 X[398] + 11 X[43633], 3 X[16964] - 7 X[41100], 6 X[16964] - 7 X[41108], 5 X[16964] - 14 X[42148], X[16964] - 7 X[42158], 17 X[16964] - 14 X[42164], 10 X[16964] - 7 X[42432], 3 X[16964] - 5 X[42521], 13 X[16964] - 28 X[42924], 9 X[16964] - 28 X[43109], 9 X[16964] - 14 X[43229], 2 X[16964] + 7 X[43633], 5 X[41100] - 6 X[42148], X[41100] - 3 X[42158], 17 X[41100] - 6 X[42164], 10 X[41100] - 3 X[42432], 7 X[41100] - 5 X[42521], 13 X[41100] - 12 X[42924], 3 X[41100] - 4 X[43109], 3 X[41100] - 2 X[43229], 2 X[41100] + 3 X[43633], 5 X[41108] - 12 X[42148], X[41108] - 6 X[42158], 17 X[41108] - 12 X[42164], 5 X[41108] - 3 X[42432], 7 X[41108] - 10 X[42521], 13 X[41108] - 24 X[42924], 3 X[41108] - 8 X[43109], 3 X[41108] - 4 X[43229], X[41108] + 3 X[43633], 2 X[42148] - 5 X[42158], 17 X[42148] - 5 X[42164], 4 X[42148] - X[42432], 42 X[42148] - 25 X[42521], 13 X[42148] - 10 X[42924], 9 X[42148] - 10 X[43109], 9 X[42148] - 5 X[43229], 4 X[42148] + 5 X[43633], 17 X[42158] - 2 X[42164], 10 X[42158] - X[42432], 21 X[42158] - 5 X[42521], 13 X[42158] - 4 X[42924], 9 X[42158] - 4 X[43109], 9 X[42158] - 2 X[43229], 2 X[42158] + X[43633], 20 X[42164] - 17 X[42432], 42 X[42164] - 85 X[42521], 13 X[42164] - 34 X[42924], 9 X[42164] - 34 X[43109], 9 X[42164] - 17 X[43229], 4 X[42164] + 17 X[43633], 21 X[42432] - 50 X[42521], 13 X[42432] - 40 X[42924], 9 X[42432] - 40 X[43109], 9 X[42432] - 20 X[43229], X[42432] + 5 X[43633], 65 X[42521] - 84 X[42924], 15 X[42521] - 28 X[43109], 15 X[42521] - 14 X[43229], 10 X[42521] + 21 X[43633], 9 X[42924] - 13 X[43109], 18 X[42924] - 13 X[43229], 8 X[42924] + 13 X[43633], 8 X[43109] + 9 X[43633], 4 X[43229] + 9 X[43633]

X(46334) lies on these lines: {2, 10646}, {3, 41121}, {4, 41944}, {5, 42909}, {6, 15685}, {13, 8703}, {14, 15682}, {15, 3534}, {16, 3830}, {17, 10304}, {18, 15687}, {20, 41974}, {30, 62}, {61, 15681}, {376, 5352}, {381, 5237}, {382, 16268}, {395, 12817}, {396, 15690}, {397, 15686}, {530, 11129}, {549, 42165}, {550, 16962}, {1657, 42586}, {3090, 42958}, {3146, 42993}, {3180, 33611}, {3412, 17538}, {3524, 42161}, {3525, 43201}, {3543, 16963}, {3545, 42937}, {3843, 42978}, {3845, 19106}, {3849, 5858}, {3850, 43100}, {3860, 23303}, {5054, 42813}, {5055, 5351}, {5059, 42991}, {5066, 16242}, {5238, 15689}, {5318, 12100}, {5321, 42507}, {5334, 43233}, {5335, 15697}, {5340, 15688}, {5343, 42436}, {5350, 15699}, {5366, 15708}, {5863, 35695}, {6778, 8591}, {6779, 36363}, {7865, 11296}, {8353, 12155}, {10109, 42137}, {10645, 15695}, {10653, 11001}, {10654, 42429}, {11480, 43418}, {11481, 19709}, {11486, 41972}, {11488, 33604}, {11540, 43104}, {11541, 42515}, {11648, 41406}, {11812, 16966}, {12101, 16809}, {12811, 42793}, {14093, 42156}, {14269, 36843}, {14855, 30439}, {14891, 42598}, {14893, 16773}, {15640, 19107}, {15683, 42157}, {15684, 22238}, {15692, 42162}, {15693, 37832}, {15696, 42992}, {15698, 18582}, {15700, 42936}, {15702, 42581}, {15704, 42990}, {15706, 43491}, {15709, 42921}, {15711, 23302}, {15712, 42592}, {15714, 43107}, {15715, 43546}, {15716, 42128}, {15719, 33417}, {15759, 43416}, {15764, 42562}, {16241, 19708}, {16967, 41106}, {17504, 42166}, {19710, 36967}, {23046, 42580}, {25235, 36344}, {33458, 35696}, {33923, 43424}, {34755, 36970}, {35434, 42519}, {36450, 42275}, {36467, 42276}, {36994, 41029}, {37641, 42113}, {38071, 42944}, {40694, 42636}, {41099, 42141}, {42085, 43481}, {42089, 42505}, {42099, 43106}, {42108, 42634}, {42109, 42913}, {42115, 43475}, {42125, 43400}, {42126, 43637}, {42130, 42509}, {42135, 43640}, {42140, 43499}, {42143, 43025}, {42147, 44903}, {42154, 42508}, {42159, 42801}, {42163, 42694}, {42430, 43006}, {42434, 42779}, {42497, 44016}, {42501, 42683}, {42532, 42584}, {42596, 43550}, {42689, 43483}, {42900, 43029}, {42910, 43226}, {42911, 44015}, {42912, 43207}, {42967, 43632}, {43002, 43004}, {43011, 43541}, {43031, 43324}, {43108, 43300}, {43194, 43775}, {43237, 43402}, {43310, 44245}, {43326, 43331}

X(46334) = reflection of X(i) in X(j) for these {i,j}: {41108, 41100}, {43229, 43109}
X(46334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36968, 42631}, {2, 42631, 10646}, {14, 42510, 42977}, {16, 3830, 41122}, {376, 16267, 5352}, {376, 16965, 16267}, {376, 42588, 41112}, {395, 33699, 12817}, {3534, 41107, 15}, {3534, 42155, 41107}, {3543, 16963, 42814}, {3543, 42151, 16963}, {5066, 42123, 42792}, {5066, 42792, 16242}, {5340, 15688, 41943}, {8703, 42502, 42504}, {10653, 11001, 41101}, {15640, 41113, 19107}, {15682, 42120, 42510}, {15682, 42510, 14}, {15684, 22238, 42972}, {16809, 43401, 43399}, {16964, 41100, 42521}, {19106, 42943, 37835}, {19107, 42533, 41113}, {19708, 41119, 16241}, {19710, 42118, 43228}, {19710, 43228, 36967}, {36968, 36969, 10646}, {36968, 42086, 36969}, {36969, 42631, 2}, {41100, 41108, 62}, {41101, 42100, 11001}, {41107, 42976, 42974}, {41112, 42588, 16965}, {41119, 42091, 19708}, {41972, 43419, 11486}, {42100, 43244, 10653}, {42107, 43200, 37835}, {42123, 42941, 16242}, {42127, 42625, 37832}, {42148, 42432, 62}, {42158, 43633, 62}, {42431, 43193, 5237}, {42792, 42941, 5066}, {43109, 43229, 41100}


X(46335) = REFLECTION OF X(41107) IN X(41101)

Barycentrics    -19*a^4 + 11*a^2*b^2 + 8*b^4 + 11*a^2*c^2 - 16*b^2*c^2 + 8*c^4 + 6*Sqrt[3]*a^2*S : :
X(46335) 11 X[61] - 8 X[397], 7 X[61] - 4 X[16965], 3 X[61] - 4 X[41101], 3 X[61] - 2 X[41107], 5 X[61] - 8 X[42147], X[61] - 4 X[42157], 17 X[61] - 8 X[42165], 5 X[61] - 2 X[42431], 21 X[61] - 20 X[42520], 13 X[61] - 16 X[42925], 9 X[61] - 16 X[43108], 9 X[61] - 8 X[43228], X[61] + 2 X[43632], 14 X[397] - 11 X[16965], 6 X[397] - 11 X[41101], 12 X[397] - 11 X[41107], 5 X[397] - 11 X[42147], 2 X[397] - 11 X[42157], 17 X[397] - 11 X[42165], 20 X[397] - 11 X[42431], 42 X[397] - 55 X[42520], 13 X[397] - 22 X[42925], 9 X[397] - 22 X[43108], 9 X[397] - 11 X[43228], 4 X[397] + 11 X[43632], 3 X[16965] - 7 X[41101], 6 X[16965] - 7 X[41107], 5 X[16965] - 14 X[42147], X[16965] - 7 X[42157], 17 X[16965] - 14 X[42165], 10 X[16965] - 7 X[42431], 3 X[16965] - 5 X[42520], 13 X[16965] - 28 X[42925], 9 X[16965] - 28 X[43108], 9 X[16965] - 14 X[43228], 2 X[16965] + 7 X[43632], 5 X[41101] - 6 X[42147], X[41101] - 3 X[42157], 17 X[41101] - 6 X[42165], 10 X[41101] - 3 X[42431], 7 X[41101] - 5 X[42520], 13 X[41101] - 12 X[42925], 3 X[41101] - 4 X[43108], 3 X[41101] - 2 X[43228], 2 X[41101] + 3 X[43632], 5 X[41107] - 12 X[42147], X[41107] - 6 X[42157], 17 X[41107] - 12 X[42165], 5 X[41107] - 3 X[42431], 7 X[41107] - 10 X[42520], 13 X[41107] - 24 X[42925], 3 X[41107] - 8 X[43108], 3 X[41107] - 4 X[43228], X[41107] + 3 X[43632], 2 X[42147] - 5 X[42157], 17 X[42147] - 5 X[42165], 4 X[42147] - X[42431], 42 X[42147] - 25 X[42520], 13 X[42147] - 10 X[42925], 9 X[42147] - 10 X[43108], 9 X[42147] - 5 X[43228], 4 X[42147] + 5 X[43632], 17 X[42157] - 2 X[42165], 10 X[42157] - X[42431], 21 X[42157] - 5 X[42520], 13 X[42157] - 4 X[42925], 9 X[42157] - 4 X[43108], 9 X[42157] - 2 X[43228], 2 X[42157] + X[43632], 20 X[42165] - 17 X[42431], 42 X[42165] - 85 X[42520], 13 X[42165] - 34 X[42925], 9 X[42165] - 34 X[43108], 9 X[42165] - 17 X[43228], 4 X[42165] + 17 X[43632], 21 X[42431] - 50 X[42520], 13 X[42431] - 40 X[42925], 9 X[42431] - 40 X[43108], 9 X[42431] - 20 X[43228], X[42431] + 5 X[43632], 65 X[42520] - 84 X[42925], 15 X[42520] - 28 X[43108], 15 X[42520] - 14 X[43228], 10 X[42520] + 21 X[43632], 9 X[42925] - 13 X[43108], 18 X[42925] - 13 X[43228], 8 X[42925] + 13 X[43632], 8 X[43108] + 9 X[43632], 4 X[43228] + 9 X[43632]

X(46335) lies on these lines: {2, 10645}, {3, 41122}, {4, 41943}, {5, 42908}, {6, 15685}, {13, 15682}, {14, 8703}, {15, 3830}, {16, 3534}, {17, 15687}, {18, 10304}, {20, 41973}, {30, 61}, {62, 15681}, {376, 5351}, {381, 5238}, {382, 16267}, {395, 15690}, {396, 12816}, {398, 15686}, {531, 11128}, {549, 42164}, {550, 16963}, {1657, 42587}, {3090, 42959}, {3146, 42992}, {3181, 33610}, {3411, 17538}, {3524, 42160}, {3525, 43202}, {3543, 16962}, {3545, 42936}, {3843, 42979}, {3845, 19107}, {3849, 5859}, {3850, 43107}, {3860, 23302}, {5054, 42814}, {5055, 5352}, {5059, 42990}, {5066, 16241}, {5237, 15689}, {5318, 42506}, {5321, 12100}, {5334, 15697}, {5335, 43232}, {5339, 15688}, {5344, 42435}, {5349, 15699}, {5365, 15708}, {5862, 35691}, {6777, 8591}, {6780, 36362}, {7865, 11295}, {8353, 12154}, {10109, 42136}, {10646, 15695}, {10653, 42430}, {10654, 11001}, {11480, 19709}, {11481, 43419}, {11485, 41971}, {11489, 33605}, {11540, 43101}, {11541, 42514}, {11648, 41407}, {11812, 16967}, {12101, 16808}, {12811, 42794}, {14093, 42153}, {14269, 36836}, {14855, 30440}, {14891, 42599}, {14893, 16772}, {15640, 19106}, {15683, 42158}, {15684, 22236}, {15692, 42159}, {15693, 37835}, {15696, 42993}, {15698, 18581}, {15700, 42937}, {15702, 42580}, {15704, 42991}, {15706, 43492}, {15709, 42920}, {15711, 23303}, {15712, 42593}, {15714, 43100}, {15715, 43547}, {15716, 42125}, {15719, 33416}, {15759, 43417}, {15764, 42565}, {16242, 19708}, {16966, 41106}, {17504, 42163}, {19710, 36968}, {23046, 42581}, {25236, 36319}, {33459, 35692}, {33923, 43425}, {34754, 36969}, {35434, 42518}, {36449, 42276}, {36468, 42275}, {36775, 44678}, {36992, 41028}, {37640, 42112}, {38071, 42945}, {40693, 42635}, {41099, 42140}, {42086, 43482}, {42092, 42504}, {42100, 43105}, {42108, 42912}, {42109, 42633}, {42116, 43476}, {42127, 43636}, {42128, 43399}, {42131, 42508}, {42138, 43639}, {42141, 43500}, {42146, 43024}, {42148, 44903}, {42155, 42509}, {42162, 42802}, {42166, 42695}, {42429, 43007}, {42433, 42780}, {42496, 44015}, {42500, 42682}, {42533, 42585}, {42597, 43551}, {42688, 43484}, {42901, 43028}, {42910, 44016}, {42911, 43227}, {42913, 43208}, {42966, 43633}, {43003, 43005}, {43010, 43540}, {43030, 43325}, {43109, 43301}, {43193, 43776}, {43236, 43401}, {43311, 44245}, {43327, 43330}

X(46335) = reflection of X(i) in X(j) for these {i,j}: {41107, 41101}, {43228, 43108}
X(46335) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36967, 42632}, {2, 42632, 10645}, {13, 42511, 42976}, {15, 3830, 41121}, {376, 16268, 5351}, {376, 16964, 16268}, {376, 42589, 41113}, {396, 33699, 12816}, {3534, 41108, 16}, {3534, 42154, 41108}, {3543, 16962, 42813}, {3543, 42150, 16962}, {5066, 42122, 42791}, {5066, 42791, 16241}, {5339, 15688, 41944}, {8703, 42503, 42505}, {10654, 11001, 41100}, {15640, 41112, 19106}, {15682, 42119, 42511}, {15682, 42511, 13}, {15684, 22236, 42973}, {16808, 43402, 43400}, {16965, 41101, 42520}, {19106, 42532, 41112}, {19107, 42942, 37832}, {19708, 41120, 16242}, {19710, 42117, 43229}, {19710, 43229, 36968}, {36967, 36970, 10645}, {36967, 42085, 36970}, {36970, 42632, 2}, {41100, 42099, 11001}, {41101, 41107, 61}, {41108, 42977, 42975}, {41113, 42589, 16964}, {41120, 42090, 19708}, {41971, 43418, 11485}, {42099, 43245, 10654}, {42110, 43199, 37832}, {42122, 42940, 16241}, {42126, 42626, 37835}, {42147, 42431, 61}, {42157, 43632, 61}, {42432, 43194, 5238}, {42791, 42940, 5066}, {43108, 43228, 41101}


X(46336) = EULER LINE INTERCEPT OF X(69)X(3266)

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

X(46336) lies on these lines: {2, 3}, {69, 3266}, {110, 25406}, {141, 8547}, {146, 10293}, {182, 37645}, {251, 40320}, {315, 11059}, {323, 14912}, {373, 31670}, {388, 5297}, {394, 8550}, {497, 7292}, {1216, 18916}, {1350, 37648}, {1352, 5650}, {1899, 3819}, {1992, 23061}, {1993, 44503}, {2549, 3291}, {2896, 30793}, {2979, 11433}, {3003, 7736}, {3060, 18928}, {3066, 29181}, {3218, 26939}, {3219, 26929}, {3292, 11179}, {3434, 19804}, {3448, 44833}, {3580, 10519}, {3619, 5888}, {3620, 18935}, {3763, 45303}, {3818, 15082}, {3917, 6515}, {4549, 37470}, {4857, 5272}, {5012, 37669}, {5063, 7735}, {5085, 11064}, {5157, 28708}, {5181, 9140}, {5268, 5270}, {5314, 20266}, {5422, 44492}, {5646, 10516}, {5651, 46264}, {5800, 37633}, {5972, 17508}, {6504, 7607}, {6776, 15066}, {7703, 15435}, {7738, 9465}, {7768, 40123}, {7771, 37803}, {7800, 30749}, {7999, 11411}, {8024, 19583}, {8585, 43619}, {9214, 15899}, {10159, 40178}, {10192, 34944}, {10327, 44720}, {10717, 25051}, {11003, 41615}, {11444, 18909}, {11457, 11487}, {11677, 16706}, {12324, 15056}, {13857, 38064}, {14561, 22112}, {15048, 40126}, {15051, 18933}, {15067, 18917}, {15080, 35260}, {15820, 31455}, {16187, 29012}, {17008, 19577}, {18950, 45794}, {19467, 44862}, {20481, 43448}, {23291, 37636}, {31884, 32269}, {32064, 44299}, {32273, 45311}, {32821, 45201}, {33884, 37644}, {35259, 44882}, {35283, 36990}, {37643, 41462}, {37775, 42119}, {37776, 42120}, {43650, 44470}

X(46336) = anticomplement of X(11284)
X(46336) = isotomic conjugate of the isogonal conjugate of X(32621)
X(46336) = barycentric product X(76)*X(32621)
X(46336) = barycentric quotient X(32621)/X(6)
X(46336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 7493}, {2, 20, 1995}, {2, 23, 40132}, {2, 376, 26255}, {2, 1370, 6997}, {2, 3522, 4232}, {2, 3523, 7495}, {2, 4189, 26256}, {2, 4190, 4239}, {2, 5169, 3090}, {2, 6636, 6353}, {2, 7378, 37990}, {2, 7386, 1370}, {2, 7391, 7392}, {2, 7396, 5133}, {2, 7496, 631}, {2, 7500, 5020}, {2, 7519, 16042}, {2, 10304, 7426}, {2, 10989, 3545}, {2, 15246, 7494}, {2, 16063, 4}, {2, 31099, 5}, {2, 31100, 6856}, {2, 31101, 8889}, {2, 31105, 5071}, {2, 31106, 5084}, {2, 31107, 14064}, {2, 32965, 26257}, {3, 140, 35486}, {3, 1656, 16618}, {3, 3526, 34351}, {3, 6816, 37201}, {3, 30739, 2}, {3, 34664, 20}, {4, 7386, 16063}, {4, 7392, 7533}, {4, 16063, 1370}, {5, 10300, 31152}, {5, 31152, 31099}, {23, 40132, 26255}, {140, 1368, 5094}, {140, 5094, 2}, {376, 40132, 23}, {377, 2478, 17677}, {427, 16419, 2}, {549, 32216, 2}, {631, 6643, 6815}, {631, 16051, 2}, {858, 40916, 2}, {1368, 3548, 16051}, {1368, 7484, 2}, {1368, 7734, 7484}, {1370, 7493, 37201}, {1656, 16618, 3542}, {1657, 5020, 10301}, {1657, 10301, 7500}, {2045, 2046, 7383}, {3522, 4232, 22}, {3526, 37454, 2}, {3538, 6804, 20}, {3548, 7516, 631}, {3580, 21766, 10519}, {5002, 5003, 35513}, {5020, 7667, 7500}, {5094, 7484, 140}, {6676, 31255, 2}, {6804, 34664, 6816}, {6816, 7493, 6997}, {6921, 30776, 2}, {7386, 16051, 6643}, {7386, 30739, 6816}, {7391, 7533, 4}, {7484, 7516, 7496}, {7485, 7495, 3523}, {7493, 30552, 22}, {7496, 37126, 7485}, {7499, 30771, 2}, {7574, 18420, 4}, {7667, 10301, 1657}, {7907, 30777, 2}, {7998, 18911, 69}, {8359, 11336, 2}, {10303, 30769, 2}, {10303, 37444, 6803}, {14813, 14814, 7529}, {15692, 44440, 3537}, {15702, 30775, 2}, {18537, 26255, 6997}, {30739, 43957, 3}


X(46337) = X(6)X(23)∩X(39)X(524)

Barycentrics    a^2*(2*(b^2+c^2)*a^4+2*(2*b^4+7*b^2*c^2+2*c^4)*a^2+(b^2+c^2)*(2*b^4+b^2*c^2+2*c^4)) : :
X(46337) = 3*X(6)-X(30489)

See Antreas Hatzipolakis and César Lozada, euclid 3507.

X(46337) lies on these lines: {6, 23}, {39, 524}, {141, 15302}, {597, 9465}, {1180, 8584}, {2493, 25488}, {3291, 3589}, {8542, 42852}, {9019, 44500}, {9872, 39389}, {11580, 38402}, {11594, 15048}, {20965, 46154}, {32621, 40689}

X(46337) = crosssum of X(6) and X(15810)


X(46338) = X(5)X(14357)∩X(30)X(67)

Barycentrics    (a^4 - a^2*b^2 + b^4 - c^4)*(a^4 - b^4 - a^2*c^2 + c^4)*(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 + 10*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - 9*b^6*c^2 - 5*a^4*c^4 - 2*a^2*b^2*c^4 + 16*b^4*c^4 + 3*a^2*c^6 - 9*b^2*c^6 + c^8) : :

X(46338) lies on the cubic K1251 and these lines: {5, 14357}, {30, 67}, {111, 468}, {523, 18907}, {3455, 7575}, {7426, 10511}, {10295, 46105}, {10297, 34897}


X(46339) = X(2)X(11657)∩X(4)X(541)

Barycentrics    5*a^12 - a^10*b^2 - 17*a^8*b^4 + 8*a^6*b^6 + 13*a^4*b^8 - 7*a^2*b^10 - b^12 - a^10*c^2 + 19*a^8*b^2*c^2 - 54*a^4*b^6*c^2 + 25*a^2*b^8*c^2 + 11*b^10*c^2 - 17*a^8*c^4 + 78*a^4*b^4*c^4 - 18*a^2*b^6*c^4 - 35*b^8*c^4 + 8*a^6*c^6 - 54*a^4*b^2*c^6 - 18*a^2*b^4*c^6 + 50*b^6*c^6 + 13*a^4*c^8 + 25*a^2*b^2*c^8 - 35*b^4*c^8 - 7*a^2*c^10 + 11*b^2*c^10 - c^12 : :

X(46339) lies on the Hutson-Parry circle, the cubics K876 and K1251, and on these lines: on lines {2, 11657}, {4, 541}, {111, 1302}, {376, 9159}, {1992, 9003}, {4240, 40138}, {7493, 11628}, {15360, 43453}

X(46339) = psi-transform of X(11656)


X(46340) = X(30)X(112)∩X(1297)X(8749)

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

X(46340) lies on the cubic K1251 and these lines: {30, 112}, {1297, 8749}, {16165, 28343}, {18876, 46105}

X(46340) = barycentric product X(23)*X(2697)
X(46340) = barycentric quotient X(i)/X(j) for these {i,j}: {2697, 18019}, {18374, 2781}


X(46341) = X(4)X(6128)∩X(74)X(46233)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(a^12 - a^10*b^2 - a^8*b^4 + a^4*b^8 + a^2*b^10 - b^12 - a^10*c^2 - a^8*b^2*c^2 + 4*a^6*b^4*c^2 + 10*a^4*b^6*c^2 - 11*a^2*b^8*c^2 - b^10*c^2 - a^8*c^4 + 4*a^6*b^2*c^4 - 26*a^4*b^4*c^4 + 10*a^2*b^6*c^4 + 13*b^8*c^4 + 10*a^4*b^2*c^6 + 10*a^2*b^4*c^6 - 22*b^6*c^6 + a^4*c^8 - 11*a^2*b^2*c^8 + 13*b^4*c^8 + a^2*c^10 - b^2*c^10 - c^12) : :

X(46341) lies on the cubic K1251 and these lines: {4, 6128}, {74, 46233}, {113, 6794}, {2394, 2986}, {7464, 32640}, {14094, 15291}, {14915, 32681}, {15738, 18877}, {40352, 44468}

X(46341) = symgonal image of X(14685)


X(46342) = X(13)X(15)∩X(62)X(32906)

Barycentrics    a^2*(Sqrt[3]*(a^6 - a^2*b^4 - a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 + b^2*c^4) + (-2*a^4 + 2*a^2*b^2 + 4*b^4 + 2*a^2*c^2 - 10*b^2*c^2 + 4*c^4)*S)*(3*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) + 4*S*(Sqrt[3]*a^2 + S)) : :

X(46342) lies on the cubic K1251 and these lines: {13, 15}, {62, 32906}, {111, 3457}, {187, 11142}, {5523, 8737}, {8739, 16459}, {16461, 36757}, {21466, 37775}

X(46342) = barycentric product X(i)*X(j) for these {i,j}: {13, 37776}, {476, 11617}, {11081, 21468}
X(46342) = barycentric quotient X(i)/X(j) for these {i,j}: {11617, 3268}, {37776, 298}
X(46342) = {X(3457),X(5995)}-harmonic conjugate of X(41406)


X(46343) = X(14)X(16)∩X(61)X(32908)

Barycentrics    a^2*(Sqrt[3]*(a^6 - a^2*b^4 - a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 + b^2*c^4) - (-2*a^4 + 2*a^2*b^2 + 4*b^4 + 2*a^2*c^2 - 10*b^2*c^2 + 4*c^4)*S)*(3*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - 4*(Sqrt[3]*a^2 - S)*S) : :

X(46343) lies on the cubic K1251 and these lines: {14, 16}, {61, 32908}, {111, 3458}, {187, 11141}, {5523, 8738}, {8740, 16460}, {16462, 36758}, {21467, 37776}

X(46343) = barycentric product X(i)*X(j) for these {i,j}: {14, 37775}, {476, 11618}, {11086, 21469}
X(46343) = barycentric quotient X(i)/X(j) for these {i,j}: {11618, 3268}, {37775, 299}
X(46343) = {X(3458),X(5994)}-harmonic conjugate of X(41407)


X(46344) = X(1)X(8074)∩X(2)X(77)

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

X(46344) lies on the cubic K1251 and these lines: {1, 8074}, {2, 77}, {9, 109}, {19, 25}, {614, 3554}, {1035, 1212}, {1038, 6554}, {1742, 1750}, {2270, 33849}, {4296, 27541}, {5819, 9817}, {7129, 40943}, {8270, 40869}, {9502, 28043}, {15849, 26020}, {16589, 37324}, {21147, 23058}


X(46345) = X(2)X(7)∩X(11)X(19)

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

X(46345) lies on the cubic K1252 and these lines: {2, 7}, {11, 19}, {25, 1436}, {56, 7079}, {282, 604}, {610, 33849}, {612, 2256}, {614, 1108}, {936, 9310}, {1210, 2082}, {1723, 5121}, {1781, 7988}, {2272, 30223}, {2347, 33995}, {3086, 7719}, {3554, 38375}, {3673, 29464}, {3692, 5205}, {6700, 17742}, {21153, 41423}, {37697, 43065}

X(46345) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 40127, 40131}


X(46346) = X(2)X(253)∩X(25)X(28782)

Barycentrics    5*a^16 - 4*a^14*b^2 - 52*a^10*b^6 + 114*a^8*b^8 - 76*a^6*b^10 + 8*a^4*b^12 + 4*a^2*b^14 + b^16 - 4*a^14*c^2 + 52*a^10*b^4*c^2 - 72*a^8*b^6*c^2 - 28*a^6*b^8*c^2 + 80*a^4*b^10*c^2 - 20*a^2*b^12*c^2 - 8*b^14*c^2 + 52*a^10*b^2*c^4 - 84*a^8*b^4*c^4 + 104*a^6*b^6*c^4 - 136*a^4*b^8*c^4 + 36*a^2*b^10*c^4 + 28*b^12*c^4 - 52*a^10*c^6 - 72*a^8*b^2*c^6 + 104*a^6*b^4*c^6 + 96*a^4*b^6*c^6 - 20*a^2*b^8*c^6 - 56*b^10*c^6 + 114*a^8*c^8 - 28*a^6*b^2*c^8 - 136*a^4*b^4*c^8 - 20*a^2*b^6*c^8 + 70*b^8*c^8 - 76*a^6*c^10 + 80*a^4*b^2*c^10 + 36*a^2*b^4*c^10 - 56*b^6*c^10 + 8*a^4*c^12 - 20*a^2*b^2*c^12 + 28*b^4*c^12 + 4*a^2*c^14 - 8*b^2*c^14 + c^16 : :

X(46346) lies on the cubic K1252 and these lines: {2, 253}, {25, 28782}, {122, 393}, {2060, 8778}, {3344, 14642}, {15341, 18337}


X(46347) = X(2)X(1032)∩X(25)X(393)

Barycentrics    a^16 + 6*a^14*b^2 - 42*a^12*b^4 + 86*a^10*b^6 - 80*a^8*b^8 + 34*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 - b^16 + 6*a^14*c^2 + 68*a^12*b^2*c^2 - 86*a^10*b^4*c^2 - 6*a^6*b^8*c^2 - 12*a^4*b^10*c^2 + 22*a^2*b^12*c^2 + 8*b^14*c^2 - 42*a^12*c^4 - 86*a^10*b^2*c^4 + 160*a^8*b^4*c^4 - 28*a^6*b^6*c^4 + 102*a^4*b^8*c^4 - 78*a^2*b^10*c^4 - 28*b^12*c^4 + 86*a^10*c^6 - 28*a^6*b^4*c^6 - 168*a^4*b^6*c^6 + 54*a^2*b^8*c^6 + 56*b^10*c^6 - 80*a^8*c^8 - 6*a^6*b^2*c^8 + 102*a^4*b^4*c^8 + 54*a^2*b^6*c^8 - 70*b^8*c^8 + 34*a^6*c^10 - 12*a^4*b^2*c^10 - 78*a^2*b^4*c^10 + 56*b^6*c^10 - 6*a^4*c^12 + 22*a^2*b^2*c^12 - 28*b^4*c^12 + 2*a^2*c^14 + 8*b^2*c^14 - c^16 : :

X(46347) lies on the cubic K1252 and these lines: {2, 1032}, {25, 393}, {1249, 1301}, {14092, 45141}, {37487, 37689}


X(46348) = X(2)X(77)∩X(25)X(7037)

Barycentrics    a*(a^12 + 2*a^11*b - 2*a^10*b^2 - 6*a^9*b^3 - a^8*b^4 + 4*a^7*b^5 + 4*a^6*b^6 + 4*a^5*b^7 - a^4*b^8 - 6*a^3*b^9 - 2*a^2*b^10 + 2*a*b^11 + b^12 + 2*a^11*c - 4*a^10*b*c + 6*a^9*b^2*c + 12*a^8*b^3*c - 28*a^7*b^4*c - 8*a^6*b^5*c + 28*a^5*b^6*c - 8*a^4*b^7*c - 6*a^3*b^8*c + 12*a^2*b^9*c - 2*a*b^10*c - 4*b^11*c - 2*a^10*c^2 + 6*a^9*b*c^2 - 22*a^8*b^2*c^2 + 24*a^7*b^3*c^2 + 12*a^6*b^4*c^2 - 12*a^5*b^5*c^2 - 12*a^4*b^6*c^2 - 8*a^3*b^7*c^2 + 22*a^2*b^8*c^2 - 10*a*b^9*c^2 + 2*b^10*c^2 - 6*a^9*c^3 + 12*a^8*b*c^3 + 24*a^7*b^2*c^3 - 16*a^6*b^3*c^3 - 20*a^5*b^4*c^3 + 8*a^4*b^5*c^3 - 8*a^3*b^6*c^3 - 16*a^2*b^7*c^3 + 10*a*b^8*c^3 + 12*b^9*c^3 - a^8*c^4 - 28*a^7*b*c^4 + 12*a^6*b^2*c^4 - 20*a^5*b^3*c^4 + 26*a^4*b^4*c^4 + 28*a^3*b^5*c^4 - 20*a^2*b^6*c^4 + 20*a*b^7*c^4 - 17*b^8*c^4 + 4*a^7*c^5 - 8*a^6*b*c^5 - 12*a^5*b^2*c^5 + 8*a^4*b^3*c^5 + 28*a^3*b^4*c^5 + 8*a^2*b^5*c^5 - 20*a*b^6*c^5 - 8*b^7*c^5 + 4*a^6*c^6 + 28*a^5*b*c^6 - 12*a^4*b^2*c^6 - 8*a^3*b^3*c^6 - 20*a^2*b^4*c^6 - 20*a*b^5*c^6 + 28*b^6*c^6 + 4*a^5*c^7 - 8*a^4*b*c^7 - 8*a^3*b^2*c^7 - 16*a^2*b^3*c^7 + 20*a*b^4*c^7 - 8*b^5*c^7 - a^4*c^8 - 6*a^3*b*c^8 + 22*a^2*b^2*c^8 + 10*a*b^3*c^8 - 17*b^4*c^8 - 6*a^3*c^9 + 12*a^2*b*c^9 - 10*a*b^2*c^9 + 12*b^3*c^9 - 2*a^2*c^10 - 2*a*b*c^10 + 2*b^2*c^10 + 2*a*c^11 - 4*b*c^11 + c^12) : :

X(46348) lies on the cubic K1252 and these lines: {2, 77}, {25, 7037}, {34, 5514}, {3342, 7118}, {40131, 45141}


X(46349) = X(4)X(10545)∩X(20)X(64)

Barycentrics    5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 22*a^4*b^6 - 7*a^2*b^8 - b^10 - 5*a^8*c^2 + 72*a^6*b^2*c^2 - 46*a^4*b^4*c^2 - 24*a^2*b^6*c^2 + 3*b^8*c^2 - 14*a^6*c^4 - 46*a^4*b^2*c^4 + 62*a^2*b^4*c^4 - 2*b^6*c^4 + 22*a^4*c^6 - 24*a^2*b^2*c^6 - 2*b^4*c^6 - 7*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(46349) = 7 X[3528] - 4 X[46261], X[5059] + 2 X[18396], 3 X[10304] - 2 X[35259], 11 X[21735] - 8 X[43586]

X(46349) lies on these lines: {4, 10545}, {20, 64}, {30, 26869}, {376, 5891}, {1370, 2777}, {1593, 38110}, {2071, 35260}, {2854, 37749}, {3153, 40196}, {3528, 46261}, {3543, 20192}, {5059, 18396}, {5656, 11413}, {7464, 37645}, {10304, 35259}, {11001, 17702}, {11738, 42021}, {12244, 41465}, {13445, 35513}, {14912, 15072}, {15080, 35483}, {15683, 44555}, {16111, 34802}, {18911, 45088}, {21735, 43586}, {35237, 35485}


X(46350) = X(2)X(280)∩X(9)X(271)

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

X(46350) lies on the curve Q172 and these lines: {2, 280}, {9, 271}, {329, 14365}, {5587, 39130}, {7078, 13138}

X(46350) = cevapoint of X(1490) and X(3341)
X(46350) = crosspoint of X(312) and X(33672)
X(46350) = X(i)-isoconjugate of X(j) for these (i,j): {56, 3342}, {221, 3345}, {223, 7152}, {2199, 41514}, {2360, 8811}, {7114, 7149}
X(46350) = barycentric product X(i)*X(j) for these {i,j}: {282, 33672}, {312, 3341}, {1490, 34404}, {3176, 44189}, {14302, 44327}
X(46350) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 3342}, {280, 41514}, {282, 3345}, {1035, 6611}, {1490, 223}, {1903, 8811}, {2192, 7152}, {3176, 196}, {3197, 221}, {3341, 57}, {5932, 14256}, {7003, 7149}, {7367, 7037}, {13614, 1817}, {14302, 14837}, {33672, 40702}


X(46351) = X(2)X(253)∩X(3)X(15394)

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

X(46351) lies on the curves K099 and Q172 and these lines: {2, 253}, {3, 15394}, {20, 2130}, {77, 271}, {216, 40813}, {3343, 6617}, {5085, 14379}, {6527, 6616}, {14615, 44326}, {34403, 40680}

X(46351) = isogonal conjugate of polar conjugate of X(47435)
X(46351) = isotomic conjugate of X(46353)
X(46351) = isotomic conjugate of the polar conjugate of X(3343)
X(46351) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 15394}, {34415, 64}
X(46351) = X(i)-cross conjugate of X(j) for these (i,j): {1498, 6617}, {41085, 1073}
X(46351) = cevapoint of X(i) and X(j) for these (i,j): {1073, 2130}, {1498, 3343}
X(46351) = crosspoint of X(69) and X(6527)
X(46351) = X(i)-isoconjugate of X(j) for these (i,j): {19, 3344}, {204, 3346}, {3213, 8805}, {7156, 8810}
X(46351) = barycentric product X(i)*X(j) for these {i,j}: {69, 3343}, {253, 6617}, {1073, 6527}, {1498, 34403}, {3926, 41085}, {14361, 15394}
X(46351) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 3344}, {1033, 6525}, {1073, 3346}, {1498, 1249}, {3343, 4}, {6527, 15466}, {6617, 20}, {14361, 14249}, {14379, 28783}, {15394, 1032}, {41085, 393}
X(46351) = {X(16096),X(41005)}-harmonic conjugate of X(253)


X(46352) = X(2)X(342)∩X(7)X(1034)

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

X(46352) lies on the curve Q172 and these lines: {2, 342}, {7, 1034}, {77, 3345}, {3342, 7013}

X(46352) = X(57)-cross conjugate of X(14256)
X(46352) = cevapoint of X(57) and X(3345)
X(46352) = X(i)-isoconjugate of X(j) for these (i,j): {55, 3341}, {282, 3197}, {1490, 2192}, {2188, 3176}, {2357, 13614}, {14302, 32652}
X(46352) = barycentric product X(i)*X(j) for these {i,j}: {85, 3342}, {347, 41514}, {1034, 14256}, {3345, 40702}
X(46352) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 3341}, {196, 3176}, {221, 3197}, {223, 1490}, {1817, 13614}, {3342, 9}, {3345, 282}, {6611, 1035}, {7037, 7367}, {7149, 7003}, {7152, 2192}, {8811, 1903}, {14256, 5932}, {14837, 14302}, {40702, 33672}, {41514, 280}


X(46353) = X(2)X(3346)∩X(4)X(1032)

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

X(46353) lies on the curves K647 and Q172 and these lines: {2, 3346}, {4, 1032}, {20, 3344}, {264, 34403}, {1105, 20792}, {2052, 31943}, {6616, 37669}

X(46353) = isotomic conjugate of X(46351)
X(46353) = polar conjugate of X(3343)
X(46353) = polar conjugate of the isogonal conjugate of X(3344)
X(46353) = X(4)-cross conjugate of X(14249)
X(46353) = cevapoint of X(4) and X(3346)
X(46353) = X(i)-isoconjugate of X(j) for these (i,j): {48, 3343}, {255, 41085}, {1498, 19614}, {1712, 14379}, {2155, 6617}
X(46353) = barycentric product X(i)*X(j) for these {i,j}: {264, 3344}, {1032, 14249}, {3346, 15466}
X(46353) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 3343}, {20, 6617}, {393, 41085}, {1032, 15394}, {1249, 1498}, {3344, 3}, {3346, 1073}, {6525, 1033}, {14249, 14361}, {15466, 6527}, {28783, 14379}


X(46354) = X(3)X(15474)∩X(942)X(39267)

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

See Angel Montesdeoca, HG121221 .

X(46354) lies on these lines: {3, 15474}, {942, 39267}, {4303, 28082}, {7742, 13397}

X(46354) = X(i)-isoconjugate of X(j) for these (i,j): {1708, 2911}, {1780, 41538}, {3811, 37579}
X(46354) = barycentric product X(15474)*X(43740)
X(46354) = barycentric quotient X(i)/X(j) for these {i,j}: {39943, 3811}, {43740, 17776}


X(46355) = X(1)X(280)∩X(4)X(189)

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

See Angel Montesdeoca, HG121221 .

X(46355) lies on the Feuerbach circumhyperbola and these lines: {1, 280}, {4, 189}, {7, 309}, {8, 44189}, {9, 271}, {84, 44075}, {282, 40957}, {285, 1172}, {1413, 9372}, {1433, 40396}, {1440, 8809}, {3577, 39130}, {7157, 17097}, {7338, 10538}, {27383, 44327}, {36121, 40836}

X(46355) = X(i)-cross conjugate of X(j) for these (i,j): {84, 280}, {7003, 189}
X(46355) = cevapoint of X(84) and X(1256)
X(46355) = X(i)-isoconjugate of X(j) for these (i,j): {6, 40212}, {40, 221}, {56, 1103}, {198, 223}, {208, 7078}, {227, 2360}, {329, 2199}, {347, 2187}, {2324, 6611}, {2331, 7011}, {3195, 7013}, {3318, 24027}, {7114, 7952}
X(46355) = barycentric product X(i)*X(j) for these {i,j}: {84, 34404}, {189, 280}, {282, 309}, {312, 1256}, {2192, 44190}, {7020, 41081}, {7058, 7157}, {40836, 44189}
X(46355) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40212}, {9, 1103}, {84, 223}, {189, 347}, {268, 7078}, {280, 329}, {282, 40}, {285, 1817}, {309, 40702}, {1146, 3318}, {1256, 57}, {1413, 6611}, {1433, 7011}, {1436, 221}, {1440, 14256}, {1903, 227}, {2192, 198}, {2208, 2199}, {7003, 7952}, {7008, 2331}, {7118, 2187}, {7129, 208}, {7151, 3209}, {7154, 3195}, {7157, 6354}, {7367, 7074}, {34404, 322}, {40836, 196}, {41081, 7013}


X(46356) = X(1)X(44301)∩X(8)X(8051)

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

See Angel Montesdeoca, HG121221 .

X(46356) lies on the Feuerbach circumhyperbola and these lines: {1, 44301}, {8, 8051}, {9, 2137}, {3680, 6553}

X(46356) = X(1616)-isoconjugate of X(2136)
X(46356) = barycentric product X(6553)*X(8051)
X(46356) = barycentric quotient X(i)/X(j) for these {i,j}: {2137, 23511}, {6553, 8055}, {8051, 4452}


X(46357) = 1ST INTERCEPT, OTHER THAN X(3), OF LINE X(3)X(2574) AND McCAY CUBIC

Barycentrics    a*((2*S*b*c*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*OH-a*((b^2+c^2)*a^6-(3*b^4-2*b^2*c^2+3*c^4)*a^4+(b^2+c^2)*(3*b^4-5*b^2*c^2+3*c^4)*a^2-(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2))*K+2*S*a*(-2*(-a^2+b^2+c^2)*S*OH+3*a*b*c*(-a^2+b^2+c^2))*OH) : :
Barycentrics    a*(2*OH*(OH-3*R)*S*SA*a+((S^2-3*SB*SC)*OH*b*c+(3*S^2-2*SB*SC-(18*R^2-5*SA)*SA)*S*a)*K) : :, where K=OH*(OH-3*R)*sqrt(2*R*OH^3-S^2-SW^2-18*R^2*(3*R^2-SW))/(2*R*OH^3-S^2-SW^2-18*R^2*(3*R^2-SW))

See Antreas Hatzipolakis, Francisco Javier García Capitán, César Lozada, and Bernard Gibert, euclid 3550.

X(46357) lies on cubics K003, K019, K187, K376, K443, K810, K851; curves Q007, Q008, Q009, Q010, Q020, Q063, Q113; and this line: {3, 2574}

X(46357) = reflection of X(46358) in X(3)
X(46357) = isogonal conjugate of X(46358)
X(46357) = X(3)-vertex conjugate of-X(46358)
X(46357) = 1st focus of the inconic centered at X(3) (see cubic K003)


X(46358) = 2ND INTERCEPT, OTHER THAN X(3), OF LINE X(3)X(2574) AND McCAY CUBIC

Barycentrics    a*(-(2*S*b*c*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*OH-a*((b^2+c^2)*a^6-(3*b^4-2*b^2*c^2+3*c^4)*a^4+(b^2+c^2)*(3*b^4-5*b^2*c^2+3*c^4)*a^2-(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2))*K+2*S*a*(-2*(-a^2+b^2+c^2)*S*OH+3*a*b*c*(-a^2+b^2+c^2))*OH) : :
Barycentrics    a*(2*OH*(OH-3*R)*S*SA*a-((S^2-3*SB*SC)*OH*b*c+(3*S^2-2*SB*SC-(18*R^2-5*SA)*SA)*S*a)*K) : :, where K=OH*(OH-3*R)*sqrt(2*R*OH^3-S^2-SW^2-18*R^2*(3*R^2-SW))/(2*R*OH^3-S^2-SW^2-18*R^2*(3*R^2-SW))

See Antreas Hatzipolakis, Francisco Javier García Capitán, César Lozada, and Bernard Gibert, euclid 3550.

X(46358) lies on cubics K003, K019, K187, K376, K443, K810, K851; curves Q007, Q008, Q009, Q010, Q020, Q063, Q113; and this line: {3, 2574}

X(46358) = reflection of X(46350) in X(3)
X(46358) = isogonal conjugate of X(46357)
X(46358) = X(3)-vertex conjugate of-X(46357)
X(46358) = 2nd focus of the inconic centered at X(3) (see cubic K003)


X(46359) = BARYCENTRIC QUOTIENT X(39)/X(515)

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

X(46359) lies on these lines: {38, 46152}, {102, 110}, {660, 23691}, {670, 34393}, {3917, 46153}

X(46359) = crosspoint of X(102) and X(34393)
X(46359) = X(i)-isoconjugate of X(j) for these (i,j): {82, 515}, {83, 2182}, {8755, 34055}
X(46359) = barycentric product X(i)*X(j) for these {i,j}: {38, 36100}, {39, 34393}, {102, 141}, {1930, 32677}, {2399, 46153}, {3665, 15629}, {20883, 36055}
X(46359) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 515}, {102, 83}, {141, 35516}, {1401, 34050}, {1843, 8755}, {1964, 2182}, {4553, 42718}, {32677, 82}, {34393, 308}, {35325, 7452}, {36055, 34055}, {36100, 3112}, {46152, 24035}, {46153, 2406}


X(46360) = X(4)X(3527)∩X(8573)X(11433)

Barycentrics    (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 3*a^4*c^2 - 6*a^2*b^2*c^2 + b^4*c^2 + 3*a^2*c^4 + b^2*c^4 - c^6)*(2*a^12 - 9*a^10*b^2 + 17*a^8*b^4 - 18*a^6*b^6 + 12*a^4*b^8 - 5*a^2*b^10 + b^12 - 9*a^10*c^2 + 18*a^8*b^2*c^2 - 10*a^6*b^4*c^2 - 4*a^4*b^6*c^2 + 11*a^2*b^8*c^2 - 6*b^10*c^2 + 17*a^8*c^4 - 10*a^6*b^2*c^4 - 16*a^4*b^4*c^4 - 6*a^2*b^6*c^4 + 15*b^8*c^4 - 18*a^6*c^6 - 4*a^4*b^2*c^6 - 6*a^2*b^4*c^6 - 20*b^6*c^6 + 12*a^4*c^8 + 11*a^2*b^2*c^8 + 15*b^4*c^8 - 5*a^2*c^10 - 6*b^2*c^10 + c^12) : :

See Antreas Hatzipolakis and Peter Moses, euclid 3542.

X(46360) = lies on these lines: {4,3527}, {8573,11433}


X(46361) = (name (pending)

Barycentrics    (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 3*a^4*c^2 - 6*a^2*b^2*c^2 + b^4*c^2 + 3*a^2*c^4 + b^2*c^4 - c^6)*(a^12 - 4*a^10*b^2 + 7*a^8*b^4 - 8*a^6*b^6 + 7*a^4*b^8 - 4*a^2*b^10 + b^12 - 6*a^10*c^2 + 10*a^8*b^2*c^2 - 4*a^6*b^4*c^2 - 4*a^4*b^6*c^2 + 10*a^2*b^8*c^2 - 6*b^10*c^2 + 15*a^8*c^4 - 8*a^6*b^2*c^4 - 14*a^4*b^4*c^4 - 8*a^2*b^6*c^4 + 15*b^8*c^4 - 20*a^6*c^6 - 4*a^4*b^2*c^6 - 4*a^2*b^4*c^6 - 20*b^6*c^6 + 15*a^4*c^8 + 12*a^2*b^2*c^8 + 15*b^4*c^8 - 6*a^2*c^10 - 6*b^2*c^10 + c^12)*(a^12 - 6*a^10*b^2 + 15*a^8*b^4 - 20*a^6*b^6 + 15*a^4*b^8 - 6*a^2*b^10 + b^12 - 4*a^10*c^2 + 10*a^8*b^2*c^2 - 8*a^6*b^4*c^2 - 4*a^4*b^6*c^2 + 12*a^2*b^8*c^2 - 6*b^10*c^2 + 7*a^8*c^4 - 4*a^6*b^2*c^4 - 14*a^4*b^4*c^4 - 4*a^2*b^6*c^4 + 15*b^8*c^4 - 8*a^6*c^6 - 4*a^4*b^2*c^6 - 8*a^2*b^4*c^6 - 20*b^6*c^6 + 7*a^4*c^8 + 10*a^2*b^2*c^8 + 15*b^4*c^8 - 4*a^2*c^10 - 6*b^2*c^10 + c^12) : :

See Antreas Hatzipolakis and Peter Moses, euclid 3542.

X(46361) = lies on these lines: { }


X(46362) = X(1)X(4014)∩X(40)X(550)

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

See Angel Montesdeoca, euclid 3557.

X(46362) = lies on these lines: {1,4014}, {40,550}, {1385,32486}, {5258,31662}, {5400,7987}, {10609,21362}, {11372,40256}


X(46363) = X(3)X(6)∩X(51)X(3089)

Barycentrics    a^2 (-a^12 (b^2+c^2)-2 a^2 (b^2-c^2)^4 (2 b^4+b^2 c^2+2 c^4)+a^10 (4 b^4+6 b^2 c^2+4 c^4)+(b^2-c^2)^4 (b^6+b^4 c^2+b^2 c^4+c^6)+a^4 (b^2-c^2)^2 (5 b^6-17 b^4 c^2-17 b^2 c^4+5 c^6)-a^8 (5 b^6+17 b^4 c^2+17 b^2 c^4+5 c^6)+4 a^6 (7 b^6 c^2+2 b^4 c^4+7 b^2 c^6)) : :

See Antreas Hatzipolakis and Angel Montesdeoca, euclid 3560.

X(46363) = lies on these lines: {3,6}, {51,3089}, {185,12250}, {373,43841}, {1596,10110} {2393,11745}, {3567,6353}, {5462,6677}, {5562,6804}, {5907,11411}, {6000,12241}, {6403,17040}, {6467,7487}, {7392,12282}, {7401,14913}, {9306,12166}, {9825,34382}, {11431,14531}, {11695,23292}, {11793,13567}, {12007,41589}, {12161,41619}, {12242,22530}, {12294,18909}, {13474,34780}, {15585,32191}, {18925,40673}, {32366,34782}, {32411,37971}


X(46364) = (name pending)

Barycentrics    4 a^34-25 a^32 (b^2+c^2)-(b^2-c^2)^12 (b^2+c^2)^3 (2 b^4+5 b^2 c^2+2 c^4)+a^30 (50 b^4+204 b^2 c^2+50 c^4)-a^28 (b^6+508 b^4 c^2+508 b^2 c^4+c^6)+a^26 (-116 b^8+82 b^6 c^2+2092 b^4 c^4+82 b^2 c^6-116 c^8)+2 a^2 (b^2-c^2)^10 (b^2+c^2)^2 (6 b^8-19 b^6 c^2-70 b^4 c^4-19 b^2 c^6+6 c^8)-2 a^18 (b^2-c^2)^4 (44 b^8-2315 b^6 c^2-7550 b^4 c^4-2315 b^2 c^6+44 c^8)+a^24 (65 b^10+1410 b^8 c^2-2691 b^6 c^4-2691 b^4 c^6+1410 b^2 c^8+65 c^10)+2 a^22 (111 b^12-564 b^10 c^2-2075 b^8 c^4+5888 b^6 c^6-2075 b^4 c^8-564 b^2 c^10+111 c^12)-a^4 (b^2-c^2)^8 (27 b^14-168 b^12 c^2+42 b^10 c^4+1507 b^8 c^6+1507 b^6 c^8+42 b^4 c^10-168 b^2 c^12+27 c^14)-a^20 (297 b^14+2824 b^12 c^2-13546 b^10 c^4+10681 b^8 c^6+10681 b^6 c^8-13546 b^4 c^10+2824 b^2 c^12+297 c^14)+a^16 (b^2-c^2)^2 (407 b^14+226 b^12 c^2-21124 b^10 c^4+17291 b^8 c^6+17291 b^6 c^8-21124 b^4 c^10+226 b^2 c^12+407 c^14)+2 a^6 (b^2-c^2)^6 (17 b^16+30 b^14 c^2+1076 b^12 c^4-430 b^10 c^6-3434 b^8 c^8-430 b^6 c^10+1076 b^4 c^12+30 b^2 c^14+17 c^16)+2 a^10 (b^2-c^2)^4 (62 b^16+439 b^14 c^2-5030 b^12 c^4-1079 b^10 c^6+15312 b^8 c^8-1079 b^6 c^10-5030 b^4 c^12+439 b^2 c^14+62 c^16)-2 a^14 (b^2-c^2)^2 (121 b^16+2364 b^14 c^2-7492 b^12 c^4-9756 b^10 c^6+26454 b^8 c^8-9756 b^6 c^10-7492 b^4 c^12+2364 b^2 c^14+121 c^16)-a^12 (b^2-c^2)^2 (59 b^18-2894 b^16 c^2-5351 b^14 c^4+42427 b^12 c^6-33217 b^10 c^8-33217 b^8 c^10+42427 b^6 c^12-5351 b^4 c^14-2894 b^2 c^16+59 c^18)-a^8 (b^2-c^2)^4 (61 b^18+1118 b^16 c^2-1185 b^14 c^4-12083 b^12 c^6+13113 b^10 c^8+13113 b^8 c^10-12083 b^6 c^12-1185 b^4 c^14+1118 b^2 c^16+61 c^18) : :

See Antreas Hatzipolakis and Angel Montesdeoca, euclid 3560.

X(46364) lies on these lines: { }


X(46365) = (name pending)

Barycentrics    a/(3*a^10*b^2 - 2*a^9*b^3 - 14*a^8*b^4 + 6*a^7*b^5 + 24*a^6*b^6 - 6*a^5*b^7 - 18*a^4*b^8 + 2*a^3*b^9 + 5*a^2*b^10 + 10*a^10*b*c + 2*a^9*b^2*c - 10*a^8*b^3*c + 2*a^7*b^4*c - 10*a^6*b^5*c + 10*a^5*b^6*c + 26*a^4*b^7*c - 18*a^3*b^8*c - 16*a^2*b^9*c + 4*a*b^10*c + 3*a^10*c^2 + 2*a^9*b*c^2 + 16*a^8*b^2*c^2 - 8*a^7*b^3*c^2 - 21*a^6*b^4*c^2 + 20*a^5*b^5*c^2 + 5*a^4*b^6*c^2 - 2*a^2*b^8*c^2 - 14*a*b^9*c^2 - b^10*c^2 - 2*a^9*c^3 - 10*a^8*b*c^3 - 8*a^7*b^2*c^3 + 30*a^6*b^3*c^3 - 24*a^5*b^4*c^3 - 26*a^4*b^5*c^3 + 40*a^3*b^6*c^3 + 10*a^2*b^7*c^3 - 6*a*b^8*c^3 - 4*b^9*c^3 - 14*a^8*c^4 + 2*a^7*b*c^4 - 21*a^6*b^2*c^4 - 24*a^5*b^3*c^4 + 26*a^4*b^4*c^4 - 24*a^3*b^5*c^4 - 3*a^2*b^6*c^4 + 30*a*b^7*c^4 - 4*b^8*c^4 + 6*a^7*c^5 - 10*a^6*b*c^5 + 20*a^5*b^2*c^5 - 26*a^4*b^3*c^5 - 24*a^3*b^4*c^5 + 12*a^2*b^5*c^5 - 14*a*b^6*c^5 + 4*b^7*c^5 + 24*a^6*c^6 + 10*a^5*b*c^6 + 5*a^4*b^2*c^6 + 40*a^3*b^3*c^6 - 3*a^2*b^4*c^6 - 14*a*b^5*c^6 + 10*b^6*c^6 - 6*a^5*c^7 + 26*a^4*b*c^7 + 10*a^2*b^3*c^7 + 30*a*b^4*c^7 + 4*b^5*c^7 - 18*a^4*c^8 - 18*a^3*b*c^8 - 2*a^2*b^2*c^8 - 6*a*b^3*c^8 - 4*b^4*c^8 + 2*a^3*c^9 - 16*a^2*b*c^9 - 14*a*b^2*c^9 - 4*b^3*c^9 + 5*a^2*c^10 + 4*a*b*c^10 - b^2*c^10) : :

See Angel Montesdeoca and Peter Moses, euclid 3563

X(46365) = lies on these lines: { }


X(46366) = X(1)X(3)∩X(920)X(1069)

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

Let A' = X(1)-line conjugate of the anticevian triangle of X(3), and define B' and C' cyclically. Then A'B'C' is perspective to the cevian triangle of X(920), and the perspector is X(46366).

X(46366) lies on these lines: {1, 3}, {920, 1069}, {1826, 8609}

X(46366) = crosspoint of X(1068) and X(3193)
X(46366) = barycentric product X(i)*X(j) for these {i,j}: {46, 45206}, {1195, 20930}, {1858, 5905}
X(46366) = barycentric quotient X(i)/X(j) for these {i,j}: {1195, 90}, {1858, 2994}, {45206, 20570}


X(46367) = X(6)X(9050)∩X(7)X(145)

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

Let A' = X(1)-line conjugate of the anticevian triangle of X(9), and define B' and C' cyclically. Then A'B'C' is perspective to the cevian triangle of X(19604), and the perspector is X(46367).

X(46367) lies on these lines: {6, 9050}, {7, 145}, {1122, 45205}, {7023, 16945}

X(46367) = crosssum of X(3158) and X(6555)
X(46367) = X(i)-isoconjugate of X(j) for these (i,j): {145, 1261}, {1222, 3158}, {1476, 6555}, {3161, 23617}, {4162, 8706}, {4936, 40420}, {40528, 44724}
X(46367) = barycentric product X(i)*X(j) for these {i,j}: {1, 45205}, {1122, 8056}, {1201, 27818}, {1828, 27832}, {3663, 40151}, {3752, 19604}, {16079, 45204}, {16945, 26563}
X(46367) = barycentric quotient X(i)/X(j) for these {i,j}: {1122, 18743}, {1201, 3161}, {2347, 6555}, {3663, 44723}, {3752, 44720}, {6363, 4521}, {16945, 23617}, {19604, 32017}, {20228, 3158}, {23845, 30720}, {38266, 1261}, {38828, 8706}, {40151, 1222}, {42336, 4394}, {45205, 75}


X(46368) = X(81)X(213)∩X(354)X(10458)

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

Let A' = X(1)-line conjugate of the anticevian triangle of X(42), and define B' and C' cyclically. Then A'B'C' is perspective to the cevian triangle of X(81), and the perspector is X(46368).

X(46368) lies on these lines: {81, 213}, {354, 10458}, {1206, 16819}, {3720, 18166}

X(46368) = X(81)-Ceva conjugate of X(1206)
X(46368) = barycentric product X(i)*X(j) for these {i,j}: {1206, 16748}, {16819, 18166}, {17175, 45223}


X(46369) = X(1)X(39)∩X(99)X(4367)

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

Let A' = X(1)-line conjugate of the anticevian triangle of X(512), and define B' and C' cyclically. Then A'B'C' is perspective to the cevian triangle of X(1), and the perspector is X(46369).

X(46369) lies on these lines: {1, 39}, {99, 4367}, {3903, 4879}, {4436, 17136}, {4553, 46177}, {21051, 27133}

X(46369) = X(39292)-Ceva conjugate of X(2238)
X(46369) = crosspoint of X(i) and X(j) for these (i,j): {1, 9424}, {99, 3903}
X(46369) = crosssum of X(i) and X(j) for these (i,j): {1, 7170}, {512, 4367}


X(46370) = X(1)X(167)∩X(4)X(8140)

Barycentrics    a*((b - c)*(8*S^2 - (a - b - c)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c + 2*a*b*c + 5*b^2*c - a*c^2 + 5*b*c^2 - c^3)*Sin[A/2]) + (a - b + c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 - 2*a^3*c + a^2*b*c - 4*a*b^2*c - 3*b^3*c + 3*a*b*c^2 + b^2*c^2 + 2*a*c^3 + 3*b*c^3 - c^4)*Sin[B/2] - (a + b - c)*(a^4 - 2*a^3*b + 2*a*b^3 - b^4 + a^3*c + a^2*b*c + 3*a*b^2*c + 3*b^3*c - a^2*c^2 - 4*a*b*c^2 + b^2*c^2 - a*c^3 - 3*b*c^3)*Sin[C/2]) : :

Let HA be the hyperbola through X(1) with foci B and C, and define HB and HC cyclically. The three hyperbolas meet in X(1) and X(46370). (Peter Moses, December 18, 2021)

X(46370) lies on the curve Q104 and these lines: {1, 167}, {4, 8140}, {40, 43192}, {1490, 15502}

X(46370) = reflection of X(1) in X(13443)
X(46370) = isogonal conjugate of X(46705)
X(46370) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {177, 6585, 1}, {7590, 16012, 1}, {8091, 8351, 8422}


X(46371) = X(4)X(512)∩X(235)X(523)

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

See Antreas Hatzipolakis and César Lozada, euclid 3578.

X(46371) lies on these lines: {4, 512}, {107, 13494}, {235, 523}, {525, 41587}, {2501, 5254}, {3574, 23290}, {5664, 39606}, {10018, 44814}, {14249, 18504}, {14457, 15328}, {16230, 41079}

X(46371) = crossdifference of every pair of points on line {X(3289), X(41615)}
X(46371) = trilinear product X(2501)*X(17882)
X(46371) = {X(4), X(14618)}-harmonic conjugate of X(23105)


X(46372) = X(3)-OF-ANTICEVIAN TRIANGLE OF X(3)

Barycentrics    a^2*(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 + 10*a^10*b^2*c^2 - 13*a^8*b^4*c^2 + 28*a^6*b^6*c^2 - 31*a^4*b^8*c^2 + 10*a^2*b^10*c^2 + b^12*c^2 + 9*a^10*c^4 - 13*a^8*b^2*c^4 - 30*a^6*b^4*c^4 + 22*a^4*b^6*c^4 + 21*a^2*b^8*c^4 - 9*b^10*c^4 - 5*a^8*c^6 + 28*a^6*b^2*c^6 + 22*a^4*b^4*c^6 - 52*a^2*b^6*c^6 + 7*b^8*c^6 - 5*a^6*c^8 - 31*a^4*b^2*c^8 + 21*a^2*b^4*c^8 + 7*b^6*c^8 + 9*a^4*c^10 + 10*a^2*b^2*c^10 - 9*b^4*c^10 - 5*a^2*c^12 + b^2*c^12 + c^14) : :

X(46372) lies on these lines: {3, 22658}, {4, 6}, {64, 2063}, {154, 22467}, {155, 15311}, {184, 36982}, {394, 5894}, {399, 13093}, {1147, 6000}, {1619, 12174}, {1993, 5895}, {2072, 14216}, {2777, 16266}, {2781, 9914}, {3292, 30443}, {3357, 15068}, {3515, 15647}, {3548, 6247}, {5020, 32184}, {5504, 12085}, {5663, 32321}, {5878, 18445}, {5907, 44883}, {6225, 43605}, {6241, 43617}, {6644, 6759}, {6696, 17814}, {7506, 32063}, {7517, 9934}, {7729, 17928}, {8567, 15066}, {9306, 31978}, {10249, 33537}, {10605, 45172}, {11477, 32602}, {12161, 12897}, {12163, 45171}, {13371, 40285}, {13861, 15012}, {17837, 22647}, {18381, 18418}, {18390, 22968}, {18439, 18466}, {22972, 26958}, {32284, 34779}, {34148, 36983}, {39568, 44668}

X(46372) = midpoint of X(9914) and X(12164)
X(46372) = reflection of X(46373) in X(46374)
X(46372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1181, 1498, 2883}, {1181, 2883, 34117}, {8550, 19149, 34117}


X(46373) = X(4)-OF-ANTICEVIAN TRIANGLE OF X(3)

Barycentrics    a^2*(a^14 - 3*a^12*b^2 + a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - a^4*b^10 + 3*a^2*b^12 - b^14 - 3*a^12*c^2 + 18*a^10*b^2*c^2 - 13*a^8*b^4*c^2 - 36*a^6*b^6*c^2 + 51*a^4*b^8*c^2 - 14*a^2*b^10*c^2 - 3*b^12*c^2 + a^10*c^4 - 13*a^8*b^2*c^4 + 82*a^6*b^4*c^4 - 50*a^4*b^6*c^4 - 35*a^2*b^8*c^4 + 15*b^10*c^4 + 5*a^8*c^6 - 36*a^6*b^2*c^6 - 50*a^4*b^4*c^6 + 92*a^2*b^6*c^6 - 11*b^8*c^6 - 5*a^6*c^8 + 51*a^4*b^2*c^8 - 35*a^2*b^4*c^8 - 11*b^6*c^8 - a^4*c^10 - 14*a^2*b^2*c^10 + 15*b^4*c^10 + 3*a^2*c^12 - 3*b^2*c^12 - c^14) : :
X(46373) = 3 X[32357] - 4 X[32401]

X(46373) lies on the Feuerbach circumhyperbola of the tangential triangle and these lines: {1, 7169}, {3, 1661}, {4, 45045}, {6, 64}, {20, 159}, {25, 2929}, {30, 9937}, {66, 43690}, {154, 16936}, {155, 6000}, {184, 30443}, {195, 13093}, {378, 12250}, {394, 36982}, {399, 12315}, {541, 19908}, {610, 3556}, {1092, 1498}, {1103, 12335}, {1204, 44079}, {1503, 19588}, {1597, 6247}, {1619, 6225}, {1853, 11403}, {1885, 34944}, {2071, 32605}, {2777, 2931}, {2916, 35240}, {2917, 5925}, {2918, 35243}, {2930, 17845}, {2935, 15063}, {3343, 33583}, {3357, 9729}, {5020, 5893}, {5663, 12301}, {5898, 17800}, {6642, 22802}, {6696, 11479}, {6759, 35237}, {7395, 10606}, {7484, 8567}, {7503, 15740}, {10117, 15750}, {11441, 36983}, {15047, 35450}, {15066, 43813}, {15136, 40285}, {17837, 17847}, {18916, 35502}, {32125, 37197}, {32357, 32401}, {37201, 41602}

X(46373) = reflection of X(46372) in X(46374)
X(46373) = reflection of X(i) in X(j) for these {i,j}: {9914, 3}, {43695, 2883}
X(46373) = isotomic conjugate of the polar conjugate of X(17807)
X(46373) = tangential isogonal conjugate of X(3515)
X(46373) = X(i)-Ceva conjugate of X(j) for these (i,j): {1619, 159}, {6225, 1498}, {11413, 3}, {37669, 6}
X(46373) = X(17807)-cross conjugate of X(40221)
X(46373) = crosssum of X(i) and X(j) for these (i,j): {512, 39020}, {523, 35968}
X(46373) = barycentric product X(i)*X(j) for these {i,j}: {20, 40221}, {69, 17807}
X(46373) = barycentric quotient X(i)/X(j) for these {i,j}: {17807, 4}, {40221, 253}
X(46373) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 64, 31978}, {6225, 11413, 1619}, {6293, 12379, 64}


X(46374) = X(5)-OF-ANTICEVIAN TRIANGLE OF X(3)

Barycentrics    a^2*(a^14 - 4*a^12*b^2 + 5*a^10*b^4 - 5*a^6*b^8 + 4*a^4*b^10 - a^2*b^12 - 4*a^12*c^2 + 14*a^10*b^2*c^2 - 13*a^8*b^4*c^2 - 4*a^6*b^6*c^2 + 10*a^4*b^8*c^2 - 2*a^2*b^10*c^2 - b^12*c^2 + 5*a^10*c^4 - 13*a^8*b^2*c^4 + 26*a^6*b^4*c^4 - 14*a^4*b^6*c^4 - 7*a^2*b^8*c^4 + 3*b^10*c^4 - 4*a^6*b^2*c^6 - 14*a^4*b^4*c^6 + 20*a^2*b^6*c^6 - 2*b^8*c^6 - 5*a^6*c^8 + 10*a^4*b^2*c^8 - 7*a^2*b^4*c^8 - 2*b^6*c^8 + 4*a^4*c^10 - 2*a^2*b^2*c^10 + 3*b^4*c^10 - a^2*c^12 - b^2*c^12) : :

X(46374) lies on these lines: {3, 1177}, {6, 32184}, {49, 20427}, {54, 10606}, {64, 34148}, {110, 5895}, {154, 33524}, {156, 2777}, {184, 5894}, {569, 23328}, {578, 6696}, {974, 2904}, {1092, 2883}, {1147, 15311}, {1498, 43574}, {1503, 13346}, {1614, 5925}, {1620, 19128}, {2071, 6293}, {2935, 6241}, {3088, 34118}, {3146, 15139}, {3292, 36982}, {3357, 45957}, {3534, 32379}, {5012, 8567}, {5878, 22115}, {5893, 9306}, {6000, 41597}, {6247, 13352}, {6759, 15704}, {9786, 19142}, {9833, 37477}, {10117, 11449}, {10192, 43652}, {10323, 32391}, {10628, 32138}, {11424, 23332}, {11425, 44883}, {11468, 17835}, {11598, 15463}, {12041, 34114}, {12111, 17847}, {13198, 34469}, {13348, 35228}, {14216, 37495}, {15033, 40686}, {15072, 17824}, {17704, 41593}, {31978, 34986}, {37498, 44668}

X(46374) = midpoint of X(46372) and X(46373)
X(46374) = {X(5012),X(43813)}-harmonic conjugate of X(8567)


X(46375) = X(6)-OF-ANTICEVIAN TRIANGLE OF X(3)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^10 + a^8*b^2 - 8*a^6*b^4 + 8*a^4*b^6 - a^2*b^8 - b^10 + a^8*c^2 + 6*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 - 8*a^6*c^4 - 4*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 2*b^6*c^4 + 8*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(46375) lies on these lines: {5, 6}, {14642, 14961}, {15905, 32661}, {20233, 22120}


X(46376) = X(55)X(1151)∩X(57)X(30279)

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

X(46376) lies on the cubic K1253 and these lines: {55, 1151}, {57, 30279}, {165, 6213}, {198, 1615}, {222, 2066}, {354, 16214}, {5273, 30303}, {7177, 13389}

X(46376) = X(34125)-cross conjugate of X(6502)
X(46376) = X(i)-isoconjugate of X(j) for these (i,j): {175, 7133}, {2362, 30413}
X(46376) = barycentric product X(i)*X(j) for these {i,j}: {6502, 40699}, {13389, 15891}
X(46376) = barycentric quotient X(i)/X(j) for these {i,j}: {1124, 31547}, {2066, 30413}, {6502, 175}, {30336, 7090}


X(46377) = X(55)X(1152)∩X(57)X(7133)

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

X(46377) lies on the cubic K1253 and these lines: {55, 1152}, {57, 7133}, {165, 6212}, {198, 1615}, {222, 5414}, {354, 16213}, {1155, 13455}, {5273, 30302}, {7177, 13388}

X(46377) = isogonal conjugate of the anticomplement of X(45704)
X(46377) = X(34121)-cross conjugate of X(2067)
X(46377) = X(i)-isoconjugate of X(j) for these (i,j): {176, 42013}, {16232, 30412}
X(46377) = barycentric product X(i)*X(j) for these {i,j}: {2067, 40700}, {13388, 15892}
X(46377) = barycentric quotient X(i)/X(j) for these {i,j}: {1335, 31548}, {2067, 176}, {5414, 30412}, {30335, 14121}


X(46378) = X(19)X(25)∩X(57)X(2067)

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

X(46378) lies on the cubic K1253 and these lines: {19, 25}, {57, 2067}, {165, 6213}, {610, 5414}, {2066, 2270}, {5273, 7090}, {7291, 13388}, {7348, 30385}, {9778, 30413}, {11051, 13456}, {11349, 13389}, {16441, 30557}

X(46378) = X(6213)-Ceva conjugate of X(7133)
X(46378) = X(i)-isoconjugate of X(j) for these (i,j): {6502, 40699}, {13389, 15891}
X(46378) = barycentric product X(i)*X(j) for these {i,j}: {175, 7133}, {2362, 30413}
X(46378) = barycentric quotient X(7133)/X(40699)
X(46378) = {X(19),X(34121)}-harmonic conjugate of X(7133)
X(46378) = {X(19),X(5338)}-harmonic conjugate of X(46379)


X(46379) = X(19)X(25)∩X(57)X(6502)

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

X(46379) lies on the cubic K1253 and these lines: {19, 25}, {57, 6502}, {165, 6212}, {610, 2066}, {2270, 5414}, {5273, 14121}, {7291, 13389}, {7347, 30386}, {9778, 30412}, {11051, 13427}, {11349, 13388}, {16440, 30556}

X(46379) = X(6212)-Ceva conjugate of X(42013)
X(46379) = X(i)-isoconjugate of X(j) for these (i,j): {2067, 40700}, {13388, 15892}
X(46379) = barycentric product X(i)*X(j) for these {i,j}: {176, 42013}, {16232, 30412}
X(46379) = barycentric quotient X(42013)/X(40700)
X(46379) = {X(19),X(34125)}-harmonic conjugate of X(42013)
X(46379) = {X(19),X(5338)}-harmonic conjugate of X(46378)






leftri   Crossdifferences: X(1)X(k): X(46380) - X(46393)  rightri
This preamble is contributed by Clark Kimberling and Peter Moses, December 21, 2021. The appearance of (j,k) in the following list means that the crossdifference of X(1) and X(j) is X(k):

(2,649), (3,650), (4,652), (5,654), (6,513), (7,657), (8,649), (9,513), (10,649), (11,654), (12,654), (19,656), (20,657), (21,661), (22,46380), (23,46381), (25,2522), (27,46382), (28,656), (29,822), (30,9404), (31,661), (32,1491), (33,652), (34,652), (35,650), (36,650), (37,513), (38,661), (39,659), (40,650), (41,2254), (42,649), (43,649), (44,513), (45,513), (46,650), (47,661), (48,656), (50,18116), (54,2600), (55,650), (56,650), (57,650), (58,661), (592,46383), (60,2610), (63,661), (65,650), (69,2484), (71,46384), (72,513), (73,652), (75,798), (76,46385), (77,657), (78,649), (79,9404), (80,654), (81,661), (82,8061), (83,46386), (84,14298), (85,46387), (86,798), (87,20979), (88,1635), (89,4893), (90,46388), (92,822), (99,46389), (100,1635), (102,46390), (103,46391), (104,46392), (108,46393), (109,46394)

For every point U, the crossdifference of X(1) and U lies on the anti-orthic axis, X(44) X(513).

underbar



X(46380) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(22)

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

X(46380) lies on these lines: {44, 513}, {647, 826}, {665, 2523}, {824, 16757}, {905, 16892}, {4024, 6591}, {4025, 14838}, {4705, 8646}, {6588, 11125}, {6590, 16612}, {8635, 8678}, {16751, 30913}, {21122, 21761}, {29021, 45745}

X(46380) = X(839)-complementary conjugate of X(21235)
X(46380) = X(14542)-Ceva conjugate of X(3270)
X(46380) = crossdifference of every pair of points on line {1, 22}
X(46380) = barycentric product X(i)*X(j) for these {i,j}: {521, 11392}, {1577, 4280}
X(46380) = barycentric quotient X(i)/X(j) for these {i,j}: {4280, 662}, {11392, 18026}
X(46380) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 2509, 661}, {650, 2522, 649}


X(46381) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(23)

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

X(46381) lies on these lines: {39, 647}, {44, 513}, {1021, 16549}, {3700, 17369}, {3960, 16892}, {4024, 16612}, {4750, 14838}, {26035, 26080}

X(46381) = crossdifference of every pair of points on line {1, 23}


X(46382) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(27)

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

X(46382) lies on these lines: {44, 513}, {647, 810}, {1021, 1577}, {21761, 43925}, {22382, 23189}, {24018, 24562}

X(46382) = crosssum of X(7490) and X(17925)
X(46382) = crossdifference of every pair of points on line {1, 27}
X(46382) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36077}, {286, 36080}, {811, 2215}
X(46382) = barycentric product X(i)*X(j) for these {i,j}: {71, 23882}, {405, 656}, {520, 39585}, {647, 5271}, {649, 42706}, {810, 44140}, {1459, 5295}, {5320, 14208}, {8611, 37543}
X(46382) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36077}, {405, 811}, {2200, 36080}, {3049, 2215}, {5271, 6331}, {5320, 162}, {23882, 44129}, {39585, 6528}, {42706, 1978}
X(46382) = {X(652),X(656)}-harmonic conjugate of X(822)


X(46383) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(51)

Barycentrics    a*(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(46383) lies on these lines: {6, 4976}, {44, 513}, {323, 401}, {522, 22383}, {647, 21173}, {693, 28983}, {900, 7252}, {1021, 22086}, {2298, 2423}, {2523, 21189}, {4024, 21758}, {4391, 26652}, {15150, 17926}, {20293, 21719}, {20980, 45745}

X(46383) = isotomic conjugate of trilinear pole of line X(5)X(75)
X(46383) = crossdifference of every pair of points on line {1, 51}
X(46383) = barycentric product X(i)*X(j) for these {i,j}: {649, 19811}, {693, 26890}
X(46383) = barycentric quotient X(i)/X(j) for these {i,j}: {19811, 1978}, {26890, 100}


X(46384) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(59)

Barycentrics    a*(a - b - c)^2*(b - c)^3*(a^2 - b^2 + b*c - c^2) : :
X(46384) = 3 X[1635] - 2 X[2182]

X(46384) lies on these lines: {44, 513}, {514, 22464}, {1443, 3960}, {1769, 8609}, {2323, 3738}, {3737, 4282}, {4530, 14393}

X(46384) = X(i)-Ceva conjugate of X(j) for these (i,j): {523, 41218}, {10015, 1647}, {23838, 2310}
X(46384) = crosspoint of X(655) and X(40450)
X(46384) = crosssum of X(59) and X(1983)
X(46384) = crossdifference of every pair of points on line {1, 59}
X(46384) = perspector of hyperbola {{A,B,C,X(1),X(11)}}
X(46384) = X(i)-isoconjugate of X(j) for these (i,j): {59, 655}, {80, 4619}, {1411, 31615}, {2149, 35174}, {2222, 4564}, {4998, 32675}, {24027, 36804}
X(46384) = barycentric product X(i)*X(j) for these {i,j}: {11, 3738}, {36, 42455}, {654, 4858}, {1146, 3960}, {1443, 23615}, {2170, 3904}, {2245, 40213}, {2310, 4453}, {2323, 40166}, {2610, 26856}, {3218, 42462}, {3900, 4089}, {4511, 21132}, {7004, 44428}, {8648, 34387}, {21666, 22379}, {21758, 23978}
X(46384) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 35174}, {654, 4564}, {1146, 36804}, {2170, 655}, {2323, 31615}, {3271, 2222}, {3738, 4998}, {3960, 1275}, {4089, 4569}, {7113, 4619}, {8648, 59}, {21132, 18815}, {21758, 1262}, {35128, 4585}, {42455, 20566}, {42462, 18359}
X(46384) = {X(654),X(2600)}-harmonic conjugate of X(2610)


X(46385) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(71)

Barycentrics    a*(b - c)*(a^3 - a*b^2 - 2*a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2) : :
X(46385) = X[650] - X[7655], 3 X[656] - 2 X[7655], 3 X[2457] - 4 X[14837], X[4498] + 2 X[4833]

X(46385) lies on these lines: {1, 28147}, {44, 513}, {242, 514}, {522, 3465}, {523, 663}, {667, 8672}, {693, 8062}, {832, 4705}, {834, 4498}, {2402, 23696}, {2457, 4778}, {2517, 29051}, {2533, 6133}, {2605, 4449}, {3716, 7650}, {4041, 15313}, {4063, 7654}, {4086, 29066}, {4139, 4775}, {4379, 30911}, {4468, 23874}, {4490, 38469}, {4560, 28623}, {4762, 45686}, {4777, 42312}, {4794, 28161}, {4824, 23655}, {4874, 28116}, {4977, 7178}, {7199, 17215}, {7253, 17494}, {14838, 23800}, {21007, 45755}, {25667, 27416}

X(46385) = midpoint of X(i) and X(j) for these {i,j}: {4724, 17418}, {7253, 17494}
X(46385) = reflection of X(i) in X(j) for these {i,j}: {656, 650}, {693, 8062}, {1459, 3737}, {2533, 6133}, {4449, 2605}, {7650, 3716}, {23752, 7649}, {23800, 14838}
X(46385) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36080}, {72, 36077}, {190, 2215}, {651, 2335}
X(46385) = crossdifference of every pair of points on line {1, 71}
X(46385) = barycentric product X(i)*X(j) for these {i,j}: {1, 23882}, {42, 15417}, {405, 514}, {513, 5271}, {522, 37543}, {649, 44140}, {905, 39585}, {1019, 5295}, {1451, 4391}, {3261, 5320}, {14549, 17494}
X(46385) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36080}, {405, 190}, {663, 2335}, {667, 2215}, {1451, 651}, {1474, 36077}, {5271, 668}, {5295, 4033}, {5320, 101}, {15417, 310}, {23882, 75}, {37543, 664}, {39585, 6335}, {44140, 1978}


X(46386) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(76)

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

X(46386) lies on these lines: {44, 513}, {213, 667}, {514, 21763}, {669, 688}, {788, 14436}, {790, 40495}, {802, 18197}, {838, 2084}, {1107, 4083}, {1924, 8637}, {2978, 4079}, {3063, 8640}, {3250, 16514}, {4063, 16552}, {4367, 23572}, {7192, 21225}, {8631, 16695}, {17458, 20598}, {20981, 22384}

X(46386) = isogonal conjugate of X(37133)
X(46386) = isogonal conjugate of the isotomic conjugate of X(3250)
X(46386) = isotomic conjugate of trilinear pole of line X(75)X(1502)
X(46386) = X(i)-Ceva conjugate of X(j) for these (i,j): {1492, 40935}, {2279, 3248}, {37133, 1}
X(46386) = X(17415)-cross conjugate of X(1491)
X(46386) = X(i)-isoconjugate of X(j) for these (i,j): {1, 37133}, {2, 789}, {6, 46132}, {75, 4586}, {76, 1492}, {101, 871}, {190, 870}, {239, 41072}, {274, 4613}, {350, 37207}, {513, 5388}, {561, 825}, {668, 14621}, {670, 40747}, {799, 40718}, {985, 1978}, {1502, 34069}, {1920, 30670}, {1921, 30664}, {2344, 4572}, {3113, 33946}, {3114, 3888}, {3261, 5384}, {4817, 7035}, {6386, 40746}, {9063, 16584}, {20234, 33514}
X(46386) = cevapoint of X(1) and X(39338)
X(46386) = crosspoint of X(1) and X(37133)
X(46386) = crosssum of X(i) and X(j) for these (i,j): {649, 21352}, {870, 4817}, {1491, 3721}
X(46386) = crossdifference of every pair of points on line {1, 76}
X(46386) = barycentric product X(i)*X(j) for these {i,j}: {1, 788}, {6, 3250}, {31, 1491}, {32, 824}, {75, 8630}, {88, 14436}, {213, 4481}, {512, 3736}, {513, 869}, {514, 40728}, {649, 2276}, {663, 1469}, {667, 984}, {669, 30966}, {672, 29956}, {692, 4475}, {693, 18900}, {694, 30654}, {798, 40773}, {875, 3783}, {893, 45882}, {904, 3805}, {1019, 3774}, {1397, 4522}, {1911, 30665}, {1914, 30671}, {1917, 30870}, {1919, 3661}, {1922, 4486}, {1927, 30639}, {1977, 3807}, {1980, 33931}, {2206, 4122}, {3049, 31909}, {3063, 7146}, {3248, 3799}, {3572, 16514}, {3835, 40736}, {3862, 8632}, {4517, 43924}, {7204, 8641}, {8640, 45782}, {14599, 23596}, {17415, 40415}
X(46386) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 46132}, {6, 37133}, {31, 789}, {32, 4586}, {101, 5388}, {513, 871}, {560, 1492}, {667, 870}, {669, 40718}, {788, 75}, {824, 1502}, {869, 668}, {984, 6386}, {1469, 4572}, {1491, 561}, {1501, 825}, {1911, 41072}, {1917, 34069}, {1918, 4613}, {1919, 14621}, {1922, 37207}, {1924, 40747}, {1977, 4817}, {1980, 985}, {2276, 1978}, {3117, 33946}, {3249, 43266}, {3250, 76}, {3736, 670}, {3774, 4033}, {4475, 40495}, {4481, 6385}, {4486, 44169}, {4522, 40363}, {8630, 1}, {9006, 3778}, {14436, 4358}, {14598, 30664}, {16514, 27853}, {17415, 2887}, {18900, 100}, {23596, 44170}, {29956, 18031}, {30654, 3978}, {30665, 18891}, {30671, 18895}, {30966, 4609}, {40370, 43289}, {40415, 9063}, {40728, 190}, {40736, 4598}, {40773, 4602}, {45882, 1920}
X(46386) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 20979, 659}, {16695, 21791, 8631}


X(46387) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(83)

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

X(46387) lies on these lines: {44, 513}, {688, 3005}, {3249, 14419}, {3271, 6377}, {3570, 21362}, {3716, 29955}, {3777, 23572}, {4380, 20906}, {4553, 35309}, {8632, 22384}, {17277, 29546}, {29428, 37686}, {29545, 33295}

X(46387) = X(i)-Ceva conjugate of X(j) for these (i,j): {660, 40936}, {3572, 2084}, {35333, 1964}
X(46387) = crosspoint of X(i) and X(j) for these (i,j): {660, 40432}, {812, 8632}, {1019, 3572}
X(46387) = crosssum of X(i) and X(j) for these (i,j): {659, 2295}, {813, 4562}, {1018, 3570}
X(46387) = crossdifference of every pair of points on line {1, 83}
X(46387) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36081}, {82, 4562}, {83, 660}, {251, 4583}, {308, 34067}, {334, 4628}, {813, 3112}, {2295, 41209}, {3952, 39276}, {4579, 14970}, {4584, 18082}, {4589, 18098}, {4599, 43534}, {5378, 10566}, {18047, 43763}, {18099, 37134}
X(46387) = barycentric product X(i)*X(j) for these {i,j}: {38, 659}, {39, 812}, {141, 8632}, {238, 2530}, {239, 21123}, {427, 22384}, {826, 5009}, {1401, 3716}, {1914, 16892}, {1964, 3766}, {2084, 30940}, {3005, 33295}, {3688, 43041}, {4010, 17187}, {4093, 7192}, {4124, 46153}, {4448, 46150}, {4455, 16887}, {4553, 27846}, {7193, 21108}, {16696, 21832}, {20663, 35367}, {27918, 46148}, {35333, 38989}
X(46387) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36081}, {38, 4583}, {39, 4562}, {659, 3112}, {812, 308}, {1178, 41209}, {1923, 34067}, {1964, 660}, {2530, 334}, {3005, 43534}, {3051, 813}, {3688, 36801}, {3766, 18833}, {4093, 3952}, {4455, 18082}, {5009, 4577}, {5027, 18099}, {8623, 18047}, {8632, 83}, {14599, 4628}, {16696, 4639}, {16892, 18895}, {17187, 4589}, {21123, 335}, {22384, 1799}, {30940, 37204}, {33295, 689}, {39786, 18070}


X(46388) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(85)

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

X(46388) lies on these lines: {6, 22384}, {9, 3716}, {41, 8648}, {44, 513}, {101, 34905}, {512, 10581}, {665, 20662}, {692, 2874}, {928, 14825}, {1025, 4763}, {1334, 4895}, {1475, 14413}, {1919, 8642}, {2488, 3709}, {2491, 3725}, {3063, 8641}, {3271, 6139}, {3572, 23569}, {3691, 14430}, {3730, 3887}, {3762, 16552}, {3960, 4253}, {4010, 28143}, {4079, 33525}, {4369, 21390}, {4775, 17425}, {5013, 22437}, {8632, 20672}, {9436, 31286}, {9605, 23141}, {16560, 21382}, {17463, 21339}, {17754, 25380}, {18155, 21388}, {40978, 42666}

X(46388) = isogonal conjugate of X(34085)
X(46388) = X(i)-Ceva conjugate of X(j) for these (i,j): {101, 42079}, {103, 24012}, {813, 55}, {1024, 663}, {34085, 1}, {36039, 31}, {40730, 15615}
X(46388) = crosspoint of X(i) and X(j) for these (i,j): {1, 34085}, {101, 2195}, {663, 1024}, {665, 926}, {692, 911}, {813, 40730}
X(46388) = crosssum of X(i) and X(j) for these (i,j): {57, 43041}, {514, 9436}, {650, 20358}, {658, 24015}, {664, 1025}, {666, 927}, {672, 4449}, {693, 30807}, {2254, 17451}, {4077, 16609}
X(46388) = crossdifference of every pair of points on line {1, 85}
X(46388) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34085}, {2, 927}, {6, 46135}, {7, 666}, {56, 36803}, {75, 36146}, {76, 32735}, {85, 36086}, {100, 34018}, {105, 4554}, {109, 18031}, {279, 36802}, {294, 4569}, {514, 39293}, {651, 2481}, {653, 31637}, {658, 14942}, {664, 673}, {668, 1462}, {883, 6185}, {885, 1275}, {919, 6063}, {934, 36796}, {1016, 43930}, {1416, 1978}, {1438, 4572}, {1814, 18026}, {4573, 13576}, {4625, 18785}, {4626, 6559}, {5222, 41075}, {5377, 24002}, {6180, 14727}, {20567, 32666}, {21609, 36041}, {28071, 36838}
X(46388) = barycentric product X(i)*X(j) for these {i,j}: {1, 926}, {9, 665}, {41, 918}, {55, 2254}, {75, 8638}, {101, 17435}, {241, 657}, {284, 24290}, {318, 23225}, {513, 2340}, {518, 663}, {521, 2356}, {522, 2223}, {649, 3693}, {650, 672}, {652, 5089}, {656, 37908}, {667, 3717}, {884, 4712}, {885, 42079}, {1024, 6184}, {1025, 14936}, {1026, 3271}, {1253, 43042}, {1458, 3900}, {1566, 36039}, {1818, 18344}, {1861, 1946}, {2170, 2284}, {2194, 4088}, {2195, 3126}, {2283, 2310}, {2342, 42758}, {2428, 38375}, {3022, 41353}, {3063, 3912}, {3064, 20752}, {3252, 4435}, {3286, 4041}, {3675, 3939}, {3709, 18206}, {3716, 40730}, {3737, 20683}, {3930, 7252}, {4105, 34855}, {4391, 9454}, {4560, 39258}, {4895, 34230}, {8641, 9436}, {9439, 42341}, {9455, 35519}, {14411, 37131}, {23351, 35293}, {23696, 42071}, {34085, 39014}, {36037, 42771}
X(46388) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 46135}, {6, 34085}, {9, 36803}, {31, 927}, {32, 36146}, {41, 666}, {518, 4572}, {560, 32735}, {649, 34018}, {650, 18031}, {657, 36796}, {663, 2481}, {665, 85}, {672, 4554}, {692, 39293}, {918, 20567}, {926, 75}, {1253, 36802}, {1458, 4569}, {1919, 1462}, {1946, 31637}, {1980, 1416}, {2175, 36086}, {2223, 664}, {2254, 6063}, {2340, 668}, {2356, 18026}, {3063, 673}, {3248, 43930}, {3286, 4625}, {3693, 1978}, {3717, 6386}, {8638, 1}, {8641, 14942}, {9439, 14727}, {9447, 919}, {9448, 32666}, {9454, 651}, {9455, 109}, {15615, 2254}, {17435, 3261}, {23225, 77}, {24290, 349}, {37908, 811}, {39258, 4552}, {39686, 1025}, {42079, 883}, {42771, 36038}


X(46389) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(90)

Barycentrics    a*(a - b - c)*(b - c)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c + b^2*c - a*c^2 + b*c^2 - c^3) : :
Trilinears    (cos B) (cos B - cos C - cos A) - (cos C) (cos C - cos A - cos B) : :
X(46389) = 3 X[650] - 2 X[14300], 3 X[650] - 4 X[40137], X[13401] - 4 X[14298], 3 X[13401] - 4 X[14300], 3 X[13401] - 8 X[40137], 3 X[14298] - X[14300], 3 X[14298] - 2 X[40137]

X(46389) lies on these lines: {6, 3657}, {44, 513}, {198, 42769}, {521, 3700}, {924, 2501}, {926, 2520}, {1252, 34151}, {3064, 15313}, {3239, 3738}, {3309, 11927}, {3900, 4820}, {4017, 10397}, {4106, 5928}, {4131, 4885}, {4776, 28834}, {6003, 14331}, {6588, 22383}, {6590, 9001}, {8676, 18344}, {12664, 30199}, {14115, 46101}, {14330, 42325}, {14589, 15632}, {20980, 36054}, {34032, 43049}, {42762, 43932}

X(46389) = reflection of X(i) in X(j) for these {i,j}: {650, 14298}, {4131, 4885}, {11934, 2520}, {13401, 650}, {14300, 40137}
X(46389) = X(i)-complementary conjugate of X(j) for these (i,j): {42, 136}, {91, 21252}, {925, 3741}, {1918, 39013}, {2165, 116}, {2351, 2968}, {8750, 1147}, {32734, 1125}, {36145, 3739}, {41271, 44311}
X(46389) = X(i)-Ceva conjugate of X(j) for these (i,j): {651, 3157}, {1813, 65}, {3064, 650}, {13397, 55}, {36599, 2310}
X(46389) = crosspoint of X(i) and X(j) for these (i,j): {4, 651}, {1800, 1813}
X(46389) = crosssum of X(i) and X(j) for these (i,j): {3, 650}, {6, 34948}
X(46389) = crossdifference of every pair of points on line {1, 90}
X(46389) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36082}, {90, 651}, {101, 7318}, {108, 6513}, {109, 2994}, {653, 1069}, {658, 7072}, {664, 2164}, {1415, 20570}, {1461, 36626}, {1813, 7040}, {4636, 7363}, {6512, 36127}, {13395, 46038}
X(46389) = barycentric product X(i)*X(j) for these {i,j}: {9, 21188}, {46, 522}, {513, 5552}, {521, 1068}, {523, 3193}, {650, 5905}, {651, 6506}, {656, 3559}, {661, 31631}, {663, 20930}, {1406, 4397}, {1800, 24006}, {2178, 4391}, {3064, 6505}, {3157, 44426}, {3737, 21077}, {4560, 21853}
X(46389) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36082}, {46, 664}, {513, 7318}, {522, 20570}, {650, 2994}, {652, 6513}, {663, 90}, {1068, 18026}, {1406, 934}, {1800, 4592}, {1946, 1069}, {2178, 651}, {3063, 2164}, {3157, 6516}, {3193, 99}, {3559, 811}, {3900, 36626}, {5552, 668}, {5905, 4554}, {6506, 4391}, {8641, 7072}, {18344, 7040}, {20930, 4572}, {21188, 85}, {21853, 4552}, {31631, 799}, {36054, 6512}
X(46389) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {652, 661, 650}, {14298, 14300, 40137}, {14300, 40137, 650}


X(46390) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(99)

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

X(46390) lies on these lines: {44, 513}, {351, 865}, {645, 3570}, {812, 39028}, {891, 16589}, {1213, 3837}, {1960, 20970}, {2533, 22224}, {3709, 4093}, {4010, 4839}, {4079, 8663}, {14436, 21838}, {14838, 21763}, {17990, 18001}, {21385, 46196}

X(46390) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 38978}, {2107, 11}
X(46390) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 38978}, {1018, 4094}, {3570, 4093}, {3572, 512}, {18001, 8663}, {18785, 2643}, {18793, 4117}, {21832, 4155}, {27853, 740}, {37128, 4128}
X(46390) = X(2086)-cross conjugate of X(2238)
X(46390) = crosspoint of X(i) and X(j) for these (i,j): {512, 3572}, {740, 27853}, {3903, 37128}, {4455, 21832}
X(46390) = crosssum of X(i) and X(j) for these (i,j): {99, 3570}, {1019, 33295}, {2238, 4367}, {3572, 46159}, {4444, 18827}, {4584, 4589}
X(46390) = crossdifference of every pair of points on line {1, 99}
X(46390) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36066}, {56, 36806}, {58, 4639}, {81, 4589}, {86, 4584}, {99, 37128}, {110, 40017}, {291, 4610}, {292, 4623}, {334, 4556}, {593, 4583}, {660, 1509}, {662, 18827}, {670, 18268}, {741, 799}, {757, 4562}, {805, 8033}, {813, 873}, {875, 34537}, {876, 4590}, {1414, 36800}, {2311, 4625}, {3572, 24037}, {4367, 39292}, {4444, 24041}, {4576, 39276}, {4593, 46159}, {4612, 7233}, {17103, 37134}
X(46390) = barycentric product X(i)*X(j) for these {i,j}: {1, 4155}, {10, 4455}, {37, 21832}, {42, 4010}, {181, 3716}, {238, 4705}, {239, 4079}, {512, 740}, {523, 3747}, {594, 8632}, {649, 4037}, {656, 862}, {659, 756}, {661, 2238}, {663, 7235}, {669, 35544}, {798, 3948}, {812, 1500}, {872, 3766}, {876, 4094}, {882, 4154}, {1018, 39786}, {1084, 27853}, {1284, 4041}, {1334, 7212}, {1577, 41333}, {1914, 4024}, {2086, 27805}, {2171, 4435}, {2210, 4036}, {2333, 24459}, {2643, 3573}, {3124, 3570}, {3572, 35068}, {3709, 16609}, {3985, 7180}, {4017, 4433}, {7064, 43041}, {7140, 22384}, {9402, 39926}, {27846, 40521}, {36815, 42666}
X(46390) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 36806}, {31, 36066}, {37, 4639}, {42, 4589}, {213, 4584}, {238, 4623}, {512, 18827}, {659, 873}, {661, 40017}, {669, 741}, {688, 46159}, {740, 670}, {756, 4583}, {798, 37128}, {862, 811}, {872, 660}, {1084, 3572}, {1284, 4625}, {1500, 4562}, {1914, 4610}, {1924, 18268}, {2086, 4369}, {2238, 799}, {3124, 4444}, {3570, 34537}, {3573, 24037}, {3684, 4631}, {3709, 36800}, {3716, 18021}, {3747, 99}, {3948, 4602}, {4010, 310}, {4024, 18895}, {4036, 44172}, {4037, 1978}, {4079, 335}, {4093, 4576}, {4094, 874}, {4117, 875}, {4154, 880}, {4155, 75}, {4433, 7257}, {4455, 86}, {4705, 334}, {5027, 17103}, {7064, 36801}, {7109, 813}, {7235, 4572}, {8632, 1509}, {14599, 4556}, {21727, 40094}, {21832, 274}, {27853, 44168}, {35068, 27853}, {35544, 4609}, {39786, 7199}, {40729, 37134}, {41333, 662}


X(46391) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(102)

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

X(46391) lies on these lines: {44, 513}, {109, 1783}, {1636, 18675}, {7004, 7117}, {8611, 36054}, {14331, 21186}, {22383, 40628}

X(46391) = isogonal conjugate of the polar conjugate of X(14304)
X(46391) = X(i)-Ceva conjugate of X(j) for these (i,j): {2765, 55}, {24035, 515}, {36044, 33}, {36050, 42076}
X(46391) = crosspoint of X(i) and X(j) for these (i,j): {63, 36037}, {515, 24035}, {905, 37628}, {13138, 36100}
X(46391) = crosssum of X(i) and X(j) for these (i,j): {19, 1769}, {652, 1457}, {1783, 23706}, {2182, 6129}, {32667, 36040}
X(46391) = crossdifference of every pair of points on line {1, 102}
X(46391) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36067}, {75, 32667}, {92, 36040}, {102, 653}, {108, 36100}, {196, 6081}, {264, 32643}, {651, 36121}, {15629, 36118}, {17080, 36108}, {18026, 32677}, {32674, 34393}
X(46391) = barycentric product X(i)*X(j) for these {i,j}: {1, 39471}, {3, 14304}, {271, 6087}, {515, 521}, {1809, 42755}, {1946, 35516}, {2182, 6332}, {2406, 34591}, {7117, 42718}, {10017, 36037}, {23987, 24031}, {24035, 35072}
X(46391) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36067}, {32, 32667}, {184, 36040}, {515, 18026}, {521, 34393}, {652, 36100}, {663, 36121}, {1455, 36118}, {1946, 102}, {2182, 653}, {2188, 6081}, {2425, 7128}, {6087, 342}, {9247, 32643}, {10017, 36038}, {14304, 264}, {23986, 24035}, {23987, 24032}, {34050, 13149}, {34591, 2399}, {39471, 75}, {42076, 23987}


X(46392) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(103)

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

X(46392) lies on these lines: {44, 513}, {294, 2338}, {676, 9502}, {1212, 14414}, {2310, 3119}, {3716, 28132}, {4105, 4171}

X(46392) = X(i)-Ceva conjugate of X(j) for these (i,j): {294, 2310}, {1783, 42077}, {24015, 516}, {36146, 4319}
X(46392) = crosspoint of X(i) and X(j) for these (i,j): {516, 24015}, {658, 14942}
X(46392) = crosssum of X(i) and X(j) for these (i,j): {651, 41353}, {657, 1458}
X(46392) = crossdifference of every pair of points on line {1, 103}
X(46392) = X(i)-isoconjugate of X(j) for these (i,j): {2, 24016}, {75, 32668}, {103, 658}, {279, 677}, {651, 43736}, {911, 4569}, {934, 36101}, {1088, 36039}, {1262, 2400}, {1275, 2424}, {1461, 18025}, {1815, 36118}, {2338, 4626}, {4619, 15634}, {7056, 40116}, {9503, 41353}, {13149, 36056}
X(46392) = barycentric product X(i)*X(j) for these {i,j}: {200, 676}, {516, 3900}, {522, 41339}, {650, 40869}, {657, 30807}, {910, 3239}, {1021, 17747}, {1456, 4163}, {2310, 2398}, {2426, 24026}, {4130, 43035}, {4171, 14953}, {7079, 39470}, {8641, 35517}, {9502, 28132}, {14936, 42719}, {23973, 24010}, {24015, 35508}, {34591, 41321}
X(46392) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 24016}, {32, 32668}, {516, 4569}, {657, 36101}, {663, 43736}, {676, 1088}, {910, 658}, {1253, 677}, {1456, 4626}, {1886, 13149}, {2310, 2400}, {2426, 7045}, {3900, 18025}, {8641, 103}, {14827, 36039}, {14953, 4635}, {23972, 24015}, {23973, 24011}, {40869, 4554}, {41339, 664}, {42077, 23973}, {43035, 36838}
X(46392) = {X(650),X(4724)}-harmonic conjugate of X(21127)


X(46393) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(104)

Barycentrics    a*(a - b - c)*(b - c)*(a^2*b - b^3 + a^2*c - 2*a*b*c + b^2*c + b*c^2 - c^3) : :
Trilinears    (A-power of B-outer Yff circle) - (A-power of C-outer Yff circle) : :

X(46393) lies on these lines: {9, 14418}, {11, 1146}, {44, 513}, {55, 14392}, {101, 108}, {908, 36038}, {972, 2291}, {1459, 40134}, {1512, 14330}, {1637, 2294}, {1769, 3310}, {2161, 2432}, {2316, 3738}, {2814, 5400}, {2821, 3030}, {3064, 3239}, {3700, 42337}, {3762, 14554}, {4105, 11934}, {4120, 42462}, {4171, 4944}, {4521, 14331}, {4728, 40166}, {6139, 11124}, {6591, 10397}, {8677, 42772}, {10015, 42762}, {13576, 28132}, {21801, 42763}, {23893, 24297}, {25666, 28834}, {25900, 31287}, {25924, 28984}, {26545, 27014}, {39534, 42756}

X(46393) = isogonal conjugate of X(37136)
X(46393) = isotomic conjugate of trilinear pole of line X(75)X(77)
X(46393) = polar conjugate of trilinear pole of line X(57)X(92)
X(46393) = X(31)-complementary conjugate of X(38981)
X(46393) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 38981}, {57, 35065}, {80, 2310}, {514, 23757}, {908, 35015}, {1465, 35014}, {2222, 55}, {2316, 2170}, {2427, 21801}, {3738, 4895}, {10015, 1769}, {14554, 11}, {24029, 517}, {32665, 17452}, {34234, 7004}, {36106, 212}, {37136, 1}
X(46393) = crosspoint of X(i) and X(j) for these (i,j): {1, 37136}, {514, 23838}, {517, 24029}, {651, 1320}, {1465, 23706}, {1897, 34234}, {2804, 10015}
X(46393) = crosssum of X(i) and X(j) for these (i,j): {56, 21786}, {57, 3960}, {101, 23703}, {650, 1319}, {1459, 2183}, {2720, 32641}
X(46393) = crossdifference of every pair of points on line {1, 104}
X(46393) = Stevanovic-circle-inverse of X(45884)
X(46393) = X(i)-isoconjugate of X(j) for these (i,j): {1, 37136}, {2, 2720}, {7, 32641}, {56, 13136}, {57, 36037}, {59, 2401}, {63, 36110}, {69, 32702}, {75, 32669}, {100, 34051}, {104, 651}, {109, 34234}, {222, 1309}, {348, 14776}, {653, 1795}, {658, 2342}, {664, 909}, {901, 40218}, {1262, 43728}, {1414, 2250}, {1415, 18816}, {1459, 39294}, {1809, 32714}, {1813, 36123}, {2405, 15405}, {2423, 4998}, {4554, 34858}, {4565, 38955}, {7128, 37628}, {14578, 18026}, {15501, 37141}, {15635, 31615}, {16082, 36059}, {35011, 43043}, {36146, 36819}, {43933, 44717}
X(46393) = barycentric product X(i)*X(j) for these {i,j}: {1, 2804}, {8, 1769}, {9, 10015}, {55, 36038}, {78, 39534}, {100, 35015}, {210, 23788}, {312, 3310}, {318, 8677}, {513, 6735}, {517, 522}, {521, 1785}, {643, 42759}, {644, 42754}, {650, 908}, {663, 3262}, {859, 4086}, {952, 37629}, {1145, 23838}, {1146, 24029}, {1320, 23757}, {1457, 4397}, {1465, 3239}, {1897, 35014}, {2170, 2397}, {2183, 4391}, {2427, 4858}, {2968, 23706}, {3326, 36037}, {3699, 42753}, {3737, 17757}, {3900, 22464}, {4041, 17139}, {4551, 14010}, {4560, 21801}, {4768, 14260}, {6332, 14571}, {6740, 42768}, {7257, 42752}, {8851, 42766}, {14942, 42758}, {21664, 37628}, {22350, 44426}, {23981, 24026}, {24028, 43728}, {41798, 42762}, {42750, 44693}
X(46393) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 37136}, {9, 13136}, {25, 36110}, {31, 2720}, {32, 32669}, {33, 1309}, {41, 32641}, {55, 36037}, {517, 664}, {522, 18816}, {649, 34051}, {650, 34234}, {663, 104}, {859, 1414}, {908, 4554}, {926, 36819}, {1457, 934}, {1465, 658}, {1635, 40218}, {1769, 7}, {1783, 39294}, {1785, 18026}, {1875, 36118}, {1946, 1795}, {1973, 32702}, {2170, 2401}, {2183, 651}, {2212, 14776}, {2310, 43728}, {2427, 4564}, {2804, 75}, {3063, 909}, {3064, 16082}, {3239, 36795}, {3262, 4572}, {3270, 37628}, {3310, 57}, {3326, 36038}, {3709, 2250}, {4041, 38955}, {4814, 36921}, {4895, 36944}, {6735, 668}, {8641, 2342}, {8677, 77}, {10015, 85}, {14010, 18155}, {14571, 653}, {17139, 4625}, {18344, 36123}, {21801, 4552}, {22350, 6516}, {22464, 4569}, {23220, 603}, {23980, 24029}, {23981, 7045}, {24029, 1275}, {35014, 4025}, {35015, 693}, {36038, 6063}, {37629, 46136}, {39534, 273}, {42072, 23706}, {42078, 23981}, {42752, 4017}, {42753, 3676}, {42754, 24002}, {42757, 22464}, {42758, 9436}, {42759, 4077}, {42762, 37780}, {42768, 41804}, {42771, 2254}
X(46393) = trilinear product X(i)*X(j) for these {i,j}: {6, 2804}, {8, 3310}, {9, 1769}, {11, 2427}, {41, 36038}, {55, 10015}, {101, 35015}, {281, 8677}, {517, 650}, {521, 14571}, {522, 2183}, {649, 6735}, {652, 1785}, {657, 22464}, {663, 908}, {859, 3700}, {1146, 23981}, {1334, 23788}, {1457, 3239}, {1465, 3900}, {1639, 14260}, {1783, 35014}, {2310, 24029}, {2316, 23757}, {2397, 3271}, {2431, 25640}, {3063, 3262}, {3064, 22350}, {3259, 5548}, {3326, 32641}, {3709, 17139}, {3737, 21801}, {4559, 14010}, {7017, 23220}, {7252, 17757}, {23706, 34591}
X(46393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 654, 1635}, {650, 14298, 652}, {657, 4893, 650}, {2590, 2591, 652}


X(46394) = BARYCENTRIC SQUARE OF X(216)

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

X(46394) lies on these lines: {3, 1625}, {5, 53}, {32, 26880}, {39, 12233}, {184, 36433}, {217, 418}, {327, 37186}, {2207, 26898}, {3164, 18027}, {3331, 26897}, {6292, 6509}, {8571, 39170}, {14374, 15167}, {14375, 15166}, {15526, 36952}, {26907, 40588}

X(46394) = complement of the isotomic conjugate of X(42487)
X(46394) = X(42487)-complementary conjugate of X(2887)
X(46394) = crosspoint of X(i) and X(j) for these (i,j): {2, 42487}, {216, 418}
X(46394) = crosssum of X(i) and X(j) for these (i,j): {6, 1629}, {275, 8795}
X(46394) = crossdifference of every pair of points on line {6130, 23286}
X(46394) = barycentric square of X(216)
X(46394) = X(i)-isoconjugate of X(j) for these (i,j): {275, 40440}, {276, 2190}, {2167, 8795}, {2616, 42405}
X(46394) = barycentric product X(i)*X(j) for these {i,j}: {5, 418}, {51, 5562}, {110, 34983}, {216, 216}, {217, 343}, {250, 41212}, {311, 44088}, {577, 36412}, {1625, 17434}, {6056, 41279}, {14570, 42293}, {14585, 45793}, {15451, 23181}, {19210, 23607}, {23357, 39019}, {30493, 44707}
X(46394) = barycentric quotient X(i)/X(j) for these {i,j}: {51, 8795}, {216, 276}, {217, 275}, {418, 95}, {1625, 42405}, {3199, 8794}, {5562, 34384}, {27374, 19174}, {34983, 850}, {36412, 18027}, {39019, 23962}, {40981, 8884}, {41212, 339}, {42293, 15412}, {44088, 54}


X(46395) = PERSPECTOR OF THE PRIVALOV CONIC

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

The Privalov conic is defined at X(5452).

X(46395 lies on the cubic K925 and these lines: {11, 5452}, {3434, 23989}, {5101, 12586}, {10947, 11927}, {17625, 30617}, {17658, 30615}

X(46395) = isotomic conjugate of the anticomplement of X(16283)
X(46395) = X(i)-cross conjugate of X(j) for these (i,j): {14935, 650}, {16283, 2}


X(46396) = COMPLEMENT OF X(652)

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

X(46396) lies on these lines: {2, 652}, {141, 8999}, {142, 7658}, {226, 3239}, {306, 17894}, {513, 3716}, {520, 6130}, {522, 23806}, {812, 28984}, {1459, 26146}, {2550, 4105}, {3900, 20314}, {4025, 5249}, {4728, 29005}, {6589, 17056}, {8611, 17896}, {8676, 17072}, {9240, 34831}, {16612, 23724}, {17069, 21195}, {17924, 24018}, {18134, 35519}, {18589, 20319}, {25259, 31019}, {25604, 41867}, {26571, 27014}, {26596, 27193}

X(46396) = midpoint of X(i) and X(j) for these {i,j}: {8611, 17896}, {17924, 24018}
X(46396) = complement of X(652)
X(46396) = complement of the isogonal conjugate of X(653)
X(46396) = medial isogonal conjugate of X(16596)
X(46396) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 16596}, {2, 123}, {4, 26932}, {6, 35072}, {9, 40616}, {19, 1146}, {27, 34589}, {28, 4858}, {33, 13609}, {34, 1086}, {57, 2968}, {65, 15526}, {73, 16595}, {81, 34588}, {92, 124}, {107, 6708}, {108, 2}, {109, 1214}, {112, 40937}, {162, 5745}, {190, 34823}, {196, 7358}, {225, 8287}, {226, 34846}, {273, 116}, {278, 11}, {281, 5514}, {331, 21252}, {393, 6506}, {607, 35508}, {608, 1015}, {644, 42018}, {648, 960}, {651, 3}, {653, 10}, {658, 34822}, {662, 34851}, {664, 18589}, {811, 21246}, {823, 34831}, {934, 17073}, {1020, 18641}, {1041, 1565}, {1119, 4904}, {1172, 34591}, {1214, 122}, {1395, 6377}, {1396, 244}, {1400, 16573}, {1409, 35071}, {1411, 42761}, {1415, 216}, {1426, 17058}, {1435, 3756}, {1441, 127}, {1461, 17102}, {1465, 10017}, {1783, 9}, {1847, 17059}, {1876, 35094}, {1880, 115}, {1897, 3452}, {2405, 25640}, {4551, 440}, {4552, 21530}, {4554, 1368}, {4559, 18591}, {4564, 20315}, {4565, 37565}, {4566, 18642}, {4569, 18639}, {5089, 1566}, {6335, 1329}, {6516, 6389}, {6529, 9119}, {6591, 46101}, {6648, 37613}, {7012, 514}, {7115, 650}, {7128, 522}, {8735, 34530}, {8750, 1212}, {8751, 17435}, {13149, 2886}, {15742, 20317}, {17080, 38977}, {17924, 46100}, {18026, 141}, {23984, 521}, {23985, 6588}, {24019, 40942}, {24033, 14837}, {24035, 117}, {30456, 39020}, {32647, 14571}, {32660, 828}, {32667, 8607}, {32674, 37}, {32688, 5089}, {32702, 8609}, {32714, 1}, {32726, 33572}, {34051, 35014}, {36044, 34050}, {36059, 6509}, {36067, 1465}, {36099, 958}, {36110, 3911}, {36118, 142}, {36127, 226}, {37790, 3259}, {37799, 5520}, {40117, 281}, {40149, 125}, {40397, 7004}, {40446, 24237}, {41207, 37370}, {43923, 6547}, {46102, 513}, {46152, 6292}
X(46396) = crossdifference of every pair of points on line {2176, 10537}
X(46396) = barycentric product X(514)*X(25252)
X(46396) = barycentric quotient X(25252)/X(190)


X(46397) = COMPLEMENT OF X(654)

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

X(46397) lies on these lines: {2, 654}, {116, 124}, {118, 31844}, {142, 44902}, {226, 918}, {513, 3716}, {908, 1639}, {924, 30476}, {926, 2886}, {1638, 5249}, {2826, 21635}, {3310, 5718}, {3452, 45326}, {4106, 28984}, {4453, 31019}, {5880, 9511}, {6139, 6690}, {17069, 23806}, {22086, 35466}, {24462, 33111}, {25511, 26596}, {30565, 31053}

X(46397) = reflection of X(6139) in X(6690)
X(46397) = complement of X(654)
X(46397) = complement of the isogonal conjugate of X(655)
X(46397) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 35128}, {80, 26932}, {109, 16586}, {651, 214}, {655, 10}, {759, 4858}, {1020, 6739}, {1411, 1086}, {1807, 16596}, {2006, 11}, {2161, 1146}, {2222, 2}, {2341, 34591}, {4552, 31845}, {4559, 35069}, {14628, 3259}, {16577, 3258}, {18359, 124}, {18815, 116}, {21741, 18334}, {23592, 3738}, {24624, 34589}, {32675, 37}, {34242, 40626}, {35174, 141}, {36069, 16579}, {36078, 16577}, {36804, 1329}, {36910, 5514}, {37140, 4999}, {43048, 35587}
X(46397) = crossdifference of every pair of points on line {2176, 45937}


X(46398) = COMPLEMENT OF X(655)

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

X(46398) lies on these lines: {2, 655}, {7, 37136}, {11, 522}, {214, 516}, {338, 1577}, {514, 26932}, {523, 46100}, {527, 39063}, {905, 1086}, {908, 1465}, {1861, 21664}, {2972, 34588}, {3126, 42757}, {3218, 14920}, {4466, 38372}, {5289, 14260}, {5886, 24410}, {6739, 45022}, {11729, 38617}, {13136, 46136}, {23593, 45274}

X(46398) = midpoint of X(908) and X(22464)
X(46398) = reflection of X(655) in X(40536)
X(46398) = complement of X(655)
X(46398) = anticomplement of X(40536)
X(46398) = complement of the isogonal conjugate of X(654)
X(46398) = complement of the isotomic conjugate of X(3904)
X(46398) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 3738}, {31, 10015}, {36, 4885}, {41, 1639}, {522, 21237}, {649, 1737}, {650, 3814}, {654, 10}, {663, 908}, {1333, 21180}, {1983, 3035}, {2148, 6369}, {2150, 6370}, {2323, 513}, {2361, 514}, {2423, 12736}, {2600, 1209}, {2610, 34829}, {3063, 44}, {3218, 17072}, {3724, 1577}, {3738, 141}, {3904, 2887}, {3960, 2886}, {4282, 523}, {4453, 17046}, {4511, 3835}, {7113, 522}, {7252, 758}, {8648, 2}, {16944, 44902}, {17515, 30476}, {21758, 1}, {21828, 442}, {22379, 17073}, {32851, 21260}, {44428, 20305}
X(46398) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 10015}, {7, 3738}, {264, 6369}, {36917, 522}
X(46398) = X(i)-isoconjugate of X(j) for these (i,j): {2149, 40437}, {2222, 32641}, {32675, 36037}, {35321, 36078}
X(46398) = crosspoint of X(2) and X(3904)
X(46398) = crosssum of X(6) and X(32675)
X(46398) = barycentric product X(i)*X(j) for these {i,j}: {320, 35015}, {331, 38353}, {1845, 17880}, {2804, 4453}, {3738, 36038}, {3904, 10015}, {4089, 6735}, {4858, 16586}, {14010, 41804}, {18155, 42768}, {32851, 42754}, {34387, 34586}, {45950, 46136}
X(46398) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 40437}, {654, 32641}, {1769, 2222}, {1845, 7012}, {2600, 35321}, {3259, 14584}, {3310, 32675}, {3738, 36037}, {3904, 13136}, {3960, 37136}, {10015, 655}, {14010, 6740}, {16586, 4564}, {17923, 39294}, {21758, 32669}, {34586, 59}, {35014, 1807}, {35015, 80}, {36038, 35174}, {38353, 219}, {42753, 1411}, {42754, 2006}, {42768, 4551}, {44428, 1309}, {45950, 952}
X(46398) = {X(2),X(655)}-harmonic conjugate of X(40536)


X(46399) = COMPLEMENT OF X(657)

Barycentrics    (b - c)*(-(a^3*b) + 2*a^2*b^2 - a*b^3 - a^3*c + a^2*b*c - a*b^2*c + b^3*c + 2*a^2*c^2 - a*b*c^2 - 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(46399) = 3 X[4728] - X[23819], 3 X[4927] - X[23769]

X(46399) lies on these lines: {2, 657}, {57, 22443}, {116, 46100}, {141, 9000}, {142, 522}, {226, 21960}, {513, 3716}, {514, 40465}, {656, 7658}, {693, 21127}, {926, 17066}, {1021, 25604}, {1024, 17282}, {1459, 4648}, {3239, 15413}, {3261, 17234}, {3912, 20907}, {4106, 17410}, {4131, 26017}, {4147, 9443}, {4728, 23819}, {4791, 17758}, {4869, 20293}, {4927, 23769}, {6586, 17245}, {7650, 23806}, {9029, 21262}, {26571, 26854}

X(46399) = midpoint of X(i) and X(j) for these {i,j}: {693, 21127}, {4106, 17410}
X(46399) = reflection of X(21195) in X(142)
X(46399) = complement of X(657)
X(46399) = complement of the isogonal conjugate of X(658)
X(46399) = medial-isogonal conjugate of X(13609)
X(46399) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 13609}, {2, 5514}, {6, 35508}, {7, 26932}, {57, 1146}, {63, 40616}, {77, 16596}, {81, 34591}, {85, 124}, {100, 6554}, {109, 1212}, {220, 17426}, {222, 35072}, {241, 1566}, {269, 1086}, {278, 6506}, {279, 11}, {348, 123}, {479, 4904}, {644, 5574}, {651, 9}, {653, 20262}, {658, 10}, {664, 3452}, {738, 3756}, {927, 34852}, {934, 2}, {1014, 4858}, {1020, 1213}, {1042, 16592}, {1086, 34530}, {1088, 116}, {1106, 6377}, {1170, 3119}, {1212, 38973}, {1254, 6627}, {1262, 650}, {1275, 513}, {1332, 42018}, {1407, 1015}, {1414, 5745}, {1415, 16588}, {1426, 6388}, {1427, 115}, {1434, 34589}, {1439, 15526}, {1446, 125}, {1461, 37}, {1462, 17435}, {3668, 8287}, {3669, 46101}, {4350, 40615}, {4551, 38930}, {4554, 1329}, {4564, 4521}, {4565, 40937}, {4566, 1211}, {4569, 141}, {4572, 21244}, {4573, 960}, {4616, 3739}, {4617, 1}, {4619, 24036}, {4625, 21246}, {4626, 142}, {4635, 3741}, {4637, 1125}, {4998, 20317}, {6610, 35091}, {6614, 3752}, {7045, 514}, {7128, 3239}, {7177, 2968}, {7339, 905}, {7365, 5517}, {7366, 16614}, {8269, 17279}, {13149, 5}, {14256, 7358}, {17093, 5511}, {18026, 41883}, {23062, 17059}, {23586, 3900}, {23971, 6129}, {23973, 39063}, {23984, 14298}, {24002, 46100}, {24013, 7658}, {24015, 118}, {24016, 241}, {24027, 6586}, {31615, 3039}, {32668, 8608}, {32674, 20310}, {32714, 6}, {34056, 33573}, {34855, 35094}, {36079, 1427}, {36118, 226}, {36146, 40869}, {36838, 2886}, {37139, 5199}, {37141, 281}, {38459, 40629}, {38859, 40619}, {41353, 16593}, {43932, 6547}
X(46399) = crossdifference of every pair of points on line {2176, 3010}
X(46399) = barycentric product X(514)*X(25242)
X(46399) = barycentric quotient X(25242)/X(190)


X(46400) = ANTICOMPLEMENT OF X(652)

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

X(46400) lies on these lines: {2, 652}, {7, 4025}, {8, 17894}, {69, 8999}, {320, 350}, {329, 3239}, {340, 520}, {521, 17896}, {522, 16091}, {1021, 23806}, {3664, 23801}, {3738, 4077}, {3900, 20297}, {4105, 17784}, {4329, 20298}, {5712, 6589}, {5905, 25259}, {7658, 9776}, {8676, 21302}, {14298, 25009}, {21173, 23725}, {21189, 23724}, {22383, 26146}, {34408, 43933}

X(46400) = reflection of X(1021) in X(23806)
X(46400) = anticomplement of X(652)
X(46400) = anticomplement of the isogonal conjugate of X(653)
X(46400) = isotomic conjugate of the anticomplement of X(38983)
X(46400) = isotomic conjugate of the isogonal conjugate of X(39199)
X(46400) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2, 34188}, {4, 37781}, {19, 39351}, {34, 4440}, {65, 39352}, {92, 33650}, {107, 92}, {108, 2}, {109, 6360}, {162, 63}, {225, 21221}, {273, 150}, {278, 149}, {331, 21293}, {608, 9263}, {648, 3869}, {651, 20}, {653, 8}, {664, 4329}, {811, 20245}, {934, 347}, {1020, 3152}, {1214, 34186}, {1395, 21224}, {1396, 17154}, {1414, 17134}, {1415, 3164}, {1441, 13219}, {1783, 144}, {1876, 39353}, {1880, 148}, {1897, 329}, {2405, 34550}, {4551, 3151}, {4554, 1370}, {4559, 18666}, {4564, 20294}, {4565, 20222}, {4566, 2897}, {4573, 20243}, {4625, 18659}, {5089, 14732}, {6335, 3436}, {6516, 6527}, {6591, 17036}, {7012, 514}, {7115, 17494}, {7128, 522}, {8750, 3177}, {13149, 3434}, {15742, 4462}, {18026, 69}, {23984, 521}, {24035, 151}, {32674, 192}, {32714, 145}, {34922, 1577}, {36093, 7291}, {36098, 3101}, {36110, 3218}, {36118, 7}, {36127, 5905}, {36146, 3100}, {36797, 18750}, {37136, 10538}, {37141, 280}, {40149, 3448}, {41207, 14956}, {46102, 513}, {46152, 2896}
X(46400) = X(38983)-cross conjugate of X(2)
X(46400) = X(8750)-isoconjugate of X(43724)
X(46400) = crosspoint of X(i) and X(j) for these (i,j): {86, 18026}, {95, 664}, {668, 40424}
X(46400) = crosssum of X(i) and X(j) for these (i,j): {42, 1946}, {51, 663}, {667, 40958}, {8641, 40957}
X(46400) = crossdifference of every pair of points on line {213, 217}
X(46400) = barycentric product X(i)*X(j) for these {i,j}: {76, 39199}, {7412, 15413}
X(46400) = barycentric quotient X(i)/X(j) for these {i,j}: {905, 43724}, {7412, 1783}, {38983, 652}, {39199, 6}


X(46401) = ANTICOMPLEMENT OF X(654)

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

X(46401) lies on these lines: {2, 654}, {7, 4453}, {150, 928}, {320, 350}, {329, 30565}, {812, 43991}, {850, 924}, {918, 5905}, {926, 3434}, {1639, 31018}, {2826, 9809}, {3738, 36038}, {3909, 21272}, {9034, 40166}, {20525, 32946}, {22086, 24597}, {23725, 23801}

X(46401) = anticomplement of X(654)
X(46401) = anticomplement of the isogonal conjugate of X(655)
X(46401) = isotomic conjugate of the anticomplement of X(38984)
X(46401) = isotomic conjugate of the isogonal conjugate of X(39200)
X(46401) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {80, 37781}, {476, 14213}, {651, 6224}, {655, 8}, {934, 41803}, {1411, 4440}, {2006, 149}, {2161, 39351}, {2222, 2}, {16577, 14731}, {18359, 33650}, {18815, 150}, {23592, 3738}, {32675, 192}, {35174, 69}, {36069, 18662}, {36078, 17479}, {36804, 3436}, {37136, 36944}, {37140, 2975}
X(46401) = X(38984)-cross conjugate of X(2)
X(46401) = crosspoint of X(i) and X(j) for these (i,j): {86, 35174}, {99, 39277}
X(46401) = crosssum of X(i) and X(j) for these (i,j): {42, 8648}, {663, 20962}
X(46401) = crossdifference of every pair of points on line {213, 45937}
X(46401) = barycentric product X(76)*X(39200)
X(46401) = barycentric quotient X(i)/X(j) for these {i,j}: {38984, 654}, {39200, 6}
X(46401) = {X(4106),X(4131)}-harmonic conjugate of X(693)


X(46402) = ANTICOMPLEMENT OF X(657)

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(46402) = 3 X[21297] - 2 X[23819]

X(46402) lies on these lines: {2, 657}, {7, 522}, {8, 20907}, {69, 3261}, {320, 350}, {521, 24002}, {926, 4374}, {1024, 3662}, {1459, 3945}, {3664, 21173}, {4380, 17410}, {4449, 41352}, {4474, 36854}, {4648, 6586}, {5232, 20316}, {8058, 30181}, {9029, 21304}, {9443, 20906}, {17096, 23800}, {17300, 21225}, {17494, 21127}, {20294, 30805}, {21195, 45755}, {34399, 43930}

X(46402) = reflection of X(i) in X(j) for these {i,j}: {4380, 17410}, {17494, 21127}, {45755, 21195}
X(46402) = anticomplement of X(657)
X(46402) = anticomplement of the isogonal conjugate of X(658)
X(46402) = isotomic conjugate of the anticomplement of X(14714)
X(46402) = isotomic conjugate of the isogonal conjugate of X(44408)
X(46402) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {7, 37781}, {57, 39351}, {85, 33650}, {99, 18750}, {100, 30695}, {108, 30694}, {109, 3177}, {241, 14732}, {269, 4440}, {279, 149}, {348, 34188}, {651, 144}, {653, 5942}, {658, 8}, {662, 45738}, {664, 329}, {927, 30807}, {934, 2}, {1020, 1654}, {1042, 21220}, {1088, 150}, {1106, 21224}, {1170, 44005}, {1262, 17494}, {1275, 513}, {1407, 9263}, {1414, 63}, {1415, 21218}, {1427, 148}, {1439, 39352}, {1446, 3448}, {1461, 192}, {3668, 21221}, {3669, 17036}, {4554, 3436}, {4564, 4468}, {4566, 2895}, {4569, 69}, {4572, 21286}, {4573, 3869}, {4616, 75}, {4617, 145}, {4625, 20245}, {4626, 7}, {4635, 17135}, {4637, 1}, {4998, 4462}, {6613, 312}, {6614, 3210}, {6648, 43216}, {7045, 514}, {7128, 25259}, {7204, 39345}, {7339, 17496}, {8269, 346}, {13149, 4}, {17093, 34547}, {23586, 3900}, {24013, 4025}, {24015, 152}, {24027, 21225}, {32714, 193}, {34056, 45293}, {34855, 39353}, {36048, 3219}, {36079, 18663}, {36118, 5905}, {36146, 10025}, {36838, 3434}, {41353, 20533}
X(46402) = X(14714)-cross conjugate of X(2)
X(46402) = crosspoint of X(i) and X(j) for these (i,j): {86, 4569}, {664, 40419}
X(46402) = crosssum of X(i) and X(j) for these (i,j): {42, 8641}, {649, 23653}, {663, 21746}, {667, 20978}, {669, 40984}
X(46402) = crossdifference of every pair of points on line {213, 3010}
X(46402) = barycentric product X(i)*X(j) for these {i,j}: {76, 44408}, {693, 37659}, {4219, 15413}, {7192, 45744}
X(46402) = barycentric quotient X(i)/X(j) for these {i,j}: {4219, 1783}, {14714, 657}, {37659, 100}, {44408, 6}, {45744, 3952}
X(46402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 3261, 20293}, {693, 4131, 7192}


X(46403) = ANTICOMPLEMENT OF X(659)

Barycentrics    (b - c)*(-a^3 - a*b^2 + a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(46403) = 3 X[2] - 4 X[3837], 9 X[2] - 10 X[30795], 5 X[2] - 4 X[45314], 7 X[2] - 8 X[45340], 5 X[631] - 4 X[44805], 2 X[650] - 3 X[44429], 3 X[659] - 5 X[30795], 5 X[659] - 6 X[45314], 7 X[659] - 12 X[45340], 2 X[676] - 3 X[4927], 4 X[676] - 3 X[44433], 3 X[693] - 2 X[7662], 3 X[1635] - 2 X[4830], 3 X[1635] - 4 X[25380], 4 X[1960] - 5 X[3616], 7 X[3622] - 6 X[25569], 2 X[3716] - 3 X[4728], 2 X[3762] - 3 X[30709], 6 X[3837] - 5 X[30795], 5 X[3837] - 3 X[45314], 7 X[3837] - 6 X[45340], 2 X[4010] - 3 X[21297], 2 X[4458] - 3 X[6545], 2 X[4491] - 3 X[26144], 4 X[4782] - 5 X[27013], 4 X[4806] - 5 X[26798], 2 X[4809] - 3 X[6548], 4 X[4874] - 5 X[26985], 2 X[5592] - 3 X[14432], X[6161] - 3 X[30592], 2 X[9508] - 3 X[36848], 2 X[13246] - 3 X[21204], 3 X[14419] - 4 X[19947], 3 X[16173] - 2 X[41191], 3 X[30574] - 4 X[44314], 25 X[30795] - 18 X[45314], 35 X[30795] - 36 X[45340], 7 X[45314] - 10 X[45340]

X(46403) lies on these lines: {2, 659}, {4, 2826}, {8, 891}, {10, 21385}, {11, 13266}, {145, 21343}, {149, 900}, {291, 812}, {320, 350}, {388, 30725}, {514, 4088}, {522, 4382}, {523, 2528}, {631, 44805}, {649, 24720}, {650, 44429}, {667, 23815}, {669, 26854}, {676, 4927}, {764, 2787}, {804, 5992}, {814, 3777}, {830, 4978}, {876, 30669}, {918, 20539}, {962, 2821}, {1019, 23789}, {1491, 17494}, {1635, 4830}, {1734, 29302}, {1960, 3616}, {2526, 4762}, {2530, 4560}, {2550, 4925}, {2788, 42758}, {2789, 21105}, {2827, 34789}, {2832, 3762}, {3120, 17197}, {3254, 23836}, {3436, 24128}, {3621, 25574}, {3622, 25569}, {3716, 4728}, {3733, 18108}, {3766, 20345}, {3835, 4724}, {3904, 29240}, {3909, 3952}, {4080, 23345}, {4083, 21302}, {4120, 4778}, {4170, 42325}, {4367, 31291}, {4449, 28470}, {4458, 6545}, {4491, 26144}, {4498, 17072}, {4782, 27013}, {4784, 26853}, {4789, 28209}, {4801, 8678}, {4806, 26798}, {4809, 6548}, {4874, 26985}, {4876, 23656}, {4895, 28521}, {4905, 29013}, {4963, 28213}, {4977, 18004}, {5080, 6550}, {5592, 14432}, {6008, 7659}, {6084, 20344}, {6085, 17777}, {6161, 30592}, {6373, 17794}, {9508, 36848}, {13246, 21204}, {14349, 29186}, {14419, 19947}, {16173, 41191}, {17418, 30094}, {18197, 23791}, {19882, 23814}, {20060, 24097}, {20293, 20983}, {21118, 28487}, {21173, 23803}, {21176, 21201}, {21303, 30665}, {21612, 33931}, {23765, 29324}, {23818, 27345}, {23838, 46150}, {30574, 44314}, {30578, 44008}

X(46403) = reflection of X(i) in X(j) for these {i,j}: {145, 21343}, {649, 24720}, {659, 3837}, {667, 23815}, {1019, 23789}, {3733, 40086}, {4498, 17072}, {4560, 2530}, {4724, 3835}, {4830, 25380}, {7192, 21146}, {13266, 11}, {17166, 4978}, {17494, 1491}, {17496, 3777}, {20295, 24719}, {21222, 764}, {21385, 10}, {26853, 4784}, {31291, 4367}, {44433, 4927}
X(46403) = anticomplement of X(659)
X(46403) = circumcircle-of-anticomplementary-triangle-inverse of X(10773)}
X(46403) = anticomplement of the isogonal conjugate of X(660)
X(46403) = anticomplement of the isotomic conjugate of X(4583)
X(46403) = isotomic conjugate of the anticomplement of X(40623)
X(46403) = isotomic conjugate of the isogonal conjugate of X(21003)
X(46403) = polar conjugate of the isogonal conjugate of X(22155)
X(46403) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {6, 39362}, {100, 17794}, {101, 33888}, {190, 20345}, {291, 149}, {292, 4440}, {334, 21293}, {335, 150}, {660, 8}, {668, 20554}, {692, 30667}, {741, 17154}, {805, 38}, {813, 2}, {1911, 9263}, {1922, 21224}, {3252, 39353}, {3862, 39345}, {4518, 33650}, {4557, 39367}, {4562, 69}, {4583, 6327}, {4584, 75}, {4589, 17135}, {4639, 17137}, {4876, 37781}, {5378, 513}, {7077, 39351}, {8684, 32937}, {18047, 25332}, {18829, 17153}, {30664, 24349}, {34067, 192}, {36066, 17140}, {36081, 17165}, {36801, 3436}, {37134, 17152}, {37207, 4441}, {43534, 3448}
X(46403) = X(4583)-Ceva conjugate of X(2)
X(46403) = X(40623)-cross conjugate of X(2)
X(46403) = X(i)-isoconjugate of X(j) for these (i,j): {101, 39979}, {692, 39714}
X(46403) = cevapoint of X(21003) and X(22155)
X(46403) = crosspoint of X(i) and X(j) for these (i,j): {86, 4562}, {668, 673}, {18827, 37205}
X(46403) = crosssum of X(i) and X(j) for these (i,j): {42, 8632}, {649, 20456}, {667, 672}
X(46403) = crossdifference of every pair of points on line {213, 5007}
X(46403) = barycentric product X(i)*X(j) for these {i,j}: {1, 20950}, {76, 21003}, {264, 22155}, {514, 32922}, {693, 33854}, {4583, 40623}
X(46403) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 39979}, {514, 39714}, {20950, 75}, {21003, 6}, {22155, 3}, {29955, 3783}, {32922, 190}, {33854, 100}, {40623, 659}
X(46403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 3837, 2}, {659, 28399, 27675}, {4830, 25380, 1635}, {27015, 27140, 2}, {27075, 27194, 2}, {27294, 27347, 2}


X(46404) = ISOTOMIC CONJUGATE OF X(652)

Barycentrics    (a - b)*b^2*(a - c)*(a + b - c)*c^2*(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(46404) lies on these lines: {75, 24031}, {76, 40701}, {85, 1969}, {92, 18031}, {108, 789}, {109, 22456}, {226, 46273}, {264, 21666}, {273, 31002}, {278, 32020}, {331, 20568}, {349, 33805}, {653, 799}, {658, 3261}, {664, 811}, {668, 18026}, {1441, 14009}, {1813, 42405}, {1897, 46107}, {4554, 6335}, {4593, 32674}, {6063, 7017}, {16089, 16091}, {17984, 17985}, {18033, 46108}, {40017, 40149}, {46111, 46277}

X(46404) = isotomic conjugate of X(652)
X(46404) = polar conjugate of X(663)
X(46404) = isotomic conjugate of the isogonal conjugate of X(653)
X(46404) = polar conjugate of the isotomic conjugate of X(4572)
X(46404) = polar conjugate of the isogonal conjugate of X(664)
X(46404) = X(6331)-Ceva conjugate of X(4554)
X(46404) = X(i)-cross conjugate of X(j) for these (i,j): {664, 4572}, {3261, 1969}, {4391, 44130}, {6332, 75}, {18134, 4998}, {21957, 10}, {35519, 6063}, {46110, 264}
X(46404) = cevapoint of X(i) and X(j) for these (i,j): {65, 21348}, {75, 6332}, {85, 3261}, {92, 46107}, {264, 46110}, {514, 17861}, {653, 664}, {693, 17862}, {1441, 4391}, {1577, 18692}, {3239, 17860}, {6335, 18026}, {7017, 35519}
X(46404) = trilinear pole of line {75, 225}
X(46404) = X(i)-isoconjugate of X(j) for these (i,j): {3, 3063}, {6, 1946}, {21, 3049}, {25, 36054}, {31, 652}, {32, 521}, {41, 1459}, {48, 663}, {55, 22383}, {78, 1919}, {108, 39687}, {184, 650}, {212, 649}, {213, 23189}, {219, 667}, {222, 8641}, {228, 7252}, {283, 798}, {284, 810}, {294, 23225}, {332, 1924}, {345, 1980}, {512, 2193}, {520, 2204}, {522, 9247}, {560, 6332}, {577, 18344}, {603, 657}, {607, 23224}, {644, 22096}, {647, 2194}, {669, 1812}, {692, 7117}, {822, 2299}, {884, 20752}, {905, 2175}, {906, 3271}, {926, 32658}, {1172, 39201}, {1402, 23090}, {1409, 21789}, {1415, 3270}, {1437, 3709}, {1501, 35518}, {1802, 43924}, {1814, 8638}, {1977, 4571}, {2170, 32656}, {2200, 3737}, {2206, 8611}, {2208, 10397}, {2212, 4091}, {2310, 32660}, {2637, 34078}, {2638, 32674}, {3248, 4587}, {4025, 9447}, {4105, 7099}, {4391, 14575}, {4516, 32661}, {4631, 23216}, {4895, 32659}, {6056, 6591}, {7004, 32739}, {7107, 21761}, {9448, 15413}, {9454, 23696}, {14395, 40352}, {14585, 44426}, {14936, 36059}, {15416, 41280}, {23614, 23985}, {32727, 33572}
X(46404) = barycentric product X(i)*X(j) for these {i,j}: {4, 4572}, {34, 6386}, {75, 18026}, {76, 653}, {85, 6335}, {92, 4554}, {108, 561}, {109, 18022}, {190, 331}, {225, 670}, {226, 6331}, {264, 664}, {273, 668}, {278, 1978}, {305, 36127}, {307, 6528}, {312, 13149}, {318, 4569}, {349, 648}, {646, 1847}, {651, 1969}, {658, 7017}, {799, 40149}, {811, 1441}, {823, 1231}, {1275, 46110}, {1502, 32674}, {1783, 20567}, {1813, 18027}, {1861, 46135}, {1880, 4602}, {1897, 6063}, {3261, 46102}, {3596, 36118}, {4552, 44129}, {4566, 44130}, {4620, 14618}, {4625, 41013}, {4998, 46107}, {5236, 36803}, {7012, 40495}, {7101, 36838}, {8750, 41283}, {18833, 46152}, {24032, 35518}, {28659, 32714}, {34085, 46108}, {40701, 44327}
X(46404) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1946}, {2, 652}, {4, 663}, {7, 1459}, {19, 3063}, {27, 7252}, {29, 21789}, {33, 8641}, {34, 667}, {57, 22383}, {59, 32656}, {63, 36054}, {65, 810}, {73, 39201}, {75, 521}, {76, 6332}, {77, 23224}, {85, 905}, {86, 23189}, {92, 650}, {99, 283}, {100, 212}, {107, 2299}, {108, 31}, {109, 184}, {158, 18344}, {162, 2194}, {190, 219}, {225, 512}, {226, 647}, {264, 522}, {273, 513}, {278, 649}, {281, 657}, {286, 3737}, {307, 520}, {318, 3900}, {321, 8611}, {329, 10397}, {331, 514}, {333, 23090}, {342, 6129}, {348, 4091}, {349, 525}, {514, 7117}, {521, 2638}, {522, 3270}, {561, 35518}, {608, 1919}, {644, 1802}, {645, 2327}, {646, 3692}, {648, 284}, {651, 48}, {652, 39687}, {653, 6}, {658, 222}, {662, 2193}, {664, 3}, {668, 78}, {670, 332}, {693, 7004}, {799, 1812}, {811, 21}, {823, 1172}, {883, 1818}, {927, 36057}, {934, 603}, {1016, 4587}, {1020, 1409}, {1025, 20752}, {1119, 43924}, {1214, 822}, {1231, 24018}, {1262, 32660}, {1275, 1813}, {1309, 2342}, {1331, 6056}, {1332, 2289}, {1395, 1980}, {1400, 3049}, {1414, 1437}, {1415, 9247}, {1434, 7254}, {1441, 656}, {1442, 23226}, {1443, 22379}, {1447, 22384}, {1457, 23220}, {1458, 23225}, {1783, 41}, {1813, 577}, {1826, 3709}, {1847, 3669}, {1855, 10581}, {1861, 926}, {1870, 8648}, {1874, 4455}, {1877, 1960}, {1880, 798}, {1897, 55}, {1940, 21761}, {1943, 22382}, {1969, 4391}, {1978, 345}, {1981, 1951}, {2052, 3064}, {2356, 8638}, {2481, 23696}, {2973, 21132}, {3064, 14936}, {3212, 22090}, {3261, 26932}, {3676, 3937}, {3699, 1260}, {3732, 7124}, {3882, 22074}, {3888, 20753}, {3911, 22086}, {3952, 2318}, {4025, 1364}, {4033, 3694}, {4077, 18210}, {4242, 2361}, {4358, 14418}, {4391, 34591}, {4551, 228}, {4552, 71}, {4554, 63}, {4559, 2200}, {4561, 1259}, {4563, 6514}, {4564, 906}, {4566, 73}, {4569, 77}, {4572, 69}, {4573, 1790}, {4589, 1808}, {4605, 2197}, {4617, 7099}, {4620, 4558}, {4625, 1444}, {4626, 7053}, {4998, 1331}, {5125, 8676}, {5236, 665}, {5930, 42658}, {6063, 4025}, {6331, 333}, {6332, 35072}, {6335, 9}, {6386, 3718}, {6516, 255}, {6517, 1092}, {6528, 29}, {6648, 2359}, {6649, 3955}, {6742, 8606}, {7012, 692}, {7017, 3239}, {7035, 4571}, {7045, 36059}, {7046, 4105}, {7101, 4130}, {7115, 32739}, {7128, 1415}, {7176, 22093}, {7182, 4131}, {7257, 1792}, {7282, 2605}, {7649, 3271}, {8736, 4079}, {8750, 2175}, {9312, 22091}, {13138, 2188}, {13149, 57}, {14206, 14395}, {14594, 7085}, {14618, 21044}, {15352, 8748}, {15418, 6518}, {15466, 14331}, {15742, 3939}, {17136, 22361}, {17496, 38344}, {17862, 40628}, {17906, 2347}, {17923, 654}, {17924, 2170}, {17985, 5075}, {18020, 4636}, {18022, 35519}, {18026, 1}, {18027, 46110}, {18816, 37628}, {18831, 35196}, {20567, 15413}, {21272, 22072}, {21609, 24562}, {21666, 23615}, {22464, 8677}, {23067, 4055}, {23703, 23202}, {23710, 6139}, {23984, 32674}, {24002, 3942}, {24006, 4516}, {24019, 2204}, {24031, 23614}, {24032, 108}, {24035, 2182}, {27808, 3710}, {28659, 15416}, {28660, 15411}, {30545, 25098}, {30806, 14414}, {31623, 1021}, {32660, 14585}, {32674, 32}, {32714, 604}, {34085, 1814}, {34388, 4064}, {35154, 17973}, {35174, 1807}, {35312, 22053}, {35338, 22079}, {35516, 39471}, {35518, 24031}, {35519, 2968}, {36038, 35014}, {36110, 34858}, {36118, 56}, {36124, 884}, {36127, 25}, {36146, 32658}, {36797, 2328}, {36838, 7177}, {37136, 14578}, {37137, 7116}, {37790, 1635}, {38461, 14413}, {38462, 4895}, {39060, 2636}, {39294, 32641}, {40117, 7118}, {40149, 661}, {40152, 32320}, {40495, 17880}, {40701, 14837}, {40717, 3716}, {41013, 4041}, {41207, 2249}, {43040, 22092}, {43923, 3248}, {43924, 22096}, {44129, 4560}, {44130, 7253}, {44146, 14432}, {44327, 268}, {44426, 2310}, {44721, 4546}, {46102, 101}, {46106, 14400}, {46107, 11}, {46109, 1639}, {46110, 1146}, {46135, 31637}, {46152, 1964}, {46153, 20775}, {46177, 22368}, {46254, 4612}
X(46404) = {X(6335),X(13149)}-harmonic conjugate of X(4554)


X(46405) = ISOTOMIC CONJUGATE OF X(654)

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

X(46405) lies on these lines: {655, 799}, {668, 35174}, {789, 2222}, {850, 4998}, {2006, 32020}, {3261, 4554}, {4593, 32675}, {18031, 18359}, {18815, 31002}, {20566, 35517}, {20920, 21587}

X(46405) = isotomic conjugate of X(654)
X(46405) = isotomic conjugate of the isogonal conjugate of X(655)
X(46405) = X(i)-cross conjugate of X(j) for these (i,j): {3904, 75}, {3936, 4998}
X(46405) = X(i)-isoconjugate of X(j) for these (i,j): {6, 8648}, {31, 654}, {32, 3738}, {36, 3063}, {55, 21758}, {512, 4282}, {560, 3904}, {607, 22379}, {649, 2361}, {663, 7113}, {667, 2323}, {1919, 4511}, {1980, 32851}, {1983, 3271}, {2150, 42666}, {2175, 3960}, {2194, 21828}, {3049, 17515}, {3724, 7252}, {4453, 9447}, {9247, 44428}
X(46405) = cevapoint of X(i) and X(j) for these (i,j): {75, 3904}, {514, 24209}, {850, 3936}, {3262, 4391}, {35174, 36804}
X(46405) = trilinear pole of line {75, 311} (the isotomic conjugate of the isogonal conjugate of line X(1)X(5))
X(46405) = barycentric product X(i)*X(j) for these {i,j}: {75, 35174}, {76, 655}, {80, 4572}, {85, 36804}, {561, 2222}, {664, 20566}, {668, 18815}, {1411, 6386}, {1502, 32675}, {1978, 2006}, {4554, 18359}, {4625, 15065}, {35139, 40999}
X(46405) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8648}, {2, 654}, {12, 42666}, {57, 21758}, {75, 3738}, {76, 3904}, {77, 22379}, {80, 663}, {85, 3960}, {100, 2361}, {190, 2323}, {226, 21828}, {264, 44428}, {311, 6369}, {349, 4707}, {651, 7113}, {655, 6}, {662, 4282}, {664, 36}, {668, 4511}, {811, 17515}, {1411, 667}, {1807, 1946}, {1978, 32851}, {2006, 649}, {2161, 3063}, {2222, 31}, {2594, 14270}, {3904, 35128}, {4453, 3025}, {4551, 3724}, {4552, 2245}, {4554, 3218}, {4564, 1983}, {4566, 1464}, {4569, 1443}, {4572, 320}, {4585, 34544}, {6063, 4453}, {6358, 2610}, {6369, 41218}, {6740, 21789}, {14213, 2600}, {14584, 1960}, {14616, 3737}, {14628, 1635}, {15065, 4041}, {16577, 2624}, {18026, 1870}, {18359, 650}, {18815, 513}, {20566, 522}, {23592, 32675}, {24624, 7252}, {32675, 32}, {34388, 6370}, {35139, 3615}, {35174, 1}, {36804, 9}, {36910, 657}, {37140, 2150}, {40999, 526}, {41226, 9404}


X(46406) = ISOTOMIC CONJUGATE OF X(657)

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

X(46406) lies on these lines: {75, 24010}, {85, 17451}, {279, 32020}, {658, 799}, {664, 4449}, {668, 883}, {789, 934}, {811, 4625}, {1088, 31002}, {1446, 40017}, {1461, 4593}, {3732, 34085}, {4554, 36838}, {6063, 34387}, {20567, 20925}

X(46406) = isotomic conjugate of X(657)
X(46406) = isotomic conjugate of the isogonal conjugate of X(658)
X(46406) = X(i)-cross conjugate of X(j) for these (i,j): {3239, 75}, {3261, 6063}, {4554, 4572}, {15413, 310}, {17234, 4998}, {18153, 31625}, {20946, 7035}, {30805, 7182}
X(46406) = cevapoint of X(i) and X(j) for these (i,j): {75, 3239}, {514, 3673}, {693, 20905}, {3261, 6063}, {3676, 41777}, {4391, 20880}, {4554, 4569}, {7182, 30805}
X(46406) = trilinear pole of line {75, 1088} (the isotomic conjugate of the isogonal conjugate of the Soddy line)
X(46406) = X(i)-isoconjugate of X(j) for these (i,j): {6, 8641}, {31, 657}, {32, 3900}, {41, 663}, {55, 3063}, {200, 1919}, {213, 21789}, {220, 667}, {294, 8638}, {346, 1980}, {513, 14827}, {522, 9447}, {560, 3239}, {604, 4105}, {607, 1946}, {649, 1253}, {650, 2175}, {652, 2212}, {669, 2287}, {692, 14936}, {798, 2328}, {810, 2332}, {1021, 1918}, {1043, 1924}, {1333, 4524}, {1397, 4130}, {1415, 3022}, {1461, 24012}, {1501, 4397}, {1576, 36197}, {1977, 4578}, {2194, 3709}, {2205, 7253}, {2206, 4171}, {2310, 32739}, {3049, 4183}, {4148, 14598}, {4391, 9448}, {4435, 18265}, {4477, 7104}, {4612, 7063}, {6059, 36054}, {6139, 18889}, {6602, 43924}, {7071, 22383}, {9455, 28132}, {15416, 44162}
X(46406) = barycentric product X(i)*X(j) for these {i,j}: {7, 4572}, {75, 4569}, {76, 658}, {85, 4554}, {109, 41283}, {269, 6386}, {279, 1978}, {304, 13149}, {305, 36118}, {310, 4566}, {312, 36838}, {313, 4616}, {321, 4635}, {349, 4573}, {561, 934}, {646, 23062}, {651, 20567}, {664, 6063}, {668, 1088}, {670, 3668}, {799, 1446}, {1020, 6385}, {1042, 4609}, {1275, 3261}, {1427, 4602}, {1441, 4625}, {1461, 1502}, {3596, 4626}, {4397, 24011}, {4617, 28659}, {4637, 27801}, {6614, 40363}, {7045, 40495}, {7182, 18026}, {7204, 46132}, {9436, 46135}, {32714, 40364}, {34085, 40704}
X(46406) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8641}, {2, 657}, {7, 663}, {8, 4105}, {10, 4524}, {57, 3063}, {75, 3900}, {76, 3239}, {77, 1946}, {85, 650}, {86, 21789}, {99, 2328}, {100, 1253}, {101, 14827}, {108, 2212}, {109, 2175}, {142, 10581}, {190, 220}, {226, 3709}, {269, 667}, {273, 18344}, {274, 1021}, {279, 649}, {310, 7253}, {312, 4130}, {321, 4171}, {331, 3064}, {348, 652}, {349, 3700}, {479, 43924}, {514, 14936}, {522, 3022}, {555, 6729}, {561, 4397}, {644, 6602}, {646, 728}, {648, 2332}, {651, 41}, {653, 607}, {658, 6}, {664, 55}, {668, 200}, {670, 1043}, {693, 2310}, {799, 2287}, {811, 4183}, {883, 2340}, {927, 2195}, {934, 31}, {1020, 213}, {1042, 669}, {1088, 513}, {1106, 1980}, {1231, 8611}, {1262, 32739}, {1269, 4990}, {1275, 101}, {1323, 6139}, {1332, 1802}, {1407, 1919}, {1414, 2194}, {1415, 9447}, {1427, 798}, {1434, 7252}, {1439, 810}, {1441, 4041}, {1443, 8648}, {1446, 661}, {1458, 8638}, {1461, 32}, {1577, 36197}, {1847, 6591}, {1897, 7071}, {1909, 4477}, {1920, 4529}, {1921, 4148}, {1978, 346}, {3239, 35508}, {3261, 1146}, {3264, 4528}, {3596, 4163}, {3668, 512}, {3671, 8653}, {3673, 17115}, {3676, 3271}, {3699, 480}, {3732, 30706}, {3900, 24012}, {4025, 3270}, {4033, 4515}, {4077, 4516}, {4091, 39687}, {4131, 2638}, {4320, 8646}, {4350, 8642}, {4358, 14427}, {4391, 3119}, {4397, 24010}, {4552, 1334}, {4554, 9}, {4561, 1260}, {4563, 2327}, {4566, 42}, {4569, 1}, {4572, 8}, {4573, 284}, {4601, 7259}, {4605, 1500}, {4610, 7054}, {4616, 58}, {4617, 604}, {4619, 23990}, {4620, 5546}, {4623, 1098}, {4624, 34820}, {4625, 21}, {4626, 56}, {4635, 81}, {4637, 1333}, {4847, 6607}, {4998, 3939}, {5249, 33525}, {6063, 522}, {6173, 17425}, {6331, 2322}, {6335, 7079}, {6354, 4079}, {6359, 21761}, {6386, 341}, {6516, 212}, {6517, 6056}, {6606, 10482}, {6614, 1397}, {6649, 2330}, {7035, 4578}, {7045, 692}, {7056, 1459}, {7177, 22383}, {7182, 521}, {7183, 36054}, {7196, 3287}, {7204, 788}, {7205, 3907}, {7216, 3121}, {7243, 4501}, {7340, 4636}, {7365, 2484}, {8269, 7084}, {9436, 926}, {10030, 4435}, {10481, 2488}, {13149, 19}, {15413, 34591}, {15467, 23289}, {17078, 654}, {17095, 9404}, {17206, 23090}, {18026, 33}, {18031, 28132}, {18033, 3716}, {19804, 4827}, {20567, 4391}, {20880, 6608}, {23062, 3669}, {23586, 1461}, {23989, 42462}, {24002, 2170}, {24011, 934}, {24015, 910}, {27808, 4082}, {30805, 35072}, {30806, 14392}, {31625, 6558}, {32714, 1973}, {33765, 21007}, {34018, 1024}, {34085, 294}, {34387, 23615}, {35157, 4845}, {35171, 42064}, {35312, 2293}, {35341, 8551}, {35519, 4081}, {36079, 33581}, {36118, 25}, {36127, 6059}, {36803, 6559}, {36838, 57}, {37139, 18889}, {37141, 7118}, {37757, 22108}, {38459, 8645}, {39126, 4162}, {40364, 15416}, {40495, 24026}, {40702, 14298}, {41283, 35519}, {41353, 2223}, {43932, 3248}, {44129, 17926}, {44327, 7367}, {46107, 42069}, {46135, 14942}


X(46407) = CIRCUMCIRCLE-INVERSE OF X(649)

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

X(46407) lies on the Brocard circle and these lines: {2, 5991}, {3, 649}, {6, 31}, {901, 38884}, {1252, 3730}, {1316, 24275}, {1331, 10756}, {2265, 14439}, {3735, 4414}, {4813, 36280}, {4988, 36205}, {20999, 46148}, {23988, 32739}, {24047, 41405}, {39640, 43079}

X(46407) = circumcircle-inverse of X(649)
X(46407) = psi-transform of X(101)
X(46407) = crossdifference of every pair of points on line {514, 3011}
X(46407) = isogonal conjugate of antitomic conjugate of X(675)
X(46407) = X(675)-of-1st-Brocard-triangle


X(46408) = CIRCUMCIRCLE-INVERSE OF X(650)

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

X(46408) lies on these lines: {3, 650}, {19, 25}, {1465, 14878}, {5514, 6174}, {14667, 14936}, {22108, 41155}

X(46408) = circumcircle-inverse of X(650)
X(46408) = Stevanovic-circle-inverse of X(3)


X(46409) = CIRCUMCIRCLE-INVERSE OF X(659)

Barycentrics    a*(a^7 - 2*a^6*b + a^5*b^2 - a^3*b^4 + 2*a^2*b^5 - a*b^6 - 2*a^6*c + 2*a^5*b*c + 2*a^4*b^2*c - 2*a^3*b^3*c - a^2*b^4*c + a*b^5*c + a^5*c^2 + 2*a^4*b*c^2 - 5*a^3*b^2*c^2 + 3*a^2*b^3*c^2 - 3*a*b^4*c^2 + b^5*c^2 - 2*a^3*b*c^3 + 3*a^2*b^2*c^3 + 4*a*b^3*c^3 - b^4*c^3 - a^3*c^4 - a^2*b*c^4 - 3*a*b^2*c^4 - b^3*c^4 + 2*a^2*c^5 + a*b*c^5 + b^2*c^5 - a*c^6) : :
X(46409) = (X[104] - 3 X[38694], X[1292] - 3 X[34474], X[5540] + 3 X[15015], X[10743] - 3 X[38752], 2 X[11730] - 3 X[34123]

X(46409) = lies on these lines: {2, 11}, {3, 659}, {104, 38694}, {214, 2809}, {952, 38603}, {1083, 3887}, {1292, 34474}, {1358, 6516}, {2795, 35204}, {2802, 11716}, {2836, 34583}, {5150, 24494}, {5220, 14191}, {5511, 5840}, {5540, 15015}, {10743, 38752}, {11730, 34123}, {28915, 33814}

X(46409) = midpoint of X(100) and X(105)
X(46409) = reflection of X(i) in X(j) for these {i,j}: {11, 6714}, {120, 3035}
X(46409) = complement of X(10773)
X(46409) = circumcircle-inverse of X(659)
X(46409) = psi-transform of X(3573)


X(46410) = CIRCUMCIRCLE-INVERSE OF X(663)

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

X(46410) lies on the Brocard circle and these lines: {3, 663}, {6, 41}, {1262, 10571}, {1813, 10764}, {9317, 19950}, {24248, 24279}

X(46410) = circumcircle-inverse of X(663)
X(46410) = psi-transform of X(109)
X(46410) = X(1311)-of-1st-Brocard-triangle


X(46411) = PERSPECTOR OF THE 1ST LOZADA CONIC

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

The 1st Lozada conic is defined at X(9724).

See Peter Moses, euclid 3605.

X(46411) = lies on these lines: { }


X(46412) = X(3)X(6749)∩X(394)X(549)

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

See Antreas Hatzipolakis and César Lozada, euclid 3608.

X(46412) lies on these lines: {3, 6749}, {97, 3524}, {376, 31626}, {394, 549}, {631, 14919}, {1073, 5054}, {3926, 44148}, {15701, 36609}

X(46412) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}} and {{A, B, C, X(4), X(549)}}


X(46413) = X(114)X(34349)∩X(2679)X(2881)

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

See Antreas Hatzipolakis and César Lozada, euclid 3613.

X(46413) lies on the nine-point circle and these lines: {114, 34349}, {804, 33504}, {2679, 2881}, {2794, 41175}, {2799, 36471}

X(46413) = Poncelet point of X(2794)


X(46414) = X(526)X(35588)∩X(17702)X(42424)

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

See Antreas Hatzipolakis and César Lozada, euclid 3613.

X(46414) lies on the nine-point circle and these lines: {526, 35588}, {17702, 42424}

X(46414) = Poncelet point of X(17702)


X(46415) = COMPLEMENT OF X(14733)

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

See Antreas Hatzipolakis and César Lozada, euclid 3615.

X(46415) lies on the nine-point circle and these lines: {2, 14733}, {11, 3900}, {115, 656}, {116, 46100}, {118, 3814}, {119, 971}, {120, 5123}, {124, 17072}, {513, 5514}, {517, 44993}, {1566, 3126}, {1861, 25640}, {2550, 33331}, {3820, 31841}

X(46415) = complement of X(14733)
X(46415) = complementary conjugate of X(6366)
X(46415) = center of the circumconic {{A, B, C, X(4), X(10426)}}
X(46415) = Poncelet point of X(10426)


X(46416) = X(114)X(35282)∩X(125)X(40550)

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

See Antreas Hatzipolakis and César Lozada, euclid 3615.

X(46416) lies on the nine-point circle and these lines: {114, 35282}, {125, 40550}, {3258, 14417}, {6334, 38971}, {7473, 42426}, {16177, 45689}, {23967, 38975}, {24284, 36471}, {32313, 35582}


X(46417) = X(525)X(22239)∩X(1301)X(39447)

Barycentrics    (a^16-(b^2+c^2)*a^14+(b^4-b^2*c^2+c^4)*a^12-7*(b^4-c^4)*(b^2-c^2)*a^10+(5*b^4+28*b^2*c^2+5*c^4)*(b^2-c^2)^2*a^8+(b^4-c^4)*(b^2-c^2)*(9*b^4-38*b^2*c^2+9*c^4)*a^6-(b^2-c^2)^2*(9*b^8+9*c^8+(3*b^4-40*b^2*c^2+3*c^4)*b^2*c^2)*a^4-(b^4-c^4)*(b^2-c^2)^3*(b^2-4*b*c+c^2)*(b^2+4*b*c+c^2)*a^2+2*(b^2+c^2)^2*(b^2-c^2)^6)*(a^10-(b^2+c^2)*a^8-(2*b^2+b*c-2*c^2)*(2*b^2-b*c-2*c^2)*a^6+8*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(5*b^4+13*b^2*c^2+5*c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(b^4+4*b^2*c^2+c^4))*(a^2-b^2+c^2)*(a^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2) : :

See Antreas Hatzipolakis and César Lozada, euclid 3615.

X(46417) lies on these lines: {525, 22239}, {1301, 39447}


X(46418) = X(514)X(1309)∩X(653)X(1845)

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

See Antreas Hatzipolakis and César Lozada, euclid 3615.

X(46418) lies on these lines: {514, 1309}, {653, 1845}, {3732, 8677}


X(46419) = X(6)X(1012)∩X(73)X(4304)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 3616.

X(46419) lies on these lines: {6,1012}, {30,34586}, {73,4304}, {946,1201}, {1777,3157}, {2650,2800}, {2823,18675}, {7004,10122}, {22300,23845}, {33811,37195}


X(46420) = (name pending)

Barycentrics    a^2*(a^14*b^2 - 3*a^13*b^3 - 5*a^12*b^4 + 12*a^11*b^5 + 11*a^10*b^6 - 15*a^9*b^7 - 15*a^8*b^8 + 15*a^6*b^10 + 15*a^5*b^11 - 11*a^4*b^12 - 12*a^3*b^13 + 5*a^2*b^14 + 3*a*b^15 - b^16 - 3*a^13*b^2*c - 5*a^12*b^3*c + 10*a^11*b^4*c + 22*a^10*b^5*c - 5*a^9*b^6*c - 35*a^8*b^7*c - 20*a^7*b^8*c + 20*a^6*b^9*c + 35*a^5*b^10*c + 5*a^4*b^11*c - 22*a^3*b^12*c - 10*a^2*b^13*c + 5*a*b^14*c + 3*b^15*c - a^14*c^2 - 2*a^13*b*c^2 - 2*a^12*b^2*c^2 + 8*a^11*b^3*c^2 + 24*a^10*b^4*c^2 + 2*a^9*b^5*c^2 - 35*a^8*b^6*c^2 - 24*a^7*b^7*c^2 - 9*a^6*b^8*c^2 + 10*a^5*b^9*c^2 + 48*a^4*b^10*c^2 + 16*a^3*b^11*c^2 - 30*a^2*b^12*c^2 - 10*a*b^13*c^2 + 5*b^14*c^2 + 2*a^12*b*c^3 + 12*a^11*b^2*c^3 + 16*a^10*b^3*c^3 - 6*a^9*b^4*c^3 - 24*a^8*b^5*c^3 - 16*a^7*b^6*c^3 - 16*a^6*b^7*c^3 - 20*a^5*b^8*c^3 + 18*a^4*b^9*c^3 + 52*a^3*b^10*c^3 + 16*a^2*b^11*c^3 - 22*a*b^12*c^3 - 12*b^13*c^3 + 6*a^12*c^4 + 10*a^11*b*c^4 - 7*a^9*b^3*c^4 - 19*a^8*b^4*c^4 - 20*a^7*b^5*c^4 + 8*a^6*b^6*c^4 - 6*a^5*b^7*c^4 - 32*a^4*b^8*c^4 + 18*a^3*b^9*c^4 + 48*a^2*b^10*c^4 + 5*a*b^11*c^4 - 11*b^12*c^4 - 10*a^10*b*c^5 - 21*a^9*b^2*c^5 - 17*a^8*b^3*c^5 - 4*a^7*b^4*c^5 + 8*a^6*b^5*c^5 + 10*a^5*b^6*c^5 - 6*a^4*b^7*c^5 - 20*a^3*b^8*c^5 + 10*a^2*b^9*c^5 + 35*a*b^10*c^5 + 15*b^11*c^5 - 15*a^10*c^6 - 20*a^9*b*c^6 + a^8*b^2*c^6 + 8*a^7*b^3*c^6 + 8*a^5*b^5*c^6 + 8*a^4*b^6*c^6 - 16*a^3*b^7*c^6 - 9*a^2*b^8*c^6 + 20*a*b^9*c^6 + 15*b^10*c^6 + 20*a^8*b*c^7 + 24*a^7*b^2*c^7 + 8*a^6*b^3*c^7 - 4*a^5*b^4*c^7 - 20*a^4*b^5*c^7 - 16*a^3*b^6*c^7 - 24*a^2*b^7*c^7 - 20*a*b^8*c^7 + 20*a^8*c^8 + 20*a^7*b*c^8 + a^6*b^2*c^8 - 17*a^5*b^3*c^8 - 19*a^4*b^4*c^8 - 24*a^3*b^5*c^8 - 35*a^2*b^6*c^8 - 35*a*b^7*c^8 - 15*b^8*c^8 - 20*a^6*b*c^9 - 21*a^5*b^2*c^9 - 7*a^4*b^3*c^9 - 6*a^3*b^4*c^9 + 2*a^2*b^5*c^9 - 5*a*b^6*c^9 - 15*b^7*c^9 - 15*a^6*c^10 - 10*a^5*b*c^10 + 16*a^3*b^3*c^10 + 24*a^2*b^4*c^10 + 22*a*b^5*c^10 + 11*b^6*c^10 + 10*a^4*b*c^11 + 12*a^3*b^2*c^11 + 8*a^2*b^3*c^11 + 10*a*b^4*c^11 + 12*b^5*c^11 + 6*a^4*c^12 + 2*a^3*b*c^12 - 2*a^2*b^2*c^12 - 5*a*b^3*c^12 - 5*b^4*c^12 - 2*a^2*b*c^13 - 3*a*b^2*c^13 - 3*b^3*c^13 - a^2*c^14 + b^2*c^14)*(a^14*b^2 - 6*a^12*b^4 + 15*a^10*b^6 - 20*a^8*b^8 + 15*a^6*b^10 - 6*a^4*b^12 + a^2*b^14 + 2*a^13*b^2*c - 2*a^12*b^3*c - 10*a^11*b^4*c + 10*a^10*b^5*c + 20*a^9*b^6*c - 20*a^8*b^7*c - 20*a^7*b^8*c + 20*a^6*b^9*c + 10*a^5*b^10*c - 10*a^4*b^11*c - 2*a^3*b^12*c + 2*a^2*b^13*c - a^14*c^2 + 3*a^13*b*c^2 + 2*a^12*b^2*c^2 - 12*a^11*b^3*c^2 + 21*a^9*b^5*c^2 - a^8*b^6*c^2 - 24*a^7*b^7*c^2 - a^6*b^8*c^2 + 21*a^5*b^9*c^2 - 12*a^3*b^11*c^2 + 2*a^2*b^12*c^2 + 3*a*b^13*c^2 - b^14*c^2 + 3*a^13*c^3 + 5*a^12*b*c^3 - 8*a^11*b^2*c^3 - 16*a^10*b^3*c^3 + 7*a^9*b^4*c^3 + 17*a^8*b^5*c^3 - 8*a^7*b^6*c^3 - 8*a^6*b^7*c^3 + 17*a^5*b^8*c^3 + 7*a^4*b^9*c^3 - 16*a^3*b^10*c^3 - 8*a^2*b^11*c^3 + 5*a*b^12*c^3 + 3*b^13*c^3 + 5*a^12*c^4 - 10*a^11*b*c^4 - 24*a^10*b^2*c^4 + 6*a^9*b^3*c^4 + 19*a^8*b^4*c^4 + 4*a^7*b^5*c^4 + 4*a^5*b^7*c^4 + 19*a^4*b^8*c^4 + 6*a^3*b^9*c^4 - 24*a^2*b^10*c^4 - 10*a*b^11*c^4 + 5*b^12*c^4 - 12*a^11*c^5 - 22*a^10*b*c^5 - 2*a^9*b^2*c^5 + 24*a^8*b^3*c^5 + 20*a^7*b^4*c^5 - 8*a^6*b^5*c^5 - 8*a^5*b^6*c^5 + 20*a^4*b^7*c^5 + 24*a^3*b^8*c^5 - 2*a^2*b^9*c^5 - 22*a*b^10*c^5 - 12*b^11*c^5 - 11*a^10*c^6 + 5*a^9*b*c^6 + 35*a^8*b^2*c^6 + 16*a^7*b^3*c^6 - 8*a^6*b^4*c^6 - 10*a^5*b^5*c^6 - 8*a^4*b^6*c^6 + 16*a^3*b^7*c^6 + 35*a^2*b^8*c^6 + 5*a*b^9*c^6 - 11*b^10*c^6 + 15*a^9*c^7 + 35*a^8*b*c^7 + 24*a^7*b^2*c^7 + 16*a^6*b^3*c^7 + 6*a^5*b^4*c^7 + 6*a^4*b^5*c^7 + 16*a^3*b^6*c^7 + 24*a^2*b^7*c^7 + 35*a*b^8*c^7 + 15*b^9*c^7 + 15*a^8*c^8 + 20*a^7*b*c^8 + 9*a^6*b^2*c^8 + 20*a^5*b^3*c^8 + 32*a^4*b^4*c^8 + 20*a^3*b^5*c^8 + 9*a^2*b^6*c^8 + 20*a*b^7*c^8 + 15*b^8*c^8 - 20*a^6*b*c^9 - 10*a^5*b^2*c^9 - 18*a^4*b^3*c^9 - 18*a^3*b^4*c^9 - 10*a^2*b^5*c^9 - 20*a*b^6*c^9 - 15*a^6*c^10 - 35*a^5*b*c^10 - 48*a^4*b^2*c^10 - 52*a^3*b^3*c^10 - 48*a^2*b^4*c^10 - 35*a*b^5*c^10 - 15*b^6*c^10 - 15*a^5*c^11 - 5*a^4*b*c^11 - 16*a^3*b^2*c^11 - 16*a^2*b^3*c^11 - 5*a*b^4*c^11 - 15*b^5*c^11 + 11*a^4*c^12 + 22*a^3*b*c^12 + 30*a^2*b^2*c^12 + 22*a*b^3*c^12 + 11*b^4*c^12 + 12*a^3*c^13 + 10*a^2*b*c^13 + 10*a*b^2*c^13 + 12*b^3*c^13 - 5*a^2*c^14 - 5*a*b*c^14 - 5*b^2*c^14 - 3*a*c^15 - 3*b*c^15 + c^16) : :

Let A'B'C' be the intouch triangle, Oa the circumcenter of AB'C' and Ac, Ab the reflections of Oa in A'B', A'C', resp. Define Ba, Bc, Cb, Ca cyclically. The six points lie on a conic centered at X(942). Its perspector is X(46420)

See Elias M. Hagos and Peter Moses, euclid 3619.

X(46420) lies on these lines: { }


X(46421) = X(2)X(175)∩X(8)X(20)

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

X(46421) lies on the cubic K332 and these lines: {2, 175}, {8, 20}, {144, 13387}, {176, 6360}, {190, 13458}, {200, 31563}, {329, 31547}, {1271, 4329}, {2324, 3084}, {3666, 19066}, {4641, 19065}, {6347, 20262}, {11680, 16028}, {13425, 14829}, {17134, 32793}, {17594, 26300}, {20223, 31550}

X(46421) = anticomplement of X(13390)
X(46421) = anticomplement of the isogonal conjugate of X(5414)
X(46421) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 176}, {55, 13386}, {212, 46413}, {606, 175}, {1805, 75}, {2066, 31552}, {2067, 7}, {5414, 8}, {7090, 21270}, {7133, 4}, {13388, 3434}, {30557, 69}
X(46421) = X(i)-Ceva conjugate of X(j) for these (i,j): {329, 46422}, {31547, 144}
X(46421) = barycentric product X(75)*X(32556)
X(46421) = barycentric quotient X(i)/X(j) for these {i,j}: {30557, 34907}, {32556, 1}, {34910, 14121}
X(46421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 63, 46422}, {40, 189, 46422}, {13388, 14121, 2}


X(46422) = X(2)X(176)∩X(8)X(20)

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

X(46422) lies on the cubic K332 and these lines: {2, 176}, {8, 20}, {69, 13461}, {144, 13386}, {165, 8984}, {175, 6360}, {190, 13425}, {200, 31564}, {329, 31548}, {1270, 4329}, {2324, 3083}, {3666, 19065}, {4641, 19066}, {6348, 20262}, {11681, 16028}, {13458, 14829}, {17134, 32794}, {17594, 26301}, {20223, 31549}

X(46422) = anticomplement of X(1659)
X(46422) = anticomplement of the isogonal conjugate of X(2066)
X(46422) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 175}, {55, 13387}, {212, 46412}, {605, 176}, {1806, 75}, {2066, 8}, {5414, 31551}, {6502, 7}, {13389, 3434}, {14121, 21270}, {30556, 69}, {42013, 4}
X(46422) = X(i)-Ceva conjugate of X(j) for these (i,j): {329, 46421}, {31548, 144}
X(46422) = cevapoint of X(40) and X(38004)
X(46422) = barycentric product X(75)*X(32555)
X(46422) = barycentric quotient X(i)/X(j) for these {i,j}: {30556, 34908}, {32555, 1}, {34909, 7090}
X(46422) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 63, 46421}, {40, 189, 46421}, {7090, 13389, 2}


X(46423) = ISOGONAL CONJUGATE OF X(7728)

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

See Antreas Hatzipolakis and César Lozada, euclid 3621.

X(46423) lies on these lines: {3, 34209}, {4, 46424}, {50, 15262}, {186, 34170}, {477, 6344}, {2071, 5663}, {3520, 14385}, {10564, 31941}, {12028, 38701}, {36164, 43917}

X(46423) = reflection of X(4) in X(46424)
X(46423) = isogonal conjugate of X(7728)
X(46423) = cevapoint of X(3) and X(12302)
X(46423) = X(i)-vertex conjugate of-X(j) for these (i, j): {4, 30}, {64, 186}
X(46423) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(50)}} and {{A, B, C, X(4), X(2071)}}


X(46424) = X(5)X(14385)∩X(2072)X(5663)

Barycentrics    (b^2+c^2)*a^20-(3*b^4+4*b^2*c^2+3*c^4)*a^18-(b^2+c^2)*(3*b^4-16*b^2*c^2+3*c^4)*a^16+(22*b^8+22*c^8-b^2*c^2*(23*b^4+18*b^2*c^2+23*c^4))*a^14-(b^2+c^2)*(28*b^8+28*c^8-b^2*c^2*(17*b^4+27*b^2*c^2+17*c^4))*a^12+(95*b^8+95*c^8-24*b^2*c^2*(5*b^4-2*b^2*c^2+5*c^4))*b^2*c^2*a^10+(b^4-c^4)*(b^2-c^2)*(28*b^8+28*c^8-b^2*c^2*(93*b^4-40*b^2*c^2+93*c^4))*a^8-(b^2-c^2)^2*(22*b^12+22*c^12-(3*b^8+3*c^8+2*b^2*c^2*(37*b^4-30*b^2*c^2+37*c^4))*b^2*c^2)*a^6+(b^4-c^4)*(b^2-c^2)^3*(3*b^8+3*c^8+b^2*c^2*(27*b^4-31*b^2*c^2+27*c^4))*a^4+(3*b^8+3*c^8-b^2*c^2*(b^4+12*b^2*c^2+c^4))*(b^2-c^2)^6*a^2-(b^2-c^2)^8*(b^2+c^2)*(b^4+3*b^2*c^2+c^4) : :

See Antreas Hatzipolakis and César Lozada, euclid 3621.

X(46424) lies on these lines: {4, 46423}, {5, 14385}, {2072, 5663}, {16177, 17854}

X(46424) = midpoint of X(4) and X(46423)


X(46425) = X(115)X(122)∩X(230)X(231)

Barycentrics   a^2*(a^8-2*(b^2+c^2)*a^6+7*b^2*c^2*a^4+2*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2-(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2)*(b^2-c^2) : :
X(46425) = X(686)-3*X(2433)

See Antreas Hatzipolakis and César Lozada, euclid 3627.

X(46425) lies on these lines: {6, 1636}, {25, 2881}, {111, 1297}, {112, 1301}, {115, 122}, {186, 15292}, {230, 231}, {526, 686}, {1196, 2508}, {2079, 3569}, {2395, 40347}, {5972, 13526}, {6128, 45319}, {7663, 10278}, {8552, 14566}, {8770, 14998}, {14346, 32320}, {15421, 41079}, {23292, 45325}, {44564, 44817}

X(46425) = midpoint of X(i) and X(j) for these {i, j}: {25, 42665}, {15421, 41079}
X(46425) = complement of the isogonal conjugate of X(32715)
X(46425) = crossdifference of every pair of points on line {X(3), X(113)}
X(46425) = crosspoint of X(i) and X(j) for these (i, j): {2, 1304}, {107, 2986}, {112, 34570}
X(46425) = crosssum of X(i) and X(j) for these (i, j): {6, 9033}, {30, 6587}, {520, 3003}
X(46425) = X(2)-Ceva conjugate of-X(16177)
X(46425) = X(i)-complementary conjugate of-X(j) for these (i, j): (31, 16177), (560, 39008), (1304, 2887)
X(46425) = X(i)-Dao conjugate of-X(j) for these (i, j): (403, 16237), (1084, 11744)
X(46425) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 22239}, {662, 11744}, {823, 40082}
X(46425) = X(i)-line conjugate of-X(j) for these (i, j): (112, 1624), (115, 122), (1301, 1624)
X(46425) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 22239), (512, 11744)
X(46425) = perspector of the circumconic {{A, B, C, X(4), X(2071)}}
X(46425) = center of the circumconic {{A, B, C, X(15421), X(41079)}}
X(46425) = intersection, other than A, B, C, of circumconics {{A, B, C, X(111), X(16318)}} and {{A, B, C, X(112), X(6587)}}
X(46425) = midpoint of hyperbola {{A,B,C,X(2),X(3)}} intercepts of the orthic axis
X(46425) = barycentric product X(i)*X(j) for these {i, j}: {520, 34170}, {523, 2071}, {525, 15262}, {1304, 16177}
X(46425) = barycentric quotient X(i)/X(j) for these (i, j): (25, 22239), (512, 11744), (2071, 99)
X(46425) = trilinear product X(i)*X(j) for these {i, j}: {656, 15262}, {661, 2071}, {822, 34170}
X(46425) = trilinear quotient X(i)/X(j) for these (i, j): (19, 22239), (661, 11744), (822, 40082), (2071, 662)
X(46425) = {X(647), X(6587)}-harmonic conjugate of X(16040)


X(46426) = ISOGONAL CONJUGATE OF X(5972)

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

See Antreas Hatzipolakis and César Lozada, euclid 3627.

X(46426) lies on these lines: {4, 39190}, {6, 38861}, {232, 15262}, {250, 20975}, {264, 2452}, {325, 5159}, {511, 2071}, {523, 11596}, {648, 34978}, {974, 2693}, {1316, 9307}, {1593, 35908}, {2407, 46087}, {2715, 46252}, {3091, 14356}, {5020, 5968}, {6530, 10151}, {11007, 22468}, {13479, 30716}, {19189, 37917}, {34233, 36176}

X(46426) = isogonal conjugate of X(5972)
X(46426) = antigonal conjugate of the isogonal conjugate of X(14673)
X(46426) = Cevapoint of X(i) and X(j) for these (i, j): {6, 20975}, {523, 34978}
X(46426) = crosssum of X(402) and X(31945)
X(46426) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 17882), (136, 46371)
X(46426) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 17468}, {6, 17882}
X(46426) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 17882), (31, 17468)
X(46426) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(10422)}} and {{A, B, C, X(3), X(10151)}}
X(46426) = trilinear pole of the line {2079, 3569}
X(46426) = 1st Saragossa point of X(250)
X(46426) = barycentric quotient X(i)/X(j) for these (i, j): (1, 17882), (31, 17468)
X(46426) = trilinear quotient X(i)/X(j) for these (i, j): (2, 17882), (6, 17468)


X(46427) = ISOGONAL CONJUGATE OF X(14643)

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

See Antreas Hatzipolakis and César Lozada, euclid 3627.

Let P and U be the intersections of the 1st and 2nd Droz-Farny circles. Then X(46427) is the cevapoint of P and U. (Randy Hutson, January 11, 2022)

X(46427) lies on these lines: {5, 14611}, {137, 18809}, {974, 46423}, {1154, 2071}, {11062, 15262}, {14865, 38937}

X(46427) = isogonal conjugate of X(14643)
X(46427) = crosssum of X(5) and X(33505)
X(46427) = trilinear pole of line X(2081)X(46425)
X(46427) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(5627)}} and {{A, B, C, X(4), X(2071)}}
X(46427) = barycentric quotient X(1989)/X(10688)
X(46427) = trilinear quotient X(2166)/X(10688)


X(46428) = ISOGONAL CONJUGATE OF X(38794)

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

See Antreas Hatzipolakis and César Lozada, euclid 3627.

X(46428) lies on these lines: {2071, 3581}, {13596, 38937}

X(46428) = isogonal conjugate of X(38794)
X(46428) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(2071)}} and {{A, B, C, X(6), X(186)}}


X(46429) = ISOGONAL CONJUGATE OF X(16111)

Barycentrics    a^2*(a^10+3*(b^2-c^2)*a^8-(11*b^4-6*b^2*c^2-2*c^4)*a^6+(5*b^6+2*c^6+(13*b^2-18*c^2)*b^2*c^2)*a^4+(b^2-c^2)*(6*b^6+3*c^6-(16*b^2+3*c^2)*b^2*c^2)*a^2-(b^2-c^2)^3*(4*b^4+6*b^2*c^2+c^4))*(a^10-3*(b^2-c^2)*a^8+(2*b^4+6*b^2*c^2-11*c^4)*a^6+(2*b^6+5*c^6-(18*b^2-13*c^2)*b^2*c^2)*a^4-(b^2-c^2)*(3*b^6+6*c^6-(3*b^2+16*c^2)*b^2*c^2)*a^2+(b^4+6*b^2*c^2+4*c^4)*(b^2-c^2)^3) : :

See Antreas Hatzipolakis and César Lozada, euclid 3627.

X(46429) lies on these lines: {24, 38937}, {2071, 14157}

X(46429) = isogonal conjugate of X(16111)
X(46429) = anticomplement of complementary conjugate of X(46686)
X(46429) = X(i)-vertex conjugate of-X(j) for these (i, j): {3, 10419}, {250, 46423}
X(46429) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(2071)}} and {{A, B, C, X(24), X(30)}}


X(46430) = X(4)X(974)∩X(125)X(389)

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^4-3*b^2*c^2+5*c^4)*a^8-2*(4*b^4-5*b^2*c^2+4*c^4)*b^2*c^2*a^6-(b^4-c^4)*(b^2-c^2)*(5*b^4-12*b^2*c^2+5*c^4)*a^4+2*(b^2-c^2)^2*(2*b^8+2*c^8-3*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^2-(b^6+c^6)*(b^2-c^2)^4) : :
X(46430) = X(3)+2*X(12236), X(4)+2*X(974), X(4)-4*X(11746), 2*X(4)+X(17854), 4*X(5)-X(12825), X(52)+2*X(6699), X(74)+2*X(1112), X(74)+5*X(3567), X(74)-4*X(16270), X(110)-4*X(9826), X(110)-7*X(15043), X(974)+2*X(11746), 4*X(974)-X(17854), 2*X(1112)-5*X(3567), X(1112)+2*X(16270), X(1511)-4*X(12006), X(1511)+2*X(13358), 5*X(3567)+4*X(16270), 8*X(11746)+X(17854), 2*X(12006)+X(13358)

See Antreas Hatzipolakis and César Lozada, euclid 3627.

X(46430) lies on these lines: {3, 12236}, {4, 974}, {5, 12825}, {6, 15463}, {24, 13198}, {51, 2777}, {52, 6699}, {54, 1511}, {74, 1112}, {110, 6642}, {113, 5462}, {125, 389}, {143, 12041}, {182, 22109}, {185, 7687}, {186, 44668}, {265, 14708}, {381, 5640}, {511, 38727}, {526, 42731}, {542, 16223}, {568, 15061}, {569, 12893}, {631, 41673}, {973, 10821}, {1154, 34128}, {1199, 3043}, {1503, 16227}, {1539, 10095}, {1899, 44795}, {2781, 14853}, {2854, 14912}, {2931, 36752}, {2935, 10982}, {3047, 20771}, {3060, 15055}, {3448, 7544}, {3518, 15647}, {5050, 14914}, {5446, 16111}, {5504, 17928}, {5562, 6723}, {5622, 39588}, {5876, 11704}, {5889, 12358}, {5892, 38793}, {5943, 36518}, {5972, 21649}, {6102, 7723}, {6241, 12133}, {6243, 38728}, {6746, 7730}, {6776, 32246}, {7401, 18932}, {7722, 15081}, {9729, 11800}, {9730, 12022}, {9781, 10721}, {9786, 19457}, {9934, 10594}, {10110, 13202}, {10111, 14516}, {10113, 13630}, {10574, 10733}, {10990, 11807}, {11245, 32423}, {11402, 32609}, {11412, 13416}, {11424, 13293}, {11432, 19504}, {11438, 32607}, {11557, 16003}, {11561, 13365}, {11562, 36253}, {11598, 14865}, {11709, 31760}, {12052, 46045}, {12140, 34224}, {12228, 36753}, {12244, 15151}, {12273, 15028}, {12281, 13148}, {12284, 15024}, {12295, 40647}, {13160, 46085}, {13201, 15057}, {13321, 15041}, {13366, 17701}, {13417, 20417}, {13474, 17856}, {13754, 23515}, {14049, 34564}, {14831, 45311}, {15063, 41671}, {15085, 15805}, {15118, 19161}, {16625, 38729}, {18560, 43904}, {20379, 38898}, {21663, 32411}, {23315, 45089}, {25487, 37472}, {31763, 32311}, {32111, 44084}, {32191, 40949}, {33547, 43817}, {37853, 45186}, {38723, 40280}

X(46430) = midpoint of X(i) and X(j) for these {i, j}: {568, 15061}, {3060, 15055}, {5890, 14644}
X(46430) = reflection of X(i) in X(j) for these (i, j): (12824, 16222), (14644, 12099), (16222, 5946), (36518, 5943), (38793, 5892)
X(46430) = crosssum of X(3) and X(14643)
X(46430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 974, 17854), (4, 17854, 46431), (74, 3567, 1112), (110, 15043, 9826), (125, 389, 1986), (125, 3574, 32743), (185, 7687, 12292), (265, 37481, 14708), (974, 11746, 4), (1112, 16270, 74), (3047, 44802, 20771), (5462, 11806, 113), (5889, 15059, 12358), (6102, 20304, 7723), (6642, 19456, 110), (7722, 15081, 15738), (9729, 11800, 16163), (10110, 17855, 13202), (10574, 10733, 44573), (12006, 13358, 1511), (15151, 16105, 12244)


X(46431) = X(4)X(974)∩X(25)X(74)

Barycentrics    a^2*((b^2+c^2)*a^12-2*(2*b^4-3*b^2*c^2+2*c^4)*a^10+(b^2+c^2)*(5*b^4-11*b^2*c^2+5*c^4)*a^8-2*(3*b^2-4*c^2)*(4*b^2-3*c^2)*b^2*c^2*a^6-(b^4-c^4)*(b^2-c^2)*(5*b^4-28*b^2*c^2+5*c^4)*a^4+2*(b^2-c^2)^2*(2*b^8+2*c^8+b^2*c^2*(b^4-15*b^2*c^2+c^4))*a^2-(b^4-c^4)*(b^2-c^2)^3*(b^4+7*b^2*c^2+c^4)) : :
X(46431) = 3*X(4)-2*X(974), 5*X(4)-4*X(11746), X(74)-3*X(11455), 5*X(974)-6*X(11746), 4*X(974)-3*X(17854), 3*X(1539)-2*X(11561), 4*X(1539)-3*X(12824), 3*X(1986)-4*X(11807), 3*X(3830)-2*X(12236), 2*X(6699)-3*X(16194), 2*X(7687)-3*X(32062), X(7731)-3*X(10721), X(7731)+3*X(12290), 3*X(11381)-X(21650), 3*X(11455)-2*X(12133), 8*X(11561)-9*X(12824), 8*X(11746)-5*X(17854), 2*X(11807)-3*X(13202), 2*X(12140)-3*X(16658), 3*X(12292)-2*X(21650)

See Antreas Hatzipolakis and César Lozada, euclid 3627.

X(46431) lies on these lines: {4, 974}, {25, 74}, {30, 12825}, {110, 12085}, {113, 858}, {125, 13474}, {146, 7391}, {186, 11598}, {265, 44276}, {378, 9934}, {382, 5663}, {389, 17856}, {541, 34603}, {1112, 6241}, {1495, 25564}, {1498, 15463}, {1511, 14157}, {1539, 11561}, {1986, 6000}, {2071, 20771}, {2777, 6240}, {2781, 9973}, {3028, 9629}, {3043, 12112}, {3520, 15647}, {3529, 41673}, {3830, 12236}, {5946, 18550}, {6699, 16194}, {7687, 32062}, {7722, 16105}, {7723, 18565}, {7728, 18569}, {9826, 15072}, {10540, 25487}, {10628, 13433}, {10706, 34609}, {10752, 34777}, {11439, 15055}, {11456, 15472}, {11559, 16835}, {12041, 32137}, {12244, 15738}, {12279, 44573}, {12315, 19504}, {12358, 15305}, {12900, 14855}, {13198, 35502}, {13293, 26883}, {13416, 15058}, {13491, 16222}, {14641, 38793}, {15030, 37853}, {15081, 15151}, {16659, 17702}, {17812, 19457}, {18781, 19223}, {38727, 44870}

X(46431) = midpoint of X(10721) and X(12290)
X(46431) = reflection of X(i) in X(j) for these (i, j): (74, 12133), (125, 13474), (1986, 13202), (3529, 41673), (6241, 1112), (7722, 16105), (12041, 32137), (12244, 15738), (12279, 44573), (12292, 11381), (17854, 4), (17856, 389)
X(46431) = crosssum of X(3) and X(20127)
X(46431) = {X(74), X(11455)}-harmonic conjugate of X(12133)
X(46431) = {X(4), X(17854)}-harmonic conjugate of X(46430)


X(46432) = X(3)X(6)∩X(115)X(393)

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

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 3630.

X(46432) lies on these lines: {3,6}, {53,44226}, {115,393}, {232,34481}, {419,9307}, {608,14936}, {1033,14581}, {1196,45141}, {1249,3767}, {1843,33578}, {1974,20975}, {1990,44960}, {2197,14827}, {2207,31942}, {3087,7747}, {3186,11596}, {3269,14642}, {5475,44920}, {7735,38282} ,{7737,40065}, {7748,42459}, {7755,40138}, {8541,40981}, {9722,18362}, {15525,23976}, {19118,42671}, {20232,42295}, {23583,41770}, {26958,40995}, {30457,35508}, {33581,44079}, {36212,40318}, {37689,45245}


X(46433) = ISOGONAL CONJUGATE OF X(32555)

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

X(46433) lies on the cubics K332 and K414 and on these lines: {40, 30556}, {196, 13390}, {223, 13389}, {282, 2262}, {329, 31548}, {946, 7090}, {1703, 7348}, {2956, 6212}, {6213, 15892}, {14256, 31540}, {34495, 42872}

X(46433) = isogonal conjugate of X(32555)
X(46433) = X(34908)-Ceva conjugate of X(1)
X(46433) = X(2362)-cross conjugate of X(1)
X(46433) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32555}, {6, 46422}, {6502, 34909}
X(46433) = barycentric product X(1659)*X(34908)
X(46433) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 46422}, {6, 32555}, {7133, 34909}
X(46433) = {X(40),X(38004)}-harmonic conjugate of X(32555)


X(46434) = ISOGONAL CONJUGATE OF X(32556)

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

X(46434) lies on the cubics K332 and K414 and on these lines: {40, 30557}, {196, 1659}, {223, 13388}, {282, 2262}, {329, 31547}, {946, 14121}, {1702, 7347}, {2956, 6213}, {6212, 15891}, {14256, 31541}, {34494, 42872}

X(46434) = isogonal conjugate of X(32556)
X(46434) = X(34907)-Ceva conjugate of X(1)
X(46434) = X(16232)-cross conjugate of X(1)
X(46434) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32556}, {6, 46421}, {2067, 34910}
X(46434) = barycentric product X(13390)*X(34907)
X(46434) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 46421}, {6, 32556}, {42013, 34910}


X(46435) = ISOGONAL CONJUGATE OF X(2077)

Barycentrics    (a^5 - a^3*b^2 - a^2*b^3 + b^5 - a^4*c + 3*a^3*b*c + 3*a*b^3*c - b^4*c - 2*a^3*c^2 - a^2*b*c^2 - a*b^2*c^2 - 2*b^3*c^2 + 2*a^2*c^3 - 3*a*b*c^3 + 2*b^2*c^3 + a*c^4 + b*c^4 - c^5)*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 + 3*a^3*b*c - a^2*b^2*c - 3*a*b^3*c + b^4*c - a^3*c^2 - a*b^2*c^2 + 2*b^3*c^2 - a^2*c^3 + 3*a*b*c^3 - 2*b^2*c^3 - b*c^4 + c^5) : :
X(46435) = 3 X[5658] - X[13199], 3 X[5660] - 2 X[12332], 4 X[6702] - 3 X[14647], 4 X[6705] - 5 X[31272], X[7992] - 3 X[37718], 2 X[12114] - 3 X[16173]

X(46435) lies on the Feuerbach circumhyperbola, the cubic K1254, and on these lines: {1, 1537}, {4, 12736}, {7, 15528}, {8, 153}, {9, 119}, {11, 84}, {21, 10165}, {30, 6596}, {80, 6001}, {90, 1768}, {100, 6260}, {104, 1519}, {149, 6223}, {515, 1320}, {516, 25438}, {517, 12641}, {528, 42470}, {908, 2077}, {943, 12775}, {946, 1476}, {952, 3680}, {971, 3254}, {1000, 12115}, {1156, 10265}, {1317, 12678}, {1389, 10728}, {1490, 5840}, {1699, 7284}, {1709, 8068}, {1836, 3577}, {1877, 36121}, {2771, 6598}, {2801, 6601}, {2802, 12667}, {2827, 43728}, {3035, 10270}, {3065, 11219}, {3255, 10202}, {3296, 10531}, {3667, 46041}, {3738, 43737}, {5424, 16154}, {5533, 10085}, {5559, 12749}, {5658, 13199}, {5660, 12332}, {5787, 22938}, {6003, 14224}, {6245, 10308}, {6246, 7319}, {6261, 12119}, {6700, 21635}, {6702, 14647}, {6705, 31272}, {7160, 10956}, {7285, 13226}, {7992, 36599}, {10073, 15071}, {10269, 12611}, {10596, 18490}, {10742, 22792}, {11609, 29057}, {12019, 33576}, {12114, 16173}, {12247, 43734}, {12619, 45631}, {12680, 13274}, {12687, 37726}, {12688, 13273}, {12750, 41690}, {12764, 18838}, {15017, 16209}, {15446, 22775}, {16127, 43740}, {18391, 38307}, {24703, 38759}, {37826, 43166}

X(46435) = midpoint of X(149) and X(6223)
X(46435) = reflection of X(i) in X(j) for these {i,j}: {80, 12761}, {84, 11}, {100, 6260}, {2950, 119}, {5787, 22938}, {10742, 22792}, {12119, 6261}, {12665, 34293}, {12751, 6256}
X(46435) = isogonal conjugate of X(2077)
X(46435) = antigonal image of X(84)
X(46435) = symgonal image of X(6260)
X(46435) = X(i)-cross conjugate of X(j) for these (i,j): {909, 2006}, {12764, 80}, {18838, 1}
X(46435) = cevapoint of X(513) and X(35015)
X(46435) = trilinear pole of line {650, 1108}
X(46435) = Feuerbach-hyperbola-antipode of X(84)
X(46435) = inner-Garcia-to-ABC similarity image of X(12666)
X(46435) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2077}, {3, 15500}, {12665, 36052}
X(46435) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 2077}, {19, 15500}, {8609, 12665}
X(46435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {153, 39776, 12751}, {12676, 12679, 84}


X(46436) = X(2)X(477)∩X(4)X(841)

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

See Antreas Hatzipolakis and Peter Moses, euclid 3642.

X(46436) lies on the nine-point circle and these lines: {2, 477}, {4, 841}, {113, 858}, {115, 3154}, {125, 8675}, {127, 37985}, {128, 30745}, {131, 5159}, {133, 468}, {427, 18809}, {1368, 42424}, {1560, 1990}, {1650, 38971}, {3134, 5099}, {4549, 16167}, {5094, 14685}, {5512, 36189}, {14672, 37987}, {14995, 31655}, {16188, 30739}, {25642, 37167}

X(46436) = midpoint of X(4) and X(841)
X(46436) = complement of X(9060)
X(46436) = orthoptic-circle-of-Steiner-inellipse-inverse of X(477)
X(46436) = complement of the isogonal conjugate of X(9003)
X(46436) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 9003}, {656, 10297}, {661, 44569}, {9003, 10}, {10295, 8062}, {40112, 4369} X(46436) = X(4)-Ceva conjugate of X(9003)


X(46437) = X(133)X(186)∩X(137)X(3154)

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

See Antreas Hatzipolakis and Peter Moses, euclid 3642.

X(46437) lies on the nine-point circle and these lines: {2, 16166}, {113, 37938}, {114, 30745}, {133, 186}, {137, 3154}, {140, 25641}, {858, 44953}, {1594, 18809}, {20625, 37985}, {36189, 45161}, {37452, 42424}

X(46437) = complement of X(16166)
X(46437) = X(i)-complementary conjugate of X(j) for these (i,j): {656, 18403}, {13619, 8062}, {18365, 14838}


X(46438) = X(114)X(7426)∩X(115)X(6070)

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

See Antreas Hatzipolakis and Peter Moses, euclid 3642.

X(46438) lies on the nine-point circle and these lines: {113, 41586}, {114, 7426}, {115, 6070}, {126, 34827}, {131, 18323}, {3845, 25641}, {5169, 16188}, {10254, 42424}, {10301, 42426}, {13413, 45180}, {14120, 34113}

X(46438) = X(i)-complementary conjugate of X(j) for these (i,j): {661, 40112}, {44555, 4369}


X(46439) = X(23)X(114)∩X(30)X(128)

Barycentrics    (b - c)^2*(b + c)^2*(-a^6 + 3*a^4*b^2 - 3*a^2*b^4 + b^6 + 3*a^4*c^2 + a^2*b^2*c^2 - b^4*c^2 - 3*a^2*c^4 - b^2*c^4 + c^6)*(-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(46439) = 3 X[381] - X[14980], X[1157] - 3 X[37943], 3 X[5642] - 2 X[43969], 3 X[16532] - X[35729]

See Antreas Hatzipolakis and Peter Moses, euclid 3642.

X(46439) lies on the nine-point circle and these lines: {2, 1291}, {4, 14979}, {5, 45180}, {23, 114}, {30, 128}, {113, 1154}, {115, 12077}, {125, 1510}, {131, 18403}, {137, 523}, {381, 14980}, {403, 10214}, {428, 42426}, {546, 25641}, {858, 31843}, {1157, 37943}, {1209, 33333}, {2070, 19552}, {5133, 16188}, {5642, 43969}, {6070, 8902}, {6150, 44234}, {10024, 42424}, {10096, 10227}, {14140, 43893}, {14857, 43958}, {15169, 19939}, {16532, 35729}, {20392, 34836}, {30436, 31841}, {30446, 42422}, {31655, 37454}, {33545, 36161}

X(46439) = midpoint of X(i) and X(j) for these {i,j}: {4, 14979}, {2070, 19552}, {14140, 43893}, {14857, 43958}
X(46439) = reflection of X(i) in X(j) for these {i,j}: {6150, 44234}, {16337, 403}, {45180, 5}
X(46439) = complement of X(1291)
X(46439) = reflection of X(137) in the Euler line
X(46439) -= complement of the isogonal conjugate of X(45147)
X(46439) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 45147}, {661, 323}, {1749, 523}, {2616, 46114}, {2618, 16336}, {6140, 37}, {10413, 8287}, {11063, 14838}, {37779, 4369}, {37943, 8062}, {45147, 10}
X(46439) = X(4)-Ceva conjugate of X(45147)
X(46439) = X(1141)-of-(reflection of Euler triangle in Euler line)
X(46439) = barycentric product X(24978)*X(45147)
X(46439) = barycentric quotient X(10413)/X(33565)


X(46440) = CENTER OF THE HATZIPOLAKIS - SUPPA ELLIPSE

Barycentrics    a^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+a^4 b^4 c^2+2 a^2 b^6 c^2+2 a^6 c^4+a^4 b^2 c^4-3 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) : :
Barycentrics    (SB+SC) (S^2 (17 R^2-2 SW)-SA (3 R^2 SA+16 R^2 SW-6 SA SW)) : :

Let P be a point on the Euler line and A'B'C' the cevian triangle of P. Let Ra be the radical axis of the circumcircles of the triangles PBC' and PCB'. Define Rb, Rc cyclically. The reflections of Ra, Rb, Rc in BC, CA, AB, resp. concur at a point on an ellipse passing through X(i) for these i: {4, 5, 6, 399, 11061, 11441, 14627}. This ellipse is named here Hatzipolakis-Suppa ellipse. Its perspector is X(323) and its center X(46440)

See Antreas Hatzipolakis and Ercole Suppa, euclid 3644.

X(46440) lies on these lines: {23,110}, {146,12605}, {399,546}, {428,9143}, {1994,5480}, {2914,5609}, {3448,5133}, {5663,13353}, {5898,14449}, {7527,15102}, {7550,15101}, {10192,17847}, {11819,12383}, {12022,43605}, {12308,15032}, {15018,45303}, {25329,37784}

X(46440) = midpoint of X(399) and X(14627)


X(46441) = X(1)X(21)∩X(60)X(65)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 3644.

X(46441) lies on the Hatzipolakis-Suppa ellipse and these lines: {1,21}, {4,1029}, {6,2476}, {10,37783}, {46,37294}, {60,65}, {110,942}, {229,5902}, {399,6841}, {411,5396}, {484,15792}, {501,3336}, {757,1442}, {940,24936}, {1210,3615}, {1393,23692}, {1411,17097}, {1812,14005}, {1963,27577}, {3017,17577}, {4278,14799}, {5425,37816}, {5707,6828}, {5814,40571}, {5903,9275}, {6175,41501}, {6842,14627}, {6852,45931}, {6853,37509}, {6856,24898}, {6857,14996}, {7424,37730}, {7548,45926}, {8614,18625}, {12047,24624}, {13746,18391}, {14009,33142}, {22136,37635}, {24880,32911}, {24902,37680}, {36279,37405}, {37369,39542}, {37418,37584}

X(46441) = X(661)-he conjugate of X(2640)
X(46441) = X(i)-isoconjugate of X(j) for these (i,j): (65,15910), (523,39630)
X(46441) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {163,39630}, {284,15910}
X(46441) = barycentric product X(333)*X(15932)
X(46441) = barycentric quotient X(i)/X(j) for these {i,j}: {163,39630}, {284,15910}
X(46441) = trilinear product X(21)*X(15932)
X(46441) = trilinear quotient X(i)/X(j) for these (i,j): (21,15910), (110,39630)
X(46441) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (46,40214,37294), (60,65,1325), (5902,17104,229)


X(46442) = X(4)X(193)∩X(22)X(69)

Barycentrics    2 a^8-a^6 b^2-a^4 b^4+a^2 b^6-b^8-a^6 c^2+a^2 b^4 c^2-a^4 c^4+a^2 b^2 c^4+2 b^4 c^4+a^2 c^6-c^8 : :
Barycentrics    S^2 (SW-2 R^2) (2 SA-SW)+SB SC SW^2 : :
X(46442) = 3*X(2)-4*X(13562), 4*X(6)-3*X(45968), 3*X(5093)-2*X(32358)

See Antreas Hatzipolakis and Ercole Suppa, euclid 3644.

X(46442) lies on the Hatzipolakis-Suppa ellipse and these lines: {2,13562}, {4,193}, {6,5133}, {22,69}, {66,858}, {67,110}, {343,19121}, {399,15760}, {511,14516}, {524,9973}, {542,6467}, {648,41375}, {1352,11441}, {1353,7403}, {1370,20079}, {1503,12111}, {1594,19139}, {1899,26206}, {1974,3580}, {3164,9863}, {3547,31831}, {3589,19122}, {3620,7494}, {3630,12367}, {3933,5938}, {5093,32358}, {6403,12134}, {6776,7503}, {7387,11898}, {7404,14912}, {7500,20080}, {7553,34380}, {7566,14853}, {8681,40316}, {9306,26156}, {9818,39899}, {9967,34224}, {11160,34608}, {11416,15583}, {11440,44882}, {11443,32455}, {12168,12317}, {12278,29181}, {12359,19128}, {12412,45170}, {12827,41593}, {14003,23163}, {15066,15812}, {15069,19149}, {16386,34778}, {19126,37636}, {19132,37638}, {19155,34826}, {21243,21637}, {22151,23300}, {28708,30744}, {33878,44831}, {37491,45794}, {37900,40317}, {40867,41237}, {45016,45178}

X(46442) = reflection of X(i) in X(j) for these (i,j): (6403,12134), (12225,41716), (26926,13562), (34224,9967)
X(46442) = anticomplement of X(26926)
X(46442) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (66,20806,858), (69,5596,22), (141,1176,7495), (343,34774,19121), (13562,26926,2), (19122,23293,3589)


X(46443) = X(6)X(70)∩X(68)X(403)

Barycentrics    (a^2+b^2-c^2) (a^2-b^2+c^2) (2 a^12-9 a^10 b^2+17 a^8 b^4-18 a^6 b^6+12 a^4 b^8-5 a^2 b^10+b^12-9 a^10 c^2+20 a^8 b^2 c^2-12 a^6 b^4 c^2-2 a^4 b^6 c^2+5 a^2 b^8 c^2-2 b^10 c^2+17 a^8 c^4-12 a^6 b^2 c^4+4 a^4 b^4 c^4-b^8 c^4-18 a^6 c^6-2 a^4 b^2 c^6+4 b^6 c^6+12 a^4 c^8+5 a^2 b^2 c^8-b^4 c^8-5 a^2 c^10-2 b^2 c^10+c^12) : :
Barycentrics    SB SC (4 R^4-2 R^2 SA+2 SA^2-4 R^2 SW-SA SW+SW^2) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3644.

X(46443) lies on the Hatzipolakis-Suppa ellipse and these lines: {4,13292}, {6,70}, {24,6193}, {25,32358}, {52,1986}, {68,403}, {235,399}, {343,10018}, {378,18909}, {427,14627}, {569,37118}, {1593,43588}, {1595,32165}, {1614,41729}, {3518,18947}, {3541,11245}, {3542,3564}, {6146,6241}, {6225,35490}, {6247,15472}, {6776,34207}, {10295,17834}, {12235,14516}, {13371,19504}, {14111,27376}, {18356,37981}, {22750,32234}

X(46443) = {X(68),X(35603)}-harmonic conjugate of X(403)


X(46444) = X(6)X(666)∩X(25)X(193)

Barycentrics    (a^2+b^2-c^2) (a^2-b^2+c^2) (4 a^4-3 a^2 b^2+b^4-3 a^2 c^2+2 b^2 c^2+c^4) : :
Barycentrics    SB SC (4 SA^2-3 SA SW+SW^2) : :
X(46444) = X(35219)-3*X(41719), 3*X(35264)-X(40317)

See Antreas Hatzipolakis and Ercole Suppa, euclid 3644.

X(46444) lies on the Hatzipolakis-Suppa ellipse and these lines: {4,1353}, {6,66}, {24,34380}, {25,193}, {69,468}, {110,40316}, {141,44102}, {235,3564}, {399,1596}, {428,1992}, {460,9308}, {524,1974}, {1112,1843}, {1351,3575}, {1503,11470}, {1570,27376}, {1593,14912}, {1595,14627}, {1885,6225}, {1906,39871}, {1907,39588}, {1994,15809}, {3542,11898}, {3589,15471}, {3620,37453}, {3751,12135}, {3867,8584}, {3933,44162}, {5032,5064}, {5052,12143}, {5186,5477}, {5596,10602}, {5921,37197}, {6353,20080}, {6467,34774}, {7399,35603}, {7716,15534}, {8541,32455}, {8550,12294}, {10151,18440}, {10733,12596}, {11363,34379}, {11443,39884}, {12007,19124}, {13562,41614}, {14853,23047}, {14913,44084}, {15069,45004}, {15583,21639}, {18438,44239}, {18533,44456}, {18919,20079}, {19121,34397}, {19459,35219}, {19504,25321}, {21213,37491}, {26206,30739}, {33878,37931}, {35264,40317}, {39874,44438}, {41585,44091}

X(46444) = reflection of X(41584) in X(1974)
X(46444) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (69,19118,468), (1843,5095,3629)


X(46445) = X(110)X(1209)∩X(399)X(3153)

Barycentrics    3 a^16-12 a^14 b^2+16 a^12 b^4-4 a^10 b^6-10 a^8 b^8+12 a^6 b^10-8 a^4 b^12+4 a^2 b^14-b^16-12 a^14 c^2+22 a^12 b^2 c^2-16 a^8 b^6 c^2+4 a^6 b^8 c^2+6 a^4 b^10 c^2-8 a^2 b^12 c^2+4 b^14 c^2+16 a^12 c^4-13 a^8 b^4 c^4+4 a^6 b^6 c^4-3 a^4 b^8 c^4-4 b^12 c^4-4 a^10 c^6-16 a^8 b^2 c^6+4 a^6 b^4 c^6+10 a^4 b^6 c^6+4 a^2 b^8 c^6-4 b^10 c^6-10 a^8 c^8+4 a^6 b^2 c^8-3 a^4 b^4 c^8+4 a^2 b^6 c^8+10 b^8 c^8+12 a^6 c^10+6 a^4 b^2 c^10-4 b^6 c^10-8 a^4 c^12-8 a^2 b^2 c^12-4 b^4 c^12+4 a^2 c^14+4 b^2 c^14-c^16 : :
Barycentrics    S^2 (-3 R^4+10 R^2 SA-2 R^2 SW-4 SA SW)-SA (3 R^2-2 SW)^2 (SA-SW) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3655.

X(46445) lies on the Hatzipolakis - Suppa ellipse and these lines: {5,14683}, {110,1209}, {399,3153}, {511,7731}, {2070,5898}, {3448,13353}, {3518,18947}, {5900,15246}, {6152,23236}, {9143,34397}, {10114,24981}, {12168,12317}, {14627,32423}

X(46445) = reflection of X(i) in X(j) for these (i,j): (4,46440), (3448,13353)


X(46446) = X(110)X(34483)∩X(399)X(43893)

Barycentrics    4 a^16-19 a^14 b^2+33 a^12 b^4-19 a^10 b^6-15 a^8 b^8+31 a^6 b^10-21 a^4 b^12+7 a^2 b^14-b^16-19 a^14 c^2+38 a^12 b^2 c^2-3 a^10 b^4 c^2-28 a^8 b^6 c^2+3 a^6 b^8 c^2+18 a^4 b^10 c^2-13 a^2 b^12 c^2+4 b^14 c^2+33 a^12 c^4-3 a^10 b^2 c^4-6 a^8 b^4 c^4-a^6 b^6 c^4-16 a^4 b^8 c^4-3 a^2 b^10 c^4-4 b^12 c^4-19 a^10 c^6-28 a^8 b^2 c^6-a^6 b^4 c^6+38 a^4 b^6 c^6+9 a^2 b^8 c^6-4 b^10 c^6-15 a^8 c^8+3 a^6 b^2 c^8-16 a^4 b^4 c^8+9 a^2 b^6 c^8+10 b^8 c^8+31 a^6 c^10+18 a^4 b^2 c^10-3 a^2 b^4 c^10-4 b^6 c^10-21 a^4 c^12-13 a^2 b^2 c^12-4 b^4 c^12+7 a^2 c^14+4 b^2 c^14-c^16 : :
Barycentrics    S^2 (3 R^2+8 SA-6 SW) (5 R^2-2 SW)-SB SC (3 R^2+2 SW)^2 : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3655.

X(46446) lies on the Hatzipolakis - Suppa ellipse and these lines: {110,34483}, {140,5900}, {399,43893}

X(46446) = reflection of X(5) in X(46440)


X(46447) = X(110)X(34437)∩X(399)X(511)

Barycentrics    a^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^2-12 a^8 b^2 c^2+4 a^6 b^4 c^2+8 a^4 b^6 c^2-2 a^2 b^8 c^2+4 b^10 c^2-a^8 c^4+4 a^6 b^2 c^4+7 a^4 b^4 c^4-6 a^2 b^6 c^4-b^8 c^4+4 a^6 c^6+8 a^4 b^2 c^6-6 a^2 b^4 c^6-8 b^6 c^6-a^4 c^8-2 a^2 b^2 c^8-b^4 c^8-2 a^2 c^10+4 b^2 c^10+c^12) : :
Barycentrics    (SB+SC) (-SA SW (3 R^2 SA+16 R^2 SW-6 SA SW)+S^2 (9 R^4-3 R^2 SW+2 SW^2)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3655.

X(46447) lies on the Hatzipolakis - Suppa ellipse and these lines: {5,25335}, {110,34437}, {399,511}, {542,14627}, {599,11441}, {13353,16010}

X(46447) = reflection of X(i) in X(j) for these (i,j): (6,46440), (16010,13353)


X(46448) = X(110)X(18125)∩X(399)X(18358)

Barycentrics    a^8-b^8+a^4 b^2 c^2+3 a^2 b^4 c^2+3 a^2 b^2 c^4+2 b^4 c^4-c^8 : :
Barycentrics    S^2 SA (R^2-SW)-SB SC SW^2 : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3655.

X(46448) lies on the Hatzipolakis - Suppa ellipse and these lines: {4,69}, {6,3410}, {66,3619}, {110,18125}, {141,2916}, {399,18358}, {1503,37126}, {1614,24206}, {2888,5480}, {3448,3589}, {3564,14627}, {3618,11442}, {3620,20062}, {3763,6800}, {5189,15321}, {6776,13353}, {7514,18440}, {10516,11441}, {11646,23642}, {13562,22151}, {14826,28408}, {19140,33565}, {20021,40425}, {20079,34118}, {32255,32366}, {37334,45799}, {38317,43808}

X(46448) = reflection of X(i) in X(j) for these (i,j): (11061,46440), (6776,13353)


X(46449) = X(5663)X(14627)∩X(7731)X(18859)

Barycentrics    a^2 (a^20-6 a^18 b^2+13 a^16 b^4-8 a^14 b^6-14 a^12 b^8+28 a^10 b^10-14 a^8 b^12-8 a^6 b^14+13 a^4 b^16-6 a^2 b^18+b^20-6 a^18 c^2+30 a^16 b^2 c^2-60 a^14 b^4 c^2+60 a^12 b^6 c^2-24 a^10 b^8 c^2-24 a^8 b^10 c^2+60 a^6 b^12 c^2-60 a^4 b^14 c^2+30 a^2 b^16 c^2-6 b^18 c^2+13 a^16 c^4-60 a^14 b^2 c^4+101 a^12 b^4 c^4-66 a^10 b^6 c^4+12 a^8 b^8 c^4-36 a^6 b^10 c^4+77 a^4 b^12 c^4-54 a^2 b^14 c^4+13 b^16 c^4-8 a^14 c^6+60 a^12 b^2 c^6-66 a^10 b^4 c^6+50 a^8 b^6 c^6-4 a^6 b^8 c^6-66 a^4 b^10 c^6+42 a^2 b^12 c^6-8 b^14 c^6-14 a^12 c^8-24 a^10 b^2 c^8+12 a^8 b^4 c^8-4 a^6 b^6 c^8+72 a^4 b^8 c^8-12 a^2 b^10 c^8-14 b^12 c^8+28 a^10 c^10-24 a^8 b^2 c^10-36 a^6 b^4 c^10-66 a^4 b^6 c^10-12 a^2 b^8 c^10+28 b^10 c^10-14 a^8 c^12+60 a^6 b^2 c^12+77 a^4 b^4 c^12+42 a^2 b^6 c^12-14 b^8 c^12-8 a^6 c^14-60 a^4 b^2 c^14-54 a^2 b^4 c^14-8 b^6 c^14+13 a^4 c^16+30 a^2 b^2 c^16+13 b^4 c^16-6 a^2 c^18-6 b^2 c^18+c^20) : :
Barycentrics    (SB+SC) (-3 R^2 SA (24 R^4+R^2 SA-2 SA SW)+S^2 (179 R^4-74 R^2 SW+8 SW^2)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3655.

X(46449) lies on the Hatzipolakis - Suppa ellipse and these lines: {5663,14627}, {7731,18859}, {43704,44056}

X(46449) = reflection of X(11441) in X(46440)


X(46450) = EULER LINE INTERCEPT OF X(52)X(43808)

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^2-3 a^6 b^2 c^2+2 a^4 b^4 c^2-a^2 b^6 c^2+3 b^8 c^2-2 a^6 c^4+2 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 : :
Barycentrics    2 R^2 S^2+SB SC (3 R^2-2 SW) : :
X(46450) = 3*X(2)-4*X(37938),9*X(2)-8*X(44234),4*X(3)-3*X(35489),2*X(3)-3*X(44450),X(4)+2*X(5189),X(4)-4*X(7574),7*X(4)-4*X(18325),3*X(4)-4*X(18403),5*X(4)-8*X(18572),5*X(4)-4*X(31726),9*X(4)-8*X(44283),4*X(5)-X(20063),4*X(23)-7*X(3090),2*X(23)-3*X(37943),4*X(140)-3*X(37922),4*X(186)-5*X(631),3*X(186)-4*X(10257),3*X(376)-4*X(2071),X(376)-4*X(10989),3*X(376)-2*X(13619),9*X(376)-8*X(44246),3*X(381)-X(37949),3*X(381)-2*X(43893),8*X(403)-9*X(3545),4*X(468)-3*X(37939),5*X(631)-8*X(858),3*X(858)-2*X(10257),5*X(1656)-4*X(10096),5*X(1656)-3*X(37956),3*X(2070)-4*X(44234),X(2071)-3*X(10989),3*X(2071)-2*X(44246),8*X(2072)-7*X(3090),4*X(2072)-3*X(37943),3*X(3060)-4*X(11692),7*X(3090)-6*X(37943),5*X(3091)-4*X(11563),5*X(3091)-2*X(37924),X(3146)+2*X(35001),7*X(3153)-2*X(18325),3*X(3153)-2*X(18403),5*X(3153)-4*X(18572),5*X(3153)-2*X(31726),9*X(3153)-4*X(44283),7*X(3523)-6*X(37955),9*X(3524)-8*X(15646),7*X(3526)-6*X(16532),7*X(3528)-8*X(34152),X(3529)-4*X(7464),9*X(3545)-4*X(37925),8*X(3628)-5*X(37923),5*X(3843)-4*X(11558),5*X(5071)-2*X(37901),8*X(5159)-5*X(37953),X(5189)+2*X(7574),7*X(5189)+2*X(18325),3*X(5189)+2*X(18403),5*X(5189)+4*X(18572),5*X(5189)+2*X(31726),9*X(5189)+4*X(44283),4*X(6676)-3*X(37932),3*X(7426)-4*X(44911),7*X(7574)-X(18325),3*X(7574)-X(18403),5*X(7574)-2*X(18572),5*X(7574)-X(31726),9*X(7574)-2*X(44283),7*X(9781)-8*X(13376),4*X(10096)-3*X(37956),2*X(10295)-3*X(37948),4*X(10296)-X(33703),4*X(10297)-X(37946),4*X(10540)-5*X(20125),6*X(10989)-X(13619),9*X(10989)-2*X(44246),3*X(13619)-4*X(44246),5*X(15081)-2*X(15107),4*X(15122)-3*X(37941),9*X(15709)-8*X(44214),9*X(15710)-8*X(44280),8*X(16531)-7*X(37957),5*X(17538)-8*X(37950),3*X(18325)-7*X(18403),5*X(18325)-7*X(31726),5*X(18403)-6*X(18572),5*X(18403)-3*X(31726),3*X(18403)-2*X(44283),9*X(18572)-5*X(44283),5*X(30745)-3*X(37940),5*X(30745)-4*X(44452),9*X(31726)-10*X(44283),3*X(32609)-4*X(46114),X(33703)+4*X(37944),5*X(37760)-4*X(37936),3*X(37901)-4*X(37947),3*X(37909)-4*X(44282),3*X(37938)-2*X(44234),3*X(37940)-4*X(44452)

As a point on the Euler line, X(46450) has Shinagawa coefficients (2e,-5e-8f).

See Antreas Hatzipolakis and Ercole Suppa, Euclid 3656 .

X(46450) lies on these lines: {2,3}, {52,43808}, {54,44829}, {69,11649}, {110,44407}, {143,43816}, {265,5900}, {511,25739}, {523,15099}, {539,23061}, {543,15070}, {758,15095}, {1058,10149}, {1154,3448}, {1157,14651}, {1272,1273}, {1568,14157}, {2888,6101}, {2979,18474}, {3060,11692}, {3289,15340}, {3410,23039}, {3818,44834}, {3917,41171}, {6000,13203}, {6288,10627}, {7706,20791}, {8718,43831}, {9306,43579}, {9781,13376}, {10116,15801}, {10264,32608}, {10540,20125}, {11412,12325}, {11433,32411}, {11459,11550}, {11572,15644}, {11750,12254}, {12038,41482}, {12244,13445}, {12289,13346}, {12290,22555}, {12317,12319}, {12383,18400}, {13419,43598}, {13470,37472}, {13630,15800}, {13851,18933}, {14627,43838}, {14644,29317}, {14864,43895}, {15077,17711}, {15081,15107}, {16266,34799}, {20424,43845}, {23293,37478}, {25563,32365}, {30522,37477}, {32609,46114}

X(46450) = midpoint of X(i) and X(j) for these {i,j}: {3153,5189}, {10296,37944}
X(46450) = reflection of X(i) in X(j) for these (i,j): (4,3153), (20,18859), (23,2072), (186,858), (2070,37938), (3153,7574), (5899,5), (12244,13445), (12383,43574), (13619,2071), (14157,1568), (20063,5899), (31726,18572), (32608,10264), (35489,44450), (37899,37942), (37900,37971), (37910,44912), (37924,11563), (37925,403), (37945,11799), (37949,43893), (37967,46031)
X(46450) = reflection of X(1325) in X(523)
X(46450) = anticomplement of X(2070)
X(46450) = anticomplementary conjugate of the anticomplement of X(33565)
X(46450) = circumperp conjugate of X(14118)
X(46450) = anticomplementary-circle-inverse of X(3)
X(46450) = de-Longchamps-circle-inverse of X(7488)
X(46450) = polar-circle-inverse of X(6756)
X(46450) = X(i)-vertex conjugate of X(j) for these (i,j): (523,7512), (7512,523)
X(46450) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,20,7502), (2,31723,4), (2,44831,7556), (3,382,45971), (3,31181,31074), (3,39504,2), (4,1370,376), (4,3524,18420), (4,3525,7544), (4,5067,7528), (4,5071,7394), (4,6643,3090), (4,6816,3855), (4,11001,44440), (4,18537,41099), (4,34938,33703), (20,3146,18565), (20,18569,4), (20,35473,376), (20,44441,35473), (22,7577,7552), (23,2072,37943), (186,45181,37943), (376,3090,7494), (376,8889,631), (381,7485,14789), (381,37949,43893), (550,31724,34007), (1113,1114,7512), (1312,1313,14788), (1656,37956,10096), (2070,18403,11818), (2070,37938,2), (2071,13619,376), (2072,37943,3090), (3146,18404,4), (3548,31304,44879), (5189,7574,4), (5189,10296,34938), (5189,10989,1370), (7391,18531,4), (7391,37444,18531), (7488,13371,6143), (7565,15246,37347), (7574,35001,18404), (10750,10751,546), (11750,34148,12254), (11819,37452,44802), (12225,23335,3520), (12362,15559,35500), (14784,14785,2937), (14790,18531,7391), (14790,37444,4), (14791,31723,2), (14807,14808,3), (14864,45187,43895), (16063,18420,3524), (21312,34725,35480), (23039,34514,3410), (30745,37940,44452), (31724,34007,4), (35732,42282,17714)


X(46451) = EULER LINE INTERCEPT OF X(146)X(32223)

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^6 b^2 c^2+9 a^2 b^6 c^2-3 b^8 c^2+2 a^6 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 : :
Barycentrics    6 R^2 SB SC+S^2 (7 R^2-2 SW) : :
X(46451) = X(2)+8*X(44266),5*X(2)-8*X(44282),X(3)-4*X(10096),X(3)+2*X(43893),X(4)+2*X(2070),X(4)-4*X(11563),X(4)+8*X(25338),2*X(5)+X(5899),8*X(5)+X(20063),X(20)-4*X(186),X(20)+8*X(11799),X(20)-10*X(37760),5*X(20)-8*X(44246),X(23)+2*X(403),4*X(23)+5*X(3091),2*X(23)+X(3153),5*X(23)+4*X(10297),X(23)-4*X(37971),4*X(140)-X(35452),X(146)+8*X(32223),X(186)+2*X(11799),2*X(186)-5*X(37760),5*X(186)-2*X(44246),X(382)-4*X(11558),X(382)+8*X(44264),8*X(403)-5*X(3091),4*X(403)-X(3153),5*X(403)-2*X(10297),X(403)+2*X(37971),4*X(468)-X(2071),5*X(468)-2*X(16976),4*X(546)+5*X(37923),5*X(631)-2*X(18859),5*X(631)-8*X(44234),X(858)-4*X(37942),2*X(858)+X(37945),2*X(1533)+X(13445),X(1533)+2*X(44673),2*X(1568)+X(15107),5*X(1656)+X(37949),X(2070)+2*X(11563),X(2070)-4*X(25338),4*X(2071)-7*X(3523),5*X(2071)-8*X(16976),4*X(2072)-X(5189),X(2072)+2*X(16619),2*X(2072)+X(37925),7*X(3090)+2*X(37924),7*X(3090)-4*X(37938),5*X(3091)-2*X(3153),X(3146)+8*X(7575),X(3146)+2*X(13619),X(3146)-4*X(31726),5*X(3153)-8*X(10297),X(3153)+8*X(37971),X(3448)+2*X(14157),5*X(3522)-8*X(15646),5*X(3522)+4*X(18325),X(3529)-10*X(37958),X(3543)+8*X(7426),X(3543)+4*X(37940),7*X(3832)-4*X(18403),7*X(3832)+8*X(37936),X(3839)+2*X(37909),3*X(3839)+4*X(37939),X(5059)+8*X(44267),X(5189)+8*X(16619),X(5189)+2*X(37925),4*X(5899)-X(20063),X(5921)+8*X(32217),X(7464)-4*X(44452),X(7574)+2*X(37947),X(7574)-4*X(46031),4*X(7575)-X(13619),2*X(7575)+X(31726),7*X(9781)-4*X(11692),2*X(10096)+X(43893),4*X(10151)-X(10296),X(10151)+2*X(37897),4*X(10257)-X(37944),X(10296)+8*X(37897),X(10297)+5*X(37971),X(10304)-4*X(37907),3*X(10304)-4*X(37941),4*X(10540)-X(14683),X(11558)+2*X(44264),X(11563)+2*X(25338),4*X(11799)+5*X(37760),5*X(11799)+X(44246),X(13445)-4*X(44673),X(13619)+2*X(31726),X(13851)+2*X(32237),4*X(14156)-X(43576),X(15640)+8*X(44265),2*X(15646)+X(18325),5*X(15692)-4*X(37948),5*X(15692)-8*X(44214),5*X(15697)-8*X(44280),X(16386)-4*X(37935),2*X(16386)-5*X(37952),4*X(16619)-X(37925),5*X(17578)-8*X(44283),X(18403)+2*X(37936),X(18403)-4*X(44961),X(18859)-4*X(44234),5*X(30745)-8*X(44911),3*X(37907)-X(37941),3*X(37909)-2*X(37939),X(37924)+2*X(37938),4*X(37931)-7*X(37957),8*X(37935)-5*X(37952),X(37936)+2*X(44961),8*X(37942)+X(37945),X(37943)+4*X(44266),5*X(37943)-4*X(44282),4*X(37943)-X(44450),X(37947)+2*X(46031),X(37950)-4*X(44900),5*X(44266)+X(44282)

As a point on the Euler line, X(46451) has Shinagawa coefficients (e + 8f, -6e).

See Antreas Hatzipolakis and Ercole Suppa, Euclid 3656 .

X(46451) lies on these lines: {2,3}, {146,32223}, {343,15052}, {539,9143}, {1533,13445}, {1568,15107}, {3410,46261}, {3448,14157}, {3582,4351}, {3584,4354}, {5655,38898}, {5921,32217}, {5944,43818}, {7605,14845}, {8718,43817}, {9140,9934}, {9781,11692}, {10540,14683}, {11177,21458}, {11649,14853}, {13391,14643}, {13851,32237}, {14156,43576}, {14644,44407}, {18390,26881}, {35265,44665}, {41587,43605}

X(46451) = midpoint of X(i) and X(j) for these {i,j}: {381,37956}, {16532,43893}
X(46451) = reflection of X(i) in X(j) for these (i,j): (2,37943), (3,16532), (376,37955), (16532,10096), (35489,37922), (37940,7426), (37948,44214), (44450,2)
X(46451) = complement of the circumperp conjugate of X(35500)
X(46451) = anticomplement of the circumperp conjugate of X(12086)
X(46451) = X(523)-vertex conjugate of X(44802)
X(46451) = barycentric product X(94)*X(40640)
X(46451) = trilinear product X(2166)*X(40640)
X(46451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,3146,44441), (4,10201,2), (23,403,3153), (381,7552,2), (381,44278,7552), (403,3153,3091), (403,37971,23), (1113,1114,44802), (1533,44673,13445), (2070,11563,4), (2072,16619,37925), (2072,37925,5189), (3518,15761,34007), (6143,34330,2), (7505,44441,2), (7575,31726,13619), (10096,43893,3), (10201,44275,10254), (11563,25338,2070), (11799,37760,20), (13406,18378,4), (13406,44278,10201), (13619,31726,3146), (16386,37935,37952), (18531,37913,20), (18859,44234,631), (37936,44961,18403), (37947,46031,7574), (44211,44458,22467)


X(46452) = ISOGONAL CONJUGATE OF X(22233)

Barycentrics    (8*a^8-(29*b^2+35*c^2)*a^6+(39*b^4+29*b^2*c^2+54*c^4)*a^4-(b^2-c^2)*(23*b^4-6*b^2*c^2-35*c^4)*a^2+(5*b^2-8*c^2)*(b^2-c^2)^3)*(8*a^8-(35*b^2+29*c^2)*a^6+(54*b^4+29*b^2*c^2+39*c^4)*a^4-(b^2-c^2)*(35*b^4+6*b^2*c^2-23*c^4)*a^2+(8*b^2-5*c^2)*(b^2-c^2)^3) : :

See Antreas Hatzipolakis and César Lozada, euclid 3658.

X(46452) lies on this line: {11539, 40684}

X(46452) = isogonal conjugate of X(22233)
X(46452) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(140)}} and {{A, B, C, X(3), X(11539)}}


X(46453) = X(4)X(230)∩X(32)X(631)

Barycentrics    11 a^4-4 a^2 (b^2+c^2)+(b^2-c^2)^2 : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 3660.

X(46453) lies on these lines: {2,1285}, {3,5304}, {4,230}, {6,3524}, {30,37689}, {32,631}, {39,10299}, {69,7835}, {112,2374}, {115,15682}, {183,14039}, {186,1249}, {187,376}, {193,35297}, {315,33189}, {385,32817}, {439,7754}, {549,21309}, {571,40065}, {574,14482}, {598,23053}, {599,20194}, {609,5218}, {626,33195}, {691,36877}, {754,37690}, {966,33628}, {1003,37667}, {1007,7926}, {1078,16045}, {1620,41369}, {1627,7494}, {1691,14912}, {1992,2030}, {2420,6792}, {2548,3533}, {2996,33250}, {3003,5702}, {3089,8778}, {3090,5475}, {3147,40320}, {3291,33885}, {3314,33224}, {3407,7793}, {3522,5305}, {3523,14930}, {3525,22331}, {3528,5023}, {3529,3767}, {3530,43136}, {3543,43291}, {3545,7737}, {3552,32822}, {3618,7771}, {3620,33220}, {3734,37809}, {3785,7868}, {3793,11288}, {3815,15702}, {3855,7746}, {3933,33205}, {3972,34229}, {4045,8182}, {4232,16317}, {4262,37642}, {5008,15719}, {5024,15692}, {5067,7745}, {5071,37637}, {5206,5355}, {5210,5306}, {5254,17538}, {5277,16845}, {5319,15513}, {5485,11164}, {6179,6337}, {6392,33235}, {6423,44594}, {6424,44597}, {6636,40179}, {6680,33194}, {6722,44678}, {7031,7288}, {7426,41394}, {7581,12968}, {7582,12963}, {7714,10986}, {7739,8588}, {7750,32951}, {7761,33196}, {7762,32989}, {7767,33181}, {7773,32958}, {7774,33216}, {7776,33203}, {7778,33231}, {7779,10351}, {7784,32953}, {7785,32977}, {7787,32978}, {7797,33226}, {7799,11008}, {7806,32986}, {7812,34803}, {7823,32969}, {7831,7943}, {7848,33197}, {7857,32006}, {7875,16043}, {7898,14064}, {7904,33221}, {7908,14023}, {7919,14907}, {7921,33206}, {7925,20065}, {7941,33262}, {8369,15589}, {8587,32532}, {8779,18931}, {9605,15717}, {9741,22253}, {10304,15048}, {11001,43448}, {11179,38010}, {11580,26255}, {12082,34809}, {13638,26619}, {13758,26620}, {14033,17008}, {14712,16041}, {15603,34200}, {15700, 22246}, {16318,37460}, {16976,38292}, {16984,33223}, {16989,33215}, {17004,32983}, {17561,37675}, {18841,32960}, {18843,32883}, {20088,33000}, {23334,44401}, {31404,44535}, {31859,35287}, {32640,36875}, {32816,32959}, {38282,41370}, {41099,43620}, {41134,41672}


X(46454) = X(54)X(549)∩X(235)X(933)

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

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 3660.

X(46454) lies on these lines: {5,23338}, {54,549}, {235,933}, {252,632}, {550,1157}, {1141,3627}, {1166,7405}, {6150,35720}, {7399,19179}, {8901,13371}, {15801,38710}, {16035,22467}, {25042,44682}


X(46455) = X(3146)X(4993)∩X(5056)X(37638)

Barycentrics    (3 a^8+12 a^6 b^2-30 a^4 b^4+12 a^2 b^6+3 b^8+4 a^6 c^2-4 a^4 b^2 c^2-4 a^2 b^4 c^2+4 b^6 c^2-30 a^4 c^4-44 a^2 b^2 c^4-30 b^4 c^4+36 a^2 c^6+36 b^2 c^6-13 c^8) (3 a^8+4 a^6 b^2-30 a^4 b^4+36 a^2 b^6-13 b^8+12 a^6 c^2-4 a^4 b^2 c^2-44 a^2 b^4 c^2+36 b^6 c^2-30 a^4 c^4-4 a^2 b^2 c^4-30 b^4 c^4+12 a^2 c^6+4 b^2 c^6+3 c^8) : :
Barycentrics    (11 S^2-2 (12 R^2 SB-3 SB^2+4 SA SC)) (3 S^2-2 SC (12 R^2+SC-4 SW)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3661.

X(46455) lies on these lines: {3146,4993}, {5056,37638}


X(46456) = ISOTOMIC CONJUGATE OF X(8552)

Barycentrics    b^2*(a^2-b^2)*c^2*(a^2-c^2)*(a^12-(b^2-c^2)^6-a^10*(b^2+c^2)+a^2*(b^2-c^2)^4*(b^2+c^2)-a^8*(b^4-3*b^2*c^2+c^4)+a^4*(b^2-c^2)^2*(b^4-3*b^2*c^2+c^4)) : :
Barycentrics    SB*(-SA^2+SB^2)*(-S^2+3*SB^2)*SC*(S^2-3*SC^2)*(SA^2-SC^2) : :
Barycentrics    (sec A) csc(B - C)/(1 + 2 cos 2A) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3677.

X(46456) lies on these lines: {94,16080}, {107,476}, {250,23290}, {264,34370}, {328,6330}, {648,14618}, {653,7115}, {685,10412}, {687,14590}, {1897,36129}, {1989,16081}, {2410,16237}, {6344,17983}, {6528,41392}, {14165,18883}, {14570,38342}, {14592,15459}, {16813,23582}, {22456,23969}, {30529,37766}, {41079,44769}

X(46456) = isotomic conjugate of X(8552)
X(46456) = polar conjugate of X(526)
X(46456) = X(i)-cross conjugate of X(j) for these (i,j): (476,35139), (4240,6528)
X(46456) = X(i)-isoconjugate of X(j) for these (i,j): (3,2624), (31,8552), (48,526), (50,656), (63,14270)
X(46456) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {2,8552}, {4,526}, {19,2624}, {24,44808}, {25,14270}
X(46456) = X(1745)-Zayin conjugate of X(2624)
X(46456) = cevapoint of X(i)and X(j) for these {i,j}: {2,41079}, {94,14592}, {403,2501}, {647,13851}, {1625,15329}
X(46456) = pole wrt polar circle of trilinear polar of X(526) (line X(2088)X(16186))
X(46456) = trilinear pole of line X(4)X(94)
X(46456) = barycentric product X(i)*X(j) for these (i,j): (4,35139), (75,36129), (92,32680), (94,648), (99,6344)
X(46456) = barycentric quotient X(i)/X(j) for these {i,j}: {4,526}, {19,2624}, {24,44808}, {25,14270}, {53,2081}
X(46456) = trilinear product X(i)*X(j) for these (i,j): (2,36129), (4,32680), (19,35139), (92,476), (94,162)
X(46456) = trilinear quotient X(i)/X(j) for these (i,j): (4,2624), (19,14270), (75,8552), (92,526), (94,656)


X(46457) = X(99)X(101)∩X(115)X(2642)

Barycentrics    (2*a - b - c)*(b - c)*(2*a^3 - 2*a^2*b + b^3 - 2*a^2*c + 2*a*b*c - b^2*c - b*c^2 + c^3) : :
X(46457) = 3 X[41138] - 2 X[45661]

X(46457) lies on the cubic K1255 and these lines: {99, 101}, {115, 2642}, {545, 4750}, {900, 1635}, {903, 45674}, {6084, 40520}, {24506, 24956}, {30190, 44432}, {41138, 45661}

X(46457) = reflection of X(i) in X(j) for these {i,j}: {903, 45674}, {4120, 4370}, {14442, 1635}, {30190, 44432}
X(46457) = crossdifference of every pair of points on line {106, 3122}
X(46457) = barycentric product X(4530)*X(45273)
X(46457) = barycentric quotient X(i)/X(j) for these {i,j}: {5170, 4591}, {42084, 39155}


X(46458) = X(11)X(244)∩X(86)X(99)

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

X(46458) lies on the cubic K1255 and these lines: {11, 244}, {86, 99}, {190, 17719}, {537, 24222}, {1411, 24836}, {2643, 6089}, {3125, 14442}, {4427, 4440}, {7200, 21135}, {21035, 21725}, {21200, 24185}

X(46458) = midpoint of X(4427) and X(4440)
X(46458) = reflection of X(3120) in X(1086)
X(46458) = X(6551)-isoconjugate of X(39155)
X(46458) = crossdifference of every pair of points on line {101, 14407}
X(46458) = barycentric product X(i)*X(j) for these {i,j}: {5170, 21207}, {21132, 45273}
X(46458) = barycentric quotient X(5170)/X(4570)
X(46458) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {244, 1086, 24188}, {244, 1769, 3122}, {4440, 33148, 24416}


X(46459) = X(69)X(74)∩X(122)X(125)

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

X(46459) lies on the cubic K1255 and these lines: {69, 74}, {110, 39352}, {122, 125}, {648, 5972}, {2799, 16278}, {9530, 13202}, {30211, 34950}

X(46459) = midpoint of X(110) and X(39352)
X(46459) = reflection of X(i) in X(j) for these {i,j}: {125, 15526}, {648, 5972}
X(46459) = crossdifference of every pair of points on line {112, 14398}
X(46459) = barycentric product X(3267)*X(42654)
X(46459) = barycentric quotient X(42654)/X(112)


X(46460) = X(81)X(99)∩X(244)X(665)

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

X(46460) lies on the cubic K1255 and these lines: {81, 99}, {244, 665}, {291, 21888}, {668, 36226}, {812, 7200}, {4128, 4155}, {9263, 33888}

X(46460) = reflection of X(3125) in X(1015)
X(46460) = crossdifference of every pair of points on line {100, 14404}
X(46460) = barycentric product X(693)*X(42655)
X(46460) = barycentric quotient X(42655)/X(100)


X(46461) = X(6)X(99)∩X(351)X(865)

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

X(46461) lies on the cubic K1255 and these lines: {6, 99}, {351, 865}, {694, 2854}, {4576, 25054}, {45672, 45914}

X(46461) = midpoint of X(4576) and X(25054)
X(46461) = reflection of X(3124) in X(1084)
X(46461) = X(799)-isoconjugate of X(39442)
X(46461) = crossdifference of every pair of points on line {99, 888}
X(46461) = barycentric quotient X(669)/X(39442)


X(46462) = X(99)X(1380)∩X(523)X(13636)

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

X(46462) lies on the cubic K1255 and these lines: {99, 1380}, {523, 13636}, {1648, 1649}, {2028, 3906}, {2793, 14502}, {3413, 9180}, {5639, 5648}, {13722, 44398}, {30508, 39366}

X(46462) = midpoint of X(30508) and X(39366)
X(46462) = reflection of X(13636) in X(39023)
X(46462) = reflection of X(46463) in X(1649)
X(46462) = X(22245)-Ceva conjugate of X(13722)
X(46462) = crossdifference of every pair of points on line {691, 1379}
X(46462) = X(i)-isoconjugate of X(j) for these (i,j): {1379, 36085}, {6190, 36142}
X(46462) = barycentric product X(i)*X(j) for these {i,j}: {524, 13636}, {690, 3413}, {1648, 6189}, {5638, 35522}
X(46462) = barycentric quotient X(i)/X(j) for these {i,j}: {351, 1379}, {690, 6190}, {1648, 3414}, {3413, 892}, {5638, 691}, {13636, 671}, {21906, 5639}, {33919, 13722}
X(46462) = {X(1648),X(23992)}-harmonic conjugate of X(46463)


X(46463) = X(99)X(1379)∩X(523)X(13722)

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

X(46463) lies on the cubic K1255 and these lines: {99, 1379}, {523, 13722}, {1648, 1649}, {2029, 3906}, {2793, 14501}, {3414, 9180}, {5638, 5648}, {13636, 44398}, {30509, 39365}

X(46463) = midpoint of X(30509) and X(39365)
X(46463) = reflection of X(46462) in X(1649)
X(46463) = reflection of X(13722) in X(39022)
X(46463) = X(22244)-Ceva conjugate of X(13636)
X(46463) = crossdifference of every pair of points on line {691, 1380}
X(46463) = X(i)-isoconjugate of X(j) for these (i,j): {1380, 36085}, {6189, 36142}
X(46463) = barycentric product X(i)*X(j) for these {i,j}: {524, 13722}, {690, 3414}, {1648, 6190}, {5639, 35522}
X(46463) = barycentric quotient X(i)/X(j) for these {i,j}: {351, 1380}, {690, 6189}, {1648, 3413}, {3414, 892}, {5639, 691}, {13722, 671}, {21906, 5638}, {33919, 13636}
X(46463) = {X(1648),X(23992)}-harmonic conjugate of X(46462)


X(46464) = X(99)X(524)∩X(892)X(11053)

Barycentrics    (b^2 - c^2)^2*(-2*a^2 + b^2 + c^2)*(-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(46464) = 3 X[42344] - 4 X[44398]

X(46464) lies on the cubic K1255 and these lines: {99, 524}, {892, 11053}, {1648, 1649}, {5468, 39356}, {33919, 41177}, {42344, 44398}

X(46464) = midpoint of X(5468) and X(39356)
X(46464) = reflection of X(i) in X(j) for these {i,j}: {892, 11053}, {1648, 23992}
X(46464) = crossdifference of every pair of points on line {691, 9171}
X(46464) = barycentric product X(i)*X(j) for these {i,j}: {1648, 44372}, {35522, 39527}
X(46464) = barycentric quotient X(39527)/X(691)


X(46465) = X(4)X(14)∩X(13)X(125)

Barycentrics    Sqrt[3]*(2*a^10 - 2*a^8*b^2 - 5*a^6*b^4 + 7*a^4*b^6 - a^2*b^8 - b^10 - 2*a^8*c^2 + 12*a^6*b^2*c^2 - 7*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 - 5*a^6*c^4 - 7*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 2*b^6*c^4 + 7*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) + 2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)^2*S : :
X(46465) = 2 X[2] + X[41092], 7 X[2] - X[41132], X[5668] + 2 X[6111], 2 X[5668] + X[38944], 4 X[6111] - X[38944], 7 X[41092] + 2 X[41132]

X(46465) lies on the the circumcircle of the outer Napoleon triangle, the cubics K874, K884, K952, and these lines: {2, 41092}, {3, 5623}, {4, 14}, {13, 125}, {16, 16319}, {17, 39377}, {61, 23721}, {477, 5995}, {2777, 3163}, {5335, 30465}, {5464, 23871}, {5890, 30439}, {17702, 41889}, {18777, 42155}, {25641, 40579}, {36186, 36839}, {41040, 41066}

X(46465) = midpoint of X(13) and X(36788)
X(46465) = reflection of X(46466) in X(3163)
X(46465) = {X(5668),X(6111)}-harmonic conjugate of X(38944)


X(46466) = X(4)X(13)∩X(14)X(125)

Barycentrics    Sqrt[3]*(2*a^10 - 2*a^8*b^2 - 5*a^6*b^4 + 7*a^4*b^6 - a^2*b^8 - b^10 - 2*a^8*c^2 + 12*a^6*b^2*c^2 - 7*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 - 5*a^6*c^4 - 7*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 2*b^6*c^4 + 7*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) - 2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)^2*S : :
X(46466) = X[5669] + 2 X[6110], 2 X[5669] + X[38943], 4 X[6110] - X[38943]

X(46466) lies on the the circumcircle of the outer Napoleon triangle, the cubics K874, K884, K952, and these lines: {3, 5624}, {4, 13}, {14, 125}, {15, 16319}, {18, 39378}, {62, 23722}, {477, 5994}, {2777, 3163}, {5334, 30468}, {5463, 23870}, {5663, 41889}, {5890, 30440}, {18776, 42154}, {25641, 40578}, {36185, 36840}, {41041, 41067}

X(46466) = reflection of X(46465) in X(3163)
X(46466) = {X(5669),X(6110)}-harmonic conjugate of X(38943)


X(46467) =  EULER LINE INTERCEPT OF X(33)X(500)

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

As a point on the Euler line, X(46467) has Shinagawa coefficients (4 r^2 (r+2 R)^2 - S^2, 5 S^2 -4 r^2 (r+2 R) (r+6 R)).

See Antreas Hatzipolakis and Ercole Suppa, euclid 3698.

X(46467) lies on these lines: {2,3}, {19,9958} ,{33,500}, {225,6357}, {511,1872}, {1770,1882}, {1824,13754}, {1826,3579}, {1838,18400}, {1839,15946}, {1844,17637}, {1865,45930}, {1868,37585}, {1869,18480}, {1871,6000}, {5307,12699}, {5453,6198}, {37826,44665}

X(46467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,27,15763), (4,28,44225), (4,7414,430), (4,14016,6841), (4,14018,381), (4,31902,15762), (4,37381,546), (4,37395,7524)


X(46468) =  EULER LINE INTERCEPT OF X(500)X(1442)

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

As a point on the Euler line, X(46468) has Shinagawa coefficients (4 r^2 (r+2 R)^2 - S^2, 4S^2 -8 r^2 (r+2 R) (r+3 R)).

See Antreas Hatzipolakis and Ercole Suppa, euclid 3699.

X(46468) lies on these lines: {2,3}, {500,1442}, {516,23555}, {1068,13408}, {1770,40149}, {1825,41562}, {1826,31730}, {1838,35201}, {1869,31673}, {5307,41869}, {5905,44665}, {6000,42448}, {6637,37755}, {12528,13754}, {14206,41013}, {18400,42759}

X(46468) = X(29)-beth conjugate of X(44225)
X(46468) = X(92)-Ceva conjugate of X(40942)
X(46468) = trilinear product X(4292)*X(6198)
X(46468) = trilinear quotient X(4292)/X(7100)
X(46468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,7554,37372), (4,31900,15763), (4,37168,44225), (2475,3559,860)


X(46469) = X(4)X(65)∩X(521)X(8062)

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

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 3708.

X(46469) lies on these lines: {4,65}, {521,8062}


X(46470) = EULER LINE INTERCEPT OF X(13)X(74)

Barycentrics    3*sqrt(3)*(a^2-b^2+c^2)*(a^4-2*(b^2+c^2)*a^2+b^4+4*b^2*c^2+c^4)*(a^2+b^2-c^2)*a^2+8*S^3*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2) : :
X(46470) = X(4)+2*X(23721)

See Kadir Altintas and César Lozada, euclid 3712.

X(46470) lies on these lines: {2, 3}, {13, 74}, {15, 36299}, {617, 15928}, {5890, 30439}, {8919, 16962}, {16163, 22796}


X(46471) = EULER LINE INTERCEPT OF X(14)X(74)

Barycentrics    3*sqrt(3)*(a^2-b^2+c^2)*(a^4-2*(b^2+c^2)*a^2+b^4+4*b^2*c^2+c^4)*(a^2+b^2-c^2)*a^2-8*S^3*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2) : :
X(46471) = X(4)+2*X(23722)

See Kadir Altintas and César Lozada, euclid 3712.

X(46471) lies on these lines: {2, 3}, {14, 74}, {16, 36298}, {616, 15928}, {5890, 30440}, {8918, 16963}, {16163, 22797}


X(46472) = EULER LINE INTERCEPT OF X(1294)X(34601)

Barycentrics    (2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*(2*a^12-2*(b^2+c^2)*a^10-(11*b^4-24*b^2*c^2+11*c^4)*a^8+24*(b^4-c^4)*(b^2-c^2)*a^6-16*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)*a^4+2*(b^4-c^4)*(b^2-c^2)*(b^4+10*b^2*c^2+c^4)*a^2+(b^4+4*b^2*c^2+c^4)*(b^2-c^2)^4) : :
X(46472) = 4*X(3)-3*X(1651), 2*X(4)-3*X(1650), 4*X(140)-3*X(11251), 16*X(140)-15*X(15183), 3*X(376)-2*X(15774), 6*X(402)-7*X(3523), 4*X(550)-3*X(12113), 2*X(550)-3*X(35241

See Kadir Altintas and César Lozada, euclid 3712.

X(46472) lies on these lines: {2, 3}, {1294, 34601}, {3184, 16240}, {5882, 12626}, {9033, 10990}, {11623, 13179}, {12244, 38591}, {12369, 16534}, {12438, 43174}, {12696, 13464}, {13212, 20417}, {13268, 20418}, {15354, 38791}, {34507, 39886}, {41963, 44610}, {41964, 44611}

X(46472) = reflection of X(i) in X(j) for these (i, j): (3081, 376), (12113, 35241), (34601, 1294)


X(46473) = X(1587)X(3388)∩X(1588)X(3374)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 3718.

X(46473) lies on the Kiepert circumhyperbola, the cubics K329, K1227 and these lines: {3,42647}, {4,41979}, {6,3091}, {20,42645}, {376,41976}, {381,42725}, {631,41980}, {1587,3388}, {1588,3374}, {3146,42730}, {3371,23259}, {3385,23249}, {3387,9541}, {3523,43622}, {3526,43628}, {3545,42784}, {3830,43629}, {3839,42646}, {5066,42726}, {5067,41975}, {5072,42648}, {7486,43623}, {8981,14785}, {13665,14782}, {13785,14783}, {13966,14784}, {15683,43624}


X(46474) = X(3)X(42647)∩X(5)X(11425)

Barycentrics    12 a^12-11 a^10 b^2-53 a^8 b^4+114 a^6 b^6-94 a^4 b^8+41 a^2 b^10-9 b^12-11 a^10 c^2-70 a^8 b^2 c^2+126 a^6 b^4 c^2+56 a^4 b^6 c^2-155 a^2 b^8 c^2+54 b^10 c^2-53 a^8 c^4+126 a^6 b^2 c^4+76 a^4 b^4 c^4+114 a^2 b^6 c^4-135 b^8 c^4+114 a^6 c^6+56 a^4 b^2 c^6+114 a^2 b^4 c^6+180 b^6 c^6-94 a^4 c^8-155 a^2 b^2 c^8-135 b^4 c^8+41 a^2 c^10+54 b^2 c^10-9 c^12+6 Sqrt[2] (6 a^10-17 a^8 b^2+14 a^6 b^4-4 a^2 b^8+b^10-17 a^8 c^2+24 a^6 b^2 c^2+8 a^4 b^4 c^2-12 a^2 b^6 c^2-3 b^8 c^2+14 a^6 c^4+8 a^4 b^2 c^4+32 a^2 b^4 c^4+2 b^6 c^4-12 a^2 b^2 c^6+2 b^4 c^6-4 a^2 c^8-3 b^2 c^8+c^10) S : :
Barycentrics    18 S^4-6 Sqrt[2] S^3 (SA-2 SW)+S^2 (9 SA-4 SW) (SA-SW)+3 Sqrt[2] S SA (16 R^2-3 SW) (SA-SW)+8 SA (4 R^2-SW) (SA-SW) SW : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3718.

X(46474) lies on these lines: {3,42647}, {5,11425}, {578,42648}, {1192,42783}


X(46475) = X(1)X(256)∩X(3)X(37)

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

See Kadir Altintas and César Lozada, euclid 3722.

X(46475) lies on these lines: {1, 256}, {3, 37}, {4, 17321}, {5, 4657}, {9, 182}, {10, 24257}, {30, 41312}, {31, 11203}, {40, 31395}, {44, 5050}, {45, 5085}, {63, 37527}, {75, 6998}, {140, 17279}, {238, 38029}, {344, 631}, {355, 4026}, {381, 41311}, {474, 25099}, {549, 41313}, {575, 1743}, {576, 1449}, {581, 37819}, {612, 37619}, {692, 15296}, {726, 31981}, {971, 1001}, {988, 9737}, {1100, 1351}, {1108, 37492}, {1279, 10246}, {1350, 16777}, {1352, 4357}, {1486, 7387}, {1503, 4364}, {1621, 15503}, {1656, 17384}, {1961, 20368}, {2456, 36405}, {2808, 6176}, {3098, 3247}, {3526, 17357}, {3553, 4260}, {3564, 4643}, {3576, 7611}, {3666, 19544}, {3672, 7390}, {3717, 38116}, {3723, 33878}, {3731, 5092}, {3932, 26446}, {4078, 6684}, {4220, 28606}, {4223, 24554}, {4664, 13634}, {4687, 21554}, {5054, 41310}, {5093, 16666}, {5097, 16667}, {5138, 8557}, {5145, 9619}, {5171, 37552}, {5287, 37521}, {5480, 17045}, {5587, 29061}, {5751, 37615}, {6776, 17257}, {6889, 28420}, {6940, 28978}, {7330, 13323}, {7380, 17322}, {7385, 17302}, {7609, 16468}, {8424, 9959}, {8550, 17332}, {8609, 36740}, {10516, 17325}, {10519, 17316}, {11108, 25887}, {11477, 16884}, {11482, 16668}, {11898, 17344}, {12017, 16814}, {12610, 36674}, {13727, 30273}, {14561, 17023}, {14810, 16673}, {14853, 26626}, {15069, 17253}, {16434, 44307}, {16593, 38122}, {16670, 39561}, {16672, 31884}, {16676, 17508}, {17073, 25365}, {17272, 34507}, {17296, 40107}, {17306, 24206}, {18589, 43160}, {20336, 37151}, {20872, 32613}, {24320, 40937}, {24328, 34381}, {24357, 29010}, {24547, 37149}, {24701, 41007}, {26635, 33849}, {29077, 36663}, {29598, 38317}, {32555, 43121}, {32556, 43120}

X(46475) = reflection of X(37474) in X(1385)
X(46475) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 8245, 6210), (3, 20430, 1766)


X(46476) = X(3)X(42648)∩X(4)X(41980)

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

X(46476) lies on the Kiepert circumhyperbola, the cubics K329 and K1227, and these lines: {3, 42648}, {4, 41980}, {6, 3091}, {20, 42646}, {376, 41975}, {381, 42726}, {631, 41979}, {1587, 3387}, {1588, 3373}, {3146, 42729}, {3372, 23259}, {3386, 23249}, {3388, 9541}, {3523, 43623}, {3526, 43629}, {3545, 42783}, {3830, 43628}, {3839, 42645}, {5066, 42725}, {5067, 41976}, {5072, 42647}, {7486, 43622}, {8981, 14784}, {13665, 14783}, {13785, 14782}, {13966, 14785}, {15683, 43625}

X(46476) = X(i)-cross conjugate of X(j) for these (i,j): {20, 46473}, {42646, 4}
X(46476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3091, 46473}, {42163, 42983, 46473}, {42166, 42982, 46473}


X(46477) = X(3)X(42648)∩X(5)X(11425)

Barycentrics    12*a^12 - 11*a^10*b^2 - 53*a^8*b^4 + 114*a^6*b^6 - 94*a^4*b^8 + 41*a^2*b^10 - 9*b^12 - 11*a^10*c^2 - 70*a^8*b^2*c^2 + 126*a^6*b^4*c^2 + 56*a^4*b^6*c^2 - 155*a^2*b^8*c^2 + 54*b^10*c^2 - 53*a^8*c^4 + 126*a^6*b^2*c^4 + 76*a^4*b^4*c^4 + 114*a^2*b^6*c^4 - 135*b^8*c^4 + 114*a^6*c^6 + 56*a^4*b^2*c^6 + 114*a^2*b^4*c^6 + 180*b^6*c^6 - 94*a^4*c^8 - 155*a^2*b^2*c^8 - 135*b^4*c^8 + 41*a^2*c^10 + 54*b^2*c^10 - 9*c^12 - 6*Sqrt[2]*(6*a^10 - 17*a^8*b^2 + 14*a^6*b^4 - 4*a^2*b^8 + b^10 - 17*a^8*c^2 + 24*a^6*b^2*c^2 + 8*a^4*b^4*c^2 - 12*a^2*b^6*c^2 - 3*b^8*c^2 + 14*a^6*c^4 + 8*a^4*b^2*c^4 + 32*a^2*b^4*c^4 + 2*b^6*c^4 - 12*a^2*b^2*c^6 + 2*b^4*c^6 - 4*a^2*c^8 - 3*b^2*c^8 + c^10)*S : :

X(46477) lies on these lines: {3, 42648}, {5, 11425}, {578, 42647}, {1192, 42784}

X(46477) = {X(5),X(11425)}-harmonic conjugate of X(46474)


X(46478) = X(1)X(14749)∩X(11)X(1402)

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

See Floor van Lamoen and Francisco Javier García Capitán, euclid 3745.

X(46478) lies on these lines: {1,14749}, {10,13731}, {11,1402}, {3646,16288}

X(46478) = midpoint of X(1) and X(43739)


X(46479) = (name pending)

Barycentrics    a*(a^11*b^3 - 4*a^9*b^5 + 6*a^7*b^7 - 4*a^5*b^9 + a^3*b^11 + 3*a^11*b^2*c + a^10*b^3*c - 2*a^9*b^4*c + 2*a^8*b^5*c - 4*a^7*b^6*c - 4*a^6*b^7*c + 2*a^5*b^8*c - 2*a^4*b^9*c + a^3*b^10*c + 3*a^2*b^11*c + 4*a^11*b*c^2 + 3*a^10*b^2*c^2 + 12*a^9*b^3*c^2 + 16*a^8*b^4*c^2 - 6*a^6*b^6*c^2 + 16*a^4*b^8*c^2 + 12*a^3*b^9*c^2 + 3*a^2*b^10*c^2 + 4*a*b^11*c^2 + 2*a^11*c^3 + 4*a^10*b*c^3 + 18*a^9*b^2*c^3 + 26*a^8*b^3*c^3 + 32*a^7*b^4*c^3 + 14*a^6*b^5*c^3 + 14*a^5*b^6*c^3 + 32*a^4*b^7*c^3 + 26*a^3*b^8*c^3 + 18*a^2*b^9*c^3 + 4*a*b^10*c^3 + 2*b^11*c^3 + 2*a^10*c^4 + 2*a^9*b*c^4 + 20*a^8*b^2*c^4 + 38*a^7*b^3*c^4 + 18*a^6*b^4*c^4 + 16*a^5*b^5*c^4 + 18*a^4*b^6*c^4 + 38*a^3*b^7*c^4 + 20*a^2*b^8*c^4 + 2*a*b^9*c^4 + 2*b^10*c^4 - 6*a^9*c^5 + 2*a^8*b*c^5 - 4*a^7*b^2*c^5 - 2*a^6*b^3*c^5 - 6*a^5*b^4*c^5 - 6*a^4*b^5*c^5 - 2*a^3*b^6*c^5 - 4*a^2*b^7*c^5 + 2*a*b^8*c^5 - 6*b^9*c^5 - 6*a^8*c^6 - 10*a^7*b*c^6 - 8*a^6*b^2*c^6 - 30*a^5*b^3*c^6 - 40*a^4*b^4*c^6 - 30*a^3*b^5*c^6 - 8*a^2*b^6*c^6 - 10*a*b^7*c^6 - 6*b^8*c^6 + 6*a^7*c^7 - 2*a^6*b*c^7 - 4*a^5*b^2*c^7 - 14*a^4*b^3*c^7 - 14*a^3*b^4*c^7 - 4*a^2*b^5*c^7 - 2*a*b^6*c^7 + 6*b^7*c^7 + 6*a^6*c^8 + 14*a^5*b*c^8 - 11*a^3*b^3*c^8 + 14*a*b^5*c^8 + 6*b^6*c^8 - 2*a^5*c^9 - 2*a^4*b*c^9 - 11*a^3*b^2*c^9 - 11*a^2*b^3*c^9 - 2*a*b^4*c^9 - 2*b^5*c^9 - 2*a^4*c^10 - 10*a^3*b*c^10 - 15*a^2*b^2*c^10 - 10*a*b^3*c^10 - 2*b^4*c^10 - 2*a^2*b*c^11 - 2*a*b^2*c^11)*(2*a^11*b^3 + 2*a^10*b^4 - 6*a^9*b^5 - 6*a^8*b^6 + 6*a^7*b^7 + 6*a^6*b^8 - 2*a^5*b^9 - 2*a^4*b^10 + 4*a^11*b^2*c + 4*a^10*b^3*c + 2*a^9*b^4*c + 2*a^8*b^5*c - 10*a^7*b^6*c - 2*a^6*b^7*c + 14*a^5*b^8*c - 2*a^4*b^9*c - 10*a^3*b^10*c - 2*a^2*b^11*c + 3*a^11*b*c^2 + 3*a^10*b^2*c^2 + 18*a^9*b^3*c^2 + 20*a^8*b^4*c^2 - 4*a^7*b^5*c^2 - 8*a^6*b^6*c^2 - 4*a^5*b^7*c^2 - 11*a^3*b^9*c^2 - 15*a^2*b^10*c^2 - 2*a*b^11*c^2 + a^11*c^3 + a^10*b*c^3 + 12*a^9*b^2*c^3 + 26*a^8*b^3*c^3 + 38*a^7*b^4*c^3 - 2*a^6*b^5*c^3 - 30*a^5*b^6*c^3 - 14*a^4*b^7*c^3 - 11*a^3*b^8*c^3 - 11*a^2*b^9*c^3 - 10*a*b^10*c^3 - 2*a^9*b*c^4 + 16*a^8*b^2*c^4 + 32*a^7*b^3*c^4 + 18*a^6*b^4*c^4 - 6*a^5*b^5*c^4 - 40*a^4*b^6*c^4 - 14*a^3*b^7*c^4 - 2*a*b^9*c^4 - 2*b^10*c^4 - 4*a^9*c^5 + 2*a^8*b*c^5 + 14*a^6*b^3*c^5 + 16*a^5*b^4*c^5 - 6*a^4*b^5*c^5 - 30*a^3*b^6*c^5 - 4*a^2*b^7*c^5 + 14*a*b^8*c^5 - 2*b^9*c^5 - 4*a^7*b*c^6 - 6*a^6*b^2*c^6 + 14*a^5*b^3*c^6 + 18*a^4*b^4*c^6 - 2*a^3*b^5*c^6 - 8*a^2*b^6*c^6 - 2*a*b^7*c^6 + 6*b^8*c^6 + 6*a^7*c^7 - 4*a^6*b*c^7 + 32*a^4*b^3*c^7 + 38*a^3*b^4*c^7 - 4*a^2*b^5*c^7 - 10*a*b^6*c^7 + 6*b^7*c^7 + 2*a^5*b*c^8 + 16*a^4*b^2*c^8 + 26*a^3*b^3*c^8 + 20*a^2*b^4*c^8 + 2*a*b^5*c^8 - 6*b^6*c^8 - 4*a^5*c^9 - 2*a^4*b*c^9 + 12*a^3*b^2*c^9 + 18*a^2*b^3*c^9 + 2*a*b^4*c^9 - 6*b^5*c^9 + a^3*b*c^10 + 3*a^2*b^2*c^10 + 4*a*b^3*c^10 + 2*b^4*c^10 + a^3*c^11 + 3*a^2*b*c^11 + 4*a*b^2*c^11 + 2*b^3*c^11) : :

X(46479) is the perspector of the conic defined in the following posting: Floor van Lamoen and Peter Moses, euclid 3752.

X(46479) lies on these lines: { }


X(46480) = X(4427)X(4551)∩X(17301)X(39974)

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

See Ercole Suppa, euclid 3774.

X(46480) lies on these lines: {4427,4551}, {17301,39974}

X(46480) = trilinear pole of the line {65,1125}
X(46480) = X(5434)-cross conjugate of X(4998)
X(46480) = X(i)-isoconjugate of X(j) for these (i,j): (522,5035), (663,37633), (2175,4828), (4828,2175) ,(5035,522)
X(46480) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {85,4828}, {651,37633}, {1415,5035}, {4552,31025}
X(46480) = cevapoint of X(i)and X(j) for these {i,j}: {226,43052}, {514,5718}, {3669,4031}
X(46480) = barycentric product X(i)*X(j) for these (i,j): (664,42285), (4554,39974)
X(46480) = barycentric quotient X(i)/X(j) for these {i,j}: {85,4828}, {651,37633}, {1415,5035}, {4552,31025}
X(46480) = trilinear product X(i)*X(j) for these (i,j): (651,42285), (664,39974)
X(46480) = trilinear quotient X(i) /X(j) for these (i,j): (109,5035), (664,37633)


X(46481) = (name pending)

Barycentrics    a (a^8 b^2+2 a^8 b c+a^8 c^2-5 a^7 b^3-7 a^7 b^2 c-7 a^7 b c^2-5 a^7 c^3+10 a^6 b^4+7 a^6 b^3 c+10 a^6 b^2 c^2+7 a^6 b c^3+10 a^6 c^4-10 a^5 b^5+4 a^5 b^4 c+4 a^5 b c^4-10 a^5 c^5+5 a^4 b^6-14 a^4 b^5 c-a^4 b^4 c^2-4 a^4 b^3 c^3-a^4 b^2 c^4-14 a^4 b c^5+5 a^4 c^6-a^3 b^7+11 a^3 b^6 c-13 a^3 b^5 c^2+3 a^3 b^4 c^3+3 a^3 b^3 c^4-13 a^3 b^2 c^5+11 a^3 b c^6-a^3 c^7-3 a^2 b^7 c+14 a^2 b^6 c^2-11 a^2 b^5 c^3-11 a^2 b^3 c^5+14 a^2 b^2 c^6-3 a^2 b c^7-4 a b^7 c^2+12 a b^6 c^3-8 a b^5 c^4-8 a b^4 c^5+12 a b^3 c^6-4 a b^2 c^7-2 b^7 c^3+8 b^6 c^4-12 b^5 c^5+8 b^4 c^6-2 b^3 c^7) : :

See Floor van Lamoen and Francisco Javier García Capitán, euclid 3793.

X(46481) lies on this line: {1, 14746}


X(46482) = (name pending)

Barycentrics    a^14 b^6 - 5 a^12 b^8 + 10 a^10 b^10 - 10 a^8 b^12 + 5 a^6 b^14 - a^4 b^16 - a^14 b^4 c^2 + 3 a^12 b^6 c^2 - 5 a^10 b^8 c^2 + 5 a^8 b^10 c^2 - 4 a^4 b^14 c^2 + 2 a^2 b^16 c^2 - a^14 b^2 c^4 + 4 a^12 b^4 c^4 - 3 a^10 b^6 c^4 - a^8 b^8 c^4 - 3 a^6 b^10 c^4 + 12 a^4 b^12 c^4 - 7 a^2 b^14 c^4 - b^16 c^4 + a^14 c^6 + 3 a^12 b^2 c^6 - 3 a^10 b^4 c^6 + 4 a^8 b^6 c^6 - 6 a^4 b^10 c^6 + 9 a^2 b^12 c^6 + 6 b^14 c^6 - 5 a^12 c^8 - 5 a^10 b^2 c^8 - a^8 b^4 c^8 - 2 a^4 b^8 c^8 - 4 a^2 b^10 c^8 - 15 b^12 c^8 + 10 a^10 c^10 + 5 a^8 b^2 c^10 - 3 a^6 b^4 c^10 - 6 a^4 b^6 c^10 - 4 a^2 b^8 c^10 + 20 b^10 c^10 - 10 a^8 c^12 + 12 a^4 b^4 c^12 + 9 a^2 b^6 c^12 - 15 b^8 c^12 + 5 a^6 c^14 - 4 a^4 b^2 c^14 - 7 a^2 b^4 c^14 + 6 b^6 c^14 - a^4 c^16 + 2 a^2 b^2 c^16 - b^4 c^16 : :

See Floor van Lamoen and Francisco Javier García Capitán, euclid 3803.

X(46482) lies on this line: {13413, 39506}


X(46483) = X(4)X(81)∩X(30)X(944)

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

See Antreas Hatzipolakis and César Lozada, euclid 3820.

X(46483) lies on these lines: {3, 3936}, {4, 81}, {8, 3564}, {20, 17778}, {30, 944}, {58, 8229}, {182, 4202}, {184, 24984}, {221, 388}, {377, 6776}, {511, 3868}, {515, 2650}, {631, 30831}, {860, 1437}, {964, 1352}, {1330, 4220}, {1899, 24537}, {2292, 2792}, {2975, 4388}, {3146, 20090}, {3487, 13442}, {4340, 26118}, {4683, 8235}, {5051, 37527}, {5767, 6917}, {6193, 6850}, {6998, 26064}, {7413, 26131}, {9306, 25017}, {11064, 27686}, {11179, 17679}, {12115, 44665}, {13407, 39572}, {13731, 29984}, {13732, 18139}, {16066, 26540}, {20077, 37443}, {23536, 39870}, {36496, 36746}

X(46483) = reflection of X(4) in X(13408)
X(46483) = X(13408)-of-anti-Euler triangle
X(46483) = {X(37527), X(37823)}-harmonic conjugate of X(5051)


X(46484) = EULER LINE INTERCEPT OF X(522)X(1491)

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

X(46484) lies on these lines: {2, 3}, {522, 1491}, {1764, 21243}, {1961, 2647}, {29821, 33178}


X(46485) = EULER LINE INTERCEPT OF X(1491)X(4728)

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

X(46485) lies on these lines: {2, 3}, {1491, 4728}


X(46486) = EULER LINE INTERCEPT OF X(1491)X(4802)

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

X(464846) lies on these lines: {2, 3}, {1491, 4802}


X(46487) = EULER LINE INTERCEPT OF X900)X(1491)

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

X(46487) lies on these lines: {2, 3}, {900, 1491}, {1764, 37636}, {3704, 3869}, {3712, 5057}, {3743, 12047}, {3936, 17139}, {17011, 45230}, {24624, 35466}


X(46488) = EULER LINE INTERCEPT OF X(1491)X(2977)

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

X(46488) lies on these lines: {2, 3}, {200, 1079}, {1491, 2977}, {3935, 40612}


X(46489) = EULER LINE INTERCEPT OF X(1491)X(4926)

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

X(46489) lies on these lines: {2, 3}, {1491, 4926}


X(46490) = EULER LINE INTERCEPT OF X(1491)X(28195)

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

X(46490) lies on these lines: {2, 3}, {1491, 28195}


X(46491) = EULER LINE INTERCEPT OF X(1491)X(28138)

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

X(46491) lies on these lines: {2, 3}, {1491, 28183}


X(46492) = EULER LINE INTERCEPT OF X(1491)X(28175)

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

X(46492) lies on these lines: {2, 3}, {1491, 28175}


X(46493) = EULER LINE INTERCEPT OF X(1491)X(28138)

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

X(46493) lies on these lines: {2, 3}, {3978, 10330}, {5027, 7927}, {19596, 25051}, {26881, 40814}


X(46494) = (name pending)

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

X(46494) lies on this line: {2, 3}


X(46495) = EULER LINE INTERCEPT OF X(2407)X(11123)

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

X(46495) lies on these lines: {2, 3}, {2407, 11123}, {5467, 10190}, {5468, 31614}, {23342, 37879}


X(46496) = (name pending)

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

X(46496) lies on this line:: {2, 3}


X(46497) = EULER LINE INTERCEPT OF X(115)X(5991)

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

X(46497) lies on these lines: {2, 3}, {115, 5991}, {349, 4456}, {664, 14963}, {798, 812}, {3732, 39690}, {16600, 18097}


X(46498) = EULER LINE INTERCEPT OF X(812)X(1019)

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

X(46498) lies on these lines: {2, 3}, {812, 1019}


X(46499) = EULER LINE INTERCEPT OF X(190)X(646)

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

X(46499) lies on these lines: {2, 3}, {190, 646}, {4482, 29732}


X(46500) = (name pending)

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

X(46500) lies on this line: {2, 3}


X(46501) = EULER LINE INTERCEPT OF X(100)X(3948)

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

X(46501) lies on these lines: {2, 3}, {100, 3948}, {294, 39690}, {651, 44112}, {661, 830}, {1376, 27040}, {1633, 2245}, {2238, 20672}, {7676, 22369}


X(46502) = EULER LINE INTERCEPT OF X(100)X(29511)

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

X(46502) lies on these lines: {2, 3}, {100, 29511}, {1019, 3960}, {2287, 29497}


X(46503) = EULER LINE INTERCEPT OF X(112)X(743)

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

X(46503) lies on these lines: {2, 3}, {19, 16872}, {31, 1932}, {112, 743}, {292, 1474}, {648, 43095}, {893, 2299}, {2309, 2354}


X(46504) = EULER LINE INTERCEPT OF X(112)X(721)

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

X(46504) lies on these lines: {2, 3}, {112, 721}


X(46505) = EULER LINE INTERCEPT OF X(112)X(707)

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

X(46505) lies on these lines: {2, 3}, {112, 707}, {1501, 40372}, {1843, 45210}, {1974, 9468}, {3186, 3511}, {16584, 22364}, {41293, 41331}


X(46506) = EULER LINE INTERCEPT OF X(1928)X(1969)

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

X(46506) lies on these lines: {2, 3}, {1928, 1969}


X(46507) = X(1)X(19)∩(X(75)X(9239)

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

X(46507) lies on these lines: {1, 19}, {75, 9239}, {92, 1934}, {1928, 1969}, {2201, 41269}, {3056, 3721}, {3708, 4008}, {16706, 20272}, {17473, 17871}


X(46508) = EULER LINE INTERCEPT OF X(626)X(20819)

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

X(46508) lies on these lines: {2, 3}, {626, 20819}, {7852, 44099}, {7853, 40325}, {14820, 39691}, {40359, 40360}


X(46509) = EULER LINE INTERCEPT OF X(8265)X(23209)

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

X(46509) lies on these lines: {2, 3}, {8265, 23209}


X(46510) = EULER LINE INTERCEPT OF X(1897)X(17987)

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

X(46510) lies on these lines: {2, 3}, {1897, 17987}, {18070, 24006}


X(46511) = EULER LINE INTERCEPT OF X(232)X(538)

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

X(46511) lies on these lines: {2, 3}, {232, 538}, {264, 33885}, {287, 14157}, {385, 8744}, {393, 9462}, {524, 2211}, {1235, 3199}, {1992, 36879}, {2207, 8667}, {2489, 4580}, {3934, 44142}, {3972, 10986}, {5182, 19128}, {6403, 22486}, {7757, 39575}, {7773, 28417}, {7804, 10985}, {8743, 14614}, {10312, 12150}, {28441, 32823}


X(46512) = EULER LINE INTERCEPT OF X(39)X(35606)

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

X(46512) lies on these lines: {2, 3}, {39, 35606}, {76, 5468}, {83, 5466}, {110, 38664}, {338, 6593}, {476, 38680}, {575, 5967}, {576, 46124}, {597, 9214}, {1078, 34245}, {1648, 7745}, {2930, 25051}, {3329, 36822}, {5254, 41939}, {5640, 31850}, {5972, 38734}, {6033, 31127}, {7762, 45291}, {7793, 40871}, {9168, 11638}, {11183, 23105}, {11422, 40814}, {35282, 38740}, {35360, 41253}


X(46513) = EULER LINE INTERCEPT OF X(649)X(834)

Barycentrics    a^2 (a + b) (a + c) (a^3 b^2 - a b^4 - a^2 b^2 c + b^4 c + a^3 c^2 - 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(46513) lies on these lines: {2, 3}, {649, 834}, {896, 23363}, {1403, 2206}, {3187, 23160}, {3670, 18202}, {20878, 29632}, {23197, 40940}


X(46514) = EULER LINE INTERCEPT OF X(116)X(14964)

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

X(46514) lies on these lines: {2, 3}, {116, 14964}, {514, 1921}, {16699, 17181}, {17911, 18659}, {18180, 26531}


X(46515) = EULER LINE INTERCEPT OF X(11)X(16752)

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

X(46515) lies on these lines: {2, 3}, {11, 16752}, {274, 11680}, {693, 784}


X(46516) = EULER LINE INTERCEPT OF X(768)X(3261)

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

X(46516) lies on these lines: {2, 3}, {768, 3261}


X(46517) = EULER LINE INTERCEPT OF X(66)X(40341)

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

X(46517) lies on these lines: {2, 3}, {66, 40341}, {125, 29181}, {325, 33799}, {523, 2525}, {570, 16308}, {576, 11245}, {1503, 3292}, {1899, 11477}, {3098, 45303}, {3258, 44955}, {3284, 16318}, {3313, 3631}, {3448, 34380}, {3564, 23061}, {3629, 15826}, {3793, 31125}, {5157, 32217}, {5522, 16188}, {5972, 29323}, {7756, 15820}, {7998, 18358}, {11064, 29012}, {14927, 26864}, {15019, 45298}, {15066, 39884}, {15437, 39951}, {15581, 41602}, {15598, 16325}, {18390, 44935}, {18911, 21850}, {20190, 37649}, {24855, 40350}, {29317, 32269}, {30737, 40996}, {37775, 42136}, {37776, 42137}, {40126, 43448}, {42426, 46662}

X(46517) = reflection of X(468) in X(858)
X(46517) = reflection of X(37899) in X(468)
X(46517) = reflection of X(47312) in X(2)
X(46517) = reflection of X(37899) in the orthic axis
X(46517) = complement of X(37900)
X(46517) = anticomplement of X(37897)


X(46518) = EULER LINE INTERCEPT OF X(99)X(20022)

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

X(46518) lies on these lines: {2, 3}, {99, 20022}, {263, 46264}, {511, 25046}, {512, 14712}, {2387, 20065}, {3060, 11257}, {4324, 40790}, {5012, 12110}, {5201, 25051}, {6781, 8623}, {7748, 41278}, {9019, 14570}, {17500, 41328}, {20021, 29012}, {22735, 38741}, {29317, 36213}


X(46519) = EULER LINE INTERCEPT OF X(42)X(1770)

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

X(46519) lies on these lines: {2, 3}, {42, 1770}, {43, 4333}, {148, 5990}, {390, 37635}, {513, 4380}, {2895, 17784}, {4294, 26131}, {4295, 17018}, {4299, 11269}, {4305, 29814}, {4316, 33140}, {4324, 29640}, {4338, 42042}, {5088, 37782}, {17778, 20075}, {18663, 20011}, {18666, 20061}, {18668, 44661}, {26013, 28164}


X(46520) = EULER LINE INTERCEPT OF X(513)X(4382)

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

X(46520) lies on these lines: {2, 3}, {513, 4382}, {11269, 12953}, {26013, 28150}


X(46521) = EULER LINE INTERCEPT OF X(513)X(4379)

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

X(46521) lies on these lines: {2, 3}, {513, 4379}, {1464, 3720}, {3683, 30970}, {4683, 24703}, {8299, 30981}, {11238, 11269}, {17605, 22053}, {26013, 28194}, {30979, 30980}, {30996, 30999}, {31136, 31165}


X(46522) = EULER LINE INTERCEPT OF X(39)X(40325)

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

X(46522) lies on these lines: {2, 3}, {39, 40325}, {112, 5970}, {160, 44526}, {187, 44099}, {232, 2971}, {512, 1692}, {682, 3767}, {1843, 33843}, {1968, 44162}, {1974, 5033}, {2386, 20975}, {2387, 5028}, {2549, 20775}, {2782, 44145}, {3289, 5167}, {3331, 9418}, {3455, 39644}, {5186, 44146}, {6392, 19597}, {7737, 40981}, {7748, 23208}, {7761, 22062}, {8744, 44090}, {8749, 16098}, {8753, 17980}, {9917, 32006}, {12143, 44142}, {15270, 44518}, {16084, 17984}, {38294, 44371}


X(46523) = EULER LINE INTERCEPT OF X(514)X(4374)

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

X(46523) lies on these lines: {2, 3}, {514, 4374}


X(46524) = EULER LINE INTERCEPT OF X(649)X(4083)

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

X(46524) lies on these lines: {2, 3}, {649, 4083}, {20335, 20757}


X(46525) = EULER LINE INTERCEPT OF X(824)X(4391)

Barycentrics    a^4 b^3 - b^7 + 2 a^5 b c - a^3 b^3 c - a b^5 c - a^2 b^3 c^2 + b^5 c^2 + a^4 c^3 - a^3 b c^3 - a^2 b^2 c^3 + 2 a b^3 c^3 - a b c^5 + b^2 c^5 - c^7 : :

X(46525) lies on these lines: {2, 3}, {824, 4391}


X(46526) = EULER LINE INTERCEPT OF X(321)X(693)

Barycentrics    a^4 b^3 - b^7 - 2 a^5 b c + a^3 b^3 c + a b^5 c - a^2 b^3 c^2 + b^5 c^2 + a^4 c^3 + a^3 b c^3 - a^2 b^2 c^3 - 2 a b^3 c^3 + a b c^5 + b^2 c^5 - c^7 : :

X(46526) lies on these lines: {2, 3}, {321, 693}, {3570, 21287}


X(46527) = EULER LINE INTERCEPT OF X(824)X(4791)

Barycentrics    2 a^4 b^3 - 2 b^7 + 2 a^5 b c - a^3 b^3 c - a b^5 c - 2 a^2 b^3 c^2 + 2 b^5 c^2 + 2 a^4 c^3 - a^3 b c^3 - 2 a^2 b^2 c^3 + 2 a b^3 c^3 - a b c^5 + 2 b^2 c^5 - 2 c^7 : :

X(46527) lies on these lines: {2, 3}, {824, 4791}


X(46528) = EULER LINE INTERCEPT OF X(824)X(4823)

Barycentrics    2 a^4 b^3 - 2 b^7 - 2 a^5 b c + a^3 b^3 c + a b^5 c - 2 a^2 b^3 c^2 + 2 b^5 c^2 + 2 a^4 c^3 + a^3 b c^3 - 2 a^2 b^2 c^3 - 2 a b^3 c^3 + a b c^5 + 2 b^2 c^5 - 2 c^7 : :

X(46528) lies on these lines: {2, 3}, {824, 4823}


X(46529) = EULER LINE INTERCEPT OF X(824)X(3762)

Barycentrics    a^4 b^3 - b^7 + 4 a^5 b c - 2 a^3 b^3 c - 2 a b^5 c - a^2 b^3 c^2 + b^5 c^2 + a^4 c^3 - 2 a^3 b c^3 - a^2 b^2 c^3 + 4 a b^3 c^3 - 2 a b c^5 + b^2 c^5 - c^7 : :

X(46529) lies on these lines: {2, 3}, {824, 3762}


X(46530) = EULER LINE INTERCEPT OF X(824)X(4978)

Barycentrics    a^4 b^3 - b^7 - 4 a^5 b c + 2 a^3 b^3 c + 2 a b^5 c - a^2 b^3 c^2 + b^5 c^2 + a^4 c^3 + 2 a^3 b c^3 - a^2 b^2 c^3 - 4 a b^3 c^3 + 2 a b c^5 + b^2 c^5 - c^7 : :

X(46530) lies on these lines: {2, 3}, {824, 4978}


X(46531) = EULER LINE INTERCEPT OF X(824)X(6586)

Barycentrics    -2 a^7 + a^5 b^2 + a^3 b^4 + a^2 b^5 - b^7 + a^5 c^2 - 2 a^3 b^2 c^2 - a^2 b^3 c^2 - a^2 b^2 c^3 + b^4 c^3 + a^3 c^4 + b^3 c^4 + a^2 c^5 - c^7 : :

X(46531) lies on these lines: {2, 3}, {824, 6586}


X(46532) = EULER LINE INTERCEPT OF X(4024)X(4705)

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

X(46532) lies on these lines: {2, 3}, {4024, 4705}


X(46533) = EULER LINE INTERCEPT OF X(918)X(1086)

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

X(46533) lies on these lines: {2, 3}, {918, 1086}


X(46534) = EULER LINE INTERCEPT OF X(850)X(1577)

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

X(46534) lies on these lines: {2, 3}, {850, 1577}, {3007, 15526}, {7291, 23674}


X(46535) = EULER LINE INTERCEPT OF X(1111)X(3120)

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

X(46535) lies on these lines: {2, 3}, {1111, 3120}, {20294, 42761}


X(46536) = EULER LINE INTERCEPT OF X(115)X(2223)

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

X(46536) lies on these lines: {2, 3}, {115, 2223}, {512, 661}, {4433, 10026}, {4436, 44396}, {4447, 23947}, {5949, 8053}, {8299, 20337}, {8818, 15624}, {20975, 44670}, {21010, 23903}


X(46537) = EULER LINE INTERCEPT OF X(812)X(1015))

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

X(46537) lies on these lines: {2, 3}, {812, 1015}


X(46538) = EULER LINE INTERCEPT OF X(8061)X(16892)

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

X(46538) lies on these lines: {2, 3}, {8061, 16892}


X(46539) = EULER LINE INTERCEPT OF X(826)X(2474)

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

X(46539) lies on these lines: {2, 3}, {826, 2474}, {3917, 14378}, {6030, 8725}, {8623, 39691}, {9821, 23293}, {9918, 28436}, {12144, 26177}, {17949, 20021}


X(46540) = EULER LINE INTERCEPT OF X(2084)X(2530)

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

X(46540) lies on these lines: {2, 3}, {2084, 2530}


X(46541) = EULER LINE INTERCEPT OF X(99)X(9088)

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

X(46541) lies on these lines: {2, 3}, {99, 9088}, {107, 1293}, {108, 34594}, {110, 32704}, {112, 9059}, {162, 190}, {902, 46109}, {933, 26713}, {1304, 2692}, {4781, 17906}, {16077, 35169}


X(46542) = EULER LINE INTERCEPT OF X(242)X(514)

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

X(46542) lies on these lines: {242, 514}, {6591, 40086}


X(46543) = EULER LINE INTERCEPT OF X(112)X(9069)

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

X(46543) lies on these lines: {2, 3}, {112, 9069}, {648, 4577}


X(46544) = EULER LINE INTERCEPT OF X(339)X(44089)

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

X(46544) lies on these lines: {2, 3}, {339, 44089}, {2548, 16335}, {2549, 31267}, {16313, 30435}


X(46545) = (name pending)

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

X(46545) lies on this line: {2, 3}


X(46546) = EULER LINE INTERCEPT OF X(32)X(20859)

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

X(46546) lies on these lines: {2, 3}, {32, 20859}, {39, 1501}, {141, 33801}, {157, 22062}, {160, 2916}, {184, 30270}, {206, 20819}, {511, 34396}, {574, 8627}, {577, 9475}, {594, 7087}, {626, 4159}, {1086, 1631}, {1634, 35707}, {3001, 19127}, {3060, 3398}, {3094, 18898}, {3095, 5012}, {3098, 3506}, {3117, 5162}, {3313, 14575}, {3917, 42671}, {4414, 8628}, {5007, 21969}, {5989, 20023}, {6664, 8177}, {7795, 10328}, {8588, 41273}, {9155, 35268}, {12203, 39906}, {12220, 37893}, {14602, 32452}, {15080, 35002}, {15107, 26316}, {16893, 23208}, {19126, 23635}, {37485, 40947}


X(46547) = (name pending)

Barycentrics    a^14 - a^10 b^4 + a^10 b^2 c^2 + b^12 c^2 - a^10 c^4 - b^10 c^4 - b^4 c^10 + b^2 c^12 : :

X(46547) lies on this line: {2, 3}


X(46548) = EULER LINE INTERCEPT OF X(56)X(43066)

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

X(46548) lies on these lines: {2, 3}, {56, 43066}, {238, 28283}, {514, 659}, {528, 23854}, {4433, 32847}, {4653, 5277}, {5045, 29819}, {21808, 24929}


X(46549) = EULER LINE INTERCEPT OF X(55)X(13097)

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

X(46549) lies on these lines: {2, 3}, {55, 13097}, {522, 659}, {846, 7322}, {1283, 1284}, {1697, 11533}, {3556, 3913}, {8666, 29844}, {24928, 29818}, {25968, 29291}


X(46550) = EULER LINE INTERCEPT OF X(513)X(4088)

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

X(46550) lies on these lines: {2, 3}, {513, 4088}, {1279, 3120}


X(46551) = EULER LINE INTERCEPT OF X(513)X(168922)

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

X(46551) lies on these lines: {2, 3}, {513, 16892}, {15621, 34666}


X(46552) = EULER LINE INTERCEPT OF X(513)X(4468)

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

X(46552) lies on these lines: {2, 3}, {513, 4468}, {1565, 37782}


X(46553) = EULER LINE INTERCEPT OF X(63)X(3966)

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

X(46553) lies on these lines: {2, 3}, {63, 3966}, {513, 3004}, {3743, 10624}, {26013, 28845}


X(46554) = EULER LINE INTERCEPT OF X(650)X(4802)

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

X(46554) lies on these lines: {2, 3}, {650, 4802}


X(46555) = EULER LINE INTERCEPT OF X(37)X(650)

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

X(46555) lies on these lines: {2, 3}, {37, 650}, {1104, 1647}, {1125, 42753}, {3695, 17780}, {9458, 32777}


X(46556) = (name pending)

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

X(46556) lies on this line: {2, 3}


X(46557) = EULER LINE INTERCEPT OF X(1826)X(7649)

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

X(46557) lies on these lines: {2, 3}, {1826, 7649}


X(46558) = EULER LINE INTERCEPT OF X(242)X(8735)

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

X(46558) lies on these lines: {2, 3}, {242, 8735}


X(46559) = EULER LINE INTERCEPT OF X(1874)X(5236)

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

X(46559) lies on these lines: {2, 3}, {1874, 5236}


X(46560) = EULER LINE INTERCEPT OF X(316)X(44089)

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

X(46560) lies on these lines: {2, 3}, {316, 44089}, {16221, 44947}, {35524, 44146}


X(46561) = EULER LINE INTERCEPT OF X(3906)X(9148)

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

X(46561) lies on these lines: {2, 3}, {3906, 9148}, {7697, 7703}, {30789, 35002}, {31127, 32515}


X(46562) = (name pending)

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

X(46562) lies on this line: {2, 3}


X(46563) = EULER LINE INTERCEPT OF X(313)X(3261)

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

X(46563) lies on these lines: {2, 3}, {313, 3261}


X(46564) = EULER LINE INTERCEPT OF X(650)X(3250)

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

X(46564) lies on these lines: {2, 3}, {650, 3250}, {17046, 22449}


X(46565) = EULER LINE INTERCEPT OF X(29017)X(35519)

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

X(46565) lies on these lines: {2, 3}, {29017, 35519}


X(46566) = EULER LINE INTERCEPT OF X(42)X(649)

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

X(46566) lies on these lines: {2, 3}, {42, 649}, {27846, 40956}


X(46567) = (name pending)

Barycentrics    a^4 b^6 - b^10 - a^5 b^4 c + a b^8 c - a^2 b^6 c^2 + b^8 c^2 + a^3 b^4 c^3 - a b^6 c^3 - a^5 b c^4 + a^3 b^3 c^4 + a^4 c^6 - a^2 b^2 c^6 - a b^3 c^6 + a b c^8 + b^2 c^8 - c^10 : :

X(46567) lies on this line: {2, 3}


X(46568) = EULER LINE INTERCEPT OF X(37)X(513)

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

X(46568) lies on these lines: {2, 3}, {37, 513}, {1104, 27846}, {3695, 23354}, {20777, 26012}


X(46569) = EULER LINE INTERCEPT OF X(1577)X(1930)

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

X(46569) lies on these lines: {2, 3}, {1577, 1930}


X(46570) = EULER LINE INTERCEPT OF X(14208)X(20910)

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

X(46570) lies on these lines: {2, 3}, {14208, 20910}


X(46571) = EULER LINE INTERCEPT OF X(6)X(44136)

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

X(46571) lies on these lines: {2, 3}, {6, 44136}, {287, 44768}, {323, 1236}, {338, 22151}, {1994, 7894}, {3260, 37784}, {3978, 23962}, {6748, 26156}, {9544, 39646}, {10358, 11451}, {13449, 15059}


X(46572) = (name pending)

Barycentrics    a^4 b^6 - b^10 + a^5 b^4 c - a b^8 c - a^2 b^6 c^2 + b^8 c^2 - a^3 b^4 c^3 + a b^6 c^3 + a^5 b c^4 - a^3 b^3 c^4 + a^4 c^6 - a^2 b^2 c^6 + a b^3 c^6 - a b c^8 + b^2 c^8 - c^10 : :

X(46572) lies on this line: {2, 3}


X(46573) = (name pending)

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

X(46573) lies on this line: {2, 3}


X(46574) = EULER LINE INTERCEPT OF X(649)X(693)

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

X(46574) lies on these lines: {2, 3}, {649, 693}, {673, 17963}, {3002, 5088}, {17026, 21370}, {24592, 24633}


X(46575) = EULER LINE INTERCEPT OF X(812)X(4391)

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

X(46575) lies on these lines: {2, 3}, {812, 4391}


X(46576) = EULER LINE INTERCEPT OF X(513)X(3261)

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

X(46576) lies on these lines: {2, 3}, {513, 3261}


X(46577) = EULER LINE INTERCEPT OF X(3766)X(4083)

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

X(46577) lies on these lines: {2, 3}, {3766, 4083}


X(46578) = EULER LINE INTERCEPT OF X(513)X(1919)

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

X(46578) lies on these lines: {2, 3}, {513, 1919}


X(46579) = EULER LINE INTERCEPT OF X(650)X(8632)

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

X(46579) lies on these lines: {2, 3}, {650, 8632}


X(46580) = EULER LINE INTERCEPT OF X(918)X(3837)

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

X(46580) lies on these lines: {2, 3}, {918, 3837}


X(46581) = EULER LINE INTERCEPT OF X(3910)X(4486)

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

X(46581) lies on these lines: {2, 3}, {3910, 4486}


X(46582) = EULER LINE INTERCEPT OF X(150)X(14964)

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

X(46582) lies on these lines: {2, 3}, {150, 14964}, {812, 4481}, {17086, 17171}


X(46583) = EULER LINE INTERCEPT OF X(513)X(894)

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

X(46583) lies on these lines: {2, 3}, {513, 894}, {1026, 1089}


X(46584) = EULER LINE INTERCEPT OF X(f239)X(18107)

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

X(46584) lies on these lines: {2, 3}, {239, 18107}




leftri   Euler Line Intercepts: X(46585) - X(46596)  rightri

This preamble is contributed by Clark Kimberling and Peter Moses, January 11, 2022. In the plane of a triangle ABC with circumcircle (O) and Euler line L, let U1 be a point on (O), and let

U1 = an arbitrary point on (O), and T1 = line tangent to (O) at U1;
U2 = reflection of U1 in L, and T2 = line tangent to (O) at U2;
U3 = antipode of U1, and T3 = line tangent to (O) at U3;
U4 = antipode of U2, and T4 = line tangent to (O) at U4;
P1 = T1∩T2; P2 = T2∩T3; P3 = T3∩T4; P4 = T4∩T1.

The points P1, P2, P3, P4 are the vertices of a parallelogram. The following table shows results for several choices of the point U1. In the table, each index k represents the triangle center X(k).

U1 U2 U3 U4 P1 P2 P3 P4
74 477 110 476 46585 46616 15329 46608
98 842 99 691 7418 46609 11634 44823
100 1290 104 2687 13583 46610 14127 46611
101 2690 103 2688 46595 46596
105 2752 1292 2691 46586 46593
107 1304 1294 2693 46587 46614 46613
108 2766 1295 2694 46588
111 2770 1296 2770 46589
112 935 1297 2697 46592 46614 46594 46615
930 1291 1141 14979 46590
933 972 18401 945 46591


The midpoints of segments U1U2, U2U3, U3U4, U4U1 are vertices of another parallelogram, as represented by the following table.

U1 m(U1,U2) m(U2,U3) m(U3,U4) m(U4,U1)
74 36164 14934 7471 46632
98 36166 46634 7472 46333
100 36167 46636 46618 46635
112 46619 46631 46620 46637


If you have Geogebra, you can download Three Parallelograms. (The vertices are U1, U2, U3, U4; P1, P2, P3, P4; m1, m2, m3, m4. Drag D to vary the line OD; drag U1 to vary the 12 vertices.)

underbar



X(46585) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(74)

Barycentrics    a^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*c^2 + 4*a^10*b^2*c^2 - 7*a^8*b^4*c^2 - 10*a^6*b^6*c^2 + 17*a^4*b^8*c^2 - 2*a^2*b^10*c^2 - 3*b^12*c^2 - 5*a^10*c^4 - 7*a^8*b^2*c^4 + 38*a^6*b^4*c^4 - 22*a^4*b^6*c^4 - 13*a^2*b^8*c^4 + 9*b^10*c^4 + 10*a^8*c^6 - 10*a^6*b^2*c^6 - 22*a^4*b^4*c^6 + 32*a^2*b^6*c^6 - 6*b^8*c^6 - 10*a^6*c^8 + 17*a^4*b^2*c^8 - 13*a^2*b^4*c^8 - 6*b^6*c^8 + 5*a^4*c^10 - 2*a^2*b^2*c^10 + 9*b^4*c^10 - a^2*c^12 - 3*b^2*c^12) : :
X(46585) = X[15035] - 2 X[42742], 3 X[15055] - 2 X[39987]

X(46585) lies on these lines: {2, 3}, {74, 526}, {98, 43660}, {477, 16171}, {841, 842}, {1294, 1300}, {1299, 5897}, {1495, 7740}, {1624, 10721}, {1986, 40948}, {2693, 32710}, {2777, 39985}, {2972, 12292}, {5467, 43576}, {5502, 14157}, {6000, 14264}, {9717, 12112}, {12041, 14933}, {14915, 33927}, {15035, 42742}, {15055, 39987}, {21663, 39174}, {39434, 39437}

X(46585) = reflection of X(i) in X(j) for these {i,j}: {4, 3134}, {14264, 16186}, {14933, 12041}, {15329, 3}
X(46585) = circumcircle-inverse of X(36164)
X(46585) = crosspoint of X(74) and X(477)
X(46585) = crosssum of X(i) and X(j) for these (i,j): {30, 5663}, {9033, 37985}
X(46585) = crossdifference of every pair of points on line {647, 3163}
X(46585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 7464, 11634}, {1113, 1114, 36164}, {3651, 36001, 13589}, {7440, 7454, 7429}, {14157, 14385, 5502}, {40894, 40895, 4230}, {42789, 42790, 4240}


X(46586) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(105)

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

X(46586) lies on these lines: {2, 3}, {104, 9061}, {105, 659}, {111, 759}, {2373, 39439}, {2374, 39435}, {2770, 12030}, {7292, 42753}, {9078, 28476}, {15344, 26703}, {24403, 41230}, {24822, 27543}

X(46586) = crosspoint of X(105) and X(2752)
X(46586) = crosssum of X(518) and X(2836)
X(46586) = crossdifference of every pair of points on line {647, 6184}
X(46586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 23, 13589}, {21, 1325, 11634}, {468, 867, 2}, {4228, 7469, 15329}, {7423, 7458, 7448}


X(46587) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(107)

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

X(46587) lines on these lines: {2, 3}, {107, 1624}, {110, 1301}, {111, 38867}, {112, 9064}, {476, 22239}, {685, 878}, {925, 30249}, {1289, 1302}, {1304, 5502}, {1495, 43952}, {5667, 43919}, {6000, 39174}, {9060, 10423}, {16186, 35908}, {23181, 30441}, {30510, 40596}, {39575, 46128}

X(46587) = circumcircle-inverse of X(31510)
X(46587) = polar-circle-inverse of X(37985)
X(46587) = isogonal conjugate of X(43701)
X(46587) = isotomic conjugate of the polar conjugate of X(2442)
X(46587) = isogonal conjugate of the polar conjugate of X(2404)
X(46587) = X(i)-Ceva conjugate of X(j) for these (i,j): {250, 40948}, {2404, 2442}, {44769, 112}
X(46587) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43701}, {19, 2416}, {92, 2430}, {656, 1294}, {2972, 36043}, {15404, 36035}
X(46587) = crosspoint of X(107) and X(1304)
X(46587) = crosssum of X(520) and X(9033)
X(46587) = crossdifference of every pair of points on line {647, 1562}
X(46587) = barycentric product X(i)*X(j) for these {i,j}: {3, 2404}, {69, 2442}, {107, 44436}, {133, 44769}, {648, 6000}, {15459, 40948}
X(46587) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 2416}, {6, 43701}, {112, 1294}, {133, 41079}, {184, 2430}, {2404, 264}, {2442, 4}, {6000, 525}, {32640, 15404}, {40948, 41077}, {44436, 3265}
X(46587) = trilinear product X(i)*X(j) for these {i,j}: {48, 2404}, {63, 2442}, {133, 36034}, {162, 6000}
X(46587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 468, 7418}, {25, 44889, 4}, {28, 2074, 14127}, {235, 36179, 4}, {1113, 1114, 31510}, {4230, 7473, 11634}, {4240, 7480, 15329}, {4240, 15329, 4230}, {4246, 37966, 13589}


X(46588) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(108)

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

X(46588) lies on these lines: {2, 3}, {100, 40097}, {107, 30250}, {108, 676}, {1289, 9070}, {1301, 6011}, {1870, 42753}, {2222, 23706}, {9107, 26706}, {30249, 44065}, {36110, 36113}

X(46588) = X(37140)-Ceva conjugate of X(112)
X(46588) = X(656)-isoconjugate of X(39435)
X(46588) = crosspoint of X(108) and X(2766)
X(46588) = crosssum of X(521) and X(2850)
X(46588) = crossdifference of every pair of points on line {647, 35072}
X(46588) = barycentric product X(653)*X(45272)
X(46588) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 39435}, {45272, 6332}
X(46588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 186, 14127}, {4238, 7476, 11634}, {4242, 37964, 13589}, {4246, 37966, 15329}


X(46589) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(111)

Barycentrics    a^2*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8 + a^8*c^2 - 8*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 + a^6*c^4 + 4*a^4*b^2*c^4 - 20*a^2*b^4*c^4 + 3*b^6*c^4 - a^4*c^6 + 10*a^2*b^2*c^6 + 3*b^4*c^6 - a^2*c^8 - 3*b^2*c^8) : :

X(46589) lies on these lines: {2, 3}, {98, 9084}, {111, 351}, {842, 10102}, {2373, 2374}, {14700, 15916}, {23342, 26276}, {40282, 44420}

X(46589) = circumcircle-inverse of X(36168)
X(46589) = crosspoint of X(111) and X(2770)
X(46589) = crosssum of X(524) and X(2854)
X(46589) = crossdifference of every pair of points on line {647, 2482}
X(46589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 23, 11634}, {468, 3143, 2}, {1113, 1114, 36168}, {1995, 7426, 15329}


X(46590) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(930)

Barycentrics    a^2*(a - b)*(a + b)*(a - c)*(a + c)*(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 - 8*a^8*b^2*c^2 + 13*a^6*b^4*c^2 - 12*a^4*b^6*c^2 + 12*a^2*b^8*c^2 - 6*b^10*c^2 - 3*a^8*c^4 + 13*a^6*b^2*c^4 + 2*a^4*b^4*c^4 - 9*a^2*b^6*c^4 + 15*b^8*c^4 + 2*a^6*c^6 - 12*a^4*b^2*c^6 - 9*a^2*b^4*c^6 - 20*b^6*c^6 + 2*a^4*c^8 + 12*a^2*b^2*c^8 + 15*b^4*c^8 - 3*a^2*c^10 - 6*b^2*c^10 + c^12) : :

X(46590) lies on these lines: {2, 3}, {110, 33639}, {925, 30248}, {930, 25149}, {933, 20185}, {6799, 13398}, {10420, 13863}

X(46590) = crosspoint of X(930) and X(1291)
X(46590) = crosssum of X(1510) and X(45147)
X(46590) = crossdifference of every pair of points on line {647, 39018}


X(46591) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(933)

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

X(46591) lies on these lines: {2, 3}, {107, 30248}, {110, 6799}, {930, 20626}, {933, 46062}, {1301, 33639}, {1304, 13863}

X(46591) = crossdifference of every pair of points on line {647, 39019}
X(46591) = X(656)-isoconjugate of X(39431)
X(46591) = barycentric product X(18315)*X(44057)
X(46591) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 39431}, {10214, 24978}, {44057, 18314}


X(46592) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(935)

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

X(46592) lies on these lines: {2, 3}, {99, 1289}, {107, 30247}, {110, 39382}, {112, 1576}, {159, 35902}, {691, 10423}, {925, 30251}, {1296, 1301}, {1304, 10098}, {1986, 38551}, {2420, 2445}, {2696, 22239}, {3565, 39417}, {10097, 32729}, {14580, 34158}, {20187, 30249}, {20626, 44061}, {32649, 32662}, {32696, 32708}, {34131, 39841}

X(46592) = isogonal conjugate of orthocenter of X(3)X(6)X(66)
X(46592) = circumcircle-inverse of X(46619)
X(46592) = X(691)-Ceva conjugate of X(112)
X(46592) = X(42665)-cross conjugate of X(2393)
X(46592) = cevapoint of X(i) and X(j) for these (i,j): {2393, 42665}, {42659, 44102}
X(46592) = crosspoint of X(112) and X(935)
X(46592) = crosssum of X(i) and X(j) for these (i,j): {520, 14417}, {525, 9517}
X(46592) = trilinear pole of line {2393, 14580}
X(46592) = crossdifference of every pair of points on line {647, 15526}
X(46592) = X(i)-isoconjugate of X(j) for these (i,j): {647, 37220}, {656, 2373}, {810, 46140}, {1177, 14208}, {1577, 18876}, {10423, 17879}, {15526, 36095}
X(46592) = barycentric product X(i)*X(j) for these {i,j}: {99, 14580}, {107, 14961}, {110, 5523}, {112, 858}, {162, 18669}, {648, 2393}, {691, 1560}, {1634, 21459}, {8750, 17172}, {12827, 32708}, {17708, 20410}, {20884, 32676}, {23582, 42665}
X(46592) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 2373}, {162, 37220}, {648, 46140}, {858, 3267}, {1560, 35522}, {1576, 18876}, {2393, 525}, {5181, 45807}, {5523, 850}, {14580, 523}, {14961, 3265}, {18669, 14208}, {20410, 9979}, {32729, 41511}, {35325, 46165}, {41937, 10423}, {42665, 15526}


X(46593) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(1292)

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

X(46593) lies on these lines: {2, 3}, {99, 30257}, {1292, 6084}, {1296, 6011}, {9070, 30256}, {20187, 30250}, {30247, 44065}

X(46593) = crosspoint of X(1292) and X(2691)
X(46593) = crosssum of X(2775) and X(3309)


X(46594) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(1297)

Barycentrics    a^2*(a^16*b^2 - 3*a^14*b^4 + a^12*b^6 + 5*a^10*b^8 - 5*a^8*b^10 - a^6*b^12 + 3*a^4*b^14 - a^2*b^16 + a^16*c^2 + 2*a^12*b^4*c^2 - 6*a^10*b^6*c^2 - 2*a^8*b^8*c^2 + 4*a^6*b^10*c^2 + 2*a^4*b^12*c^2 + 2*a^2*b^14*c^2 - 3*b^16*c^2 - 3*a^14*c^4 + 2*a^12*b^2*c^4 + 7*a^8*b^6*c^4 - 3*a^6*b^8*c^4 - 10*a^2*b^12*c^4 + 7*b^14*c^4 + a^12*c^6 - 6*a^10*b^2*c^6 + 7*a^8*b^4*c^6 - 5*a^4*b^8*c^6 + 6*a^2*b^10*c^6 - 3*b^12*c^6 + 5*a^10*c^8 - 2*a^8*b^2*c^8 - 3*a^6*b^4*c^8 - 5*a^4*b^6*c^8 + 6*a^2*b^8*c^8 - b^10*c^8 - 5*a^8*c^10 + 4*a^6*b^2*c^10 + 6*a^2*b^6*c^10 - b^8*c^10 - a^6*c^12 + 2*a^4*b^2*c^12 - 10*a^2*b^4*c^12 - 3*b^6*c^12 + 3*a^4*c^14 + 2*a^2*b^2*c^14 + 7*b^4*c^14 - a^2*c^16 - 3*b^2*c^16) : :

X(46594) lies on these lines: {2, 3}, {98, 34168}, {111, 5897}, {684, 1297}, {1294, 2373}, {1300, 39436}, {2374, 39434}

X(46594) = circumcircle-inverse of X(46620)
X(46594) = crosspoint of X(1297) and X(2697)
X(46594) = crosssum of X(1503) and X(2781)
X(46594) = crossdifference of every pair of points on line {647, 23976}


X(46595) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(101)

Barycentrics    a^2*(a - b)*(a - c)*(a^4*b^2 - a^3*b^3 - a^2*b^4 + a*b^5 + a^3*b^2*c - a^2*b^3*c - a*b^4*c + b^5*c + a^4*c^2 + a^3*b*c^2 + 2*a^2*b^2*c^2 - a^3*c^3 - 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(46595)lies on these lines: {2, 3}, {101, 692}, {1305, 26705}, {1983, 21789}, {9057, 44876}

X(46595) = X(656)-isoconjugate of X(39438)
X(46595) = crosspoint of X(101) and X(2690)
X(46595) = crosssum of X(514) and X(2774)
X(46595) = crossdifference of every pair of points on line {647, 1086}
X(46595) = barycentric quotient X(112)/X(39438)


X(46596) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(2688)

Barycentrics   a^2*(a^10*b^2 - 2*a^9*b^3 - 2*a^8*b^4 + 6*a^7*b^5 - 6*a^5*b^7 + 2*a^4*b^8 + 2*a^3*b^9 - a^2*b^10 + a^10*c^2 + 4*a^8*b^2*c^2 - 4*a^7*b^3*c^2 - 5*a^6*b^4*c^2 - 6*a^5*b^5*c^2 + 7*a^4*b^6*c^2 + 8*a^3*b^7*c^2 - 4*a^2*b^8*c^2 + 2*a*b^9*c^2 - 3*b^10*c^2 - 2*a^9*c^3 - 4*a^7*b^2*c^3 + 8*a^6*b^3*c^3 + 12*a^5*b^4*c^3 - 12*a^4*b^5*c^3 - 4*a^3*b^6*c^3 - 2*a*b^8*c^3 + 4*b^9*c^3 - 2*a^8*c^4 - 5*a^6*b^2*c^4 + 12*a^5*b^3*c^4 + 6*a^4*b^4*c^4 - 6*a^3*b^5*c^4 - 3*a^2*b^6*c^4 - 6*a*b^7*c^4 + 4*b^8*c^4 + 6*a^7*c^5 - 6*a^5*b^2*c^5 - 12*a^4*b^3*c^5 - 6*a^3*b^4*c^5 + 16*a^2*b^5*c^5 + 6*a*b^6*c^5 - 4*b^7*c^5 + 7*a^4*b^2*c^6 - 4*a^3*b^3*c^6 - 3*a^2*b^4*c^6 + 6*a*b^5*c^6 - 2*b^6*c^6 - 6*a^5*c^7 + 8*a^3*b^2*c^7 - 6*a*b^4*c^7 - 4*b^5*c^7 + 2*a^4*c^8 - 4*a^2*b^2*c^8 - 2*a*b^3*c^8 + 4*b^4*c^8 + 2*a^3*c^9 + 2*a*b^2*c^9 + 4*b^3*c^9 - a^2*c^10 - 3*b^2*c^10) : :

X(46596 lies on these lines: {2, 3}, {103, 926}, {917, 41905}, {1294, 39438}

X(46596) = crosspoint of X(103) and X(2688)
X(46596) = crosssum of X(516) and X(2772)
X(46596) = crossdifference of every pair of points on line {647, 23972}


X(46597) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(190)

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

X(46597) lies on these lines: {2, 3}, {36, 27846}, {99, 27853}, {100, 932}, {101, 29329}, {109, 29325}, {110, 6010}, {667, 3573}, {3572, 17940}, {3733, 4585}, {3799, 8671}, {9058, 39631}, {18266, 40155}

X(46597) = crosspoint of X(2702) and X(34071)
X(46597) = crosssum of X(2786) and X(3835)
X(46597) = crossdifference of every pair of points on line {647, 6377}


X(46598) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(670)

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

X(46598) lies on these lines: {2, 3}, {99, 3222}, {110, 30254}, {669, 2396}, {17938, 17941}, {21006, 23342}

X(46598) = crosssum of X(804) and X(23301)


X(46599) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(671)

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

X(46599) lies on these lines: {2, 3}, {187, 5968}, {2079, 33900}, {3455, 34010}, {11643, 23288}, {14263, 40350}, {14995, 26613}, {21445, 34810}

X(46599) = circumcircle-inverse of X(36196)
X(46599) = crosssum of X(i) and X(j) for these (i,j): {125, 33921}, {543, 625}


X(46600) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(6189)

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

X(46600) lies on these lines: {2, 3}, {110, 1380}, {323, 38597}, {669, 30509}, {1340, 5640}, {1341, 15080}, {1379, 15107}, {1634, 6189}, {3060, 3557}, {3414, 36829}, {3558, 11422}, {5012, 14631}, {5201, 6190}, {6141, 11673}, {14630, 15019}

X(46600) = crosssum of X(512) and X(13636)
X(46600) = crossdifference of every pair of points on line {647, 13722}
X(46600) = barycentric product X(3557)*X(6189)
X(46600) = barycentric quotient X(i)/X(j) for these {i,j}: {1380, 6177}, {3557, 3414}
X(46600) = {X(2),X(237)}-harmonic conjugate of X(46601)
X(46600) = {X(3),X(23)}-harmonic conjugate of X(46601)


X(46601) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(6190)

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

X(46601) lies on these lines: {2, 3}, {110, 1379}, {323, 38596}, {669, 30508}, {1340, 15080}, {1341, 5640}, {1380, 15107}, {1634, 6190}, {3060, 3558}, {3413, 36829}, {3557, 11422}, {5012, 14630}, {5201, 6189}, {6142, 11673}, {14631, 15019}

X(46601) = crosssum of X(512) and X(13722)
X(46601) = crossdifference of every pair of points on line {647, 13636}
X(46601) = barycentric product X(3558)*X(6190)
X(46601) = barycentric quotient X(i)/X(j) for these {i,j}: {1379, 6178}, {3558, 3413}
X(46601) = {X(2),X(237)}-harmonic conjugate of X(46600)
X(46601) = {X(3),X(23)}-harmonic conjugate of X(46600)


X(46602) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(43091)

Barycentrics    a^2*(4*a^10 - 7*a^8*b^2 + a^6*b^4 - a^4*b^6 + 7*a^2*b^8 - 4*b^10 - 7*a^8*c^2 + 16*a^6*b^2*c^2 - 4*a^4*b^4*c^2 - 10*a^2*b^6*c^2 + 5*b^8*c^2 + a^6*c^4 - 4*a^4*b^2*c^4 + 8*a^2*b^4*c^4 - b^6*c^4 - a^4*c^6 - 10*a^2*b^2*c^6 - b^4*c^6 + 7*a^2*c^8 + 5*b^2*c^8 - 4*c^10) : :

X(46602) lies on these lines: {2, 3}, {1495, 33927}, {5467, 15107}, {6800, 14687}, {9717, 35265}, {15080, 46127}


X(46603) = ISOGONAL CONJUGATE OF X(9512)

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

See Antreas Hatzipolakis and César Lozada, euclid 3864.

X(46603) lies on these lines: {3448, 14721}, {5012, 36830}, {9513, 9514}, {21243, 44155}

X(46603) = isogonal conjugate of X(9512)
X(46603) = isotomic conjugate of X(46247)
X(46603) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 9514}, {1577, 46248}
X(46603) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (54, 39843), (110, 9514), (1576, 46248)
X(46603) = cevapoint of PU(145)
X(46603) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(5012)}} and {{A, B, C, X(3), X(41203)}}
X(46603) = barycentric product X(110)*X(46246)
X(46603) = barycentric quotient X(i)/X(j) for these (i, j): (54, 39843), (110, 9514), (1576, 46248)
X(46603) = trilinear product X(163)*X(46246)
X(46603) = trilinear quotient X(i)/X(j) for these (i, j): (163, 46248), (662, 9514), (2167, 39843)


X(46604) = X(311)X(930)∩X(570)X(8603)

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

See Antreas Hatzipolakis and César Lozada, euclid 3864.

X(46604) lies on these lines: {140, 21394}, {311, 930}, {570, 8603}, {34507, 39171}

X(46604) = center of the circumconic {{A, B, C, X(930), X(32737)}}
X(46604) = center of the perspeconic of these triangles: ABC and Kosnita


X(46605) = (name pending)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 3882.

X(46605) lies on these lines: { }

X(46605) = cevapoint of X(119) and X(650)


X(46606) = X(2)X(14265)∩X(2421)X(4226)

Barycentrics    (a^2-b^2)(a^2-c^2)(a^6 b^2-3 a^4 b^4+3 a^2 b^6-b^8+3 a^6 c^2-3 a^4 b^2 c^2+a^2 b^4 c^2+3 b^6 c^2-2 a^4 c^4-3 a^2 b^2 c^4-3 b^4 c^4+3 a^2 c^6+b^2 c^6) (3 a^6 b^2-2 a^4 b^4+3 a^2 b^6+a^6 c^2-3 a^4 b^2 c^2-3 a^2 b^4 c^2+b^6 c^2-3 a^4 c^4+a^2 b^2 c^4-3 b^4 c^4+3 a^2 c^6+3 b^2 c^6-c^8) : :
Barycentrics    (SA-SB) (SA-SC) (-2 S^4-S^2 (2 SC-SW) SW+SC^2 SW^2) (2 S^4+2 S^2 SB SW+SW^2 (SB SC+SC^2+SA SW-SW^2)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3882.

X(46606) lies on the curve Q066 and these lines: {2,14265}, {147,34174}, {2421,4226}, {5968,7736}, {25046,46039}, {35910,35922}

X(46606) = isotomic conjugate of the anticomplement of X(2395)
X(46606) = X(2395)-cross conjugate of X(2)
X(46606) = X(i)-vertex conjugate of X(j) for these (i,j): (4226,4230) ,(4230,4226)
X(46606) = cevapoint of X(i)and X(j) for these {i,j}: {114,523}, {512,11672}
X(46606) = trilinear pole of line X(230)X(511) (the axis of parabola {{A,B,C,X(511),X(805)}}, and the Simson line of X(115) wrt the medial triangle)
X(46606) = barycentric product X(290)*X(43942)
X(46606) = trilinear product X(1821)*X(43942)


X(46607) = (name pending)

Barycentrics    (a^2-b^2)(a^2-c^2)(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+5 a^10 b^2 c^2-4 a^8 b^4 c^2-12 a^6 b^6 c^2+25 a^4 b^8 c^2-17 a^2 b^10 c^2+4 b^12 c^2+3 a^10 c^4-7 a^8 b^2 c^4+16 a^6 b^4 c^4-32 a^4 b^6 c^4+25 a^2 b^8 c^4-5 b^10 c^4-2 a^8 c^6+2 a^6 b^2 c^6+16 a^4 b^4 c^6-12 a^2 b^6 c^6-2 a^6 c^8-7 a^4 b^2 c^8-4 a^2 b^4 c^8+5 b^6 c^8+3 a^4 c^10+5 a^2 b^2 c^10-4 b^4 c^10-a^2 c^12+b^2 c^12) (a^12 b^2-3 a^10 b^4+2 a^8 b^6+2 a^6 b^8-3 a^4 b^10+a^2 b^12-a^12 c^2-5 a^10 b^2 c^2+7 a^8 b^4 c^2-2 a^6 b^6 c^2+7 a^4 b^8 c^2-5 a^2 b^10 c^2-b^12 c^2+4 a^10 c^4+4 a^8 b^2 c^4-16 a^6 b^4 c^4-16 a^4 b^6 c^4+4 a^2 b^8 c^4+4 b^10 c^4-5 a^8 c^6+12 a^6 b^2 c^6+32 a^4 b^4 c^6+12 a^2 b^6 c^6-5 b^8 c^6-25 a^4 b^2 c^8-25 a^2 b^4 c^8+5 a^4 c^10+17 a^2 b^2 c^10+5 b^4 c^10-4 a^2 c^12-4 b^2 c^12+c^14) : :
Barycentrics    (SA-SB) (SA-SC) (S^2 (-13 R^2+SA)+36 R^4 SB-3 R^2 SB^2-SB^3+18 R^2 SA SC-2 SA^2 SC-SA SC^2+SB SC^2) (S^2 (5 R^2-SW)+SC (36 R^4+15 R^2 SC-18 R^2 SW-3 SC SW+2 SW^2)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3882.

X(46607) lies on these lines: { }

X(46607) = cevapoint of X(113) and X(647)
X(46607) = trilinear pole of line X(30)X(974) (the Simson line of X(125) wrt the orthic triangle)


X(46608) = CROSSPOINT OF X(74) AND X(476)

Barycentrics    a^2*(b^2 - c^2)*(a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8 - 4*a^8*c^2 + 7*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 + 6*a^6*c^4 - 5*a^4*b^2*c^4 - 6*a^2*b^4*c^4 + 3*b^6*c^4 - 4*a^4*c^6 + 5*a^2*b^2*c^6 + 3*b^4*c^6 + a^2*c^8 - 3*b^2*c^8) : :
X(46608) = 4 X[8562] - 3 X[34291]

X(46608) lies on the cubic K723 and these lines: {3, 523}, {74, 526}, {157, 669}, {186, 18808}, {476, 10412}, {512, 4550}, {520, 7689}, {924, 3357}, {1510, 15062}, {1609, 45801}, {2433, 11074}, {3005, 5888}, {3050, 18573}, {3098, 8675}, {5961, 13289}, {7691, 14329}, {8057, 9938}, {8266, 45839}, {9003, 32305}, {9033, 12901}, {14977, 35296}, {16868, 34963}, {18310, 37344}

X(46608) = reflection of X(3) in X(14809)
X(46608) = circumcircle-inverse of X(46632)
X(46608) = X(39290)-Ceva conjugate of X(6)
X(46608) = crosspoint of X(i) and X(j) for these (i,j): {74, 476}, {1304, 38534}
X(46608) = crosssum of X(i) and X(j) for these (i,j): {30, 526}, {512, 6128}, {523, 20304}, {2072, 9033}
X(46608) = crossdifference of every pair of points on line {3003, 3163}


X(46609) = CROSSPOINT OF X(99) AND X(842)

Barycentrics    a^2*(b^2 - 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 + 5*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 + 5*a^2*b^2*c^4 + a^2*c^6 - 3*b^2*c^6) : :
X(46609) = 3 X[3] - 2 X[44821], X[44821] - 3 X[44822], 4 X[44821] - 3 X[44823], 4 X[44822] - X[44823]

X(46609) lies on these lines: {3, 523}, {6, 39495}, {22, 669}, {23, 9168}, {25, 10190}, {26, 32204}, {99, 670}, {159, 3566}, {511, 8723}, {512, 3098}, {690, 11616}, {842, 7418}, {1499, 33532}, {1649, 1995}, {2422, 3094}, {2793, 44826}, {2799, 14270}, {3050, 44453}, {3534, 25423}, {5466, 7496}, {7484, 10278}, {7485, 8029}, {7492, 44010}, {8266, 21395}, {8371, 40916}, {9479, 41078}, {9723, 22089}, {10189, 16419}, {10280, 13154}, {23301, 31152}, {39513, 39560}

X(46609) = reflection of X(i) in X(j) for these {i,j}: {3, 44822}, {6, 39495}, {44823, 3}
X(46609) = reflection of X(44823) in the Euler line
X(46609) = circumcircle-inverse of X(46634)
X(46609) = X(6035)-Ceva conjugate of X(6)
X(46609) = crosspoint of X(99) and X(842)
X(46609) = crosssum of X(512) and X(542)
X(46609) = crossdifference of every pair of points on line {1084, 3003}


X(46610) = CROSSPOINT OF X(104) AND X(1290)

Barycentrics    a*(b - c)*(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 + a*b^3*c^2 + a*b^2*c^3 - 2*b^3*c^3 + a^2*c^4 - 2*a*b*c^4 + b*c^5) : :
X(46610) = 3 X[39478] - 2 X[44805], X[44805] - 3 X[44807]

X(46610) lies on these lines: {1, 13868}, {3, 523}, {104, 900}, {513, 1385}, {659, 1623}, {1290, 13589}, {2320, 4367}, {2605, 21842}, {3733, 11101}, {12262, 15313}, {13743, 28217}, {27685, 31946}, {39478, 44805}

X(46610) = reflection of X(39478) in X(44807)
X(46610) = circumcircle-inverse of X(46636)
X(46610) = crosspoint of X(104) and X(1290)
X(46610) = crosssum of X(i) and X(j) for these (i,j): {517, 8674}, {8677, 18455}
X(46610) = crossdifference of every pair of points on line {3003, 23980}


X(46611) = CROSSPOINT OF X(100) AND X(2687)

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

X(46611) lies on these lines: {3, 523}, {100, 190}, {513, 3579}, {526, 12778}, {2605, 5697}, {2687, 14127}, {2804, 39478}, {3733, 37405}, {3737, 11010}, {8674, 44812}, {15313, 40660}, {16117, 28217}, {27553, 31946}

X(46611) = circumcircle-inverse of X(46635)
X(46611) = crosspoint of X(100) and X(2687)
X(46611) = crosssum of X(i) and X(j) for these (i,j): {512, 3013}, {513, 2771}
X(46611) = crossdifference of every pair of points on line {1015, 3003}


X(46612) = CROSSPOINT OF X(1294) AND X(1304)

Barycentrics    a^2*(b^2 - c^2)*(a^16 - 5*a^14*b^2 + 9*a^12*b^4 - 5*a^10*b^6 - 5*a^8*b^8 + 9*a^6*b^10 - 5*a^4*b^12 + a^2*b^14 - 5*a^14*c^2 + 21*a^12*b^2*c^2 - 29*a^10*b^4*c^2 + 7*a^8*b^6*c^2 + 17*a^6*b^8*c^2 - 13*a^4*b^10*c^2 + a^2*b^12*c^2 + b^14*c^2 + 9*a^12*c^4 - 29*a^10*b^2*c^4 + 50*a^8*b^4*c^4 - 34*a^6*b^6*c^4 - 11*a^4*b^8*c^4 + 15*a^2*b^10*c^4 - 5*a^10*c^6 + 7*a^8*b^2*c^6 - 34*a^6*b^4*c^6 + 58*a^4*b^6*c^6 - 17*a^2*b^8*c^6 - 9*b^10*c^6 - 5*a^8*c^8 + 17*a^6*b^2*c^8 - 11*a^4*b^4*c^8 - 17*a^2*b^6*c^8 + 16*b^8*c^8 + 9*a^6*c^10 - 13*a^4*b^2*c^10 + 15*a^2*b^4*c^10 - 9*b^6*c^10 - 5*a^4*c^12 + a^2*b^2*c^12 + a^2*c^14 + b^2*c^14) : :

X(46612) lies on these lines: {3, 523}, {26, 8057}, {159, 9007}, {206, 8675}, {520, 6759}, {526, 9934}, {1294, 6086}, {1304, 5502}, {9033, 13289}, {23286, 38808}

X(46612) = crosspoint of X(1294) and X(1304)
X(46612) = crosssum of X(i) and X(j) for these (i,j): {520, 34842}, {6000, 9033}
X(46612) = crossdifference of every pair of points on line {3003, 39008}


X(46613) = CROSSPOINT OF X(107) AND X(2693)

Barycentrics    a^2*(b^2 - c^2)*(a^16 - 5*a^14*b^2 + 9*a^12*b^4 - 5*a^10*b^6 - 5*a^8*b^8 + 9*a^6*b^10 - 5*a^4*b^12 + a^2*b^14 - 5*a^14*c^2 + 17*a^12*b^2*c^2 - 25*a^10*b^4*c^2 + 27*a^8*b^6*c^2 - 23*a^6*b^8*c^2 + 7*a^4*b^10*c^2 + 5*a^2*b^12*c^2 - 3*b^14*c^2 + 9*a^12*c^4 - 25*a^10*b^2*c^4 + 6*a^8*b^4*c^4 + 6*a^6*b^6*c^4 + 29*a^4*b^8*c^4 - 29*a^2*b^10*c^4 + 4*b^12*c^4 - 5*a^10*c^6 + 27*a^8*b^2*c^6 + 6*a^6*b^4*c^6 - 62*a^4*b^6*c^6 + 23*a^2*b^8*c^6 + 11*b^10*c^6 - 5*a^8*c^8 - 23*a^6*b^2*c^8 + 29*a^4*b^4*c^8 + 23*a^2*b^6*c^8 - 24*b^8*c^8 + 9*a^6*c^10 + 7*a^4*b^2*c^10 - 29*a^2*b^4*c^10 + 11*b^6*c^10 - 5*a^4*c^12 + 5*a^2*b^2*c^12 + 4*b^4*c^12 + a^2*c^14 - 3*b^2*c^14) : :

X(46613) lies on these lines: {3, 523}, {107, 1624}, {520, 3357}, {8057, 12084}, {9033, 13293}, {14380, 38937}

X(46613) = crosspoint of X(107) and X(2693)
X(46613) = crosssum of X(520) and X(2777)
X(46613) = crossdifference of every pair of points on line {3003, 35071}


X(46614) = CROSSPOINT OF X(935) AND X(1297)

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

X(46614) lies on these lines: {3, 523}, {161, 23616}, {525, 15577}, {684, 1297}, {935, 46592}, {2799, 39854}, {3265, 26283}

X(46614) = circumcircle-inverse of X(46631)
X(46614) = crosspoint of X(935) and X(1297)
X(46614) = crosssum of X(1503) and X(9517)
X(46614) = crossdifference of every pair of points on line {3003, 23976}


X(46615) = CROSSPOINT OF X(112) AND X(2697)

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

X(46615) lies on these lines: {3, 523}, {25, 6587}, {112, 1576}, {157, 21397}, {206, 512}, {525, 44883}, {571, 42658}, {1968, 2485}, {2697, 46594}, {2799, 39860}, {2848, 44806}, {9178, 41890}, {25644, 34217}

X(46615) = circumcircle-inverse of X(46637)
X(46615) = crosspoint of X(112) and X(2697)
X(46615) = crosssum of X(525) and X(2781)
X(46615) = crossdifference of every pair of points on line {3003, 15526}


X(46616) = CROSSPOINT OF X(110) AND X(477)

Barycentrics    a^2*(b^2 - c^2)*(a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8 - 4*a^8*c^2 + 11*a^6*b^2*c^2 - 9*a^4*b^4*c^2 + a^2*b^6*c^2 + b^8*c^2 + 6*a^6*c^4 - 9*a^4*b^2*c^4 + 6*a^2*b^4*c^4 - b^6*c^4 - 4*a^4*c^6 + a^2*b^2*c^6 - b^4*c^6 + a^2*c^8 + b^2*c^8) : :
X(46616) = 3 X[3] - 2 X[14809], 4 X[8562] - X[14380], 2 X[39477] - 3 X[44808]

X(46616) lies on these lines: {3, 523}, {54, 8562}, {110, 351}, {182, 8675}, {477, 16171}, {512, 8717}, {520, 1147}, {647, 5063}, {924, 6759}, {1510, 8718}, {2436, 32663}, {3520, 18808}, {5926, 15577}, {8057, 9932}, {9003, 12584}, {9033, 12893}, {13293, 13496}, {22962, 37084}

X(46616) = circumcircle-inverse of X(14934)
X(46616) = X(30528)-Ceva conjugate of X(6)
X(46616) = crosspoint of X(110) and X(477)
X(46616) = crosssum of X(i) and X(j) for these (i,j): {512, 3018}, {523, 5663}
X(46616) = crossdifference of every pair of points on line {115, 3003}
X(46616) = barycentric product X(525)*X(15463)
X(46616) = barycentric quotient X(15463)/X(648)


X(46617) = EULER LINE INTERCEPT OF X(542)X(3416)

Barycentrics    2 a^7+3 a^6 b+2 a^5 b^2-a^4 b^3-4 a^3 b^4-a^2 b^5-b^7+3 a^6 c+8 a^5 b c-7 a^3 b^3 c-3 a^2 b^4 c-a b^5 c+2 a^5 c^2-4 a^3 b^2 c^2-4 a^2 b^3 c^2+2 b^5 c^2-a^4 c^3-7 a^3 b c^3-4 a^2 b^2 c^3+2 a b^3 c^3-b^4 c^3-4 a^3 c^4-3 a^2 b c^4-b^3 c^4-a^2 c^5-a b c^5+2 b^2 c^5-c^7 : :
X(46617) = 3*X(5055)-2*X(38330)

As a point on the Euler line, X(46617) has Shinagawa coefficients (r*R+2s^2,3*(r^2+r*R-s^2)) .

See Kadir Altintas and Ercole Suppa, Euclid 3886 .

X(46617) lies on these lines: {2,3}, {542,3416}, {34773,39766}

X(46617) = reflection of X(3) in X(38430)


X(46618) = MIDPOINT OF X(104) AND X(2687)

Barycentrics    a*(a^12 - a^11*b - 3*a^10*b^2 + 3*a^9*b^3 + 2*a^8*b^4 - 2*a^7*b^5 + 2*a^6*b^6 - 2*a^5*b^7 - 3*a^4*b^8 + 3*a^3*b^9 + a^2*b^10 - a*b^11 - a^11*c + 5*a^10*b*c - a^9*b^2*c - 9*a^8*b^3*c + 7*a^7*b^4*c - 2*a^6*b^5*c - 5*a^5*b^6*c + 10*a^4*b^7*c - 2*a^3*b^8*c - 3*a^2*b^9*c + 2*a*b^10*c - b^11*c - 3*a^10*c^2 - a^9*b*c^2 + 13*a^8*b^2*c^2 - 6*a^7*b^3*c^2 - 12*a^6*b^4*c^2 + 14*a^5*b^5*c^2 - 2*a^4*b^6*c^2 - 6*a^3*b^7*c^2 + 3*a^2*b^8*c^2 - a*b^9*c^2 + b^10*c^2 + 3*a^9*c^3 - 9*a^8*b*c^3 - 6*a^7*b^2*c^3 + 25*a^6*b^3*c^3 - 7*a^5*b^4*c^3 - 14*a^4*b^5*c^3 + 12*a^3*b^6*c^3 - 5*a^2*b^7*c^3 - 2*a*b^8*c^3 + 3*b^9*c^3 + 2*a^8*c^4 + 7*a^7*b*c^4 - 12*a^6*b^2*c^4 - 7*a^5*b^3*c^4 + 18*a^4*b^4*c^4 - 7*a^3*b^5*c^4 - 4*a^2*b^6*c^4 + 7*a*b^7*c^4 - 4*b^8*c^4 - 2*a^7*c^5 - 2*a^6*b*c^5 + 14*a^5*b^2*c^5 - 14*a^4*b^3*c^5 - 7*a^3*b^4*c^5 + 16*a^2*b^5*c^5 - 5*a*b^6*c^5 - 2*b^7*c^5 + 2*a^6*c^6 - 5*a^5*b*c^6 - 2*a^4*b^2*c^6 + 12*a^3*b^3*c^6 - 4*a^2*b^4*c^6 - 5*a*b^5*c^6 + 6*b^6*c^6 - 2*a^5*c^7 + 10*a^4*b*c^7 - 6*a^3*b^2*c^7 - 5*a^2*b^3*c^7 + 7*a*b^4*c^7 - 2*b^5*c^7 - 3*a^4*c^8 - 2*a^3*b*c^8 + 3*a^2*b^2*c^8 - 2*a*b^3*c^8 - 4*b^4*c^8 + 3*a^3*c^9 - 3*a^2*b*c^9 - a*b^2*c^9 + 3*b^3*c^9 + a^2*c^10 + 2*a*b*c^10 + b^2*c^10 - a*c^11 - b*c^11) : :

X(46618) lies on these lines: {2, 3}, {36, 29008}, {74, 6003}, {104, 523}, {477, 759}, {517, 31523}, {915, 2694}, {1290, 38693}, {2693, 39439}, {2695, 14987}, {2716, 43655}, {2829, 5520}, {6713, 42422}, {32710, 39435}

X(46618) = midpoint of X(i) and X(j) for these {i,j}: {20, 36175}, {104, 2687}, {1325, 6909}
X(46618) = reflection of X(i) in X(j) for these {i,j}: {1532, 44898}, {36167, 3}, {42422, 6713}
X(46618) = circumcircle-inverse of X(14127)


X(46619) = MIDPOINT OF X(112) AND X(935)

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

X(46619) lies on these lines: {2, 3}, {99, 250}, {107, 10098}, {112, 523}, {476, 39382}, {691, 1289}, {1296, 22239}, {1301, 2696}, {1304, 30247}, {1554, 2777}, {2697, 38699}, {2794, 42426}, {6720, 38971}, {10420, 30251}, {34978, 39832}

X(46619) = midpoint of X(112) and X(935)
X(46619) = reflection of X(38971) in X(6720)
X(46619) = circumcircle-inverse of X(46592)
X(46619) = isogonal conjugate of orthocenter of X(4)X(6)X(67)
X(46619) = Euler line intercept, other than X(2), of circle {{X(2),X(107),X(112)}}


X(46620) = MIDPOINT OF X(1297) AND X(2697)

Barycentrics    2*a^20 - 4*a^18*b^2 - a^16*b^4 + 3*a^14*b^6 + 3*a^12*b^8 + 3*a^10*b^10 - 11*a^8*b^12 + a^6*b^14 + 7*a^4*b^16 - 3*a^2*b^18 - 4*a^18*c^2 + 14*a^16*b^2*c^2 - 7*a^14*b^4*c^2 - 7*a^12*b^6*c^2 - 9*a^10*b^8*c^2 + 11*a^8*b^10*c^2 + 15*a^6*b^12*c^2 - 17*a^4*b^14*c^2 + 5*a^2*b^16*c^2 - b^18*c^2 - a^16*c^4 - 7*a^14*b^2*c^4 + 10*a^12*b^4*c^4 + 6*a^10*b^6*c^4 - a^8*b^8*c^4 - 11*a^6*b^10*c^4 + 4*a^4*b^12*c^4 - 4*a^2*b^14*c^4 + 4*b^16*c^4 + 3*a^14*c^6 - 7*a^12*b^2*c^6 + 6*a^10*b^4*c^6 + 2*a^8*b^6*c^6 - 5*a^6*b^8*c^6 - 7*a^4*b^10*c^6 + 12*a^2*b^12*c^6 - 4*b^14*c^6 + 3*a^12*c^8 - 9*a^10*b^2*c^8 - a^8*b^4*c^8 - 5*a^6*b^6*c^8 + 26*a^4*b^8*c^8 - 10*a^2*b^10*c^8 - 4*b^12*c^8 + 3*a^10*c^10 + 11*a^8*b^2*c^10 - 11*a^6*b^4*c^10 - 7*a^4*b^6*c^10 - 10*a^2*b^8*c^10 + 10*b^10*c^10 - 11*a^8*c^12 + 15*a^6*b^2*c^12 + 4*a^4*b^4*c^12 + 12*a^2*b^6*c^12 - 4*b^8*c^12 + a^6*c^14 - 17*a^4*b^2*c^14 - 4*a^2*b^4*c^14 - 4*b^6*c^14 + 7*a^4*c^16 + 5*a^2*b^2*c^16 + 4*b^4*c^16 - 3*a^2*c^18 - b^2*c^18 : :

X(46620) lies on these lines: {2, 3}, {523, 1297}, {842, 34168}, {935, 38717}, {1554, 5972}, {2373, 2693}, {2770, 5897}, {32710, 39436}, {34841, 42426}, {39434, 40119}

X(46620) = midpoint of X(i) and X(j) for these {i,j}: {1297, 2697}
X(46620) = reflection of X(i) in X(j) for these {i,j}: {1529, 5159}, {1554, 5972}, {42426, 34841}
X(46620) = circumcircle-inverse of X(46594)


X(46621) = X(4)X(371)∩X(54)X(216)

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

See Antreas Hatzipolakis and Peter Moses, euclid 3903.

X(46621) is closely related to X(46622).

X(46621) lies on these lines: {4, 371}, {54, 216}, {186, 8954}, {324, 16032}, {1151, 10605}, {1199, 32589}, {1589, 6515}, {1599, 8909}, {3090, 10960}, {3156, 3311}, {3364, 46112}, {3389, 46113}, {5012, 8961}, {6200, 6458}, {6419, 26894}, {6425, 12964}, {8908, 11463}, {8963, 43651}, {18909, 44616}, {21640, 26916}

X(46621) = X(13450)-Ceva conjugate of X(46622)
X(46621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 216, 46622), (371, 6413, 4)


X(46622) = X(4)X(372)∩X(54)X(216)

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

X(46622) is closely related to X(46621).

X(46622) lies on these lines: {4, 372}, {54, 216}, {186, 32589}, {324, 16037}, {1152, 10605}, {1199, 8954}, {1590, 6515}, {3090, 10962}, {3155, 3312}, {3365, 46112}, {3390, 46113}, {6396, 6457}, {6420, 26919}, {6426, 12970}, {8961, 34148}, {18909, 44617}

X(46622) = X(13450)-Ceva conjugate of X(46621)
X(46622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {54, 216, 46621}, {372, 6414, 4}


X(46623) = X(1)X(3)∩X(4)X(25446)

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

X(46623) lies on the cubic K1256 and these lines: {1, 3}, {4, 25446}, {20, 19642}, {58, 37425}, {184, 23059}, {185, 411}, {283, 851}, {404, 5650}, {511, 3651}, {573, 19548}, {580, 4192}, {582, 19543}, {1006, 15488}, {1150, 5178}, {1408, 15447}, {1444, 5929}, {1792, 10381}, {2328, 28258}, {3781, 25440}, {3917, 35976}, {4220, 35203}, {5752, 6102}, {5907, 6905}, {5972, 24882}, {6045, 7580}, {9306, 37264}, {13323, 37400}, {13329, 19513}, {18180, 37286}, {19771, 20846}, {21363, 36558}, {22076, 35979}, {37510, 37732}

X(46623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 45923, 1385}


X(46624) = X(1885)-CEVA CONJUGATE OF X(4)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(3*a^12 - 7*a^10*b^2 - a^8*b^4 + 14*a^6*b^6 - 11*a^4*b^8 + a^2*b^10 + b^12 - 7*a^10*c^2 + 37*a^8*b^2*c^2 - 42*a^6*b^4*c^2 - 2*a^4*b^6*c^2 + 17*a^2*b^8*c^2 - 3*b^10*c^2 - a^8*c^4 - 42*a^6*b^2*c^4 + 74*a^4*b^4*c^4 - 18*a^2*b^6*c^4 + 3*b^8*c^4 + 14*a^6*c^6 - 2*a^4*b^2*c^6 - 18*a^2*b^4*c^6 - 2*b^6*c^6 - 11*a^4*c^8 + 17*a^2*b^2*c^8 + 3*b^4*c^8 + a^2*c^10 - 3*b^2*c^10 + c^12) : :

X(46624) lies on the cubic K1256 and these lines: {4, 40196}, {20, 3186}, {378, 3462}, {1249, 1968}, {3068, 26936}, {5254, 5894}, {5667, 18560}

X(46624) = X(1885)-Ceva conjugate of X(4)


X(46625) = X(20)X(3186)∩X(147)X(185)

Barycentrics    a^14*b^2 - 5*a^12*b^4 + 9*a^10*b^6 - 6*a^8*b^8 - a^6*b^10 + 3*a^4*b^12 - a^2*b^14 + a^14*c^2 + a^12*b^2*c^2 + a^10*b^4*c^2 - 13*a^8*b^6*c^2 + 15*a^6*b^8*c^2 - 5*a^4*b^10*c^2 - a^2*b^12*c^2 + b^14*c^2 - 5*a^12*c^4 + a^10*b^2*c^4 + a^8*b^4*c^4 - 2*a^6*b^6*c^4 - 13*a^4*b^8*c^4 + 5*a^2*b^10*c^4 - 3*b^12*c^4 + 9*a^10*c^6 - 13*a^8*b^2*c^6 - 2*a^6*b^4*c^6 + 14*a^4*b^6*c^6 - 3*a^2*b^8*c^6 + 3*b^10*c^6 - 6*a^8*c^8 + 15*a^6*b^2*c^8 - 13*a^4*b^4*c^8 - 3*a^2*b^6*c^8 - 2*b^8*c^8 - a^6*c^10 - 5*a^4*b^2*c^10 + 5*a^2*b^4*c^10 + 3*b^6*c^10 + 3*a^4*c^12 - a^2*b^2*c^12 - 3*b^4*c^12 - a^2*c^14 + b^2*c^14 : :

X(46625) lies on the Steiner/Wallace right hyperbola, the Kiepert circumhyperbola of the anticomplementary triangle, the cubic K1256, and these lines: {20, 3186}, {147, 185}, {2896, 8920}, {3504, 17928}, {6815, 45029}, {32974, 41914}


X(46626) = X(147)X(185)∩X(3493)X(8841)

Barycentrics    a^2*(a^18*b^2 - 3*a^16*b^4 + 3*a^14*b^6 - 3*a^12*b^8 + 6*a^10*b^10 - 6*a^8*b^12 + 3*a^6*b^14 - 3*a^4*b^16 + 3*a^2*b^18 - b^20 + a^18*c^2 - a^14*b^4*c^2 + 6*a^12*b^6*c^2 - 26*a^10*b^8*c^2 + 34*a^8*b^10*c^2 - 21*a^6*b^12*c^2 + 14*a^4*b^14*c^2 - 9*a^2*b^16*c^2 + 2*b^18*c^2 - 3*a^16*c^4 - a^14*b^2*c^4 + 14*a^12*b^4*c^4 - 23*a^10*b^6*c^4 + 25*a^8*b^8*c^4 - a^6*b^10*c^4 - 14*a^4*b^12*c^4 + 9*a^2*b^14*c^4 - 6*b^16*c^4 + 3*a^14*c^6 + 6*a^12*b^2*c^6 - 23*a^10*b^4*c^6 + 40*a^8*b^6*c^6 - 37*a^6*b^8*c^6 + 22*a^4*b^10*c^6 - 11*a^2*b^12*c^6 + 16*b^14*c^6 - 3*a^12*c^8 - 26*a^10*b^2*c^8 + 25*a^8*b^4*c^8 - 37*a^6*b^6*c^8 - 6*a^4*b^8*c^8 + 8*a^2*b^10*c^8 - 17*b^12*c^8 + 6*a^10*c^10 + 34*a^8*b^2*c^10 - a^6*b^4*c^10 + 22*a^4*b^6*c^10 + 8*a^2*b^8*c^10 + 12*b^10*c^10 - 6*a^8*c^12 - 21*a^6*b^2*c^12 - 14*a^4*b^4*c^12 - 11*a^2*b^6*c^12 - 17*b^8*c^12 + 3*a^6*c^14 + 14*a^4*b^2*c^14 + 9*a^2*b^4*c^14 + 16*b^6*c^14 - 3*a^4*c^16 - 9*a^2*b^2*c^16 - 6*b^4*c^16 + 3*a^2*c^18 + 2*b^2*c^18 - c^20) : :

X(46626) lies on the cubic K1256 and these lines: {147, 185}, {3493, 8841}


X(46627) = X(32)X(512)∩X(114)X(325)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^10*b^2 + 2*a^6*b^6 + a^2*b^10 + a^10*c^2 - 6*a^8*b^2*c^2 + a^6*b^4*c^2 - 5*a^4*b^6*c^2 - 2*a^2*b^8*c^2 - b^10*c^2 + a^6*b^2*c^4 + 8*a^4*b^4*c^4 + a^2*b^6*c^4 + 2*b^8*c^4 + 2*a^6*c^6 - 5*a^4*b^2*c^6 + a^2*b^4*c^6 - 2*b^6*c^6 - 2*a^2*b^2*c^8 + 2*b^4*c^8 + a^2*c^10 - b^2*c^10) : :
X(46627) = 3 X[9753] - X[13137]

X(46627) lies on the cubic K1257 and these lines: {32, 512}, {114, 325}, {2794, 44011}, {9753, 13137}, {32484, 35436}

X(46627) = crossdifference of every pair of points on line {325, 2422}


X(46628) = X(4)X(39299)∩X(114)X(4558)

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

X(46628) lies on the cubic K1257 and these lines: {4, 39299}, {114, 4558}, {230, 1313}, {511, 1114}, {1113, 44099}, {13414, 44127}

X(46628) = orthic-isogonal conjugate of X(13414)
X(46628) = X(4)-Ceva conjugate of X(13414)


X(46629) = X(4)X(39298)∩X(114)X(4558)

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

X(46629) lies on the cubic K1257 and these lines: {4, 39298}, {114, 4558}, {230, 1312}, {511, 1113}, {1114, 44099}, {13415, 44127}

X(46629) = orthic-isogonal conjugate of X(13415)
X(46629) = X(4)-Ceva conjugate of X(13415)


X(46630) = X(511)X(38642)∩X(1976)X(2396)

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

X(46630) lies on the cubic K1257 and these lines: {511, 38642}, {1976, 2396}


X(46631) = MIDPOINT OF X(935) AND X(1297)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^18 - 4*a^16*b^2 + a^14*b^4 + 2*a^12*b^6 - 5*a^10*b^8 + 8*a^8*b^10 - a^6*b^12 - 6*a^4*b^14 + 3*a^2*b^16 - 4*a^16*c^2 + 10*a^14*b^2*c^2 - 6*a^12*b^4*c^2 + a^10*b^6*c^2 - 5*a^8*b^8*c^2 - 4*a^6*b^10*c^2 + 16*a^4*b^12*c^2 - 7*a^2*b^14*c^2 - b^16*c^2 + a^14*c^4 - 6*a^12*b^2*c^4 + 10*a^10*b^4*c^4 - 3*a^8*b^6*c^4 - 5*a^6*b^8*c^4 - 8*a^4*b^10*c^4 + 6*a^2*b^12*c^4 + 5*b^14*c^4 + 2*a^12*c^6 + a^10*b^2*c^6 - 3*a^8*b^4*c^6 + 20*a^6*b^6*c^6 - 2*a^4*b^8*c^6 - 9*a^2*b^10*c^6 - 9*b^12*c^6 - 5*a^10*c^8 - 5*a^8*b^2*c^8 - 5*a^6*b^4*c^8 - 2*a^4*b^6*c^8 + 14*a^2*b^8*c^8 + 5*b^10*c^8 + 8*a^8*c^10 - 4*a^6*b^2*c^10 - 8*a^4*b^4*c^10 - 9*a^2*b^6*c^10 + 5*b^8*c^10 - a^6*c^12 + 16*a^4*b^2*c^12 + 6*a^2*b^4*c^12 - 9*b^6*c^12 - 6*a^4*c^14 - 7*a^2*b^2*c^14 + 5*b^4*c^14 + 3*a^2*c^16 - b^2*c^16) : :
X(46631) = X[2697] - 3 X[38717]

X(46631) lies on these lines: {3, 523}, {30, 935}, {339, 36166}, {2072, 38953}, {2697, 38717}, {10242, 18323}, {34841, 38971}, {38624, 46620}, {38741, 44246}

X(46631) = midpoint of X(935) and X(1297)
X(46631) = reflection of X(i) in X(j) for these {i,j}: {38971, 34841}, {46620, 38624}, {46637, 3}
X(46631) = reflection of X(46637) in the Euler line
X(46631) = circumcircle inverse of X(46614)


X(46632) = MIDPOINT OF X(74) AND X(476)

Barycentrics    2*a^16 - 6*a^14*b^2 + 3*a^12*b^4 + 5*a^10*b^6 - 12*a^6*b^10 + 11*a^4*b^12 - 3*a^2*b^14 - 6*a^14*c^2 + 22*a^12*b^2*c^2 - 21*a^10*b^4*c^2 - 15*a^8*b^6*c^2 + 40*a^6*b^8*c^2 - 24*a^4*b^10*c^2 + 3*a^2*b^12*c^2 + b^14*c^2 + 3*a^12*c^4 - 21*a^10*b^2*c^4 + 48*a^8*b^4*c^4 - 30*a^6*b^6*c^4 - 3*a^4*b^8*c^4 + 9*a^2*b^10*c^4 - 6*b^12*c^4 + 5*a^10*c^6 - 15*a^8*b^2*c^6 - 30*a^6*b^4*c^6 + 32*a^4*b^6*c^6 - 9*a^2*b^8*c^6 + 15*b^10*c^6 + 40*a^6*b^2*c^8 - 3*a^4*b^4*c^8 - 9*a^2*b^6*c^8 - 20*b^8*c^8 - 12*a^6*c^10 - 24*a^4*b^2*c^10 + 9*a^2*b^4*c^10 + 15*b^6*c^10 + 11*a^4*c^12 + 3*a^2*b^2*c^12 - 6*b^4*c^12 - 3*a^2*c^14 + b^2*c^14 : :
X(467632) = 3 X[74] - X[14508], X[110] - 3 X[38700], 3 X[476] + X[14508], X[477] - 3 X[15055], 2 X[546] - 3 X[21315], 2 X[3154] - 3 X[15061], 3 X[5627] - X[10733], 2 X[10264] - 3 X[40630], 4 X[12068] - 3 X[14643], X[14480] - 3 X[15035], 3 X[14644] - X[44967], 3 X[14993] + X[20127], 5 X[15021] + X[38677], 5 X[15040] - 2 X[30221], 3 X[15041] + X[38580], 3 X[15061] - X[20957], 2 X[16319] - 3 X[44214], 2 X[21269] - 3 X[34150], X[21269] - 3 X[34209], 2 X[31379] - 3 X[38727], 4 X[31945] - 5 X[38794]

X(46632) lies on the cubic K905 and these lines: {3, 523}, {5, 46045}, {30, 74}, {110, 38700}, {113, 22104}, {125, 36184}, {185, 36159}, {399, 3233}, {477, 15055}, {541, 1553}, {546, 21315}, {1511, 14611}, {1552, 11251}, {2072, 10745}, {2777, 25641}, {2780, 9179}, {3154, 15061}, {3258, 6699}, {3627, 21316}, {5663, 7471}, {6070, 17702}, {7728, 36169}, {10620, 36193}, {11657, 11799}, {12041, 16168}, {12068, 14643}, {12103, 21317}, {12236, 16978}, {12244, 36172}, {13630, 36161}, {14480, 15035}, {14644, 44967}, {14830, 44265}, {15021, 38677}, {15040, 30221}, {15041, 38580}, {16171, 39987}, {16319, 44214}, {31379, 38727}, {31945, 38794}, {36177, 40280}

X(46632) = midpoint of X(i) and X(j) for these {i,j}: {74, 476}, {10620, 36193}, {12244, 36172}, {14677, 18319}
X(46632) = reflection of X(i) in X(j) for these {i,j}: {113, 22104}, {265, 12079}, {399, 3233}, {3258, 6699}, {3627, 21316}, {7471, 38609}, {7728, 36169}, {11799, 11657}, {14611, 1511}, {14934, 3}, {16978, 12236}, {20957, 3154}, {21317, 12103}, {34150, 34209}, {36164, 12041}, {36184, 125}, {46045, 5}
X(46632) = reflection of X(14934) in the Euler line
X(46632) = circumcircle-inverse of X(46608)
X(46632) = {X(15061),X(20957)}-harmonic conjugate of X(3154)


X(46633) = MIDPOINT OF X(98) AND X(691)

Barycentrics    2*a^14 - 6*a^12*b^2 + 5*a^10*b^4 + 2*a^8*b^6 - 6*a^6*b^8 + 4*a^4*b^10 - a^2*b^12 - 6*a^12*c^2 + 18*a^10*b^2*c^2 - 18*a^8*b^4*c^2 + 15*a^6*b^6*c^2 - 9*a^4*b^8*c^2 + a^2*b^10*c^2 - b^12*c^2 + 5*a^10*c^4 - 18*a^8*b^2*c^4 + 3*a^4*b^6*c^4 + 5*a^2*b^8*c^4 + 3*b^10*c^4 + 2*a^8*c^6 + 15*a^6*b^2*c^6 + 3*a^4*b^4*c^6 - 10*a^2*b^6*c^6 - 2*b^8*c^6 - 6*a^6*c^8 - 9*a^4*b^2*c^8 + 5*a^2*b^4*c^8 - 2*b^6*c^8 + 4*a^4*c^10 + a^2*b^2*c^10 + 3*b^4*c^10 - a^2*c^12 - b^2*c^12 : :
X(46633) = X[23] - 3 X[21445], X[99] - 3 X[38702], X[842] - 3 X[34473], 2 X[14120] - 3 X[38224], 3 X[14639] - X[44969], 3 X[14651] - X[36174], 2 X[16320] - 3 X[44214], 2 X[16760] - 3 X[38737], 2 X[36180] - 3 X[38225]

X(46633) lies on these lines: {3, 523}, {23, 21445}, {30, 98}, {99, 38702}, {114, 40544}, {230, 11799}, {325, 15122}, {385, 7464}, {524, 11579}, {542, 9181}, {842, 34473}, {1499, 18332}, {2072, 10749}, {2420, 34369}, {2682, 33511}, {2782, 7472}, {2794, 16188}, {3398, 36157}, {3564, 15545}, {5099, 6036}, {5191, 7471}, {5663, 14999}, {6033, 36170}, {9155, 14611}, {9179, 15566}, {9862, 36173}, {10104, 36165}, {10796, 36183}, {12042, 36166}, {14120, 38224}, {14639, 44969}, {14651, 36174}, {14666, 44265}, {16320, 44214}, {16760, 38737}, {22104, 35282}, {23967, 25641}, {26316, 36177}, {32515, 37950}, {34209, 39295}, {34365, 43090}, {36180, 38225}, {38552, 46619}, {38553, 46620}

X(46633) = midpoint of X(i) and X(j) for these {i,j}: {98, 691}, {385, 7464}, {9862, 36173}, {38741, 38953}
X(46633) = reflection of X(i) in X(j) for these {i,j}: {114, 40544}, {325, 15122}, {2682, 33511}, {5099, 6036}, {6033, 36170}, {7472, 38611}, {11799, 230}, {36166, 12042}
X(46633) = circumcircle-inverse of X(44823)


X(46634) = MIDPOINT OF X(99) AND X(842)

Barycentrics    2*a^14 - 6*a^12*b^2 + 7*a^10*b^4 - 2*a^8*b^6 - 6*a^6*b^8 + 8*a^4*b^10 - 3*a^2*b^12 - 6*a^12*c^2 + 14*a^10*b^2*c^2 - 14*a^8*b^4*c^2 + 9*a^6*b^6*c^2 - 7*a^4*b^8*c^2 + 3*a^2*b^10*c^2 + b^12*c^2 + 7*a^10*c^4 - 14*a^8*b^2*c^4 + 12*a^6*b^4*c^4 - 3*a^4*b^6*c^4 - a^2*b^8*c^4 - 3*b^10*c^4 - 2*a^8*c^6 + 9*a^6*b^2*c^6 - 3*a^4*b^4*c^6 + 2*a^2*b^6*c^6 + 2*b^8*c^6 - 6*a^6*c^8 - 7*a^4*b^2*c^8 - a^2*b^4*c^8 + 2*b^6*c^8 + 8*a^4*c^10 + 3*a^2*b^2*c^10 - 3*b^4*c^10 - 3*a^2*c^12 + b^2*c^12 : :
X(46634) = X[98] - 3 X[38704], 3 X[186] - X[385], 2 X[230] - 3 X[44214], X[691] - 3 X[21166], 3 X[2072] - 4 X[44377], 3 X[15561] - 2 X[36170], 3 X[15561] - X[38953], 3 X[21445] - 5 X[37952], 3 X[38748] - 2 X[40544]

X(46634) lies on these lines: {3, 523}, {30, 99}, {98, 38704}, {115, 16760}, {186, 385}, {230, 44214}, {524, 3581}, {525, 18332}, {549, 16092}, {620, 16188}, {691, 21166}, {1511, 14999}, {2072, 44377}, {2080, 36180}, {2782, 36166}, {2967, 46619}, {3095, 36156}, {5099, 23698}, {5191, 14611}, {6023, 15452}, {6321, 14120}, {7471, 9155}, {7472, 33813}, {7575, 32515}, {7782, 38528}, {7789, 43090}, {11171, 36177}, {11649, 14962}, {11799, 16320}, {13172, 36174}, {15561, 36170}, {18579, 22329}, {21445, 37952}, {23967, 31378}, {30717, 34978}, {31859, 37930}, {38748, 40544}

X(46634) = midpoint of X(i) and X(j) for these {i,j}: {99, 842}, {13172, 36174}
X(46634) = reflection of X(i) in X(j) for these {i,j}: {115, 16760}, {2080, 36180}, {6321, 14120}, {7472, 33813}, {11799, 16320}, {14999, 1511}, {16092, 549}, {16188, 620}, {22329, 18579}, {36166, 38613}, {38953, 36170}
X(46634) = circumcircle-inverse of X(46609)
X(46634) = crossdifference of every pair of points on line {3003, 6041}
X(46634) = {X(15561),X(38953)}-harmonic conjugate of X(36170)


X(46635) = MIDPOINT OF X(100) AND X(2687)

Barycentrics    a*(a^12 - a^11*b - 3*a^10*b^2 + 3*a^9*b^3 + 2*a^8*b^4 - 2*a^7*b^5 + 2*a^6*b^6 - 2*a^5*b^7 - 3*a^4*b^8 + 3*a^3*b^9 + a^2*b^10 - a*b^11 - a^11*c + 3*a^10*b*c + a^9*b^2*c - 6*a^8*b^3*c + 3*a^7*b^4*c - 5*a^5*b^6*c + 6*a^4*b^7*c + 2*a^3*b^8*c - 3*a^2*b^9*c - 3*a^10*c^2 + a^9*b*c^2 + 9*a^8*b^2*c^2 - 6*a^7*b^3*c^2 - 8*a^6*b^4*c^2 + 10*a^5*b^5*c^2 + 2*a^4*b^6*c^2 - 6*a^3*b^7*c^2 - a^2*b^8*c^2 + a*b^9*c^2 + b^10*c^2 + 3*a^9*c^3 - 6*a^8*b*c^3 - 6*a^7*b^2*c^3 + 15*a^6*b^3*c^3 - a^5*b^4*c^3 - 9*a^4*b^5*c^3 + 2*a^3*b^6*c^3 + 2*a*b^8*c^3 + 2*a^8*c^4 + 3*a^7*b*c^4 - 8*a^6*b^2*c^4 - a^5*b^3*c^4 + 6*a^4*b^4*c^4 - a^3*b^5*c^4 + 3*a*b^7*c^4 - 4*b^8*c^4 - 2*a^7*c^5 + 10*a^5*b^2*c^5 - 9*a^4*b^3*c^5 - a^3*b^4*c^5 + 6*a^2*b^5*c^5 - 5*a*b^6*c^5 + 2*a^6*c^6 - 5*a^5*b*c^6 + 2*a^4*b^2*c^6 + 2*a^3*b^3*c^6 - 5*a*b^5*c^6 + 6*b^6*c^6 - 2*a^5*c^7 + 6*a^4*b*c^7 - 6*a^3*b^2*c^7 + 3*a*b^4*c^7 - 3*a^4*c^8 + 2*a^3*b*c^8 - a^2*b^2*c^8 + 2*a*b^3*c^8 - 4*b^4*c^8 + 3*a^3*c^9 - 3*a^2*b*c^9 + a*b^2*c^9 + a^2*c^10 + b^2*c^10 - a*c^11) : :
X(46635) = X[1290] - 3 X[34474]

X(46635) lies on these lines: {3, 523}, {30, 100}, {186, 1897}, {758, 12778}, {952, 46618}, {1290, 34474}, {2677, 17702}, {3035, 42422}, {3109, 11849}, {5520, 5840}, {13199, 36175}, {13869, 37535}, {33814, 36167}

X(46635) = midpoint of X(i) and X(j) for these {i,j}: {100, 2687}, {13199, 36175}
X(46635) = reflection of X(i) in X(j) for these {i,j}: {36167, 33814}, {42422, 3035}
X(46635) = circumcircle-inverse of X(46611)


X(46636) = MIDPOINT OF X(104) AND X(1290)

Barycentrics    a*(a^12 - a^11*b - 3*a^10*b^2 + 3*a^9*b^3 + 2*a^8*b^4 - 2*a^7*b^5 + 2*a^6*b^6 - 2*a^5*b^7 - 3*a^4*b^8 + 3*a^3*b^9 + a^2*b^10 - a*b^11 - a^11*c + 3*a^10*b*c + a^9*b^2*c - 6*a^8*b^3*c + a^7*b^4*c + a^5*b^6*c + 6*a^4*b^7*c - 4*a^3*b^8*c - 3*a^2*b^9*c + 2*a*b^10*c - 3*a^10*c^2 + a^9*b*c^2 + 9*a^8*b^2*c^2 - 4*a^7*b^3*c^2 - 8*a^6*b^4*c^2 + 6*a^5*b^5*c^2 - 4*a^3*b^7*c^2 + 3*a^2*b^8*c^2 + a*b^9*c^2 - b^10*c^2 + 3*a^9*c^3 - 6*a^8*b*c^3 - 4*a^7*b^2*c^3 + 15*a^6*b^3*c^3 - 3*a^5*b^4*c^3 - 9*a^4*b^5*c^3 + 8*a^3*b^6*c^3 - 4*a*b^8*c^3 + 2*a^8*c^4 + a^7*b*c^4 - 8*a^6*b^2*c^4 - 3*a^5*b^3*c^4 + 10*a^4*b^4*c^4 - 3*a^3*b^5*c^4 - 4*a^2*b^6*c^4 + a*b^7*c^4 + 4*b^8*c^4 - 2*a^7*c^5 + 6*a^5*b^2*c^5 - 9*a^4*b^3*c^5 - 3*a^3*b^4*c^5 + 6*a^2*b^5*c^5 + a*b^6*c^5 + 2*a^6*c^6 + a^5*b*c^6 + 8*a^3*b^3*c^6 - 4*a^2*b^4*c^6 + a*b^5*c^6 - 6*b^6*c^6 - 2*a^5*c^7 + 6*a^4*b*c^7 - 4*a^3*b^2*c^7 + a*b^4*c^7 - 3*a^4*c^8 - 4*a^3*b*c^8 + 3*a^2*b^2*c^8 - 4*a*b^3*c^8 + 4*b^4*c^8 + 3*a^3*c^9 - 3*a^2*b*c^9 + a*b^2*c^9 + a^2*c^10 + 2*a*b*c^10 - b^2*c^10 - a*c^11) : :
X(46636) = X[100] - 3 X[38711], X[2687] - 3 X[38693]

X(46636) lies on these lines: {3, 523}, {30, 104}, {100, 38711}, {952, 36167}, {1623, 7575}, {2072, 10746}, {2677, 6699}, {2687, 38693}, {2829, 42422}, {3109, 37535}, {5520, 6713}, {11849, 13869}, {32153, 36154}, {38602, 46618}

X(46636) = midpoint of X(104) and X(1290)
X(46636) = reflection of X(i) in X(j) for these {i,j}: {2677, 6699}, {5520, 6713}, {46618, 38602}
X(46636) = circumcircle-inverse of X(46610)


X(46637) = MIDPOINT OF X(112) AND X(2697)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^18 - 4*a^16*b^2 - a^14*b^4 + 6*a^12*b^6 - 3*a^10*b^8 + a^6*b^12 - 2*a^4*b^14 + a^2*b^16 - 4*a^16*c^2 + 14*a^14*b^2*c^2 - 10*a^12*b^4*c^2 - a^10*b^6*c^2 + 5*a^8*b^8*c^2 - 12*a^6*b^10*c^2 + 8*a^4*b^12*c^2 - a^2*b^14*c^2 + b^16*c^2 - a^14*c^4 - 10*a^12*b^2*c^4 + 10*a^10*b^4*c^4 - 5*a^8*b^6*c^4 + 25*a^6*b^8*c^4 - 8*a^4*b^10*c^4 - 6*a^2*b^12*c^4 - 5*b^14*c^4 + 6*a^12*c^6 - a^10*b^2*c^6 - 5*a^8*b^4*c^6 - 28*a^6*b^6*c^6 + 2*a^4*b^8*c^6 + 17*a^2*b^10*c^6 + 9*b^12*c^6 - 3*a^10*c^8 + 5*a^8*b^2*c^8 + 25*a^6*b^4*c^8 + 2*a^4*b^6*c^8 - 22*a^2*b^8*c^8 - 5*b^10*c^8 - 12*a^6*b^2*c^10 - 8*a^4*b^4*c^10 + 17*a^2*b^6*c^10 - 5*b^8*c^10 + a^6*c^12 + 8*a^4*b^2*c^12 - 6*a^2*b^4*c^12 + 9*b^6*c^12 - 2*a^4*c^14 - a^2*b^2*c^14 - 5*b^4*c^14 + a^2*c^16 + b^2*c^16) : :
X(46637) = X[935] - 3 X[38699]

X(46637) lies on these lines: {3, 523}, {30, 112}, {935, 38699}, {2071, 41676}, {2072, 6033}, {2794, 38971}, {5159, 9775}, {6720, 42426}, {38608, 46619}

X(46637) = midpoint of X(112) and X(2697)
X(46637) = reflection of X(i) in X(j) for these {i,j}: {42426, 6720}, {46619, 38608}
X(46637) = reflection of X(46631) in the Euler line
X(46637) = circumcircle-inverse of X(46615)


X(46638) = ISOGONAL CONJUGATE OF X(8610)

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

See Antreas Hatzipolakis and César Lozada, euclid 3914.

X(46638) lies on MacBeath circumconic and these lines: {6, 36791}, {110, 4248}, {145, 595}, {519, 15383}, {651, 3187}, {1332, 18743}, {1797, 2403}, {1813, 5435}, {2316, 39698}, {4558, 41629}, {7754, 43190}, {9059, 23644}

X(46638) = isogonal conjugate of X(8610)
X(46638) = isotomic conjugate of the anticomplement of X(3977)
X(46638) = Cevapoint of X(6) and X(519)
X(46638) = X(6)-cross conjugate of-X(15383)
X(46638) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 1739), (214, 17465)
X(46638) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1739}, {42, 16753}, {44, 39264}, {88, 23644}
X(46638) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 1739), (44, 17465), (81, 16753), (106, 39264)
X(46638) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(145)}} and {{A, B, C, X(6), X(16947)}}
X(46638) = trilinear pole of the line {3, 3667}
X(46638) = orthocorrespondent of X(121)
X(46638) = barycentric product X(69)*X(40101)
X(46638) = barycentric quotient X(i)/X(j) for these (i, j): (1, 1739), (44, 17465), (81, 16753), (106, 39264), (519, 121), (902, 23644)
X(46638) = trilinear product X(63)*X(40101)
X(46638) = trilinear quotient X(i)/X(j) for these (i, j): (2, 1739), (44, 23644), (86, 16753), (88, 39264), (519, 17465)


X(46639) = ISOGONAL CONJUGATE OF X(6587)

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

See Antreas Hatzipolakis and César Lozada, euclid 3914.

X(46639) lies on MacBeath circumconic and these lines: {6, 15394}, {64, 895}, {69, 14390}, {110, 1301}, {162, 13138}, {193, 253}, {394, 3343}, {459, 2986}, {520, 15384}, {648, 2404}, {1073, 1993}, {1332, 7259}, {1813, 5546}, {1992, 34403}, {2063, 40221}, {2987, 40318}, {3964, 14092}, {4563, 34211}, {8798, 15801}, {10733, 38956}, {11064, 46065}, {11441, 41085}, {12111, 39268}, {12164, 31942}, {12272, 33584}, {13157, 41628}, {14362, 36413}, {14379, 34148}, {15905, 46351}, {28785, 35602}, {34570, 37672}, {41679, 44769}

X(46639) = isogonal conjugate of X(6587)
X(46639) = isotomic conjugate of the polar conjugate of X(1301)
X(46639) = Cevapoint of X(i) and X(j) for these (i, j): {6, 520}, {58, 23090}, {112, 1301}, {521, 9119}
X(46639) = X(i)-cross conjugate of-X(j) for these (i, j): (6, 15384), (112, 110), (520, 15394), (1461, 662)
X(46639) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 17898), (125, 1562), (1511, 14345)
X(46639) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 17898}, {19, 8057}, {20, 661}, {37, 21172}, {57, 14308}
X(46639) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 17898), (25, 44705), (55, 14308), (58, 21172)
X(46639) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(2404)}} and {{A, B, C, X(6), X(2445)}}
X(46639) = trilinear pole of the line {3, 64} (the line through X(3) perpendicular to the trilinear polar of X(3))
X(46639) = 1st Saragossa point of X(32713)
X(46639) = orthocorrespondent of X(122)
X(46639) = barycentric product X(i)*X(j) for these {i, j}: {6, 44326}, {64, 99}, {69, 1301}, {107, 15394}, {109, 5931}, {110, 253}
X(46639) = barycentric quotient X(i)/X(j) for these (i, j): (1, 17898), (25, 44705), (55, 14308), (58, 21172), (64, 523), (99, 14615)
X(46639) = trilinear product X(i)*X(j) for these {i, j}: {31, 44326}, {63, 1301}, {64, 662}, {99, 2155}, {110, 2184}, {112, 19611}
X(46639) = trilinear quotient X(i)/X(j) for these (i, j): (2, 17898), (9, 14308), (19, 44705), (21, 14331), (48, 42658), (64, 661)


X(46640) = ISOGONAL CONJUGATE OF X(6588)

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

See Antreas Hatzipolakis and César Lozada, euclid 3914.

X(46640) lies on MacBeath circumconic and these lines: {{6, 23983}, {110, 7435}, {193, 1814}, {521, 15385}, {651, 2405}, {895, 43703}, {1783, 44765}, {1797, 42467}, {1813, 3882}, {1993, 23122}, {2988, 3187}, {2990, 6515}, {2991, 40318}, {8759, 12649}, {11609, 40454}

X(46640) = isogonal conjugate of X(6588)
X(46640) = isotomic conjugate of the polar conjugate of X(40097)
X(46640) = Cevapoint of X(i) and X(j) for these (i, j): {6, 521}, {520, 2092}, {522, 24005}, {650, 22760}
X(46640) = X(i)-cross conjugate of-X(j) for these (i, j): (6, 15385), (1415, 100)
X(46640) = X(9)-Dao conjugate of-X(21186)
X(46640) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 21186}, {123, 32674}, {197, 514}, {205, 693}
X(46640) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 21186), (100, 3436), (101, 1766), (108, 14257)
X(46640) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(2405)}} and {{A, B, C, X(81), X(32714)}}
X(46640) = trilinear pole of the line {3, 960}
X(46640) = orthocorrespondent of X(123)
X(46640) = barycentric product X(i)*X(j) for these {i, j}: {69, 40097}, {99, 43703}, {190, 42467}, {651, 34277}, {668, 3435}
X(46640) = barycentric quotient X(i)/X(j) for these (i, j): (1, 21186), (100, 3436), (101, 1766), (108, 14257), (109, 21147), (110, 16049)
X(46640) = trilinear product X(i)*X(j) for these {i, j}: {63, 40097}, {100, 42467}, {109, 34277}, {190, 3435}, {653, 39167}, {662, 43703}
X(46640) = trilinear quotient X(i)/X(j) for these (i, j): (2, 21186), (100, 1766), (101, 197), (109, 478), (162, 41364), (190, 3436)


X(46641) = X(2)X(3603)∩X(356)X(357)

Barycentrics    a*y*z*(x^2+x*(cos(C)*y+cos(B)*z)-y*z*cos(A)) : :, where x:y:z=cos(A/3) : :

See Antreas Hatzipolakis and César Lozada, euclid 3914.

X(46641) lies on these lines: {2, 3603}, {356, 357}

X(46641) = orthocorrespondent of X(357)


X(46642) = X(2)X(3602)∩X(356)X(1134)

Barycentrics    a*y*z*(x^2+x*(cos(C)*y+cos(B)*z)-y*z*cos(A)) : :, where x:y:z=cos(A/3-4*Pi/3) : :

See Antreas Hatzipolakis and César Lozada, euclid 3914.

X(46642) lies on these lines: {2, 3602}, {356, 1134}

X(46642) = orthocorrespondent of X(1134)


X(46643) = X(2)X(3604)∩X(1136)X(1137)

Barycentrics    a*y*z*(x^2+x*(cos(C)*y+cos(B)*z)-y*z*cos(A)) : :, where x:y:z=cos(A/3-2*Pi/3) : :

See Antreas Hatzipolakis and César Lozada, euclid 3914.

X(46643) lies on these lines: {2, 3604}, {1136, 1137}

X(46643) = orthocorrespondent of X(1136)


X(46644) = X(2)X(664)∩X(1155)X(1156)

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

See Antreas Hatzipolakis and César Lozada, euclid 3914.

X(46644) lies on these lines: {2, 664}, {1155, 1156}

X(46644) = X(1055)-isoconjugate-of-X(34919)
X(46644) = X(1156)-reciprocal conjugate of-X(34919)
X(46644) = trilinear pole of the line {8545, 14077}
X(46644) = orthocorrespondent of X(1156)
X(46644) = barycentric product X(i)*X(j) for these {i, j}: {1121, 8545}, {1996, 41798}
X(46644) = barycentric quotient X(i)/X(j) for these (i, j): (1156, 34919), (1996, 37780)
X(46644) = trilinear product X(i)*X(j) for these {i, j}: {1121, 37541}, {1156, 8545}, {1996, 4845}
X(46644) = trilinear quotient X(i)/X(j) for these (i, j): (1121, 34919), (1996, 1323)


X(46645) = X(67)X(32424)∩X(599)X(2549)

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

See Antreas Hatzipolakis and César Lozada, euclid 3915.

X(46645) lies on these lines: {67, 32424}, {599, 2549}, {5094, 22110}, {10130, 42850}

X(46645) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(67)}} and {{A, B, C, X(69), X(9164)}}


X(46646) = X(530)X(11119)∩X(5472)X(11080)

Barycentrics    -2*sqrt(3)*(8*a^14-19*(b^2+c^2)*a^12-(20*b^4+29*b^2*c^2+20*c^4)*a^10+4*(b^2+c^2)*(23*b^4-5*b^2*c^2+23*c^4)*a^8-5*(16*b^8+16*c^8-3*(5*b^4+7*b^2*c^2+5*c^4)*b^2*c^2)*a^6+(b^4-c^4)*(b^2-c^2)*(5*b^4-99*b^2*c^2+5*c^4)*a^4+5*(b^2-c^2)^4*(4*b^4+11*b^2*c^2+4*c^4)*a^2-6*(b^2+c^2)*(b^2-c^2)^6)*S+2*a^16-47*(b^2+c^2)*a^14+(161*b^4+187*b^2*c^2+161*c^4)*a^12-(b^2+c^2)*(178*b^4-121*b^2*c^2+178*c^4)*a^10-(26*b^8+26*c^8+(281*b^4+255*b^2*c^2+281*c^4)*b^2*c^2)*a^8+(b^2+c^2)*(197*b^8+197*c^8-(148*b^4+123*b^2*c^2+148*c^4)*b^2*c^2)*a^6-(b^2-c^2)^2*(139*b^8+139*c^8-4*(13*b^4+75*b^2*c^2+13*c^4)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)^3*(28*b^4-107*b^2*c^2+28*c^4)*a^2+2*(b^4+11*b^2*c^2+c^4)*(b^2-c^2)^6 : :

See Antreas Hatzipolakis and César Lozada, euclid 3915.

X(46646) lies on these lines: {530, 11119}, {5472, 11080}, {11581, 36307}


X(46647) = X(531)X(11120)∩X(5471)X(11085)

Barycentrics    2*sqrt(3)*(8*a^14-19*(b^2+c^2)*a^12-(20*b^4+29*b^2*c^2+20*c^4)*a^10+4*(b^2+c^2)*(23*b^4-5*b^2*c^2+23*c^4)*a^8-5*(16*b^8+16*c^8-3*(5*b^4+7*b^2*c^2+5*c^4)*b^2*c^2)*a^6+(b^4-c^4)*(b^2-c^2)*(5*b^4-99*b^2*c^2+5*c^4)*a^4+5*(b^2-c^2)^4*(4*b^4+11*b^2*c^2+4*c^4)*a^2-6*(b^2+c^2)*(b^2-c^2)^6)*S+2*a^16-47*(b^2+c^2)*a^14+(161*b^4+187*b^2*c^2+161*c^4)*a^12-(b^2+c^2)*(178*b^4-121*b^2*c^2+178*c^4)*a^10-(26*b^8+26*c^8+(281*b^4+255*b^2*c^2+281*c^4)*b^2*c^2)*a^8+(b^2+c^2)*(197*b^8+197*c^8-(148*b^4+123*b^2*c^2+148*c^4)*b^2*c^2)*a^6-(b^2-c^2)^2*(139*b^8+139*c^8-4*(13*b^4+75*b^2*c^2+13*c^4)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)^3*(28*b^4-107*b^2*c^2+28*c^4)*a^2+2*(b^4+11*b^2*c^2+c^4)*(b^2-c^2)^6 : :

See Antreas Hatzipolakis and César Lozada, euclid 3915.

X(46647) lies on these lines: {531, 11120}, {5471, 11085}, {11582, 36310}


X(46648) = X(542)X(34238)∩X(2065)X(2782)

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

See Antreas Hatzipolakis and César Lozada, euclid 3915.

X(46648) lies on these lines: {542, 34238}, {2065, 2782}


X(46649) = ISOGONAL CONJUGATE OF X(3025)

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

See Antreas Hatzipolakis and César Lozada, euclid 3915.

X(46649) lies on these lines: {59, 952}, {80, 23592}, {528, 36590}, {655, 900}, {14204, 18815}

X(46649) = isogonal conjugate of X(3025)
X(46649) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(528)}} and {{A, B, C, X(8), X(952)}}
X(46649) = perspector of ABC and the reflection of the intouch triangle in line X(1)X(5)
X(46649) = barycentric product X(i)*X(j) for these {i, j}: {8, 23592}, {765, 34535}
X(46649) = barycentric quotient X(i)/X(j) for these (i, j): (55, 35128), (655, 4453), (1110, 34544), (1252, 4996)
X(46649) = trilinear product X(i)*X(j) for these {i, j}: {9, 23592}, {1252, 34535}
X(46649) = trilinear quotient X(i)/X(j) for these (i, j): (9, 35128), (655, 3960), (765, 4996), (1110, 215), (1252, 34544)


X(46650) = COMPLEMENT OF X(5995)

Barycentrics    (b^2 - c^2)^2*(Sqrt[3]*(-a^2 + b^2 + c^2) + 2*S)*(Sqrt[3]*(-a^4 + b^4 + c^4) - 2*(a^2 - b^2 - c^2)*S) : :
X(46650) = X[5668] - 5 X[40334]

X(46650) lies on the nine-point circle and these lines: {2, 5995}, {113, 623}, {114, 618}, {115, 23871}, {132, 7684}, {512, 46651}, {624, 16188}, {5668, 40334}, {6111, 31705}, {7685, 45158}, {15526, 23872}, {15609, 25173}

X(46650) = midpoint of X(623) and X(33501)
X(46650) = complement of X(5995)
X(46650) = complement of the isogonal conjugate of X(23870)
X(46650) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23870}, {15, 14838}, {298, 4369}, {470, 8062}, {661, 396}, {1577, 623}, {2151, 647}, {2154, 1637}, {2624, 40696}, {3384, 23873}, {6137, 37}, {8739, 16612}, {9204, 16597}, {17402, 16598}, {23870, 10}, {30465, 8287}, {32679, 619}, {39152, 21192}
X(46650) = X(4)-Ceva conjugate of X(23870)


X(46651) = COMPLEMENT OF X(5994)

Barycentrics    (b^2 - c^2)^2*(Sqrt[3]*(-a^2 + b^2 + c^2) - 2 S)*(Sqrt[3]*(-a^4 + b^4 + c^4) + 2*(a^2 - b^2 - c^2)*S) : :
X(46651) = X[5669] - 5 X[40335]

X(46651) lies on the nine-point circle and these lines: {2, 5994}, {113, 624}, {114, 619}, {115, 23870}, {132, 7685}, {512, 46650}, {623, 16188}, {5669, 40335}, {6110, 31706}, {7684, 45158}, {15526, 23873}, {15610, 25178}

X(46651) = midpoint of X(624) and X(33499)
X(46651) = complement of X(5994)
X(46651) = complement of the isogonal conjugate of X(23871)
X(46651) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23871}, {16, 14838}, {299, 4369}, {471, 8062}, {661, 395}, {1577, 624}, {2152, 647}, {2153, 1637}, {2624, 40695}, {3375, 23872}, {6138, 37}, {8740, 16612}, {9205, 16597}, {17403, 16598}, {23871, 10}, {30468, 8287}, {32679, 618}, {39153, 21192}
X(46651) = X(4)-Ceva conjugate of X(23871)


X(46652) = COMPLEMENT OF X(16806)

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

X(46652) lies on the nine-point circle and these lines: {2, 16806}, {114, 629}, {128, 618}, {636, 31843}, {32552, 33526}, {33496, 41022}

X(46652) = complement of X(16806)
X(46652) = complement of the isogonal conjugate of X(23872)
X(46652) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23872}, {61, 14838}, {302, 4369}, {473, 8062}, {656, 465}, {661, 23302}, {1577, 635}, {3376, 23871}, {10642, 16612}, {23872, 10}
X(46652) = X(4)-Ceva conjugate of X(23872)


X(46653) = COMPLEMENT OF X(16807)

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

X(46653) lies on the nine-point circle and these lines: {2, 16807}, {114, 630}, {128, 619}, {635, 31843}, {32553, 33527}, {33497, 41023}

X(46653) = complement of X(16807)
X(46653) = complement of the isogonal conjugate of X(23873)
X(46653) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23873}, {62, 14838}, {303, 4369}, {472, 8062}, {656, 466}, {661, 23303}, {1577, 636}, {3383, 23870}, {10641, 16612}, {23873, 10}
X(46653) = X(4)-Ceva conjugate of X(23873)


X(46654) = COMPLEMENT OF X(827)

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

X(46654) lies on the nine-point circle and these lines: {2, 827}, {4, 14378}, {5, 44953}, {20, 44943}, {113, 37347}, {114, 140}, {115, 9479}, {126, 21248}, {132, 1594}, {133, 42874}, {137, 868}, {186, 42426}, {339, 23285}, {826, 35584}, {3005, 3258}, {3143, 45161}, {3150, 20625}, {3269, 33504}, {3934, 13499}, {4577, 26197}, {5971, 30745}, {6143, 33695}, {7574, 25641}, {7759, 28672}, {7845, 15573}, {7853, 44947}, {7858, 28688}, {8623, 38975}, {10173, 45163}, {16188, 37938}, {21249, 31845}, {31842, 37452}, {35605, 36471}, {36189, 46439}

X(46654) = midpoint of X(i) and X(j) for these {i,j}: {4, 29011}, {20, 44943}
X(46654) = reflection of X(44953) in X(5)
X(46654) = complement of X(827)
X(46654) = orthoptic-circle-of-Steiner-inellipse-inverse of X(9076)
X(46654) = complement of the isogonal conjugate of X(826)
X(46654) = complement of the isotomic conjugate of X(23285)
X(46654) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 826}, {41513, 523}
X(46654) = crosspoint of X(i) and X(j) for these (i,j): {2, 23285}, {427, 31067}
X(46654) = crosssum of X(6) and X(4630)
X(46654) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 826}, {2, 8060}, {38, 523}, {39, 14838}, {65, 4142}, {141, 4369}, {427, 8062}, {512, 16600}, {513, 29654}, {523, 1215}, {561, 688}, {594, 29512}, {656, 6676}, {661, 3589}, {688, 16584}, {798, 1194}, {826, 10}, {850, 21238}, {897, 32193}, {1109, 7668}, {1235, 21259}, {1577, 3934}, {1581, 5113}, {1634, 16598}, {1843, 16612}, {1910, 14316}, {1928, 42291}, {1930, 512}, {1964, 647}, {2084, 39}, {2156, 23881}, {2525, 18589}, {2528, 21249}, {2530, 1125}, {2642, 7664}, {2643, 3124}, {3005, 37}, {3125, 21208}, {3404, 2799}, {3708, 339}, {3954, 514}, {4017, 17061}, {4077, 17049}, {4576, 21254}, {7178, 17048}, {8024, 42327}, {8061, 2}, {14208, 11574}, {14424, 16597}, {15523, 513}, {16696, 21196}, {16732, 44312}, {16892, 3739}, {17187, 31947}, {17442, 525}, {17957, 9479}, {20883, 30476}, {21035, 650}, {21108, 942}, {21123, 3666}, {21814, 6586}, {23285, 2887}, {23881, 21247}, {24006, 5943}, {31067, 28595}, {35309, 4422}, {35325, 16599}, {39691, 8287}, {46149, 4458}, {46151, 23998}, {46153, 34977}, {46160, 6370}
X(46654) = barycentric product X(i)*X(j) for these {i,j}: {7768, 39691}, {8061, 18076}
X(46654) = barycentric quotient X(i)/X(j) for these {i,j}: {15449, 14378}, {18076, 4593}, {37085, 4630}, {39691, 15321}


X(46655) = COMPLEMENT OF X(32692)

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

X(46655) lies on the nine-point circle and these lines: {2, 32692}, {114, 12134}, {128, 6069}, {132, 5446}, {1209, 31842}, {18314, 38970}

X(46655) = complement of X(32692)
X(46655) = circumcircle-inverse of X(112)-of-tangential-triangle
X(46655) = X(i)-complementary conjugate of X(j) for these (i,j): {52, 14838}, {467, 8062}, {924, 16577}, {1577, 1216}, {1748, 6368}, {1953, 2501}, {2180, 647}, {2617, 46184}, {2618, 343}, {6368, 18588}, {6563, 21231}, {14213, 924}, {14576, 16612}, {18314, 34825}, {21011, 46389}, {39113, 4369}


X(46656) = COMPLEMENT OF X(26714)

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

X(46656) lies on the nine-point circle and these lines: {2, 26714}, {4, 14383}, {114, 141}, {132, 19130}, {625, 33330}, {1560, 37648}, {3580, 38975}, {6388, 35971}, {15526, 38974}

X(46656) = complement of X(26714)
X(46656) = complement of the isogonal conjugate of X(23878)
X(46656) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23878}, {182, 14838}, {183, 4369}, {458, 8062}, {523, 16603}, {661, 3815}, {798, 3117}, {897, 45336}, {1577, 24206}, {1755, 33569}, {2349, 45319}, {3288, 37}, {3403, 512}, {6784, 16592}, {10311, 16612}, {20023, 42327}, {23878, 10}, {24018, 42353}, {39680, 18904}, {42711, 3835}, {44144, 21259}
X(46656) = X(4)-Ceva conjugate of X(23878)


X(46657) = COMPLEMENT OF X(11636)

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

X(46657) lies on the nine-point circle and these lines: {2, 6325}, {4, 14388}, {113, 24206}, {114, 549}, {115, 17416}, {126, 626}, {132, 7577}, {141, 13234}, {1506, 1560}, {3096, 9999}, {5031, 44956}, {5094, 15922}, {7818, 30789}, {10295, 42426}, {10748, 11569}, {15357, 35582}, {15526, 38971}, {36189, 46438}

X(46657) = midpoint of X(4) and X(14388)
X(46657) = complement of X(11636)
X(46657) = orthoptic-circle-of-Steiner-inellipse-inverse of X(6325)
X(46657) = complement of isogonal conjugate of X(3906)
X(46657) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 3906}, {574, 14838}, {599, 4369}, {661, 597}, {798, 9465}, {2643, 6791}, {3906, 10}, {5094, 8062}, {8288, 8287}, {8541, 16612}, {9145, 16598}, {9146, 21254}, {9464, 42327}, {10130, 8060}, {17414, 37}, {23288, 4892}, {36263, 523}
X(46657) = X(4)-Ceva conjugate of X(3906)
X(46657) = crossdifference of every pair of points on line {35357, 36828}
X(46657) = barycentric product X(i)*X(j) for these {i,j}: {599, 38361}, {7850, 8288}
X(46657) = barycentric quotient X(38361)/X(598)


X(46658) = X(113)X(389)∩X(114)X(6677)

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

X(46658) lies on the nine-point circle and these lines: {113, 389}, {114, 6677}, {128, 43809}, {133, 44226}, {2970, 16178}, {3124, 33504}, {25641, 31726}, {37777, 42426}

X(46658) = X(i)-complementary conjugate of X(j) for these (i,j): {235, 8062}, {656, 16196}, {774, 523}, {800, 14838}, {1624, 16598}, {2643, 3269}, {13567, 4369}, {17858, 512}, {18603, 21196}, {24006, 5907}, {44079, 16612}, {44131, 21259}


X(46659) = MIDPOINT OF X(4) AND X(843)

Barycentrics    (b^2 - c^2)^2*(4*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 4*b^2*c^2 + c^4)*(-a^6 + 5*a^4*b^2 - 5*a^2*b^4 + b^6 + 5*a^4*c^2 - a^2*b^2*c^2 - 5*a^2*c^4 + c^6) : :
X(46659) = X[352] - 3 X[38227]

X(46659) lies on the nine-point circle and these lines: {2, 2709}, {4, 843}, {5, 44956}, {20, 44946}, {114, 524}, {115, 1499}, {126, 511}, {352, 38227}, {512, 5512}, {542, 16341}, {1648, 9193}, {2793, 35586}, {3849, 11569}, {5476, 9169}, {5480, 16188}, {6092, 7617}, {6791, 8704}, {6792, 9753}, {9152, 24206}, {20389, 35605}

X(46659) = complement of X(2709)
X(46659) = midpoint of X(i) and X(j) for these {i,j}: {4, 843}, {20, 44946}
X(46659) = reflection of X(44956) in X(5)
X(46659) = complement of the isogonal conjugate of X(2793)
X(46659) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2793}, {661, 22110}, {2030, 14838}, {2793, 10}, {9135, 37}, {17959, 1499}, {22329, 4369}, {23894, 19662}, {34245, 21254}
X(46659) = X(4)-Ceva conjugate of X(2793)
X(46659) = X(843)-of-Euler-triangle
X(46659) = X(44956)-of-Johnson-triangle
X(46659) = barycentric product X(2793)*X(39905)
X(46659) = barycentric quotient X(39905)/X(46144)


X(46660) = MIDPOINT OF X(4) AND X(28173)

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

X(46660) lies on the nine-point circle and these lines: {2, 8701}, {4, 28173}, {114, 41820}, {115, 244}, {119, 9947}, {121, 3831}, {1086, 38960}, {1125, 27592}, {1566, 4988}, {1647, 15611}, {3756, 5515}, {5511, 26933}, {5520, 6075}

X(46660) = complement of X(8701)
X(46660) = midpoint of X(4) and X(28173)
X(46660) = orthoptic-circle-of-Steiner-inellipse inverse of X(9108)
X(46660) = X(28173)-of-Euler-triangle
X(46660) = complement of the isogonal conjugate of X(4977)
X(46660) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 4977}, {58, 8043}, {244, 3120}, {513, 3634}, {514, 17239}, {553, 4885}, {649, 44307}, {661, 41809}, {757, 6367}, {1015, 16726}, {1019, 6707}, {1100, 514}, {1125, 513}, {1213, 4129}, {1269, 21260}, {1962, 661}, {2308, 650}, {2355, 3239}, {3683, 4521}, {3686, 20317}, {3733, 3743}, {3737, 18253}, {3916, 20315}, {4359, 3835}, {4427, 24003}, {4647, 31946}, {4976, 3452}, {4977, 10}, {4978, 141}, {4979, 2}, {4983, 1213}, {4984, 16594}, {4985, 1329}, {4988, 1211}, {4992, 34832}, {7192, 27798}, {8025, 4369}, {16709, 512}, {16726, 24185}, {30581, 21196}, {30591, 3454}, {30724, 142}, {31900, 8062}, {32636, 522}, {35327, 24036}, {35342, 4422}, {36075, 16578}, {46542, 942}
X(46660) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 4977}, {13476, 6367}


X(46661) = X(2)X(43658)∩X(113)X(15060)

Barycentrics    (b^2 - c^2)^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 - 2*a^2*c^4 - b^2*c^4 + c^6)*(-a^8 + 2*a^6*b^2 - 2*a^2*b^6 + b^8 + 2*a^6*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(46661) lies on the nine-point circle and these lines: {2, 43658}, {113, 15060}, {114, 7495}, {6070, 38971}, {18572, 25641}, {37969, 42426}

X(46661) = orthoptic-circle-of-Steiner-inellipse-inverse of X(43658)
X(46661) = X(i)-complementary conjugate of X(j) for these (i,j): {566, 14838}, {661, 14389}, {7577, 8062}, {18117, 37}, {24006, 5946}, {36829, 16598}


X(46662) = X(113)X(6823)∩X(114)X(7386)

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

X(46662) lies on the nine-point circle and these lines: {113, 6823}, {114, 7386}, {115, 2972}, {132, 37439}, {133, 3091}, {1650, 15613}, {3937, 31653}

X(46662) = X(i)-complementary conjugate of X(j) for these (i,j): {631, 8062}, {656, 1656}, {661, 11433}, {11402, 16612}, {36748, 14838}, {44149, 21259}


X(46663) = COMPLEMENT OF X(8059)

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

X(46663) lies on the nine-point circle and these lines: {2, 8059}, {10, 25640}, {11, 7358}, {117, 1329}, {118, 20307}, {119, 6260}, {123, 44313}, {223, 30757}, {2550, 20622}, {3452, 44993}, {5513, 38015}, {7952, 20619}, {20206, 21244}

X(46663) = complement of X(8059)
X(46663) = complement of the isogonal conjugate of X(8058)
X(46663) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 8058}, {33, 14331}, {37, 24018}, {40, 522}, {65, 17898}, {198, 905}, {208, 21172}, {221, 6129}, {223, 7658}, {227, 656}, {322, 17072}, {329, 4885}, {346, 20318}, {347, 3900}, {513, 3086}, {522, 946}, {650, 57}, {651, 40555}, {663, 1108}, {1783, 40535}, {1817, 17069}, {2187, 6589}, {2324, 514}, {2331, 14837}, {3195, 6588}, {3239, 20205}, {3318, 7358}, {3900, 281}, {4041, 1901}, {4391, 21239}, {4397, 20306}, {5514, 26932}, {6129, 1}, {7074, 650}, {7080, 513}, {7358, 123}, {7952, 521}, {8058, 10}, {10397, 1214}, {14298, 2}, {14302, 20210}, {14837, 142}, {15501, 2804}, {17896, 2886}, {21871, 1577}, {27398, 4369}, {38357, 11}, {40702, 46399}, {40971, 3239}
X(46663) = X(4)-Ceva conjugate of X(8058)


X(46664) = X(3)X(14980)∩X(23)X(132)

Barycentrics    (b^2 - c^2)^2*(-a^2 + b^2 + c^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)*(-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^6*b^2*c^2 + 3*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*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(46664) lies on the nine-point circle and these lines: {3, 14980}, {23, 132}, {30, 18402}, {113, 10540}, {115, 16040}, {125, 6368}, {128, 2072}, {133, 11563}, {523, 20625}, {546, 18809}, {1650, 46437}, {5133, 42426}, {5159, 31843}, {6676, 16188}, {10024, 12091}, {12605, 42424}, {12606, 33333}, {24977, 46439}

X(46664) = reflection of X(20625) in the Euler line
X(46664) = X(i)-complementary conjugate of X(j) for these (i,j): {656, 37938}, {810, 50}, {2070, 8062}, {9380, 14838}, {24978, 20305}


X(46665) = COMPLEMENT OF X(7953)

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

X(46665) lies on the nine-point circle and these lines: {2, 7953}, {4, 14381}, {5, 45165}, {20, 45155}, {114, 3628}, {115, 15527}, {132, 15559}, {868, 11792}, {2679, 35605}, {19577, 31655}, {25641, 37924}, {37943, 42426}

X(46665) = midpoint of X(i) and X(j) for these {i,j}: {4, 29316}, {20, 45155}
X(46665) = reflection of X(45165) in X(5)
X(46665) = complement of X(7953)
X(46665) = complement of the isogonal conjugate of X(7927)
X(46665) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 7927}, {428, 8062}, {512, 28594}, {523, 28595}, {656, 10691}, {661, 34573}, {1577, 7849}, {2642, 31128}, {2643, 39691}, {3589, 4369}, {5007, 14838}, {7927, 10}, {8664, 37}, {10330, 21254}, {17457, 3005}, {17469, 523}, {21802, 514}, {39998, 42327}, {44091, 16612}, {44142, 21259}
X(46665) = X(4)-Ceva conjugate of X(7927)
X(46665) = X(29316)-of-Euler-triangle
X(46665) = X(45165)-of-Johnson-triangle
X(46665) = barycentric quotient X(15527)/X(14381)


X(46666) = COMPLEMENT OF X(36515)

Barycentrics    (b^2 - c^2)^2*(-2*a^10 + 4*a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 - 4*a^2*b^8 + 2*b^10 + 4*a^8*c^2 - 9*a^6*b^2*c^2 + 6*a^4*b^4*c^2 + 5*a^2*b^6*c^2 - 6*b^8*c^2 - 2*a^6*c^4 + 6*a^4*b^2*c^4 - 2*a^2*b^4*c^4 + 4*b^6*c^4 + 2*a^4*c^6 + 5*a^2*b^2*c^6 + 4*b^4*c^6 - 4*a^2*c^8 - 6*b^2*c^8 + 2*c^10 + 2*Sqrt[3]*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)*(-4*a^8 + 4*a^6*b^2 + 6*a^4*b^4 - 8*a^2*b^6 + 2*b^8 + 4*a^6*c^2 - a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 2*b^6*c^2 + 6*a^4*c^4 + 5*a^2*b^2*c^4 - 8*a^2*c^6 - 2*b^2*c^6 + 2*c^8 - 2*Sqrt[3]*a^2*(2*a^4 - 4*a^2*b^2 + 2*b^4 - 4*a^2*c^2 - b^2*c^2 + 2*c^4)*S) : :

X(46666) lies on the nine-point circle and these lines: {2, 36515}, {114, 1080}, {115, 30452}, {512, 15610}, {621, 1338}, {623, 33498}, {3440, 14372}

X(46666) = midpoint of X(i) and X(j) for these {i,j}: {621, 1338}, {3440, 14372}
X(46666) = reflection of X(33498) in X(623)
X(46666) = complement of X(36515)
X(46666) = X(i)-complementary conjugate of X(j) for these (i,j): {661, 298}, {3180, 4369}, {19780, 14838}


X(46667) = COMPLEMENT OF X(36514)

Barycentrics    (b^2 - c^2)^2*(-2*a^10 + 4*a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 - 4*a^2*b^8 + 2*b^10 + 4*a^8*c^2 - 9*a^6*b^2*c^2 + 6*a^4*b^4*c^2 + 5*a^2*b^6*c^2 - 6*b^8*c^2 - 2*a^6*c^4 + 6*a^4*b^2*c^4 - 2*a^2*b^4*c^4 + 4*b^6*c^4 + 2*a^4*c^6 + 5*a^2*b^2*c^6 + 4*b^4*c^6 - 4*a^2*c^8 - 6*b^2*c^8 + 2*c^10 - 2*Sqrt[3]*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)*(-4*a^8 + 4*a^6*b^2 + 6*a^4*b^4 - 8*a^2*b^6 + 2*b^8 + 4*a^6*c^2 - a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 2*b^6*c^2 + 6*a^4*c^4 + 5*a^2*b^2*c^4 - 8*a^2*c^6 - 2*b^2*c^6 + 2*c^8 + 2*Sqrt[3]*a^2*(2*a^4 - 4*a^2*b^2 + 2*b^4 - 4*a^2*c^2 - b^2*c^2 + 2*c^4)*S) : :

X(46667) lies on the nine-point circle and these lines: {2, 36514}, {114, 383}, {115, 30453}, {512, 15609}, {622, 1337}, {624, 33500}, {3441, 14373}

X(46667) = midpoint of X(i) and X(j) for these {i,j}: {622, 1337}, {3441, 14373}
X(46667) = reflection of X(33500) in X(624)
X(46667) = complement of X(36514)
X(46667) = X(i)-complementary conjugate of X(j) for these (i,j): {661, 299}, {3181, 4369}, {19781, 14838}


X(46668) = COMPLEMENT OF X(2702)

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

X(46668) lies on the nine-point circle and these lines: {2, 2702}, {4, 2700}, {11, 4369}, {114, 516}, {115, 514}, {116, 512}, {118, 511}, {121, 625}, {125, 3835}, {126, 20339}, {2681, 2786}, {5031, 20551}, {5074, 20529}, {5513, 6651}, {7683, 45158}, {20541, 20546}, {41323, 41324}

X(46668) = midpoint of X(4) and X(2700)
X(46668) = complement of X(2702)
X(46668) = complement of the isogonal conjugate of X(2786)
X(46668) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2786}, {423, 8062}, {513, 239}, {523, 20337}, {661, 10026}, {1326, 14838}, {1577, 20546}, {1757, 514}, {1931, 523}, {2786, 10}, {5029, 37}, {6541, 4129}, {6542, 513}, {8298, 27929}, {9508, 2}, {17731, 4369}, {17735, 650}, {17990, 16589}, {18004, 1211}, {18266, 6586}, {20693, 661}, {20947, 3835}, {27929, 17793}, {28602, 16594}, {38348, 17755}, {40740, 30665}, {40794, 812}
X(46668) = X(4)-Ceva conjugate of X(2786)
X(46668) = polar conjugate of isogonal conjugate of X(47428)
X(46668) = X(2700)-of-Euler-triangle


X(46669) = X(114)X(5999)∩X(115)X(826)

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

X(46669) lies on the nine-point circle and these lines: {114, 5999}, {115, 826}, {511, 44953}, {647, 35971}, {5103, 13499}, {5207, 19558}

X(46669) = Moses-radical-circle-inverse of X(35971)
X(46669) = complement of the isogonal conjugate of X(9479)
X(46669) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 9479}, {420, 8062}, {661, 385}, {1577, 5103}, {2076, 14838}, {5113, 37}, {7779, 4369}, {8061, 15573}, {9479, 10}, {17799, 523}, {17997, 16600}, {18010, 1215}, {34054, 826}, {40850, 8060}, {44090, 16612}
X(46669) = X(4)-Ceva conjugate of X(9479)
X(46669) = complement of X(46970)
X(46669) = barycentric product X(9479)*X(14316)


X(46670) = COMPLEMENT OF X(2701)

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

X(4666) lies on the nine-point circle and these lines: {2, 2701}, {4, 2708}, {114, 515}, {115, 522}, {116, 17066}, {117, 511}, {124, 512}, {125, 17072}, {625, 31844}, {20546, 31845}

X(46670) = midpoint of X(4) and X(2708)
X(46670) = complement of X(2701)
X(46670) = complement of the isogonal conjugate of X(2785)
X(46670) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2785}, {415, 8062}, {513, 33140}, {650, 1944}, {1758, 522}, {2651, 523}, {2785, 10}, {4516, 41182}, {5060, 14838}, {5075, 37}, {17942, 34977}, {17950, 4885}, {17966, 905}, {17985, 521}, {17992, 2092}, {18006, 442}, {40882, 4369}
X(46670) = X(4)-Ceva conjugate of X(2785)
X(46670) = X(2708)-of-Euler-triangle


X(46671) = COMPLEMENT OF X(2703)

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

X(46671) lies on the nine-point circle and these lines: {2, 2703}, {4, 2699}, {11, 512}, {114, 517}, {115, 513}, {116, 42327}, {119, 511}, {125, 21260}, {2680, 2787}, {3110, 37715}, {3814, 45162}, {3836, 31845}, {5006, 5061}, {5164, 38472}, {5958, 11792}, {6547, 15611}

X(46671) = midpoint of X(4) and X(2699)
X(46671) = reflection of X(5164) in X(38472)
X(46671) = complement of X(2703)
X(46671) = complement of the isogonal conjugate of X(2787)
X(46671) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2787}, {42, 2511}, {422, 8062}, {661, 44396}, {2787, 10}, {5006, 14838}, {5040, 37}, {5061, 522}, {5209, 512}, {5291, 514}, {17763, 513}, {17790, 3835}, {17977, 20315}, {17987, 20316}, {17989, 1213}, {18003, 3454}, {19623, 4369}
X(46671) = X(4)-Ceva conjugate of X(2787)
X(46671) = X(2699)-of-Euler-triangle
X(46671) = barycentric quotient X(2787)/X(43189)


X(46672) = (name pending)

Barycentrics   (10*a^8-(11*b^2+10*c^2)*a^6-3*(2*b^4+11*b^2*c^2+10*c^4)*a^4-(11*b^6-46*c^6+3*(11*b^2+10*c^2)*b^2*c^2)*a^2+2*(b^2-c^2)*(5*b^6-15*b^2*c^4+8*c^6))*(10*a^8-(10*b^2+11*c^2)*a^6-3*(10*b^4+11*b^2*c^2+2*c^4)*a^4+(46*b^6-11*c^6-3*(10*b^2+11*c^2)*b^2*c^2)*a^2-2*(b^2-c^2)*(8*b^6-15*b^4*c^2+5*c^6)) : :

See Antreas Hatzipolakis and César Lozada, euclid 3930.

X(46672) lies on these lines: { }


X(46673) = X(3)X(13378)∩X(5)X(10168)

Barycentrics    12*a^10-19*(b^2+c^2)*a^8-5*(b^4+4*b^2*c^2+c^4)*a^6-3*(b^2+c^2)*(b^4+4*b^2*c^2+c^4)*a^4+(29*b^8+29*c^8-2*(8*b^4+21*b^2*c^2+8*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(-14*b^4+32*b^2*c^2-14*c^4) : :
X(46673) = X(3)-3*X(13378), 3*X(381)-X(31748), 3*X(10162)-X(31731), X(31729)-3*X(34512)

See Antreas Hatzipolakis and César Lozada, euclid 3930.

X(46673) lies on these lines: {3, 13378}, {5, 10168}, {381, 31748}, {9830, 31749}, {10162, 31731}, {31729, 34512}


X(46674) = X(5)X(539)∩X(54)X(21265)

Barycentrics    (-a^2 b^2+b^4-a^2 c^2-2 b^2 c^2+c^4) (-a^18+6 a^16 b^2-16 a^14 b^4+27 a^12 b^6-36 a^10 b^8+41 a^8 b^10-36 a^6 b^12+21 a^4 b^14-7 a^2 b^16+b^18+6 a^16 c^2-26 a^14 b^2 c^2+47 a^12 b^4 c^2-45 a^10 b^6 c^2+13 a^8 b^8 c^2+32 a^6 b^10 c^2-51 a^4 b^12 c^2+31 a^2 b^14 c^2-7 b^16 c^2-16 a^14 c^4+47 a^12 b^2 c^4-51 a^10 b^4 c^4+18 a^8 b^6 c^4+2 a^6 b^8 c^4+27 a^4 b^10 c^4-47 a^2 b^12 c^4+20 b^14 c^4+27 a^12 c^6-45 a^10 b^2 c^6+18 a^8 b^4 c^6+4 a^6 b^6 c^6+3 a^4 b^8 c^6+21 a^2 b^10 c^6-28 b^12 c^6-36 a^10 c^8+13 a^8 b^2 c^8+2 a^6 b^4 c^8+3 a^4 b^6 c^8+4 a^2 b^8 c^8+14 b^10 c^8+41 a^8 c^10+32 a^6 b^2 c^10+27 a^4 b^4 c^10+21 a^2 b^6 c^10+14 b^8 c^10-36 a^6 c^12-51 a^4 b^2 c^12-47 a^2 b^4 c^12-28 b^6 c^12+21 a^4 c^14+31 a^2 b^2 c^14+20 b^4 c^14-7 a^2 c^16-7 b^2 c^16+c^18) : :
Barycentrics    (S^2+SB SC)(16 R^6+7 R^2 S^2+16 R^4 SA-3 S^2 SA+10 R^2 SB SC+(-24 R^4-S^2-8 R^2 SA-4 SB SC) SW+(9 R^2+SA) SW^2-SW^3) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3934.

X(46674) lies on these lines: {5,539}, {54,21265}, {143,36412}, {265,40448}, {1173,3078}, {15780,33664}, {18370,39284}, {30483,34826}

X(46674) = Orion transform of X(5)


X(46675) = X(165)X(2324)∩X(480)X(19605)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 3934.

X(46675) lies on these lines: {165,2324}, {480,19605}, {1174,8012}, {3256,6602}, {5537,11051}, {6244,7368}, {10310,45721}, {11227,34867}

X(46675) = Orion transform of X(9)


X(46676) = X(10)X(4682)∩X(12)X(21081)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 3934.

X(46676) lies on these lines: {10,4682}, {12,21081}, {306,39583}, {502,6057}, {1126,1224}

X(46676) = Orion transform of X(10)


X(46677) = X(3)X(200)∩X(8)X(210)

Barycentrics    a (a-b-c) (a^4 b-2 a^2 b^3+b^5+a^4 c-2 a^2 b^2 c+b^4 c-2 a^2 b c^2+8 a b^2 c^2-2 b^3 c^2-2 a^2 c^3-2 b^2 c^3+b c^4+c^5) : :
Barycentrics    a (a-b-c) ((2 a-b-c) S^2+2 a SA^2) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 3934.

X(46677) lies on these lines: {3,200}, {8,210}, {10,17658}, {40,18239}, {56,2057}, {65,6735}, {72,1145}, {78,1319}, {100,12680}, {354,5552}, {404,9850}, {452,18247}, {480,11510}, {517,45631}, {518,1788}, {1158,5687}, {1259,3689}, {1260,1728}, {1329,17642}, {1532,21075}, {1864,3913}, {3059,5220}, {3436,7957}, {3522,12125}, {3555,6745}, {3697,4187}, {3698,4197}, {3711,10966}, {3832,14923}, {3870,25875}, {3871,14100}, {3872,25917}, {3873,27525}, {3895,9848}, {3967,23528}, {3983,6734}, {4420,37605}, {4853,5044}, {4861,17536}, {4882,5119}, {5176,6895}, {5177,5836}, {5815,6925}, {6762,41426}, {7962,15347}, {9954,12526}, {10395,38211}, {11678,20070}, {12053,18236}, {12688,17615}, {15558,17648}, {17609,27385}, {17857,18237}, {27383,34791}, {34619,44547}, {35460,40263}

X(46677) = reflection of X(37566) in X(37828)
X(46677) = crossdifference of every pair of points on line X(7661)-X(43924)
X(46677) = extouch-isogonal conjugate of X(8)
X(46677) = {X(6736),X(14740)}-harmonic conjugate of X(72)


X(46678) = X(9)X(55)∩X(220)X(15931)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 3934.

X(46678) lies on these lines: {9,55}, {220,15931}, {2078,6602}, {8012,38849}, {10857,34867}, {11508,15662}, {34526,41338}

X(46678) = extouch-isogonal conjugate of X(9)


X(46679) = X(10)X(37)∩X(8013)X(33771)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 3934.

X(46679) lies on these lines: {10,37}, {8013,33771}, {20654,35468}

X(46679) = (cevian triangle of X(10))-isogonal conjugate of X(10)


X(46680) = X(6)X(1092)∩X(54)X(1249)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 3946.

X(46680) lies on these lines: {6,1092}, {32,23606}, {54,1249}, {83,11427}, {184,2207}, {578,1217}, {1970,10984}, {1974,14585}, {7763,40405}

X(46680) = X(i)-isoconjugate of X(j) for these (i,j): (75,11433), (92,40680), (304,3089), (561,8573), (1181,1969)
X(46680) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {32,11433}, {184,40680}, {1217,18022}, {1501,8573}, {1974,3089}
X(46680) = barycentric product X(184)*X(1217)
X(46680) = barycentric quotient X(i)/X(j) for these {i,j}: {32,11433}, {184,40680}, {1217,18022}, {1501,8573}, {1974,3089}
X(46680) = trilinear product X(1217)*X(9247)
X(46680) = trilinear quotient X(i)/X(j) for these (i,j): (31,11433), (48,40680), (560,8573), (1217,1969), (1973,3089)





leftri  Mutual-reflections conics: X(46681) - X(46696)  rightri

This preamble and centers X(46681)-X(46696) were contributed by César Eliud Lozada, January 14, 2022.

Let T'=A'B'C' and T"=A"B"C" be two triangles, A1 the reflection of A' in B"C" and A2 the reflection of A" in B'C'. Define B1, B2, C1, C2 cyclically. For some selected pairs of triangles T' and T", these six points lie on a conic, here named the mutual-reflections conic of T' and T" or, shortly, the MR-conic of T' and T".

The appearance of (T', T", n) in the following partial list means that the center of the MR-conic of triangles T' and T" is X(n):

(ABC, ABC-X3 reflections, 3), (ABC, anticomplementary, 3), (ABC, outer-Garcia, 10), (ABC, Gossard, 402), (ABC, intouch, 5083), (ABC, medial, 5), (ABC, 5th mixtilinear, 1), (ABC, tangential, 125), (ABC-X3 reflections, anti-Euler, 3), (ABC-X3 reflections, anti-Hutson intouch, 16163), (anti-Aquila, Ehrmann-mid, 9955), (anti-Aquila, incircle-circles, 46681), (anti-Aquila, medial, 1125), (anti-Ara, orthic, 46682), (anti-Ascella, 2nd anti-extouch, 12161), (1st anti-Auriga, 2nd anti-Auriga, 1), (2nd anti-circumperp-tangential, anti-tangential-midarc, 46683), (2nd anti-circumperp-tangential, Mandart-incircle, 1), (1st anti-circumperp, 3rd anti-Euler, 3), (1st anti-circumperp, circumorthic, 3), (anti-Conway, 2nd anti-extouch, 32046), (2nd anti-Conway, orthic, 143), (anti-Ehrmann-mid, anti-Euler, 5), (anti-Ehrmann-mid, Aquila, 18480), (4th anti-Euler, circumorthic, 3), (anti-excenters-reflections, orthic, 4), (anti-Honsberger, anti-Ursa minor, 3589), (anti-Honsberger, Ehrmann-vertex, 19130), (anti-Honsberger, 2nd Ehrmann, 6), (anti-Honsberger, Trinh, 5092), (anti-Hutson intouch, tangential, 3), (anti-incircle-circles, anti-inverse-in-incircle, 5), (anti-incircle-circles, 1st excosine, 6759), (anti-incircle-circles, X3-ABC reflections, 265), (anti-inverse-in-incircle, anticomplementary, 110), (anti-Mandart-incircle, 2nd circumperp tangential, 3), (anti-Mandart-incircle, 1st circumperp, 46684), (1st anti-Parry, 2nd anti-Parry, 3), (anti-tangential-midarc, intangents, 1), (anti-Ursa minor, Kosnita, 140), (anti-Ursa minor, medial, 5972), (anti-Wasat, circumorthic, 389), (anti-Wasat, orthic, 5), (anti-X3-ABC reflections, Ehrmann-mid, 5), (anti-X3-ABC reflections, Kosnita, 6699), (anti-inner-Yff, outer-Johnson, 5), (anti-outer-Yff, inner-Johnson, 5), (anticomplementary, Aquila, 10), (anticomplementary, inner-Conway, 46685), (anticomplementary, X3-ABC reflections, 5), (Aquila, outer-Garcia, 355), (1st Auriga, 2nd Auriga, 55), (7th Brocard, 10th Brocard, 182), (circumorthic, Ehrmann-side, 5), (2nd circumperp tangential, 2nd circumperp, 214), (1st circumperp, 2nd circumperp, 3), (1st circumperp, excentral, 3), (2nd circumperp, hexyl, 3), (2nd circumperp, Wasat, 1125), (inner-Conway, Honsberger, 9), (3rd Conway, inverse-in-Conway, 10441), (Ehrmann-mid, Ehrmann-vertex, 46686), (Ehrmann-vertex, Kosnita, 5), (2nd Ehrmann, Kosnita, 575), (Euler, Johnson, 5), (Euler, medial, 5), (2nd Euler, orthic, 5), (3rd Euler, 4th Euler, 5), (3rd Euler, Wasat, 5), (excenters-reflections, excentral, 1), (excentral, 6th mixtilinear, 40), (1st excosine, tangential, 26), (inner-Fermat, 1st half-diamonds, 18), (outer-Fermat, 2nd half-diamonds, 17), (Garcia-reflection, 2nd Schiffler, 11), (1st half-squares, outer-Vecten, 641), (2nd half-squares, inner-Vecten, 642), (Honsberger, Ursa-minor, 5572), (Hutson intouch, intouch, 1), (Hutson intouch, 5th mixtilinear, 15558), (incircle-circles, 2nd Zaniah, 1125), (intangents, Mandart-incircle, 46687), (intouch, inverse-in-incircle, 942), (intouch, Ursa-minor, 1), (Johnson, X3-ABC reflections, 4), (1st Kenmotu-centers, 1st Kenmotu diagonals, 46688), (2nd Kenmotu-centers, 2nd Kenmotu diagonals, 46689), (Kosnita, Trinh, 3), (Lucas central, Lucas tangents, 46690), (Lucas(-1) central, Lucas(-1) tangents, 46691), (Lucas inner, Lucas inner tangential, 46692), (Lucas(-1) inner, Lucas(-1) inner tangential, 46693), (medial, 2nd Zaniah, 46694), (midarc, 2nd midarc, 1), (midarc, tangential-midarc, 46695), (2nd midarc, 2nd tangential-midarc, 46696)

underbar

X(46681) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: ANTI-AQUILA AND INCIRCLE-CIRCLES

Barycentrics    a*((b+c)*a^5-(b^2-6*b*c+c^2)*a^4-(b+c)*(2*b^2+3*b*c+2*c^2)*a^3+(2*b^4+2*c^4-(7*b^2-18*b*c+7*c^2)*b*c)*a^2+(b^2-c^2)*(b-c)*(b^2+5*b*c+c^2)*a-(b^2-c^2)*(b-c)*(b^3+c^3)) : :
X(46681) = 3*X(1)+X(11570) = 7*X(1)+X(11571) = 5*X(1)-X(12758) = 3*X(1)-X(15558) = X(11)-5*X(17609) = X(214)+3*X(3892) = 3*X(354)+X(1317) = 3*X(354)-X(12736) = 9*X(354)-X(17636) = 3*X(1317)+X(17636) = 3*X(5083)-X(11570) = 7*X(5083)-X(11571) = 5*X(5083)+X(12758) = 3*X(5083)+X(15558) = 7*X(11570)-3*X(11571) = 5*X(11570)+3*X(12758) = 5*X(11571)+7*X(12758) = 3*X(11571)+7*X(15558) = 3*X(12736)-X(17636) = 3*X(12758)-5*X(15558)

X(46681) lies on these lines: {1, 104}, {7, 14217}, {11, 17609}, {80, 1056}, {100, 3333}, {119, 11019}, {149, 11037}, {153, 10580}, {214, 999}, {226, 16174}, {354, 1317}, {388, 6246}, {495, 6702}, {551, 18254}, {758, 25405}, {938, 12751}, {942, 2802}, {952, 5045}, {1058, 34789}, {1125, 46694}, {1210, 10956}, {1320, 11529}, {1387, 2801}, {1537, 14100}, {2829, 16215}, {3035, 34791}, {3036, 3742}, {3085, 38133}, {3241, 39776}, {3295, 46684}, {3304, 12739}, {3338, 10087}, {3361, 34474}, {3487, 16173}, {3555, 14740}, {3600, 12119}, {3616, 46685}, {3660, 28234}, {3881, 24928}, {3947, 23513}, {4298, 5840}, {4314, 38761}, {5434, 12743}, {5531, 30343}, {5533, 13407}, {5541, 10980}, {5542, 21630}, {6049, 37625}, {6265, 7373}, {6326, 11025}, {6713, 13405}, {6767, 12515}, {7993, 30350}, {8083, 8098}, {9654, 38161}, {9850, 38038}, {9946, 12737}, {9951, 10569}, {10090, 41553}, {10265, 41556}, {10404, 13274}, {11021, 35636}, {11033, 12748}, {11035, 15009}, {11038, 12757}, {11041, 26726}, {11374, 32557}, {12019, 12128}, {12532, 38314}, {12665, 40269}, {12832, 31397}, {15888, 20118}, {17644, 38156}, {18527, 22799}, {18530, 38756}, {21625, 21635}, {35620, 38484}

X(46681) = midpoint of X(i) and X(j) for these {i, j}: {1, 5083}, {942, 12735}, {1317, 12736}, {3035, 34791}, {3555, 14740}, {9946, 12737}, {11570, 15558}, {15528, 25485}
X(46681) = reflection of X(i) in X(j) for these (i, j): (18240, 5045), (46694, 1125)
X(46681) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 11570, 15558), (354, 1317, 12736), (3555, 34123, 14740), (5083, 15558, 11570), (17609, 17624, 21620)


X(46682) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: ANTI-ARA AND ORTHIC

Barycentrics    (2*a^8-2*(b^2+c^2)*a^6-(b^4-4*b^2*c^2+c^4)*a^4+(b^4-c^4)^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
X(46682) = 3*X(428)-X(1112) = 3*X(7540)+X(7723) = 3*X(7576)+X(12292) = 3*X(13490)-X(14708) = 3*X(16658)+X(17854) = X(16659)+3*X(46430)

X(46682) lies on these lines: {4, 110}, {24, 6699}, {25, 125}, {30, 13416}, {33, 46687}, {34, 46683}, {67, 7716}, {74, 7487}, {235, 7687}, {265, 1598}, {378, 38726}, {403, 44407}, {427, 5972}, {428, 542}, {468, 6723}, {541, 7576}, {974, 16655}, {1495, 37981}, {1503, 11746}, {1511, 1595}, {1560, 20998}, {1593, 16163}, {1594, 12900}, {1596, 10113}, {1597, 12121}, {1843, 13417}, {1974, 15118}, {2777, 3575}, {3088, 15035}, {3089, 14644}, {3448, 6995}, {3515, 38727}, {3517, 15061}, {3518, 20397}, {3541, 38793}, {3542, 23515}, {3867, 6593}, {5064, 5642}, {5095, 12167}, {5412, 46688}, {5413, 46689}, {5663, 6756}, {6353, 15059}, {6800, 35488}, {7408, 14683}, {7507, 36518}, {7540, 7723}, {7553, 12358}, {7713, 13211}, {7714, 9140}, {7715, 10264}, {7718, 7984}, {7728, 18494}, {10018, 17712}, {10151, 18400}, {10272, 16198}, {10594, 36253}, {11363, 11735}, {11382, 32241}, {11744, 15811}, {12041, 37458}, {12173, 13202}, {12902, 18535}, {13198, 31383}, {13490, 14708}, {15066, 35490}, {15080, 16868}, {15088, 37942}, {15115, 20771}, {16003, 37122}, {16111, 18533}, {16658, 17854}, {16659, 46430}, {18405, 37197}, {19504, 24981}, {20304, 21841}, {21243, 41674}, {21659, 26864}, {22970, 32340}, {32257, 41584}, {33547, 45179}

X(46682) = midpoint of X(i) and X(j) for these {i, j}: {4, 12140}, {974, 16655}, {1843, 32239}, {3575, 12133}, {7553, 12358}, {7687, 13419}
X(46682) = reflection of X(15473) in X(6756)
X(46682) = crosssum of X(3) and X(41673)


X(46683) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: 2nd ANTI-CIRCUMPERP-TANGENTIAL AND ANTI-TANGENTIAL-MIDARC

Barycentrics    (2*a^8-2*(b^2+c^2)*a^6-(b^4-4*b^2*c^2+c^4)*a^4-2*(b^2-c^2)^2*b*c*a^2+(b^4-c^4)*(b^2-c^2)*(b+c)^2)*(a-b+c)*(a+b-c) : :
X(46683) = 3*X(1)-X(12896) = X(3028)-3*X(5434) = X(12896)+3*X(18968) = 2*X(12896)-3*X(46687) = 2*X(18968)+X(46687)

X(46683) lies on these lines: {1, 12888}, {11, 7687}, {12, 5972}, {34, 46682}, {35, 38726}, {36, 6699}, {55, 16163}, {56, 125}, {57, 13211}, {74, 4293}, {110, 388}, {113, 1478}, {226, 11720}, {265, 999}, {495, 1511}, {496, 10113}, {497, 10733}, {498, 38793}, {499, 23515}, {541, 7727}, {542, 3023}, {1056, 12383}, {1319, 11735}, {1354, 4092}, {1428, 15118}, {1469, 32243}, {1479, 12295}, {1870, 12140}, {2067, 46688}, {2192, 11744}, {2777, 3024}, {3085, 15035}, {3086, 14644}, {3295, 12121}, {3304, 12904}, {3333, 12407}, {3448, 3600}, {3476, 7984}, {3585, 46686}, {4295, 7978}, {4299, 10065}, {4311, 11709}, {4315, 13605}, {4317, 10081}, {5181, 12588}, {5204, 38727}, {5218, 15051}, {5270, 16534}, {5298, 45311}, {5433, 6723}, {5563, 36253}, {5642, 11237}, {5663, 18990}, {6502, 46689}, {7286, 29012}, {7288, 15059}, {7373, 12902}, {7728, 9655}, {7951, 12900}, {8998, 31472}, {9033, 11905}, {9613, 12368}, {9654, 14643}, {9657, 12373}, {9659, 22109}, {9672, 32607}, {10054, 11656}, {10088, 30714}, {10117, 18954}, {10832, 19457}, {10895, 36518}, {11723, 12047}, {12261, 24928}, {12374, 12943}, {13182, 16278}, {13990, 44622}, {15325, 20304}, {15326, 37853}, {19111, 31408}, {19472, 32378}, {19505, 36201}, {31479, 38794}, {32250, 39892}

X(46683) = midpoint of X(i) and X(j) for these {i, j}: {1, 18968}, {1469, 32243}, {3024, 7354}
X(46683) = reflection of X(46687) in X(1)
X(46683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (56, 12903, 125), (1478, 10091, 113), (4299, 10065, 16111), (12374, 12943, 13202)


X(46684) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE AND 1st CIRCUMPERP

Barycentrics    a*(2*a^5-3*(b+c)*a^4-2*(b^2-5*b*c+c^2)*a^3+(b+c)*(4*b^2-9*b*c+4*c^2)*a^2-4*(b-c)^2*b*c*a-(b^3+c^3)*(b-c)^2) : :
X(46684) = X(1)-3*X(38693) = 3*X(3)-X(6265) = 2*X(4)-3*X(38161) = 2*X(5)-3*X(38133) = 3*X(40)+X(6264) = X(100)-3*X(165) = 3*X(100)-X(5531) = 3*X(100)+X(13243) = 3*X(104)-X(6264) = X(149)+3*X(9778) = X(149)-3*X(11219) = 3*X(165)+X(1768) = 9*X(165)-X(5531) = 9*X(165)+X(13243) = 3*X(214)-2*X(6265) = X(214)+2*X(12515) = 3*X(1768)+X(5531) = 3*X(1768)-X(13243) = X(6265)+3*X(12515) = 4*X(6702)-3*X(38161)

Let OA, OB, OC be the circles with collinear centers described at X(5531) and Hyacinthos #21433 (Barry Wolk, January 2013). Let A'B'C' be the triangle formed by the radical axes of these circles and the corresponding mixtilinear excircle. Then X(46684) = X(6)-of-A'B'C'. (Randy Hutson, April 16, 2022)

X(46684) lies on these lines: {1, 38693}, {2, 34789}, {3, 214}, {4, 6702}, {5, 38133}, {10, 2829}, {11, 516}, {20, 80}, {30, 6246}, {35, 11570}, {36, 12758}, {40, 104}, {46, 10058}, {55, 5083}, {56, 15558}, {57, 18240}, {63, 100}, {109, 24025}, {119, 3647}, {140, 12611}, {149, 9778}, {210, 17661}, {355, 38213}, {376, 12119}, {381, 38104}, {484, 6909}, {515, 15863}, {517, 4973}, {519, 13528}, {528, 13226}, {546, 38182}, {548, 952}, {659, 2827}, {758, 2077}, {946, 6713}, {950, 12832}, {962, 16173}, {991, 17601}, {993, 3359}, {1125, 1537}, {1145, 3916}, {1156, 2951}, {1158, 5720}, {1317, 37568}, {1320, 7991}, {1376, 5779}, {1385, 25485}, {1387, 4301}, {1519, 6681}, {1699, 9352}, {1702, 19081}, {1703, 19082}, {1764, 38484}, {1770, 8068}, {2096, 45701}, {2771, 9943}, {2821, 41191}, {2950, 10270}, {2975, 39776}, {3035, 3452}, {3036, 34862}, {3057, 41554}, {3065, 33557}, {3070, 8988}, {3071, 13976}, {3218, 5537}, {3295, 46681}, {3522, 6224}, {3534, 12747}, {3576, 10698}, {3651, 12691}, {3678, 12665}, {3683, 31235}, {3754, 6906}, {3814, 32554}, {3817, 6667}, {3874, 11248}, {3881, 26877}, {3884, 37561}, {3887, 19921}, {3892, 10679}, {3898, 10269}, {4299, 10057}, {4302, 10073}, {4868, 37469}, {5010, 11571}, {5119, 10074}, {5184, 9441}, {5204, 12740}, {5217, 12739}, {5248, 12775}, {5250, 16209}, {5267, 31788}, {5445, 37437}, {5480, 38197}, {5493, 20418}, {5541, 38669}, {5587, 10728}, {5657, 12248}, {5660, 9809}, {5731, 7972}, {5805, 38207}, {5840, 10265}, {5851, 6594}, {5884, 26285}, {6154, 7964}, {6174, 13257}, {6244, 13205}, {6284, 20118}, {6326, 12520}, {6361, 14217}, {6459, 19077}, {6460, 19078}, {6840, 15228}, {7004, 23703}, {7987, 13253}, {8148, 38637}, {9616, 19113}, {9841, 38665}, {9951, 13279}, {9955, 34126}, {9956, 22799}, {9964, 37105}, {10165, 11729}, {10167, 17660}, {10427, 43151}, {10434, 35649}, {10724, 37718}, {10742, 26446}, {11012, 18861}, {11218, 26842}, {11717, 41343}, {11849, 12005}, {12512, 24466}, {12532, 15071}, {12699, 16174}, {12702, 12737}, {12729, 16190}, {12743, 15338}, {12764, 24914}, {12767, 15015}, {13464, 38032}, {13624, 19907}, {14110, 17654}, {14151, 31508}, {15326, 18976}, {15599, 37998}, {15626, 23832}, {16128, 38752}, {17009, 34339}, {18232, 34293}, {18481, 19914}, {18483, 23513}, {19925, 34122}, {20095, 43161}, {22938, 28146}, {26364, 46435}, {28174, 41347}, {30329, 37541}, {31445, 38757}, {31806, 38722}, {33709, 38038}, {33898, 37828}, {35445, 37736}

X(46684) = midpoint of X(i) and X(j) for these {i, j}: {3, 12515}, {20, 80}, {40, 104}, {100, 1768}, {355, 38753}, {484, 6909}, {1155, 17613}, {1156, 2951}, {1320, 7991}, {3065, 33557}, {3218, 5537}, {5493, 21630}, {5531, 13243}, {5541, 38669}, {6361, 14217}, {6840, 15228}, {9778, 11219}, {10265, 31730}, {12119, 12247}, {12248, 12751}, {12532, 15071}, {12702, 12737}, {14110, 17654}, {18481, 19914}
X(46684) = reflection of X(i) in X(j) for these (i, j): (4, 6702), (119, 6684), (214, 3), (946, 6713), (1145, 43174), (1519, 6681), (1537, 1125), (3874, 15528), (4297, 38759), (4301, 1387), (6246, 12619), (10427, 43151), (11715, 38602), (12611, 140), (12665, 3678), (12699, 16174), (19907, 13624), (21630, 20418), (21635, 3035), (22799, 9956), (24466, 12512), (25485, 1385), (31803, 18254), (33814, 31663), (35016, 17009)
X(46684) = complement of X(34789)
X(46684) = X(643)-beth conjugate of-X(14740)
X(46684) = X(1026)-Zayin conjugate of-X(516)
X(46684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 40256, 3878), (4, 6702, 38161), (46, 10058, 12736), (63, 100, 14740), (100, 13243, 5531), (165, 1768, 100), (376, 12247, 12119), (946, 6713, 32557), (1158, 25440, 31803), (1537, 21154, 1125), (1768, 5531, 13243), (5657, 12248, 12751), (6326, 35242, 34474), (10164, 21635, 3035), (12767, 16192, 15015), (19914, 38754, 18481)


X(46685) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: ANTICOMPLEMENTARY AND INNER-CONWAY

Barycentrics    a*((b+c)*a^4-2*(b^2+b*c+c^2)*a^3+3*(b+c)*b*c*a^2+2*(b^4+c^4-(b^2+b*c+c^2)*b*c)*a-(b^2-c^2)*(b^3-c^3)) : :
X(46685) = 3*X(2)-4*X(46694) = X(100)-3*X(3681) = X(149)+3*X(4661) = 3*X(210)-2*X(3035) = 3*X(210)-X(17660) = 3*X(354)-4*X(6667) = 3*X(392)-2*X(12735) = 2*X(942)-3*X(34122) = 5*X(3616)-4*X(46681) = 3*X(3679)-X(11571) = 3*X(3681)-2*X(14740) = 6*X(3740)-5*X(31235) = 2*X(3754)-3*X(38213) = 3*X(3873)-4*X(18240) = 3*X(3873)-5*X(31272) = 2*X(3881)-3*X(32557) = 3*X(4134)-X(33337) = 4*X(5044)-3*X(34123) = 2*X(12532)+X(39776) = 4*X(18240)-5*X(31272)

X(46685) lies on these lines: {1, 18254}, {2, 5083}, {8, 153}, {9, 37736}, {10, 11570}, {11, 518}, {63, 100}, {65, 3036}, {72, 952}, {78, 104}, {80, 3436}, {119, 6734}, {144, 20095}, {145, 15558}, {149, 329}, {210, 3035}, {214, 2975}, {354, 6667}, {392, 12735}, {517, 38389}, {519, 12758}, {528, 17781}, {529, 18976}, {758, 1109}, {912, 6735}, {914, 3717}, {942, 34122}, {956, 6265}, {958, 12739}, {960, 1317}, {997, 10074}, {1145, 2771}, {1156, 34784}, {1320, 11682}, {1329, 20118}, {1331, 2342}, {1387, 3555}, {1537, 5777}, {2098, 11256}, {2284, 38358}, {2802, 3632}, {2810, 22321}, {2829, 14872}, {3059, 5851}, {3219, 41553}, {3305, 14151}, {3419, 10742}, {3421, 12247}, {3434, 34789}, {3616, 46681}, {3679, 11571}, {3687, 34458}, {3699, 34234}, {3738, 4088}, {3740, 31235}, {3754, 38213}, {3811, 10058}, {3868, 12736}, {3870, 30223}, {3871, 41562}, {3872, 10698}, {3873, 18240}, {3874, 6702}, {3881, 32557}, {3916, 33814}, {3927, 12331}, {3935, 41166}, {3940, 12773}, {3951, 38665}, {3962, 17636}, {3984, 38669}, {4134, 33337}, {4420, 17100}, {4430, 5748}, {4468, 37998}, {4511, 11715}, {4551, 16586}, {4651, 20879}, {4652, 34474}, {4847, 21635}, {4853, 13253}, {4855, 38693}, {4861, 20117}, {4863, 13271}, {4882, 12767}, {4996, 12757}, {5044, 34123}, {5080, 6246}, {5220, 41701}, {5231, 15017}, {5249, 38211}, {5289, 20586}, {5440, 38602}, {5533, 21616}, {5541, 12526}, {5552, 15528}, {5686, 12755}, {5687, 12515}, {5692, 7972}, {5730, 12737}, {5794, 12763}, {5795, 41558}, {5815, 9803}, {5854, 17638}, {6174, 27778}, {6583, 38182}, {6713, 27385}, {6765, 13278}, {7330, 12775}, {7672, 31164}, {7686, 38156}, {7993, 10971}, {8068, 21077}, {9024, 43216}, {9802, 9804}, {10057, 41686}, {10087, 12514}, {10265, 21075}, {10427, 40659}, {10707, 11678}, {10916, 39692}, {10956, 24987}, {11415, 14217}, {11679, 35649}, {11680, 15064}, {12005, 27529}, {12513, 12740}, {12607, 20612}, {12611, 24390}, {12619, 17757}, {12675, 21154}, {12680, 38759}, {12831, 25006}, {12832, 24982}, {13265, 44694}, {13274, 24703}, {14213, 17165}, {14923, 31803}, {15104, 44447}, {15556, 20060}, {17658, 17661}, {18253, 33667}, {19907, 31835}, {20116, 38216}, {24465, 41539}, {34339, 38128}, {35614, 38484}, {39778, 40661}, {45393, 45632}

X(46685) = midpoint of X(i) and X(j) for these {i, j}: {8, 12532}, {80, 5904}, {1156, 34784}, {3869, 12531}, {3962, 17636}
X(46685) = reflection of X(i) in X(j) for these (i, j): (1, 18254), (65, 3036), (100, 14740), (145, 15558), (214, 3678), (908, 17615), (1145, 34790), (1317, 960), (1537, 5777), (3555, 1387), (3868, 12736), (3874, 6702), (5083, 46694), (9809, 13227), (10427, 40659), (11570, 10), (12680, 38759), (17660, 3035), (19907, 31835), (25485, 20117), (33667, 18253), (39776, 8), (39778, 40661), (41558, 5795)
X(46685) = anticomplement of X(5083)
X(46685) = X(8)-beth conjugate of-X(11570)
X(46685) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (100, 3681, 14740), (200, 1768, 100), (210, 17660, 3035), (3873, 31272, 18240), (5083, 46694, 2)


X(46686) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: EHRMANN-MID AND EHRMANN-VERTEX

Barycentrics    2*a^10-3*(3*b^4-4*b^2*c^2+3*c^4)*a^6+(b^2+c^2)*(7*b^4-12*b^2*c^2+7*c^4)*a^4+(b^2-c^2)^2*(b^2-3*c^2)*(3*b^2-c^2)*a^2-3*(b^4-c^4)*(b^2-c^2)^3 : :
X(46686) = 3*X(2)+X(10721) = X(3)-3*X(36518) = 3*X(4)+X(110) = 5*X(4)-X(10733) = 3*X(4)-X(12295) = 7*X(4)+X(12383) = 2*X(4)+X(16534) = 11*X(4)+5*X(20125) = 5*X(4)+X(30714) = X(110)-3*X(113) = 5*X(110)+3*X(10733) = 7*X(110)-3*X(12383) = 2*X(110)-3*X(16534) = 11*X(110)-15*X(20125) = 5*X(110)-3*X(30714) = 5*X(113)+X(10733) = 3*X(113)+X(12295) = 7*X(113)-X(12383) = 11*X(113)-5*X(20125) = 5*X(113)-X(30714) = 2*X(12900)+X(13202) = 2*X(12900)-3*X(36518) = X(13202)+3*X(36518)

X(46686) lies on these lines: {2, 10721}, {3, 12900}, {4, 110}, {5, 1539}, {20, 15036}, {25, 12893}, {30, 5972}, {52, 12825}, {74, 3091}, {125, 381}, {140, 34584}, {146, 3832}, {182, 19506}, {185, 16222}, {235, 15473}, {265, 3527}, {382, 14643}, {389, 546}, {399, 36749}, {403, 32110}, {427, 33547}, {515, 11723}, {542, 1353}, {567, 43831}, {974, 5462}, {1112, 10151}, {1495, 18323}, {1511, 3627}, {1514, 10297}, {1531, 11799}, {1533, 7574}, {1553, 36184}, {1568, 31726}, {1593, 12901}, {1595, 23306}, {1597, 12302}, {1598, 2931}, {1656, 20127}, {1657, 15046}, {1699, 12368}, {1986, 12162}, {2574, 32549}, {2575, 32550}, {2771, 5806}, {2794, 33511}, {2935, 6642}, {3047, 15033}, {3090, 15055}, {3146, 15035}, {3448, 3839}, {3526, 38788}, {3529, 15029}, {3544, 15021}, {3545, 12244}, {3574, 15089}, {3583, 46687}, {3585, 46683}, {3817, 11709}, {3818, 32271}, {3830, 5642}, {3850, 20304}, {3851, 10990}, {3853, 10272}, {3856, 13566}, {3858, 10264}, {3859, 20396}, {3861, 6053}, {5055, 38728}, {5066, 15088}, {5072, 15041}, {5073, 38723}, {5076, 32609}, {5095, 18440}, {5181, 31670}, {5198, 12168}, {5446, 44226}, {5449, 35488}, {5655, 12902}, {5892, 44920}, {5893, 9826}, {5907, 11807}, {5943, 17855}, {6000, 14708}, {6033, 16278}, {6560, 13990}, {6561, 8998}, {6564, 46688}, {6565, 46689}, {6644, 13293}, {6759, 12228}, {7517, 22109}, {7526, 13289}, {7699, 37077}, {7722, 15305}, {7723, 13417}, {8717, 18531}, {8994, 42265}, {9140, 41099}, {9730, 17854}, {9818, 10117}, {9919, 11479}, {9927, 45010}, {9955, 11735}, {10110, 12236}, {10114, 18379}, {10118, 37697}, {10170, 13416}, {10257, 20725}, {10575, 46431}, {10628, 44870}, {10657, 43227}, {10658, 43226}, {10750, 14500}, {10751, 14499}, {10752, 32275}, {10819, 22615}, {10820, 22644}, {10895, 12374}, {10896, 12373}, {10982, 19456}, {11381, 16223}, {11454, 16868}, {11558, 13391}, {11561, 32137}, {11562, 12292}, {11563, 41674}, {11597, 32340}, {11720, 31673}, {11744, 37475}, {11805, 22804}, {12038, 20771}, {12133, 23047}, {12219, 15058}, {12227, 32139}, {12242, 15807}, {12281, 16261}, {12310, 18535}, {12358, 16105}, {12811, 40685}, {12891, 35764}, {12892, 35765}, {12896, 18514}, {13203, 18537}, {13211, 18492}, {13419, 18567}, {13488, 15115}, {13568, 15114}, {13969, 42262}, {14448, 22584}, {14853, 41737}, {15054, 15081}, {15101, 16776}, {15118, 19130}, {15123, 37984}, {15647, 18475}, {15687, 34153}, {17812, 37514}, {18358, 32257}, {18376, 34155}, {18403, 44407}, {18451, 19504}, {18513, 18968}, {18560, 43839}, {18572, 29012}, {19059, 42561}, {19060, 31412}, {19110, 23249}, {19111, 23259}, {19481, 40240}, {19505, 37696}, {22251, 33699}, {23698, 33512}, {25564, 37814}, {25641, 46045}, {32223, 44961}, {34484, 46027}, {37197, 37489}, {44673, 46031}

X(46686) = midpoint of X(i) and X(j) for these {i, j}: {3, 13202}, {4, 113}, {5, 1539}, {52, 12825}, {110, 12295}, {125, 7728}, {146, 16003}, {265, 15063}, {382, 16163}, {1495, 18323}, {1511, 3627}, {1514, 10297}, {1531, 11799}, {1533, 7574}, {1553, 36184}, {1568, 31726}, {1986, 12162}, {3818, 32271}, {3830, 5642}, {3853, 10272}, {5095, 18440}, {5181, 31670}, {5907, 11807}, {6033, 16278}, {7687, 38791}, {7723, 13417}, {10575, 46431}, {10721, 16111}, {10733, 30714}, {10750, 14500}, {10751, 14499}, {10752, 32275}, {10990, 38790}, {11561, 32137}, {11562, 12292}, {11597, 32340}, {11720, 31673}, {11805, 22804}, {12133, 25711}, {12358, 16105}, {12824, 16194}, {12902, 24981}, {14448, 22584}, {25641, 46045}
X(46686) = reflection of X(i) in X(j) for these (i, j): (3, 12900), (74, 20397), (974, 5462), (6699, 5), (7687, 546), (11735, 9955), (11806, 11746), (12041, 6723), (12236, 10110), (14708, 41671), (15118, 19130), (16534, 113), (19481, 40240), (20304, 3850), (20417, 20304), (32223, 44961), (32257, 18358), (36253, 7687), (37853, 140), (38726, 5972), (40647, 9826), (40685, 12811), (44673, 46031), (45311, 5066)
X(46686) = complement of X(16111)
X(46686) = complementary conjugate of the complement of X(46429)
X(46686) = inverse of X(10151) in Hatzipolakis-Lozada hyperbola
X(46686) = X(113)-of-Euler-triangle
X(46686) = X(6699)-of-Johnson-triangle
X(46686) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 10721, 16111), (3, 36518, 12900), (4, 110, 12295), (4, 5448, 12897), (5, 12041, 6723), (5, 14677, 34128), (74, 3091, 23515), (74, 23515, 20397), (113, 12295, 110), (146, 3832, 14644), (146, 14644, 16003), (265, 38789, 15063), (381, 7728, 125), (382, 14643, 16163), (546, 38791, 36253), (1656, 20127, 38727), (1657, 15046, 38794), (3545, 12244, 15059), (3843, 38789, 265), (3851, 38790, 15061), (5655, 12902, 24981), (6723, 12041, 6699), (11562, 16194, 12292), (12292, 12824, 11562), (13202, 36518, 3), (13417, 15030, 7723), (15061, 38790, 10990), (20304, 20417, 38725)


X(46687) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: INTANGENTS AND MANDART-INCIRCLE

Barycentrics    (2*a^8-2*(b^2+c^2)*a^6-(b^4-4*b^2*c^2+c^4)*a^4+2*(b^2-c^2)^2*b*c*a^2+(b^4-c^4)*(b^2-c^2)*(b-c)^2)*(-a+b+c) : :
X(46687) = 3*X(1)-X(18968) = X(3024)-3*X(3058) = 3*X(12896)+X(18968) = 2*X(12896)+X(46683) = 2*X(18968)-3*X(46683)

X(46687) lies on these lines: {1, 12888}, {11, 5972}, {12, 7687}, {33, 46682}, {35, 6699}, {36, 38726}, {55, 125}, {56, 16163}, {67, 10387}, {74, 4294}, {110, 497}, {113, 1479}, {221, 11744}, {265, 3295}, {388, 10733}, {390, 3448}, {495, 10113}, {496, 1511}, {498, 23515}, {499, 38793}, {541, 19470}, {542, 3024}, {999, 12121}, {1058, 12383}, {1365, 6062}, {1456, 6357}, {1478, 12295}, {1697, 13211}, {2066, 46688}, {2293, 38535}, {2330, 15118}, {2646, 11735}, {2771, 31795}, {2777, 3028}, {3056, 32297}, {3057, 10693}, {3085, 14644}, {3086, 15035}, {3303, 12903}, {3486, 7984}, {3583, 46686}, {3586, 12368}, {3746, 36253}, {4302, 10081}, {4304, 11709}, {4309, 10065}, {4314, 13605}, {4857, 16534}, {4995, 45311}, {5160, 29012}, {5181, 12589}, {5217, 38727}, {5218, 15059}, {5414, 46689}, {5432, 6723}, {5642, 11238}, {5663, 15171}, {5722, 12778}, {6198, 12140}, {6767, 12902}, {7288, 15051}, {7728, 9668}, {7741, 12900}, {7978, 30305}, {8998, 44623}, {9033, 11906}, {9140, 10385}, {9659, 32607}, {9669, 14643}, {9670, 12374}, {9672, 22109}, {10070, 11656}, {10091, 30714}, {10117, 10833}, {10118, 36201}, {10149, 18400}, {10264, 10386}, {10831, 19457}, {10896, 36518}, {11720, 12053}, {11723, 30384}, {12261, 24929}, {12310, 16541}, {12373, 12953}, {12407, 31393}, {13183, 16278}, {13990, 44624}, {15172, 32423}, {15338, 37853}, {19052, 31474}, {22954, 32350}, {32250, 39891}

X(46687) = midpoint of X(i) and X(j) for these {i, j}: {1, 12896}, {3028, 6284}, {3056, 32297}
X(46687) = reflection of X(46683) in X(1)
X(46687) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (55, 12904, 125), (1479, 10088, 113), (4302, 10081, 16111), (12373, 12953, 13202)


X(46688) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: 1st KENMOTU-CENTERS AND 1st KENMOTU DIAGONALS

Barycentrics    (a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*a^2+(b^2-c^2)^2*(-a^2+b^2+c^2)*S : :
X(46688) = 3*X(371)+X(35834) = 3*X(35822)+X(35826)

X(46688) lies on these lines: {2, 13990}, {3, 8994}, {4, 19044}, {5, 13915}, {6, 67}, {49, 43863}, {74, 1587}, {110, 3068}, {113, 485}, {141, 32303}, {265, 3311}, {371, 12891}, {372, 6699}, {486, 23515}, {541, 35822}, {542, 32787}, {590, 5972}, {615, 6723}, {1151, 16163}, {1152, 38727}, {1511, 8981}, {1588, 14644}, {1986, 12239}, {2066, 46687}, {2067, 46683}, {2777, 3070}, {3024, 19030}, {3028, 19028}, {3069, 15059}, {3071, 7687}, {3312, 13969}, {3448, 7585}, {3594, 38729}, {5412, 46682}, {5418, 10820}, {5465, 13908}, {5504, 19062}, {5622, 39875}, {5642, 13846}, {5663, 7583}, {6143, 43825}, {6199, 12902}, {6200, 38726}, {6221, 12121}, {6398, 38728}, {6417, 19051}, {6419, 36253}, {6420, 20397}, {6427, 15027}, {6449, 38723}, {6459, 10733}, {6460, 15055}, {6560, 16111}, {6561, 12295}, {6564, 46686}, {6593, 13910}, {7581, 19059}, {7582, 15081}, {7584, 20304}, {7728, 13665}, {7735, 13654}, {7736, 13774}, {7968, 11735}, {7984, 19066}, {8960, 12376}, {8976, 14643}, {8983, 11720}, {8991, 11598}, {8995, 11597}, {9140, 19054}, {9540, 15035}, {10088, 13905}, {10091, 13904}, {10113, 42215}, {10117, 44598}, {10264, 19117}, {10272, 13925}, {10576, 12900}, {10620, 18512}, {10721, 23249}, {10778, 19113}, {10817, 42638}, {10819, 30714}, {10880, 12140}, {11005, 19056}, {11006, 19058}, {11744, 19088}, {12041, 42216}, {12240, 46430}, {12244, 23267}, {12903, 18996}, {12904, 19038}, {13171, 19006}, {13202, 23251}, {13211, 18991}, {13287, 36201}, {13903, 32609}, {13909, 46085}, {13966, 34128}, {13979, 19116}, {15088, 18762}, {19096, 33565}, {23236, 31487}, {32788, 45311}, {35770, 38725}, {36518, 42265}, {37853, 42259}, {43808, 43826}

X(46688) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 19110, 13990), (6, 125, 46689), (110, 3068, 8998), (3312, 15061, 13969), (3448, 7585, 19111), (5418, 10820, 38793), (6417, 38724, 19051)


X(46689) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: 2nd KENMOTU-CENTERS AND 2nd KENMOTU DIAGONALS

Barycentrics    (a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*a^2-(b^2-c^2)^2*(-a^2+b^2+c^2)*S : :
X(46689) = 3*X(372)+X(35835) = 3*X(35823)+X(35827)

X(46689) lies on these lines: {2, 8998}, {3, 13969}, {4, 19043}, {5, 13979}, {6, 67}, {49, 43864}, {74, 1588}, {110, 3069}, {113, 486}, {141, 32304}, {265, 3312}, {371, 6699}, {372, 12892}, {485, 23515}, {541, 35823}, {542, 32788}, {590, 6723}, {615, 5972}, {1151, 38727}, {1152, 16163}, {1511, 13966}, {1587, 14644}, {1986, 12240}, {2777, 3071}, {3024, 19029}, {3028, 19027}, {3068, 15059}, {3070, 7687}, {3311, 8994}, {3448, 7586}, {3592, 38729}, {5413, 46682}, {5414, 46687}, {5420, 10819}, {5465, 13968}, {5504, 19061}, {5622, 39876}, {5642, 13847}, {5663, 7584}, {6143, 43826}, {6221, 38728}, {6395, 12902}, {6396, 38726}, {6398, 12121}, {6418, 19052}, {6419, 20397}, {6420, 36253}, {6428, 15027}, {6450, 38723}, {6459, 15055}, {6460, 10733}, {6502, 46683}, {6560, 12295}, {6561, 16111}, {6565, 46686}, {6593, 13972}, {7581, 15081}, {7582, 19060}, {7583, 20304}, {7728, 13785}, {7735, 13774}, {7736, 13654}, {7969, 11735}, {7984, 19065}, {8981, 34128}, {9140, 19053}, {10088, 13963}, {10091, 13962}, {10113, 42216}, {10117, 44599}, {10264, 19116}, {10272, 13993}, {10577, 12900}, {10620, 18510}, {10721, 23259}, {10778, 19112}, {10818, 42637}, {10820, 30714}, {10881, 12140}, {11005, 19055}, {11006, 19057}, {11597, 13986}, {11598, 13980}, {11720, 13971}, {11744, 19087}, {12041, 42215}, {12239, 46430}, {12244, 23273}, {12375, 16534}, {12903, 18995}, {12904, 19037}, {13171, 19005}, {13202, 23261}, {13211, 18992}, {13288, 36201}, {13915, 19117}, {13935, 15035}, {13951, 14643}, {13961, 32609}, {13970, 46085}, {15088, 18538}, {19095, 33565}, {32787, 45311}, {35771, 38725}, {36518, 42262}, {37853, 42258}, {43808, 43825}

X(46689) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 19111, 8998), (6, 125, 46688), (110, 3069, 13990), (3311, 15061, 8994), (3448, 7586, 19110), (5420, 10819, 38793), (6418, 38724, 19052)


X(46690) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: LUCAS CENTRAL AND LUCAS TANGENTS

Barycentrics    (-4*a^12+b^12+c^12+17*(b^2+c^2)*a^10-2*(11*b^4+4*b^2*c^2+11*c^4)*a^8+(b^2+c^2)*(23*b^4-113*b^2*c^2+23*c^4)*a^6-(19*b^8+19*c^8-2*(52*b^4+61*b^2*c^2+52*c^4)*b^2*c^2)*a^4+(8*b^8+8*c^8-(9*b^4+16*b^2*c^2+9*c^4)*b^2*c^2)*b^2*c^2+(b^2+c^2)*(4*b^8+4*c^8-(75*b^4-82*b^2*c^2+75*c^4)*b^2*c^2)*a^2+(22*(b^2+c^2)*a^8-2*(17*b^4+74*b^2*c^2+17*c^4)*a^6+2*(b^2+c^2)*(14*b^4+27*b^2*c^2+14*c^4)*a^4-2*(15*b^8+15*c^8+2*(2*b^4-27*b^2*c^2+2*c^4)*b^2*c^2)*a^2+2*(b^2+c^2)*(3*b^8+3*c^8-(9*b^4+8*b^2*c^2+9*c^4)*b^2*c^2))*S)*a^2 : :
X(46690) = X(7598)-3*X(11199)

X(46690) lies on these lines: {7598, 11199}


X(46691) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: LUCAS(-1) CENTRAL AND LUCAS(-1) TANGENTS

Barycentrics    a^2*(-4*a^12+b^12+c^12+17*(b^2+c^2)*a^10-2*(11*b^4+4*b^2*c^2+11*c^4)*a^8+(b^2+c^2)*(23*b^4-113*b^2*c^2+23*c^4)*a^6-(19*b^8+19*c^8-2*(52*b^4+61*b^2*c^2+52*c^4)*b^2*c^2)*a^4+(8*b^8+8*c^8-(9*b^4+16*b^2*c^2+9*c^4)*b^2*c^2)*b^2*c^2+(b^2+c^2)*(4*b^8+4*c^8-(75*b^4-82*b^2*c^2+75*c^4)*b^2*c^2)*a^2-(22*(b^2+c^2)*a^8-2*(17*b^4+74*b^2*c^2+17*c^4)*a^6+2*(b^2+c^2)*(14*b^4+27*b^2*c^2+14*c^4)*a^4-2*(15*b^8+15*c^8+2*(2*b^4-27*b^2*c^2+2*c^4)*b^2*c^2)*a^2+2*(b^2+c^2)*(3*b^8+3*c^8-(9*b^4+8*b^2*c^2+9*c^4)*b^2*c^2))*S) : :
X(46691) = X(7599)-3*X(32074)

X(46691) lies on these lines: {7599, 32074}


X(46692) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: LUCAS INNER AND LUCAS INNER TANGENTIAL

Barycentrics    a^2*(400*a^12-490*b^12-490*c^12-2090*(b^2+c^2)*a^10+20*(173*b^4+166*b^2*c^2+173*c^4)*a^8-2*(b^2+c^2)*(1195*b^4-2341*b^2*c^2+1195*c^4)*a^6-2*(25*b^8+25*c^8+2*(1481*b^4+755*b^2*c^2+1481*c^4)*b^2*c^2)*a^4+2*(134*b^8+134*c^8+(1353*b^4-2164*b^2*c^2+1353*c^4)*b^2*c^2)*b^2*c^2+2*(b^2+c^2)*(580*b^8+580*c^8+(1767*b^4-2678*b^2*c^2+1767*c^4)*b^2*c^2)*a^2-(600*a^10+590*(b^2+c^2)*a^8-10*(377*b^4+734*b^2*c^2+377*c^4)*a^6+2*(b^2+c^2)*(2530*b^4-81*b^2*c^2+2530*c^4)*a^4-(3270*b^8+3270*c^8+(277*b^4-4182*b^2*c^2+277*c^4)*b^2*c^2)*a^2+(b^2+c^2)*(390*b^8+390*c^8-(4173*b^4-5614*b^2*c^2+4173*c^4)*b^2*c^2))*S) : :
X(46692) = X(7601)-3*X(32072)

X(46692) lies on these lines: {7601, 32072}


X(46693) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: LUCAS(-1) INNER AND LUCAS(-1) INNER TANGENTIAL

Barycentrics    a^2*(400*a^12-490*b^12-490*c^12-2090*(b^2+c^2)*a^10+20*(173*b^4+166*b^2*c^2+173*c^4)*a^8-2*(b^2+c^2)*(1195*b^4-2341*b^2*c^2+1195*c^4)*a^6-2*(25*b^8+25*c^8+2*(1481*b^4+755*b^2*c^2+1481*c^4)*b^2*c^2)*a^4+2*(134*b^8+134*c^8+(1353*b^4-2164*b^2*c^2+1353*c^4)*b^2*c^2)*b^2*c^2+2*(b^2+c^2)*(580*b^8+580*c^8+(1767*b^4-2678*b^2*c^2+1767*c^4)*b^2*c^2)*a^2+(600*a^10+590*(b^2+c^2)*a^8-10*(377*b^4+734*b^2*c^2+377*c^4)*a^6+2*(b^2+c^2)*(2530*b^4-81*b^2*c^2+2530*c^4)*a^4-(3270*b^8+3270*c^8+(277*b^4-4182*b^2*c^2+277*c^4)*b^2*c^2)*a^2+(b^2+c^2)*(390*b^8+390*c^8-(4173*b^4-5614*b^2*c^2+4173*c^4)*b^2*c^2))*S) : :
X(46693) = X(7602)-3*X(32073)

X(46693) lies on these lines: {7602, 32073}


X(46694) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: MEDIAL AND 2nd ZANIAH

Barycentrics    a*((b+c)*a^3-(b+c)^2*a^2-(b+c)*(b^2-3*b*c+c^2)*a+(b^2+3*b*c+c^2)*(b-c)^2)*(-a+b+c) : :
X(46694) = 3*X(2)+X(46685) = X(11)+3*X(210) = X(72)+3*X(34122) = 3*X(210)-X(14740) = X(1145)-5*X(3697) = X(1317)-5*X(25917) = 5*X(1698)-X(11570) = X(3035)-3*X(3740) = 5*X(3617)-X(39776) = 3*X(3679)+X(12758) = 3*X(3681)+5*X(31272) = X(3878)+3*X(38213) = 7*X(3983)+X(17638) = X(5887)+3*X(38128) = 7*X(9780)+X(12532) = X(9946)-3*X(38752) = 3*X(10176)+X(15863) = X(12736)-3*X(34122) = 3*X(15064)+X(46684) = X(15528)-3*X(38133)

X(46694) lies on these lines: {2, 5083}, {8, 4939}, {9, 100}, {10, 119}, {11, 210}, {72, 12736}, {80, 2551}, {104, 936}, {149, 18228}, {214, 958}, {518, 6667}, {527, 24465}, {528, 18227}, {756, 16579}, {758, 5123}, {952, 5044}, {960, 2802}, {997, 11715}, {1125, 46681}, {1145, 3697}, {1158, 34293}, {1215, 41797}, {1317, 25917}, {1320, 15829}, {1329, 3678}, {1376, 5779}, {1387, 34790}, {1698, 11570}, {1768, 8580}, {2284, 25069}, {2550, 34789}, {2801, 3035}, {2827, 4925}, {3305, 41553}, {3617, 39776}, {3679, 12758}, {3681, 30827}, {3754, 10592}, {3820, 12619}, {3878, 11928}, {3911, 17615}, {3928, 11678}, {3952, 4858}, {3983, 17638}, {4521, 37998}, {4551, 16578}, {4662, 5854}, {4679, 13274}, {5234, 15015}, {5325, 6174}, {5438, 38693}, {5531, 30393}, {5660, 38057}, {5770, 15528}, {5784, 17661}, {5791, 9946}, {5811, 46435}, {5840, 12572}, {6265, 9708}, {6700, 6713}, {7308, 37736}, {8582, 12832}, {9519, 38390}, {9623, 10698}, {9709, 12515}, {9780, 12532}, {9951, 13996}, {10090, 41229}, {10176, 15863}, {11571, 19875}, {11681, 15556}, {12059, 24914}, {12611, 31419}, {14110, 38156}, {14872, 21154}, {16174, 21616}, {17660, 31235}, {18229, 35649}, {18976, 34606}, {19113, 31438}, {19861, 41554}, {21630, 21631}, {24003, 34589}, {24025, 24433}, {25096, 38358}, {25681, 32557}, {30294, 34711}, {31165, 38099}, {31424, 34474}, {31445, 33814}, {31803, 37828}, {34894, 42015}, {35628, 38484}

X(46694) = midpoint of X(i) and X(j) for these {i, j}: {8, 15558}, {10, 18254}, {11, 14740}, {72, 12736}, {960, 3036}, {1158, 34293}, {1387, 34790}, {1768, 13227}, {3678, 6702}, {3911, 17615}, {5083, 46685}, {9951, 13996}
X(46694) = reflection of X(i) in X(j) for these (i, j): (18240, 6667), (46681, 1125)
X(46694) = complement of X(5083)
X(46694) = inverse of X(124) in Spieker circle
X(46694) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 46685, 5083), (11, 210, 14740), (72, 34122, 12736), (210, 18236, 3452)


X(46695) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: MIDARC AND TANGENTIAL-MIDARC

Barycentrics    a*(4*b*c*(b-c)*(2*a^2-2*(b+c)*a-b*c)*sin(A/2)+2*c*((3*b+c)*a^3-(3*b^2-b*c+2*c^2)*a^2+(b-c)*(b^2+4*b*c-c^2)*a-(b^2-c^2)*(b-c)*b)*sin(B/2)-2*b*((b+3*c)*a^3-(2*b^2-b*c+3*c^2)*a^2+(b-c)*(b^2-4*b*c-c^2)*a-(b^2-c^2)*(b-c)*c)*sin(C/2)+(b-c)*(a^4-2*(b+c)*a^3+(2*b^2+b*c+2*c^2)*a^2-2*(b^3+c^3)*a+(b^2+3*b*c+c^2)*(b-c)^2)) : :
X(46695) = X(10506)-3*X(11191)

X(46695) lies on these lines: {1, 6724}, {177, 10501}, {5045, 5571}, {10491, 10506}, {13092, 13560}

X(46695) = midpoint of X(177) and X(10501)
X(46695) = reflection of X(46696) in X(1)
X(46695) = X(125)-of-midarc-triangle


X(46696) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: 2ND MIDARC AND 2ND TANGENTIAL-MIDARC

Barycentrics    a*(4*b*c*(b-c)*(2*a^3-(2*b^2+7*b*c+2*c^2)*a+b*c*(b+c))*sin(A/2)+2*c*((5*b-c)*a^4+(11*b+c)*c*a^3-(6*b^3-c^3+b*c*(b+10*c))*a^2+(b^2-c^2)*(3*b+c)*c*a+(b^2-c^2)^2*b)*sin(B/2)+2*b*((b-5*c)*a^4-(b+11*c)*b*a^3-(b^3-6*c^3-b*c*(10*b+c))*a^2+(b^2-c^2)*(b+3*c)*b*a-(b^2-c^2)^2*c)*sin(C/2)-(b-c)*(a^5-(b+c)*a^4+13*b*c*a^3-13*(b+c)*b*c*a^2-(b^4+c^4+b*c*(b^2-12*b*c+c^2))*a+(b^2-c^2)*(b-c)*(b^2+3*b*c+c^2))) : :
X(46696) = X(10501)-3*X(11234)

X(46696) lies on these lines: {1, 6724}, {8422, 10506}, {10501, 11234}, {31766, 31792}

X(46696) = midpoint of X(8422) and X(10506)
X(46696) = reflection of X(46695) in X(1)
X(46696) = X(125)-of-2nd-midarc-triangle


X(46697) = (name pending)

Barycentrics    a^2*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 + 6*a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 + 3*b^2*c^4 - c^6)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - a^4*c^2 + 6*a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6)*(a^22*b^2 - 7*a^20*b^4 + 21*a^18*b^6 - 35*a^16*b^8 + 34*a^14*b^10 - 14*a^12*b^12 - 14*a^10*b^14 + 34*a^8*b^16 - 35*a^6*b^18 + 21*a^4*b^20 - 7*a^2*b^22 + b^24 + a^22*c^2 - 8*a^20*b^2*c^2 + 41*a^18*b^4*c^2 - 122*a^16*b^6*c^2 + 206*a^14*b^8*c^2 - 220*a^12*b^10*c^2 + 214*a^10*b^12*c^2 - 256*a^8*b^14*c^2 + 257*a^6*b^16*c^2 - 156*a^4*b^18*c^2 + 49*a^2*b^20*c^2 - 6*b^22*c^2 - 7*a^20*c^4 + 41*a^18*b^2*c^4 - 86*a^16*b^4*c^4 + 128*a^14*b^6*c^4 - 170*a^12*b^8*c^4 + 2*a^10*b^10*c^4 + 448*a^8*b^12*c^4 - 680*a^6*b^14*c^4 + 441*a^4*b^16*c^4 - 131*a^2*b^18*c^4 + 14*b^20*c^4 + 21*a^18*c^6 - 122*a^16*b^2*c^6 + 128*a^14*b^4*c^6 + 168*a^12*b^6*c^6 - 202*a^10*b^8*c^6 - 416*a^8*b^10*c^6 + 848*a^6*b^12*c^6 - 576*a^4*b^14*c^6 + 165*a^2*b^16*c^6 - 14*b^18*c^6 - 35*a^16*c^8 + 206*a^14*b^2*c^8 - 170*a^12*b^4*c^8 - 202*a^10*b^6*c^8 + 380*a^8*b^8*c^8 - 390*a^6*b^10*c^8 + 306*a^4*b^12*c^8 - 94*a^2*b^14*c^8 - b^16*c^8 + 34*a^14*c^10 - 220*a^12*b^2*c^10 + 2*a^10*b^4*c^10 - 416*a^8*b^6*c^10 - 390*a^6*b^8*c^10 - 72*a^4*b^10*c^10 + 18*a^2*b^12*c^10 + 20*b^14*c^10 - 14*a^12*c^12 + 214*a^10*b^2*c^12 + 448*a^8*b^4*c^12 + 848*a^6*b^6*c^12 + 306*a^4*b^8*c^12 + 18*a^2*b^10*c^12 - 28*b^12*c^12 - 14*a^10*c^14 - 256*a^8*b^2*c^14 - 680*a^6*b^4*c^14 - 576*a^4*b^6*c^14 - 94*a^2*b^8*c^14 + 20*b^10*c^14 + 34*a^8*c^16 + 257*a^6*b^2*c^16 + 441*a^4*b^4*c^16 + 165*a^2*b^6*c^16 - b^8*c^16 - 35*a^6*c^18 - 156*a^4*b^2*c^18 - 131*a^2*b^4*c^18 - 14*b^6*c^18 + 21*a^4*c^20 + 49*a^2*b^2*c^20 + 14*b^4*c^20 - 7*a^2*c^22 - 6*b^2*c^22 + c^24) : :

See Antreas Hatzipolakis and Peter Moses, euclid 3953.

X(46697) lies on this line: {5065, 6641}


X(46698) = NINE-POINT-CIRCLE-INVERSE OF X(1113)

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

X(46698) lies on these lines: {2, 3}, {113, 32549}

X(46698) = midpoint of PU(199)
X(46698) = nine-point-circle-inverse of X(1113)
X(46698) = crosssum of X(184) and X(15166)


X(46699) = NINE-POINT-CIRCLE-INVERSE OF X(1114)

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

X(46699) lies on these lines: {2, 3}, {113, 32550}

X(46699) = midpoint of PU(200)
X(46699) = nine-point-circle-inverse of X(1114)
X(46699) = crosssum of X(184) and X(15167)


X(46700) = X(4)X(6)∩X(253)X(7398)

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

See Antreas Hatzipolakis and César Lozada, euclid 3962.

X(46700) lies on these lines: {4, 6}, {25, 15594}, {107, 35283}, {253, 7398}, {1368, 20204}, {3589, 32713}, {5020, 15259}, {6525, 32000}, {9825, 15312}, {13562, 27373}, {14615, 34412}

X(46700) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(34412)}} and {{A, B, C, X(253), X(5286)}}


X(46701) = (name pending)

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

See Antreas Hatzipolakis and César Lozada, euclid 3962.

X(46701) lies on the circumconic centered at X(5139) and this line: {25, 7795}

X(46701) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(25)}} and {{A, B, C, X(66), X(76)}}


X(46702) = EULER LINE INTERCEPT OF X(577)X(6116)

Barycentrics    -8*S^3*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)+sqrt(3)*(-a^2+b^2+c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^2+b^2-c^2) : :
Barycentrics   (S^2-3*SB*SC)*S^3+sqrt(3)*(S^2+SB*SC)*SA*SB*SC : :

See Kadir Altintas and César Lozada, euclid 3969.

X(46702) lies on these lines: {2, 3}, {577, 6116}, {1092, 41888}, {3643, 11793}, {5872, 40665}, {5889, 11078}, {6759, 41023}, {10654, 39571}, {11543, 42459}, {18381, 41022}, {23325, 44666}

X(46702) = reflection of X(46703) in X(5)
X(46702) = X(46703)-of-Johnson-triangle
X(46702) = intersection, other than A, B, C, of circumconics {{A, B, C, X(68), X(19773)}} and {{A, B, C, X(265), X(46703)}}
X(46702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 19772, 3), (18586, 18587, 473)


X(46703) = EULER LINE INTERCEPT OF X(577)X(6117)

Barycentrics    8*S^3*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)+sqrt(3)*(-a^2+b^2+c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^2+b^2-c^2) : :
Barycentrics   -(S^2-3*SB*SC)*S^3+sqrt(3)*(S^2+SB*SC)*SA*SB*SC : :

See Kadir Altintas and César Lozada, euclid 3969.

X(46703) lies on these lines: {2, 3}, {577, 6117}, {1092, 41887}, {3642, 11793}, {5873, 40666}, {5889, 11092}, {6759, 41022}, {10653, 39571}, {11542, 42459}, {18381, 41023}, {23325, 44667}

X(46703) = reflection of X(46702) in X(5)
X(46703) = X(46702)-of-Johnson-triangle
X(46703) = intersection, other than A, B, C, of circumconics {{A, B, C, X(68), X(19772)}} and {{A, B, C, X(265), X(46702)}}
X(46703) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 19773, 3), (18586, 18587, 472)


X(46704) = 68TH HATZIPOLAKIS-MOSES-EULER POINT

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

See Antreas Hatzipolakis and Peter Moses, euclid 3975.

X(46704) lies on these lines: {2, 3}, {171, 3585}, {355, 511}, {500, 515}, {517, 4647}, {944, 5453}, {946, 36250}, {1460, 18961}, {1478, 5711}, {1503, 13408}, {3436, 5774}, {4299, 15447}, {4442, 22791}, {5492, 29057}, {5786, 36742}, {7009, 18447}, {7683, 45926}, {9958, 10526}, {10888, 37531}, {16792, 29012}, {18492, 20368}, {18513, 37603}, {26446, 35203}

X(46704) = midpoint X(4) and X(15971)
X(46704) = reflection of X(i) in X(j) for these {i,j}: {3,15973}, {944,5453}, {9840,5}
X(46704) = X(15971)-of-Euler-triangle
X(46704) = X(9840)-of-Johnson-triangle


X(46705) = ISOGONAL CONJUGATE OF X(46370)

Barycentrics    a*((c-a)*(a-b+c)*((b^3+(a+c)*b^2-b*(c-a)^2-(a+c)*(c^2-6*c*a+a^2))*sin(B/2)+(2*c+2*a)*b^2-2*b*(c-a)^2-2*(c^2-a^2)*(c-a)+2*b^3)+(a+b-c)*(b^4+(c-2*a)*b^3-c*(c-a)*b^2-(c-a)*(c^2+5*c*a+2*a^2)*b-(c^2-a^2)*a*(-a+3*c))*sin(C/2)-(-a+b+c)*(b^4-(2*c-a)*b^3+a*(c-a)*b^2+(c-a)*(2*c^2+5*c*a+a^2)*b-(c^2-a^2)*c*(-3*a+c))*sin(A/2))*((a-b)*(a+b-c)*((c^3+(a+b)*c^2-c*(a-b)^2-(a+b)*(a^2-6*a*b+b^2))*sin(C/2)+(2*a+2*b)*c^2-2*c*(a-b)^2-2*(a^2-b^2)*(a-b)+2*c^3)+(-a+b+c)*(c^4+(a-2*b)*c^3-a*(a-b)*c^2-(a-b)*(a^2+5*a*b+2*b^2)*c-(a^2-b^2)*b*(-b+3*a))*sin(A/2)-(a-b+c)*(c^4-(2*a-b)*c^3+b*(a-b)*c^2+(a-b)*(2*a^2+5*a*b+b^2)*c-(a^2-b^2)*a*(-3*b+a))*sin(B/2)) : :

See Kadir Altintas and César Lozada, euclid 3990.

X(46705) lies on the curve Q104 and this line: {259, 2956}

X(46705) = isogonal conjugate of X(46370)





leftri  Points on cubics: X(46706) - X(46726)  rightri

This preamble is contributed by Clark Kimberling and Peter Moses, January 18, 2022.

Let P = p : q : r be a point that is not on a sideline BC, CA, AB of a triangle ABC. Let A' be the point, other than A, in which the cevian line AP intersects the Steiner circumellipse, and define B' and C' cyclically. Then

A' = -a q r : (b r + c q) q : (b r + c q) r

Let A'' be the points, other than A, in which the anticevian line of P intersects the Steiner circumellipse, and define B'' and C'' cyclically. Then

A" = a q r : (c q – b r) q : (b r – c q) r

Then A'B'C' is perspective to the anticomplementary triangle, and the perspector is the point

U(P) = p^2*q^2 + p^2*r^2 - q^2*r^2 : :

Moreover, A''B''C'' is also perspective to the anticomplementary triangle, with perspector U(P), which is the anticomplement of isotomic conjugate of P^2. The appearance of (i,j) in the following list means that if X(i) = p:q:r, then X(j) = U(P).

(1,194), (2,2), (4,6392), (6,8264), (7,4452), (8,30695), (31,40382), (32,40381), (66,33785), (69,6527), (75,69), (76,315), (83,7760), (85,6604), (86,4360), (87,32033), (92,6515), (98,36849), (99,99), (174,3210), (188,3177), (190,190), (264,317), (274,17143), (290,290), (308,33769), (335,6653), (365,17486), (366,192), (508,145), (556,329), (561,33796), (648,648), (662,14570), (664,664), (666,666), (668,668), (670,670), (671,671), (673,32029), (799,4576), (886,886), (889,889), (892,892), (903,903),

Note that i = j if and only if X(i) lies on the Steiner circumellipse.

underbar



X(46706) = X(220)-CEVA CONJUGATE OF X(2)

Barycentrics    a^6*b^2 - 4*a^5*b^3 + 6*a^4*b^4 - 4*a^3*b^5 + a^2*b^6 + a^6*c^2 - 5*a^4*b^2*c^2 + 4*a^3*b^3*c^2 + a^2*b^4*c^2 - b^6*c^2 - 4*a^5*c^3 + 4*a^3*b^2*c^3 - 4*a^2*b^3*c^3 + 4*b^5*c^3 + 6*a^4*c^4 + a^2*b^2*c^4 - 6*b^4*c^4 - 4*a^3*c^5 + 4*b^3*c^5 + a^2*c^6 - b^2*c^6 : :
Barycentrics    ra2 - rb2 - rc2 : :, where ra, rb, rc are the radii of the mixtilinear incircles

X(46706) lies on these lines: {2, 31618}, {9, 3177}, {144, 4499}, {192, 3870}, {1655, 30695}, {7674, 20111}, {11677, 14732}, {25243, 43989}, {26125, 30694}

X(46706) = anticomplement of isogonal conjugate of X(14827)
X(46706) = anticomplement of isotomic conjugate of X(220)
X(46706) = anticomplement of polar conjugate of X(7071)
X(46706) = anticomplement of barycentric square of X(85)
X(46706) = isotomic conjugate of isogonal conjugate of X(35215)
X(46706) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {9, 21280}, {31, 6604}, {32, 36845}, {41, 3434}, {55, 21285}, {200, 315}, {220, 6327}, {341, 33796}, {346, 21275}, {480, 21286}, {560, 4452}, {657, 21293}, {692, 46402}, {1253, 69}, {1501, 17480}, {1802, 1370}, {2175, 7}, {2194, 20244}, {2206, 17158}, {2287, 17138}, {2328, 17137}, {2332, 20242}, {4524, 21294}, {4578, 21304}, {6066, 21272}, {6602, 3436}, {7071, 21270}, {7079, 11442}, {7256, 21305}, {7259, 44445}, {8641, 150}, {9447, 145}, {9448, 3210}, {14827, 8}, {24027, 4569}, {32739, 3900}
X(46706) = X(220)-Ceva conjugate of X(2)
X(46706) = barycentric product X(76)*X(35215)
X(46706) = barycentric quotient X(35215)/X(6)


X(46707) = X(594)-CEVA CONJUGATE OF X(2)

Barycentrics    a^4 + 2*a^3*b - a^2*b^2 - 2*a*b^3 - b^4 + 2*a^3*c - 4*a*b^2*c - 2*b^3*c - a^2*c^2 - 4*a*b*c^2 - b^2*c^2 - 2*a*c^3 - 2*b*c^3 - c^4 : :
X(46707) = 3 X[2] - 4 X[6537]

X(46707) lies on these lines: {1, 20536}, {2, 1171}, {8, 148}, {10, 894}, {69, 27269}, {194, 5739}, {315, 17343}, {333, 20337}, {524, 23905}, {596, 39348}, {599, 26147}, {1655, 2895}, {2134, 35216}, {3578, 19570}, {4643, 44370}, {6626, 10026}, {14555, 27318}, {16826, 17778}, {17344, 25994}, {17346, 26081}, {17685, 33297}, {17781, 29615}, {20090, 33770}, {21220, 37656}, {23942, 41135}, {24051, 24090}, {24504, 33299}, {26064, 40721}, {35511, 36223}

X(46707) = reflection of X(i) in X(j) for these {i,j}: {1509, 6537}, {32004, 23905}
X(46707) = anticomplement of X(1509)
X(46707) = anticomplement of isogonal conjugate of X(1500)
X(46707) = anticomplement of isotomic conjugate of X(594)
X(46707) = isotomic conjugate of isogonal conjugate of X(35216)
X(46707) = anticomplementary isogonal conjugate of X(17143)
X(46707) = X(594)-Ceva conjugate of X(2)
X(46707) = X(58)-isoconjugate of X(2135)
X(46707) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 17143}, {6, 17140}, {9, 35614}, {10, 17137}, {12, 21285}, {31, 4360}, {37, 17135}, {41, 2975}, {42, 75}, {43, 34086}, {55, 21273}, {65, 20244}, {71, 20243}, {72, 18659}, {100, 17159}, {101, 17166}, {181, 7}, {210, 20245}, {213, 1}, {228, 17134}, {321, 17138}, {594, 6327}, {692, 17161}, {756, 69}, {762, 1330}, {765, 4576}, {798, 17154}, {813, 4155}, {872, 2}, {1018, 512}, {1042, 17158}, {1089, 315}, {1110, 99}, {1245, 39731}, {1252, 21295}, {1254, 6604}, {1334, 3869}, {1400, 3873}, {1402, 3875}, {1500, 8}, {1824, 17220}, {1826, 20242}, {1918, 17147}, {2171, 3434}, {2175, 18662}, {2194, 18654}, {2200, 20222}, {2205, 17148}, {2333, 3868}, {2350, 13476}, {3690, 4329}, {3949, 1370}, {3952, 17217}, {4024, 21293}, {4033, 44445}, {4037, 20554}, {4079, 149}, {4103, 21301}, {4551, 4374}, {4557, 7192}, {4705, 150}, {6057, 21286}, {6187, 39765}, {6358, 21280}, {6378, 10453}, {6535, 21287}, {6541, 20560}, {7035, 670}, {7064, 329}, {7109, 192}, {7140, 21270}, {7148, 21281}, {18098, 17142}, {20693, 20351}, {21759, 17155}, {21803, 30660}, {21816, 2891}, {21859, 21302}, {23493, 17144}, {23990, 6758}, {27808, 21305}, {28654, 21275}, {28658, 17146}, {34857, 17139}, {40504, 8049}, {40521, 20295}, {40607, 40007}, {40729, 38}
X(46707) = barycentric product X(i)*X(j) for these {i,j}: {76, 35216}, {321, 2134}
X(46707) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 2135}, {2134, 81}, {35216, 6}
X(46707) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1509, 6537, 2}, {1654, 6625, 10}


X(46708) = X(11080)-CEVA CONJUGATE OF X(2)

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

X(46708) lies on these lines: {2, 2981}, {13, 533}, {115, 40901}, {146, 148}, {194, 616}, {299, 5025}, {303, 22847}, {315, 40899}, {395, 30471}, {628, 22511}, {3411, 36781}, {5617, 13571}, {6298, 22496}, {6772, 40898}, {7785, 22796}, {14145, 16530}, {20088, 41745}, {33255, 37641}

X(46708) = anticomplement of X(11129)
X(46708) = anticomplement of isotomic conjugate of X(11080)
X(46708) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {11080, 6327}, {36839, 17217}
X(46708) = X(11080)-Ceva conjugate of X(2)
X(46708) = {X(3180),X(11121)}-harmonic conjugate of X(13)


X(46709) = X(11085)-CEVA CONJUGATE OF X(2)

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

X(46709) lies on these lines: {2, 6151}, {14, 532}, {115, 40900}, {146, 148}, {194, 617}, {298, 5025}, {302, 22893}, {315, 40898}, {396, 30472}, {627, 22510}, {3412, 44029}, {5613, 13571}, {6299, 22495}, {6775, 40899}, {7785, 22797}, {14144, 16529}, {20088, 41746}, {33255, 37640}

X(46709) = anticomplement of X(11128)
X(46709) = anticomplement of isotomic conjugate of X(11085)
X(46709) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {11085, 6327}, {36840, 17217}
X(46709) = X(11085)-Ceva conjugate of X(2)
X(46709) = {X(3181),X(11122)}-harmonic conjugate of X(14)


X(46710) = X(17)X(623)∩X(148)X(16001)

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

X(46710) lies on these lines: {17, 623}, {148, 16001}, {182, 193}, {194, 617}, {299, 7939}, {315, 40901}, {2996, 21845}, {3181, 16241}, {7764, 40900}, {7826, 40899}


X(46711) = X(18)X(624)∩X(148)X(16002)

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

X(46711) lies on these lines: {18, 624}, {148, 16002}, {182, 193}, {194, 616}, {298, 7939}, {315, 40900}, {2996, 21846}, {3180, 16242}, {7764, 40901}, {7826, 40898}


X(46712) = X(2207)-CEVA CONJUGATE OF X(2)

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

X(46712) lies on these lines: {2, 40831}, {6, 194}, {19, 21216}, {69, 3981}, {148, 36851}, {193, 1843}, {385, 37491}, {393, 6339}, {3618, 4074}, {7766, 36432}, {7793, 37485}, {30676, 30688}

X(46712) = anticomplement of isogonal conjugate of X(36417)
X(46712) = anticomplement of isotomic conjugate of X(2207)
X(46712) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {107, 21305}, {158, 33796}, {393, 21275}, {560, 6527}, {1096, 315}, {1924, 34186}, {1973, 1370}, {1974, 4329}, {2203, 18659}, {2207, 6327}, {5317, 17138}, {6059, 21286}, {7337, 21285}, {24000, 670}, {24019, 44445}, {32713, 17217}, {36417, 8}, {41937, 21295}, {44162, 6360}
X(46712) = X(2207)-Ceva conjugate of X(2)


X(46713) = X(36421)-CEVA CONJUGATE OF X(2)

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

X(46713) lies on these lines: {29, 3868}, {63, 26647}, {193, 20008}, {1993, 3177}, {3732, 5889}, {6225, 20061}, {6515, 30694}, {17147, 40571}, {31294, 39351}

X(46713) = anticomplement of isotomic conjugate of X(36421)
X(46713) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2204, 3152}, {2299, 2897}, {2326, 1370}, {24022, 18026}, {36420, 36845}, {36421, 6327}
X(46713) = X(36421)-Ceva conjugate of X(2)


X(46714) = X(1500)-CEVA CONJUGATE OF X(2)

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

X(46714) lies on these lines: {2, 34022}, {37, 1655}, {192, 25054}, {194, 966}, {1654, 4651}, {2663, 17499}, {17300, 21220}, {21226, 24437}, {24478, 24505}

X(46714) = anticomplement of isogonal conjugate of X(7109)
X(46714) = anticomplement of isotomic conjugate of X(1500)
X(46714) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {31, 17143}, {32, 17140}, {37, 17138}, {41, 35614}, {42, 17137}, {181, 21285}, {213, 17135}, {228, 18659}, {560, 4360}, {594, 21275}, {692, 17159}, {756, 315}, {765, 670}, {872, 69}, {1018, 44445}, {1089, 33796}, {1110, 4576}, {1402, 20244}, {1500, 6327}, {1918, 75}, {1924, 17154}, {2171, 21280}, {2175, 21273}, {2200, 20243}, {2205, 1}, {2209, 34086}, {2333, 20242}, {3952, 21305}, {4079, 21293}, {4557, 17217}, {7064, 21286}, {7109, 8}, {9447, 2975}, {9448, 18662}, {18267, 18827}, {23990, 21295}, {32739, 17166}, {40521, 21304}, {40729, 17153}
X(46714) = X(1500)-Ceva conjugate of X(2)


X(46715) = X(8041)-CEVA CONJUGATE OF X(2)

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

X(46715) lies on these lines: {2, 689}, {38, 21217}, {1369, 7779}, {2896, 3118}, {3410, 39346}, {7791, 40382}, {33021, 39953}

X(46715) = anticomplement of isotomic conjugate of X(8041)
X(46715) = anticomplementary isogonal conjugate of X(33769)
X(46715) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 33769}, {31, 33798}, {39, 21278}, {560, 7760}, {1923, 6}, {1964, 76}, {2084, 25051}, {2531, 21221}, {3051, 17165}, {4020, 12220}, {7794, 21275}, {8041, 6327}, {9247, 19121}, {23995, 4577}, {41267, 3770}, {41331, 17489}
X(46715) = X(8041)-Ceva conjugate of X(2)


X(46716) = X(1407)-CEVA CONJUGATE OF X(2)

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

X(46716) lies on these lines: {2, 32017}, {57, 1999}, {192, 5256}, {194, 712}, {4320, 17480}, {9263, 9965}, {17143, 24621}, {17490, 27002}, {19825, 27318}, {29529, 37652}

X(46716) = anticomplement of isotomic conjugate of X(1407)
X(46716) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {56, 21286}, {269, 315}, {279, 21275}, {560, 30695}, {604, 3436}, {738, 21280}, {934, 21304}, {1042, 21287}, {1088, 33796}, {1106, 69}, {1397, 329}, {1398, 21270}, {1407, 6327}, {1408, 20245}, {1435, 11442}, {1461, 21301}, {2206, 18750}, {4616, 21305}, {4637, 44445}, {7023, 21285}, {7099, 1370}, {7250, 21294}, {7342, 21273}, {7366, 3434}, {16947, 3869}, {23979, 3952}, {24027, 668}, {41280, 3177}
X(46716) = X(1407)-Ceva conjugate of X(2)
X(46716) = {X(3210),X(39694)}-harmonic conjugate of X(57)


X(46717) = X(394)-CEVA CONJUGATE OF X(2)

Barycentrics    a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 + a^2*b^10 + a^10*c^2 - a^8*b^2*c^2 - 2*a^6*b^4*c^2 + 2*a^4*b^6*c^2 + a^2*b^8*c^2 - b^10*c^2 - 4*a^8*c^4 - 2*a^6*b^2*c^4 + 4*a^4*b^4*c^4 - 2*a^2*b^6*c^4 + 4*b^8*c^4 + 6*a^6*c^6 + 2*a^4*b^2*c^6 - 2*a^2*b^4*c^6 - 6*b^6*c^6 - 4*a^4*c^8 + a^2*b^2*c^8 + 4*b^4*c^8 + a^2*c^10 - b^2*c^10 : :
X(46717) = 3 X[2] - 4 X[6509]

X(46717) lies on the Steiner/Wallace right hyperbola (Kiepert circumhyperbola of anticomplementary triangle) and these lines: {1, 10538}, {2, 216}, {4, 13409}, {20, 2979}, {22, 6194}, {63, 1943}, {69, 8612}, {147, 1370}, {148, 6504}, {194, 401}, {253, 41914}, {394, 8613}, {426, 41204}, {627, 19772}, {628, 19773}, {631, 32078}, {852, 3168}, {1075, 41481}, {1764, 7560}, {3552, 46625}, {3917, 42329}, {5905, 44354}, {6503, 40888}, {7396, 9742}, {7493, 7616}, {8782, 40870}, {12012, 40329}, {14361, 41678}, {14461, 41588}, {14570, 37669}, {14919, 35061}, {38283, 42453}, {39352, 45794}

X(46717) = reflection of X(2052) in X(6509)
X(46717) = isotomic conjugate of X(34287)
X(46717) = anticomplement of X(2052)
X(46717) = anticomplement of isogonal conjugate of X(577)
X(46717) = anticomplement of isotomic conjugate of X(394)
X(46717) = isotomic conjugate of isogonal conjugate of X(41373)
X(46717) = isotomic conjugate of polar conjugate of X(1075)
X(46717) = anticomplementary isogonal conjugate of X(317)
X(46717) = X(38257)-complementary conjugate of X(20305)
X(46717) = X(i)-Ceva conjugate of X(j) for these (i,j): {394, 2}, {20477, 20}
X(46717) = X(41373)-cross conjugate of X(1075)
X(46717) = X(i)-isoconjugate of X(j) for these (i,j): {19, 13855}, {31, 34287}
X(46717) = crossdifference of every pair of points on line {30442, 39201}
X(46717) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 317}, {3, 21270}, {6, 5906}, {31, 6515}, {48, 4}, {63, 11442}, {163, 520}, {184, 5905}, {255, 69}, {326, 315}, {394, 6327}, {520, 21294}, {560, 6392}, {563, 6193}, {577, 8}, {822, 3448}, {906, 20293}, {1092, 4329}, {1259, 21286}, {1437, 17220}, {1790, 20242}, {1804, 21285}, {1820, 68}, {2148, 5889}, {2169, 264}, {2289, 3436}, {3682, 21287}, {3926, 21275}, {3990, 1330}, {4055, 2895}, {4091, 21293}, {4100, 20}, {4558, 21300}, {4575, 850}, {6056, 329}, {6507, 1370}, {7125, 3434}, {7183, 21280}, {7335, 7}, {9247, 193}, {14575, 21216}, {14585, 192}, {18604, 17135}, {19210, 21271}, {19614, 32001}, {22341, 2893}, {23224, 150}, {23606, 6360}, {23995, 648}, {24000, 6528}, {24027, 18026}, {28724, 21278}, {32656, 4391}, {32660, 521}, {32661, 7253}, {35200, 340}, {36054, 33650}, {36059, 46400}, {36060, 41724}, {39201, 21221}
X(46717) = barycentric product X(i)*X(j) for these {i,j}: {69, 1075}, {76, 41373}, {95, 41481}
X(46717) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 34287}, {3, 13855}, {1075, 4}, {41373, 6}, {41481, 5}
X(46717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 40896, 324}, {2, 43988, 3164}, {394, 20477, 8613}, {2052, 6509, 2}, {6360, 7361, 63}, {6389, 11547, 2}, {15466, 44436, 2}


X(46718) = X(2)X(18023)∩X(67)X(14712)

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

X(46718) lies on these lines: {2, 18023}, {67, 14712}, {895, 39356}, {1632, 39346}, {2453, 32528}, {7836, 45809}, {11061, 40871}


X(46719) = X(2)X(4403)∩X(80)X(20072)

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

X(46719) lies on these lines: {2, 4403}, {80, 20072}, {148, 3732}, {194, 30694}, {1320, 39349}, {6224, 40860}, {14206, 19570}, {17279, 18159}, {20085, 39364}

X(46719) = X(34535)-anticomplementary conjugate of X(21280)


X(46720) = X(593)-CEVA CONJUGATE OF X(2)

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

X(46720) lies on these lines: {2, 1240}, {75, 18601}, {81, 4360}, {192, 19717}, {239, 33792}, {3210, 23958}, {3264, 26747}, {3995, 41242}, {8267, 17486}, {9263, 20086}, {10330, 33767}, {14829, 17495}, {16049, 20222}, {17143, 18171}, {17160, 29766}, {18654, 18662}, {31036, 32026}

X(46720) = anticomplement of X(28654)
X(46720) = anticomplement of isotomic conjugate of X(593)
X(46720) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {58, 21287}, {60, 21286}, {593, 6327}, {757, 315}, {763, 17138}, {849, 69}, {873, 33796}, {1101, 668}, {1333, 1330}, {1408, 2893}, {1509, 21275}, {2150, 3436}, {2206, 2895}, {3733, 21294}, {4556, 21301}, {7341, 21285}, {7342, 7}, {16947, 2475}, {23357, 3952}, {23995, 190}, {36420, 5906}
X(46720) = X(593)-Ceva conjugate of X(2)
X(46720) = {X(17147),X(35058)}-harmonic conjugate of X(81)


X(46721) = X(6)X(6664)∩X(69)X(20859)

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

X(46721) lies on these lines: {6, 6664}, {69, 20859}, {82, 17489}, {193, 2854}, {194, 3618}, {1974, 41676}, {8264, 14570}, {27375, 32451}, {43996, 46288}

X(46721) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {46288, 21289}, {46289, 1369}
X(46721) = crosssum of X(3005) and X(38996)
X(46721) = {X(6),X(6664)}-harmonic conjugate of X(33798)


X(46722) = X(2226)-CEVA CONJUGATE OF X(2)

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

X(46722) lies on these lines: {2, 646}, {88, 17160}, {190, 17147}, {194, 21224}, {519, 46150}, {668, 26844}, {1797, 2403}, {3210, 23958}, {4576, 33296}, {9263, 20092}, {14570, 41629}, {16726, 42051}

X(46722) = anticomplement of X(36791)
X(46722) = anticomplement of isogonal conjugate of X(41935)
X(46722) = anticomplement of isotomic conjugate of X(2226)
X(46722) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {679, 315}, {1318, 21286}, {2226, 6327}, {4618, 21304}, {4638, 21301}, {9456, 21290}, {41935, 8}
X(46722) = X(2226)-Ceva conjugate of X(2)
X(46722) = crossdifference of every pair of points on line {8660, 23644}
X(46722) = {X(17495),X(39698)}-harmonic conjugate of X(88)


X(46723) = X(2)X(2986)∩X(94)X(11071)

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

X(46723) lies on these lines: {2, 2986}, {94, 11071}, {648, 14129}, {2407, 30529}, {18122, 40604}, {18300, 36853}, {32027, 41254}

X(46723) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2166, 1272}, {14595, 6360}, {14859, 21271}, {23588, 6758}
X(46723) = {X(13582),X(37779)}-harmonic conjugate of X(94)


X(46724) = ANTICOMPLEMENT OF X(36412)

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

X(46724) lies on these lines: {2, 10979}, {3, 95}, {6, 35941}, {20, 317}, {30, 32002}, {69, 74}, {76, 10323}, {97, 43988}, {141, 35937}, {160, 1632}, {183, 16276}, {186, 44131}, {206, 35278}, {216, 401}, {286, 6906}, {290, 8266}, {297, 34828}, {305, 15574}, {311, 1078}, {315, 40697}, {316, 39113}, {325, 7667}, {340, 550}, {418, 16089}, {458, 36751}, {548, 41008}, {577, 648}, {1232, 18354}, {1238, 7768}, {1609, 40814}, {1799, 20564}, {1843, 11676}, {1975, 37198}, {3148, 32085}, {3260, 44180}, {3522, 6527}, {3525, 8797}, {3528, 32000}, {3589, 40884}, {3964, 44133}, {4226, 19121}, {6394, 46546}, {6636, 30737}, {7488, 44138}, {7771, 44837}, {7782, 9723}, {7802, 44128}, {8553, 41760}, {8719, 9924}, {9308, 36748}, {9737, 44443}, {9822, 35919}, {11057, 38434}, {11257, 40947}, {15696, 40995}, {17538, 32001}, {17907, 37188}, {19126, 35926}, {30716, 37918}, {37688, 44210}, {37765, 42459}, {39352, 40897}, {39646, 44200}, {40896, 43980}, {40996, 44245}, {43459, 44135}

X(46724) = reflection of X(32002) in X(45198)
X(46724) = isotomic conjugate of X(6662)
X(46724) = isotomic conjugate of anticomplement of X(6663)
X(46724) = isotomic conjugate of isogonal conjugate of X(1614)
X(46724) = isogonal conjugate of perspector of Steiner circumellipse of orthic triangle
X(46724) = anticomplement of X(36412)
X(46724) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2148, 17035}, {2167, 2888}, {46089, 6360}
X(46724) = X(6663)-cross conjugate of X(2)
X(46724) = X(31)-isoconjugate of X(6662)
X(46724) = cevapoint of X(3) and X(43988)
X(46724) = crosssum of X(15451) and X(34980)
X(46724) = crossdifference of every pair of points on line {14398, 42293}
X(46724) = barycentric product X(76)*X(1614)
X(46724) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6662}, {1614, 6}, {6663, 36412}, {46093, 35071}
X(46724) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 264, 95}, {3, 20477, 264}, {20, 40680, 317}, {216, 401, 36794}, {577, 3164, 648}, {7782, 14615, 9723}


X(46725) = X(1252)-CEVA CONJUGATE OF X(2)

Barycentrics    (a - b)*(a - c)*(a^2*b^2 - a*b^3 + 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(46725) = 3 X[2] - 4 X[23988], 2 X[44312] - 3 X[46125]

X(46725) lies on these lines: {2, 4554}, {100, 17494}, {194, 21224}, {514, 46148}, {693, 27134}, {1331, 2398}, {1621, 40637}, {2481, 26846}, {4576, 33946}, {4586, 10330}, {4762, 35310}, {5701, 27190}, {6758, 31296}, {8267, 17486}, {14570, 43191}, {17147, 32029}, {20095, 39350}, {20974, 25049}, {26795, 26824}, {26985, 28743}, {44312, 46125}

X(46725) = reflection of X(i) in X(j) for these {i,j}: {23989, 23988}, {25049, 20974}
X(46725) = isotomic conjugate of trilinear pole of line X(116)X(926) (the tangent to the nine-point circle at X(116))
X(46725) = anticomplement of X(23989)
X(46725) = anticomplement of isogonal conjugate of X(23990)
X(46725) = anticomplement of isotomic conjugate of X(1252)
X(46725) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {59, 21285}, {101, 21293}, {692, 150}, {765, 315}, {1016, 21275}, {1101, 17143}, {1110, 69}, {1252, 6327}, {2149, 3434}, {4557, 21294}, {4564, 21280}, {4567, 17138}, {4570, 17137}, {6065, 21286}, {6066, 329}, {7035, 33796}, {9447, 17036}, {23357, 17140}, {23979, 36845}, {23990, 8}, {23995, 4360}, {24027, 6604}, {32739, 149}
X(46725) = X(1252)-Ceva conjugate of X(2)
X(46725) = X(513)-isoconjugate of X(2141)
X(46725) = cevapoint of X(17494) and X(40637)
X(46725) = crosspoint of X(190) and X(31624)
X(46725) = crossdifference of every pair of points on line {8638, 20974}
X(46725) = barycentric product X(i)*X(j) for these {i,j}: {190, 2140}, {765, 19594}
X(46725) = barycentric quotient X(i)/X(j) for these {i,j}: {101, 2141}, {2140, 514}, {19594, 1111}
X(46725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5701, 40619, 27190}, {23988, 23989, 2}


X(46726) = X(23357)-CEVA CONJUGATE OF X(2)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^4*b^4 - a^2*b^6 + 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 - a^2*c^6 - b^2*c^6) : :
X(46726) = 3 X[2] - 4 X[23584]

X(46726) lies on these lines: {2, 6331}, {110, 9514}, {194, 11004}, {850, 45215}, {3164, 7492}, {4226, 35311}, {5012, 40642}, {5661, 36901}, {8267, 36849}, {10330, 14570}, {14683, 39355}, {23878, 35319}

X(46726) = reflection of X(23962) in X(23584)
X(46726) = isogonal conjugate of X(36198)
X(46726) = anticomplement of X(23962)
X(46726) = anticomplement of isogonal conjugate of X(23963)
X(46726) = anticomplement of isotomic conjugate of X(23357)
X(46726) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {249, 21275}, {1101, 315}, {1576, 21294}, {14574, 21221}, {23357, 6327}, {23963, 8}, {23995, 69}, {24037, 33797}, {24041, 33796}, {41937, 5906}
X(46726) = X(23357)-Ceva conjugate of X(2)
X(46726) = cevapoint of X(31296) and X(40642)
X(46726) = trilinear product X(662)*X(34845)
X(46726) = trilinear quotient X(34845)/X(661)
X(46726) = barycentric product X(i)*X(j) for these {i,j}: {99, 34845}, {249, 36199}
X(46726) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 36198}, {34845, 523}, {36199, 338}
X(46726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11794, 31296, 110}, {23584, 23962, 2}


X(46727) = X(2)X(9833)∩X(262)X(6146)

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

See Antreas Hatzipolakis and Peter Moses, euclid 4004.

X(46727) lies on the Kiepert circumhyperbola and these lines: {2, 9833}, {262, 6146}, {1503, 13599}, {2052, 6756}, {3517, 16080}, {7566, 40393}, {10982, 14492}, {13380, 16655}, {18396, 45300}, {31363, 34781}

X(46727) = isogonal conjugate of X(46728)


X(46728) = X(3)X(6)∩X(20)X(2888)

Barycentrics    a^2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*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 + 5*a^2*c^6 + 2*b^2*c^6 - 2*c^8) : :
Barycentrics    Sin[A]^2*(Cot[A] + 1 / (Csc[A]*Csc[B]*Csc[C] - 3*Cot[w])) : :
X(46728) = 3 X[3] - X[36747], 5 X[3] - 3 X[37506], X[4] - 3 X[43653], 3 X[376] - X[19467], 3 X[578] - 2 X[36747], X[578] + 2 X[37486], 5 X[578] - 6 X[37506], 3 X[3796] - X[12160], 3 X[8703] - X[43595], 3 X[19126] - 2 X[44480], X[36747] + 3 X[37486], 5 X[36747] - 9 X[37506], 5 X[37486] + 3 X[37506]

See Antreas Hatzipolakis and Peter Moses, euclid 4004.

X(46728) lies on these lines: {3, 6}, {4, 33522}, {20, 2888}, {22, 5562}, {23, 11444}, {24, 3917}, {25, 11793}, {26, 1216}, {51, 7509}, {68, 44829}, {69, 9833}, {74, 17538}, {110, 38435}, {141, 6756}, {156, 7555}, {184, 7512}, {185, 10323}, {186, 43652}, {343, 18381}, {376, 1204}, {394, 9715}, {524, 31804}, {546, 33533}, {548, 43588}, {550, 7689}, {599, 34726}, {1092, 2979}, {1147, 5944}, {1154, 7525}, {1209, 31723}, {1297, 6570}, {1352, 13419}, {1370, 20299}, {1595, 29181}, {1614, 35268}, {1658, 10627}, {2777, 37201}, {2937, 10539}, {3060, 37126}, {3088, 46026}, {3089, 11821}, {3090, 34417}, {3091, 15107}, {3292, 9707}, {3517, 17811}, {3518, 5651}, {3546, 44673}, {3547, 18388}, {3567, 43650}, {3574, 7558}, {3627, 4550}, {3796, 12160}, {3818, 7553}, {3819, 6642}, {5059, 15062}, {5067, 38848}, {5446, 7514}, {5447, 6644}, {5449, 14791}, {5462, 7516}, {5889, 6636}, {5891, 7517}, {5907, 7387}, {5921, 41464}, {5943, 7393}, {6000, 11414}, {6247, 44683}, {6800, 43844}, {7395, 10110}, {7404, 31670}, {7484, 11695}, {7487, 10519}, {7496, 15028}, {7499, 45089}, {7503, 45186}, {7528, 24206}, {7540, 11178}, {7550, 9781}, {7592, 14531}, {7998, 44802}, {8542, 12061}, {8567, 17822}, {8703, 43595}, {8717, 13491}, {9545, 23061}, {9818, 13598}, {9909, 17814}, {9927, 34115}, {10170, 13861}, {10274, 41590}, {10299, 43597}, {10303, 41462}, {10304, 43601}, {10605, 37198}, {11003, 15801}, {11204, 11413}, {11381, 12082}, {11411, 46264}, {11424, 35921}, {11439, 37945}, {11456, 45187}, {11459, 12088}, {11591, 17714}, {12083, 12162}, {12087, 15305}, {12103, 32138}, {12106, 32142}, {12111, 41466}, {12134, 16789}, {12163, 35243}, {12225, 34786}, {12233, 16197}, {12307, 34783}, {12362, 18390}, {13289, 41673}, {13322, 34850}, {13367, 44837}, {13474, 39568}, {13564, 18436}, {14641, 33532}, {14786, 19130}, {14790, 21243}, {15004, 43651}, {15024, 22112}, {15043, 15246}, {15053, 15717}, {15058, 37925}, {15067, 37440}, {15072, 16661}, {15682, 43613}, {16266, 18475}, {16618, 22660}, {18534, 44870}, {18535, 33537}, {18570, 32196}, {18912, 41586}, {18914, 44882}, {20427, 35513}, {20806, 23042}, {21230, 34514}, {21735, 34564}, {22549, 33542}, {23325, 37444}, {23335, 44201}, {32767, 37638}, {34779, 41716}, {34785, 44239}, {34788, 41614}, {35228, 41589}, {35240, 35481}, {35475, 43576}, {43598, 44082}

X(46728) = midpoint of X(i) and X(j) for these {i,j}: {3, 37486}, {1350, 37485}
X(46728) = reflection of X(i) in X(j) for these {i,j}: {576, 44491}, {578, 3}, {12233, 16197}
X(46728) = isogonal conjugate of X(46727)
X(46728) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 52, 182}, {3, 389, 37515}, {3, 568, 13336}, {3, 1350, 15644}, {3, 1351, 37476}, {3, 6243, 569}, {3, 9730, 13347}, {3, 9786, 16836}, {3, 10625, 13346}, {3, 11432, 5085}, {3, 13336, 17508}, {3, 15644, 37480}, {3, 17834, 389}, {3, 33878, 37498}, {3, 36749, 37513}, {3, 36752, 5092}, {3, 37484, 13352}, {3, 37489, 9729}, {3, 37494, 52}, {3, 37495, 39242}, {3, 37498, 11430}, {22, 5562, 6759}, {26, 1216, 9306}, {394, 9715, 10282}, {569, 6243, 576}, {1092, 7488, 11202}, {1351, 37476, 37505}, {1352, 31305, 13419}, {2937, 23039, 10539}, {2979, 7488, 1092}, {3098, 37478, 11438}, {3518, 7999, 5651}, {5092, 16625, 36752}, {5889, 6636, 10984}, {6101, 7502, 1147}, {7395, 33586, 10110}, {7512, 11412, 184}, {9729, 14810, 3}, {9786, 31884, 3}, {10282, 15606, 394}, {11459, 12088, 26883}, {11591, 17714, 46261}, {14531, 22352, 7592}


X(46729) = X(2)X(11449)∩X(275)X(7507)

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

See Antreas Hatzipolakis and Peter Moses, euclid 4011.

X(46729) lies on the Kiepert circumhyperbola and these lines: {2, 11449}, {76, 12362}, {262, 12241}, {275, 7507}, {671, 34725}, {1503, 13380}, {2052, 3575}, {3515, 16080}, {5392, 12225}, {6146, 13599}, {6776, 31363}, {9825, 37874}, {18396, 40448}, {38444, 42410}

X(46729) = isogonal conjugate of X(46730)
X(46729) = X(41362)-cross conjugate of X(4)


X(46730) = X(3)X(6)∩X(22)X(185)

Barycentrics    a^2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*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 + 5*a^2*c^6 + 2*b^2*c^6 - 2*c^8) : :
Barycentrics    Sin[A]^2*(Cot[A] + 1 / (2*Csc[A]*Csc[B]*Csc[C] - 3*Cot[w])) : :
X(46730) = 5 X[3] - 3 X[37497], 3 X[3] - X[37498], 3 X[26] - X[32139], 3 X[154] - X[12164], 3 X[154] - 5 X[16195], X[155] - 3 X[14070], 3 X[182] - 2 X[44469], 2 X[1147] - 3 X[11202], 3 X[1147] - 4 X[32171], X[1498] - 3 X[9909], 4 X[1658] - 3 X[11202], 3 X[1658] - 2 X[32171], 3 X[3167] - 5 X[17821], 3 X[3357] - 4 X[32138], 2 X[5448] - 3 X[10201], 4 X[5449] - 3 X[23325], 3 X[6759] - 2 X[32139], 3 X[7689] - 2 X[32138], 2 X[9820] - 3 X[34351], 3 X[10154] - 2 X[16252], 3 X[10192] - 4 X[44277], 7 X[10244] - 3 X[32063], 9 X[10245] - 5 X[14530], 2 X[10282] - 3 X[14070], 9 X[11202] - 8 X[32171], 3 X[11204] - 2 X[12084], 2 X[12038] - 3 X[18324], 4 X[12107] - X[15083], X[12164] - 5 X[16195], X[12250] + 3 X[34621], X[12324] + 3 X[34608], X[13346] + 2 X[17834], 5 X[13346] - 6 X[37497], 3 X[13346] - 2 X[37498], 3 X[14852] - 2 X[18383], X[16266] - 3 X[18324], 5 X[17834] + 3 X[37497], 3 X[17834] + X[37498], 3 X[18281] - 4 X[20191], 2 X[18569] - 3 X[23325], 2 X[19139] - 3 X[23042], 3 X[23329] - 2 X[23335], 3 X[23329] - 4 X[44158], 4 X[25563] - 3 X[44441], 3 X[34609] - 5 X[40686], 3 X[34726] + X[34780], 3 X[37488] - X[44492], 9 X[37497] - 5 X[37498]

See Antreas Hatzipolakis and Peter Moses, euclid 4011.

X(46730) lies on these lines: {2, 3574}, {3, 6}, {4, 14860}, {5, 11745}, {20, 1204}, {22, 185}, {23, 12111}, {24, 5562}, {25, 5907}, {26, 6759}, {30, 3357}, {51, 7503}, {64, 39568}, {68, 18400}, {74, 3529}, {110, 14448}, {113, 41674}, {125, 37444}, {141, 9825}, {154, 12164}, {155, 10282}, {156, 12107}, {184, 5889}, {186, 1092}, {206, 41589}, {235, 32269}, {323, 11449}, {343, 3575}, {376, 18916}, {378, 45186}, {394, 3515}, {517, 8144}, {542, 9833}, {546, 4550}, {548, 45969}, {550, 12370}, {1147, 1154}, {1181, 9715}, {1216, 6644}, {1352, 7487}, {1370, 26937}, {1495, 11441}, {1498, 9909}, {1531, 35488}, {1568, 7505}, {1593, 13598}, {1598, 44870}, {1614, 7556}, {1974, 41716}, {1986, 22109}, {1993, 13367}, {2070, 10539}, {2904, 16879}, {2931, 10628}, {2937, 32608}, {2979, 22467}, {3060, 11424}, {3088, 31670}, {3091, 34417}, {3146, 11440}, {3147, 5972}, {3167, 17821}, {3517, 17814}, {3518, 11459}, {3522, 43601}, {3523, 15053}, {3524, 43597}, {3542, 32223}, {3543, 15062}, {3545, 38848}, {3548, 44673}, {3549, 18388}, {3564, 34776}, {3567, 35921}, {3580, 12225}, {3628, 33533}, {3818, 6756}, {3917, 17928}, {5059, 13445}, {5446, 7526}, {5448, 10201}, {5449, 18569}, {5462, 7514}, {5651, 11444}, {5663, 17714}, {5876, 37440}, {5890, 7512}, {5891, 7506}, {5892, 7516}, {5899, 18439}, {5943, 7395}, {5965, 6193}, {6000, 7387}, {6101, 37814}, {6102, 7502}, {6146, 44239}, {6241, 12088}, {6515, 10112}, {6636, 10574}, {6642, 11793}, {6676, 12233}, {6696, 23300}, {6815, 43653}, {6823, 13568}, {7393, 11695}, {7401, 24206}, {7404, 19130}, {7412, 10441}, {7464, 11468}, {7507, 37638}, {7517, 12162}, {7525, 13630}, {7550, 15024}, {7592, 14831}, {8263, 34507}, {8548, 34788}, {8681, 34787}, {9545, 15801}, {9707, 43844}, {9714, 18451}, {9781, 35500}, {9818, 10110}, {9820, 34351}, {10154, 16252}, {10192, 44277}, {10244, 32063}, {10245, 14530}, {10263, 18570}, {10298, 34148}, {10303, 43584}, {10311, 22416}, {10545, 15022}, {10575, 12083}, {10594, 15030}, {10605, 11414}, {10982, 21849}, {10996, 33522}, {11204, 12084}, {11250, 13391}, {11413, 21663}, {11442, 31304}, {11454, 12086}, {11457, 44831}, {11479, 17810}, {11591, 12106}, {11645, 34726}, {11750, 25738}, {11800, 19457}, {12038, 16266}, {12087, 12279}, {12160, 19357}, {12161, 18475}, {12241, 41588}, {12250, 34621}, {12290, 37925}, {12307, 23039}, {12310, 17835}, {12324, 34608}, {12362, 13567}, {12412, 15085}, {12429, 17845}, {12605, 18390}, {13148, 16165}, {13383, 22660}, {13399, 20062}, {13434, 15004}, {13474, 18534}, {13595, 15056}, {14216, 29012}, {14790, 20299}, {14852, 18383}, {15028, 22112}, {15043, 37126}, {15058, 34484}, {15578, 32184}, {15750, 35602}, {16163, 35503}, {16261, 26863}, {18281, 20191}, {18378, 18435}, {18418, 44960}, {18909, 46264}, {19139, 23042}, {19506, 46085}, {20417, 32273}, {21230, 38322}, {21844, 43574}, {23292, 31802}, {23294, 46450}, {23329, 23335}, {25563, 44441}, {26881, 43605}, {29317, 34938}, {30552, 37853}, {32140, 44407}, {32345, 34751}, {34609, 40686}, {34785, 44665}, {34799, 41482}, {34826, 44288}, {35268, 38435}, {38443, 43689}

X(46730) = midpoint of X(i) and X(j) for these {i,j}: {3, 17834}, {64, 39568}, {1350, 37491}, {7387, 12163}, {9833, 11411}, {12310, 17835}, {12412, 15085}, {12429, 17845}, {14216, 31305}
X(46730) = reflection of X(i) in X(j) for these {i,j}: {113, 41674}, {155, 10282}, {156, 12107}, {576, 44470}, {1147, 1658}, {3357, 7689}, {6759, 26}, {13346, 3}, {14790, 20299}, {15083, 156}, {16266, 12038}, {18381, 12359}, {18569, 5449}, {19506, 46085}, {22660, 13383}, {23335, 44158}, {34786, 9927}, {34788, 8548}
X(46730) = isogonal conjugate of X(46729)
X(46730) = X(20)-of-Kosnita-triangle
X(46730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 52, 578}, {3, 389, 182}, {3, 568, 569}, {3, 1350, 13348}, {3, 1351, 11425}, {3, 6243, 13352}, {3, 9729, 13347}, {3, 9730, 37515}, {3, 9786, 9729}, {3, 10625, 37480}, {3, 11432, 37476}, {3, 14627, 14805}, {3, 36747, 11430}, {3, 36753, 37513}, {3, 37472, 39242}, {3, 37475, 17704}, {3, 37481, 13336}, {3, 37486, 15644}, {3, 37489, 389}, {3, 37490, 9730}, {3, 37493, 37506}, {3, 37494, 10625}, {3, 37514, 5092}, {3, 37515, 17508}, {20, 1899, 44829}, {23, 12111, 26883}, {24, 5562, 9306}, {52, 578, 576}, {155, 14070, 10282}, {186, 11412, 1092}, {1147, 1658, 11202}, {1192, 1350, 3}, {1495, 45187, 11441}, {1593, 33586, 13598}, {1993, 38444, 13367}, {2070, 18436, 10539}, {2937, 32608, 34783}, {2979, 22467, 43652}, {3060, 14118, 11424}, {3581, 37478, 11438}, {5092, 15012, 37514}, {5449, 18569, 23325}, {5876, 37440, 46261}, {5889, 7488, 184}, {5890, 7512, 10984}, {6515, 19467, 10112}, {10625, 32110, 3}, {11432, 37476, 575}, {11438, 37478, 3098}, {11440, 15107, 3146}, {11444, 44802, 5651}, {12160, 19357, 34986}, {12164, 16195, 154}, {12307, 45735, 23039}, {12605, 41587, 18390}, {13367, 14531, 1993}, {14810, 17704, 3}, {15043, 37126, 43650}, {16266, 18324, 12038}, {23335, 44158, 23329}, {32110, 37494, 37480}, {36752, 37498, 44469}, {37493, 37505, 15520}, {37493, 37506, 37505}, {41482, 41724, 34799}


X(46731) = (name pending)

Barycentrics    (a^2-2 b^2-2 c^2) (9 a^4+14 a^2 b^2+9 b^4-14 a^2 c^2-14 b^2 c^2+5 c^4) (9 a^4-14 a^2 b^2+5 b^4+14 a^2 c^2-14 b^2 c^2+9 c^4) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 4016.

X(46731) lies on this line: {1503, 3839}


X(46732) = X(4)X(575)∩X(20)X(13378)

Barycentrics    28 a^10 - 51 a^8 b^2 - 25 a^6 b^4 + 37 a^4 b^6 + 33 a^2 b^8 - 22 b^10 - 51 a^8 c^2 + 8 a^6 b^2 c^2 - 33 a^4 b^4 c^2 - 30 a^2 b^6 c^2 + 74 b^8 c^2 - 25 a^6 c^4 - 33 a^4 b^2 c^4 - 6 a^2 b^4 c^4 - 52 b^6 c^4 + 37 a^4 c^6 - 30 a^2 b^2 c^6 - 52 b^4 c^6 + 33 a^2 c^8 + 74 b^2 c^8 - 22 c^10 : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 4016.

X(46732) lies on these lines: {4, 575}, {20, 13378}


X(46733) = X(4)X(50)∩X(32)X(3567)

Barycentrics    a^4*(a^12-4*(b^2+c^2)*a^10+(7*b^4+11*b^2*c^2+7*c^4)*a^8-2*(b^2+c^2)*(4*b^4+b^2*c^2+4*c^4)*a^6+(7*b^8+7*c^8+(2*b^4+3*b^2*c^2+2*c^4)*b^2*c^2)*a^4-2*(b^4-c^4)*(b^2-c^2)*(2*b^4+b^2*c^2+2*c^4)*a^2+(b^8+c^8+(b^4-b^2*c^2+c^4)*b^2*c^2)*(b^2-c^2)^2) : :
Barycentrics    (SB+SC)^2*(S^4+(48*R^4-4*(3*SA+8*SW)*R^2+9*SA^2+5*SW^2)*S^2+3*(4*R^2-SW)*SA^2*SW) : :

See Kadir Altintas and César Lozada, euclid 4024.

X(46733) lies on these lines: {4, 50}, {32, 3567}, {577, 11459}, {8565, 39575}


X(46734) = X(2)X(9872)∩X(111)X(5476)

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

See Kadir Altintas and César Lozada, euclid 4024.

X(46734) lies on these lines: {2, 9872}, {111, 5476}, {182, 352}


X(46735) = X(3)X(3186)∩X(194)X(394)

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

See Antreas Hatzipolakis and César Lozada, euclid 4030.

X(46735) lies on these lines: {3, 3186}, {194, 394}, {1073, 41235}, {3682, 21080}, {3926, 6374}, {3998, 22028}

X(46735) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}} and {{A, B, C, X(6), X(40830)}}
X(46735) = trilinear pole of the line {520, 23301}


X(46736) = PERSPECTOR OF THE TAYLOR CIRCLE

Barycentrics    a^2*((b^2+c^2)*a^10-(5*b^4+3*b^2*c^2+4*c^4)*a^8+2*(5*b^6+3*c^6+(b^2+c^2)*b^2*c^2)*a^6-2*(b^2-c^2)*(5*b^6-2*c^6+(2*b^2-c^2)*b^2*c^2)*a^4+(5*b^6+c^6-(b^2+c^2)*b^2*c^2)*(b^2-c^2)^2*a^2-(b^2-c^2)^5*b^2)*((b^2+c^2)*a^10-(4*b^4+3*b^2*c^2+5*c^4)*a^8+2*(3*b^6+5*c^6+(b^2+c^2)*b^2*c^2)*a^6-2*(b^2-c^2)*(2*b^6-5*c^6+(b^2-2*c^2)*b^2*c^2)*a^4+(b^6+5*c^6-(b^2+c^2)*b^2*c^2)*(b^2-c^2)^2*a^2+(b^2-c^2)^5*c^2) : :
Barycentrics    (3*S^2+4*R^2*(4*R^2-SC-SW)-2*SA*SB+SC^2)*(3*S^2+4*R^2*(4*R^2-SB-SW)-2*SA*SC+SB^2)*(SB+SC) : :

See Antreas Hatzipolakis, César Lozada, and Peter Moses, euclid 4046 and euclid 4059

X(46736) lies on this line: {53, 389}

X(46736) = isogonal conjugate of X(46760)
X(46736) = perspector of the Taylor circle
X(46736) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(389)}} and {{A, B, C, X(6), X(51)}}


X(46737) = MIDPOINT OF X(3162) AND X(15255)

Barycentrics    a^2*((b^2+c^2)*a^10+(b^4+4*b^2*c^2+c^4)*a^8-2*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^6-2*(b^8+c^8+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)*(b^2-c^2)*a^2+(b^4+c^4)*(b^4-c^4)^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
Barycentrics    SB*SC*(SB+SC)*((4*R^2*(4*R^2-SW)-SW^2)*S^2+((2*R^2+SW)*(S^2-SB*SC+SW^2)-6*R^2*SW^2)*SW) : :

See Antreas Hatzipolakis, César Lozada, and Peter Moses, euclid 4046 and euclid 4059

X(46737) lies on this line: {25, 32}

X(46737) = midpoint of X(3162) and X(15255)





leftri   Points on cubics pK(m^2 n^2, m^2 n^2 q r): X(46738) -X(46759)   rightri

This preamble is contributed by Clark Kimberling and Peter Moses, January 24, 2022.

In the plane of a triangle ABC, let L, given by l x + m y + n z = 0, be a line, and let P = p : q : r be a point not on L and not on a sideline BC, CA, AB. Let

Ap = L∩AP,      Bp = L∩BP,      Cp = L∩CP.

Let A'B'C' be the cevian triangle of a point X = x : y : z, so that

A' = 0 : y : z ,      B' = x : 0 : z,      C' = x : y : 0.

The locus of X such that A'B'C' is perspective to the (degenerate) triangle ApBpCp is the cubic pK(m^2 n^2, m^2 n^2 q r), given by

p (m^2 q y^2 z - n^2 r y z^2) + (cyclic) = 0.

The appearance of {{i,j}, {{Knnn}, {h1, h2, ...}}} in the following list means that if l : m : n = X(i) and P = X(j), then the cubic is Knnn in Bernard Gibert's catalogue (CTC), and that the cubic passes through the points X(h1), X(h2), . . .

{{1,1},{{},{1,75,92,304,561,1760,46244}}}
{{1,2},{{K184},{2,69,75,76,85,264,312,15466,34403,34404,40702}}}
{{1,4},{{},{2,4,75,76,253,305,341,1088,1370,14615,20914,40009,40015,46738,46739,46740,46741}}}
{{1,10},{{},{2,10,75,76,310,4043,17135,40004,40005}}}
{{1,20},{{},{20,75,253,14615,15466,34403,41530}}}
{{1,63},{{},{63,75,92,304,1969,20571,44179}}}
{{1,69},{{},{69,75,264,491,492,20570,20930,24243,24244,34391,34392,40697,46742,46743,46744,46745,46746}}}
{{1,76},{{},{2,75,76,2998,6374,6376,6384}}}
{{1,83},{{},{2,75,76,83,1031,1369,8024,20933,33938,40035,40036,40037,40038,46747,46748}}}
{{1,92},{{},{75,85,92,304,309,312,322,18750}}}
{{1,94},{{},{2,75,76,94,1272,7799,40705}}}
{{1,95},{{},{69,75,95,264,302,303,311,19712,19713,34389,34390,45799,46749,46750,46751,46752,46753,46754,46755,46756,46757,46758,}}}
{1,523,{{},{75,141,308,523,670,4033,6189,6190,7199}}}
{{2,1},{{K034},{1,2,7,8,63,75,92,280,347,1895,19611}}}
{{2,3},{{K045},{2,3,4,69,254,264,1993,5392,40697,40698}}}
{{2,4},{{K007},{2,4,7,8,20,69,189,253,329,1032,1034,5932,14361,14362,14365,34162,39158,39159,39160,39161,41080,42427,42428}}}
{{2,6},{{K141},{2,4,6,22,69,76,1670,1671,18018,19613,41361}}}
{{2,7},{{K200},{2,7,8,144,175,176,1143,1274,10405,13386,13387,20534,31527,40699,40700}}}
{{2,8},{{K1078},{2,7,8,145,4373,7048,7057,8051,8055,24313,24314}}}
{{2,10},{{},{1,2,10,75,86,3995,18133,39747,39748}}}
{{2,19},{{K605},{1,2,19,75,279,304,346,2184,4329,7219,10327,18596,18750,39732,39733}}}
{{2,21},{{},{2,7,8,21,1441,2475,3219,30690,34772,41808}}}
{{2,37},{{},{1,2,37,75,274,4651,16552,39734,39735}}}
{{2,39},{{},{2,6,39,76,308,8266,30505}}}
{{2,40},{{K133},{2,40,77,189,280,309,318,329,347,962}}}
{{2,52},{{},{2,52,54,68,311,317,1993,5392,11412,34385}}}
{{2,54},{{},{2,4,54,69,311,1994,2888,3459,7488,11140,45799}}}
{{2,63},{{},{2,63,92,2994,5905,13386,13387,19217,19218}}}
{{2,64},{{K235},{2,4,64,69,394,2052,3346,6225,6527,11413,14615}}}
{{2,65},{{K254},{1,2,4,65,69,75,81,314,321,1764,2995,3869,16049,17751,20028}}}
{{2,66},{{},{2,4,66,69,315,1370,5596,13575}}}
{{2,67},{{K008},{2,4,67,69,316,524,671,858,2373,11061,13574,14360,14364,34163,34164,34165,34166,39157}}}
{{2,68},{{},{2,4,68,69,317,6193,6504,6515}}}
{{2,69},{{K170},{2,4,69,193,487,488,2996,13386,13387,13428,13439,19583,24243,24244}}}
{{2,70},{{},{2,4,69,70,13579,37444,44128,44177,45794}}}
{{2,71},{{},{2,4,69,71,4184,17220,17911,44129}}}
{{2,72},{{K610},{2,4,21,63,69,72,92,286,1441,2997,3868,40571,43675}}}
{{2,74},{{K279},{2,4,69,74,94,146,323,1138,1272,2071,3260}}}
{{2,75},{{},{1,2,75,192,330,3223,17149}}}
{{2,79},{{K455},{2,7,8,10,79,86,319,1029,2895,3648,17781}}}
{{2,80},{{K311},{2,7,8,80,320,369,519,903,908,3232,6224,8046,30578,34234,36917,36918}}}
{{2,81},{{},{2,81,321,1029,2895,13386,13387}}}
{{2,82},{{},{1,2,75,82,1930,17280,20934,21289,21378,33091,39724,39725,39726,39727,39728,46759}}}
{{2,84},{{K154},{2,7,8,78,84,273,322,6223,41514}}}
{{2,91},{{},{1,2,75,91,5552,7318,44179}}}
{{2,95},{{},{2,5,95,627,628,11143,11144,17035,19712,19713}}}
{{2,104},{{},{2,7,8,104,153,3262,4511,18815}}}
{{2,113},{{},{2,74,113,2986,3260,3580,5627,6148,15454,40423}}}
{2,523,{{K242},{2,99,523,1113,1114,3413,3414,6189,6190,22339,22340,30508,30509}}}
{{3,4},{{},{4,76,264,2052,16246,17907,18022,40009}}}
{{3,92},{{},{75,92,264,331,1969,7017,40701}}}
{{3,94},{{},{76,94,264,2052,40705,44138,46106}}}
{{3,98},{{},{76,98,264,305,1093,2052,6330,35142}}}
{{4,1},{{},{1,63,69,304,1265,7056,19611}}}
{{4,2},{{},{2,69,345,348,3926,6527,34403,37669}}}
{{4,3},{{},{2,3,69,305,1370,3926,20806}}}
{{4,39},{{},{3,39,69,305,1176,14376,34254}}}
{{4,63},{{},{63,69,75,304,326,345,348,18750,44189}}}
{{6,2},{{},{2,76,264,305,315,1502,40421}}}
{{6,75},{{},{75,76,304,561,1969,3596,6063}}}
{{7,9},{{},{2,8,9,78,312,318,329,346,46350}}}
{{7,33},{{},{7,8,9,33,312,3718,5423,27540,41791,44692}}}
{{7,37},{{},{8,9,21,37,281,312,345,3701}}}
{{8,1},{{},{1,2,7,279,1088,1445,36845}}}
{{8,2},{{},{2,7,279,4452,5435,18886,21456,27818}}}
{{8,34},{{},{7,8,34,57,85,479,7182,8809,28739,33673}}}
{{8,57},{{},{2,7,57,77,85,189,273,279,14256,44697,46352}}}
{{8,81},{{},{2,7,81,279,1029,1442,1446,18625}}}
{{8,88},{{},{2,7,88,279,1443,8046,18815,37789}}}
{{8,105},{{},{2,7,8,105,279,479,4318,7291,43736,43760}}}
{{9,7},{{},{7,75,85,309,331,348,1088,6063}}}
{{10,57},{{},{27,57,75,81,86,274,757,14829,17206}}}
{{10,63},{{},{27,63,85,86,286,1444,2185,17206}}}
{{10,81},{{},{81,86,274,286,333,1434,1444}}}
{{19,69},{{},{69,76,304,305,3718,3926,7182,14615}}}
{{27,72},{{},{72,306,307,321,3710,3998,20336}}}
{{31,76},{{},{76,305,561,1502,18022,20567,28659}}}
{{37,7},{{},{7,76,86,274,286,310,1509,18021}}}
{{37,69},{{},{69,261,274,286,6063,17206,44129}}}
{{42,85},{{},{85,274,310,561,873,6385,44129}}}
{{57,8},{{},{8,75,312,322,341,345,3596,7017}}}
{{57,10},{{},{8,10,312,318,333,3596,3718,30713}}}
{{63,4},{{K647},{2,4,92,253,264,273,318,342,2052,7020,14249,46353}}}
{{63,10},{{},{2,10,29,75,92,158,2052,5125}}}
{{63,76},{{},{2,76,92,393,2052,2998,6392}}}
{{65,2},{{},{2,261,314,333,3596,28660,31623}}}
{{69,1},{{},{1,4,158,920,1068,1123,1336,7040}}}
{{69,2},{{K1046},{2,4,393,1123,1336,3068,3069,6353,6392,13429,13440,34208}}}
{{69,6},{{K621},{2,4,6,24,393,847,2052,6515}}}
{{69,10},{{},{1,4,10,158,1714,8747,39748}}}
{{69,19},{{},{1,4,19,92,158,196,278,281,2184,7003}}}
{{69,24},{{},{4,24,847,7505,10880,10881,13429,13440}}}
{{69,25},{{},{2,4,25,264,393,8743,13575,41766,43678}}}
{{69,37},{{},{1,2,4,37,158,393,1172,1713,30733,40149}}}
{{69,54},{{},{4,54,3459,13429,13440,13450,46621,46622}}}
{{69,75},{{},{1,4,75,158,1096,3223,33781}}}
{{69,111},{{},{2,4,111,393,8744,13574,37777,37778,46105}}}
{{75,2},{{K102},{1,2,6,43,87,194,3224,15963,15964,15965,15966,15967,15968,39641,39642,40139}}}
{{75,3},{{K006},{1,3,4,46,90,155,254,371,372,485,486,487,488,6212,6213,8946,8947,8948,8949}}}
{{75,4},{{K003},{1,3,4,1075,1745,3362,13855,39641,39642,46357,46358}}}
{{75,6},{{K002},{1,2,3,4,6,9,57,223,282,1073,1249,3341,3342,3343,3344,3349,3350,3351,3352,3356,14481,39162,39163,39164,39165,40989,40990,40991,40992}}}
{{75,9},{{K1079},{1,9,57,173,258,1743,2136,2137,8056,8078,24242}}}
{{75,10},{{},{1,10,58,3216,39641,39642,39748}}}
{{75,16},{{},{1,14,16,17,61,7150,41225}}}
{{75,19},{{K343},{1,9,19,40,57,63,84,610,1712,2184}}}
{{75,25},{{K169},{1,2,6,20,25,64,69,159,200,269,1763,2138,2139,7097,13575,17742,40187,40188,40189,40190,40219,40220,40221,40222,40223,40224,40225,40226,40227}}}
{{75,31},{{K968},{1,19,31,63,75,2172,19616}}}
{{75,32},{{K1027},{1,32,76,1670,1671,1676,1677,1759,7096,18796,18797,18798,18799,19612}}}
{{75,37},{{},{1,2,6,37,81,3293,17147,39949,39964}}}
{{75,39},{{},{1,39,83,1342,1343,5403,5404,16549}}}
{{75,42},{{},{1,2,6,42,86,3294,8049,8053,39950}}}
{{75,48},{{},{1,19,47,48,63,91,92}}}
{{75,54},{{K005},{1,3,4,5,17,18,54,61,62,195,627,628,2120,2121,3336,3459,3460,3461,3462,3463,3467,3468,3469,3470,3471,3489,3490,6191,6192,7344,7345,8837,8839,8918,8919,8929,8930,38931,38932,38933,38934,38935,39261,39262,46035,46036,46037}}}
{{75,55},{{K1059},{1,7,9,55,57,218,277,3174}}}
{{75,56},{{K692},{1,8,40,56,84,2122,2123}}}
{{75,57},{{K351},{1,9,57,165,364,2124,2125,3062,6212,6213,7001,7010,15891,15892}}}
{{75,58},{{},{1,10,58,191,267,2126,2127,6212,6213}}}
{{75,61},{{},{1,17,61,3389,3390,3391,3392}}}
{{75,62},{{},{1,18,62,3364,3365,3366,3367}}}
{{75,63},{{K1039},{1,19,63,1707,2128,2129,3377,3378,6203,6204,6212,6213,7347,7348,8769,19213,19214,19215,19216,19217,19218}}}
{{75,64},{{K004},{1,3,4,20,40,64,84,1490,1498,2130,2131,3182,3183,3345,3346,3347,3348,3353,3354,3355,3472,3473,3637,40851,40852,40993,40994,42411,42412}}}
{{75,66},{{},{1,3,4,22,66,159,8270,13575}}}
{{75,67},{{},{1,3,4,23,67,2930,13574}}}
{{75,69},{{},{1,3,4,25,69,1716,3186,3504,7093,19588}}}
{{75,71},{{K109},{1,3,4,19,27,63,71,226,284,579,1751,1780,23604,41342,43729}}}
{{75,74},{{K001},{1,3,4,13,14,15,16,30,74,370,399,484,616,617,1138,1157,1263,1276,1277,1337,1338,2132,2133,3065,3440,3441,3464,3465,3466,3479,3480,3481,3482,3483,3484,5623,5624,5667,5668,5669,5670,5671,5672,5673,5674,5675,5676,5677,5678,5679,5680,5681,5682,5683,5684,5685,7059,7060,7164,7165,7325,7326,7327,7328,7329,8172,8173,8174,8175,8431,8432,8433,8434,8435,8436,8437,8438,8439,8440,8441,8442,8443,8444,8445,8446,8447,8448,8449,8450,8451,8452,8453,8454,8455,8456,8457,8458,8459,8460,8461,8462,8463,8464,8465,8466,8467,8468,8469,8470,8471,8472,8473,8474,8475,8476,8477,8478,8479,8480,8481,8482,8483,8484,8485,8486,8487,8488,8489,8490,8491,8492,8493,8494,8495,8496,8497,8498,8499,8500,8501,8502,8503,8504,8505,8506,8507,8508,8509,8510,8511,8512,8513,8514,8515,8516,8517,8518,8519,8520,8521,8522,8523,8524,8525,8526,8527,8528,8529,8530,8531,8532,8533,8534,8535,8536,16882,16883}}}
{{75,81},{{K1146},{1,37,81,846,2134,2135,13610,42677,42680}}}
{{75,84},{{K414},{1,40,84,164,505,2956,3645,6212,6213,32555,32556,34494,34495,46433,46434}}}
{{75,88},{{},{1,44,88,9324,9325,39150,39151}}}
{{75,99},{{K021},{1,99,512,2142,2143,5539,7315}}}
{{75,102},{{K269},{1,36,40,80,84,102,515,6326,8072,8073,10692,39146,39147}}}
{{75,103},{{},{1,103,516,6212,6213,32622,32623,39144,39145}}}
{{75,104},{{},{1,104,517,11752,11789,39150,39151}}}
{{75,111},{{K1156},{1,2,6,111,524,2930,5524,5525,7312,7313,8591,13574}}}
{{76,1},{{},{1,6,31,1740,2162,2176,34248}}}
{{76,3},{{K171},{3,6,25,3053,8770,8946,8948,10132,10133,15369,19588,20032,34121,34125,44192,44193}}}
{{76,21},{{},{6,21,55,56,172,893,1402}}}
{{76,24},{{},{6,24,2351,3155,3156,44192,44193}}}
{{76,25},{{K172},{3,6,25,55,56,64,154,198,1033,1035,1436,7037,28781,28782,28783,28784,28785,34167}}}
{{76,31},{{K175},{1,6,19,31,48,55,56,204,221,2192,19614}}}
{{76,32},{{K177},{2,3,6,25,32,66,206,1676,1677,3162,19615,41378,41379}}}
{{76,41},{{},{6,41,55,56,57,2191,21059}}}
{{76,48},{{},{6,19,48,2164,2178,19215,19216,34121,34125}}}
{{76,56},{{},{6,55,56,3207,11051,20673,30335,30336,34121,34125}}}
{{76,63},{{},{6,19,48,63,1973,2129,21775}}}
{{76,74},{{},{6,74,1495,3440,3441,9412,11081,11086}}}
{{76,98},{{},{3,6,25,98,237,694,1691,1971,1987,3511,46272}}}
{{76,103},{{},{6,103,1458,2195,3207,9500,11051,20672}}}
{{76,105},{{},{6,55,56,105,292,1914,2110,2223}}}
{{81,12},{{},{2,10,12,313,321,3436,3596,20336,22020,28654,41013}}}
{514,6,{{},{6,190,4360,14087,31625}}}
{514,7,{{},{7,190,344,4076,14087}}}
{523,1,{{},{1,99,1016,1509,4593,14089,24037}}}
{523,2,{{},{2,99,4590,6189,6190,14089,39298,39299}}}
{523,20,{{},{20,99,3926,14089,23582}}}

Each of these cubics is unicursal with node and singularity m n : n l : l m. As noted above, each cubic is of type pK(m^2 n^2, m^2 n^2 q r), which is equivalent to cK(# m n , m^2, n^2 q r). See Special Isocubics in the Triangle Plane). (Bernard Gibert, January 28, 2022)

underbar



X(46738) = ISOTOMIC CONJUGATE OF X(40188)

Barycentrics    b*c*(-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(46738) lies on the cubic pK(76,305) and these lines: {2, 37}, {4, 341}, {82, 4676}, {85, 18040}, {92, 30713}, {190, 1760}, {304, 17233}, {322, 4033}, {1111, 18065}, {1861, 3710}, {1930, 17286}, {1978, 40364}, {2064, 14615}, {2298, 3758}, {2550, 3701}, {3596, 20927}, {3673, 18044}, {3717, 12618}, {3769, 33760}, {3994, 17872}, {4110, 17788}, {4150, 20914}, {4385, 5263}, {4494, 20236}, {5016, 44720}, {7283, 13730}, {10327, 11677}, {17315, 18156}, {17353, 33937}, {17381, 39731}, {17446, 32925}, {17786, 17789}, {18133, 33736}, {20179, 33938}, {20915, 20920}, {28739, 41786}, {28753, 30701}

X(46738) = isotomic conjugate of X(40188)
X(46738) = isotomic conjugate of the isogonal conjugate of X(17742)
X(46738) = X(i)-Ceva conjugate of X(j) for these (i,j): {305, 341}, {15742, 4033}
X(46738) = X(11677)-cross conjugate of X(75)
X(46738) = X(i)-isoconjugate of X(j) for these (i,j): {31, 40188}, {32, 39732}, {1397, 41791}, {1472, 40184}, {2206, 36907}
X(46738) = barycentric product X(i)*X(j) for these {i,j}: {75, 10327}, {76, 17742}, {305, 23050}, {312, 28739}, {561, 12329}, {1978, 2509}, {3596, 8270}, {4033, 17498}
X(46738) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 40188}, {75, 39732}, {312, 41791}, {321, 36907}, {1801, 1437}, {2345, 40184}, {2509, 649}, {8270, 56}, {10327, 1}, {11677, 614}, {12329, 31}, {15487, 16502}, {17498, 1019}, {17742, 6}, {20613, 608}, {23050, 25}, {28409, 7289}, {28739, 57}, {41786, 28017}
X(46738) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 17371, 19804}, {75, 18743, 16706}, {321, 2345, 75}, {322, 30693, 4033}, {4033, 20444, 322}, {17786, 17789, 20930}


X(46739) = ISOTOMIC CONJUGATE OF X(40222)

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

X(46739) lies on the cubic pK(76,305) and these lines: {2, 3933}, {69, 14259}, {907, 3926}, {8801, 44142}, {14615, 40009}, {40123, 40189}

X(46739) = isotomic conjugate of X(40222)
X(46739) = isotomic conjugate of the isogonal conjugate of X(40189)
X(46739) = X(31)-isoconjugate of X(40222)
X(46739) = barycentric product X(i)*X(j) for these {i,j}: {76, 40189}, {18840, 40123}
X(46739) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 40222}, {18840, 40178}, {37485, 30435}, {40123, 3618}, {40189, 6}


X(46740) = ISOTOMIC CONJUGATE OF X(17742)

Barycentrics    b*c*(-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(46740) lies on the cubic pK(76,305) and these lines: {75, 1370}, {76, 5179}, {85, 16706}, {274, 40188}, {286, 16750}, {334, 20930}, {1760, 7182}, {17370, 40044}, {27826, 40014}, {39733, 40015}

X(46740) = isotomic conjugate of X(17742)
X(46740) = polar conjugate of X(23050)
X(46740) = isotomic conjugate of the isogonal conjugate of X(40188)
X(46740) = X(i)-cross conjugate of X(j) for these (i,j): {4, 1088}, {4000, 75}, {12610, 7}, {23537, 310}, {36907, 39732}
X(46740) = X(i)-isoconjugate of X(j) for these (i,j): {6, 12329}, {31, 17742}, {32, 10327}, {41, 8270}, {48, 23050}, {212, 20613}, {692, 2509}, {1801, 2333}, {2175, 28739}, {7084, 15487}
X(46740) = cevapoint of X(39732) and X(41791)
X(46740) = trilinear pole of line {693, 21174}
X(46740) = barycentric product X(i)*X(j) for these {i,j}: {75, 39732}, {76, 40188}, {85, 41791}, {274, 36907}
X(46740) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 12329}, {2, 17742}, {4, 23050}, {7, 8270}, {75, 10327}, {85, 28739}, {278, 20613}, {514, 2509}, {1444, 1801}, {3673, 11677}, {4000, 15487}, {7199, 17498}, {36907, 37}, {39732, 1}, {40188, 6}, {41791, 9}


X(46741) = ISOTOMIC CONJUGATE OF X(2139)

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

X(46741) lies on the cubic pK(76,305) and these lines: {2, 253}, {75, 17903}, {76, 17907}, {193, 15262}, {393, 41760}, {441, 1033}, {648, 28419}, {1075, 3541}, {1619, 15259}, {1853, 46700}, {3542, 41204}, {3618, 8743}, {5596, 32713}, {6225, 39268}, {6527, 41678}, {36794, 41370}, {41766, 45279}

X(46741) = isotomic conjugate of X(2139)
X(46741) = polar conjugate of X(42484)
X(46741) = isotomic conjugate of the isogonal conjugate of X(2138)
X(46741) = polar conjugate of the isogonal conjugate of X(1619)
X(46741) = X(305)-Ceva conjugate of X(4)
X(46741) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2139}, {48, 42484}, {19614, 40186}
X(46741) = cevapoint of X(1619) and X(2138)
X(46741) = barycentric product X(i)*X(j) for these {i,j}: {76, 2138}, {264, 1619}, {305, 15259}
X(46741) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2139}, {4, 42484}, {1249, 40186}, {1619, 3}, {2138, 6}, {15259, 25}
X(46741) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {459, 1249, 32000}, {6527, 42458, 41678}


X(46742) = ISOTOMIC CONJUGATE OF X(8948)

Barycentrics    b^2*c^2*(-a^2 + b^2 + c^2)*(a^2 + S) : :
Barycentrics    (cot A) (1 + csc A sin B sin C) : :

X(46742) lies on the cubic pK(76,264) and these lines: {69, 305}, {76, 485}, {264, 3127}, {1270, 3266}, {1271, 8024}, {3068, 8222}, {3595, 39998}, {11059, 32805}, {32806, 40022}, {44149, 45806}

X(46742) = isotomic conjugate of X(8948)
X(46742) = isotomic conjugate of the isogonal conjugate of X(488)
X(46742) = polar conjugate of the isogonal conjugate of X(8222)
X(46742) = X(45805)-Ceva conjugate of X(76)
X(46742) = X(i)-isoconjugate of X(j) for these (i,j): {19, 26454}, {31, 8948}, {32, 19218}, {493, 1973}, {560, 24244}
X(46742) = cevapoint of X(488) and X(8222)
X(46742) = barycentric product X(i)*X(j) for these {i,j}: {76, 488}, {264, 8222}, {305, 3068}, {561, 19215}, {670, 17431}, {1502, 10132}, {6423, 40050}, {24246, 45805}
X(46742) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8948}, {3, 26454}, {69, 493}, {75, 19218}, {76, 24244}, {305, 5490}, {487, 45596}, {488, 6}, {3068, 25}, {3933, 26347}, {4563, 1306}, {5200, 2207}, {5408, 8950}, {5590, 26373}, {6423, 1974}, {8222, 3}, {10132, 32}, {17431, 512}, {19215, 31}, {24246, 8577}, {26503, 8946}, {33364, 5411}, {39387, 5413}, {42022, 26461}
X(46742) = {X(69),X(305)}-harmonic conjugate of X(46743)


X(46743) = ISOTOMIC CONJUGATE OF X(8946)

Barycentrics    b^2*c^2*(-a^2 + b^2 + c^2)*(a^2 - S) : :
Barycentrics    (cot A) (1 - csc A sin B sin C) : :

X(46743) lies on the cubic pK(76,264) and these lines: {69, 305}, {76, 486}, {264, 3128}, {1270, 8024}, {1271, 3266}, {3069, 8223}, {3593, 39998}, {9464, 32814}, {11059, 32806}, {32805, 40022}, {44149, 45805}

X(46743) = isotomic conjugate of X(8946)
X(46743) = isotomic conjugate of the isogonal conjugate of X(487)
X(46743) = polar conjugate of the isogonal conjugate of X(8223)
X(46743) = X(45806)-Ceva conjugate of X(76)
X(46743) = X(i)-isoconjugate of X(j) for these (i,j): {19, 26461}, {31, 8946}, {32, 19217}, {494, 1973}, {560, 24243}
X(46743) = cevapoint of X(487) and X(8223)
X(46743) = barycentric product X(i)*X(j) for these {i,j}: {76, 487}, {264, 8223}, {305, 3069}, {561, 19216}, {670, 17432}, {1502, 10133}, {6424, 40050}, {24245, 45806}
X(46743) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8946}, {3, 26461}, {69, 494}, {75, 19217}, {76, 24243}, {305, 5491}, {487, 6}, {488, 45595}, {3069, 25}, {3933, 45594}, {4563, 1307}, {5591, 26374}, {6424, 1974}, {8222, 42022}, {8223, 3}, {10133, 32}, {17432, 512}, {19216, 31}, {24245, 8576}, {26494, 8948}, {33365, 5410}, {39388, 5412}
X(46743) = {X(69),X(305)}-harmonic conjugate of X(46742)


X(46744) = ISOTOMIC CONJUGATE OF X(6213)

Barycentrics    b*c*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(b*c + S) : :
Barycentrics    (cot A)/(1 - sin A) : :

The trilinear polar of X(46744) passes through X(4025).

X(46744) lies on the cubic pK(76,264) and these lines: {69, 13386}, {75, 492}, {86, 3083}, {92, 264}, {348, 1267}, {491, 14121}, {6212, 17206}, {13453, 34400}, {20930, 34392}, {24243, 41013}

X(46744) = isotomic conjugate of X(6213)
X(46744) = isotomic conjugate of the anticomplement of X(31591)
X(46744) = isotomic conjugate of the complement of X(31552)
X(46744) = isotomic conjugate of the isogonal conjugate of X(6212)
X(46744) = polar conjugate of the isogonal conjugate of X(3083)
X(46744) = X(31591)-cross conjugate of X(2)
X(46744) = X(i)-isoconjugate of X(j) for these (i,j): {6, 34121}, {19, 606}, {25, 1335}, {31, 6213}, {32, 13387}, {184, 1123}, {212, 13438}, {603, 13456}, {1973, 3084}, {1974, 5391}, {6135, 22383}
X(46744) = cevapoint of X(i) and X(j) for these (i,j): {2, 31552}, {3083, 6212}
X(46744) = barycentric product X(i)*X(j) for these {i,j}: {75, 13386}, {76, 6212}, {92, 1267}, {264, 3083}, {273, 13425}, {304, 1336}, {318, 13453}, {561, 34125}, {605, 18022}, {1124, 1969}, {3718, 13459}, {7182, 13426}
X(46744) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 34121}, {2, 6213}, {3, 606}, {63, 1335}, {69, 3084}, {75, 13387}, {92, 1123}, {273, 13437}, {278, 13438}, {281, 13456}, {304, 5391}, {318, 13454}, {605, 184}, {1124, 48}, {1267, 63}, {1336, 19}, {1897, 6135}, {3083, 3}, {3718, 13458}, {4025, 6365}, {6136, 8750}, {6212, 6}, {6364, 1459}, {7182, 13436}, {13386, 1}, {13389, 2067}, {13390, 2362}, {13424, 6212}, {13425, 78}, {13426, 33}, {13427, 607}, {13453, 77}, {13459, 34}, {13460, 608}, {14121, 7133}, {22107, 3942}, {30556, 5414}, {34125, 31}
X(46744) = {X(92),X(264)}-harmonic conjugate of X(46745)
X(46744) = {X(312),X(322)}-harmonic conjugate of X(46745)


X(46745) = ISOTOMIC CONJUGATE OF X(6212)

Barycentrics    b*c*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(b*c - S) : :
Barycentrics    (cot A)/(1 + sin A) : :

The trilinear polar of X(46745) passes through X(4025).

X(46745) lies on the cubic pK(76,264) and these lines: {69, 13387}, {75, 491}, {86, 3084}, {92, 264}, {348, 5391}, {492, 7090}, {6213, 17206}, {13436, 34400}, {20930, 34391}, {24244, 41013}

X(46745) = isotomic conjugate of X(6212)
X(46745) = isotomic conjugate of the anticomplement of X(31590)
X(46745) = isotomic conjugate of the complement of X(31551)
X(46745) = isotomic conjugate of the isogonal conjugate of X(6213)
X(46745) = polar conjugate of the isogonal conjugate of X(3084)
X(46745) = X(31590)-cross conjugate of X(2)
X(46745) = X(i)-isoconjugate of X(j) for these (i,j): {6, 34125}, {19, 605}, {25, 1124}, {31, 6212}, {32, 13386}, {184, 1336}, {212, 13460}, {603, 13427}, {1267, 1974}, {1973, 3083}, {6136, 22383}
X(46745) = cevapoint of X(i) and X(j) for these (i,j): {2, 31551}, {3084, 6213}
X(46745) = barycentric product X(i)*X(j) for these {i,j}: {75, 13387}, {76, 6213}, {92, 5391}, {264, 3084}, {273, 13458}, {304, 1123}, {318, 13436}, {561, 34121}, {606, 18022}, {1335, 1969}, {3718, 13437}, {7182, 13454}
X(46745) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 34125}, {2, 6212}, {3, 605}, {63, 1124}, {69, 3083}, {75, 13386}, {92, 1336}, {273, 13459}, {278, 13460}, {281, 13427}, {304, 1267}, {318, 13426}, {606, 184}, {1123, 19}, {1335, 48}, {1659, 16232}, {1897, 6136}, {3084, 3}, {3718, 13425}, {4025, 6364}, {5391, 63}, {6135, 8750}, {6213, 6}, {6365, 1459}, {7090, 42013}, {7182, 13453}, {13387, 1}, {13388, 6502}, {13435, 6213}, {13436, 77}, {13437, 34}, {13438, 608}, {13454, 33}, {13456, 607}, {13458, 78}, {22106, 3942}, {26871, 38003}, {30557, 2066}, {34121, 31}
X(46745) = {X(92),X(264)}-harmonic conjugate of X(46744)
X(46745) = {X(312),X(322)}-harmonic conjugate of X(46744)


X(46746) = ISOTOMIC CONJUGATE OF X(155)

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

X(46746) lies on the cubic pK(76,264) and these lines: {254, 264}, {317, 2052}, {847, 9723}, {2970, 3964}, {8795, 15316}, {16081, 31635}, {39109, 46104}

X(46746) = isotomic conjugate of X(155)
X(46746) = polar conjugate of X(1609)
X(46746) = isotomic conjugate of the anticomplement of X(12359)
X(46746) = isotomic conjugate of the complement of X(11411)
X(46746) = isotomic conjugate of the isogonal conjugate of X(254)
X(46746) = polar conjugate of the isogonal conjugate of X(6504)
X(46746) = X(i)-cross conjugate of X(j) for these (i,j): {69, 264}, {5392, 76}, {8800, 6504}, {12359, 2}
X(46746) = X(i)-isoconjugate of X(j) for these (i,j): {31, 155}, {48, 1609}, {184, 920}, {560, 40697}, {1973, 6503}, {6515, 9247}, {14575, 33808}
X(46746) = cevapoint of X(i) and X(j) for these (i,j): {2, 11411}, {254, 6504}, {525, 2970}
X(46746) = trilinear pole of line {6563, 14618}
X(46746) = barycentric product X(i)*X(j) for these {i,j}: {76, 254}, {264, 6504}, {276, 8800}, {921, 1969}, {1502, 39109}, {15316, 18027}, {16172, 40832}, {34384, 41536}, {34385, 39114}
X(46746) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 155}, {4, 1609}, {69, 6503}, {76, 40697}, {92, 920}, {254, 6}, {264, 6515}, {275, 8883}, {324, 41587}, {921, 48}, {1969, 33808}, {2052, 3542}, {2986, 15478}, {5392, 34853}, {6504, 3}, {6515, 454}, {8800, 216}, {11547, 35603}, {13398, 32661}, {13579, 18126}, {15316, 577}, {16172, 3003}, {34756, 571}, {39109, 32}, {39114, 52}, {39117, 41523}, {39416, 32734}, {41536, 51}, {44427, 44816}


X(46747) = X(2)X(37)∩X(76)X(40044)

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) : :

X(46747) lies on the cubic pK(76,8024) and these lines: {2, 37}, {76, 40044}, {82, 32930}, {83, 30133}, {190, 16566}, {304, 17240}, {341, 5015}, {1089, 5263}, {1930, 17285}, {3596, 18151}, {3701, 32850}, {3718, 17336}, {3994, 17446}, {4033, 17788}, {4385, 30145}, {4429, 36250}, {7283, 20833}, {17233, 20445}, {17352, 33937}, {17763, 33760}, {17786, 17791}, {17789, 18040}, {20915, 20928}, {20919, 28654}, {20933, 21064}, {21598, 40035}

X(46747) = isotomic conjugate of the isogonal conjugate of X(17744)
X(46747) = X(8024)-Ceva conjugate of X(33938)
X(46747) = X(32)-isoconjugate of X(39728)
X(46747) = barycentric product X(i)*X(j) for these {i,j}: {75, 33091}, {76, 17744}, {312, 28780}
X(46747) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 39728}, {17744, 6}, {28780, 57}, {33091, 1}
X(46747) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 312, 40001}, {75, 18743, 17370}, {312, 19799, 18743}, {321, 4358, 33155}, {321, 17289, 75}, {17786, 20444, 17791}


X(46748) = X(2)X(3108)∩X(76)X(40045)

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

X(46748) lies on the cubic pK(76,8024) and these lines: {2, 3108}, {69, 14250}, {76, 40045}, {315, 39989}, {3933, 7953}, {7768, 35137}, {40035, 40036}


X(46749) = ISOTOMIC CONJUGATE OF X(3467)

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) : :

X(46749) lies on the cubic pK(76,311) and these lines: {7, 8}, {76, 20932}, {264, 40716}, {304, 30596}, {311, 20565}, {313, 20924}, {870, 40044}, {1111, 4360}, {3673, 17393}, {4089, 33943}, {5361, 19804}, {9312, 44179}, {16732, 17300}, {17234, 18151}, {17241, 20927}, {17263, 30807}, {17271, 18698}, {17297, 20236}, {17322, 26563}, {17378, 17861}, {17387, 20171}, {17483, 21863}, {17788, 18143}, {17789, 18040}, {18032, 39735}, {18041, 30985}, {18133, 18159}, {18139, 20919}, {20444, 20917}, {20920, 31019}, {20951, 44188}, {21609, 33808}, {25647, 38941}, {35550, 44139}

X(46749) = isotomic conjugate of X(3467)
X(46749) = isotomic conjugate of the isogonal conjugate of X(3336)
X(46749) = X(20565)-Ceva conjugate of X(75)
X(46749) = cevapoint of X(17483) and X(27529)
X(46749) = barycentric product X(i)*X(j) for these {i,j}: {75, 17483}, {76, 3336}, {85, 27529}, {310, 21863}, {561, 21773}, {1969, 23070}, {11069, 40075}
X(46749) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3467}, {3336, 6}, {11069, 6187}, {14452, 11075}, {17483, 1}, {21773, 31}, {21863, 42}, {23070, 48}, {27529, 9}, {35195, 35192}, {35197, 2174}, {42649, 3063}
X(46749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 20930, 17791}, {85, 20930, 75}, {320, 1441, 75}, {3262, 7321, 75}, {5564, 20880, 75}, {18139, 30690, 20919}, {18143, 20956, 17788}, {20444, 20917, 40001}


X(46750) = ISOTOMIC CONJUGATE OF X(3336)

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(46750) lies on the cubic pK(76,311) and these lines: {69, 40716}, {75, 45799}, {264, 17791}, {309, 17361}, {311, 20565}, {312, 37656}, {314, 3467}, {17360, 20570}

X(46750) = isotomic conjugate of X(3336)
X(46750) = isotomic conjugate of the isogonal conjugate of X(3467)
X(46750) = X(319)-cross conjugate of X(75)
X(46750) = X(i)-isoconjugate of X(j) for these (i,j): {6, 21773}, {25, 23070}, {31, 3336}, {32, 17483}, {109, 42649}, {1333, 21863}, {1397, 27529}, {6186, 35197}, {7113, 11069}
X(46750) = barycentric product X(76)*X(3467)
X(46750) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 21773}, {2, 3336}, {10, 21863}, {63, 23070}, {75, 17483}, {80, 11069}, {312, 27529}, {650, 42649}, {3219, 35197}, {3467, 6}, {19658, 11076}


X(46751) = ISOTOMIC CONJUGATE OF X(3471)

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

X(46751) lies on the cubic pK(76,311) and these lines: {69, 74}, {264, 40705}, {3629, 44769}, {3763, 35910}, {16076, 45198}, {16077, 32002}, {34767, 40410}, {46757, 46758}

X(46751) = isotomic conjugate of X(3471)
X(46751) = isotomic conjugate of the isogonal conjugate of X(3470)
X(46751) = X(10272)-cross conjugate of X(37779)
X(46751) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3471}, {2173, 14579}, {9406, 13582}
X(46751) = cevapoint of X(10272) and X(37779)
X(46751) = barycentric product X(i)*X(j) for these {i,j}: {76, 3470}, {1494, 37779}, {1749, 33805}, {10272, 31621}, {39290, 45790}
X(46751) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3471}, {74, 14579}, {1494, 13582}, {1749, 2173}, {2914, 39176}, {3470, 6}, {5627, 11071}, {6140, 14398}, {10272, 3163}, {11063, 1495}, {14451, 11070}, {14919, 43704}, {36308, 46072}, {36311, 46076}, {37779, 30}, {37943, 1990}, {40604, 1511}, {44769, 1291}, {45147, 1637}, {45790, 5664}


X(46752) = ISOTOMIC CONJUGATE OF X(3469)

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

X(46752) lies on the cubic pK(76,311) and these lines: {75, 225}, {85, 1804}, {320, 1439}, {4554, 18695}, {7535, 20914}, {18747, 27471}

X(46752) = isotomic conjugate of X(3469)
X(46752) = isotomic conjugate of the isogonal conjugate of X(3468)
X(46752) = barycentric product X(i)*X(j) for these {i,j}: {76, 3468}, {349, 15777}, {20924, 34300}
X(46752) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3469}, {3468, 6}, {15777, 284}, {17483, 7165}, {30690, 34303}, {34300, 2161}
X(46752) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 40702, 18749}, {349, 45797, 75}


X(46753) = X(5)X(302)∩X(95)X(303)

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

X(46753) lies on the cubic pK(76,311) and these lines: {5, 302}, {69, 19772}, {95, 303}, {264, 298}, {299, 465}, {343, 8613}, {32002, 33529}

X(46753) = isotomic conjugate of the isogonal conjugate of X(8837)
X(46753) = X(311)-Ceva conjugate of X(303)
X(46753) = barycentric product X(76)*X(8837)
X(46753) = barycentric quotient X(8837)/X(6)
X(46753) = {X(95),X(33530)}-harmonic conjugate of X(303)


X(46754) = X(5)X(303)∩X(95)X(302)

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

X(46754) lies on the cubic pK(76,311) and these lines: {5, 303}, {69, 19773}, {95, 302}, {264, 299}, {298, 466}, {343, 8613}, {32002, 33530}

X(46754) = isotomic conjugate of the isogonal conjugate of X(8839)
X(46754) = X(311)-Ceva conjugate of X(302)
X(46754) = barycentric product X(76)*X(8839)
X(46754) = barycentric quotient X(8839)/X(6)
X(46754) = {X(95),X(33529)}-harmonic conjugate of X(302)


X(46755) = ISOTOMIC CONJUGATE OF X(3489)

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

X(46755) lies on the cubic pK(76,311) and these lines: {17, 76}, {69, 2993}, {95, 183}, {99, 1606}, {264, 38428}, {299, 40035}, {311, 19712}

X(46755) = isotomic conjugate of X(3489)
X(46755) = isotomic conjugate of the isogonal conjugate of X(627)
X(46755) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3489}, {560, 19712}
X(46755) = barycentric product X(76)*X(627)
X(46755) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3489}, {76, 19712}, {627, 6}, {34389, 40167}, {41000, 39134}
X(46755) = {X(305),X(44149)}-harmonic conjugate of X(46756)


X(46756) = ISOTOMIC CONJUGATE OF X(3490)

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

X(46756) lies on the cubic pK(76,311) and these lines: {18, 76}, {69, 2992}, {95, 183}, {99, 1605}, {264, 38427}, {298, 40035}, {311, 19713}

X(46756) = isotomic conjugate of X(3490)
X(46756) = isotomic conjugate of the isogonal conjugate of X(628)
X(46756) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3490}, {560, 19713}
X(46756) = barycentric product X(76)*X(628)
X(46756) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3490}, {76, 19713}, {628, 6}, {34390, 40168}, {41001, 39135}
X(46756) = {X(305),X(44149)}-harmonic conjugate of X(46755)


X(46757) = ISOTOMIC CONJUGATE OF X(38932)

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

X(46757) lies on the cubic pK(76,311) and these lines: {13, 99}, {69, 19777}, {264, 38427}, {302, 11120}, {622, 39261}, {19712, 45799}, {46751, 46758}

X(46757) = isotomic conjugate of X(38932)
X(46757) = isotomic conjugate of the isogonal conjugate of X(39261)
X(46757) = barycentric product X(i)*X(j) for these {i,j}: {76, 39261}, {622, 40706}
X(46757) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 38932}, {622, 395}, {6151, 3439}, {11094, 23715}, {14369, 19295}, {38404, 40157}, {39261, 6}, {40706, 2993}


X(46758) = ISOTOMIC CONJUGATE OF X(38931)

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

X(46758) lies on the cubic pK(76,311) and these lines: {14, 99}, {69, 19776}, {264, 38428}, {303, 11119}, {621, 39262}, {19713, 45799}, {46751, 46757}

X(46758) = isotomic conjugate of X(38931)
X(46758) = isotomic conjugate of the isogonal conjugate of X(39262)
X(46758) = barycentric product X(i)*X(j) for these {i,j}: {76, 39262}, {621, 40707}
X(46758) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 38931}, {621, 396}, {2981, 3438}, {11093, 23714}, {14368, 19294}, {38403, 40156}, {39262, 6}, {40707, 2992}


X(46759) = X(1)X(39725)∩X(2)X(39726)

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

X(46759) lies on the cubic pK(76,311) and these lines: {1, 39725}, {2, 39726}, {75, 39727}, {39724, 39728}

X(46759) = X(1930)-Ceva conjugate of X(82)
X(46759) = barycentric product X(3112)*X(35213)
X(46759) = barycentric quotient X(35213)/X(38)


X(46760) = ISOGONAL CONJUGATE OF X(46736)

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

See Antreas Hatzipolakis and Peter Moses, euclid 4059.

X(46760) lies on these lines: {2, 95}, {3, 2052}, {76, 6503}, {107, 6641}, {140, 2055}, {324, 46724}, {343, 1078}, {418, 1629}, {578, 631}, {3524, 14361}, {7484, 22712}, {7509, 40814}, {7786, 10601}, {8613, 22052}, {8884, 26876}, {14165, 26906}, {15466, 37068}, {26865, 33971}, {26907, 41204}, {35941, 41244}, {38283, 43998}

X(46760) = isogonal conjugate of X(46736)
X(46760) = {X(2),X(577)}-harmonic conjugate of X (275)


X(46761) = (name pending)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^10*b^2 + a^8*b^4 - 2*a^6*b^6 - 2*a^4*b^8 + a^2*b^10 + b^12 + a^10*c^2 + 3*a^8*b^2*c^2 - 4*a^4*b^6*c^2 - a^2*b^8*c^2 + b^10*c^2 - 4*a^6*b^2*c^4 - 38*a^4*b^4*c^4 - 4*a^2*b^6*c^4 - 2*b^8*c^4 - 2*a^6*c^6 - 4*a^4*b^2*c^6 - 2*b^6*c^6 + 3*a^2*b^2*c^8 + b^4*c^8 + a^2*c^10 + b^2*c^10)*(a^10*b^2 - 2*a^6*b^6 + a^2*b^10 + a^10*c^2 + 3*a^8*b^2*c^2 - 4*a^6*b^4*c^2 - 4*a^4*b^6*c^2 + 3*a^2*b^8*c^2 + b^10*c^2 + a^8*c^4 - 38*a^4*b^4*c^4 + b^8*c^4 - 2*a^6*c^6 - 4*a^4*b^2*c^6 - 4*a^2*b^4*c^6 - 2*b^6*c^6 - 2*a^4*c^8 - a^2*b^2*c^8 - 2*b^4*c^8 + a^2*c^10 + b^2*c^10 + c^12) : :

See Antreas Hatzipolakis and Peter Moses, euclid 4059.

X(46761) lies on these lines: { }

X(46761) = isogonal conjugate of X(46762)


X(46762) = ISOGONAL CONJUGATE OF X(46761)

Barycentrics    (a^2 - b^2 - c^2)*(a^12 + a^10*b^2 - 2*a^8*b^4 - 2*a^6*b^6 + a^4*b^8 + a^2*b^10 + a^10*c^2 - a^8*b^2*c^2 - 4*a^6*b^4*c^2 + 3*a^2*b^8*c^2 + b^10*c^2 - 2*a^8*c^4 - 4*a^6*b^2*c^4 - 38*a^4*b^4*c^4 - 4*a^2*b^6*c^4 - 2*a^6*c^6 - 4*a^2*b^4*c^6 - 2*b^6*c^6 + a^4*c^8 + 3*a^2*b^2*c^8 + a^2*c^10 + b^2*c^10) : :

See Antreas Hatzipolakis and Peter Moses, euclid 4059.

X(46762) lies on this line: {54, 69}

X(46762) = isogonal conjugate of X(46761)


X(46763) = X(4)X(46358)∩X(6)X(1344)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^8 - 2*a^6*b^2 - a^4*b^4 + b^8 - 2*a^6*c^2 + 4*a^4*b^2*c^2 - 4*b^6*c^2 - a^4*c^4 + 6*b^4*c^4 - 4*b^2*c^6 + c^8 - a^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)*J) + 4*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + 4*b^2*c^2 - 2*c^4 - a^2*(a^2 - b^2 - c^2)*J)*S^2*Sqrt[2*(-27 + J^3)*R^4 - S^2 + 18*R^2*SW - SW^2] : :

See Antreas Hatzipolakis and Peter Moses, euclid 4060.

X(46763) lies on these lines: {4, 46358}, {6, 1344}, {14709, 46357}


X(46764) = X(4)X(46357)∩X(6)X(1344)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^8 - 2*a^6*b^2 - a^4*b^4 + b^8 - 2*a^6*c^2 + 4*a^4*b^2*c^2 - 4*b^6*c^2 - a^4*c^4 + 6*b^4*c^4 - 4*b^2*c^6 + c^8 - a^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)*J) - 4*(a^4 + a^2*b^2 - 2*b^4 + a^2*c^2 + 4*b^2*c^2 - 2*c^4 - a^2*(a^2 - b^2 - c^2)*J)*S^2*Sqrt[2*(-27 + J^3)*R^4 - S^2 + 18*R^2*SW - SW^2] : :

See Antreas Hatzipolakis and Peter Moses, euclid 4060.

X(46764) lies on these lines: {4, 46357}, {6, 1344}, {14709, 46358}


X(46765) = X(4)X(251)∩X(32)X(66)

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

X(46765) lies on the Jerabek circumhyperbola, the cubic K1258, and these lines: {3, 22075}, {4, 251}, {6, 2353}, {32, 66}, {54, 34945}, {69, 10316}, {248, 27372}, {290, 11610}, {1176, 34137}, {1799, 28405}, {7819, 34138}, {8793, 40938}, {10312, 43678}, {21458, 41361}, {34207, 46288}, {38834, 43696}

X(46765) = isogonal conjugate of the isotomic conjugate of X(40404)
X(46765) = isogonal conjugate of the polar conjugate of X(16277)
X(46765) = X(i)-cross conjugate of X(j) for these (i,j): {32, 10547}, {40947, 1799}
X(46765) = X(i)-isoconjugate of X(j) for these (i,j): {10, 16715}, {22, 20883}, {38, 17907}, {63, 41375}, {75, 40938}, {92, 3313}, {162, 23881}, {304, 27373}, {315, 17442}, {427, 1760}, {1235, 2172}, {1843, 20641}, {1930, 8743}, {1969, 23208}, {4456, 16747}, {4463, 17171}, {11605, 18715}
X(46765) = cevapoint of X(32) and X(2353)
X(46765) = crosspoint of X(16277) and X(40404)
X(46765) = crosssum of X(i) and X(j) for these (i,j): {427, 19595}, {3313, 40938}
X(46765) = barycentric product X(i)*X(j) for these {i,j}: {3, 16277}, {6, 40404}, {66, 1176}, {251, 14376}, {1799, 2353}, {2156, 34055}, {10547, 18018}, {13854, 28724}, {27372, 39287}
X(46765) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 41375}, {32, 40938}, {66, 1235}, {184, 3313}, {251, 17907}, {647, 23881}, {1176, 315}, {1333, 16715}, {1799, 40073}, {1974, 27373}, {2156, 20883}, {2353, 427}, {10547, 22}, {14376, 8024}, {14575, 23208}, {16277, 264}, {28724, 34254}, {34055, 20641}, {40146, 1843}, {40404, 76}, {46288, 8743}
X(46765) = {X(16277),X(40357)}-harmonic conjugate of X(13854)


X(46766) = X(6)X(34427)∩X(32)X(66)

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

X(46766) lies on the cubic K1258 and these lines: {6, 34427}, {25, 46288}, {32, 66}, {251, 13575}, {1370, 40357}, {7735, 16277}

X(46766) = isogonal conjugate of the isotomic conjugate of X(40357)
X(46766) = X(i)-isoconjugate of X(j) for these (i,j): {1760, 39129}, {1930, 40358}, {3313, 39733}
X(46766) = barycentric product X(i)*X(j) for these {i,j}: {6, 40357}, {66, 8793}, {159, 16277}, {1176, 17407}, {3162, 40404}
X(46766) = barycentric quotient X(i)/X(j) for these {i,j}: {2353, 39129}, {8793, 315}, {16277, 40009}, {17407, 1235}, {40357, 76}, {46288, 40358}


X(46767) = X(6)X(17409)∩X(251)X(13575)

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

X(46767) lies on the cubics K429 and K1258 and these lines: {6, 17409}, {251, 13575}, {10316, 39172}, {20806, 36414}

X(46767) = isogonal conjugate of the isotomic conjugate of X(40358)
X(46767) = polar conjugate of the isotomic conjugate of X(39172)
X(46767) = X(40358)-Ceva conjugate of X(39172)
X(46767) = X(32)-cross conjugate of X(17409)
X(46767) = X(i)-isoconjugate of X(j) for these (i,j): {66, 21582}, {159, 46244}, {304, 17407}, {1930, 40357}, {18018, 18596}
X(46767) = barycentric product X(i)*X(j) for these {i,j}: {4, 39172}, {6, 40358}, {22, 34207}, {206, 13575}, {8673, 39417}, {17453, 39733}, {20806, 40144}, {20968, 40009}
X(46767) = barycentric quotient X(i)/X(j) for these {i,j}: {206, 1370}, {1974, 17407}, {2172, 21582}, {7251, 18629}, {10316, 28419}, {13575, 40421}, {17409, 41361}, {17453, 18596}, {20968, 159}, {22075, 23115}, {34207, 18018}, {39172, 69}, {40144, 43678}, {40358, 76}, {46288, 40357}


X(46768) = X(6)X(34427)∩X(32)X(19615)

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

X(46768) lies on the cubic K1258 and these lines: {6, 34427}, {32, 19615}, {251, 40358}, {10547, 17409}

X(46768) = X(20931)-isoconjugate of X(39129)
X(46768) = barycentric product X(i)*X(j) for these {i,j}: {8793, 34427}, {19615, 40357}
X(46768) = barycentric quotient X(22262)/X(39129)


X(46769) = X(6)X(39172)∩X(25)X(40144)

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

X(46769) lies on the cubic K1258 and these lines: {6, 39172}, {25, 40144}, {251, 40358}, {8743, 39417}, {34207, 46288}

X(46769) = X(40358)-Ceva conjugate of X(34207)
X(46769) = X(21582)-isoconjugate of X(34427)
X(46769) = barycentric product X(i)*X(j) for these {i,j}: {5596, 34207}, {13575, 20993}, {28696, 40144}
X(46769) = barycentric quotient X(i)/X(j) for these {i,j}: {16544, 21582}, {20993, 1370}, {22135, 28419}


X(46770) = X(32)X(184)∩X(251)X(1343)

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

X(46770) lies on the cubic K1258 and these lines: {32, 184}, {251, 1343}, {1342, 5012}, {1670, 6636}, {1671, 34945}, {1976, 12050}

X(46770) = isogonal conjugate of the isotomic conjugate of X(1342)
X(46770) = X(75)-isoconjugate of X(5403)
X(46770) = barycentric product X(6)*X(1342)
X(46770) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 5403}, {1342, 76}
X(46770) = {X(32),X(184)}-harmonic conjugate of X(41379)
X(46770) = {X(32),X(1501)}-harmonic conjugate of X(46771)
X(46770) = {X(184),X(34396)}-harmonic conjugate of X(46771)


X(46771) = X(32)X(184)∩X(251)X(1342)

Barycentrics    a^4*(a^2 + Sqrt[a^2*b^2 + a^2*c^2 + b^2*c^2]) : :

X(46771) lies on the cubic K1258 and these lines: {32, 184}, {251, 1342}, {1343, 5012}, {1670, 34945}, {1671, 6636}, {1976, 12051}

X(46771) = isogonal conjugate of the isotomic conjugate of X(1343)
X(46771) = X(75)-isoconjugate of X(5404)
X(46771) = barycentric product X(i)*X(j) for these {i,j}: {6, 1343}, {184, 16245}
X(46771) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 5404}, {1343, 76}, {16245, 18022}
X(46771) = {X(32),X(184)}-harmonic conjugate of X(41378)
X(46771) = {X(32),X(1501)}-harmonic conjugate of X(46770)
X(46771) = {X(184),X(34396)}-harmonic conjugate of X(46770)


X(46772) = ISOGONAL CONJUGATE OF X(39673)

Barycentrics    (b + c)*(2*a*b + a*c + 2*b*c)*(a*b + 2*a*c + 2*b*c) : :
X(46772) = X[42027] - 3 X[43224]

See Antreas Hatzipolakis and Peter Moses, euclid 4064.

X(46772) lies on these lines: {1, 3696}, {2, 39737}, {19, 1889}, {37, 4365}, {65, 22271}, {75, 4981}, {82, 18089}, {210, 40504}, {536, 17038}, {759, 6013}, {876, 4802}, {984, 39708}, {994, 44663}, {3896, 4751}, {4688, 13476}, {4699, 39739}, {4739, 39742}, {4967, 39712}, {22316, 27798}, {31238, 37593}, {42027, 43224}

X(46772) = isogonal conjugate of X(39673)
X(46772) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39673}, {21, 16878}, {58, 17018}, {99, 8655}, {110, 6005}, {1333, 4687}
X(46772) = trilinear pole of line {661, 21836}
X(46772) = trilinear product X(i)*X(j) for these {i,j}: {10, 10013}, {523, 6013}
X(46772) = barycentric product X(i)*X(j) for these {i,j}: {321, 10013}, {1577, 6013}
X(46772) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39673}, {10, 4687}, {37, 17018}, {661, 6005}, {798, 8655}, {1400, 16878}, {6013, 662}, {10013, 81}


X(46773) = X(58)X(40589)∩X(65)X(4649)

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

See Antreas Hatzipolakis and Peter Moses, euclid 4071.

X(46773) lies on these lines: {58, 40589}, {65, 4649}


X(46774) = (name pending)

Barycentrics    a^2*(a^6 + 2*a^5*b - 2*a^4*b^2 - 6*a^3*b^3 - 2*a^2*b^4 + 2*a*b^5 + b^6 + a^5*c - 2*a^4*b*c - 11*a^3*b^2*c - 11*a^2*b^3*c - 2*a*b^4*c + b^5*c - 3*a^4*c^2 - 12*a^3*b*c^2 - 18*a^2*b^2*c^2 - 12*a*b^3*c^2 - 3*b^4*c^2 - 4*a^3*c^3 - 10*a^2*b*c^3 - 10*a*b^2*c^3 - 4*b^3*c^3 - a^2*c^4 - a*b*c^4 - b^2*c^4 + a*c^5 + b*c^5 + c^6)*(a^6 + a^5*b - 3*a^4*b^2 - 4*a^3*b^3 - a^2*b^4 + a*b^5 + b^6 + 2*a^5*c - 2*a^4*b*c - 12*a^3*b^2*c - 10*a^2*b^3*c - a*b^4*c + b^5*c - 2*a^4*c^2 - 11*a^3*b*c^2 - 18*a^2*b^2*c^2 - 10*a*b^3*c^2 - b^4*c^2 - 6*a^3*c^3 - 11*a^2*b*c^3 - 12*a*b^2*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 + b*c^5 + c^6) : :

See Antreas Hatzipolakis and Peter Moses, euclid 4071.

X(46774) lies on these lines: { }


X(46775) = X(6)X(17)∩X(30259)X(45971)

Barycentrics    2*a^12-4*(b^2+c^2)*a^10-(5*b^4+6*b^2*c^2+5*c^4)*a^8+4*(b^2+c^2)*(5*b^4-2*b^2*c^2+5*c^4)*a^6-(20*b^8+20*c^8-(17*b^4+12*b^2*c^2+17*c^4)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)*(8*b^4-17*b^2*c^2+8*c^4)*a^2-(b^2-c^2)^6 : :

See Antreas Hatzipolakis and César Lozada, euclid 4073.

X(46775) lies on these lines: {6, 17}, {30259, 45971}


X(46776) = X(4)X(6)∩X(648)X(5895)

Barycentrics    7*a^12-11*(b^2+c^2)*a^10-4*(b^4-9*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(5*b^4-14*b^2*c^2+5*c^4)*a^6-(b^2-c^2)^4*a^4+(b^4-c^4)*(b^2-c^2)*(b^4-10*b^2*c^2+c^4)*a^2-2*(b^4+4*b^2*c^2+c^4)*(b^2-c^2)^4 : :

See Antreas Hatzipolakis and César Lozada, euclid 4073.

X(46776) lies on these lines: {4, 6}, {648, 5895}, {8567, 44134}, {30549, 44247}


X(46777) = X(2)X(6)∩X(98)X(804)

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

See Antreas Hatzipolakis and César Lozada, euclid 4073.

X(46777) lies on these lines: {2, 6}, {98, 804}, {237, 36822}, {3053, 10684}, {4108, 46589}, {6785, 13240}, {9753, 36183}, {9755, 15920}

X(46777) = crossdifference of every pair of points on line {X(512), X(11672)}
X(46777) = crosssum of X(511) and X(34383)
X(46777) = X(98)-daleth conjugate of-X(804)
X(46777) = perspector of the circumconic {{A, B, C, X(99), X(34536)}}
X(46777) = intersection, other than A, B, C, of circumconics {{A, B, C, X(98), X(2421)}} and {{A, B, C, X(325), X(43665)}}
X(46777) = {X(2), X(385)}-harmonic conjugate of X(2421)


X(46778) = X(6)X(523)∩X(99)X(670)

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

See Antreas Hatzipolakis and César Lozada, euclid 4073.

X(46778) lies on these lines: {6, 523}, {99, 670}, {183, 669}, {308, 18105}, {512, 3734}, {599, 25423}, {888, 33755}, {1975, 14824}, {3098, 32472}, {3314, 44445}, {7610, 45317}, {7770, 23099}, {7778, 23301}, {8266, 21006}, {33799, 39292}, {37637, 44451}

X(46778) = crossdifference of every pair of points on line {X(511), X(1084)}
X(46778) = crosssum of X(512) and X(34383)
X(46778) = X(99)-daleth conjugate of-X(804)
X(46778) = perspector of the circumconic {{A, B, C, X(98), X(34537)}}
X(46778) = inverse of X(6) in Kiepert parabola





leftri   Points on cubics: X(46779) - X(46815)  rightri

This preamble is contributed by Clark Kimberling and Peter Moses, January 27, 2022.

In the plane of a triangle ABC, let L, given by l x + m y + n z = 0, be a line, and let P = p : q : r be a point not on L and not on a sideline BC, CA, AB. Let

Ap = L∩AP,      Bp = L∩BP,      Cp = L∩CP.

Let A'B'C' be the cocevian triangle (TCCT, p. 200) of a point X = x : y : z, so that

A' = 0 : y : -z,      B' = -x : 0 : z,      C' = x :-y : 0.

The locus of X such that A'B'C' is perspective to the (degenerate) triangle ApBpCp is the cubic, given by

m^2 p q y^2 z + n^2 p r y z^2 + (cyclic) - 2(m n q r + n l r p + l m p q) x y z = 0.

The appearance of (k, Knnn) in the following list means that if L is the line x + y + z = 0 at infinity and P = X(k), then the cubic is Knnn in Bernard Gibert's catalogue (CTC):

(2, K015), (4, K010), (99, K185), (190, K296), (648, K953), (876, K286), (4373, K090), (5485, K408)

The appearance of {{i,j}, {h1, h2, ...}}} in the following list means that if l : m : n = X(i) and P = X(j), then the cubic passes through the points X(h1), X(h2), . . .

{1,{2,1022,1026,3572,4585,24004,24015,24029,24035,27853,46779,46780,46781,46782,}
{76,{2,4230,17941,23288,23342,23354,30508,30509}
{100,{2,88,3218,3935,4358,18359,37780,37783,41798}
{110,{2,23,94,111,323,3266,14919,18019,21907,32849,37798,46106,46783,46784,46785,46786,46787,46788,46789}. This is the isogonal conjugate of the cubic K381)
{650,{2,57,200,312,1088,1812,40149,46644}
{664,{2,527,673,1121,1948,3912,11608,14943,40843,40846,40864,40873,40875,40882,44331,46790,46791,46792,46793,,46794. This is the isogonal conjugate of the cubic K225
{666,{2,7,8,528,14947,18821,36887,43671}
{668,{2,239,335,536,3227,11611,19623,29908,40844,40862,40874,40881,44330,46795,46796,46797,46798,46799,46800,46801,46802,46803,46804,46805}
{670,{2,385,538,1916,3228,15014,17759,39925,40859,40887}
{671,{2,99,523,7473,9180,9182,14606,30508,30509}
{693,{2,81,321,4945,6605,13386,13387,43260}
{850,{2,97,251,324,8024,11078,11092,11143,11144,13428,13439,42008,46806,46807,46808,46809}
{879,{2,4,69,393,3926,6776,43718,44144}
{882,{2,6,32,76,1502,3094,3114,11325,14609}
{885,{2,7,8,279,346,390,16713,40779}
{2394,{2,4,69,3431,5967,27558,30508,30509,44135}
{2574,{2,1114,2593,8106,8116,8426,16071,22340,39298,41519,46810,46811,46812}
{2575,{2,1113,2592,8105,8115,8427,16070,22339,39299,41518,46813,46814,46815}
{2966,{2,4,69,542,5641,9214,9513,36890,44155}
{4025,{2,27,63,92,306,13386,13387,19799}
{4367,{2,256,694,1432,1909,3978,17787,28369,40790}
{4374,{2,257,385,894,1916,17752,27447,40738}
{4581,{2,7,8,941,4198,30589,30590,31011,34262,34284}
{5466,{2,1383,4232,9464,21466,21467,30508,30509}
{6332,{2,29,77,78,273,307,318,13386,13387}

underbar



X(46779) = X(2)X(45)∩X(1022)X(1023)

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

X(46779) lies on these lines: {2, 45}, {1022, 1023}, {1026, 23838}, {3573, 39154}, {4582, 24004}, {17109, 24397}, {23343, 23352}

X(46779) = isotomic conjugate of X(46781)
X(46779) = crossdifference of every pair of points on line {1960, 42084}
X(46779) = X(i)-isoconjugate of X(j) for these (i,j): {1635, 2718}, {1960, 37222}
X(46779) = barycentric product X(i)*X(j) for these {i,j}: {2802, 4555}, {3257, 30566}, {4582, 43048}
X(46779) = barycentric quotient X(i)/X(j) for these {i,j}: {901, 2718}, {2802, 900}, {3257, 37222}, {4555, 35175}, {24457, 1647}, {30566, 3762}, {37630, 14584}, {43048, 30725}
X(46779) = {X(3257),X(5376)}-harmonic conjugate of X(4585)


X(46780) = X(2)X(668)∩X(889)X(3572)

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

X(46780) lies on these lines: {2, 668}, {889, 3572}, {1022, 27853}, {4585, 5381}, {4607, 23891}, {23354, 43928}

X(46780) = isotomic conjugate of X(46782)
X(46780) = X(2382)-isoconjugate of X(3768)
X(46780) = barycentric product X(537)*X(889)
X(46780) = barycentric quotient X(i)/X(j) for these {i,j}: {537, 891}, {889, 18822}, {898, 2382}, {20331, 3768}, {36848, 19945}
X(46780) = {X(3227),X(30866)}-harmonic conjugate of X(31002)


X(46781) = X(2)X(3762)∩X(1000)X(3887)

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

X(46781) lies on these lines: {2, 3762}, {1000, 3887}, {1016, 4585}, {2718, 2726}, {14628, 30725}, {35168, 35175}

X(46781) = isotomic conjugate of X(46779)
X(46781) = X(i)-isoconjugate of X(j) for these (i,j): {2802, 32665}, {30566, 32719}
X(46781) = trilinear pole of line {900, 34590}
X(46781) = barycentric product X(i)*X(j) for these {i,j}: {900, 35175}, {3762, 37222}
X(46781) = barycentric quotient X(i)/X(j) for these {i,j}: {900, 2802}, {1647, 24457}, {2718, 901}, {3762, 30566}, {14584, 37630}, {30725, 43048}, {35175, 4555}, {37222, 3257}


X(46782) = X(2)X(812)∩X(513)X(16507)

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

X(46782) lies on these lines: {2, 812}, {513, 16507}, {536, 14433}, {899, 14434}, {1022, 3572}, {2382, 9081}, {6381, 27855}, {24004, 27853}

X(46782) = isotomic conjugate of X(46780)
X(46782) = X(i)-isoconjugate of X(j) for these (i,j): {537, 34075}, {898, 20331}
X(46782) = barycentric product X(891)*X(18822)
X(46782) = barycentric quotient X(i)/X(j) for these {i,j}: {891, 537}, {2382, 898}, {3768, 20331}, {18822, 889}, {19945, 36848}


X(46783) = X(2)X(523)∩X(6)X(10560)

Barycentrics    a^2*(a^2 + b^2 - 2*c^2)*(a^2 - 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[46783] - 4 X[3291], 2 X[3266] - 5 X[30745]

X(46783) = X(4678) lies on the cubic K792 and these lines: {2, 523}, {6, 10560}, {23, 111}, {323, 895}, {352, 42007}, {511, 36827}, {512, 46131}, {538, 42008}, {671, 10989}, {858, 31125}, {892, 5971}, {1236, 3266}, {1994, 10559}, {3231, 8705}, {7417, 46633}, {7468, 44420}, {7482, 44467}, {7664, 40544}, {8753, 37962}, {9139, 14919}, {9465, 14609}, {10558, 34545}, {10754, 14515}, {14246, 16042}, {14263, 36182}, {14908, 37980}, {15018, 21460}, {17983, 46106}, {17993, 20403}, {32729, 35265}, {34169, 36174}, {38526, 39576}

X(46783) = X(9177)-cross conjugate of X(2854)
X(46783) = X(i)-isoconjugate of X(j) for these (i,j): {524, 36150}, {896, 2770}, {14210, 32741}
X(46783) = cevapoint of X(2854) and X(9177)
X(46783) = crossdifference of every pair of points on line {187, 1649}
X(46783) = barycentric product X(i)*X(j) for these {i,j}: {671, 2854}, {5968, 37858}, {7482, 14977}, {30786, 44467}
X(46783) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 2770}, {923, 36150}, {2854, 524}, {7482, 4235}, {9177, 2482}, {14263, 34171}, {32740, 32741}, {44467, 468}, {46154, 36824}
X(46783) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {111, 691, 23}, {111, 15899, 691}, {671, 34320, 10989}, {691, 15398, 111}, {895, 32583, 323}, {15398, 15899, 23}


X(46784) = X(2)X(650)∩X(23)X(105)

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

X(46784) lies on these lines: {2, 650}, {23, 105}, {111, 927}, {323, 1814}, {673, 24585}, {4442, 14942}, {6185, 14953}, {6654, 33150}, {18019, 32849}

X(46784) = X(672)-isoconjugate of X(2752)
X(46784) = barycentric product X(2481)*X(2836)
X(46784) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 2752}, {2836, 518}, {7476, 4238}


X(46785) = X(2)X(1577)∩X(23)X(759)

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

X(46785) lies on these lines: {2, 1577}, {23, 759}, {80, 33139}, {2006, 18593}, {6740, 33305}, {14194, 24916}, {18359, 37759}, {24624, 35466}, {33134, 36815}, {34172, 36175}, {36002, 45926}

X(46785) = X(2245)-isoconjugate of X(12030)
X(46785) = barycentric quotient X(i)/X(j) for these {i,j}: {759, 12030}, {37964, 4242}


X(46786) = X(2)X(647)∩X(23)X(94)

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

X(46786) lies on these lines: {2, 647}, {23, 94}, {111, 16081}, {248, 290}, {287, 323}, {542, 36885}, {1976, 18372}, {2697, 40079}, {3266, 14919}, {5191, 7473}, {5967, 11422}, {11673, 20021}, {14999, 34369}, {15080, 35912}, {35606, 40814}

X(46786) = isotomic conjugate of X(46787)
X(46786) = isotomic conjugate of the isogonal conjugate of X(34369)
X(46786) = X(i)-isoconjugate of X(j) for these (i,j): {163, 23350}, {842, 1755}, {5641, 9417}, {6149, 34370}, {14998, 23997}
X(46786) = trilinear pole of line {542, 18312}
X(46786) = barycentric product X(i)*X(j) for these {i,j}: {76, 34369}, {290, 542}, {850, 34761}, {1640, 43187}, {2247, 46273}, {2966, 18312}, {5191, 18024}, {14999, 43665}
X(46786) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 842}, {290, 5641}, {523, 23350}, {542, 511}, {850, 34765}, {879, 35909}, {1640, 3569}, {1989, 34370}, {2247, 1755}, {2395, 14998}, {2966, 5649}, {5191, 237}, {6041, 2491}, {6103, 232}, {7473, 4230}, {14265, 34174}, {14999, 2421}, {16092, 5968}, {17986, 35908}, {18312, 2799}, {20021, 46157}, {34156, 40080}, {34175, 38939}, {34369, 6}, {34761, 110}, {43087, 14356}, {43187, 6035}, {43665, 14223}, {45662, 9155}
X(46786) = {X(16081),X(22456)}-harmonic conjugate of X(46106)


X(46787) = X(2)X(1637)∩X(23)X(110)

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

X(46787) lies on these lines: {2, 1637}, {23, 110}, {94, 18019}, {111, 14919}, {147, 34174}, {325, 34370}, {684, 5968}, {877, 7664}, {1297, 40080}, {1916, 39291}, {2396, 32458}, {2421, 36790}, {2967, 4230}, {3266, 6331}, {3569, 35910}, {5641, 7840}, {9513, 35909}, {14966, 36415}

X(46787) = isogonal conjugate of X(34369)
X(46787) = isotomic conjugate of X(46786)
X(46787) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34369}, {98, 2247}, {293, 6103}, {542, 1910}, {661, 34761}, {1640, 36084}, {1821, 5191}, {6041, 36036}, {36132, 45321}
X(46787) = trilinear pole of line {511, 23350}
X(46787) = crossdifference of every pair of points on line {1640, 5191}
X(46787) = trilinear product X(i)*X(j) for these {i,j}: {662, 23350}, {842, 1959}, {1755, 5641}, {14223, 23997}
X(46787) = barycentric product X(i)*X(j) for these {i,j}: {99, 23350}, {110, 34765}, {325, 842}, {511, 5641}, {877, 35909}, {2396, 14998}, {2421, 14223}, {2799, 5649}, {3569, 6035}, {7799, 34370}, {20022, 46157}
X(46787) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34369}, {110, 34761}, {232, 6103}, {237, 5191}, {511, 542}, {842, 98}, {1755, 2247}, {2421, 14999}, {2491, 6041}, {2799, 18312}, {3569, 1640}, {4230, 7473}, {5641, 290}, {5649, 2966}, {5968, 16092}, {6035, 43187}, {9155, 45662}, {14223, 43665}, {14356, 43087}, {14998, 2395}, {23350, 523}, {34174, 14265}, {34370, 1989}, {34765, 850}, {35908, 17986}, {35909, 879}, {38939, 34175}, {40080, 34156}, {46157, 20021}


X(46788) = X(2)X(525)∩X(23)X(74)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 + 2*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 + 4*b^4*c^4 + 3*a^2*c^6 - b^2*c^6 - c^8) : :
X(46788) = X[323] - 4 X[44436]

X(46788) lies on these lines: {2, 525}, {23, 74}, {94, 16080}, {323, 3284}, {511, 36831}, {852, 44715}, {1304, 35265}, {1494, 44555}, {2693, 15055}, {3448, 17986}, {5627, 14854}, {5663, 7480}, {11002, 35908}, {14118, 38933}, {14380, 33927}, {15072, 39174}, {17511, 34150}

X(46788) = isotomic conjugate of X(46789)
X(46788) = X(i)-isoconjugate of X(j) for these (i,j): {30, 36151}, {477, 2173}, {1495, 36102}, {1784, 32663}, {1990, 36062}, {3284, 36130}, {14401, 36117}
X(46788) = barycentric product X(i)*X(j) for these {i,j}: {74, 35520}, {1494, 5663}, {7480, 34767}, {14264, 39988}
X(46788) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 477}, {1553, 23097}, {2159, 36151}, {2349, 36102}, {2437, 41392}, {5627, 43707}, {5663, 30}, {7480, 4240}, {11251, 34334}, {14264, 39985}, {14380, 14220}, {14385, 34210}, {18877, 32663}, {34209, 14254}, {35200, 36062}, {35520, 3260}, {36063, 1784}, {36119, 36130}, {39986, 15454}, {42742, 3233}, {44769, 30528}
X(46788) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14919, 44769, 323}, {40384, 44769, 14919}


X(46789) = X(2)X(2411)∩X(23)X(477)

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

X(46789) lies on these lines: {2, 2411}, {23, 477}, {94, 14919}, {146, 39985}, {323, 648}, {1511, 4240}, {2407, 36789}, {5504, 34210}, {36102, 38340}

X(46789) = isotomic conjugate of X(46788)
X(46789) = X(32162)-cross conjugate of X(43752)
X(46789) = X(i)-isoconjugate of X(j) for these (i,j): {2159, 5663}, {18877, 36063}
X(46789) = barycentric product X(i)*X(j) for these {i,j}: {477, 3260}, {6148, 43707}, {14206, 36102}, {30528, 41079}, {36151, 46234}
X(46789) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 5663}, {477, 74}, {1784, 36063}, {3233, 42742}, {3260, 35520}, {4240, 7480}, {14220, 14380}, {14254, 34209}, {15454, 39986}, {23097, 1553}, {30528, 44769}, {32663, 18877}, {34210, 14385}, {34334, 11251}, {36062, 35200}, {36102, 2349}, {36130, 36119}, {36151, 2159}, {39985, 14264}, {41392, 2437}, {43707, 5627}


X(46790) = X(2)X(514)∩X(80)X(519)

Barycentrics    (a + b - 2*c)*(a - 2*b + c)*(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(46790) = 5 X[29590] - X[35596]

X(46790) lies on these lines: {2, 514}, {80, 519}, {88, 3008}, {239, 4080}, {527, 666}, {528, 14190}, {679, 17067}, {1121, 3912}, {3218, 21372}, {3911, 17078}, {4887, 9326}, {5723, 35113}, {6336, 26003}, {6633, 30566}, {17023, 27922}, {17310, 31051}, {17556, 36205}, {19636, 28534}, {26136, 39349}, {27739, 34362}, {29590, 35596}, {30575, 33129}, {30849, 30857}, {31222, 31226}, {35092, 37691}

X(46790) = midpoint of X(i) and X(j) for these {i,j}: {903, 3257}, {10707, 36236}
X(46790) = isotomic conjugate of X(46791)
X(46790) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14191}, {44, 840}, {902, 37131}, {2251, 18821}
X(46790) = barycentric product X(i)*X(j) for these {i,j}: {75, 14190}, {528, 903}, {1022, 42722}, {2246, 20568}, {4997, 5723}
X(46790) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14191}, {88, 37131}, {106, 840}, {528, 519}, {903, 18821}, {1642, 14439}, {1643, 1635}, {2246, 44}, {5723, 3911}, {14190, 1}, {42722, 24004}, {42763, 23757}
X(46790) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3008, 6549, 88}, {4555, 4997, 3912}


X(46791) = X(2)X(918)∩X(190)X(320)

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

X(46791) lies on these lines: {2, 918}, {190, 320}, {673, 1121}, {840, 9059}, {903, 36910}, {1227, 24004}, {3904, 36887}, {4152, 6174}, {4370, 41801}, {4437, 30731}

X(46791) = isotomic conjugate of X(46790)
X(46791) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14190}, {106, 2246}, {528, 9456}, {901, 1643}
X(46791) = trilinear pole of line {519, 4543}
X(46791) = barycentric product X(i)*X(j) for these {i,j}: {75, 14191}, {519, 18821}, {840, 3264}, {4358, 37131}
X(46791) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14190}, {44, 2246}, {519, 528}, {840, 106}, {1635, 1643}, {3911, 5723}, {14191, 1}, {14439, 1642}, {18821, 903}, {23757, 42763}, {24004, 42722}, {37131, 88}


X(46792) = X(2)X(650)∩X(518)X(30807)

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

X(46792) lies on these lines: {2, 650}, {518, 30807}, {527, 2481}, {666, 2323}, {673, 10030}, {1861, 33676}, {3912, 14943}, {3975, 36803}

X(46792) = isotomic conjugate of X(46793)
X(46792) = X(672)-isoconjugate of X(12032)
X(46792) = barycentric product X(i)*X(j) for these {i,j}: {75, 14197}, {2481, 28850}, {28143, 34085}
X(46792) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 12032}, {14197, 1}, {28850, 518}


X(46793) = X(100)X(2340)∩X(527)X(32041)

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

X(46793) lies on these lines: {100, 2340}, {527, 32041}, {673, 14943}, {1025, 6184}, {3738, 14947}, {3912, 4554}, {4876, 31637}

X(46793) = reflection of X(1025) in X(6184)
X(46793) = isotomic conjugate of X(46792)
X(46793) = antitomic image of X(1025)
X(46793) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14197}, {1438, 28850}, {28143, 32735}
X(46793) = barycentric product X(3263)*X(12032)
X(46793) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14197}, {518, 28850}, {12032, 105}


X(46794) = X(2)X(905)∩X(517)X(38955)

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

X(46794) lies on these lines: {2, 905}, {517, 38955}, {527, 18816}, {673, 1948}, {3912, 36795}, {6996, 34234}, {16082, 26001}

X(46794) = barycentric product X(75)*X(14198)
X(46794) = barycentric quotient X(14198)/X(1)


X(46795) = X(2)X(514)∩X(88)X(239)

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

X(46795) lies on these lines: {2, 514}, {88, 239}, {335, 536}, {519, 4674}, {3912, 4080}, {4358, 4945}, {4850, 35962}, {4997, 17266}, {9460, 16610}, {16826, 27922}, {23345, 36872}, {24183, 35092}, {29607, 31201}

X(46795) = isotomic conjugate of X(46797)
X(46795) = X(i)-isoconjugate of X(j) for these (i,j): {44, 2382}, {2251, 18822}
X(46795) = trilinear pole of line {537, 36848}
X(46795) = barycentric product X(i)*X(j) for these {i,j}: {537, 903}, {4555, 36848}, {20331, 20568}
X(46795) = barycentric quotient X(i)/X(j) for these {i,j}: {106, 2382}, {537, 519}, {903, 18822}, {20331, 44}, {36848, 900}, {42765, 23757}
X(46795) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {88, 4555, 239}, {3912, 6549, 4080}


X(46796) = X(2)X(513)∩X(44)X(4607)

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

X(46796) lies on these lines: {2, 513}, {44, 4607}, {239, 37129}, {536, 889}, {13466, 40552}, {31002, 41144}

X(46796) = midpoint of X(889) and X(3227)
X(46796) = reflection of X(13466) in X(40552)
X(46796) = isotomic conjugate of X(46801)
X(46796) = X(36847)-cross conjugate of X(33908)
X(46796) = cevapoint of X(33908) and X(36847)
X(46796) = trilinear pole of line {14474, 33908}
X(46796) = barycentric product X(i)*X(j) for these {i,j}: {889, 14474}, {3227, 33908}
X(46796) = barycentric quotient X(i)/X(j) for these {i,j}: {14474, 891}, {33908, 536}, {36847, 13466}


X(46797) = X(2)X(812)∩X(44)X(190)

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

X(46797) lies on these lines: {2, 812}, {44, 190}, {335, 2087}, {678, 4432}, {900, 36872}, {903, 24625}, {1023, 4366}, {2382, 9059}, {4370, 24004}, {6632, 6652}

X(46797) = reflection of X(24004) in X(4370)
X(46797) = isotomic conjugate of X(46795)
X(46797) = antitomic image of X(24004)
X(46797) = X(i)-isoconjugate of X(j) for these (i,j): {106, 20331}, {537, 9456}, {32665, 36848}
X(46797) = trilinear pole of line {519, 3251}
X(46797) = barycentric product X(i)*X(j) for these {i,j}: {519, 18822}, {2382, 3264}
X(46797) = barycentric quotient X(i)/X(j) for these {i,j}: {44, 20331}, {519, 537}, {900, 36848}, {2382, 106}, {18822, 903}, {23757, 42765}


X(46798) = X(2)X(650)∩X(44)X(666)

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

X(46798) lies on these lines: {2, 650}, {44, 666}, {105, 26247}, {239, 335}, {241, 34085}, {536, 2481}, {1921, 34852}, {4384, 35026}, {4702, 14942}, {5222, 36221}, {6185, 36802}, {10030, 39979}, {17023, 36219}

X(46798) = midpoint of X(33674) and X(33676)
X(46798) = isotomic conjugate of X(46802)
X(46798) = X(672)-isoconjugate of X(14665)
X(46798) = barycentric product X(i)*X(j) for these {i,j}: {2481, 14839}, {36796, 43063}
X(46798) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 14665}, {14839, 518}, {43063, 241}


X(46799) = X(2)X(523)∩X(239)X(897)

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

X(46799) lies on these lines: {2, 523}, {239, 897}, {524, 17497}, {536, 671}, {892, 3227}, {3263, 42008}

X(46799) = X(i)-isoconjugate of X(j) for these (i,j): {896, 35107}, {922, 35155}
X(46799) = barycentric product X(i)*X(j) for these {i,j}: {671, 35103}, {5163, 18023}
X(46799) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 35107}, {671, 35155}, {5163, 187}, {35103, 524}


X(46800) = X(2)X(1577)∩X(239)X(11611)

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

X(46800) lies on these lines: {2, 1577}, {239, 11611}, {335, 2161}, {536, 14616}, {758, 16704}, {30908, 34079}


X(46801) = X(2)X(891)∩X(239)X(37209)

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

X(46801) lies on these lines: {2, 891}, {239, 37209}, {536, 668}, {1646, 3227}, {13466, 41314}, {23891, 42083}

X(46801) = reflection of X(i) in X(j) for these {i,j}: {3227, 1646}, {41314, 13466}
X(46801) = isotomic conjugate of X(46796)
X(46801) = antitomic image of X(41314)
X(46801) = X(36847)-cross conjugate of X(536)
X(46801) = X(14474)-isoconjugate of X(34075)
X(46801) = cevapoint of X(536) and X(36847)
X(46801) = trilinear pole of line {536, 14434}
X(46801) = barycentric quotient X(i)/X(j) for these {i,j}: {536, 33908}, {891, 14474}, {13466, 36847}


X(46802) = X(2)X(665)∩X(100)X(239)

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

X(46802) lies on these lines: {2, 665}, {100, 239}, {241, 4554}, {292, 2481}, {335, 3675}, {536, 32041}, {900, 14947}, {1025, 39775}, {1026, 17755}, {4876, 39714}, {6184, 42720}

X(46802) = reflection of X(i) in X(j) for these {i,j}: {2481, 27918}, {42720, 6184}
X(46802) = isotomic conjugate of X(46798)
X(46802) = antitomic image of X(42720)
X(46802) = X(i)-isoconjugate of X(j) for these (i,j): {1438, 14839}, {2195, 43063}
X(46802) = barycentric product X(3263)*X(14665)
X(46802) = barycentric quotient X(i)/X(j) for these {i,j}: {241, 43063}, {518, 14839}, {14665, 105}


X(46803) = X(2)X(649)∩X(239)X(20332)

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

X(46803) lies on these lines: {2, 649}, {239, 20332}, {335, 20363}, {536, 3226}, {726, 23579}, {894, 3253}


X(46804) = X(2)X(905)∩X(104)X(517)

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

X(46804) lies on these lines: {2, 905}, {104, 517}, {239, 34234}, {335, 40862}, {536, 18816}, {3872, 35046}

X(46804) = isotomic conjugate of X(46805)
X(46804) = X(2183)-isoconjugate of X(2726)
X(46804) = barycentric product X(2810)*X(18816)
X(46804) = barycentric quotient X(i)/X(j) for these {i,j}: {104, 2726}, {2810, 517}, {45919, 42757}


X(46805) = X(2)X(3310)∩X(239)X(651)

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

X(46805) lies on these lines: {2, 3310}, {239, 651}, {2397, 23980}, {2726, 9058}, {6335, 14571}, {9456, 18816}

X(46805) = reflection of X(2397) in X(23980)
X(46805) = isotomic conjugate of X(46804)
X(46805) = antitomic image of X(2397)
X(46805) = X(909)-isoconjugate of X(2810)
X(46805) = barycentric product X(2726)*X(3262)
X(46805) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 2810}, {2726, 104}, {42757, 45919}


X(46806) = X(2)X(98)∩X(97)X(8024)

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

X(46806) lies on these lines: {2, 98}, {97, 8024}, {248, 290}, {251, 324}, {458, 9755}, {1297, 1972}, {1916, 2987}, {2395, 9979}, {3329, 30535}, {3407, 39685}, {3424, 37174}, {5304, 6531}, {5989, 36790}, {6394, 15589}, {7925, 40428}, {9769, 43113}, {11610, 44176}, {14601, 41231}, {16989, 31636}, {16990, 31635}, {22329, 34369}, {35909, 46245}, {36897, 39097}, {41194, 41201}, {41195, 41200}

X(46806) = isotomic conjugate of X(46807)
X(46806) = crosspoint of X(41074) and X(41174)
X(46806) = trilinear pole of line {182, 23878}
X(46806) = X(i)-isoconjugate of X(j) for these (i,j): {240, 43718}, {262, 1755}, {263, 1959}, {325, 3402}, {327, 9417}, {511, 2186}, {36132, 41167}, {46238, 46319}
X(46806) = barycentric product X(i)*X(j) for these {i,j}: {98, 183}, {182, 290}, {248, 44144}, {287, 458}, {1910, 3403}, {1976, 20023}, {2966, 23878}, {3288, 43187}, {6394, 33971}, {8842, 40820}, {18024, 34396}
X(46806) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 262}, {182, 511}, {183, 325}, {248, 43718}, {287, 42313}, {290, 327}, {458, 297}, {1910, 2186}, {1976, 263}, {2715, 26714}, {3288, 3569}, {3403, 46238}, {6784, 44114}, {9755, 1513}, {10311, 232}, {14601, 46319}, {23878, 2799}, {32545, 39682}, {33971, 6530}, {34396, 237}, {34761, 36885}, {39530, 39569}, {39683, 40804}, {41173, 6037}, {42711, 42703}, {44144, 44132}
X(46806) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5984, 40867}, {2, 40870, 110}, {98, 287, 2}, {98, 40820, 1976}, {1976, 17974, 5012}


X(46807) = X(2)X(51)∩X(97)X(251)

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

X(46807) lies on these lines: {2, 51}, {97, 251}, {147, 39682}, {237, 38383}, {297, 2967}, {323, 2857}, {324, 8024}, {325, 36790}, {327, 3314}, {385, 2987}, {401, 1297}, {850, 2525}, {1972, 30737}, {4108, 39469}, {5641, 7840}, {7774, 22240}, {7779, 9473}, {10352, 35296}, {18020, 26276}, {20022, 36212}, {37174, 37668}

X(46807) = isotomic conjugate of X(46806)
X(46807) = trilinear pole of line {2799, 41167}
X(46807) = X(i)-isoconjugate of X(j) for these (i,j): {182, 1910}, {293, 10311}, {1821, 34396}, {3288, 36084}, {3403, 14601}
X(46807) = crossdifference of every pair of points on line {3288, 34396}
X(46807) = barycentric product X(i)*X(j) for these {i,j}: {262, 325}, {297, 42313}, {327, 511}, {2186, 46238}, {34765, 36885}, {43718, 44132}
X(46807) = barycentric quotient X(i)/X(j) for these {i,j}: {232, 10311}, {237, 34396}, {262, 98}, {263, 1976}, {297, 458}, {325, 183}, {327, 290}, {511, 182}, {1513, 9755}, {2186, 1910}, {2799, 23878}, {3569, 3288}, {6037, 41173}, {6530, 33971}, {26714, 2715}, {36885, 34761}, {39569, 39530}, {39682, 32545}, {40804, 39683}, {42313, 287}, {42703, 42711}, {43718, 248}, {44114, 6784}, {44132, 44144}, {46238, 3403}, {46319, 14601}
X(46807) = {X(262),X(42313)}-harmonic conjugate of X(2)


X(46808) = X(2)X(648)∩X(30)X(74)

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

X(46808) lies on these lines: {2, 648}, {30, 74}, {297, 16076}, {1304, 37907}, {2394, 9979}, {2799, 34767}, {5055, 44715}, {7426, 17986}, {9410, 14918}, {10298, 22455}, {16077, 40885}, {31621, 44579}, {34288, 36889}, {35910, 36886}, {44555, 44769}

X(46808) = isotomic conjugate of X(46809)
X(46808) = X(40423)-Ceva conjugate of X(4550)
X(46808) = X(18487)-cross conjugate of X(381)
X(46808) = X(2173)-isoconjugate of X(3431)
X(46808) = cevapoint of X(i) and X(j) for these (i,j): {381, 18487}, {3581, 5158}
X(46808) = barycentric product X(i)*X(j) for these {i,j}: {74, 44135}, {381, 1494}, {16080, 37638}, {18487, 31621}
X(46808) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 3431}, {381, 30}, {1531, 16163}, {3581, 1511}, {4550, 10564}, {4993, 43768}, {5158, 3284}, {5627, 18316}, {16080, 43530}, {18486, 1099}, {18487, 3163}, {32225, 5642}, {34416, 9407}, {34417, 1495}, {36430, 18487}, {37638, 11064}, {44135, 3260}, {46090, 46091}
X(46808) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1494, 14919}, {2, 39358, 14920}, {1494, 16080, 2}, {11078, 11092, 10733}, {13212, 20126, 9140}, {36308, 36311, 74}


X(46809) = X(2)X(340)∩X(30)X(14920)

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

X(46809) lies on these lines: {2, 340}, {30, 14920}, {323, 1494}, {376, 3431}, {525, 1636}, {2071, 22455}, {2697, 10989}, {2986, 12028}, {3163, 46106}, {3543, 16263}, {6148, 11064}, {7552, 15786}, {10217, 11078}, {10218, 11092}, {11050, 13857}, {14919, 31621}, {15351, 44651}, {15683, 16251}, {23582, 40885}, {40506, 44576}, {40512, 44346}, {44216, 46115}

X(46809) = isotomic conjugate of X(46808)
X(46809) = X(46229)-cross conjugate of X(2407)
X(46809) = cevapoint of X(3284) and X(10564)
X(46809) = trilinear pole of line {5664, 9033}
X(46809) = X(i)-isoconjugate of X(j) for these (i,j): {381, 2159}, {2349, 34417}, {5158, 36119}, {8749, 18477}, {18486, 40353}, {33805,