Clark Kimberling's

Encyclopedia of Triangle Centers - ETC

Points II-Caph: X(32001)-X(32007)

X(32001) = POINT II-CAPH OF X(4)

X(32001) = isotomic conjugate of X(15077)
X(32001) = anticomplement of X(15905)
X(32001) = polar conjugate of isotomic conjugate of X(32831)
X(32001) = {X(4),X(69)}-harmonic conjugate of X(32000)
X(32001) = polar conjugate of isogonal conjugate of X(37672)

X(32002) = POINT II-CAPH OF X(5)

X(32002) lies on these lines: {2, 10985}, {4, 69}, {5, 95}, {53, 648}, {99, 2383}, {183, 5064}, {216, 17035}, {265, 6528}, {275, 467}, {290, 15321}, {297, 3589}, {302, 473}, {303, 472}, {325, 428}, {382, 20477}, {458, 3763}, {1007, 7714}, {1078, 15559}, {1273, 18354}, {1494, 15687}, {1907, 7750}, {1994, 14129}, {2052, 13579}, {3087, 17907}, {3518, 7769}, {3855, 8797}, {3964, 5198}, {5081, 5564}, {5976, 22480}, {6144, 9308}, {6390, 6756}, {6527, 17578}, {7282, 7321}, {7752, 9723}, {7806, 10311}, {14111, 20572}, {14516, 19169}

X(32002) = isotomic conjugate of X(3519)
X(32002) = anticomplement of X(22052)
X(32002) = polar conjugate of X(2963)

X(32003) = POINT II-CAPH OF X(7)

X(32003) lies on these lines: {2, 5543}, {7, 8}, {57, 29616}, {145, 3160}, {150, 962}, {279, 519}, {347, 4460}, {348, 3241}, {392, 28644}, {527, 30695}, {664, 20050}, {728, 1445}, {1323, 3633}, {1434, 4720}, {2481, 7319}, {3187, 18624}, {3188, 12536}, {3598, 4848}, {3621, 9312}, {3623, 31721}, {3632, 10481}, {3672, 6738}, {3875, 20008}, {3912, 5435}, {4323, 7179}, {4328, 5232}, {4350, 6765}, {4384, 5226}, {5175, 20244}, {5228, 29611}, {5273, 25935}, {5704, 24203}, {5734, 17181}, {6049, 17081}, {7264, 18391}, {10405, 20059}, {10914, 23839}, {12630, 14189}, {17077, 27253}, {20111, 26531}, {25719, 31145}

X(32003) = {X(7),X(8)}-harmonic conjugate of X(31994)

X(32004) = POINT II-CAPH OF X(86)

X(32004) lies on these lines: {1,6626}, {10,86}, {65,664}, {81,2295}, {99,3244}, {145,17103}, {274,4714}, {333,16826}, {519,1509}, {524,23905}, {648,1855}, {757,5255}, {1931,29588}, {2106,3780}, {2329,5325}, {3635,6629}, {3874,4360}, {5711,17377}, {5937,23361}, {6625,20090}, {8033,17144}, {16834,24378}, {17378,17528}, {17778,20337}

X(32005) = POINT II-CAPH OF X(192)

X(32005) lies on these lines: {1,87}, {2,20943}, {239,3928}, {333,16722}, {350,20105}, {385,5204}, {499,19570}, {1107,4699}, {1278,17448}, {1478,13571}, {1575,21219}, {1655,5550}, {2275,20081}, {3240,21223}, {3360,21762}, {3614,7777}, {3617,21226}, {3621,17759}, {3634,27318}, {4352,17383}, {5217,7783}, {5229,7774}, {7354,7837}, {7779,9597}, {7905,9651}, {9263,20050}, {16815,24621}, {16969,25269}, {17232,24215}, {19701,29595}, {19862,27269}, {20036,20072}, {27268,31997}

X(32005) = anticomplement of X(20943)

X(32006) = POINT II-CAPH OF X(69)

Let A'B'C' be the anticevian triangle of X(69). Let A" be the orthogonal projection of A' on the line through X(69) parallel to line BC, and define B" and C" cyclically. The lines AA", BB", CC" concur in X(32006) = Point II-Caph of X(69). See X(33006).png (Angel Montesdeoca, December 6, 2022)

X(32006) lies on these lines: {2, 3053}, {3, 1007}, {4, 69}, {5, 3785}, {20, 325}, {30, 3926}, {32, 14064}, {83, 18841}, {99, 3529}, {115, 14023}, {127, 28696}, {148, 7946}, {183, 3091}, {193, 5254}, {290, 15077}, {350, 5225}, {376, 7763}, {381, 7767}, {382, 3933}, {385, 14063}, {388, 25303}, {491, 6459}, {492, 6460}, {524, 6392}, {543, 7916}, {546, 14929}, {626, 7737}, {631, 7752}, {754, 3767}, {1078, 3090}, {1285, 7934}, {1369, 7394}, {1370, 3266}, {1384, 8361}, {1657, 6390}, {1909, 5229}, {1975, 3146}, {1992, 5286}, {2207, 20806}, {2548, 6683}, {2549, 7759}, {2896, 16924}, {2996, 20080}, {3096, 16045}, {3314, 14035}, {3436, 20553}, {3524, 7769}, {3525, 7771}, {3528, 7814}, {3543, 7788}, {3545, 7811}, {3618, 6656}, {3619, 7770}, {3788, 3849}, {3832, 15589}, {3855, 6249}, {3972, 14069}, {4417, 7406}, {4872, 21605}, {5025, 7735}, {5177, 16992}, {5188, 7694}, {5304, 7851}, {5319, 7861}, {5475, 7800}, {5866, 11413}, {6340, 7396}, {6655, 7738}, {6658, 7897}, {6781, 7888}, {6997, 26235}, {7386, 11059}, {7388, 9540}, {7389, 13935}, {7391, 9464}, {7503, 15574}, {7736, 7785}, {7739, 7838}, {7746, 23055}, {7747, 7795}, {7748, 7758}, {7753, 7935}, {7754, 11008}, {7756, 7903}, {7775, 7830}, {7779, 20105}, {7782, 17538}, {7799, 11001}, {7803, 7812}, {7815, 31415}, {7822, 14537}, {7832, 14039}, {7833, 7941}, {7847, 7926}, {7858, 7910}, {7862, 21843}, {7866, 18907}, {7879, 8370}, {7881, 19687}, {7890, 11648}, {7893, 14041}, {7912, 14712}, {7917, 15682}, {7921, 7924}, {7929, 16044}, {7931, 14037}, {7933, 16989}, {7938, 16898}, {7939, 11361}, {7945, 19569}, {8356, 31400}, {8357, 9605}, {8362, 15484}, {8743, 22151}, {9292, 20022}, {9723, 11414}, {10159, 18844}, {10513, 17578}, {11285, 31404}, {12215, 14927}, {14062, 17129}, {14068, 17128}, {14570, 28728}, {19695, 31859}, {20556, 21281}

X(32007) = POINT II-CAPH OF X(142)

X(32007) lies on these lines: {1, 17078}, {7, 8}, {57, 32019}, {79, 2481}, {99, 1434}, {142, 32008}, {145, 17079}, {150, 18480}, {241, 29569}, {279, 3623}, {348, 3622}, {527, 32024}, {553, 3912}, {664, 3244}, {728, 17298}, {1125, 9436}, {2099, 7185}, {3254, 4569}, {3633, 9312}, {3649, 16823}, {4089, 11009}, {4346, 15956}, {4384, 4654}, {4675, 27253}, {4872, 12699}, {4887, 6738}, {5228, 17367}, {5845, 27000}, {5905, 30854}, {7146, 24803}, {7196, 29824}, {10025, 21258}, {11553, 17320}, {17084, 24798}, {17092, 17317}, {17181, 18493}, {17776, 21454}, {21314, 25716}

Points III-Caph: X(32008)-X(32023)

X(32008) = POINT III-CAPH OF X(9)

X(32008) lies on these lines: {1, 31269}, {2, 220}, {6, 27253}, {8, 344}, {9, 85}, {10, 10482}, {29, 1861}, {92, 3305}, {189, 7367}, {190, 20880}, {218, 14828}, {257, 17260}, {312, 728}, {333, 1174}, {349, 6559}, {664, 1212}, {672, 1434}, {673, 1334}, {1121, 6606}, {1213, 27023}, {1220, 17353}, {1698, 28874}, {2338, 17095}, {2481, 3294}, {3730, 14377}, {3740, 28058}, {4422, 17947}, {4473, 17128}, {4513, 27304}, {4518, 16823}, {4997, 5316}, {5278, 29616}, {6706, 10025}, {6738, 25072}, {9312, 31169}, {14829, 29627}, {16284, 17335}, {16788, 17687}, {17338, 17743}, {18359, 26591}, {21872, 27000}, {25500, 30608}, {25878, 26059}, {27065, 30690}, {28980, 30806}

X(32008) = isogonal conjugate X(1475)
X(32008) = isotomic conjugate of X(142)
X(32008) = cevapoint of X(2) and X(9)
X(32008) = X(19)-isoconjugate of X(22053)
X(32008) = trilinear pole of line X(522)X(3935) (the isotomic conjugate of the circumconic centered at X(1212))

X(32009) = POINT III-CAPH OF X(37)

X(32009) lies on these lines: {1, 872}, {2, 1500}, {10, 30571}, {37, 274}, {57, 16831}, {75, 4099}, {81, 213}, {83, 5284}, {86, 3294}, {88, 29578}, {89, 29595}, {105, 8708}, {190, 17175}, {239, 1255}, {277, 17321}, {279, 26125}, {291, 1125}, {330, 5283}, {335, 21816}, {595, 985}, {668, 16589}, {959, 4323}, {961, 7677}, {1002, 3616}, {1107, 3227}, {1224, 17289}, {1258, 3230}, {1390, 16823}, {2664, 9401}, {3963, 25661}, {4384, 25430}, {4393, 27789}, {4698, 16819}, {5291, 16912}, {5550, 7786}, {16369, 28615}, {16818, 17263}, {17260, 20963}, {17320, 24790}, {18140, 27255}, {19742, 25417}

X(32009) = isogonal conjugate X(20963)
X(32009) = isotomic conjugate of X(3739)
X(32009) = cevapoint of X(2) and X(37)
X(32009) = X(19)-isoconjugate of X(22060)

X(32010) = POINT III-CAPH OF X(38)

X(32010)lies on these lines: {2, 694}, {38, 799}, {57, 14534}, {86, 1431}, {99, 17596}, {239, 257}, {244, 873}, {256, 314}, {261, 1178}, {354, 2668}, {756, 7035}, {805, 9073}, {846, 4154}, {870, 982}, {984, 7033}, {2669, 3752}, {3027, 9791}, {3863, 27164}, {4389, 14616}, {4562, 16587}, {4594, 27922}, {4603, 6654}, {5009, 7305}, {7192, 8034}, {16739, 18021}, {16975, 18826}, {18822, 18829}

X(32010) = isogonal conjugate X(20964)
X(32010) = isotomic conjugate of X(1215)
X(32010) = polar conjugate of X(1840)
X(32010) = cevapoint of X(2) and X(38)
X(32010) = trilinear pole of line X(812)X(4560)
X(32010) = X(19)-isoconjugate of X(22061)

X(32011) = POINT III-CAPH OF X(43)

X(32011) lies on these lines: {2, 16969}, {42, 31002}, {43, 6384}, {75, 16569}, {86, 6685}, {310, 899}, {335, 3752}, {1575, 27447}, {17490, 27494}, {17754, 27498}

X(32011) = isogonal conjugate X(22343)
X(32011) = isotomic conjugate of X(3840)
X(32011) = cevapoint of X(2) and X(43)
X(32011) = X(19)-isoconjugate of X(22066)

X(32012) = POINT III-CAPH OF X(44)

X(32012) lies on these lines: {2, 1017}, {44, 20568}, {668, 17349}, {3679, 4595}, {4671, 16816}, {5219, 25529}, {5235, 17292}, {16704, 30866}, {21385, 23598}

X(32012) = isotomic conjugate of X(3834)
X(32012) = cevapoint of X(2) and X(44)
X(32012) = X(19)-isoconjugate of X(22067)

X(32013) = POINT III-CAPH OF X(45)

X(32013) lies on these lines: {45, 20569}, {519, 16484}, {4358, 16815}, {16704, 29569}

X(32013) = isotomic conjugate of X(34824)
X(32013) = isotomic conjugate of complement of X(45)
X(32013) = cevapoint of X(2) and X(45)
X(32013) = X(19)-isoconjugate of X(22068)

X(32014) = POINT III-CAPH OF X(86)

X(31014) lies on these lines: {2, 1171}, {10, 86}, {76, 15668}, {83, 17398}, {98, 6578}, {99, 1125}, {226, 1434}, {274, 321}, {671, 23905}, {873, 18140}, {2368, 8701}, {3624, 17103}, {3634, 17731}, {4052, 16712}, {4080, 4632}, {4102, 29574}, {4596, 13576}, {4608, 5466}, {6539, 6542}, {6540, 17175}, {6626, 19862}, {6629, 19878}, {10159, 17245}, {11140, 26541}, {14534, 20337}, {18157, 30126}, {24051, 24058}, {25508, 28615}, {27797, 31011}

X(31014) = isogonal conjugate X(20970)
X(32014) = isotomic conjugate of X(1213)
X(32014) = polar conjugate of X(430)
X(32014) = cevapoint of X(2) and X(86)
X(32014) = barycentric product X(30593)*X(30594)
X(32014) = X(19)-isoconjugate of X(22080)

X(32015) = POINT III-CAPH OF X(142)

X(32015) lies on these lines: {8, 3826}, {85, 10012}, {1125, 14942}, {3912, 4102}, {6706, 31640}, {17282, 31359}, {17743, 27147}

X(32015) = isotomic conjugate of X(6666)
X(32015) = cevapoint of X(2) and X(142)

X(32016) = POINT III-CAPH OF X(244)

X(32016) lies on these lines: {239, 6631}, {244, 7035}, {350, 1266}, {4885, 27191}, {5437, 6654}, {7033, 17063}, {10436, 27922}, {27195, 31286}

X(32016) = isotomic conjugate of X(24003)
X(32016) = cevapoint of X(2) and X(244)

X(32017) = POINT III-CAPH OF X(312)

X(32017) lies on these lines: {1, 341}, {57, 312}, {75, 8056}, {76, 279}, {81, 4358}, {88, 321}, {105, 1261}, {274, 16736}, {278, 7017}, {291, 3840}, {668, 3452}, {961, 1476}, {985, 29649}, {1022, 1577}, {1224, 19864}, {1432, 3912}, {1997, 3596}, {4671, 26745}, {6685, 30571}, {14829, 29529}, {17786, 30827}, {25430, 30829}, {30710, 30818}

X(32017) = isogonal conjugate X(20228)
X(32017) = isotomic conjugate of X(3752)
X(32017) = polar conjugate of X(1828)
X(32017) = cevapoint of X(2) and X(312)
X(32017) = trilinear pole of line X(513)X(4397)
X(32017) = X(19)-isoconjugate of X(22344)

X(32018) = POINT III-CAPH OF X(319)

X(32018) lies on these lines: {2, 7230}, {75, 1089}, {76, 6539}, {79, 319}, {85, 4102}, {274, 321}, {286, 31902}, {304, 29602}, {334, 6538}, {668, 4647}, {767, 8701}, {870, 1126}, {1909, 31013}, {2481, 6540}, {4632, 18359}, {4717, 25303}, {4980, 18145}, {6385, 27801}, {7278, 17762}, {20568, 20911}, {20569, 30589}

X(32018) = isotomic conjugate of X(1100)
X(32018) = polar conjugate of X(2355)
X(32018) = cevapoint of X(2) and X(319)
X(32018) = trilinear pole of line X(693)X(4036)

X(32019) = POINT III-CAPH OF X(344)

X(32019) lies on these lines: {1, 17263}, {81, 17244}, {105, 3871}, {274, 17279}, {277, 344}, {1224, 17371}, {1255, 17367}, {2006, 30829}, {25417, 29569}

X(32019) = isotomic conjugate of X(17278)
X(32019) = cevapoint of X(2) and X(344)

X(32020) = POINT III-CAPH OF X(350)

X(32020) lies on these lines: {1, 668}, {2, 1978}, {28, 811}, {57, 4554}, {76, 330}, {81, 799}, {89, 30964}, {105, 8709}, {192, 20671}, {274, 4602}, {291, 350}, {670, 25534}, {727, 789}, {1002, 17794}, {1022, 20568}, {1221, 26971}, {1921, 20363}, {1929, 1966}, {3123, 18830}, {3227, 18145}, {3403, 8056}, {3840, 7018}, {9263, 18135}, {17027, 20457}, {18895, 27918}, {20372, 20610}, {21297, 31002}, {24625, 27853}, {29438, 29454}, {29750, 29811}

X(32020) = isogonal conjugate X(21760)
X(32020) = isotomic conjugate of X(1575)
X(32020) = cevapoint of X(2) and X(350)
X(32020) = X(19)-isoconjugate of X(20777)

X(32021) = POINT III-CAPH OF X(354)

X(32021) lies on these lines: {2481, 3742}, {4384, 5437}, {7271, 25496}

X(32021) = isotomic conjugate of X(3740)
X(32021) = cevapoint of X(2) and X(354)

X(32022) = POINT III-CAPH OF X(391)

X(32022) lies on these lines: {2, 2271}, {4, 17277}, {10, 344}, {69, 17758}, {76, 966}, {98, 25446}, {226, 4384}, {321, 28809}, {2478, 13576}, {3424, 7385}, {5224, 18840}, {5392, 26592}, {6625, 17349}, {7379, 14484}, {16827, 31405}, {17352, 18841}, {25006, 30701}

X(32022) = isogonal conjugate X(5021)
X(32022) = isotomic conjugate of X(4648)
X(32022) = polar conjugate of X(4196)
X(32022) = cevapoint of X(2) and X(391)

X(32023) = POINT III-CAPH OF X(497)

X(32023) lies on these lines: {2, 14936}, {11, 6063}, {55, 4998}, {75, 24386}, {85, 3817}, {497, 4554}, {693, 15283}, {982, 3663}, {1699, 7196}, {2481, 5274}, {3061, 3452}, {3263, 3705}, {3675, 7185}, {3794, 9309}, {6384, 27498}, {13577, 15284}, {14727, 18821}, {15149, 17917}, {20295, 26910}

X(32023) = isotomic conjugate of X(1376)
X(32023) = cevapoint of X(2) and X(497)

Points IV-Caph: X(32024)-X(32035)

X(32024) = POINT IV-CAPH OF X(9)

X(32024) lies on these lines: {1, 31169}, {8, 190}, {9, 85}, {45, 27253}, {63, 30854}, {144, 6604}, {220, 664}, {728, 25728}, {1212, 10025}, {2481, 16552}, {3730, 3732}, {3929, 4384}, {4640, 28058}, {5282, 6559}, {6554, 31640}, {6558, 25278}, {14512, 31852}, {14828, 16601}, {16284, 17336}, {17257, 26561}, {17277, 20880}, {17350, 27288}, {17781, 25935}

X(32025) = POINT IV-CAPH OF X(10)

X(32025) lies on these lines: {2, 4445}, {6, 29593}, {8, 4026}, {10, 86}, {37, 29615}, {69, 3617}, {75, 537}, {141, 27191}, {190, 594}, {192, 17251}, {239, 17239}, {313, 25280}, {320, 4691}, {391, 17354}, {519, 17322}, {524, 28604}, {536, 17252}, {599, 4699}, {894, 4690}, {966, 17233}, {1100, 29610}, {1213, 4478}, {1278, 17253}, {1698, 17394}, {2321, 17256}, {2345, 17346}, {3589, 29591}, {3626, 4357}, {3631, 26806}, {3632, 17393}, {3661, 17275}, {3662, 28634}, {3664, 4745}, {3686, 17289}, {3729, 17328}, {3739, 17287}, {3759, 4034}, {3763, 16816}, {3875, 4668}, {3949, 18714}, {3995, 4102}, {4001, 19797}, {4007, 4664}, {4021, 4746}, {4361, 17238}, {4363, 17343}, {4384, 17228}, {4389, 4452}, {4393, 17327}, {4399, 17302}, {4431, 17258}, {4464, 4701}, {4470, 20080}, {4472, 20090}, {4645, 4733}, {4651, 30966}, {4657, 29617}, {4659, 17329}, {4665, 6646}, {4669, 17320}, {4686, 17254}, {4687, 17294}, {4688, 17288}, {4698, 17310}, {4708, 17319}, {4740, 17255}, {4741, 17118}, {4751, 17296}, {4772, 7232}, {4788, 24441}, {4851, 29576}, {4852, 17326}, {4889, 29580}, {5257, 17315}, {5790, 10446}, {5839, 17381}, {6540, 30594}, {7081, 30761}, {7227, 20072}, {8013, 17731}, {10436, 17360}, {10453, 31341}, {12531, 18654}, {15668, 17373}, {16777, 20055}, {16815, 17231}, {16826, 17372}, {16831, 17386}, {16832, 17241}, {16833, 17370}, {16834, 17400}, {17045, 20016}, {17116, 17344}, {17117, 17237}, {17119, 17236}, {17121, 17385}, {17143, 18133}, {17151, 17249}, {17229, 17260}, {17230, 17259}, {17248, 17299}, {17263, 29594}, {17268, 31333}, {17280, 17330}, {17281, 17331}, {17286, 17335}, {17292, 17348}, {17293, 17349}, {17303, 17363}, {17309, 27268}, {17312, 31238}, {17317, 24603}, {17337, 29587}, {17352, 29611}, {17361, 25590}, {17374, 28633}, {17772, 19856}, {17791, 18698}, {20653, 31620}, {21277, 21677}, {25498, 29584}, {26048, 26979}, {26244, 30179}, {29446, 30866}, {31025, 31143}

X(32025) = isotomic conjugate of isogonal conjugate of X(33771)

X(32026) = POINT IV-CAPH OF X(37)

X(32026) lies on these lines: {1, 190}, {37, 274}, {39, 27195}, {192, 5283}, {194, 4704}, {213, 17261}, {350, 25092}, {536, 16819}, {668, 1500}, {1107, 4681}, {1621, 7760}, {2276, 18140}, {3616, 7757}, {3807, 4075}, {3995, 27163}, {4043, 10471}, {4098, 24215}, {4099, 17762}, {4360, 16552}, {9331, 24524}, {16589, 17759}, {16712, 27097}, {16818, 17320}, {16997, 31451}, {17160, 29773}, {17263, 24790}, {17280, 25499}, {17319, 20963}, {18145, 27020}, {18827, 24051}, {21070, 30966}

X(32027) = POINT IV-CAPH OF X(141)

X(32027) lies on these lines: {2, 7826}, {39, 31168}, {69, 3096}, {76, 338}, {83, 141}, {99, 2896}, {110, 14247}, {183, 7899}, {194, 7865}, {315, 3620}, {384, 7848}, {385, 7849}, {524, 7859}, {538, 7928}, {542, 10357}, {626, 14061}, {1078, 3314}, {1975, 7936}, {3329, 7882}, {3631, 6656}, {3734, 7929}, {3763, 7878}, {3785, 7835}, {3933, 7831}, {3934, 7809}, {5008, 19694}, {5041, 16897}, {6179, 7868}, {6292, 7779}, {6392, 7790}, {6683, 7840}, {7751, 7919}, {7752, 16990}, {7754, 7937}, {7759, 16986}, {7766, 7914}, {7767, 7832}, {7770, 7850}, {7771, 7881}, {7780, 7931}, {7786, 7788}, {7793, 7869}, {7795, 7811}, {7796, 7800}, {7801, 7904}, {7805, 7948}, {7808, 7946}, {7810, 7836}, {7812, 21356}, {7814, 15271}, {7815, 7897}, {7818, 31276}, {7822, 7893}, {7824, 7895}, {7827, 22165}, {7846, 14023}, {7853, 17129}, {7855, 7876}, {7871, 11285}, {7873, 17128}, {7885, 9466}, {7898, 17130}, {7905, 8362}, {7933, 17131}, {7935, 20081}, {7941, 31239}, {7942, 8667}, {7943, 14614}, {7949, 11174}, {8370, 10302}, {19577, 21248}

X(32028) = POINT IV-CAPH OF X(190)

X(32028) lies on these lines: {99, 666}, {144, 30225}, {190, 514}, {660, 6372}, {668, 4462}, {898, 4367}, {4378, 9266}, {4440, 6547}, {4499, 6004}, {4562, 6540}, {6546, 6634}, {6630, 17487}, {17350, 24281}, {27191, 31647}

X(32029) = POINT IV-CAPH OF X(239)

X(32029) lies on these lines: {1, 17755}, {2, 1280}, {6, 190}, {8, 26561}, {69, 1086}, {75, 16973}, {81, 4576}, {141, 27191}, {145, 20533}, {193, 4440}, {239, 335}, {291, 27919}, {511, 24813}, {524, 903}, {537, 3751}, {545, 1992}, {664, 9263}, {742, 17160}, {883, 1462}, {900, 10755}, {918, 1814}, {1015, 4561}, {1100, 24358}, {1386, 6651}, {2786, 10754}, {2796, 8593}, {2876, 25048}, {3416, 29617}, {3564, 24833}, {3570, 26273}, {3589, 29586}, {3618, 4422}, {3874, 30133}, {3881, 30130}, {3961, 24631}, {4384, 16496}, {4432, 16475}, {4716, 5847}, {5032, 17487}, {5039, 24815}, {5093, 24844}, {5263, 31317}, {5846, 6653}, {6542, 9053}, {6776, 29243}, {12167, 24814}, {14839, 20455}, {14853, 24828}, {14912, 24817}, {16593, 17316}, {16830, 31306}, {16972, 17393}, {17275, 25357}, {17449, 24602}, {18440, 24827}, {19459, 24822}, {20042, 31058}, {20132, 31314}, {20154, 27484}, {20172, 24349}, {24547, 25898}

X(32030) = POINT IV-CAPH OF X(244)

X(32030) lies on these lines: {244, 7035}, {668, 24191}, {903, 4106}, {3999, 17160}, {7192, 18822}

X(32031) = POINT IV-CAPH OF X(319)

X(32031) lies on these lines: {79, 319}, {668, 1330}, {2481, 7768}, {6327, 17143}, {7264, 17361}

X(32032) = POINT IV-CAPH OF X(320)

X(32032) lies on these lines: {2, 1017}, {69, 150}, {80, 320}, {316, 2481}, {3570, 10708}, {4555, 12531}, {4597, 6224}, {4738, 17360}, {17143, 21283}, {17378, 24222}

X(32033) = POINT IV-CAPH OF X(330)

X(32033) lies on these lines: {1, 87}, {1278, 18830}, {1575, 6384}, {2162, 4360}, {2998, 3226}, {3963, 26077}, {4361, 4598}, {4393, 21759}, {6383, 24621}, {16606, 30963}, {17302, 27341}, {21226, 26069}, {27424, 28366}

X(32034) = POINT IV-CAPH OF X(346)

X(32034) lies on these lines: {2, 20432}, {20, 190}, {279, 304}, {668, 30695}, {3227, 6553}, {3621, 30225}, {4461, 17143}, {7738, 17262}, {7791, 20073}

X(32035) = POINT IV-CAPH OF X(350)

X(32035) lies on these lines: {2, 20671}, {8, 76}, {39, 27195}, {75, 17793}, {194, 1015}, {274, 12263}, {291, 350}, {310, 4576}, {537, 4479}, {538, 3227}, {1078, 8671}, {2810, 18906}, {3097, 30963}, {4440, 18830}, {7033, 24260}, {9263, 20081}, {9902, 17144}, {12782, 18140}, {20457, 24514}, {27076, 31276}

Points Chara: X(32036)-X(32042)

X(32036) = POINT CHARA OF X(17)

X(32036) lies on the Steiner circumellipse and these lines: {2, 11087}, {17, 671}, {99, 16806}, {110, 930}, {338, 11130}, {530, 8172}, {531, 11600}, {648, 17402}, {1576, 14185}, {3228, 21461}, {4558, 23895}, {10409, 23872}, {11118, 11139}, {14570, 23896}

X(32036) = reflection of X(11117) in X(2)
X(32036) = Steiner circumellipse antipode of X(11117)
X(32036) = trilinear pole of line X(2)X(17)

X(32037) = POINT CHARA OF X(18)

X(32037) lies on the Steiner circumellipse and these lines: {2, 11082}, {18, 671}, {99, 16807}, {110, 930}, {338, 11131}, {530, 11601}, {531, 8173}, {648, 17403}, {1576, 14187}, {3228, 21462}, {4558, 23896}, {10410, 23873}, {11117, 11138}, {14570, 23895}

X(32037) = reflection of X(11118) in X(2)
X(32037) = Steiner circumellipse antipode of X(11118)
X(32037) = trilinear pole of line X(2)X(18)

X(32038) = POINT CHARA OF X(65)

X(32038) lies on the Steiner circumellipse and these lines: {99, 651}, {100, 6648}, {108, 648}, {190, 4551}, {646, 21859}, {664, 1020}, {668, 4552}, {670, 4554}, {903, 4654}, {941, 2481}, {959, 3227}, {1121, 31359}, {1415, 4612}, {2006, 14616}, {2092, 31643}, {4664, 9578}, {18816, 27339}

X(32038) = trilinear pole of line X(2)X(65)

X(32039) = POINT CHARA OF X(87)

X(32039) lies on the Steiner circumellipse and these lines: {190, 932}, {330, 3226}, {668, 4598}

X(32039) = trilinear pole of line X(2)X(87)

X(32040) = POINT CHARA OF X(165)

X(32040) lies on the Steiner circumellipse and these lines: {2, 18025}, {99, 26716}, {190, 2398}, {648, 4241}, {668, 30728}, {671, 2784}, {903, 1992}, {1121, 3241}, {1494, 31144}, {2481, 16834}, {3226, 14614}, {4569, 24015}

X(32040) = reflection of X(2) in X(23972)
X(32040) = reflection of X(18025) in X(2)
X(32040) = Steiner circumellipse antipode of X(18025)
X(32040) = antipode of X(2) in hyperbola {{A,B,C,X(2),X(658)}}
X(32040) = trilinear pole of line X(2)X(165)
X(32040) = isotomic conjugate of isogonal conjugate of X(26716)

X(32041) = POINT CHARA OF X(210)

X(32041) lies on the Steiner circumellipse and these lines: {2, 2481}, {99, 644}, {100, 666}, {190, 1026}, {376, 2808}, {528, 14947}, {646, 670}, {648, 4238}, {651, 6606}, {664, 1018}, {668, 30730}, {671, 2795}, {903, 4664}, {1002, 3227}, {1121, 3679}, {2279, 3226}, {4552, 4569}, {4876, 18827}, {7208, 9331}, {7233, 20680}, {14727, 30610}, {17294, 18025}, {17310, 18821}

X(32041) = reflection of X(2) in X(6184)
X(32041) = reflection of X(2481) in X(2)
X(32041) = isotomic conjugate of X(4762)
X(32041) = Steiner circumellipse antipode of X(2481)
X(32041) = trilinear pole of line X(2)X(210) (the line through the centroids of ABC, the intouch and extouch triangles)

X(32042) = POINT CHARA OF X(319)

X(32042) lies on the Steiner circumellipse and these lines: {99, 8652}, {100, 6540}, {668, 4427}, {903, 10436}, {1121, 3929}, {3227, 25417}, {3228, 28625}, {4632, 13486}, {17393, 30597}

X(32042) = isotomic conjugate of X(4802)
X(32042) = trilinear pole of line X(2)X(319)

X(32043) = X(2)X(4432)∩X(320)X(24628)

X(32043) lies on these lines: {2,4432}, {320,24628}, {1121,4384}, {1125,17694}, {1698,16060}, {2482,24603}, {3912,6174}, {4369,24636}, {4750,4763}, {4997,17738}, {24602,27757}

X(32044) = X(899)X(13466)∩X(1086)X(30970)

X(32044) lies on these lines: {899,13466}, {1086,30970}, {3248,30950}, {3768,4465}, {4033,30964}, {4379,17793}

X(32045) = X(2)X(24821)∩X(3227)X(16826)

X(32045) lies on these lines: {2,24821}, {3227,16826}, {4375,6544}, {4767,29584}, {5461,29610}, {24709,29615}

Circumcenters and centroids of not-equilateral central triangles: X(32046)-X(32084)

X(32046) = CIRCUMCENTER OF THE ANTI-CONWAY TRIANGLE

X(32046) is the center of the circle that is the locus of the crosssum of nine-point circle antipodes. (Randy Hutson, June 7, 2019)

Let A'B'C' be the antipedal triangle of X(3) (the tangential triangle). X(32046) is the radical center of the nine-point circles of triangles AA'X(3), BB'X(3), CC'X(3). (cf. Anopolis #2105, Antreas Hatzipolakis, December 1, 2014) (Randy Hutson, June 7, 2019)

Let AeBeCe and AiBiCi be the Ae and Ai triangles (aka K798e and K798i triangles). Let A'B'C' be the orthic triangle. X(32046) is the radical center of the circumcircles of triangles A'AeAi, B'BeBi, C'CeCi. (Randy Hutson, June 7, 2019)

X(32046) lies on these lines: {2,49}, {3,54}, {4,567}, {5,156}, {6,26}, {17,3206}, {18,3205}, {20,31815}, {22,10263}, {24,5944}, {25,10095}, {30,578}, {35,9666}, {36,9653}, {52,7502}, {68,11264}, {110,1656}, {140,141}, {154,13364}, {155,7514}, {185,18570}, {206,18583}, {215,498}, {343,7568}, {378,13491}, {381,1614}, {382,15033}, {389,1658}, {394,7516}, {399,15058}, {499,2477}, {511,7525}, {546,6759}, {548,13346}, {549,1092}, {550,10984}, {568,1199}, {575,2393}, {576,7555}, {597,23410}, {631,9545}, {1176,1351}, {1181,5663}, {1353,19131}, {1385,31811}, {1437,6924}, {1498,31861}, {1511,17928}, {1698,9622}, {1899,13561}, {1974,7715}, {1994,6243}, {2070,3567}, {2930,15462}, {2931,13358}, {2937,3060}, {3043,15061}, {3044,15561}, {3047,14643}, {3071,9677}, {3090,9544}, {3091,10540}, {3133,20775}, {3167,7393}, {3202,11272}, {3431,16867}, {3448,11597}, {3517,12167}, {3523,13339}, {3526,9703}, {3574,11750}, {3579,31812}, {3624,9621}, {3627,11424}, {3628,9306}, {3767,9604}, {3796,13391}, {3843,14157}, {3845,26883}, {5050,6642}, {5070,9705}, {5073,8718}, {5092,5447}, {5093,19121}, {5392,25043}, {5422,7506}, {5446,17714}, {5504,14528}, {5576,14389}, {5622,15132}, {5640,26882}, {5876,7503}, {6241,14130}, {6639,18912}, {6640,18911}, {6644,12006}, {6676,13292}, {6689,10116}, {6800,7517}, {7387,11426}, {7395,14128}, {7507,11565}, {7508,13323}, {7509,15067}, {7527,18439}, {7529,18874}, {7530,10982}, {7542,11245}, {7575,16227}, {7741,9667}, {7746,9697}, {7951,9652}, {8141,11428}, {8144,11429}, {8227,9587}, {8254,10274}, {8548,9937}, {9586,31423}, {9603,31401}, {9696,31455}, {9701,26363}, {9702,26364}, {9714,9777}, {9729,12038}, {9730,13367}, {9781,18378}, {9786,18324}, {9818,19347}, {9833,11818}, {9908,19139}, {10020,13567}, {10024,12022}, {10625,22352}, {11179,18281}, {11250,11430}, {11425,12084}, {11427,14790}, {11432,14070}, {11438,15331}, {11441,15060}, {11449,15045}, {11454,18364}, {11464,15037}, {11702,15101}, {11746,20773}, {11935,15720}, {12041,13148}, {12100,13347}, {12105,15826}, {12107,16881}, {12241,15761}, {12370,15760}, {12383,15089}, {13142,16618}, {13154,17811}, {13371,23292}, {13406,18390}, {13470,18569}, {13482,15681}, {13564,15080}, {14265,14355}, {14789,23236}, {14805,15032}, {14912,18951}, {15024,15047}, {15028,15038}, {15083,31834}, {18128,20299}, {18377,18388}, {18379,18396}, {18420,18925}, {18580,26937}, {19125,19155}, {19365,32047}, {19467,30522}, {22146,26216}, {23042,23326}

X(32046) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 12161}, {5, 31804}, {20, 31815}, {550, 31802}, {1181, 7526}, {1385, 31811}, {3579, 31812}, {6101, 31810}, {6102, 31807}, {12228, 13198}
X(32046) = isogonal conjugate of X(16837)
X(32046) = X(5)-of-2nd-anti-extouch triangle
X(32046) = anti-Conway-isogonal conjugate of X(12161)
X(32046) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 1993, 6101), (49, 13353, 2), (11412, 11422, 195)

X(32047) = CIRCUMCENTER OF THE ANTI-TANGENTIAL-MIDARC TRIANGLE

X(32047) lies on these lines: {1,30}, {3,1398}, {4,18447}, {5,34}, {11,15761}, {12,13371}, {20,18455}, {26,56}, {33,3627}, {35,11250}, {36,1658}, {52,1425}, {55,12084}, {65,8141}, {140,1038}, {143,19366}, {155,221}, {156,26888}, {222,24475}, {278,6917}, {347,6868}, {382,6198}, {388,14790}, {495,23335}, {498,18281}, {499,10201}, {517,4347}, {548,1040}, {550,1062}, {614,10154}, {952,21147}, {999,7387}, {1068,6923}, {1154,7352}, {1159,17016}, {1325,2906}, {1394,24467}, {1428,19154}, {1448,24470}, {1456,5887}, {1465,6924}, {1478,18569}, {1482,4318}, {1565,7210}, {1657,3100}, {1718,24914}, {1745,1807}, {2067,11265}, {3157,16266}, {3270,10575}, {3295,12085}, {3304,9645}, {3529,9538}, {3564,19471}, {3585,18377}, {3600,31305}, {3628,19372}, {3850,9817}, {3868,23070}, {3869,22136}, {4299,9630}, {4302,9627}, {4670,30147}, {5010,10226}, {5073,9642}, {5204,18324}, {5262,5708}, {5432,23336}, {5433,10020}, {5563,17714}, {5663,6238}, {5690,8270}, {5889,19368}, {6502,11266}, {6644,11398}, {7051,11267}, {7191,9909}, {7280,15331}, {7530,11399}, {7741,13406}, {7747,9595}, {7756,9594}, {7951,10224}, {9632,23251}, {9634,13903}, {9641,17800}, {10267,15832}, {11255,19369}, {11268,19373}, {11412,19367}, {11436,13630}, {11446,12290}, {11461,12279}, {11700,26286}, {12161,19349}, {13383,15325}, {15952,20254}, {18513,18567}, {18915,18951}, {19175,19210}, {19365,32046}

X(32047) = midpoint of X(i) and X(j) for these lines: {i,j}: {6238, 7355}, {19469, 19505}
X(32047) = reflection of X(8144) in X(1)
X(32047) = anti-tangential-midarc-isogonal conjugate of X(7352)
X(32047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (34, 1060, 5), (1870, 4296, 3)

X(32048) = CIRCUMCENTER OF THE ARIES TRIANGLE

X(32048) lies on these lines: {3,125}, {22,68}, {23,6193}, {24,12118}, {25,1147}, {26,19908}, {30,9932}, {154,15316}, {155,6243}, {156,14984}, {161,1498}, {403,8907}, {539,9908}, {1069,9673}, {1598,5448}, {1658,9938}, {2937,12429}, {3157,9658}, {3167,18378}, {3564,15581}, {5480,9820}, {5654,10594}, {5899,12164}, {6642,11425}, {6644,12241}, {7506,10982}, {7530,22660}, {7689,11414}, {8185,9928}, {8548,19127}, {9591,9896}, {10117,12419}, {10201,20302}, {10625,26283}, {11206,12420}, {11411,12088}, {11477,20987}, {12083,12163}, {12166,15083}, {12225,25715}, {12301,14070}, {12319,16868}, {12328,20872}, {13371,18382}, {13383,15577}, {15761,22661}

X(32048) = midpoint of X(i) and X(j) for these lines: {i,j}: {7387, 9937}, {9908, 12309}
X(32048) = reflection of X(i) in X(j) for these (i,j): (9938, 1658), (19908, 26), (22661, 15761), (23307, 13383)
X(32048) = {X(9909), X(12309)}-harmonic conjugate of X(9908)
X(32048) = Aries-isogonal conjugate of X(12420)
X(32048) = X(1158)-of-tangential-triangle if ABC is acute

X(32049) = CIRCUMCENTER OF THE GARCIA-REFLECTION TRIANGLE

X(32049) lies on these lines: {1,1329}, {2,11260}, {3,10915}, {4,3880}, {7,8}, {10,999}, {11,11256}, {40,529}, {42,30960}, {46,1145}, {56,6735}, {57,8256}, {72,12647}, {78,10944}, {80,3633}, {145,1837}, {153,12679}, {354,5554}, {355,381}, {495,28628}, {515,3913}, {516,12640}, {517,6256}, {528,2136}, {612,30778}, {758,25413}, {908,2098}, {952,3811}, {956,10039}, {958,31397}, {960,3421}, {1001,5795}, {1012,8668}, {1056,3812}, {1155,20076}, {1222,3705}, {1319,5552}, {1376,6736}, {1388,27385}, {1420,3035}, {1478,10914}, {1537,5854}, {1699,3680}, {1709,27870}, {1836,14923}, {2478,5919}, {2646,10528}, {2800,12676}, {2802,10742}, {2886,4853}, {3057,3436}, {3086,5123}, {3241,26129}, {3244,5722}, {3304,24982}, {3338,3679}, {3419,3632}, {3434,3893}, {3445,5121}, {3476,7080}, {3555,5570}, {3617,24477}, {3621,4863}, {3626,5708}, {3813,5587}, {3814,11373}, {3829,7989}, {3838,5261}, {3869,25414}, {3870,10950}, {3885,5080}, {3890,4679}, {3895,6284}, {3899,5559}, {4018,10052}, {4028,15232}, {4297,4421}, {4515,24247}, {4861,11375}, {4999,31434}, {5084,10179}, {5178,31145}, {5220,5837}, {5289,21075}, {5541,10483}, {5787,12437}, {5790,10916}, {5881,6765}, {5886,22837}, {6684,11194}, {6734,18967}, {7991,17768}, {8583,9711}, {8666,26446}, {8679,31785}, {8715,18481}, {9623,25466}, {10072,17619}, {10529,17606}, {10827,24390}, {11376,11681}, {11519,24392}, {11531,28609}, {13600,26333}, {15888,19860}, {17728,25005}, {19861,21031}, {20070,28534}, {24928,26364}

X(32049) = midpoint of X(i) and X(j) for these lines: {i,j}: {2136, 5691}, {3632, 11523}, {5881, 6765}
X(32049) = reflection of X(i) in X(j) for these (i,j): (1, 12607), (3, 10915), (1482, 21077), (3680, 13463), (10912, 946), (11256, 11), (12513, 10), (12629, 3813), (18481, 8715), (21627, 19925), (24391, 3626)
X(32049) = anticomplement of X(11260)
X(32049) = Garcia-reflection-isogonal conjugate of X(3680)
X(32049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 17757, 25681), (8, 388, 5836), (388, 5836, 5880)

X(32050) = CIRCUMCENTER OF THE 3rd HATZIPOLAKIS TRIANGLE

X(32050) lies on these lines: {6,2929}, {5946,22962}, {10574,22971}, {15026,22816}, {15045,22549}, {15087,22955}, {31985,32068}

X(32050) = 3rd-Hatzipolakis-isogonal conjugate of X(31985)

X(32051) = CIRCUMCENTER OF THE HUTSON EXTOUCH TRIANGLE

X(32051) lies on these lines: {9,946}, {516,12731}, {5918,31968}, {9943,12702}, {12699,22992}, {12857,16138}

X(32051) = reflection of X(12699) in X(22992)
X(32051) = Hutson-extouch-isogonal conjugate of X(31968)

X(32052) = CIRCUMCENTER OF THE LUCAS ANTIPODAL TRIANGLE

X(32052) lies on these lines: {3,69}, {511,12977}, {2996,19406}, {12984,13061}, {13881,19422}, {18980,23698}

X(32052) = midpoint of X(3) and X(19490)
X(32052) = Lucas-antipodal-isogonal conjugate of X(31970)
X(32052) = {X(3), X(9723)}-harmonic conjugate of X(32053)

X(32053) = CIRCUMCENTER OF THE LUCAS(-1) ANTIPODAL TRIANGLE

X(32053) lies on these lines: {3,69}, {511,13068}, {2996,19407}, {12985,13062}, {13881,19423}, {18981,23698}

X(32053) = midpoint of X(3) and X(19491)
X(32053) = Lucas(-1)-antipodal-isogonal conjugate of X(31971)
X(32053) = {X(3), X(9723)}-harmonic conjugate of X(32052)

X(32054) = CIRCUMCENTER OF THE MANDART-EXCIRCLES TRIANGLE

X(32054) lies on these lines: {19,1598}, {65,12912}, {999,12522}, {3338,12659}, {3555,17656}, {5048,12876}, {5708,12442}, {11246,31977}, {12621,17757}, {12655,25415}, {18257,25681}, {21077,21632}

X(32054) = midpoint of X(3555) and X(17656)
X(32054) = reflection of X(12522) in X(12907)
X(32054) = Mandart-excircles-isogonal conjugate of X(31977)

X(32055) = CIRCUMCENTER OF THE 1st SCHIFFLER TRIANGLE

X(32055) lies on the line {12745,31870}

X(32056) = CIRCUMCENTER OF THE SODDY TRIANGLE

X(32056) lies on the line {1,4}

X(32057) = CIRCUMCENTER OF THE 2nd INNER-SODDY TRIANGLE

Let A', B', C' be as at X(7133). A'B'C' is perspective to the 2nd inner Soddy triangle at X(32057). (Randy Hutson, June 7, 2019)

X(32057) lies on these lines: {1,372}, {482,11246}, {6284,31533}, {10252,16213}

X(32057) = midpoint of X(31533) and X(31568)
X(32057) = 2nd-inner-Soddy-isogonal conjugate of X(482)

X(32058) = CIRCUMCENTER OF THE 2nd OUTER-SODDY TRIANGLE

X(32058) lies on these lines: {1,371}, {481,11246}, {6284,31532}, {10253,16214}

X(32058) = midpoint of X(31532) and X(31567)
X(32058) = 2nd-outer-Soddy-isogonal conjugate of X(481)

X(32059) = CIRCUMCENTER OF THE INNER-SQUARES TRIANGLE

X(32059) lies on these lines: {4,371}, {11209,31987}, {11315,26958}, {31406,32060}

X(32060) = CIRCUMCENTER OF THE OUTER-SQUARES TRIANGLE

X(32060) lies on these lines: {4,372}, {11210,31988}, {11316,26958}, {31406,32059}

X(32061) = CIRCUMCENTER OF THE X-PARABOLA-TANGENTIAL TRIANGLE

X(32061) lies on these lines: {4,542}, {8029,31990}

X(32061) = X-parabola-tangential-isogonal conjugate of X(31990)

X(32062) = CENTROID OF THE ANTI-EXCENTERS-REFLECTIONS TRIANGLE

X(32062) lies on these lines: {4,51}, {5,14855}, {6,14490}, {20,3819}, {24,11204}, {25,10606}, {30,3917}, {33,32065}, {34,11189}, {52,3853}, {53,1562}, {64,5198}, {74,13603}, {125,1596}, {154,1593}, {184,1597}, {235,23332}, {373,381}, {376,5650}, {378,1495}, {382,5562}, {428,15311}, {511,3543}, {546,10575}, {1154,3627}, {1204,1598}, {1216,5073}, {1498,11402}, {1531,31723}, {1533,15760}, {1656,14641}, {1843,2781}, {1885,16621}, {1906,6247}, {1907,2883}, {1974,10249}, {2390,12688}, {2393,12294}, {2777,7576}, {2979,3146}, {3091,6688}, {3292,18451}, {3357,10594}, {3426,10605}, {3529,11793}, {3534,10170}, {3545,16836}, {3575,16656}, {3830,13754}, {3832,9729}, {3839,5943}, {3845,9730}, {3855,11695}, {3861,13491}, {4550,12083}, {5056,17704}, {5059,13348}, {5076,5446}, {5447,17800}, {5640,13570}, {5651,21312}, {5663,14831}, {5946,14893}, {6102,12102}, {7418,10568}, {7998,15683}, {9818,22352}, {10282,14865}, {10301,10990}, {10982,12315}, {11017,15712}, {11190,11471}, {11216,11470}, {11241,11473}, {11242,11474}, {11243,11475}, {11244,11476}, {11430,13596}, {11456,13366}, {11459,15682}, {11472,18534}, {11744,15321}, {11746,17856}, {11820,22112}, {12099,17853}, {12111,13598}, {12112,15033}, {12292,13417}, {13363,23046}, {13399,13567}, {13403,16659}, {13419,18560}, {13445,13595}, {13488,16655}, {14269,16226}, {15058,15644}, {15082,15692}, {15684,23039}, {15752,31978}, {15761,18488}, {16658,18400}, {16980,31673}, {18356,18555}, {19124,19153}, {19169,19209}, {19416,32070}, {19417,32071}

X(32062) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 11455}, {51, 11381}, {382, 18435}, {2979, 3146}, {3543, 15305}, {11459, 15682}, {15684, 23039}
X(32062) = reflection of X(i) in X(j) for these (i,j): (20, 3819), (51, 4), (185, 51), (2979, 5907), (3534, 10170), (3917, 15030), (5562, 18435), (5650, 16261), (5946, 14893), (9730, 3845), (11381, 11455), (11455, 13474), (14855, 5), (15030, 16194), (15072, 5943), (16226, 14269), (17853, 12099)
X(32062) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 11381, 185), (4, 12290, 389), (4, 13474, 11381)

X(32063) = CENTROID OF THE ANTI-INCIRCLE-CIRCLES TRIANGLE

X(32063) lies on these lines: {3,64}, {4,11402}, {5,32064}, {6,3531}, {20,25712}, {24,12174}, {25,5890}, {30,3167}, {51,1181}, {54,11403}, {110,11820}, {140,12324}, {156,12085}, {159,399}, {161,5899}, {184,1597}, {185,3517}, {206,10249}, {221,7373}, {376,6090}, {378,3426}, {381,597}, {382,2883}, {548,12250}, {550,6225}, {578,15811}, {999,10535}, {1154,7387}, {1173,3527}, {1351,2393}, {1384,1971}, {1398,9638}, {1495,10605}, {1593,1614}, {1596,6776}, {1625,15905}, {1656,14216}, {1657,5878}, {1660,22115}, {1853,5055}, {2192,6767}, {2390,10680}, {2777,15681}, {2979,11414}, {3089,18914}, {3197,22147}, {3295,11189}, {3311,11241}, {3312,11242}, {3332,15762}, {3515,6241}, {3516,9707}, {3526,6247}, {3534,15311}, {3542,26944}, {3796,15030}, {3830,18400}, {3843,18376}, {3851,14862}, {5020,5892}, {5054,10192}, {5064,16658}, {5070,20299}, {5073,17845}, {5076,5893}, {5093,17813}, {5596,15760}, {5644,14845}, {5663,14070}, {5895,17800}, {6001,10179}, {6199,17819}, {6221,10533}, {6395,17820}, {6398,10534}, {6623,19118}, {6688,11484}, {6696,15720}, {6800,15305}, {7485,15052}, {7507,16659}, {9715,12111}, {9777,15032}, {9899,31663}, {9909,13754}, {10117,12308}, {10182,15701}, {10193,15707}, {10306,11190}, {10620,15647}, {10675,11244}, {10676,11243}, {11216,11482}, {11381,19357}, {11410,11464}, {11425,13474}, {11472,18475}, {12163,16195}, {13488,18925}, {13567,15152}, {14269,18405}, {15693,23328}, {15694,23329}, {15696,20427}, {15750,26882}, {18358,20079}, {18494,31383}, {18909,21841}, {19173,19209}, {19418,32070}, {19419,32071}, {19709,23325}

X(32063) = midpoint of X(i) and X(j) for these lines: {i,j}: {154, 1498}, {5656, 11206}
X(32063) = reflection of X(i) in X(j) for these (i,j): (3, 154), (64, 11204), (154, 6759), (10249, 206), (10606, 11202), (11204, 10282), (14216, 23332), (23332, 16252), (32064, 5)
X(32063) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 12315, 13093), (1498, 6759, 3), (12315, 14530, 3)

X(32064) = CENTROID OF THE ANTI-INVERSE-IN-INCIRCLE TRIANGLE

X(32064) lies on these lines: {2,154}, {4,51}, {5,32063}, {6,7378}, {20,343}, {22,14927}, {25,23291}, {64,3146}, {66,69}, {107,459}, {125,6353}, {159,3619}, {161,6636}, {184,8889}, {193,15583}, {221,5261}, {376,11204}, {381,5644}, {382,12250}, {388,32065}, {394,5921}, {427,6776}, {428,26869}, {469,3332}, {497,11189}, {546,12315}, {631,9833}, {1154,11411}, {1352,3819}, {1368,14826}, {1498,3091}, {1585,5871}, {1586,5870}, {1593,18945}, {1619,1995}, {1892,10360}, {1992,11216}, {1993,8549}, {2192,5274}, {2390,3436}, {2550,11190}, {2777,15682}, {2781,3448}, {2883,3832}, {3068,11241}, {3069,11242}, {3088,6146}, {3089,16655}, {3090,6759}, {3147,23294}, {3357,3529}, {3410,16063}, {3434,21270}, {3522,6696}, {3524,23329}, {3525,10282}, {3535,14242}, {3536,14227}, {3541,18925}, {3542,16659}, {3543,15311}, {3545,23325}, {3546,12134}, {3556,5260}, {3566,8029}, {3575,18913}, {3580,7500}, {3618,5133}, {3620,9924}, {3627,13093}, {3628,14530}, {3681,3827}, {3818,6688}, {3839,23324}, {3917,9747}, {4232,26958}, {5032,23326}, {5056,16252}, {5059,5894}, {5064,11245}, {5159,8780}, {5225,6285}, {5229,7355}, {5284,18621}, {5422,19149}, {5480,7409}, {5891,6643}, {5892,7401}, {5895,17578}, {6145,15740}, {6193,23335}, {6619,11547}, {6622,26883}, {6756,26944}, {6815,20791}, {6995,13567}, {6997,11451}, {7394,7693}, {7408,17810}, {7492,15579}, {7493,23293}, {7494,21243}, {7496,15581}, {7667,10519}, {8972,17819}, {9143,15131}, {9306,16051}, {9544,15139}, {9920,21357}, {9934,15081}, {9968,15019}, {10182,15709}, {10193,15698}, {10250,14912}, {10299,25563}, {10303,17821}, {10304,23328}, {10535,10589}, {10588,26888}, {11180,31152}, {11225,20423}, {11243,11488}, {11244,11489}, {11392,18915}, {11393,18922}, {11432,16198}, {11548,12017}, {12174,23047}, {12278,30552}, {12279,31978}, {12359,31305}, {12964,31412}, {13364,18952}, {13941,17820}, {14683,23315}, {14855,18474}, {15246,15577}, {16419,18358}, {18435,18531}, {18533,18931}, {18917,31723}, {19174,19209}, {19420,32070}, {19421,32071}, {22967,31371}

X(32064) = reflection of X(i) in X(j) for these (i,j): (2, 1853), (20, 10606), (154, 23332), (193, 17813), (3543, 18405), (5596, 19153), (5656, 381), (9143, 15131), (9833, 11202), (9920, 21357), (10606, 6247), (11202, 20299), (11206, 2), (17813, 15583), (19153, 23300), (32063, 5)
X(32064) = isotomic conjugate of the isogonal conjugate of X(33582)
X(32064) = anticomplement of X(154)
X(32064) = anticomplementary conjugate of X(17037)
X(32064) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (154, 1853, 23332), (154, 23332, 2)

X(32065) = CENTROID OF THE ANTI-TANGENTIAL-MIDARC TRIANGLE

X(32065) lies on these lines: {1,6000}, {12,23332}, {31,56}, {33,32062}, {34,51}, {35,11204}, {36,11202}, {55,10606}, {64,3303}, {65,278}, {354,5603}, {388,32064}, {497,12940}, {517,11214}, {960,6349}, {999,10535}, {1038,3819}, {1058,12950}, {1060,5891}, {1062,14855}, {1154,7352}, {1394,30493}, {1398,11402}, {1428,19153}, {1464,2352}, {1469,2393}, {1498,3304}, {1503,5434}, {1853,11237}, {1870,5890}, {2067,11241}, {2260,21767}, {2330,10249}, {2781,3028}, {2818,3576}, {2979,4296}, {3058,15311}, {3295,10076}, {3357,3746}, {3584,23329}, {3585,18376}, {3868,18633}, {4309,20427}, {4317,9833}, {4857,22802}, {4995,23328}, {5270,18381}, {5298,10192}, {5563,6759}, {5895,9670}, {6198,11455}, {6247,15888}, {6502,11242}, {6688,19372}, {6767,10060}, {7051,11243}, {10571,22341}, {11216,19369}, {11244,19373}, {18435,18447}, {18915,18950}, {19175,19209}, {19370,32070}, {19371,32071}, {24308,24806}

X(32065) = midpoint of X(7355) and X(11189)
X(32065) = reflection of X(i) in X(j) for these (i,j): (6285, 11189), (11189, 1)
X(32065) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7355, 6285), (56, 221, 26888)

X(32066) = CENTROID OF THE APOLLONIUS TRIANGLE

X(32066) lies on the line {970,5529}

X(32067) = CENTROID OF THE 4th CONWAY TRIANGLE

X(32067) lies on these lines: {1,11233}, {2,10439}, {3984,11679}

X(32068) = CENTROID OF THE 3rd HATZIPOLAKIS TRIANGLE

X(32068) lies on these lines: {2,5965}, {5,15130}, {6,30771}, {51,29012}, {182,7494}, {389,12605}, {511,10691}, {539,13363}, {542,5943}, {575,13567}, {1209,15047}, {1368,5097}, {1853,5476}, {1899,19130}, {3060,19924}, {3448,12834}, {3564,6688}, {5422,21243}, {5644,10516}, {5946,18400}, {5972,13366}, {6388,14153}, {6677,12007}, {6723,15516}, {9826,19481}, {10095,18128}, {10116,15026}, {10601,24206}, {11427,22234}, {11695,13292}, {12022,16226}, {12241,15012}, {13142,17704}, {13403,18565}, {14561,18950}, {15004,18911}, {21849,29317}, {31985,32050}

X(32068) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 11225}, {5943, 11245}
X(32068) = {X(5422), X(21243)}-harmonic conjugate of X(25555)

X(32069) = CENTROID OF THE LEMOINE TRIANGLE

X(32069) lies on these lines: {2,10183}, {8029,12073}, {8145,31969}

X(32069) = reflection of X(2) in X(10183)

X(32070) = CENTROID OF THE LUCAS ANTIPODAL TANGENTIAL TRIANGLE

X(32070) lies on these lines: {51,19410}, {154,8939}, {1151,19442}, {1154,18939}, {2393,12590}, {2781,19507}, {2979,19406}, {3819,19422}, {5890,19414}, {5891,19428}, {6000,18980}, {6688,19448}, {8681,11198}, {9723,32071}, {10238,17842}, {10606,13021}, {11189,19434}, {11190,19432}, {11202,19440}, {11204,19454}, {11216,19426}, {11241,19436}, {11242,19439}, {11243,19450}, {11244,19452}, {11402,19358}, {18376,18414}, {18435,18462}, {18926,18950}, {19134,19153}, {19186,19209}, {19370,32065}, {19416,32062}, {19418,32063}, {19420,32064}, {23298,23332}

X(32070) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19358, 19404, 19408), (19446, 21642, 19410)

X(32071) = CENTROID OF THE LUCAS(-1) ANTIPODAL TANGENTIAL TRIANGLE

X(32071) lies on these lines: {51,19411}, {154,8943}, {1152,19443}, {1154,18940}, {2393,12591}, {2781,19508}, {2979,19407}, {3819,19423}, {5890,19415}, {5891,19429}, {6000,18981}, {6688,19449}, {8681,32077}, {9723,32070}, {10240,17839}, {10606,13022}, {11189,19435}, {11190,19433}, {11202,19441}, {11204,19455}, {11216,19427}, {11241,19438}, {11242,19437}, {11243,19451}, {11244,19453}, {11402,19359}, {18376,18415}, {18435,18463}, {18927,18950}, {19135,19153}, {19187,19209}, {19371,32065}, {19417,32062}, {19419,32063}, {19421,32064}, {23299,23332}

X(32071) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19359, 19405, 19409), (19447, 21643, 19411)

X(32072) = CENTROID OF THE LUCAS INNER TRIANGLE

X(32072) lies on the Parry circle and the line {356,8496}

X(32073) = CENTROID OF THE LUCAS(-1) INNER TRIANGLE

X(32073) lies on the Parry circle and these lines: {}

X(32074) = CENTROID OF THE LUCAS(-1) TANGENTS TRIANGLE

X(32074) lies on the Parry circle and these lines: {23,6454}, {352,6481}, {1152,8156}, {11171,11199}

X(32075) = CENTROID OF THE 3rd MIXTILINEAR TRIANGLE

X(32075) lies on these lines: {3,31979}, {1420,3924}

X(32076) = CENTROID OF THE 4th MIXTILINEAR TRIANGLE

X(32076) lies on these lines: {3,31980}, {165,5011}

X(32077) = CENTROID OF THE LUCAS(-1) CENTRAL TRIANGLE

X(32077) lies on these lines: {3,494}, {5409,18940}, {8156,31973}, {8373,8400}, {8681,32071}, {8780,10133}

X(32077) = {X(3), X(11950)}-harmonic conjugate of X(26293)

X(32078) = CENTROID OF THE CEVIAN TRIANGLE OF X(3)

X(32078) lies on these lines: {2,10184}, {3,54}, {4,14635}, {5,14129}, {51,216}, {110,31626}, {140,14978}, {154,157}, {184,10979}, {233,3078}, {852,6688}, {2972,3819}, {2974,6676}, {3131,10632}, {3132,10633}, {3135,23635}, {6000,23719}, {6638,11451}, {7494,17008}, {7499,30737}, {7503,23709}, {10003,30506}, {13366,22052}, {18376,18416}, {18435,18464}, {20975,23195}, {23332,26905}, {26870,32064}, {26874,30258}

X(32078) = reflection of X(i) in X(j) for these (i,j): (2, 12012), (4, 14635), (11197, 2)
X(32078) = anticomplement of X(10184)
X(32078) = isogonal conjugate of the polar conjugate of X(233)
X(32078) = X(14635)-of-anti-Euler triangle
X(32078) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 233}, {5, 22052}, {97, 3078}, {140, 216}, {217, 1232}, {343, 13366}, {577, 14978}
X(32078) = barycentric quotient X(i)/X(j) for these (i,j): (3, 31617), (140, 276), (184, 288), (217, 1173), (233, 264), (418, 31626)
X(32078) = trilinear product X(i)*X(j) for these lines: {i,j}: {48, 233}, {216, 17438}, {217, 20879}
X(32078) = trilinear quotient X(i)/X(j) for these (i,j): (48, 288), (63, 31617), (233, 92)
X(32078) = {X(216), X(26907)}-harmonic conjugate of X(418)

X(32079) = CENTROID OF THE SODDY TRIANGLE

X(32079) lies on these lines: {7,1699}, {479,17728}, {658,9778}, {3160,10164}, {10004,10171}

X(32079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (9533, 15511, 10136), (15913, 17113, 7)

X(32080) = CENTROID OF THE INNER-SODDY TRIANGLE

X(32080) lies on these lines: {}

X(32081) = CENTROID OF THE OUTER-SODDY TRIANGLE

X(32081) lies on the line {175,16214}

X(32082) = CENTROID OF THE 2nd INNER-SODDY TRIANGLE

X(32082) lies on these lines: {1,4}, {55,31538}, {176,9778}, {482,11246}, {1371,3474}, {5393,17728}, {10164,13389}, {13388,31570}, {16213,31535}

X(32082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3475, 32083), (176, 16663, 10134)

X(32083) = CENTROID OF THE 2nd OUTER-SODDY TRIANGLE

X(32083) lies on these lines: {1,4}, {55,31539}, {175,9778}, {481,11246}, {1372,3474}, {5405,17728}, {10164,13388}, {13389,31569}, {16214,31534}

X(32083) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3475, 32082), (175, 16662, 10135)

X(32084) = CENTROID OF THE YIU TRIANGLE

X(32084) lies on these lines: {5,30529}, {381,9143}, {1989,14643}, {5663,30685}, {8154,31991}

X(32085) = ISOGONAL CONJUGATE OF X(3917)

See Kadir Altintas and Ercole Suppa, Hyacinthos 28982.

Let (P_A) be the pedal circle of the A-vertex of the anticomplementary triangle (and of the A-vertex of the tangential triangle), and define (P_B) and (P_C) cyclically. Let R_A be the radical center of (O), (P_B), (P_C) (where (O) is the circumcircle). Define R_B and R_C cyclically. The lines AR_A, BR_B, CR_C concur in X(32085). (Randy Hutson, June 7, 2019)

Generalization: Let X = x : y : z and X' = 1/x : 1/y : 1/z (trilinears) be two isogonal conjugate points. Let (P_A) be the pedal circle of the A-vertex of the anticevian triangle of X (and of the A-vertex of the anticevian triangle of X'), and define (P_B) and (P_C) cyclically. Let R_A be the radical center of (O), (P_B), (P_C). Define R_B and R_C cyclically. The lines AR_A, BR_B, CR_C concur in the polar conjugate of the isotomic conjugate of the cevapoint of X and X', with trilinears 1/(x (y^2 + z^2) (a^2 - b^2 - c^2)) : :. (Randy Hutson, June 7, 2019)

X(32085) lies on the circumhyperbola {{A,B,C,X(4),X(93)}} (with center X(136)) and on these lines {2,8801}, {4,83}, {20,26224}, {25,183}, {53,6531}, {82,225}, {95,237}, {107,9076}, {235,14860}, {242,4222}, {251,393}, {297,16890}, {317,20022}, {458,18092}, {648,1843}, {689,2374}, {827,1300}, {847,10594}, {1093,1598}, {1105,3575}, {1217,7487}, {1596,16264}, {1826,2201}, {2052,16277}, {3089,18855}, {4194,27067}, {4200,27005}, {4232,10130}, {6530,6756}, {7716,9308}, {8793,11547}, {9755,14486}, {10002,10548}, {10301,17983}, {12110,14575}, {12122,22078}, {12173,18848}, {14018,29568}, {15424,26863}, {16230,18010}, {16263,18494}, {18105,23290}

X(32085) = isogonal conjugate of X(3917)
X(32085) = isotomic conjugate of X(3933)
X(32085) = cevapoint of X(i) and X(j) for these (i,j): {2, 7754}, {4, 25}, {6620, 9755}, {18101, 18108}
X(32085) = crosssum of X(3) and X(22138)
X(32085) = trilinear pole of line {419, 2501}
X(32085) = polar conjugate of X(141)
X(32085) = isogonal conjugate of the anticomplement of X(5943)
X(32085) = isogonal conjugate of the complement of X(3060)
X(32085) = isotomic conjugate of the anticomplement of X(5305)
X(32085) = isotomic conjugate of the complement of X(7754)
X(32085) = polar conjugate of the isotomic of X(83)
X(32085) = polar conjugate of the isogonal of X(251)
X(32085) = X(i)-cross conjugate of X(j) for these (i,j): {251, 83}, {428, 4}, {2489, 648}, {5305, 2}, {14618, 107}, {17922, 1897}
X(32085) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3917}, {2, 4020}, {3, 38}, {31, 3933}, {39, 63}, {48, 141}, {69, 1964}, {71, 16696}, {72, 17187}, {75, 20775}, {77, 3688}, {78, 1401}, {163, 2525}, {184, 1930}, {212, 3665}, {228, 16887}, {255, 427}, {304, 3051}, {305, 1923}, {326, 1843}, {394, 17442}, {577, 20883}, {603, 3703}, {656, 1634}, {810, 4576}, {826, 4575}, {906, 16892}, {1331, 2530}, {1332, 21123}, {1437, 15523}, {1444, 21035}, {1459, 4553}, {1790, 3954}, {2084, 4563}, {2200, 16703}, {3005, 4592}, {3990, 17171}, {4055, 16747}, {4558, 8061}, {4568, 22383}, {6507, 27376}, {7116, 16720}, {8024, 9247}, {17206, 21814}, {18604, 21016}, {19215, 26347}, {22367, 32010}
X(32085) = barycentric product of X(i)*X(j) for these lines: {i,j}: {4,83}, {19,3112}, {25,308}, {27,18082}, {29,18097}, {82,92}, {107,4580}, {162,18070}, {251,264}, {275,17500}, {286,18098}, {393,1799}, {419,14970}, {689,2489}, {733,17984}, {827,14618}, {1093,28724}, {1176,2052}, {1897,10566}, {1973,18833}, {2373,21459}, {2501,4577}, {4599,24006}, {6330,21458}, {6331,18105}, {6335,18108}, {6531,20022}, {10547,18027}, {10548,14860}, {16277,17907}
X(32085) = barycentric quotient of X(i) and X(j) for these lines: {i,j}: {2,3933}, {4,141}, {6,3917}, {19,38}, {25,39}, {27,16887}, {28,16696}, {31,4020}, {32,20775}, {82,63}, {83,69}, {92,1930}, {112,1634}, {141,4175}, {158,20883}, {251,3}, {264,8024}, {278,3665}, {281,3703}, {286,16703}, {308,305}, {393,427}, {419,732}, {427,7794}, {428,6292}, {458,14994}, {468,7813}, {523,2525}, {607,3688}, {608,1401}, {648,4576}, {827,4558}, {1096,17442}, {1176,394}, {1194,22424}, {1474,17187}, {1783,4553}, {1799,3926}, {1824,3954}, {1826,15523}, {1843,8041}, {1897,4568}, {1973,1964}, {1974,3051}, {2052,1235}, {2207,1843}, {2333,21035}, {2489,3005}, {2501,826}, {3112,304}, {4577,4563}, {4580,3265}, {4599,4592}, {4628,1331}, {5007,22078}, {6524,27376}, {6531,20021}, {6591,2530}, {6995,8362}, {7009,16720}, {7649,16892}, {8743,3313}, {8744,9019}, {8747,17171}, {8793,23115}, {8882,16030}, {8948,26347}, {10311,14096}, {10547,577}, {10549,21243}, {10551,22416}, {10566,4025}, {14273,14424}, {14569,27371}, {14618,23285}, {14885,22138}, {16277,14376}, {16890,4121}, {17409,23208}, {17500,343}, {18070,14208}, {18082,306}, {18097,307}, {18098,72}, {18099,4019}, {18101,26932}, {18105,647}, {18108,905}, {19118,3787}, {20022,6393}, {21458,441}, {21459,858}, {22105,14417}, {28724,3964}
X(32085) = trilinear product of X(i)*X(j) for these lines: {i,j}: {4,82}, {19,83}, {19,83}, {25,3112}, {25,3112}, {27,18098}, {28,18082}, {28,18082}, {92,251}, {112,18070}, {158,1176}, {308,1973}, {308,1973}, {811,18105}, {827,24006}, {1096,1799}, {1096,1799}, {1172,18097}, {1172,18097}, {1783,10566}, {1897,18108}, {1974,18833}, {1974,18833}, {2190,17500}, {2190,17500}, {2216,10550}, {2489,4593}, {2489,4593}, {2501,4599}, {2501,4599}, {3405,6531}, {4580,24019}, {4628,17924}, {4628,17924}, {6520,28724}, {6520,28724}, {7012,18101}, {7012,18101}, {8767,21458}, {8767,21458}
X(32085) = trilinear quotient of X(i) and X(j) for these lines: {i,j}: {1,3917}, {6,4020}, {19,39}, {25,1964}, {28,17187}, {31,20775}, {33,3688}, {34,1401}, {75,3933}, {158,427}, {162,1634}, {273,3665}, {318,3703}, {393,17442}, {419,2236}, {428,17457}, {811,4576}, {827,4575}, {862,4093}, {1096,1843}, {1824,21035}, {1897,4553}, {1930,4175}, {1969,8024}, {1973,3051}, {2052,20883}, {2190,16030}, {2333,21814}, {2501,8061}, {4577,4592}, {6520,27376}, {6591,21123}, {16600,22077}, {17446,22424}, {17469,22078}, {20964,22367}
X(32085) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {4,17500,10550}, {1176,17500,83}

Points V-Caph: X(32086)-X(32097)

X(32086) = POINT V-CAPH OF X(7)

X(32086) lies on these lines: {2, 10481}, {7, 8}, {12, 24797}, {226, 8055}, {279, 3616}, {348, 5550}, {479, 17169}, {664, 5543}, {728, 4454}, {938, 1111}, {1119, 5342}, {1125, 21314}, {1323, 3622}, {1358, 3485}, {1698, 20121}, {2481, 5558}, {3160, 17079}, {3241, 9312}, {3598, 16823}, {3665, 5226}, {3673, 10580}, {4308, 7223}, {4323, 27818}, {4384, 10521}, {4452, 7274}, {4872, 10248}, {4888, 6738}, {6172, 32008}, {7196, 26103}, {7288, 24805}, {7960, 24774}, {9436, 9780}, {9812, 17170}, {10588, 24798}, {18230, 32024}, {20053, 25719}

X(32086) = {X(7),X(8)}-harmonic conjugate of X(32098)
X(32086) = {X(85),X(6604)}-harmonic conjugate of X(31994)

X(32087) = POINT V-CAPH OF X(8)

X(32087) lies on these lines {1, 4460}, {2, 2321}, {6, 4371}, {7, 8}, {9, 4461}, {10, 3672}, {40, 28638}, {63, 9536}, {77, 4853}, {78, 7269}, {86, 3241}, {142, 4007}, {144, 3686}, {145, 10436}, {192, 5296}, {193, 17116}, {200, 7190}, {239, 5749}, {269, 4915}, {273, 7046}, {314, 7320}, {321, 18228}, {326, 4861}, {329, 14213}, {346, 4384}, {347, 4847}, {350, 26038}, {391, 3729}, {519, 3945}, {524, 7222}, {527, 4034}, {536, 966}, {594, 3763}, {938, 5295}, {962, 4647}, {1014, 12513}, {1058, 28644}, {1100, 4470}, {1213, 28635}, {1219, 7176}, {1266, 4678}, {1278, 17257}, {1442, 3872}, {1447, 7172}, {1654, 4740}, {1698, 4021}, {2345, 3589}, {3161, 17277}, {3187, 19825}, {3243, 4923}, {3475, 4046}, {3596, 4441}, {3616, 4360}, {3617, 4357}, {3620, 29615}, {3621, 3879}, {3622, 28626}, {3623, 4464}, {3626, 4346}, {3629, 4363}, {3632, 3664}, {3663, 3679}, {3687, 5226}, {3694, 24554}, {3706, 10580}, {3739, 5308}, {3883, 30332}, {3886, 8236}, {3932, 9780}, {3950, 16832}, {3966, 9812}, {3977, 5271}, {3986, 28313}, {4058, 17284}, {4060, 17296}, {4072, 31211}, {4328, 4882}, {4359, 34255}, {4373, 17274}, {4395, 17293}, {4398, 32025}, {4405, 7227}, {4416, 4454}, {4419, 4686}, {4445, 7263}, {4478, 7232}, {4546, 30181}, {4643, 4726}, {4644, 6144}, {4648, 4688}, {4651, 30946}, {4668, 4862}, {4677, 4888}, {4699, 17316}, {4739, 4851}, {4748, 17246}, {4764, 17256}, {4772, 6542}, {4816, 4896}, {4821, 6646}, {4859, 29594}, {4869, 17294}, {4873, 6666}, {4916, 17392}, {4971, 15668}, {4980, 5739}, {4986, 21290}, {5082, 21279}, {5435, 11679}, {5543, 20007}, {5550, 28653}, {5750, 17014}, {7319, 30479}, {11024, 28612}, {14552, 28610}, {16816, 26685}, {16833, 17355}, {17143, 30022}, {17163, 18697}, {17184, 19826}, {17233, 29627}, {17322, 19877}, {17331, 20073}, {17353, 24599}, {17377, 20053}, {17394, 20057}, {20054, 30712}, {20055, 26806}, {26626, 28604}, {27147, 29583}, {27304, 27544}

X(32087) = isotomic conjugate of X(5558)
X(32087) = anticomplement of X(3247)
X(32087) = {X(7),X(8)}-harmonic conjugate of X(32099)
X(32087) = {X(69),X(75)}-harmonic conjugate of X(31995)

X(32088) = POINT V-CAPH OF X(9)

X(32088) lies on these lines: {2, 32007}, {8, 4702}, {9, 85}, {44, 27253}, {220, 31269}, {6173, 32015}, {6604, 18230}, {17336, 20880}, {27065, 30854}

X(32088) = {X(9),X(85)}-harmonic conjugate of X(32100)

X(32089) = POINT V-CAPH OF X(10)

X(32089) lies on these lines: {2, 4399}, {10, 86}, {75, 3992}, {594, 31248}, {1698, 4360}, {3632, 30598}, {3634, 5564}, {3828, 17322}, {3932, 9780}, {4389, 5936}, {4460, 19877}, {4464, 31253}, {6535, 30594}, {17271, 21296}, {17279, 29576}, {17285, 24603}, {17311, 29593}, {17332, 28604}, {17359, 31311}, {17380, 28635}, {17384, 28633}

X(32089) = {X(10),X(86)}-harmonic conjugate of X(32101)

X(32090) = POINT V-CAPH OF X(37)

X(32090) lies on these lines: {1, 4753}, {37, 274}, {4687, 17143}, {4755, 16819}, {17264, 25512}, {18145, 27255}, {21830, 27268}

X(32090) = {X(37),X(274)}-harmonic conjugate of X(32102)

X(32091) = POINT V-CAPH OF X(44)

X(32091) lies on these lines: {44, 20568}

X(32092) = POINT V-CAPH OF X(75)

X(32092) lies on these lines: {1, 75}, {2, 3760}, {7, 9534}, {10, 3761}, {19, 16747}, {35, 16992}, {63, 169}, {76, 1698}, {85, 3339}, {192, 31996}, {194, 4699}, {213, 4363}, {239, 20893}, {310, 17210}, {321, 16831}, {330, 16829}, {350, 3624}, {609, 16915}, {980, 31993}, {1089, 30758}, {1107, 4688}, {1111, 28611}, {1125, 4441}, {1218, 2663}, {1268, 30596}, {1449, 20174}, {1909, 3679}, {1975, 5251}, {2176, 17118}, {3208, 29383}, {3294, 3729}, {3633, 25303}, {3634, 18135}, {3665, 7243}, {3673, 16832}, {3739, 5283}, {3925, 3933}, {3926, 19854}, {4000, 16818}, {4063, 23807}, {4253, 24592}, {4352, 19853}, {4358, 25585}, {4361, 20963}, {4410, 17251}, {4664, 32009}, {4668, 24524}, {4671, 29578}, {4687, 32026}, {4691, 25278}, {4726, 25130}, {4739, 16975}, {4980, 29597}, {5088, 16824}, {5271, 18206}, {5280, 11321}, {5299, 20172}, {6376, 19875}, {6381, 9780}, {6390, 24953}, {6533, 7264}, {7031, 16998}, {7176, 16821}, {11679, 21422}, {16502, 20181}, {16705, 19858}, {16748, 16887}, {16815, 30563}, {16826, 28605}, {16827, 17116}, {16830, 31130}, {16834, 21432}, {17135, 17169}, {17211, 17889}, {17303, 25499}, {17308, 20913}, {17321, 25512}, {17753, 20245}, {17754, 29433}, {17759, 27255}, {18044, 29757}, {18145, 19876}, {20911, 28612}, {21384, 29773}, {24199, 29960}, {25457, 25661}, {26035, 30107}, {26959, 27318}, {30035, 30038}

X(32092) = {X(1),X(75)}-harmonic conjugate of X(32104)

X(32093) = POINT V-CAPH OF X(145)

X(32093) lies on these lines: {2, 1743}, {7, 145}, {8, 4888}, {69, 3617}, {75, 31145}, {141, 4747}, {144, 17300}, {193, 24599}, {320, 1279}, {346, 17311}, {391, 4675}, {464, 9965}, {1122, 3873}, {3241, 4862}, {3244, 4902}, {3621, 4896}, {3623, 3663}, {3631, 4470}, {3672, 17378}, {3870, 7271}, {4454, 4851}, {4488, 29573}, {4644, 4869}, {4648, 17332}, {4678, 25590}, {4699, 11160}, {5059, 10442}, {5232, 17361}, {6646, 29624}, {7222, 17374}, {17014, 20090}, {17151, 20014}, {17316, 20059}, {17375, 29616}, {17778, 21454}, {20043, 26842}, {20080, 26806}, {29583, 31300}

X(32094) = POINT V-CAPH OF X(190)

X(32094) lies on these lines: {10, 24428}, {100, 2748}, {190, 514}, {519, 1757}, {644, 4568}, {660, 6005}, {1018, 4063}, {3218, 3912}, {3570, 4169}, {3693, 9321}, {3732, 30720}, {4422, 6547}, {4440, 31647}, {4553, 6004}, {4562, 32042}, {4760, 21821}, {6632, 10196}, {17262, 24281}, {21272, 30732}, {23891, 30731}, {24196, 24419}

X(32095) = POINT V-CAPH OF X(192)

X(32095) lies on these lines: {1, 87}, {2, 17144}, {37, 20168}, {42, 14823}, {75, 25130}, {220, 20180}, {239, 7308}, {274, 4740}, {385, 3303}, {519, 27269}, {551, 27318}, {1107, 4704}, {1278, 31997}, {1500, 7786}, {1655, 3241}, {2176, 4393}, {3058, 7823}, {3210, 29570}, {3304, 7783}, {3622, 17759}, {3623, 21226}, {3746, 7793}, {3913, 16999}, {3934, 30998}, {4309, 14712}, {4360, 16969}, {4479, 24656}, {4664, 14897}, {4699, 17143}, {7762, 15170}, {7787, 16785}, {9263, 20057}, {9331, 26959}, {16777, 20170}, {16826, 17490}, {17024, 31088}, {17242, 30038}, {17244, 20257}, {17383, 27248}, {19738, 31036}, {20081, 25303}, {21830, 27268}, {24620, 29595}, {24621, 29580}, {25107, 30963}

X(32096) = POINT V-CAPH OF X(239)

X(32096) lies on these lines: {2, 3722}, {190, 4686}, {239, 335}, {1086, 3629}, {1100, 27191}, {1279, 29607}, {4366, 4384}, {4402, 4440}, {4437, 29617}, {4974, 24715}, {6650, 28558}, {6653, 29590}, {16593, 29628}, {16816, 17755}, {16833, 17738}, {17367, 26582}, {17380, 25357}

X(32097) = POINT V-CAPH OF X(320)

X(32097) lies on these lines: {7, 21290}, {69, 1111}, {80, 320}, {668, 7321}, {4555, 26726}, {4986, 31995}, {17274, 24222}

Points VI-Caph: X(32098)-X(32109)

X(32098) = POINT VI-CAPH OF X(7)

X(32098) lies on these lines: {7, 8}, {57, 29627}, {145, 10481}, {279, 3241}, {348, 5543}, {728, 4869}, {938, 7264}, {1323, 3623}, {1565, 5734}, {2099, 24797}, {2481, 5556}, {3160, 20057}, {3244, 21314}, {3616, 9436}, {3633, 20121}, {3665, 4323}, {3912, 21454}, {4373, 20008}, {4862, 6738}, {9312, 20050}, {9812, 17753}, {9965, 25935}, {17079, 25718}, {20059, 30625}

X(32098) = {X(7),X(8)}-harmonic conjugate of X(32086)

X(32099) = POINT VI-CAPH OF X(8)

X(32099) lies on these lines: {1, 5232}, {2, 1449}, {6, 29611}, {7, 8}, {9, 29616}, {10, 3945}, {77, 200}, {78, 1442}, {86, 9780}, {141, 5222}, {142, 4034}, {144, 2321}, {145, 4357}, {150, 4738}, {189, 26872}, {193, 3661}, {239, 3620}, {269, 4882}, {279, 6743}, {306, 5273}, {307, 3160}, {314, 7319}, {318, 32001}, {326, 4420}, {329, 2893}, {344, 17295}, {346, 4416}, {347, 6737}, {355, 31780}, {391, 3912}, {519, 3672}, {524, 2345}, {527, 4007}, {594, 4644}, {599, 4000}, {651, 3713}, {894, 20080}, {914, 5744}, {938, 5814}, {966, 4690}, {1014, 1376}, {1086, 4371}, {1264, 5423}, {1266, 20052}, {1654, 5296}, {1743, 29594}, {1943, 18624}, {1992, 17289}, {3161, 17233}, {3187, 19823}, {3241, 17271}, {3421, 21279}, {3474, 4046}, {3578, 17776}, {3596, 25278}, {3616, 4966}, {3617, 5936}, {3618, 17228}, {3619, 3759}, {3621, 3875}, {3624, 4909}, {3625, 4346}, {3626, 25590}, {3629, 17293}, {3630, 4363}, {3631, 4361}, {3632, 3663}, {3633, 4021}, {3662, 4402}, {3664, 3679}, {3687, 5435}, {3694, 24635}, {3705, 15589}, {3706, 9812}, {3751, 5772}, {3758, 11008}, {3763, 4969}, {3872, 7269}, {3883, 8236}, {3886, 30332}, {3949, 18161}, {3964, 7279}, {3966, 10580}, {3974, 4872}, {3986, 29602}, {4001, 28610}, {4005, 10978}, {4042, 14828}, {4060, 4659}, {4328, 4915}, {4344, 5847}, {4358, 5739}, {4360, 20050}, {4384, 4869}, {4389, 20053}, {4399, 7232}, {4419, 4718}, {4431, 4454}, {4452, 17274}, {4464, 20014}, {4488, 17347}, {4643, 4681}, {4648, 17275}, {4657, 4725}, {4665, 7222}, {4668, 4888}, {4677, 4862}, {4678, 4967}, {4704, 6542}, {4720, 8822}, {4748, 4916}, {4788, 6646}, {4816, 4887}, {4853, 7190}, {4856, 29598}, {4886, 18141}, {4971, 17255}, {5044, 28644}, {5081, 32000}, {5226, 11679}, {5227, 7291}, {5257, 29624}, {5550, 17394}, {5815, 21270}, {5932, 31527}, {6144, 17369}, {6381, 10449}, {7046, 7282}, {7172, 7179}, {7320, 30479}, {11160, 17364}, {14555, 30829}, {15533, 17365}, {16667, 29604}, {16706, 21356}, {16786, 17349}, {16833, 21255}, {17014, 17306}, {17135, 30946}, {17184, 19824}, {17230, 26685}, {17236, 20016}, {17238, 26626}, {17248, 29585}, {17250, 20057}, {17251, 17390}, {17252, 17389}, {17253, 17388}, {17256, 17386}, {17260, 29583}, {17277, 29627}, {17282, 24599}, {17283, 31189}, {17288, 29617}, {17309, 17332}, {17310, 17331}, {17311, 17330}, {17315, 17328}, {17376, 28634}, {17378, 32025}, {18623, 26942}, {20090, 29593}, {26038, 30962}, {26041, 27097}, {28780, 28795}

X(32099) = isotomic conjugate of X(5556)
X(32099) = anticomplement of X(1449)
X(32099) = {X(7),X(8)}-harmonic conjugate of X(32087)
X(32099) = {X(69),X(75)}-harmonic conjugate of X(21296)
X(32099) = {X(17287),X(17363)}-harmonic conjugate of X(2)

X(32100) = POINT VI-CAPH OF X(9)

X(32100) lies on these lines: {8, 15481}, {9, 85}, {144, 32007}, {220, 31169}, {3219, 30854}, {6172, 6604}, {10025, 31269}, {16814, 27253}, {17335, 20880}

X(32100) = {X(9),X(85)}-harmonic conjugate of X(32088)

X(32101) = POINT VI-CAPH OF X(10)

X(32101) lies on these lines: {2, 4478}, {7, 11237}, {10, 86}, {594, 31144}, {1654, 7227}, {1698, 30598}, {3617, 3672}, {3626, 4464}, {3679, 4360}, {4021, 4691}, {4357, 4745}, {4668, 17393}, {4887, 4967}, {4888, 17270}, {5278, 30590}, {6542, 31248}, {6666, 17285}, {7277, 28604}, {9780, 17377}, {17228, 20195}, {17239, 17291}, {17268, 31311}, {17275, 17368}, {17277, 17293}, {17287, 28633}, {17295, 29576}, {17305, 28634}, {17307, 17366}, {17394, 19875}, {26842, 27790}

X(32101) = {X(10),X(86)}-harmonic conjugate of X(32089)

X(32102) = POINT VI-CAPH OF X(37)

X(32101) lies on these lines: {1, 17336}, {37, 274}, {4664, 17143}, {4681, 16819}, {4704, 5283}

X(32102) = {X(37),X(274)}-harmonic conjugate of X(32090)

X(32103) = POINT VI-CAPH OF X(44)

X(32103) lies on these lines: {44, 20568}

X(32104) = POINT VI-CAPH OF X(75)

X(32194) lies on these lines: {1, 75}, {8, 3761}, {9, 20174}, {10, 3760}, {76, 3679}, {85, 18421}, {192, 16819}, {194, 4740}, {213, 4361}, {239, 26223}, {312, 16832}, {321, 3294}, {350, 1698}, {536, 5283}, {668, 4668}, {1107, 4686}, {1269, 17270}, {1278, 25264}, {1909, 3632}, {1975, 5258}, {2176, 17119}, {2321, 17050}, {2345, 16818}, {2481, 4385}, {3501, 29433}, {3617, 6381}, {3644, 32026}, {3672, 19853}, {3729, 16552}, {3730, 24592}, {3746, 16992}, {3770, 4034}, {4050, 29699}, {4359, 16831}, {4363, 20963}, {4431, 29960}, {4461, 27304}, {4479, 18140}, {4494, 4665}, {4659, 21384}, {4669, 25278}, {4671, 16815}, {4677, 24524}, {4699, 31996}, {4714, 7264}, {4717, 24331}, {4726, 16975}, {4732, 21615}, {4751, 32009}, {4980, 16834}, {5280, 20172}, {7243, 30617}, {7773, 31159}, {7776, 31140}, {9331, 27255}, {11321, 16785}, {11520, 20880}, {11679, 20367}, {16549, 17026}, {16823, 31130}, {16828, 17321}, {17030, 17759}, {17294, 20913}, {17301, 25499}, {17320, 19871}, {17754, 29742}, {17866, 20895}, {21070, 29966}, {24170, 30942}, {24190, 31027}, {24790, 27248}, {26234, 28612}

X(32104) = {X(1),X(75)}-harmonic conjugate of X(32092)

X(32105) = POINT VI-CAPH OF X(145)

X(32105) lies on these lines: {2, 3950}, {7, 145}, {69, 20054}, {75, 3622}, {192, 24599}, {319, 31145}, {346, 17366}, {1278, 17014}, {3617, 3672}, {3621, 3663}, {3623, 30712}, {4000, 30833}, {4346, 17361}, {4402, 6666}, {4454, 4852}, {4461, 17368}, {4862, 20050}, {9797, 21314}, {17272, 20052}, {17484, 20043}, {20014, 21296}

X(32106) = POINT VI-CAPH OF X(190)

X(32106) lies on these lines: {2, 31647}, {190, 514}, {545, 6547}, {3912, 17484}, {4473, 6549}, {17496, 25267}

X(32107) = POINT VI-CAPH OF X(192)

X(32107) lies on these lines: {1, 87}, {39, 30998}, {239, 3929}, {274, 27268}, {385, 5217}, {498, 19570}, {1107, 1278}, {1479, 13571}, {1655, 9780}, {1909, 20105}, {2176, 25269}, {2276, 20081}, {3177, 11684}, {3210, 5278}, {3617, 17759}, {3621, 21226}, {3634, 27269}, {3644, 17448}, {4352, 17280}, {4699, 5283}, {4704, 31997}, {4788, 17144}, {5204, 7783}, {5225, 7774}, {5333, 29595}, {6284, 7837}, {7173, 7777}, {7779, 9598}, {7905, 9664}, {16666, 20168}, {16815, 17490}, {17129, 31448}, {17232, 24214}, {17242, 24215}, {17495, 30563}, {19862, 27318}, {20018, 20072}, {20036, 20073}, {20691, 21219}, {24621, 29578}

X(32108) = POINT VI-CAPH OF X(239)

X(32108) lies on these lines: {190, 4718}, {239, 335}, {1086, 3630}, {3759, 9055}, {4366, 16468}, {4393, 17755}, {4422, 17393}, {4437, 17367}, {4864, 17266}, {12630, 20533}, {15570, 29575}, {16593, 17389}, {17287, 27191}, {24715, 28498}, {26582, 29617}

X(32109) = POINT VI-CAPH OF X(320)

X(32109) lies on these lines: {69, 4738}, {80, 320}, {150, 21286}

Points on Walsmith rectangular hyperbola: X(32110)-X(32114) and X(32119)-X(32127)

X(32110) = MIDPOINT OF X(23) AND X(74)

X(32110) lies on the Walsmith rectangular hyperbola and these lines: {2, 4549}, {3, 6}, {4, 7703}, {5, 1531}, {22, 8717}, {23, 74}, {24, 7689}, {25, 11472}, {26, 1204}, {30, 125}, {51, 18570}, {64, 9714}, {110, 186}, {113, 468}, {155, 15750}, {184, 18324}, {185, 1658}, {323, 15035}, {376, 15360}, {382, 23325}, {512, 19902}, {517, 10149}, {541, 7426}, {549, 13857}, {550, 18555}, {858, 6699}, {1154, 14708}, {1209, 31833}, {1216, 22467}, {1495, 5663}, {1503, 8262}, {1511, 3292}, {1533, 10990}, {1594, 20191}, {1995, 4550}, {2070, 6000}, {2071, 11692}, {2072, 6723}, {2393, 11579}, {2777, 11799}, {2931, 21284}, {3066, 9818}, {3146, 11468}, {3357, 7517}, {3431, 11422}, {3515, 10539}, {3518, 11440}, {3520, 5446}, {3530, 8254}, {3564, 30714}, {3569, 14696}, {3580, 10295}, {3830, 15362}, {4846, 7493}, {5447, 7691}, {5448, 10018}, {5449, 6240}, {5462, 14118}, {5642, 18579}, {5651, 5891}, {5889, 12038}, {5890, 10298}, {5892, 15053}, {6102, 13367}, {6696, 7553}, {6756, 18488}, {7464, 15055}, {7514, 22112}, {7542, 13568}, {7556, 15072}, {7574, 15061}, {7687, 18323}, {9909, 11820}, {10110, 14130}, {10226, 10263}, {10272, 22249}, {10296, 14644}, {10297, 23515}, {10540, 12308}, {10605, 14070}, {10606, 18534}, {10619, 12899}, {11202, 18445}, {11572, 13561}, {11645, 20126}, {12088, 14641}, {12106, 15030}, {12107, 13491}, {12112, 15054}, {12307, 15606}, {12367, 16010}, {13474, 18378}, {14002, 16261}, {14927, 18931}, {15040, 22115}, {15051, 23061}, {15139, 17835}, {15712, 31802}, {18325, 20127}, {18474, 18533}, {18559, 23293}, {18572, 20304}, {19506, 31726}, {20300, 23328}, {20417, 29012}, {23329, 31723}

X(32110) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 3581}, {23, 74}, {376, 15360}, {1533, 10990}, {3580, 10295}, {7464, 15107}, {12112, 15054}, {12367, 16010}, {15139, 17835}, {18325, 20127}
X(32110) = reflection of X(i) in X(j) for these lines: {i,j}: {113, 468}, {858, 6699}, {1495, 7575}, {1511, 18571}, {1531, 5}, {1533, 16619}, {3292, 1511}, {5642, 18579}, {10272, 22249}, {13857, 549}, {18323, 7687}, {18572, 20304}, {25641, 11657}
X(32110) = reflection of X(25641) in the Orthic axis
X(32110) = circumcircle-inverse of X(14687)
X(32110) = Brocard-circle-inverse of X(39242)
X(32110) = antipode of X(113) in Walsmith rectangular hyperbola
X(32110) = orthocenter of X(6)X(1495)X(3569)
X(32110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 568, 11430}, {3, 9786, 569}, {3, 11438, 9730}, {24, 7689, 12162}, {26, 1204, 10575}, {182, 1350, 9967}, {1379, 1380, 14687}, {1620, 17834, 3}, {3515, 12163, 10539}, {5889, 21844, 12038}, {5890, 10298, 18475}, {6102, 15331, 13367}, {13349, 13350, 22463}, {15055, 15107, 7464}

X(32111) = MIDPOINT OF X(23) AND X(146)

X(32111) lies on the Walsmith rectangular hyperbola and these lines: {2, 11472}, {4, 6}, {5, 7703}, {22, 4549}, {23, 146}, {24, 5878}, {30, 110}, {54, 13488}, {64, 7505}, {74, 468}, {113, 858}, {125, 403}, {186, 10117}, {235, 6241}, {376, 20725}, {381, 18911}, {399, 18325}, {427, 7699}, {511, 1533}, {541, 7426}, {550, 26882}, {1495, 2777}, {1499, 1513}, {1531, 29012}, {1539, 18323}, {1555, 2794}, {1594, 11381}, {1596, 5890}, {1614, 1885}, {1906, 3567}, {1995, 4846}, {3146, 22660}, {3147, 12250}, {3292, 6053}, {3357, 10018}, {3426, 5094}, {3520, 16252}, {3521, 31830}, {3542, 6225}, {3564, 14094}, {3580, 5663}, {3581, 16619}, {3628, 13623}, {4550, 7495}, {5133, 16194}, {5894, 21844}, {6001, 15904}, {6240, 22802}, {6247, 16868}, {6696, 14940}, {6759, 18560}, {6823, 15058}, {7464, 11064}, {7542, 15062}, {8718, 12362}, {9820, 12086}, {9919, 21284}, {10151, 25739}, {10257, 13445}, {10294, 13202}, {10564, 16534}, {10733, 12419}, {11440, 13383}, {11457, 12315}, {11585, 12279}, {11744, 15139}, {11745, 26863}, {11820, 31152}, {12174, 18912}, {12902, 31726}, {13367, 14862}, {13474, 15559}, {13596, 23292}, {13619, 15152}, {14389, 31861}, {14643, 15122}, {14677, 18571}, {15030, 24206}, {15305, 15760}, {15531, 21850}, {15761, 18439}, {18388, 32062}

X(32111) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 12112}, {23, 146}, {399, 18325}, {1533, 15063}, {11744, 15139}
X(32111) = reflection of X(i) in X(j) for these lines: {i,j}: {4, 1514}, {74, 468}, {858, 113}, {3292, 6053}, {3580, 11799}, {3581, 16619}, {7464, 11064}, {10295, 1495}, {10564, 16534}, {13445, 10257}, {14677, 18571}, {18323, 1539}, {25739, 10151}
X(32111) = reflection of X(477) in the Orthic axis
X(32111) = crossdifference of every pair of points on line {520, 5651}
X(32111) = antipode of X(74) in Walsmith rectangular hyperbola
X(32111) = orthocenter of X(6)X(3569)X(3580)
X(32111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 5656, 11456}, {4, 11456, 12022}, {4, 15032, 16657}, {235, 6241, 26879}, {1515, 6530, 4}, {5893, 16655, 4}, {22802, 26883, 6240}

X(32112) = CROSSDIFFERENCE OF X(30) AND X(2420)

The trilinear polar of X(32112) passes through X(3569) and the complement of X(877). (Randy Hutson, June 7, 2019)

X(32112) lies on the curve Q101, the Walsmith rectangular hyperbola, and these lines: {6, 647}, {74, 512}, {110, 250}, {113, 525}, {125, 523}, {232, 3569}, {262, 2394}, {264, 850}, {325, 6333}, {511, 684}, {526, 1495}, {924, 3447}, {2931, 8673}, {3425, 8723}, {3580, 9033}, {6530, 16230}, {8552, 10564}, {9139, 9213}, {11472, 30209}

X(32112) = reflection of X(10564) in X(8552)
X(32112) = reflection of X(32119) in X(468)
X(32112) = X(i)-isoconjugate of X(j) for these (i,j): {248, 24001}, {293, 4240}, {336, 23347}, {1821, 2420}, {1910, 2407}, {2173, 2966}, {2715, 14206}
X(32112) = crossdifference of every pair of points on line {30, 2420}
X(32112) = intersection of Simson line of X(74) and trilinear polar of X(74)
X(32112) = antipode of X(32119) in Walsmith rectangular hyperbola
X(32112) = orthocenter of X(74)X(110)X(1495)
X(32112) = orthocenter of X(74)X(125)X(3580)
X(32112) = orthocenter of X(113)X(125)X(1495)
X(32112) = barycentric product X(i)*X(j) for these lines: {i,j}: {74, 2799}, {297, 14380}, {325, 2433}, {511, 2394}, {684, 16080}, {1494, 3569}, {2421, 12079}, {6333, 8749}, {14919, 16230}
X(32112) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {74, 2966}, {232, 4240}, {237, 2420}, {240, 24001}, {511, 2407}, {684, 11064}, {2211, 23347}, {2394, 290}, {2433, 98}, {2491, 1495}, {2799, 3260}, {3569, 30}, {8430, 9214}, {8749, 685}, {14380, 287}, {14919, 17932}, {16080, 22456}, {17994, 1990}, {18808, 16081}

X(32113) = MIDPOINT OF X(23) AND X(69)

X(32113) lies on the Walsmith rectangular hyperbola and these lines:: {6, 468}, {23, 69}, {30, 599}, {67, 74}, {110, 524}, {113, 511}, {125, 2393}, {141, 858}, {159, 21284}, {186, 6776}, {373, 16511}, {403, 5480}, {523, 3569}, {1316, 16321}, {1594, 12061}, {2070, 11898}, {2072, 9967}, {2452, 16324}, {2854, 3580}, {2930, 2931}, {3589, 15826}, {3619, 30745}, {3620, 5189}, {3763, 5159}, {3818, 18323}, {5654, 11477}, {7464, 10519}, {8547, 18911}, {8550, 11464}, {10117, 19596}, {10297, 10516}, {10510, 11064}, {10989, 21356}, {11179, 18579}, {11645, 16111}, {11663, 13371}, {15068, 16619}, {16776, 20113}, {17710, 26156}, {18358, 18572}, {31959, 31983}

X(32113) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 69}, {67, 12367}
X(32113) = reflection of X(i) in X(j) for these lines: {i,j}: {6, 468}, {858, 141}, {1316, 16321}, {2452, 16324}, {2453, 16334}, {3580, 8262}, {10510, 11064}, {11179, 18579}, {15826, 3589}, {18323, 3818}, {18572, 18358}
X(32113) = reflection of X(2453) in the Orthic axis
X(32113) = {X(8263),X(16789)}-harmonic conjugate of X(599)
X(32113) = crossdifference of every pair of points on line {182, 30209}
X(32113) = antipode of X(6) in Walsmith rectangular hyperbola
X(32113) = orthocenter of X(74)X(3569)X(3580)
X(32113) = orthocenter of X(113)X(1495)X(3569)

X(32114) = REFLECTION OF X(125) IN X(5181)

X(32114) lies on the Walsmith rectangular hyperbola and these lines:: {6, 5642}, {69, 74}, {110, 193}, {113, 1596}, {125, 126}, {159, 2930}, {511, 1533}, {524, 1495}, {526, 6131}, {895, 3618}, {1350, 10990}, {1351, 16534}, {2931, 19588}, {3448, 15812}, {3564, 30714}, {3569, 9033}, {3580, 8681}, {3620, 9140}, {3629, 15303}, {5486, 5651}, {5965, 25714}, {6053, 10752}, {6723, 25320}, {7699, 11188}, {7703, 12272}, {9143, 20080}, {10519, 20417}, {11472, 17702}, {11898, 23236}, {13202, 14982}, {14912, 15034}
X(32114) = midpoint of X(11898) and X(23236)
X(32114) = reflection of X(i) in X(j) for these lines: {i,j}: {125, 5181}, {895, 5972}, {1351, 16534}, {5095, 110}, {5642, 5648}, {10752, 6053}, {10990, 1350}, {13202, 14982}, {24981, 2930}
X(32114) = crossdifference of every pair of points on line {2780, 5622}
X(32114) = antipode of X(32127) in Walsmith rectangular hyperbola

Incenters of not-equilateral central triangles: X(32115)-X(32118)

X(32115) = INCENTER OF THE 6th ANTI-BROCARD TRIANGLE

X(32115) lies on these lines: {10,98}, {58,99}, {83,11599}, {182,2783}, {239,1281}, {291,4586}, {519,8298}, {740,1691}, {2456,29057}, {2792,12177}, {2796,5182}, {3573,4368}, {4154,19561}, {4672,5038}, {5977,16825}, {5988,10352}, {5992,10353}, {10131,32117}, {10789,16834}, {12151,28558}, {13196,17768}, {13355,24728}, {27838,27950}

X(32115) = inverse of X(5150) in the 1st Lemoine circle

X(32116) = INCENTER OF THE 1st ANTI-ORTHOSYMMEDIAL TRIANGLE

X(32116) lies on these lines: {28,105}, {109,1297}, {251,32118}, {2794,15971}, {2831,3744}, {2844,9157}, {5078,10016}

X(32117) = INCENTER OF THE 6th BROCARD TRIANGLE

X(32117) lies on these lines: {1,7187}, {3,1281}, {8,3177}, {20,24280}, {55,17789}, {72,15310}, {75,20992}, {76,2795}, {194,740}, {304,3685}, {384,3923}, {516,17760}, {744,24696}, {956,29010}, {1975,5695}, {2783,11257}, {2792,9863}, {2796,7833}, {2896,4655}, {3705,25083}, {3821,7876}, {4019,21299}, {4201,9791}, {4451,25252}, {4672,7787}, {5025,5988}, {5992,6655}, {7081,7580}, {7750,17768}, {7791,24248}, {7893,17770}, {8680,24351}, {9873,29097}, {9939,28558}, {10131,32115}, {16895,24295}, {17135,25257}, {17688,24342}, {20065,24695}, {20432,23407}, {27549,32034}

X(32118) = INCENTER OF THE 1st ORTHOSYMMEDIAL TRIANGLE

X(32118) lies on these lines: {1,572}, {3,25065}, {4,15314}, {21,16566}, {31,1726}, {33,57}, {46,24309}, {51,2844}, {58,3497}, {65,516}, {72,17355}, {226,12618}, {251,32116}, {354,4353}, {405,25081}, {517,12722}, {518,2321}, {527,24476}, {726,2901}, {758,3923}, {761,29044}, {942,3663}, {971,24471}, {984,3730}, {991,7146}, {1009,25078}, {1011,25080}, {1210,12610}, {1400,1736}, {1451,1825}, {1469,2801}, {1721,2955}, {1746,26000}, {1753,23052}, {1764,11031}, {1770,29050}, {1781,4223}, {1876,3668}, {2352,16577}, {2690,2711}, {2809,3751}, {2825,12294}, {2831,5480}, {2838,18907}, {3671,21629}, {3729,3868}, {3754,4660}, {3812,18252}, {3821,5883}, {4329,5807}, {4356,11997}, {4463,5294}, {5256,20243}, {5884,29057}, {5902,24248}, {8094,12728}, {9021,17351}, {9532,19161}, {10158,19744}, {10176,24295}, {10319,10382}, {10572,29024}, {11221,19732}, {11529,12717}, {12445,12727}, {12652,18421}, {17132,24473}, {18389,29069}

X(32118) = midpoint of X(i) and X(j) for these lines: {i,j}: {65, 12723}, {942, 21848}, {3729, 3868}
X(32118) = reflection of X(i) in X(j) for these (i,j): (72, 17355), (3663, 942), (4660, 3754), (12721, 4353), (18252, 3812)
X(32118) = {X(354), X(12721)}-harmonic conjugate of X(4353)

X(32119) = X(6)X(1637)∩X(74)X(98)

X(32119) lies on the Walsmith rectangular hyperbola and these lines: {6, 1637}, {74, 98}, {107, 110}, {113, 132}, {125, 526}, {520, 3580}, {523, 1495}, {542, 31953}, {684, 5972}, {2492, 6793}, {2777, 9409}, {2797, 16163}, {3569, 6103}, {7669, 10117}

X(32119) = reflection of X(i) in X(j) for these lines: {i,j}: {125, 6130}, {684, 5972}, {32112, 468}
X(32119) = crossdifference of every pair of points on line {1625, 3269}
X(32119) = antipode of X(32112) in Walsmith rectangular hyperbola
X(32119) = orthocenter of X(6)X(74)X(113)
X(32119) = orthocenter of X(74)X(1495)X(3580)

X(32120) = X(6)X(523)∩X(74)X(1499)

X(32120) lies on the Walsmith rectangular hyperbola and these lines:: {6, 523}, {74, 1499}, {110, 525}, {113, 30209}, {125, 512}, {468, 3569}, {520, 32114}, {526, 32112}, {690, 1495}, {858, 24284}, {2780, 32110}, {3566, 10117}, {3580, 9517}, {9033, 32113}, {14417, 18860}

X(32120) = reflection of X(i) in X(j) for these lines: {i,j}: {858, 24284}, {3569, 468}
X(32120) = antipode of X(3569) in Walsmith rectangular hyperbola
X(32120) = orthocenter of X(6)X(74)X(3580)
X(32120) = orthocenter of X(6)X(113)X(1495)
X(32120) = orthocenter of X(110)X(125)X(1495)

X(32121) = X(6)X(14273)∩X(74)X(2374)

X(32121) lies on the Walsmith rectangular hyperbola and these lines: {6, 14273}, {74, 2374}, {99, 110}, {113, 126}, {125, 5139}, {512, 3580}, {523, 32113}, {526, 6131}, {924, 32112}, {1495, 3566}, {1499, 32109}, {3569, 10418}, {7665, 9138}, {16316, 32111}, {20186, 32110}

X(32121) = reflection of X(32114) and X(6131)
X(32121) = crossdifference of every pair of points on line {3124, 14984}
X(32121) = orthocenter of X(6)X(110)X(113)
X(32121) = orthocenter of X(6)X(125)X(2931)
X(32121) = orthocenter of X(110)X(1495)X(3580)

X(32122) = X(6)X(9033)∩X(74)X(2373)

X(32122) lies on the Walsmith rectangular hyperbola and these lines: {6, 9033}, {74, 2373}, {110, 1289}, {125, 127}, {520, 32112}, {525, 1495}, {690, 10117}, {3580, 8673}, {8057, 32113}, {30209, 32110}

X(32122) = orthocenter of X(6)X(74)X(125)

X(32123) = X(5)X(6)∩X(74)X(858)

X(32123) lies on the Walsmith rectangular hyperbola and these lines: {4, 9938}, {5, 6}, {23, 12319}, {24, 22661}, {30, 10117}, {74, 858}, {110, 403}, {125, 1568}, {235, 12293}, {427, 11472}, {468, 2931}, {912, 15904}, {1147, 10024}, {1368, 4549}, {1495, 11799}, {1503, 15133}, {1594, 7703}, {3167, 10254}, {5133, 7699}, {5448, 5576}, {6193, 16868}, {6622, 12318}, {7505, 9932}, {9820, 13160}, {10255, 12164}, {10564, 15115}, {11064, 15136}, {11459, 12359}, {11585, 12163}, {12118, 15761}, {14984, 32112}, {15123, 23515}, {18323, 19479}, {18404, 19908}, {20427, 23335}

X(32123) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 12319}, {68, 12364}
X(32123) = reflection of X(i) in X(j) for these lines: {i,j}: {858, 23306}, {2931, 468}, {10564, 15115}, {15136, 11064}, {18323, 19479}
X(32123) = antipode of X(2931) in Walsmith rectangular hyperbola
X(32123) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {68, 5654, 15068}, {235, 23307, 12293}

X(32124) = X(6)X(23)∩X(74)X(7575)

X(32124) lies on the Walsmith rectangular hyperbola and these lines: {6, 23}, {30, 7699}, {74, 7575}, {113, 10295}, {125, 7426}, {186, 11472}, {403, 15432}, {468, 7703}, {10546, 18571}

X(32124) = midpoint of X(23) and X(7712)
X(32124) = reflection of X(7703) and X(468)
X(32124) = antipode of X(7703) in Walsmith rectangular hyperbola

X(32125) = X(6)X(66)∩X(74)X(403)

X(32125) lies on the Walsmith rectangular hyperbola and these lines: {5, 64}, {6, 66}, {23, 13203}, {30, 2931}, {74, 403}, {110, 858}, {113, 2072}, {125, 15126}, {154, 1368}, {159, 31152}, {161, 1370}, {235, 1192}, {468, 10117}, {1498, 11585}, {1594, 6241}, {1596, 31860}, {1619, 30771}, {2393, 32114}, {2450, 3566}, {2777, 11799}, {2781, 3580}, {2883, 15072}, {3357, 10024}, {3564, 17847}, {5133, 7703}, {5169, 20300}, {5576, 9730}, {5654, 13371}, {5894, 11454}, {6696, 13160}, {6823, 8567}, {7396, 28419}, {7495, 15578}, {9932, 14790}, {10192, 15080}, {10255, 13093}, {10564, 18400}, {10606, 15760}, {11206, 31101}, {12118, 23335}, {12250, 16868}, {13352, 18381}, {15138, 15142}, {15472, 25739}, {15559, 16657}, {15577, 16063}, {15761, 20427}, {17824, 18914}, {18323, 19506}, {18382, 31133}, {31074, 32064}

X(32125) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 13203}, {11744, 12379}
X(32125) = reflection of X(i) in X(j) for these lines: {i,j}: {125, 15126}, {858, 23315}, {10117, 468}, {11744, 1514}, {18323, 19506}
X(32125) = crosspoint of X(16080) and X(18018)
X(32125) = crosssum of X(206) and X(3284)
X(32125) = crossdifference of every pair of points on line {8673, 9306}
X(32125) = antipode of X(10117) in Walsmith rectangular hyperbola
X(32125) = orthocenter of X(110)X(3569)X(3580)

X(32126) = X(6)X(5089)∩X(74)X(2766)

X(32126) lies on the Walsmith rectangular hyperbola and these lines: {6, 5089}, {40, 5692}, {72, 20989}, {74, 2766}, {110, 518}, {113, 517}, {125, 3827}, {468, 15904}, {650, 3569}, {910, 21873}, {912, 2931}, {2771, 32109}, {2778, 32110}, {2836, 3580}, {3740, 7703}, {7686, 7699}, {9004, 32114}

X(32126) = reflection of X(15904) and X(468)
X(32126) = antipode of X(15904) in Walsmith rectangular hyperbola

X(32127) = REFLECTION OF X(3292) IN X(6)

X(32127) lies on the Walsmith rectangular hyperbola and these lines: {6, 373}, {74, 511}, {110, 8681}, {113, 3564}, {125, 524}, {193, 7703}, {520, 2451}, {538, 2452}, {576, 15030}, {1350, 10602}, {1351, 1597}, {1352, 1992}, {1495, 2854}, {1974, 6391}, {2030, 10765}, {2080, 22143}, {2393, 10117}, {2987, 9190}, {3003, 9145}, {6467, 8547}, {8548, 13352}, {9004, 15904}, {11003, 15531}, {18860, 20975}

X(32127) = reflection of X(3292) in X(6)
X(32127) = {X(6),X(8542)}-harmonic conjugate of X(373)
X(32127) = crossdifference of every pair of points on line {1499, 6776}
X(32127) = antipode of X(32114) in Walsmith rectangular hyperbola
X(32127) = orthocenter of X(74)X(1495)X(3569)

X(32128) = X(3)X(8)∩X(4)X(93)

See J.L. Ayme and Ercole Suppa, Hyacinthos 28984.

X(32128) lies on these lines: {3,8}, {4,93}, {498,2594}, {6928,10449}, {10441,10526}

X(32129) = CENTROID OF GEMINI TRIANGLE 104

X(32129) lies on these lines: {1, 32044}, {2, 3761}, {1978, 4664}, {4364, 30629}, {17237, 25378}, {26738, 30990}, {30967, 30991}

X(32130) = (name pending)

See Kadir Altintas and Ercole Suppa, Hyacinthos 28987.

X(32130) lies on Kiepert hyperbola and this line: {4,17952}

X(32131) = (name pending)

See Kadir Altintas and Ercole Suppa, Hyacinthos 28987.

X(32131) lies on this line: {3,6}

X(32132) = X(2)X(254)∩X(3)X(2165)

See Kadir Altintas and Ercole Suppa, Hyacinthos 28987.

Let A'B'C' be the Schroeter triangle. Let P be a point on the nine-point circle. Let A" be the intersection, other than P, of the nine-point circle and line A'P; define B" and C" cyclically. Triangle A"B"C" is perspective to ABC for all P. If P = X(135), the perspector is X(32132). (Randy Hutson, June 7, 2019)

X(32132) lies on these lines: {2,254}, {3,2165}, {24,16172}, {68,394}, {96,97}, {925,3147}, {3546,5392}, {3926,20563}, {6642,14593}

X(32133) = X(2)X(12505)∩X(67)X(10354)

See Kadir Altintas and Ercole Suppa, Hyacinthos 28988.

X(32133) lies on these lines: {2,12505}, {67,10354}, {599,5486}, {858,14262}, {1296,16063}, {5094,21448}, {5485,16051}

X(32133) = barycentric product of X(i) and X(j) for these lines: {i,j}: {338,15406}, {5485,5486}
X(32133) = barycentric quotient of X(i) and X(j) for these lines: {i,j}: {115,5512}, {5485,11185}, {5486,1992}, {15406,249}, {21448,1995}

X(32133) = trilinear product of X(i) and X(j) for these lines: {i,j}: {1109,15406}, {1109,15406}
X(32133) = trilinear quotient of X(i) and X(j) for these lines: {i,j}: {1109, 5512}

X(5)-of-central (not equilateral) triangles: X(32134)-X(32215)

X(32134) = X(5)-OF-5th ANTI-BROCARD TRIANGLE

X(32134) lies on these lines: {3,3329}, {4,11842}, {5,32}, {26,10790}, {30,3398}, {83,140}, {98,546}, {182,550}, {187,11272}, {355,10789}, {384,22521}, {495,10797}, {496,10798}, {548,12054}, {549,5171}, {632,7808}, {952,12194}, {1078,3628}, {1353,5039}, {1483,10800}, {1506,10631}, {1656,7793}, {1691,18583}, {2782,5007}, {3095,3972}, {3564,12193}, {3627,14880}, {4027,19687}, {5008,6248}, {5097,7816}, {5188,15870}, {5690,10791}, {5844,12195}, {5874,10793}, {5875,10792}, {5901,11364}, {5999,13111}, {6179,7697}, {6249,10991}, {6661,10333}, {6756,11380}, {7766,13108}, {7781,15520}, {7819,10350}, {7830,25555}, {7839,13188}, {7858,15561}, {7878,11171}, {8369,10349}, {8722,15712}, {9301,10346}, {9821,10348}, {10794,10943}, {10795,10942}, {10799,15171}, {10803,32213}, {10804,32214}, {11490,32141}, {11837,32146}, {11838,32147}, {11839,32162}, {11840,32177}, {11841,32178}, {12176,12206}, {12197,28174}, {12201,12208}, {12204,22523}, {12205,22522}, {12835,18990}, {13335,14881}, {13885,13925}, {13938,13993}, {18993,19116}, {18994,19117}, {22330,32135}, {22520,32153}

X(32134) = midpoint of X(i) and X(j) for these lines: {i,j}: {3398, 12110}, {12201, 13193}
X(32134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7787, 10788, 3), (11842, 18501, 4), (12210, 12211, 12212)

X(32135) = X(5)-OF-6th ANTI-BROCARD TRIANGLE

X(32135) lies on these lines: {2,98}, {6,1569}, {99,576}, {115,5038}, {262,8289}, {511,5026}, {543,10796}, {575,2782}, {690,25556}, {1691,5477}, {2030,12829}, {2080,2482}, {2456,29012}, {3098,10753}, {3398,14981}, {5055,10488}, {5095,14590}, {5097,5969}, {5476,6321}, {7697,10485}, {7787,22234}, {7808,20398}, {8590,8787}, {8724,11842}, {10104,20399}, {10131,32152}, {10351,11257}, {10754,15520}, {10991,12054}, {10992,12110}, {11645,22505}, {11676,22525}, {12042,20190}, {13172,20423}, {14159,25561}, {19120,19130}, {22330,32134}

X(32135) = midpoint of X(i) and X(j) for these lines: {i,j}: {99, 576}, {182, 12177}, {3098, 10753}, {8593, 11178}
X(32135) = reflection of X(i) in X(j) for these (i,j): (115, 25555), (12042, 20190)
X(32135) = {X(5182), X(12177)}-harmonic conjugate of X(182)

X(32136) = X(5)-OF-ANTI-CONWAY TRIANGLE

X(32136) lies on these lines: {3,54}, {5,11264}, {6,156}, {22,13421}, {26,17809}, {49,1199}, {110,15026}, {143,184}, {155,14128}, {182,32142}, {265,3091}, {389,32171}, {546,12241}, {567,5876}, {568,5944}, {569,11591}, {575,3564}, {576,11536}, {578,5663}, {632,3292}, {1147,12006}, {1173,7545}, {1511,9545}, {1614,14627}, {1994,10263}, {2393,22330}, {2914,15101}, {2916,11477}, {3448,11702}, {3525,9716}, {3529,31815}, {3567,9704}, {3627,21659}, {5893,12102}, {6243,11003}, {6593,22234}, {8254,21243}, {8550,13371}, {9306,32205}, {9703,15043}, {9826,13358}, {10116,12242}, {10226,13382}, {10282,16881}, {10539,13364}, {11424,32137}, {11425,32138}, {11426,32139}, {11427,32140}, {11428,32158}, {11429,32168}, {11430,32210}, {11482,19459}, {11565,18569}, {11750,20424}, {12086,13491}, {12107,16625}, {12233,30522}, {13321,26882}, {13353,15067}, {13434,15060}, {13561,23292}, {14912,18952}, {15704,31802}, {17710,19150}, {18912,20304}, {19365,32143}, {24680,31811}

X(32136) = midpoint of X(12161) and X(32046)
X(32136) = X(140)-of-2nd anti-extouch triangle
X(32136) = X(3628)-of-anti-Ascella triangle
X(32136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 11422, 1493), (195, 5012, 6101), (11422, 11423, 3)

X(32137) = X(5)-OF-ANTI-EXCENTERS-REFLECTIONS TRIANGLE

X(32137) lies on these lines: {2,11017}, {3,11439}, {4,94}, {5,10575}, {20,15060}, {24,32210}, {25,32138}, {26,11472}, {30,1216}, {33,32143}, {34,32168}, {49,13596}, {52,15687}, {64,13861}, {140,14915}, {156,1593}, {185,3845}, {195,14094}, {235,13561}, {376,11592}, {378,32171}, {381,10574}, {382,5876}, {389,3861}, {546,5462}, {550,14128}, {632,14855}, {1154,3627}, {1209,1533}, {1498,31861}, {1597,32139}, {1656,12279}, {1657,15058}, {1885,30522}, {2070,15062}, {3091,32205}, {3146,6101}, {3357,12106}, {3426,6642}, {3530,14641}, {3534,15056}, {3543,18436}, {3545,12046}, {3567,14269}, {3830,10263}, {3832,15026}, {3843,5946}, {3850,13363}, {3851,11465}, {3853,13754}, {3856,5943}, {3858,9730}, {4550,7525}, {4846,16620}, {5066,9729}, {5073,11459}, {5076,5889}, {5079,20791}, {5446,12102}, {5576,32111}, {5878,11818}, {5891,15704}, {5892,12811}, {5944,14130}, {6146,15807}, {6243,17578}, {7527,10610}, {7999,15681}, {10096,20191}, {10110,14893}, {10540,14865}, {11250,20773}, {11403,12161}, {11424,32136}, {11440,18378}, {11444,17800}, {11470,32155}, {11471,32158}, {11473,32169}, {11474,32170}, {11475,32207}, {11476,32208}, {11793,12103}, {11819,16654}, {12086,18350}, {12324,18952}, {12358,18565}, {12363,16658}, {13368,22584}, {13421,13598}, {13565,15760}, {15061,21451}, {15311,31830}, {17814,22334}, {18570,26883}, {19124,19155}, {19169,19211}, {20299,20304}, {20396,23294}, {28154,31752}, {28168,31751}

X(32137) = midpoint of X(i) and X(j) for these lines: {i,j}: {5, 11381}, {382, 5876}, {1539, 12292}, {3146, 6101}, {3627, 12162}, {6102, 18439}, {10263, 12111}, {12290, 13491}
X(32137) = reflection of X(i) in X(j) for these (i,j): (20, 32142), (143, 4), (185, 10095), (389, 3861), (550, 14128), (5446, 12102), (5889, 16982), (6146, 15807), (10627, 5907), (12103, 11793), (13421, 13598), (13491, 12006), (13630, 546), (14641, 3530)
X(32137) = anticomplement of the anticomplement of X(11017)
X(32137) = X(13491)-of-Ehrmann-mid triangle
X(32137) = X(32138)-of-anti-Ara triangle
X(32137) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 18439, 6102), (11439, 11455, 3)

X(32138) = X(5)-OF-ANTI-HUTSON INTOUCH TRIANGLE

X(32138) lies on these lines: {3,74}, {4,13561}, {5,1204}, {20,30522}, {25,32137}, {26,64}, {30,3357}, {55,32143}, {56,32168}, {143,1593}, {146,14940}, {155,8567}, {185,18570}, {186,18439}, {378,6102}, {381,11704}, {382,18379}, {511,15579}, {541,20191}, {546,11438}, {568,14865}, {1147,10226}, {1151,32169}, {1152,32170}, {1154,10606}, {1192,11472}, {1498,18324}, {1657,13445}, {1658,6000}, {2070,12290}, {2071,18436}, {2777,5449}, {2883,10020}, {2904,13148}, {2937,12279}, {3146,3581}, {3516,12161}, {3532,17814}, {3534,7691}, {3628,4550}, {3851,15053}, {5020,11017}, {5085,19155}, {5448,25563}, {5584,32158}, {5878,10201}, {5890,14130}, {5895,15114}, {5925,14852}, {6101,11413}, {6243,12086}, {6696,13371}, {6759,15331}, {7502,10575}, {7526,10605}, {7575,26883}, {7728,16868}, {9544,23040}, {9786,10095}, {9818,12006}, {9833,15138}, {10224,23329}, {10539,15646}, {10540,21844}, {11250,13754}, {11264,18917}, {11270,18350}, {11381,32110}, {11412,18859}, {11425,32136}, {11455,18378}, {11477,32155}, {11479,32205}, {11480,32207}, {11481,32208}, {11750,13399}, {12085,13391}, {12162,21663}, {13093,14070}, {13406,22802}, {14915,17714}, {15060,17928}, {15311,15761}, {15704,20725}, {16003,21659}, {17702,18356}, {18377,20299}, {18403,23294}, {18435,22467}, {18562,25739}, {18567,23325}, {18913,18952}, {19172,19211}, {22660,23328}

X(32138) = midpoint of X(i) and X(j) for these lines: {i,j}: {20, 32140}, {26, 64}, {3357, 7689}, {5894, 12359}, {12084, 12163}, {15054, 15132}
X(32138) = reflection of X(i) in X(j) for these (i,j): (3, 32210), (4, 13561), (156, 3), (382, 18379), (1147, 10226), (2883, 10020), (5448, 25563), (6759, 15331), (11477, 32155), (13371, 6696), (18377, 20299), (22660, 23336), (22802, 13406), (32139, 32171)
X(32138) = X(156)-of-ABC-X3 reflections triangle
X(32138) = X(13561)-of-anti-Euler triangle
X(32138) = X(32137)-of-Ara triangle
X(32138) = X(32143)-of-anti-Mandart-incircle triangle
X(32138) = X(32168)-of-2nd circumperp tangential triangle
X(32138) = X(32210)-of-X3-ABC reflections triangle
X(32138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 11456, 5944), (11468, 12111, 3), (32139, 32171, 156)

X(32139) = X(5)-OF-ANTI-INCIRCLE-CIRCLES TRIANGLE

Let A'B'C' be the Kosnita triangle. Let A" be the circumcenter of triangle AB'C', and define B" and C" cyclically. Then X(32139) = X(20)-of-A"B"C". (Randy Hutson, June 7, 2019)

X(32139) lies on these lines: {3,74}, {4,1994}, {5,1181}, {6,546}, {22,18436}, {24,10540}, {25,6102}, {26,6759}, {30,155}, {49,378}, {52,7530}, {54,15305}, {64,11250}, {68,15761}, {140,17814}, {143,1598}, {154,1658}, {184,7526}, {185,6644}, {195,3830}, {323,3529}, {381,7592}, {382,1993}, {389,13861}, {394,550}, {403,25738}, {511,9925}, {542,8548}, {547,15805}, {568,10594}, {569,15030}, {578,31861}, {999,32143}, {1069,32047}, {1092,10575}, {1147,6000}, {1154,7387}, {1199,3832}, {1493,11403}, {1503,18569}, {1539,19504}, {1596,13292}, {1597,32137}, {1620,18571}, {1656,13561}, {1853,10224}, {2072,11457}, {2979,8718}, {3089,18951}, {3090,15052}, {3091,15032}, {3146,12112}, {3157,8144}, {3167,12085}, {3295,32168}, {3311,32169}, {3312,32170}, {3357,12038}, {3448,16868}, {3520,9544}, {3530,17811}, {3542,18917}, {3544,15018}, {3564,19149}, {3843,15087}, {3845,10982}, {3851,5422}, {3853,15811}, {5012,15058}, {5020,12006}, {5050,19155}, {5072,15037}, {5448,18381}, {5462,15011}, {5654,13371}, {5656,6193}, {5889,7517}, {5890,7506}, {5891,7516}, {5907,7514}, {5925,17847}, {5946,7529}, {6101,11414}, {6238,26888}, {6247,9820}, {6642,13630}, {6823,31831}, {7352,10535}, {7393,14128}, {7395,15060}, {7503,18435}, {7525,31834}, {7553,31815}, {7564,18388}, {7689,10282}, {7728,12419}, {8717,13348}, {8743,22146}, {9140,11704}, {9545,14865}, {9704,14130}, {9786,12106}, {9815,23410}, {9818,19347}, {10024,11442}, {10095,11432}, {10113,19456}, {10116,18390}, {10170,13154}, {10201,12359}, {10226,10606}, {10263,12160}, {10306,32158}, {10323,23039}, {10661,10676}, {10662,10675}, {10665,12970}, {10666,12964}, {11002,26863}, {11381,13352}, {11412,12083}, {11413,22115}, {11423,16261}, {11424,16194}, {11425,11472}, {11426,32136}, {11439,15033}, {11477,11663}, {11482,32155}, {11484,32205}, {11485,32207}, {11486,32208}, {11818,12233}, {11819,31383}, {12293,17824}, {12317,14940}, {13346,14915}, {13406,14852}, {13509,22120}, {14070,14530}, {14644,18504}, {15047,19709}, {15063,21659}, {15331,17821}, {15690,16936}, {16659,31723}, {16881,17810}, {17702,22802}, {17714,17834}, {17928,18350}, {18405,18567}, {18570,19357}, {19173,19211}, {20299,31283}, {31725,32111}

X(32139) = midpoint of X(i) and X(j) for these lines: {i,j}: {155, 1498}, {5878, 12118}, {7387, 12164}, {7728, 12419}, {12085, 12315}, {12308, 12412}
X(32139) = reflection of X(i) in X(j) for these (i,j): (3, 156), (26, 6759), (64, 11250), (68, 15761), (3357, 12038), (6247, 9820), (7689, 10282), (12084, 1147), (12163, 1658), (12359, 16252), (14216, 13371), (15132, 5609), (16266, 155), (17834, 17714), (18356, 13406), (18381, 5448), (18569, 22660), (32138, 32171), (32140, 5)
X(32139) = X(156)-of-X3-ABC reflections triangle
X(32139) = X(6102)-of-Ara triangle
X(32139) = X(32140)-of-Johnson triangle
X(32139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (399, 11456, 15068), (1614, 12111, 3), (11441, 11456, 3)

X(32140) = X(5)-OF-ANTI-INVERSE-IN-INCIRCLE TRIANGLE

X(32140) lies on these lines: {2,156}, {3,70}, {4,94}, {5,1181}, {20,30522}, {26,1503}, {30,64}, {52,11550}, {66,3564}, {69,10627}, {74,12278}, {110,6640}, {125,10539}, {140,1352}, {154,10020}, {155,1853}, {182,18128}, {185,18474}, {376,2888}, {381,18912}, {388,32143}, {389,11818}, {399,10255}, {427,12161}, {497,32168}, {511,14864}, {539,13346}, {542,1147}, {578,10116}, {631,3410}, {1154,11411}, {1199,5169}, {1204,16003}, {1209,10984}, {1368,31831}, {1370,6101}, {1498,14852}, {1593,12370}, {1594,18445}, {1595,13292}, {1614,6639}, {1656,18911}, {1658,9833}, {1992,32155}, {2072,11441}, {2550,32158}, {3068,32169}, {3069,32170}, {3088,11264}, {3098,17712}, {3357,17702}, {3519,13340}, {3538,11592}, {3546,5921}, {3580,7517}, {3581,31304}, {3618,19155}, {3796,7568}, {3818,5462}, {5448,23325}, {5449,6759}, {5562,14791}, {5576,7592}, {5596,19154}, {5609,15114}, {5654,10224}, {5876,18531}, {5889,31723}, {5946,7528}, {6000,9927}, {6143,9544}, {6146,7526}, {6243,7391}, {6247,12084}, {6515,10263}, {6642,18440}, {6643,11591}, {6644,12134}, {6776,32046}, {6816,15060}, {6997,15026}, {7386,32142}, {7392,32205}, {7401,12006}, {7403,11245}, {7505,10540}, {7506,26879}, {7529,26869}, {7530,16655}, {7564,12233}, {7689,18400}, {7706,13382}, {8144,10071}, {9140,26917}, {9786,31830}, {9820,23332}, {10024,11456}, {10055,32047}, {10095,11433}, {10264,26937}, {10516,15805}, {10620,18565}, {11202,20191}, {11250,12118}, {11424,18488}, {11427,32136}, {11440,12289}, {11488,32207}, {11489,32208}, {11585,15068}, {11695,18553}, {12038,23329}, {12085,12429}, {12106,16010}, {12111,18404}, {12241,31861}, {12290,31725}, {12419,15061}, {13364,18950}, {13367,18580}, {13567,13861}, {13630,18420}, {13754,18381}, {14449,31670}, {16172,20422}, {18383,18568}, {18570,19467}, {18918,22533}, {19139,23300}, {19174,19211}

X(32140) = midpoint of X(i) and X(j) for these lines: {i,j}: {64, 12293}, {68, 14216}, {11411, 14790}, {12085, 12429}
X(32140) = reflection of X(i) in X(j) for these (i,j): (20, 32138), (26, 12359), (68, 18356), (155, 13371), (156, 13561), (1147, 20299), (1498, 15761), (5596, 19154), (5609, 15114), (6759, 5449), (9833, 1658), (12084, 6247), (12118, 11250), (16266, 23335), (18569, 18381), (19139, 23300), (32139, 5)
X(32140) = anticomplement of X(156)
X(32140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (156, 13561, 2), (11442, 11457, 3)

X(32141) = X(5)-OF-ANTI-MANDART-INCIRCLE TRIANGLE

X(32141) lies on these lines: {1,6924}, {3,8}, {4,11849}, {5,55}, {21,5790}, {26,197}, {30,4421}, {35,355}, {40,14988}, {46,24475}, {56,1483}, {119,6284}, {140,1376}, {145,6942}, {149,6949}, {155,7074}, {156,692}, {165,5534}, {200,26921}, {227,32047}, {390,6944}, {404,10246}, {411,12702}, {474,16202}, {495,11501}, {496,11502}, {497,6959}, {499,1484}, {515,26285}, {517,6796}, {519,26286}, {546,11496}, {547,4428}, {550,10310}, {571,21855}, {632,4413}, {912,3579}, {958,7508}, {1001,3628}, {1012,18518}, {1058,6970}, {1385,5836}, {1388,10090}, {1478,14882}, {1482,3871}, {1486,13861}, {1621,1656}, {1771,5399}, {2077,18481}, {2098,10087}, {2886,31659}, {3085,6917}, {3149,10679}, {3158,5709}, {3198,8141}, {3293,5398}, {3295,5901}, {3303,10283}, {3434,6863}, {3560,18357}, {3564,12328}, {3617,6875}, {3740,18233}, {3746,5886}, {3753,24299}, {3913,5844}, {4188,7967}, {4294,6929}, {4302,11698}, {5010,5881}, {5070,5284}, {5082,6954}, {5172,10573}, {5217,22758}, {5218,6862}, {5248,9956}, {5264,5396}, {5281,6824}, {5432,26470}, {5450,26086}, {5541,11014}, {5552,6928}, {5560,5587}, {5693,12738}, {5697,6265}, {5762,6600}, {5763,6985}, {5779,7676}, {5818,7489}, {5840,18242}, {5843,11495}, {5874,11498}, {5875,11497}, {6154,15908}, {6326,11010}, {6756,11383}, {6825,17784}, {6834,20075}, {6868,7080}, {6883,9709}, {6906,18525}, {6915,18493}, {6921,10806}, {6923,10786}, {6934,10528}, {6941,10738}, {6950,26321}, {6958,12116}, {6960,20095}, {6971,27529}, {7491,17757}, {8273,15712}, {9778,16117}, {9897,15446}, {10525,13205}, {10902,26446}, {10944,14793}, {10993,11826}, {11490,32134}, {11492,32146}, {11493,32147}, {11494,32151}, {11503,32177}, {11504,32178}, {11509,18990}, {11510,15325}, {11517,31789}, {11729,26358}, {11848,32162}, {12114,28224}, {12178,12339}, {12255,12535}, {12334,12341}, {12336,22558}, {12337,22557}, {12338,22556}, {12514,31835}, {12515,15071}, {12737,21842}, {12775,18542}, {13887,13925}, {13940,13993}, {14795,18395}, {14798,24914}, {15624,29010}, {16203,16371}, {17522,24808}, {17714,20872}, {18999,19116}, {19000,19117}, {20986,32046}, {21740,25413}, {22457,23981}, {22935,30144}, {24680,25439}

X(32141) = midpoint of X(i) and X(j) for these lines: {i,j}: {3913, 11249}, {5534, 24467}, {6796, 8715}, {6985, 10306}, {11248, 11500}, {12334, 13204}
X(32141) = reflection of X(i) in X(j) for these (i,j): (5450, 26086), (10943, 140), (32153, 3)
X(32141) = X(156)-of-1st circumperp triangle
X(32141) = X(1483)-of-2nd circumperp tangential triangle
X(32141) = X(13561)-of-excentral triangle
X(32141) = X(26286)-of-inner-Garcia triangle
X(32141) = X(32138)-of-2nd circumperp triangle
X(32141) = X(32153)-of-ABC-X3 reflections triangle
X(32141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 5687, 5690), (3, 18526, 104), (100, 11491, 3)

X(32142) = X(5)-OF-6th ANTI-MIXTILINEAR TRIANGLE

X(32142) lies on these lines: {2,143}, {3,74}, {4,11017}, {5,3917}, {6,13154}, {20,15060}, {26,17811}, {30,5447}, {51,13421}, {52,632}, {69,18952}, {95,19211}, {125,21230}, {140,389}, {141,12061}, {182,32136}, {185,15712}, {186,12300}, {323,1493}, {338,25043}, {394,7516}, {511,3628}, {546,10170}, {547,5446}, {548,5907}, {549,5562}, {550,5891}, {568,3525}, {599,15074}, {631,6102}, {1038,32143}, {1040,32168}, {1112,14940}, {1350,13861}, {1368,13561}, {1594,11576}, {1656,2979}, {1657,15056}, {3025,7144}, {3060,5070}, {3091,13340}, {3098,17714}, {3519,15108}, {3522,18435}, {3523,18436}, {3526,5946}, {3528,18439}, {3530,13754}, {3534,15058}, {3548,31807}, {5054,5889}, {5066,13598}, {5449,6698}, {5462,15606}, {5690,31849}, {5888,15037}, {5890,15720}, {5943,14449}, {5965,32165}, {6143,6242}, {6292,11675}, {6636,18350}, {7386,32140}, {7393,11426}, {7484,12161}, {7514,11425}, {7525,9306}, {7568,11064}, {7574,22804}, {8703,12162}, {9729,12108}, {9730,14869}, {10124,11695}, {10203,11702}, {10319,32158}, {10610,22115}, {10691,31831}, {11227,31836}, {11230,31737}, {11231,31738}, {11439,15681}, {11465,13321}, {11511,32155}, {11513,32169}, {11514,32170}, {11515,32207}, {11516,32208}, {11561,14448}, {11573,31835}, {11583,31376}, {12010,12900}, {12100,31834}, {12279,15688}, {12362,30522}, {13347,15083}, {13624,31752}, {14627,23061}, {14831,15713}, {15030,15704}, {15043,15694}, {15088,15465}, {15305,15696}, {15443,24470}, {18379,18531}, {19126,19155}, {26910,26915}, {26911,26914}, {31663,31751}

X(32142) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 11591}, {5, 10627}, {20, 32137}, {140, 1216}, {143, 6101}, {546, 15644}, {548, 5907}, {2979, 13364}, {5447, 11793}, {5462, 15606}, {5562, 13630}, {11573, 31835}, {13624, 31752}, {31663, 31751}
X(32142) = reflection of X(i) in X(j) for these (i,j): (3, 11592), (4, 11017), (143, 32205), (5446, 18874), (5462, 16239), (9729, 12108), (10095, 3628), (12006, 140), (14128, 11793), (16881, 11695), (16982, 10095)
X(32142) = complementary conjugate of X(31376)
X(32142) = anticomplement of X(32205)
X(32142) = complement of X(143)
X(32142) = X(11017)-of-anti-Euler triangle
X(32142) = X(11592)-of-X3-ABC reflections triangle
X(32142) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 143, 32205), (2, 6101, 143), (6101, 15026, 6243)

X(32143) = X(5)-OF-ANTI-TANGENTIAL-MIDARC TRIANGLE

X(32143) lies on these lines: {1,3024}, {3,19367}, {5,1425}, {12,13561}, {26,221}, {33,32137}, {34,143}, {35,32210}, {36,32171}, {55,32138}, {56,156}, {65,32158}, {388,32140}, {1038,32142}, {1060,11591}, {1154,7352}, {1398,12161}, {1428,19155}, {1870,6102}, {2067,32169}, {3585,18379}, {4296,6101}, {5876,18447}, {6502,32170}, {7051,32207}, {7354,30522}, {7355,8144}, {9641,12279}, {9642,12290}, {9817,11017}, {10095,19366}, {13491,18455}, {18915,18952}, {19175,19211}, {19349,32046}, {19365,32136}, {19369,32155}, {19372,32205}, {19373,32208}

X(32143) = midpoint of X(i) and X(j) for these lines: {i,j}: {7352, 32047}, {7355, 8144}
X(32143) = reflection of X(32168) in X(1)
X(32143) = X(156)-of-2nd anti-circumperp-tangential triangle
X(32143) = X(32138)-of-Mandart-incircle triangle
X(32143) = X(32168)-of-5th mixtilinear triangle
X(32143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7352, 32065, 32047), (19367, 19368, 3)

X(32144) = X(5)-OF-AOA TRIANGLE

As a point on the Euler line, X(32144) has Shinagawa coefficients (E-10*F, -3*E-2*F).

X(32144) lies on these lines: {2,3}, {125,13292}, {1147,23332}, {3564,6697}, {5448,6696}, {5663,22967}, {6699,13568}, {6723,10110}, {9820,20299}, {11064,31831}, {11264,15129}, {11801,25487}, {12161,19360}, {13754,32184}, {15113,15114}, {15120,32165}, {15132,15142}, {22660,23329}

X(32144) = midpoint of X(i) and X(j) for these lines: {i,j}: {140, 13371}, {546, 11250}, {548, 18377}, {5448, 6696}, {9820, 20299}, {10224, 23336}, {11801, 25487}, {13383, 23335}, {15114, 15115}
X(32144) = reflection of X(i) in X(j) for these (i,j): (3530, 5498), (10020, 16239), (15330, 11540), (15331, 12108)
X(32144) = complement of X(13383)
X(32144) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 1593, 546), (5, 3548, 140), (140, 546, 6644)

X(32145) = X(5)-OF-ARIES TRIANGLE

X(32145) lies on these lines: {25,32166}, {3564,15580}, {5448,31804}, {6193,12087}, {11206,12420}

X(32145) = midpoint of X(12420) and X(32048)
X(32145) = X(32166)-of-Ara triangle
X(32145) = {X(11206), X(12420)}-harmonic conjugate of X(32048)

X(32146) = X(5)-OF-1st AURIGA TRIANGLE

X(32146) lies on these lines: {3,5601}, {4,11875}, {5,5597}, {26,8190}, {30,9834}, {55,952}, {140,5599}, {145,11876}, {355,8186}, {495,11869}, {496,11871}, {546,8196}, {550,11822}, {1483,5598}, {3564,12415}, {5602,12645}, {5690,8197}, {5844,11253}, {5874,8199}, {5875,8198}, {5901,11366}, {6756,11384}, {8201,32177}, {8202,32178}, {9835,28224}, {10942,11867}, {10943,11865}, {11492,32141}, {11493,32153}, {11837,32134}, {11844,18526}, {11861,32151}, {11863,32162}, {11873,15171}, {11881,32213}, {11883,32214}, {12179,12476}, {12458,28174}, {12474,22668}, {13890,13925}, {13944,13993}, {18955,18990}, {19007,19116}, {19008,19117}

X(32146) = midpoint of X(11253) and X(12454)
X(32146) = reflection of X(32147) in X(55)
X(32146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5597, 8200, 5), (5601, 11843, 3)

X(32147) = X(5)-OF-2nd AURIGA TRIANGLE

X(32147) lies on these lines: {3,5602}, {4,11876}, {5,5598}, {26,8191}, {30,9835}, {55,952}, {140,5600}, {145,11875}, {355,8187}, {495,11870}, {496,11872}, {546,8203}, {550,11823}, {1483,5597}, {5601,12645}, {5690,8204}, {5844,11252}, {5874,8206}, {5875,8205}, {5901,11367}, {6756,11385}, {8208,32177}, {8209,32178}, {9834,28224}, {10942,11868}, {10943,11866}, {11492,32153}, {11493,32141}, {11838,32134}, {11843,18526}, {11862,32151}, {11874,15171}, {11882,32213}, {11884,32214}, {12180,12477}, {12459,28174}, {12475,22672}, {13891,13925}, {13945,13993}, {18956,18990}, {19009,19116}, {19010,19117}

X(32147) = midpoint of X(11252) and X(12455)
X(32147) = reflection of X(32146) in X(55)
X(32147) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5598, 8207, 5), (5602, 11844, 3)

X(32148) = X(5)-OF-AYME TRIANGLE

X(32148) lies on these lines: {5,10}, {612,32167}, {9958,11221}, {10618,30142}

X(32148) = midpoint of X(9958) and X(11259)
X(32148) = {X(9958), X(11221)}-harmonic conjugate of X(11259)

X(32149) = X(5)-OF-1st BROCARD-REFLECTED TRIANGLE

X(32149) lies on these lines: {2,51}, {182,7697}, {538,7606}, {575,3934}, {620,24256}, {2782,10168}, {5969,7619}, {6248,20190}, {6683,8179}, {6704,25555}, {10347,22521}, {14994,15516}, {22681,29012}

X(32149) = midpoint of X(i) and X(j) for these lines: {i,j}: {182, 7697}, {5476, 22712}, {11261, 31958}
X(32149) = complement of X(11261)
X(32149) = {X(2), X(31958)}-harmonic conjugate of X(11261)

X(32150) = X(5)-OF-2nd BROCARD TRIANGLE

X(32150) lies on these lines: {141,31727}, {182,9169}, {353,1352}, {511,31608}, {542,31742}, {3098,14867}, {3818,31731}, {6719,10160}, {7619,9830}, {8705,18583}

X(32150) = midpoint of X(i) and X(j) for these lines: {i,j}: {141, 31727}, {182, 31959}, {3098, 14867}, {3818, 31731}
X(32150) = X(16776)-of-McCay triangle
X(32150) = X(31744)-of-1st Brocard triangle
X(32150) = X(32150)-of-circumsymmedial triangle
X(32150) = {X(10166), X(31959)}-harmonic conjugate of X(182)

X(32151) = X(5)-OF-5th BROCARD TRIANGLE

X(32151) lies on these lines: {3,147}, {4,9301}, {5,32}, {26,10828}, {30,76}, {98,7911}, {140,3096}, {355,3099}, {381,7823}, {495,10038}, {496,10047}, {542,7830}, {546,9993}, {549,3788}, {550,1503}, {626,12042}, {632,7914}, {754,14881}, {952,9941}, {1078,6033}, {1352,2076}, {1483,9997}, {1656,10583}, {2782,7756}, {3094,3564}, {3095,7877}, {3104,9981}, {3398,7859}, {3406,10345}, {3628,7846}, {5690,9857}, {5844,12495}, {5874,9995}, {5875,9994}, {5901,11368}, {6287,12110}, {6655,12188}, {6756,11386}, {7502,15270}, {7575,16335}, {7761,14880}, {7801,8703}, {7831,12054}, {7870,12100}, {7883,14830}, {7915,13335}, {7916,9737}, {8362,10349}, {8782,13108}, {9983,22678}, {9985,12501}, {10346,11842}, {10871,10943}, {10872,10942}, {10875,32177}, {10876,32178}, {10877,15171}, {10878,32213}, {10879,32214}, {11494,32141}, {11861,32146}, {11862,32147}, {11885,32162}, {12497,28174}, {13892,13925}, {13946,13993}, {18957,18990}, {19011,19116}, {19012,19117}, {19780,22907}, {19781,22861}, {22744,32153}

X(32151) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 9863}, {9821, 9873}, {12501, 13210}
X(32151) = X(7823)-of-Ehrmann-mid triangle
X(32151) = X(19130)-of-6th Brocard triangle
X(32151) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2896, 9862, 3), (9301, 18503, 4), (9986, 9987, 3094)

X(32152) = X(5)-OF-6th BROCARD TRIANGLE

X(32152) lies on these lines: {3,114}, {4,1078}, {5,187}, {20,1352}, {30,5188}, {76,23698}, {98,6655}, {115,10104}, {140,7853}, {182,7791}, {194,5965}, {262,7823}, {315,9737}, {376,7883}, {384,24206}, {401,21243}, {491,9738}, {492,9739}, {511,7750}, {542,7833}, {543,13108}, {576,20065}, {631,7899}, {754,3095}, {1353,9607}, {1975,10992}, {2782,7756}, {3398,4045}, {5025,6036}, {6055,7841}, {6200,6290}, {6249,8150}, {6289,6396}, {6656,13335}, {6721,7907}, {6781,9996}, {7616,17578}, {7737,10358}, {7746,23514}, {7753,11272}, {7763,9734}, {7787,25555}, {7811,12251}, {7828,21445}, {7829,11842}, {7836,21166}, {7842,15980}, {7873,18860}, {7904,22712}, {8356,13334}, {10131,32135}, {10991,14880}, {11293,12975}, {11294,12974}, {12110,14712}

X(32152) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 7802}, {20, 9873}, {9863, 11257}
X(32152) = reflection of X(i) in X(j) for these (i,j): (3, 7830), (7747, 5)
X(32152) = inverse of X(19165) in the 2nd Brocard circle
X(32152) = X(7747)-of-Johnson triangle
X(32152) = X(7802)-of-Euler triangle
X(32152) = X(7830)-of-X3-ABC reflections triangle
X(32152) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 14907, 5171), (7833, 9863, 11257)

X(32153) = X(5)-OF-2nd CIRCUMPERP TANGENTIAL TRIANGLE

X(32153) lies on these lines: {1,1399}, {3,8}, {4,20067}, {5,56}, {21,10246}, {26,22654}, {30,10525}, {36,355}, {55,1483}, {119,5433}, {140,958}, {145,6950}, {153,6949}, {388,6862}, {392,24927}, {404,5790}, {405,16203}, {495,22759}, {496,22760}, {515,26286}, {517,5450}, {519,26285}, {546,18761}, {550,3428}, {912,960}, {997,31835}, {999,3485}, {1001,5843}, {1012,10680}, {1056,6892}, {1319,5887}, {1329,6713}, {1388,10074}, {1420,7330}, {1455,32047}, {1479,1484}, {1482,6906}, {1656,5253}, {1768,11014}, {2077,5288}, {2098,10058}, {3086,6929}, {3149,18519}, {3304,10283}, {3421,6961}, {3436,6958}, {3526,5260}, {3564,22595}, {3600,6824}, {3616,7489}, {3628,25524}, {3655,10902}, {3813,5840}, {3878,11715}, {4189,7967}, {4293,6917}, {4861,25413}, {5080,6971}, {5126,5777}, {5204,11499}, {5248,15178}, {5251,24954}, {5258,26446}, {5265,6944}, {5267,5882}, {5445,12751}, {5534,7987}, {5563,5886}, {5584,8703}, {5603,13743}, {5693,6265}, {5697,12737}, {5714,6913}, {5779,7677}, {5816,21773}, {5844,11248}, {5874,22757}, {5875,22756}, {5881,7280}, {5885,30147}, {6256,22775}, {6264,11010}, {6756,22479}, {6796,28204}, {6833,20076}, {6863,12115}, {6905,18525}, {6909,12702}, {6910,10805}, {6911,18357}, {6912,18493}, {6923,10527}, {6928,10785}, {6930,14986}, {6938,10529}, {6941,10742}, {6942,18524}, {6952,20060}, {6959,7288}, {6974,10597}, {6976,10586}, {6985,28186}, {7354,26470}, {7508,10267}, {8715,26086}, {10950,14793}, {10966,15171}, {11012,18481}, {11279,15175}, {11492,32147}, {11493,32146}, {11500,28224}, {11928,22938}, {12001,28444}, {13925,22763}, {13993,22764}, {14806,21855}, {16150,21669}, {16202,16370}, {19013,19116}, {19014,19117}, {19478,22586}, {21031,21154}, {22504,22780}, {22520,32134}, {22680,22779}, {22744,32151}, {22755,32162}, {22761,32177}, {22762,32178}, {22768,32213}, {22770,28174}, {22771,22773}, {22772,22774}, {22836,26287}, {23961,25440}

X(32153) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 24467}, {5450, 8666}, {11248, 12513}, {11249, 12114}, {19478, 22586}
X(32153) = reflection of X(i) in X(j) for these (i,j): (8715, 26086), (10942, 140), (22836, 26287), (32141, 3)
X(32153) = X(156)-of-2nd circumperp triangle
X(32153) = X(1483)-of-anti-Mandart-incircle triangle
X(32153) = X(13561)-of-hexyl triangle
X(32153) = X(24467)-of-anti-Aquila triangle
X(32153) = X(26285)-of-inner-Garcia triangle
X(32153) = X(32138)-of-1st circumperp triangle
X(32153) = X(32141)-of-ABC-X3 reflections triangle
X(32153) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 12773, 944), (3, 18526, 11491), (104, 2975, 3)

X(32154) = X(5)-OF-1st EHRMANN TRIANGLE

X(32154) lies on these lines: {2,67}, {3,9019}, {6,5888}, {23,16776}, {30,25488}, {140,524}, {141,3292}, {182,1511}, {187,30489}, {576,6101}, {597,13857}, {599,11422}, {1995,19127}, {2393,20190}, {2930,5012}, {3589,5159}, {5092,8705}, {5609,11178}, {7492,9971}, {7495,8262}, {7496,10510}, {7509,11477}, {7708,28662}, {7804,11594}, {8547,12017}, {9716,21356}, {10272,24206}, {10541,17928}, {11179,23236}, {12041,25489}, {13366,22165}, {16042,18374}

X(32154) = midpoint of X(i) and X(j) for these lines: {i,j}: {5092, 12039}, {8542, 8546}, {12041, 25489}
X(32154) = reflection of X(20113) in X(3589)
X(32154) = {X(182), X(8542)}-harmonic conjugate of X(8546)

X(32155) = X(5)-OF-2nd EHRMANN TRIANGLE

X(32155) lies on these lines: {3,11443}, {5,21639}, {6,156}, {26,17813}, {143,8541}, {511,32210}, {524,13561}, {542,18379}, {575,32171}, {576,5663}, {895,15132}, {1154,8548}, {1353,11264}, {1493,15531}, {1992,32140}, {5876,18449}, {6101,11416}, {6102,8537}, {8538,11591}, {8539,32158}, {8540,32168}, {8550,30522}, {9813,32205}, {10250,11250}, {10602,32046}, {11405,12161}, {11470,32137}, {11477,32138}, {11482,32139}, {11511,32142}, {13371,23326}, {18377,23048}, {18919,18952}, {19178,19211}, {19369,32143}

X(32155) = midpoint of X(i) and X(j) for these lines: {i,j}: {8548, 11255}, {11477, 32138}
X(32155) = reflection of X(i) in X(j) for these (i,j): (19155, 6), (32171, 575)
X(32155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8548, 11216, 11255), (11443, 11458, 3)

X(32156) = X(5)-OF-5th EULER TRIANGLE

X(32156) lies on these lines: {2,31744}, {3,6032}, {5,9172}, {30,31749}, {140,3849}, {381,31824}, {517,31755}, {549,31729}, {575,20379}, {632,10163}, {1154,31753}, {1656,12505}, {3525,6031}, {3526,9829}, {3628,10173}, {5055,31961}, {5946,31745}, {8704,11272}, {11230,31747}, {11231,31746}, {15060,31743}, {15067,31736}, {30516,31727}

X(32156) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 31840}, {5, 12506}, {15060, 31743}, {31749, 31762}, {31753, 31763}, {31755, 31758}
X(32156) = reflection of X(31606) in X(3628)
X(32156) = complement of X(31744)
X(32156) = X(31824)-of-Ehrmann-mid triangle
X(32156) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (10162, 12506, 5), (10173, 31606, 3628)

X(32157) = X(5)-OF-EXCENTERS-MIDPOINTS TRIANGLE

X(32157) lies on these lines: {2,13463}, {8,4421}, {10,528}, {21,13205}, {35,1145}, {40,12607}, {55,5554}, {100,32198}, {140,2802}, {165,32049}, {518,31787}, {519,12100}, {529,3579}, {549,22837}, {631,10912}, {952,26086}, {1329,5119}, {1376,27870}, {1385,5854}, {1697,3816}, {1698,3829}, {1706,3826}, {2136,9588}, {3035,3057}, {3036,10572}, {3058,25005}, {3654,3811}, {3679,5441}, {3813,26446}, {3880,6684}, {3885,5433}, {3895,24914}, {3913,5657}, {4640,6736}, {4642,17061}, {4861,13996}, {4999,10914}, {5086,6154}, {5123,10624}, {5176,15338}, {5204,12648}, {5221,11239}, {5250,9711}, {5428,5690}, {5541,24390}, {5559,15015}, {5836,6690}, {5855,11362}, {6361,11236}, {6667,12053}, {6691,9957}, {6940,22560}, {9780,11235}, {10107,13405}, {10164,11260}, {11010,17757}, {15813,26357}, {30337,31190}

X(32157) = midpoint of X(i) and X(j) for these lines: {i,j}: {40, 12607}, {100, 32198}, {3579, 10915}, {5690, 8715}, {11260, 12640}
X(32157) = complement of X(13463)
X(32157) = X(6247)-of-K798i triangle
X(32157) = X(32184)-of-excentral triangle
X(32157) = {X(10164), X(12640)}-harmonic conjugate of X(11260)

X(32158) = X(5)-OF-EXTANGENTS TRIANGLE

X(32158) lies on these lines: {3,11445}, {5,3611}, {19,143}, {26,3197}, {40,2940}, {55,156}, {65,32143}, {1154,6237}, {2550,32140}, {3101,6101}, {3925,13561}, {5415,32169}, {5416,32170}, {5584,32138}, {5876,18453}, {6102,6197}, {6243,9536}, {6253,30522}, {7688,32210}, {8251,11591}, {8539,32155}, {9537,18436}, {9816,32205}, {10095,11435}, {10306,32139}, {10319,32142}, {10636,32207}, {10637,32208}, {10902,32171}, {11406,12161}, {11428,32136}, {11471,32137}, {18379,18406}, {18921,18952}, {19133,19155}, {19181,19211}, {19350,32046}

X(32158) = reflection of X(32168) in X(156)
X(32158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6237, 11190, 8141), (11445, 11460, 3)

X(32159) = X(5)-OF-EXTOUCH TRIANGLE

X(32159) lies on these lines: {2,18260}, {40,17615}, {72,6256}, {210,1158}, {515,960}, {518,12608}, {912,18242}, {956,6261}, {971,6796}, {2829,31837}, {3697,17649}, {3740,18238}, {3820,12616}, {3916,17661}, {4662,5690}, {5044,5450}, {5570,6941}, {5657,12666}, {6245,15064}, {12675,15325}

X(32159) = midpoint of X(i) and X(j) for these lines: {i,j}: {72, 6256}, {1158, 18239}, {6261, 14872}
X(32159) = reflection of X(5450) in X(5044)
X(32159) = anticomplement of X(18260)
X(32159) = {X(210), X(18239)}-harmonic conjugate of X(1158)

X(32160) = X(5)-OF-3rd EXTOUCH TRIANGLE

X(32160) lies on these lines: {5909,6684}, {11212,11254}

X(32160) = midpoint of X(11254) and X(31965)
X(32160) = {X(11212), X(31965)}-harmonic conjugate of X(11254)

X(32161) = X(5)-OF-FEUERBACH TRIANGLE

X(32161) lies on these lines: {5,5947}, {11,10281}, {30,31750}, {517,31756}, {952,10277}, {1154,31754}, {5499,10209}, {7951,10208}

X(32161) = midpoint of X(i) and X(j) for these lines: {i,j}: {5, 5948}, {5499, 10209}, {31750, 31764}, {31754, 31765}, {31756, 31759}
X(32161) = complement of X(5) wrt Feuerbach triangle
X(32161) = {X(5947), X(5948)}-harmonic conjugate of X(5)

X(32162) = X(5)-OF-GOSSARD TRIANGLE

As a point on the Euler line, X(32162) has Shinagawa coefficients (11EF-34F²-2S²,3EF+30F²-2S²).

X(32162) lies on these lines: {2,3}, {355,11852}, {495,11905}, {496,11906}, {523,7740}, {952,12438}, {1482,16212}, {1483,11910}, {1511,9033}, {3564,12418}, {5690,11900}, {5844,12626}, {5874,11902}, {5875,11901}, {5901,11831}, {10942,11904}, {10943,11903}, {11839,32134}, {11848,32141}, {11885,32151}, {11907,32177}, {11908,32178}, {11914,32213}, {11915,32214}, {12181,12795}, {12696,28174}, {12790,12797}, {12792,22897}, {12793,22852}, {12794,22698}, {13894,13925}, {13948,13993}, {18958,18990}, {19017,19116}, {19018,19117}, {22755,32153}

X(32162) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 20128}, {3, 4240}, {4, 18508}, {402, 15774}, {11251, 12113}, {12790, 13212}
X(32162) = reflection of X(i) in X(j) for these (i,j): (5, 402), (1650, 140), (18507, 546)
X(32162) = X(18508)-of-Euler triangle
X(32162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1651, 12113, 11251), (11897, 18507, 546), (11911, 18508, 4)

X(32163) = X(5)-OF-3rd HATZIPOLAKIS TRIANGLE

X(32163) lies on the line {31985,32050}

X(32163) = midpoint of X(31985) and X(32050)
X(32163) = {X(31985), X(32068)}-harmonic conjugate of X(32050)

X(32164) = X(5)-OF-HUTSON EXTOUCH TRIANGLE

X(32164) lies on these lines: {5918,31968}, {10167,12731}

X(32164) = midpoint of X(31968) and X(32051)
X(32164) = {X(5918), X(31968)}-harmonic conjugate of X(32051)

X(32165) = X(5)-OF-1st HYACINTH TRIANGLE

X(32165) lies on these lines: {5,1199}, {6,18356}, {30,52}, {54,140}, {125,1493}, {143,10116}, {184,18282}, {265,546}, {389,6153}, {397,11600}, {539,12006}, {542,10095}, {575,3564}, {1154,27552}, {1353,13371}, {1594,2914}, {1614,25338}, {1658,18925}, {1885,7722}, {1994,15002}, {2888,15037}, {3448,14627}, {3850,18388}, {3861,18379}, {5663,19481}, {5965,32142}, {6515,7525}, {6748,15557}, {6776,17714}, {8254,13366}, {10112,13630}, {10224,12161}, {11250,18913}, {11536,25328}, {11745,16881}, {11801,25402}, {11898,13154}, {12107,31804}, {12134,13163}, {12899,13367}, {13391,18128}, {13392,16238}, {15114,15130}, {15120,32144}, {15330,19357}, {16982,29012}, {20424,25739}, {22249,32171}, {32068,32205}

X(32165) = midpoint of X(i) and X(j) for these lines: {i,j}: {143, 10116}, {389, 11264}, {10112, 13630}, {10114, 13358}
X(32165) = reflection of X(12134) in X(13163)
X(32165) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (10116, 11225, 143), (13353, 21230, 140)

X(32166) = X(5)-OF-2nd HYACINTH TRIANGLE

X(32166) lies on these lines: {25,32145}, {68,7592}, {575,3564}, {1147,11245}, {6776,32048}, {10116,12235}, {11264,13630}, {11433,12420}, {12241,13292}, {17702,18914}, {18951,19908}

X(32166) = midpoint of X(i) and X(j) for these lines: {i,j}: {1147, 12421}, {10116, 12235}
X(32166) = X(32145)-of-anti-Ara triangle
X(32166) = {X(11245), X(12421)}-harmonic conjugate of X(1147)

X(32167) = X(5)-OF-INCENTRAL TRIANGLE

Let L_A be the trilinear polar of A wrt BCX(1), and define L_B and L_C cyclically. Let L_I be the trilinear polar of X(1) wrt ABC (the antiorthic axis). Then X(32167) = QL-P11 (Nine-point Center QL-Diagonal Triangle) of quadrilateral L_AL_BL_CL_I. (Randy Hutson, June 7, 2019)

X(32167) lies on these lines: {1,3}, {81,22937}, {500,1962}, {612,32148}, {2771,3743}, {9955,15569}, {11230,24936}, {11231,24883}

X(32167) = midpoint of X(i) and X(j) for these lines: {i,j}: {500, 8143}, {3743, 5453}
X(32167) = reflection of X(1) in X(10618)
X(32167) = X(10618)-of-Aquila triangle
X(32167) = X(15557)-of-excentral triangle
X(32167) = {X(500), X(1962)}-harmonic conjugate of X(8143)
X(32167) = centroid of X(11)X(214)X(500)X(4065)
X(32167) = centroid of X(500) and the vertices of the incentral triangle
X(32167) = QA-P13 (Nine-point Center of the QA-Diagonal Triangle) of quadrangle ABCX(1)

X(32168) = X(5)-OF-INTANGENTS TRIANGLE

X(32168) lies on these lines: {1,3024}, {3,11446}, {5,3270}, {11,13561}, {26,2192}, {33,143}, {34,32137}, {35,32171}, {36,32210}, {55,156}, {56,32138}, {497,32140}, {1040,32142}, {1062,11591}, {1154,6238}, {1250,32208}, {2066,32169}, {2330,19155}, {3100,6101}, {3295,32139}, {3583,18379}, {5414,32170}, {5876,18455}, {5889,9642}, {5944,9638}, {6102,6198}, {6243,9539}, {6284,30522}, {6285,32047}, {7071,12161}, {8540,32155}, {9538,18436}, {9641,11412}, {9817,32205}, {10095,11436}, {10638,32207}, {11017,19372}, {11429,32136}, {13491,18447}, {18922,18952}, {19182,19211}

X(32168) = midpoint of X(i) and X(j) for these lines: {i,j}: {6238, 8144}, {6285, 32047}
X(32168) = reflection of X(32158) in X(156)
X(32168) = X(156)-of-Mandart-incircle triangle
X(32168) = X(32138)-of-2nd anti-circumperp-tangential triangle
X(32168) = X(32143)-of-5th mixtilinear triangle
X(32168) = reflection of X(32143) in X(1)
X(32168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6238, 11189, 8144), (11446, 11461, 3)

X(32169) = X(5)-OF-1st KENMOTU DIAGONALS TRIANGLE

X(32169) lies on these lines: {3,11447}, {5,21640}, {6,156}, {26,17819}, {143,5412}, {371,5663}, {372,32171}, {590,13561}, {1151,32138}, {1154,10665}, {2066,32168}, {2067,32143}, {3068,32140}, {3070,30522}, {3311,32139}, {5410,12161}, {5415,32158}, {5876,18457}, {5944,18459}, {6101,11417}, {6102,10880}, {6200,32210}, {6564,18379}, {10201,19061}, {10533,11266}, {10897,11591}, {10961,32205}, {11473,32137}, {11513,32142}, {13909,18356}, {18923,18952}, {19183,19211}, {19355,32046}

X(32169) = midpoint of X(10665) and X(11265)
X(32169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 156, 32170), (11447, 11462, 3)

X(32170) = X(5)-OF-2nd KENMOTU DIAGONALS TRIANGLE

X(32170) lies on these lines: {3,11448}, {5,21641}, {6,156}, {26,17820}, {143,5413}, {371,32171}, {372,5663}, {615,13561}, {1152,32138}, {1154,10666}, {3069,32140}, {3071,30522}, {3312,32139}, {5411,12161}, {5414,32168}, {5416,32158}, {5876,18459}, {5944,18457}, {6101,11418}, {6102,10881}, {6396,32210}, {6502,32143}, {6565,18379}, {10201,19062}, {10534,11265}, {10898,11591}, {10963,32205}, {11474,32137}, {11514,32142}, {13970,18356}, {18924,18952}, {19184,19211}, {19356,32046}

X(32170) = midpoint of X(10666) and X(11266)
X(32170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 156, 32169), (11448, 11463, 3)

X(32171) = X(5)-OF-KOSNITA TRIANGLE

Let N_AN_BN_C be the reflection triangle of X(5). Let O_A be the circumcenter of AN_BN_C, and define O_B and O_C cyclically; then X(32171) is the circumcenter of O_AO_BO_C. (Randy Hutson, June 7, 2019)

X(32171) lies on these lines: {2,6288}, {3,74}, {4,16665}, {5,13367}, {15,32208}, {16,32207}, {24,143}, {26,13391}, {30,5448}, {35,32168}, {36,32143}, {49,186}, {52,7575}, {54,5946}, {140,13561}, {154,12084}, {155,18324}, {184,13630}, {185,15646}, {265,14940}, {371,32170}, {372,32169}, {376,18442}, {378,32137}, {382,26882}, {389,32136}, {468,12370}, {511,12107}, {539,15330}, {542,20191}, {546,11430}, {567,15026}, {568,1493}, {569,9827}, {575,32155}, {578,10095}, {631,3410}, {1092,7502}, {1147,1154}, {1495,3627}, {1503,23336}, {1657,26881}, {2070,10263}, {3090,14805}, {3091,3431}, {3515,12161}, {3520,10540}, {5020,12046}, {5072,10546}, {5092,12108}, {5449,10125}, {5498,20299}, {5889,9703}, {5890,9704}, {6000,10226}, {6101,7488}, {6642,32205}, {6644,12006}, {6759,11250}, {7506,13364}, {7555,15644}, {7712,17538}, {9306,14128}, {9544,21844}, {9706,15087}, {9818,11017}, {9833,18281}, {10113,16868}, {10192,15761}, {10193,10212}, {10201,12118}, {10224,18400}, {10254,12278}, {10255,12289}, {10264,17701}, {10298,18436}, {10539,18570}, {10564,15704}, {10902,32158}, {11425,13861}, {13163,19130}, {13346,17714}, {13406,17702}, {13754,15331}, {14070,16266}, {15060,18350}, {15074,15462}, {15088,18396}, {15647,22802}, {15712,22352}, {15806,18388}, {16223,21660}, {18925,18952}, {19154,23041}, {19185,19211}, {19479,20773}, {22249,32165}, {23292,31830}

X(32171) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 156}, {1147, 1658}, {6759, 11250}, {10282, 12038}, {13346, 17714}, {15647, 25487}, {32138, 32139}
X(32171) = reflection of X(i) in X(j) for these (i,j): (5449, 10125), (13561, 140), (18379, 5), (20299, 5498), (32155, 575), (32210, 3)
X(32171) = X(18379)-of-Johnson triangle
X(32171) = X(32210)-of-ABC-X3 reflections triangle
X(32171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 399, 11440), (3, 1614, 13491), (3, 32139, 32138)

X(32172) = X(5)-OF-LEMOINE TRIANGLE

X(32172) lies on these lines: {5397,8523}, {8145,31969}

X(32172) = midpoint of X(8145) and X(31969)
X(32172) = {X(31969), X(32069)}-harmonic conjugate of X(8145)

X(32173) = X(5)-OF-LUCAS ANTIPODAL TRIANGLE

X(32173) lies on the line {31970,32052}

X(32173) = midpoint of X(31970) and X(32052)

X(32174) = X(5)-OF-LUCAS(-1) ANTIPODAL TRIANGLE

X(32174) lies on the line {31971,32053}

X(32174) = midpoint of X(31971) and X(32053)

X(32175) = X(5)-OF-LUCAS CENTRAL TRIANGLE

X(32175) lies on these lines: {1151,7598}, {8155,11198}

X(32175) = midpoint of X(8155) and X(31972)
X(32175) = {X(11198), X(31972)}-harmonic conjugate of X(8155)

X(32176) = X(5)-OF-LUCAS(-1) CENTRAL TRIANGLE

X(32176) lies on these lines: {1152,7599}, {8156,31973}

X(32176) = midpoint of X(8156) and X(31973)
X(32176) = {X(31973), X(32077)}-harmonic conjugate of X(8156)

X(32177) = X(5)-OF-LUCAS HOMOTHETIC TRIANGLE

X(32177) lies on these lines: {3,6462}, {4,11949}, {5,493}, {26,8194}, {30,9838}, {140,8222}, {355,8188}, {495,11930}, {496,11932}, {546,8212}, {550,11828}, {952,12440}, {1483,8210}, {3564,12426}, {5690,8214}, {5844,12636}, {5874,8218}, {5875,8216}, {5901,11377}, {6461,32178}, {6756,11394}, {8201,32146}, {8208,32147}, {10875,32151}, {10942,10951}, {10943,10945}, {11503,32141}, {11840,32134}, {11907,32162}, {11947,15171}, {11955,32213}, {11957,32214}, {12186,12994}, {12894,12998}, {12988,22908}, {12990,22863}, {12992,22709}, {13899,13925}, {13956,13993}, {18963,18990}, {19031,19116}, {19032,19117}, {22761,32153}, {22841,28174}

X(32177) = midpoint of X(i) and X(j) for these lines: {i,j}: {9838, 10669}, {12894, 13215}
X(32177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (493, 8220, 5), (6462, 11846, 3)

X(32178) = X(5)-OF-LUCAS(-1) HOMOTHETIC TRIANGLE

X(32178) lies on these lines: {3,6463}, {4,11950}, {5,494}, {26,8195}, {30,9839}, {140,8223}, {355,8189}, {495,11931}, {496,11933}, {546,8213}, {550,11829}, {952,12441}, {1483,8211}, {3564,12427}, {5690,8215}, {5844,12637}, {5874,8219}, {5875,8217}, {5901,11378}, {6461,32177}, {6756,11395}, {8202,32146}, {8209,32147}, {10876,32151}, {10942,10952}, {10943,10946}, {11504,32141}, {11841,32134}, {11908,32162}, {11948,15171}, {11956,32213}, {11958,32214}, {12187,12995}, {12895,12999}, {12989,22909}, {12991,22864}, {12993,22710}, {13900,13925}, {13957,13993}, {18964,18990}, {19033,19116}, {19034,19117}, {22762,32153}, {22842,28174}

X(32178) = midpoint of X(i) and X(j) for these lines: {i,j}: {9839, 10673}, {12895, 13216}
X(32178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (494, 8221, 5), (6463, 11847, 3)

X(32179) = X(5)-OF-LUCAS TANGENTS TRIANGLE

X(32179) lies on the line {1151,8155}

X(32179) = midpoint of X(1151) and X(31974)
X(32179) = {X(11199), X(31974)}-harmonic conjugate of X(1151)

X(32180) = X(5)-OF-LUCAS(-1) TANGENTS TRIANGLE

X(32180) lies on these lines: {1152,8156}, {6398,31973}

X(32180) = midpoint of X(1152) and X(31975)
X(32180) = {X(31975), X(32074)}-harmonic conjugate of X(1152)

X(32181) = X(5)-OF-MACBEATH TRIANGLE

X(32181) lies on these lines: {5,10274}, {5576,14674}, {8146,11197}

X(32181) = midpoint of X(8146) and X(31976)
X(32181) = {X(11197), X(31976)}-harmonic conjugate of X(8146)

X(32182) = X(5)-OF-MANDART-EXCIRCLES TRIANGLE

X(32182) lies on these lines: {4338,12659}, {11246,31977}

X(32182) = midpoint of X(31977) and X(32054)
X(32182) = {X(11246), X(31977)}-harmonic conjugate of X(32054)

X(32183) = X(5)-OF-2nd MIDARC TRIANGLE

X(32183) lies on these lines: {1,167}, {3,31800}, {30,31734}, {164,31393}, {495,12614}, {496,12622}, {517,5571}, {519,18258}, {999,12518}, {1317,10501}, {1385,31790}, {3241,11691}, {3488,12694}, {5045,31768}, {5882,8100}, {5919,17641}, {8094,10968}, {11040,11528}, {12443,24929}, {15172,31769}, {31766,31792}

X(32183) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 8422}, {5571, 31767}, {31734, 31770}
X(32183) = reflection of X(i) in X(j) for these (i,j): (5571, 31796), (12908, 1), (31766, 31792), (31768, 5045), (31769, 15172), (31790, 1385), (31800, 3)
X(32183) = inverse of X(30423) in the incircle
X(32183) = X(40)-of-incircle-circles triangle
X(32183) = X(942)-of-2nd tangential-midarc triangle
X(32183) = X(1385)-of-Hutson intouch triangle
X(32183) = X(1902)-of-2nd circumperp triangle
X(32183) = X(8422)-of-anti-Aquila triangle
X(32183) = X(9955)-of-Ursa-minor triangle
X(32183) = X(12699)-of-inverse-in-incircle triangle
X(32183) = X(12908)-of-5th mixtilinear triangle
X(32183) = X(31800)-of-ABC-X3 reflections triangle
X(32183) = {X(8422), X(11234)}-harmonic conjugate of X(1)

X(32184) = X(5)-OF-MIDHEIGHT TRIANGLE

X(32184) lies on these lines: {3,9972}, {5,22800}, {51,5894}, {52,23328}, {64,15043}, {185,23332}, {389,2781}, {974,1594}, {1154,25563}, {1192,10249}, {1498,15045}, {1503,9729}, {1620,6403}, {1853,10574}, {1885,11746}, {2393,17704}, {2777,10095}, {3060,8567}, {3091,7729}, {3357,5946}, {3567,10606}, {3574,23315}, {3850,6000}, {5462,15311}, {5640,5895}, {5890,12300}, {5892,16252}, {5893,5943}, {5925,9781}, {6102,23329}, {6247,7403}, {6746,21663}, {8991,12240}, {9786,32191}, {10193,10627}, {10263,11204}, {10575,23324}, {10628,30531}, {11598,14865}, {12239,13980}, {13358,25564}, {13491,23325}, {13630,20299}, {13754,32144}, {14644,22948}, {15026,22802}, {17845,20791}, {18381,22804}

X(32184) = midpoint of X(i) and X(j) for these lines: {i,j}: {389, 6696}, {5893, 31978}, {13358, 25564}, {13630, 20299}
X(32184) = {X(5943), X(31978)}-harmonic conjugate of X(5893)

X(32185) = X(5)-OF-MIXTILINEAR TRIANGLE

X(32185) lies on these lines: {1,32186}, {7961,8147}

X(32185) = midpoint of X(7961) and X(8147)
X(32185) = {X(7961), X(11200)}-harmonic conjugate of X(8147)

X(32186) = X(5)-OF-2nd MIXTILINEAR TRIANGLE

X(32186) lies on these lines: {1,32185}, {7960,8159}

X(32186) = midpoint of X(7960) and X(8159)
X(32186) = {X(7960), X(11201)}-harmonic conjugate of X(8159)

X(32187) = X(5)-OF-3rd MIXTILINEAR TRIANGLE

X(32187) lies on the line {3,31979}

X(32187) = midpoint of X(3) and X(31979)
X(32187) = {X(31979), X(32075)}-harmonic conjugate of X(3)

X(32188) = X(5)-OF-4th MIXTILINEAR TRIANGLE

X(32188) lies on the line {3,31980}

X(32188) = midpoint of X(3) and X(31980)
X(32188) = X(31744)-of-1st circumperp triangle
X(32188) = X(32156)-of-excentral triangle
X(32188) = {X(31980), X(32076)}-harmonic conjugate of X(3)

X(32189) = X(5)-OF-1st NEUBERG TRIANGLE

X(32189) lies on these lines: {2,39}, {3,8150}, {5,736}, {140,698}, {230,18806}, {262,7759}, {511,7780}, {626,2023}, {732,7764}, {754,14881}, {1078,1916}, {2021,7816}, {3094,7815}, {3095,7751}, {3202,3506}, {5976,7749}, {6680,24256}, {7752,9983}, {7775,10356}, {7781,11171}, {7804,13357}, {7895,14994}, {9462,18573}, {9862,18769}, {10357,13086}

X(32189) = midpoint of X(i) and X(j) for these lines: {i,j}: {3095, 7751}, {8149, 31981}
X(32189) = reflection of X(7764) in X(11272)
X(32189) = complement of X(8149)
X(32189) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 31981, 8149), (76, 7746, 3934), (76, 7786, 7836)

X(32190) = X(5)-OF-2nd NEUBERG TRIANGLE

X(32190) lies on these lines: {2,32}, {39,9478}, {114,6287}, {732,7764}, {3788,24273}, {5031,6683}, {7697,8149}, {7769,8290}, {7771,9990}, {8177,25555}

X(32190) = midpoint of X(i) and X(j) for these lines: {i,j}: {2896, 18548}, {7775, 13086}, {8150, 31982}
X(32190) = complement of X(8150)
X(32190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 31982, 8150), (1506, 6292, 83), (9765, 31268, 6308)

X(32191) = X(5)-OF-1st ORTHOSYMMEDIAL TRIANGLE

X(32191) lies on these lines: {4,15321}, {6,24}, {51,125}, {52,141}, {140,143}, {159,11432}, {182,5946}, {251,19165}, {389,1503}, {518,31760}, {524,10127}, {542,13358}, {568,1352}, {575,12107}, {576,22828}, {597,9967}, {1154,24206}, {1350,3060}, {1351,13321}, {1353,2854}, {1843,6746}, {2393,12007}, {3098,10263}, {3564,16881}, {3763,11412}, {3818,6102}, {5050,17710}, {5085,15043}, {5092,12006}, {5097,14984}, {5446,29181}, {5449,10095}, {5889,10516}, {5900,22336}, {5943,11548}, {6467,12061}, {6593,16222}, {6776,9971}, {7592,20987}, {7716,15581}, {9786,32184}, {9822,16625}, {9973,14912}, {10110,16198}, {10625,21167}, {10691,21849}, {11002,16063}, {11438,15578}, {11649,15516}, {13391,14810}, {13630,29012}, {16224,28343}, {17810,19149}, {20391,21851}

X(32191) = midpoint of X(i) and X(j) for these lines: {i,j}: {52, 141}, {389, 9969}, {568, 16776}, {1843, 8550}, {3098, 10263}, {3818, 6102}, {5462, 21852}, {5480, 19161}, {6467, 12061}, {9822, 16625}
X(32191) = reflection of X(i) in X(j) for these (i,j): (3589, 5462), (5092, 12006), (19130, 10095)
X(32191) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (51, 19161, 5480), (5480, 13567, 20300)

X(32192) = X(5)-OF-2nd ORTHOSYMMEDIAL TRIANGLE

X(32192) lies on these lines: {182,7575}, {2781,31771}, {5480,11226}

X(32192) = midpoint of X(5480) and X(31983)
X(32192) = X(31744)-of-1st orthosymmedial triangle
X(32192) = {X(11226), X(31983)}-harmonic conjugate of X(5480)

X(32193) = X(5)-OF-2nd PARRY TRIANGLE

Let A'B'C' and A"B"C" be the cevian and anticevian triangles of X(6), resp. Let (O_A) be the cevian circle of A". Let A* be the intersection, other than A', of (O_A) and line BC. Define B* and C* cyclically. X(32193) is the centroid of triangle A*B*C*. (Randy Hutson, August 10, 2020)

X(32193) lies on these lines: {2,9479}, {111,9076}, {351,523}, {525,9208}, {526,14697}, {690,5461}, {804,1637}, {826,4142}, {900,9811}, {2450,3566}, {2799,10190}, {3124,7668}, {3800,5027}, {4977,9810}, {8029,9147}, {8704,32194}, {9007,13303}, {9138,13291}, {9148,10189}, {9189,14417}, {9200,22889}, {9201,22934}, {9512,20998}, {10276,14698}, {13250,28221}, {13251,28217}, {13307,22734}, {14272,14977}

X(32193) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 14420}, {351, 9979}, {8029, 9147}, {9138, 13291}, {14272, 14977}
X(32193) = reflection of X(i) in X(j) for these (i,j): (9148, 10189), (10190, 11176), (10278, 1637), (14610, 351)
X(32193) = complement of X(14424)
X(32193) = X(550)-of-1st Parry triangle
X(32193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (9185, 9979, 351), (13319, 13320, 3569)

X(32194) = X(5)-OF-3rd PARRY TRIANGLE

X(32194) lies on these lines: {351,31986}, {523,31772}, {8704,32193}

X(32194) = midpoint of X(i) and X(j) for these lines: {i,j}: {351, 31986}, {31772, 31773}
X(32194) = {X(31986), X(11215)}-harmonic conjugate of X(351)

X(32195) = X(5)-OF-PELLETIER TRIANGLE

X(32195) lies on these lines: {1,11193}, {513,5045}, {521,3813}, {650,3746}, {676,2775}, {885,1058}, {946,3309}, {2646,11934}, {3900,5044}, {5550,30613}, {6198,18344}, {8760,15178}, {9957,14077}

X(32195) = midpoint of X(1) and X(11247)
X(32195) = X(8151)-of-incircle-circles triangle
X(32195) = X(10280)-of-Ursa-minor triangle
X(32195) = X(11247)-of-anti-Aquila triangle
X(32195) = {X(1), X(11193)}-harmonic conjugate of X(11247)

X(32196) = X(5)-OF-REFLECTION TRIANGLE

X(32196) lies on these lines: {2,13365}, {3,7730}, {4,93}, {5,11808}, {51,8254}, {54,143}, {156,195}, {206,576}, {511,6153}, {550,11802}, {568,12254}, {569,973}, {1112,11702}, {1209,6101}, {3518,11597}, {3574,13406}, {3627,10628}, {5446,11563}, {5609,14668}, {5891,20584}, {6102,10116}, {6145,15101}, {6639,12363}, {6689,15026}, {7530,17824}, {7691,13391}, {9019,9977}, {9707,12291}, {9920,12161}, {10095,12226}, {10203,15107}, {10254,12606}, {11441,12280}, {11805,22660}, {12134,14449}, {13565,15067}, {14652,15787}, {21660,22051}

X(32196) = midpoint of X(i) and X(j) for these lines: {i,j}: {195, 13423}, {2888, 6243}, {10263, 13368}, {12280, 12316}
X(32196) = reflection of X(i) in X(j) for these (i,j): (5, 11808), (54, 143), (550, 11802), (5876, 22804), (6101, 1209), (10610, 973), (11702, 1112), (13368, 6152), (15532, 1493), (20424, 5446), (21230, 6153), (21660, 22051), (22804, 11576)
X(32196) = anticomplement of the anticomplement of X(13365)
X(32196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (973, 10610, 5946), (3060, 13423, 195)

X(32197) = X(5)-OF-1st SCHIFFLER TRIANGLE

X(32197) lies on the line {11218,32055}

X(32198) = X(5)-OF-2nd SCHIFFLER TRIANGLE

X(32198) lies on these lines: {8,13205}, {9,80}, {11,8256}, {100,32157}, {529,12515}, {952,5450}, {1329,12758}, {1387,10199}, {1484,2802}, {1737,17652}, {1768,32049}, {2771,10915}, {2800,12607}, {2932,12647}, {3035,12740}, {3816,15558}, {3829,6702}, {3880,10265}, {3913,12247}, {4421,6224}, {5657,22560}, {5854,12737}, {6735,17638}, {7701,12751}, {10944,17100}, {11219,11256}, {19914,25438}

X(32198) = midpoint of X(i) and X(j) for these lines: {i,j}: {8, 13205}, {1768, 32049}, {3913, 12247}, {11256, 12641}, {19914, 25438}
X(32198) = reflection of X(i) in X(j) for these (i,j): (100, 32157), (3813, 12619), (13463, 11)
X(32198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8256, 27870, 13463), (11219, 12641, 11256)

X(32199) = X(5)-OF-SODDY TRIANGLE

X(32199) lies on the line {32056,32079}

X(32200) = X(5)-OF-2nd INNER-SODDY TRIANGLE

X(32200) lies on these lines: {176,31545}, {942,31541}

X(32201) = X(5)-OF-2nd OUTER-SODDY TRIANGLE

X(32201) lies on these lines: {175,31544}, {13390,31555}

X(32202) = X(5)-OF-INNER-SQUARES TRIANGLE

X(32202) lies on the line {11209,31987}

X(32202) = midpoint of X(31987) and X(32059)
X(32202) = {X(11209), X(31987)}-harmonic conjugate of X(32059)

X(32203) = X(5)-OF-OUTER-SQUARES TRIANGLE

X(32203) lies on the line {11210,31988}

X(32203) = midpoint of X(31988) and X(32060)
X(32203) = {X(11210), X(31988)}-harmonic conjugate of X(32060)

X(32204) = X(5)-OF-STEINER TRIANGLE

X(32204) lies on these lines: {2,10280}, {3,8151}, {4,9168}, {5,10190}, {140,523}, {195,30219}, {512,5447}, {525,1147}, {550,1499}, {632,10278}, {669,13564}, {1649,1656}, {2501,10018}, {3523,16220}, {3526,8029}, {3533,5466}, {5926,6563}, {10189,16239}

X(32204) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 8151}, {5926, 6563}
X(32204) = reflection of X(10279) in X(140)
X(32204) = anticomplement of X(10280)
X(32204) = {X(3), X(11123)}-harmonic conjugate of X(8151)

X(32205) = X(5)-OF-SUBMEDIAL TRIANGLE

X(32205) lies on these lines: {2,143}, {3,11451}, {5,113}, {26,17825}, {30,11695}, {49,15018}, {51,632}, {54,5643}, {110,15047}, {140,5446}, {156,5020}, {381,12279}, {389,547}, {511,16239}, {546,5892}, {568,5067}, {1112,6143}, {1154,3628}, {1511,13434}, {1614,15038}, {1656,5889}, {3090,6102}, {3091,32137}, {3411,11624}, {3412,11626}, {3526,5640}, {3530,10110}, {3544,18439}, {3567,5070}, {3589,10020}, {3627,14845}, {3819,14449}, {3845,27355}, {3850,9729}, {3851,11439}, {3853,16836}, {3856,14915}, {3857,10575}, {3859,13474}, {3917,13421}, {5054,9781}, {5055,5876}, {5056,15060}, {5072,10574}, {5079,5890}, {5447,10124}, {5544,7393}, {5562,15699}, {5907,12812}, {5972,8254}, {6000,12811}, {6241,19709}, {6642,32171}, {6689,13365}, {6746,14940}, {7392,32140}, {7486,18436}, {7999,13321}, {9306,32136}, {9813,32155}, {9817,32168}, {9818,32210}, {9825,30522}, {10545,18378}, {10601,32046}, {10625,11539}, {10643,32207}, {10644,32208}, {10961,32169}, {10963,32170}, {11284,12161}, {11444,15703}, {11479,32138}, {11484,32139}, {11812,13348}, {12045,15606}, {12100,13598}, {12834,14627}, {13403,15465}, {13565,14788}, {13861,15805}, {14641,14893}, {14984,25555}, {15022,18435}, {16042,18350}, {16105,30507}, {18379,18420}, {18928,18952}, {19137,19155}, {19188,19211}, {19372,32143}, {32068,32165}

X(32205) = midpoint of X(i) and X(j) for these lines: {i,j}: {5, 12006}, {140, 10095}, {143, 32142}, {389, 14128}, {3530, 10110}, {3628, 5462}, {3850, 9729}, {6689, 13365}, {10627, 16982}, {11793, 16881}
X(32205) = reflection of X(i) in X(j) for these (i,j): (5, 12046), (11017, 5), (11592, 140)
X(32205) = complement of X(32142)
X(32205) = X(11017)-of-Johnson triangle
X(32205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 143, 32142), (2, 15026, 143)

X(32206) = X(5)-OF-SYMMEDIAL TRIANGLE

X(32206) lies on these lines: {511,14133}, {1199,8718}, {8152,11205}

X(32206) = midpoint of X(8152) and X(31989)
X(32206) = {X(11205), X(31989)}-harmonic conjugate of X(8152)

X(32207) = X(5)-OF-INNER TRI-EQUILATERAL TRIANGLE

X(32207) lies on these lines: {3,11452}, {5,21647}, {6,156}, {15,5663}, {16,32171}, {26,17826}, {143,10641}, {1154,10661}, {5318,30522}, {5876,18468}, {5944,18470}, {6101,11420}, {6102,10632}, {7051,32143}, {10634,11591}, {10636,32158}, {10638,32168}, {10643,32205}, {10645,32210}, {11268,30402}, {11408,12161}, {11475,32137}, {11480,32138}, {11485,32139}, {11488,32140}, {11515,32142}, {13561,23302}, {16808,18379}, {18929,18952}, {19190,19211}, {19363,32046}

X(32207) = midpoint of X(10661) and X(11267)
X(32207) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 156, 32208), (11452, 11466, 3)

X(32208) = X(5)-OF-OUTER TRI-EQUILATERAL TRIANGLE

X(32208) lies on these lines: {3,11453}, {5,21648}, {6,156}, {15,32171}, {16,5663}, {26,17827}, {143,10642}, {1154,10662}, {1250,32168}, {5321,30522}, {5876,18470}, {5944,18468}, {6101,11421}, {6102,10633}, {10635,11591}, {10637,32158}, {10644,32205}, {10646,32210}, {11267,30403}, {11409,12161}, {11476,32137}, {11481,32138}, {11486,32139}, {11489,32140}, {11516,32142}, {13561,23303}, {16809,18379}, {18930,18952}, {19191,19211}, {19364,32046}, {19373,32143}

X(32208) = midpoint of X(10662) and X(11268)
X(32208) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 156, 32207), (11453, 11467, 3)

X(32209) = X(5)-OF-4th TRI-SQUARES TRIANGLE

X(32209) lies on these lines: {20,486}, {615,640}, {642,3069}, {6251,13951}, {6290,13961}, {8184,13972}, {8252,13921}, {12123,13939}, {12787,13942}, {12963,13821}

X(32209) = midpoint of X(13933) and X(13934)
X(32209) = X(642)-of-4th tri-squares-central triangle
X(32209) = {X(13847), X(13934)}-harmonic conjugate of X(13933)

X(32210) = X(5)-OF-TRINH TRIANGLE

X(32210) lies on these lines: {2,3521}, {3,74}, {5,21663}, {24,32137}, {26,10606}, {30,5449}, {35,32143}, {36,32168}, {64,18324}, {143,378}, {343,550}, {376,2888}, {511,32155}, {569,1204}, {1154,7689}, {1192,31861}, {1539,16868}, {1620,11472}, {1658,3357}, {1994,3520}, {2071,6101}, {2777,13406}, {2937,13445}, {3581,12086}, {3627,32110}, {3631,14810}, {5012,18364}, {5092,19155}, {5448,5498}, {5621,15074}, {5894,15761}, {5946,14130}, {6000,15331}, {6200,32169}, {6396,32170}, {6642,11017}, {7526,10601}, {7527,15026}, {7555,14641}, {7575,11381}, {7688,32158}, {7728,14940}, {8567,12084}, {9818,32205}, {10020,15311}, {10095,11438}, {10201,20427}, {10224,25563}, {10226,13754}, {10249,11255}, {10264,21659}, {10540,17506}, {10605,32046}, {10645,32207}, {10646,32208}, {11410,12161}, {11430,32136}, {11479,12046}, {11598,19506}, {12107,14915}, {12162,15646}, {12226,13340}, {13371,23328}, {13567,15807}, {15060,22467}, {15332,18400}, {18377,23329}, {18439,21844}, {18562,23294}, {18565,23293}, {18931,18952}, {19192,19211}

X(32210) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32138}, {1658, 3357}, {5894, 15761}, {7689, 11250}
X(32210) = reflection of X(i) in X(j) for these (i,j): (5448, 5498), (10224, 25563), (13406, 20191), (18379, 13561), (19155, 5092), (32171, 3)
X(32210) = X(32171)-of-ABC-X3 reflections triangle
X(32210) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 74, 13491), (3, 11468, 12041), (3, 12111, 1511)

X(32211) = X(5)-OF-X-PARABOLA-TANGENTIAL TRIANGLE

X(32211) lies on the line {8029,31990}

X(32211) = midpoint of X(31990) and X(32061)
X(32211) = {X(8029), X(31990)}-harmonic conjugate of X(32061)

X(32212) = X(5)-OF-YFF CONTACT TRIANGLE

X(32212) lies on these lines: {1,10196}, {8,5592}, {10,514}, {40,3667}, {145,31992}, {513,4662}, {1698,21204}, {3239,19582}, {3616,6544}, {4528,28521}, {6545,9780}, {14077,31792}, {14475,19877}, {19963,21211}, {20001,21143}, {21198,28155}, {21201,23757}

X(32212) = midpoint of X(8) and X(5592)
X(32212) = {X(8), X(6546)}-harmonic conjugate of X(5592)

X(32213) = X(5)-OF-INNER-YFF TANGENTS TRIANGLE

X(32213) lies on these lines: {1,5}, {3,10528}, {4,12000}, {10,13373}, {26,10834}, {30,10679}, {56,15867}, {140,956}, {145,6842}, {381,10596}, {442,12645}, {518,5690}, {546,10531}, {549,10269}, {550,11248}, {632,26364}, {912,31397}, {1056,6911}, {1329,15178}, {1385,12607}, {1532,10247}, {1656,10586}, {2077,8703}, {3421,6883}, {3564,12430}, {3621,6937}, {3623,6941}, {3627,6256}, {3845,26333}, {3871,13199}, {5554,8728}, {5840,25439}, {5844,6907}, {5874,10930}, {5875,10929}, {5885,8256}, {6735,10202}, {6756,11400}, {6767,6929}, {6831,18526}, {6834,12001}, {6863,10530}, {6882,7967}, {6959,7373}, {7491,20060}, {7680,28204}, {7715,26378}, {8666,31659}, {8727,28224}, {10056,22758}, {10246,17757}, {10386,26358}, {10532,18518}, {10599,18544}, {10680,10786}, {10803,32134}, {10965,15171}, {11112,12331}, {11509,18990}, {11881,32146}, {11882,32147}, {11914,32162}, {11929,12116}, {11955,32177}, {11956,32178}, {12189,13112}, {12513,26487}, {12608,22791}, {12703,28174}, {12905,13121}, {13104,22931}, {13109,22731}, {13906,13925}, {13964,13993}, {18242,24680}, {19047,19116}, {19048,19117}, {21075,31838}, {22768,32153}, {24927,27385}

X(32213) = midpoint of X(i) and X(j) for these lines: {i,j}: {10679, 12115}, {12905, 13217}
X(32213) = reflection of X(i) in X(j) for these (i,j): (5, 495), (956, 140)
X(32213) = X(10942)-of-inner-Yff triangle
X(32213) = X(10943)-of-1st Johnson-Yff triangle
X(32213) = outer-Yff-to-inner-Yff similarity image of X(5)
X(32213) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 10942, 5), (1, 10958, 496), (5, 1483, 32214)

X(32214) = X(5)-OF-OUTER-YFF TANGENTS TRIANGLE

X(32214) lies on these lines: {1,5}, {3,10529}, {4,12001}, {26,10835}, {30,10680}, {55,15868}, {140,5687}, {145,6882}, {381,10597}, {546,10532}, {549,4421}, {550,11249}, {632,26363}, {912,12053}, {946,3892}, {1058,3560}, {1385,3813}, {1532,18526}, {1656,10587}, {1898,30384}, {2886,15178}, {3434,16203}, {3564,12431}, {3621,6963}, {3622,6881}, {3623,6830}, {3655,15908}, {3845,26332}, {3880,5690}, {3913,26492}, {4187,12645}, {4847,31838}, {5770,9785}, {5844,6922}, {5874,10932}, {5875,10931}, {5884,21630}, {6001,22791}, {6713,8715}, {6756,11401}, {6767,6862}, {6831,10247}, {6833,12000}, {6841,10595}, {6842,7967}, {6911,14986}, {6914,15172}, {6917,7373}, {6958,10530}, {6968,18545}, {7681,28204}, {7715,26377}, {8703,11012}, {10072,11499}, {10085,12699}, {10246,24390}, {10386,26357}, {10531,18519}, {10598,18542}, {10679,10785}, {10804,32134}, {10879,32151}, {10902,15712}, {10966,15171}, {11510,15325}, {11883,32146}, {11884,32147}, {11915,32162}, {11928,12115}, {11957,32177}, {11958,32178}, {12190,13113}, {12331,13747}, {12558,13464}, {12704,28174}, {12906,13122}, {13106,22932}, {13107,22887}, {13110,22732}, {13607,24387}, {13907,13925}, {13965,13993}, {16216,21625}, {18967,18990}, {19049,19116}, {19050,19117}, {20418,26285}

X(32214) = midpoint of X(i) and X(j) for these lines: {i,j}: {10073, 12737}, {10085, 12699}, {10680, 12116}, {12906, 13218}
X(32214) = reflection of X(i) in X(j) for these (i,j): (5, 496), (5687, 140)
X(32214) = X(10942)-of-2nd Johnson-Yff triangle
X(32214) = X(10943)-of-outer-Yff triangle
X(32214) = inner-Yff-to-outer-Yff similarity image of X(5)
X(32214) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 1483, 32213), (11, 10942, 5), (1483, 1484, 5)

X(32215) = X(5)-OF-YIU TRIANGLE

X(32215) lies on these lines: {5,15869}, {30,30685}, {6750,20424}, {8154,31991}

X(32215) = midpoint of X(8154) and X(31991)
X(32215) = {X(31991), X(32084)}-harmonic conjugate of X(8154)

X(32216) = COMPLEMENT OF X(26255)

As a point on the Euler line, X(32216) has Shinagawa coefficients [4 E - 5 F, -3 E -3 F].

See Kadir Altintas and Ercole Suppa, Hyacinthos 28993.

X(32216) lies on these lines: {2,3}, {6,13857}, {115,21448}, {125,599}, {126,3014}, {524,26869}, {542,6090}, {2393,5650}, {2549,24855}, {2790,23234}, {5024,9745}, {5642,14982}, {6054,9717}, {7998,14984}, {9140,15066}, {9155,9759}, {11064,11179}, {15059,21766}, {15080,20772}, {15131,19153}, {16187,25561}, {19136,22112}

X(32216) = complement of X(26255)
X(32216) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {2,376,468}, {2,381,11284}, {2,858,381}, {2,10989,1995}, {2,16063,7426}, {381,3534,18325}, {427,468,6623}, {549,5159,2}, {1368,5159,18531}, {1995,10989,3830}, {7426,16063,3534}, {11284,21312,25}

Points associated with the Walsmith triangle: X(32217)-X(32229)

X(32217) = X(3)-OF-WALSMITH-TRIANGLE

X(32217) is the common radical trace of the harmonic circles of pairs of the Ehrmann circles. (Randy Hutson, June 7, 2019)

X(32217) lies on these lines: {6, 23}, {30, 182}, {110, 524}, {141, 468}, {184, 8584}, {186, 1350}, {206, 3629}, {237, 5467}, {265, 1177}, {511, 1511}, {523, 5027}, {576, 12105}, {691, 729}, {858, 3589}, {895, 12367}, {1112, 9019}, {1176, 6329}, {1316, 6322}, {1351, 2070}, {1428, 7286}, {1495, 2854}, {1513, 24975}, {1576, 2080}, {1976, 6094}, {2030, 28662}, {2330, 5160}, {2393, 11800}, {2781, 32110}, {3098, 18571}, {3564, 25338}, {3580, 27085}, {3581, 9970}, {3618, 5189}, {5085, 7464}, {5097, 11649}, {5159, 19126}, {5201, 9407}, {7574, 14561}, {8550, 16619}, {9306, 22165}, {9544, 15534}, {9973, 11443}, {10113, 11645}, {10295, 15472}, {10297, 19131}, {10510, 15107}, {11216, 20850}, {11692, 15516}, {12039, 16776}, {12112, 16010}, {14810, 15646}, {15118, 29012}, {16316, 19558}, {18323, 19129}, {18572, 19130}, {19118, 21284}, {23327, 31726}

X(32217) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 23}, {895, 12367}, {3581, 9970}, {10510, 15107}, {12112, 16010}
X(32217) = reflection of X(i) in X(j) for these lines: {i,j}: {141, 468}, {858, 3589}, {3098, 18571}, {15826, 6}, {18572, 19130}
X(32217) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 6800, 8546}, {19127, 19136, 597}
X(32217) = isogonal of the isotomic of X(26276)
X(32217) = crossdifference of every pair of points on line {3094, 3906}
X(32217) = barycentric product X(6)*X(26276)
X(32217) = barycentric quotient X(26276) / X(76)

X(32218) = X(5)-OF-WALSMITH-TRIANGLE

X(32218) lies on these lines: {23, 141}, {30, 14810}, {110, 524}, {373, 468}, {511, 10272}, {523, 5113}, {755, 1287}, {858, 5888}, {1352, 2070}, {1495, 8262}, {1503, 7575}, {3448, 19596}, {3619, 20063}, {3631, 13562}, {3763, 5189}, {5092, 22249}, {5972, 9019}, {6329, 15826}, {6698, 29012}, {7464, 21167}, {10096, 11649}, {11594, 16321}, {11799, 29181}, {12367, 25328}, {15067, 16619}

X(32218) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 141}, {1495, 8262}, {12367, 25328}
X(32218) = reflection of X(i) in X(j) for these lines: {i,j}: {3589, 468}, {5092, 22249}, {15826, 6329}

X(32219) = X(6)-OF-WALSMITH-TRIANGLE

X(32219) lies on these lines: {1495, 5663}, {8588, 19156}

X(32220) = X(20)-OF-WALSMITH-TRIANGLE

X(32220) lies on these lines: {6, 858}, {23, 159}, {30, 1351}, {69, 468}, {110, 524}, {323, 25321}, {399, 3564}, {403, 1352}, {511, 1986}, {542, 32111}, {576, 12022}, {895, 1503}, {1513, 2407}, {2072, 18583}, {2366, 10423}, {3618, 5159}, {3629, 8705}, {5032, 10989}, {5050, 15122}, {5093, 7574}, {5486, 6800}, {7391, 11216}, {7464, 14912}, {8550, 15072}, {8681, 24981}, {9035, 32120}, {10169, 31074}, {10297, 14853}, {11064, 15471}, {18323, 21850}, {19504, 22151}

X(32220) = midpoint of X(23) and X(193)
X(32220) = reflection of X(i) in X(j) for these lines: {i,j}: {69, 468}, {858, 6}, {11064, 15471}, {18323, 21850}
X(32220) = crossdifference of every pair of points on line {5028, 7652}

X(32221) = X(99)-OF-WALSMITH-TRIANGLE

X(32221) lies on these lines: {6, 598}, {110, 1316}, {542, 2682}, {543, 14999}, {9144, 14559}

X(32222) = X(110)-OF-WALSMITH-TRIANGLE

X(32222) lies on these lines: {6, 110}, {23, 2780}, {543, 7471}, {14688, 16165}, {15329, 15566}

X(32223) = MIDPOINT OF X(23) AND X(125)

X(32223) lies on these lines: {2, 3098}, {6, 21970}, {23, 125}, {25, 3818}, {30, 6699}, {51, 14389}, {69, 1974}, {74, 1533}, {110, 5965}, {113, 3581}, {140, 13598}, {143, 12242}, {182, 7493}, {184, 11225}, {186, 16163}, {265, 2070}, {316, 419}, {323, 5642}, {373, 7495}, {381, 31860}, {382, 25563}, {389, 13383}, {403, 1531}, {436, 32002}, {468, 511}, {476, 14595}, {541, 15361}, {542, 1495}, {575, 13394}, {826, 4142}, {858, 6723}, {1154, 10096}, {1209, 13621}, {1352, 4232}, {1539, 11563}, {1648, 8627}, {1658, 13403}, {1691, 6388}, {1853, 20850}, {1995, 24206}, {2777, 11799}, {2917, 22550}, {3147, 13346}, {3167, 6144}, {3231, 10418}, {3564, 15448}, {3589, 5943}, {3627, 20191}, {3629, 10192}, {3763, 5020}, {3819, 6677}, {4240, 14918}, {4846, 11438}, {5012, 32068}, {5112, 23698}, {5159, 29181}, {5189, 15059}, {5446, 10020}, {5449, 13419}, {5640, 25555}, {5663, 25338}, {5892, 25337}, {5907, 21841}, {6053, 13754}, {6292, 21513}, {6688, 7499}, {6689, 10095}, {6719, 22103}, {6759, 18917}, {7517, 20299}, {7542, 10110}, {7574, 23515}, {7575, 17702}, {7691, 21451}, {7820, 11328}, {8705, 15118}, {9714, 18381}, {9909, 26958}, {10112, 10282}, {10114, 20773}, {10154, 13567}, {10182, 13352}, {10201, 18388}, {11178, 26255}, {12317, 14157}, {12897, 15331}, {13163, 13565}, {13391, 14156}, {14070, 18390}, {14810, 30739}, {14915, 16619}, {15644, 16238}, {16111, 18325}, {16618, 16836}, {18534, 23329}, {21230, 30551}, {21849, 23292}

X(32223) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 125}, {74, 1533}, {113, 3581}, {1495, 3580}, {5642, 15360}, {11799, 32110}, {16111, 18325}
X(32223) = reflection of X(i) in X(j) for these lines: {i,j}: {858, 6723}, {5972, 468}
X(32223) = reflection of X(22104) in the orthic axis
X(32223) = X(i)-complementary conjugate of X(j) for these (i,j): {74, 21249}, {82, 113}, {2159, 6292}, {2349, 21248}
X(32223) = crosspoint of X(476) and X(18020)
X(32223) = crosssum of X(526) and X(20975)
X(32223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 20193, 18874}, {3580, 7426, 1495}

X(32224) = X(6)X(30)∩X(23)X(385)

X(32223) lies on these lines: {6, 30}, {23, 385}, {183, 7426}, {186, 8266}, {468, 15271}, {858, 11174}, {1316, 6322}, {2452, 8705}, {3329, 10989}, {5467, 11676}, {8177, 9462}, {8667, 16312}, {19221, 20897}

X(32224) = reflection of X(858) and X(16324)
X(32224) = crossdifference of every pair of points on line {39, 8675}

X(32225) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH AND 4th BROCARD

X(32225) lies on these lines: {2, 51}, {5, 20192}, {6, 30516}, {23, 9140}, {30, 125}, {187, 1648}, {230, 6791}, {376, 18390}, {381, 1531}, {389, 7552}, {468, 524}, {541, 11799}, {542, 1495}, {543, 5112}, {549, 10564}, {597, 16789}, {599, 5651}, {858, 19924}, {1209, 23410}, {1316, 3849}, {1352, 26255}, {1995, 11178}, {2030, 6792}, {3066, 5055}, {3906, 9208}, {4232, 11180}, {5054, 22112}, {5449, 7540}, {5648, 9027}, {5655, 13754}, {6090, 15533}, {7493, 11179}, {7495, 10168}, {7505, 14531}, {9019, 12099}, {9169, 9181}, {10201, 14831}, {10418, 15993}, {10989, 15107}, {11284, 19510}, {11317, 13378}, {12824, 25566}, {13567, 22352}, {14002, 18553}, {14915, 20126}, {15004, 18449}, {15331, 18555}, {15448, 24981}, {15682, 18376}, {16003, 16619}, {26958, 31152}, {31174, 31953}, {32113, 32127}

X(32225) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 15360}, {23, 9140}, {381, 3581}, {3580, 7426}, {10989, 15107}
X(32225) = reflection of X(i) in X(j) for these lines: {i,j}: {1495, 7426}, {1531, 381}, {3292, 5642}, {5642, 468}, {10564, 549}, {13857, 2}, {32110, 15361}
X(32225) = {X(3581),X(15362)}-harmonic conjugate of X(381),X(897)-isoconjugate of X(3431)
X(32225) = crossdifference of every pair of points on line {353, 3288}
X(32225) = X(2)-of-pedal-triangle-of-X(23)
X(32225) = barycentric product X(381) and X(524)
X(32225) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {187, 3431}, {381, 671}, {5158, 895}, {18487, 9214}

X(32226) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH AND REFLECTION TRIANGLE

X(32226) lies on these lines: {49, 11557}, {51, 110}, {54, 74}, {113, 137}, {125, 11245}, {184, 10117}, {195, 568}, {323, 27866}, {373, 9977}, {389, 3043}, {399, 11424}, {539, 32123}, {575, 15059}, {578, 21650}, {826, 32120}, {1112, 1495}, {1154, 14708}, {1594, 10114}, {1614, 11807}, {1986, 13367}, {2904, 9707}, {3292, 3580}, {3448, 7703}, {3569, 14397}, {5095, 21637}, {5562, 12228}, {5663, 15739}, {6467, 13248}, {6593, 32114}, {7699, 18390}, {10264, 32136}, {10610, 25487}, {11003, 13201}, {11381, 15472}, {11402, 17847}, {11472, 12308}, {11806, 15087}, {12161, 21649}, {12174, 17824}, {12254, 22802}, {12307, 15042}, {12893, 14831}, {13171, 17809}, {13472, 18912}, {14531, 22109}, {15020, 15801}, {18400, 32111}

X(32226) = midpoint of X(i) and X(j) for these lines: {i,j}: {54, 2914}, {195, 11597}, {1493, 11702}, {3574, 14049}
X(32226) = crossdifference of every pair of points on line {3448, 13527}
X(32226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 1994, 11800}, {184, 19504, 13417}, {389, 3043, 17701}, {12227, 15463, 185}

X(32227) = X(2)X(265)∩X(6)X(5642)

X(32227) lies on these lines: {2, 265}, {6, 5642}, {22, 20127}, {23, 7728}, {25, 113}, {110, 468}, {125, 5085}, {427, 10733}, {542, 26864}, {858, 12121}, {1495, 14982}, {1986, 6353}, {1995, 14643}, {3581, 5655}, {3618, 12099}, {5094, 17702}, {5181, 6090}, {5523, 15144}, {5663, 7493}, {5972, 11284}, {6676, 10264}, {6677, 12228}, {7484, 19457}, {7495, 15061}, {11579, 13394}, {12022, 15034}, {12827, 18440}, {12828, 19118}, {12893, 21284}, {14852, 30714}, {15035, 30739}, {16042, 25714}, {16163, 31152}

X(32228) = X(30)X(511)∩X(74)X(6325)

X(32228) lies on these lines: {30,511}, {74,6325}, {110,6236}, {1649,9126}, {3569,6032}, {9184,11568}, {9191,16235}, {9829,19902}, {10097,11564}, {10163,24284}, {10294,11215}, {13241,20404}

X(32228) = isogonal conjugate of X(32229)
X(32228) = crossdifference of every pair of points on line {6, 16510}

X(32229) = ISOGONAL CONJUGATE OF X(32228)

X(32229) lies on the circumcircle and these lines: {30,6325}, {74,8705}, {111,7575}, {381,2770}, {523,6236}, {2373,10296}, {7464,14388}, {10102,14002}

X(32229) = reflection of X(6236) in the Euler line
X(32229) = isogonal conjugate of X(32228)
X(32229) = trilinear pole of line {6, 16510}

X(32230) = X(30)X(250)∩X(107)X(523)

Line X(107)X(112) (the trilinear polar of X(32230)) is the locus of the trilinear pole of the tangent at P to hyperbola {{A,B,C,X(4),P}}, as P moves on the van Aubel line. Line X(107)X(112) is also the tangent to conic {{A,B,C,X(107),X(648)}} (the circumconic centered at X(1249)) at X(107). (Randy Hutson, June 7, 2019)

X(32230) lies on K1097 and these lines:{30,250}, {107,523}, {450,3260}, {648,8057}, {685,15352}, {1093,14254}, {1503,1559}, {1971,1990}, {2404,2409}, {2489,20031}, {6524,9214}, {16813,23286}, {23692,24000}

X(32230) = isogonal conjugate of X(2972)
X(32230) = polar conjugate of X(15526)
X(32230) = isotomic of the polar conjugate of X(23590)
X(32230) = polar conjugate of the isotomic of X(23582)
X(32230) = polar conjugate of the isogonal of X(23964)
X(32230) = X(92)-isoconjugate of X(35071)
X(32230) = complement of anticomplementary conjugate of X(35360)
X(32230) = X(i)-cross conjugate of X(j) for these (i,j): {{4, 107}, {6, 16813}, {133, 4240}, {184, 112}, {393, 15352}, {1249, 648}, {1614, 933}, {1990, 15459}, {6524, 6529}, {6759, 110}, {8779, 2966}, {9833, 925}, {11206, 99}, {14157, 1304}, {15262, 687}, {18400, 476}, {18685, 6335}, {23964, 23582}, {26883, 1301}, {31383, 1289}}
X(32230) = X(i)-isoconjugate of X(j) for these (i,j): {{1, 2972}, {3, 2632}, {25, 24020}, {48, 15526}, {63, 3269}, {115, 6507}, {122, 19614}, {125, 255}, {163, 23616}, {184, 17879}, {201, 1364}, {212, 1367}, {228, 17216}, {244, 4158}, {273, 7065}, {318, 1363}, {326, 20975}, {338, 4100}, {394, 3708}, {520, 656}, {525, 822}, {577, 20902}, {603, 7068}, {647, 24018}, {756, 7215}, {798, 4143}, {810, 3265}, {1092, 1109}, {1102, 3124}, {1425, 24031}, {1826, 16730}, {1973, 23974}, {2638, 6356}, {2643, 3964}, {2968, 7138}, {3682, 18210}, {3990, 4466}, {4064, 23224}, {4575, 5489}, {7004, 7066}, {18604, 21046}, {23606, 23994}}
X(32230) = cevapoint of X(i) and X(j) for these (i,j): {{4, 107}, {20, 110}, {112, 184}, {648, 17907}, {6524, 6529}}
X(32230) = trilinear pole of line {107, 112}
X(32230) = barycentric product X(i)*X(j) for these lines: {i,j}: {{4, 23582}, {19, 23999}, {63, 24021}, {69, 23590}, {92, 24000}, {99, 6529}, {107, 648}, {110, 15352}, {112, 6528}, {162, 823}, {249, 1093}, {250, 2052}, {264, 23964}, {304, 24022}, {305, 23975}, {393, 18020}, {811, 24019}, {877, 20031}, {1101, 6521}, {2326, 24032}, {4240, 15459}, {4590, 6524}, {6520, 24041}, {15384, 15466}}
X(32230) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {{4, 15526}, {6, 2972}, {19, 2632}, {25, 3269}, {27, 17216}, {63, 24020}, {69, 23974}, {92, 17879}, {99, 4143}, {107, 525}, {112, 520}, {158, 20902}, {162, 24018}, {249, 3964}, {250, 394}, {278, 1367}, {281, 7068}, {393, 125}, {523, 23616}, {593, 7215}, {648, 3265}, {823, 14208}, {850, 23107}, {1093, 338}, {1096, 3708}, {1101, 6507}, {1249, 122}, {1252, 4158}, {1437, 16730}, {1990, 1650}, {2052, 339}, {2189, 1364}, {2207, 20975}, {2326, 24031}, {2501, 5489}, {4590, 4176}, {5317, 18210}, {5379, 3998}, {6520, 1109}, {6521, 23994}, {6524, 115}, {6525, 1562}, {6528, 3267}, {6529, 523}, {7115, 7066}, {8747, 4466}, {10002, 12037}, {15352, 850}, {15384, 1073}, {18020, 3926}, {18831, 15414}, {20031, 879}, {23347, 1636}, {23357, 1092}, {23582, 69}, {23590, 4}, {23963, 23606}, {23964, 3}, {23975, 25}, {23984, 6356}, {23985, 1425}, {23995, 4100}, {23999, 304}, {24000, 63}, {24019, 656}, {24021, 92}, {24022, 19}, {24041, 1102}}

X(32231) = MIDPOINT OF X(3) AND X(17414)

X(32231) lies on these lines: {3, 17414}, {182, 9044}, {187, 30491}, {351, 1499}, {512, 5926}, {523, 549}, {647, 2780}, {3288, 21733}, {8552, 8675}, {8704, 11621}, {11615, 30230}, {16235, 23878}

X(32231) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 17414}, {3288, 21733}
X(32231) = reflection of X(5926) in X(9126)

X(32232) = X(523)X(5054)∩X(549)X(17414)

X(32232) lies on these lines: {523, 5054}, {549, 17414}, {5215, 8704}, {5996, 9126}

X(32233) = MIDPOINT OF X(20) AND X(11061)

See Q152, the Walsmith circular quartic.

X(32233) lies on these lines: {3, 67}, {4, 6593}, {5, 15133}, {6, 7706}, {20, 2781}, {30, 9970}, {110, 858}, {125, 5085}, {141, 15035}, {146, 14927}, {182, 265}, {186, 8262}, {382, 15140}, {511, 11562}, {524, 10295}, {611, 18968}, {613, 12896}, {631, 6698}, {895, 8550}, {974, 2854}, {1071, 2836}, {1350, 16163}, {1352, 1511}, {1428, 12904}, {1498, 15063}, {1853, 15142}, {2330, 12903}, {2777, 11820}, {3313, 10628}, {3448, 25406}, {3589, 14644}, {3818, 7579}, {4549, 5663}, {5026, 11005}, {5050, 12902}, {5092, 15061}, {5094, 5642}, {5095, 11477}, {5480, 10733}, {5609, 14791}, {5622, 6146}, {5655, 7574}, {5972, 10516}, {6102, 12118}, {7493, 16165}, {7495, 9140}, {7519, 12824}, {7728, 19140}, {9143, 16063}, {9969, 16223}, {10113, 14561}, {10249, 12827}, {10296, 22151}, {10575, 18442}, {10752, 25329}, {11744, 19149}, {11799, 18374}, {15027, 20190}, {15036, 21167}, {15106, 24981}, {16111, 25336}, {19374, 19510}

X(32233) = midpoint of X(i) and X(j) for these lines: {i,j}: {20, 11061}, {146, 14927}, {6776, 12383}
X(32233) = reflection of X(i) in X(j) for these lines: {i,j}: {4, 6593}, {67, 3}, {265, 182}, {895, 8550}, {1350, 16163}, {1352, 1511}, {2930, 30714}, {7728, 19140}, {10733, 5480}, {10752, 25329}, {11005, 5026}, {11477, 5095}, {11744, 19149}, {14982, 110}, {15069, 5181}, {25335, 16003}
X(32233) = {X(5621),X(25335)}-harmonic conjugate of X(16003)

X(32234) = MIDPOINT OF X(7731) AND X(12283)

See Q152, the Walsmith circular quartic.

X(32234) lies on these lines: {4, 542}, {6, 7699}, {24, 2930}, {54, 67}, {68, 16534}, {69, 15035}, {74, 5486}, {110, 468}, {113, 5921}, {125, 14912}, {182, 3043}, {186, 12584}, {193, 17702}, {265, 1353}, {378, 16010}, {403, 15471}, {511, 7722}, {524, 10295}, {1177, 1614}, {1351, 10733}, {1503, 10721}, {1511, 11898}, {1594, 25328}, {1986, 2854}, {2501, 14932}, {2781, 5925}, {2892, 11457}, {2914, 9976}, {4232, 9143}, {4235, 8593}, {5050, 15059}, {5093, 10113}, {5094, 9140}, {5181, 15034}, {5477, 6103}, {5663, 15531}, {5889, 13148}, {6193, 30714}, {6467, 10628}, {6593, 15069}, {7574, 11416}, {7577, 20301}, {7731, 12283}, {8548, 11441}, {9744, 9769}, {9967, 12219}, {10519, 15036}, {10990, 19467}, {11179, 13169}, {11180, 15303}, {11443, 18440}, {11482, 15044}, {11579, 15463}, {12292, 25336}, {14357, 14649}, {14913, 16223}, {14982, 25329}, {15116, 23294}, {15118, 18912}, {18449, 18572}, {18909, 20417}, {18947, 24981}

X(32234) = midpoint of X(7731) and X(12283)
X(32234) = reflection of X(i) in X(j) for these lines: {i,j}: {4, 5095}, {67, 8550}, {74, 6776}, {265, 1353}, {5921, 113}, {6403, 1986}, {10721, 10752}, {10733, 1351}, {11005, 5477}, {11180, 15303}, {11898, 1511}, {12219, 9967}, {13169, 11179}, {14094, 11061}, {14982, 25329}, {15069, 6593}
X(32234) = anticomplement of X(32275)
X(32234) = polar-circle-inverse of X(9880)
X(32234) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {67, 8550, 5622}, {5921, 25321, 113}, {17983, 20774, 4}

X(32235) = X(2)X(98)∩X(6)X(16510)

See Q152, the Walsmith circular quartic.

X(32235) lies on these lines: {2, 98}, {6, 16510}, {265, 7579}, {373, 6593}, {1350, 15106}, {1495, 5663}, {1511, 5650}, {1995, 19140}, {2088, 2502}, {2854, 3292}, {2930, 6090}, {5609, 9730}, {5640, 25556}, {5655, 7706}, {7574, 15136}, {10113, 15432}, {10264, 13394}, {10620, 12893}, {11438, 14094}, {11562, 20772}, {11801, 13413}, {12041, 14855}, {12584, 15066}, {13339, 20397}, {13352, 15132}, {14389, 20301}, {16010, 26864}

X(32235) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 5651, 5642}, {110, 9140, 11003}, {110, 11579, 184}
X(32235) = crossdifference of every pair of points on line {3569, 6032}

X(32236) = (name pending)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 28997.

X(32236) lies on this line: {2,6}

More centers related to Walsmith triangle: X(32237)-X(32317)

X(32237) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: WALSMITH TO ABC-X3 REFLECTIONS

See preamble just before X(31353).

X(32237) lies on these lines: {3,5646}, {22,3819}, {23,110}, {25,182}, {26,5907}, {30,5972}, {51,11003}, {125,7426}, {154,1351}, {184,5097}, {187,20998}, {373,14002}, {468,6723}, {542,32269}, {567,10110}, {575,6800}, {576,26864}, {858,29323}, {1112,11649}, {1350,9306}, {1503,32223}, {1533,10295}, {1614,16625}, {1658,13474}, {1995,5092}, {2030,3124}, {2070,6000}, {2080,14673}, {2393,11800}, {2937,11793}, {3129,13350}, {3130,13349}, {3291,8627}, {3448,32225}, {3518,9729}, {3581,12308}, {3818,7493}, {5050,31860}, {5085,5544}, {5640,5645}, {5650,7492}, {5663,12105}, {6030,10219}, {6353,14927}, {6644,8717}, {6660,18860}, {6688,13595}, {6759,9714}, {7464,15036}, {7517,10282}, {7530,11430}, {7555,10170}, {7556,15030}, {7575,12041}, {8547,19136}, {8589,21292}, {8681,12310}, {9544,21969}, {10154,21243}, {10244,17814}, {10254,15432}, {10298,32062}, {10301,13394}, {10330,26276}, {10564,15040}, {11002,11663}, {11064,29317}, {11202,18534}, {11284,17508}, {11381,11454}, {11472,14070}, {11695,13339}, {11799,12295}, {11801,25338}, {11807,20773}, {12039,19127}, {12045,16042}, {12088,13348}, {12106,16836}, {13335,20897}, {13383,13419}, {14169,21402}, {14170,21401}, {14683,15360}, {14913,20987}, {15606,18350}, {15644,17714}, {16619,17702}

X(32237) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 1495}, {1533, 10295}, {3292, 15107}
X(32237) = reflection of X(5972) in X(15448)
X(32237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (22, 5651, 14810), (5651, 14810, 3819)

X(32238) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-AQUILA TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32238) lies on these lines: {1,67}, {2,32278}, {10,6698}, {125,518}, {511,12261}, {515,32274}, {542,1385}, {942,15116}, {946,2781}, {960,2836}, {999,32270}, {1125,6593}, {1319,32243}, {1386,11735}, {1503,11709}, {2646,32297}, {2854,13605}, {3242,13211}, {3295,32256}, {3416,7984}, {3616,11061}, {4663,15118}, {5603,32247}, {5886,9970}, {9955,32271}, {10246,32306}, {10516,12368}, {10693,24476}, {11363,32239}, {11364,32242}, {11365,32262}, {11366,32265}, {11367,32266}, {11368,32268}, {11370,32280}, {11371,32281}, {11373,32287}, {11374,32288}, {11375,32289}, {11376,32290}, {11377,32295}, {11378,32296}, {11831,32279}, {12259,14984}, {13883,32303}, {13936,32304}, {18991,32252}, {18992,32253}

X(32238) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 67}, {3242, 13211}, {3416, 7984}, {10693, 24476}, {32261, 32298}
X(32238) = reflection of X(i) in X(j) for these (i,j): (10, 6698), (1386, 11735), (4663, 15118), (6593, 1125), (32271, 9955)
X(32238) = complement of X(32278)
X(32238) = X(67)-of-anti-Aquila-triangle
X(32238) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32261, 32298), (67, 32298, 32261)

X(32239) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ARA TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32239) lies on these lines: {4,542}, {23,32257}, {25,67}, {33,32297}, {34,32243}, {66,125}, {235,32274}, {427,6593}, {468,6698}, {511,12140}, {1205,11381}, {1503,12133}, {1593,32233}, {1598,32306}, {1843,13417}, {1853,15128}, {2781,3575}, {3541,15462}, {3867,25329}, {5090,32278}, {5169,32300}, {5410,32253}, {5411,32252}, {5596,13198}, {5622,14216}, {7487,32247}, {7519,32244}, {7530,32275}, {7713,32261}, {11363,32238}, {11380,32242}, {11383,32256}, {11384,32265}, {11385,32266}, {11386,32268}, {11388,32280}, {11389,32281}, {11390,32287}, {11391,32288}, {11392,32289}, {11393,32290}, {11394,32295}, {11395,32296}, {11396,32298}, {11398,32307}, {11399,32308}, {11400,32309}, {11401,32310}, {11746,26926}, {11832,32279}, {12134,14984}, {12294,17702}, {13884,32303}, {13937,32304}, {22479,32270}, {32246,32285}, {32251,32264}

X(32239) = reflection of X(i) in X(j) for these (i,j): (26926, 11746), (32285, 32246)
X(32239) = X(67)-of-anti-Ara-triangle

X(32240) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ASCELLA TO WALSMITH

The reciprocal orthologic center of these triangles is X(110)

X(32240) lies on these lines: {3,32244}, {4,32254}, {6,32260}, {24,9925}, {25,2930}, {110,19118}, {184,32276}, {193,12310}, {195,8537}, {427,32255}, {511,12165}, {524,21284}, {542,1593}, {895,11405}, {1177,26864}, {1398,32259}, {1598,5609}, {1993,32248}, {2781,12174}, {2836,11396}, {2854,12167}, {3043,5050}, {3515,12584}, {3516,16010}, {3564,12168}, {5094,25328}, {5410,32291}, {5411,32292}, {6467,17847}, {7071,32286}, {7395,32275}, {7484,32257}, {7592,32249}, {9777,32246}, {9818,32272}, {9924,13417}, {10602,15141}, {11160,21844}, {11216,15140}, {11245,32241}, {11284,32300}, {11402,32245}, {11403,32250}, {11406,32277}, {11408,32301}, {11409,32302}, {11410,32305}, {12160,14984}, {13171,19459}, {16030,32258}, {16176,32262}, {18386,32273}, {19404,32293}, {19405,32294}

X(32240) = reflection of X(i) in X(j) for these (i,j): (12167, 19504), (13171, 19459), (32251, 32245)
X(32240) = X(1156)-of-anti-Ascella-triangle if ABC is acute
X(32240) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2930, 5095, 25), (32245, 32251, 11402)

X(32241) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ATIK TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32241) lies on these lines: {2,32251}, {4,67}, {69,125}, {110,19119}, {511,18933}, {542,18909}, {631,5181}, {1177,6353}, {1843,13203}, {1899,32255}, {2854,18935}, {2930,6776}, {3043,14912}, {3548,23296}, {3564,18932}, {5095,11433}, {6515,32244}, {6643,14984}, {8263,22467}, {8889,15116}, {10519,19457}, {11061,32285}, {11245,32240}, {11411,32275}, {12324,32250}, {12584,18925}, {13567,32276}, {14683,26926}, {16010,18913}, {18911,32248}, {18912,32249}, {18914,32254}, {18915,32259}, {18916,32234}, {18917,32272}, {18918,32273}, {18921,32277}, {18922,32286}, {18923,32291}, {18924,32292}, {18926,32293}, {18927,32294}, {18928,32300}, {18929,32301}, {18930,32302}, {18931,32305}, {19166,32258}, {23291,25328}

X(32241) = X(1156)-of-anti-Atik-triangle if ABC is acute
X(32241) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (67, 32246, 2892), (2892, 32246, 4)

X(32242) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th ANTI-BROCARD TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32242) lies on these lines: {32,67}, {83,6593}, {98,32274}, {125,1691}, {182,265}, {511,12201}, {542,3398}, {1078,6698}, {1503,12192}, {2781,12110}, {5038,15118}, {7787,11061}, {9970,10796}, {10788,32247}, {10789,32261}, {10790,32262}, {10791,32278}, {10792,32280}, {10793,32281}, {10795,32288}, {10797,32289}, {10798,32290}, {10800,32298}, {10801,32307}, {10802,32308}, {10803,32309}, {10804,32310}, {11364,32238}, {11380,32239}, {11490,32256}, {11837,32265}, {11838,32266}, {11839,32279}, {11840,32295}, {11841,32296}, {11842,32306}, {12193,14984}, {12835,32243}, {13885,32303}, {13938,32304}, {18502,32271}, {18993,32252}, {18994,32253}, {22520,32270}

X(32242) = X(67)-of-5th-anti-Brocard-triangle

X(32243) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-CIRCUMPERP-TANGENTIAL TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32243) lies on these lines: {1,542}, {3,32307}, {4,32290}, {6,12903}, {11,32274}, {12,6593}, {34,32239}, {55,32233}, {56,67}, {57,32261}, {110,12588}, {125,1428}, {265,613}, {388,11061}, {498,15462}, {511,18968}, {999,32306}, {1319,32238}, {1352,10091}, {1503,3024}, {2099,32298}, {2781,7354}, {3056,17702}, {3585,32271}, {4293,32247}, {5095,19369}, {5252,32278}, {5433,6698}, {5621,9672}, {11509,32256}, {12835,32242}, {14984,18970}, {18954,32262}, {18955,32265}, {18956,32266}, {18957,32268}, {18958,32279}, {18959,32280}, {18960,32281}, {18961,32287}, {18962,32288}, {18963,32295}, {18964,32296}, {18965,32303}, {18966,32304}, {18967,32310}, {18995,32252}, {18996,32253}

X(32243) = reflection of X(32297) in X(1)
X(32243) = X(67)-of-2nd-anti-circumperp-tangential-triangle
X(32243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 11061, 32289), (999, 32306, 32308)

X(32244) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-CIRCUMPERP TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32244) lies on these lines: {2,5095}, {3,32240}, {4,32275}, {6,6698}, {20,542}, {22,2930}, {30,32272}, {67,524}, {69,110}, {74,3564}, {97,32258}, {125,193}, {325,9769}, {394,32276}, {511,10296}, {576,15025}, {599,6593}, {690,16093}, {1205,8681}, {1297,20404}, {1351,14644}, {1352,10752}, {1353,15061}, {1370,32255}, {1494,4226}, {1992,15118}, {1993,32251}, {2071,32305}, {2407,30789}, {2777,5921}, {2781,5895}, {2836,3962}, {2854,12220}, {2892,11442}, {2979,32248}, {3043,19131}, {3060,32246}, {3100,32286}, {3101,32277}, {3146,32250}, {3153,32273}, {3448,20080}, {3620,5972}, {3631,25329}, {4296,32259}, {5012,32245}, {5093,20304}, {5505,18125}, {5622,15057}, {5663,11898}, {5847,7984}, {5965,11579}, {6515,32241}, {6699,14912}, {6776,15055}, {7488,12584}, {7519,32239}, {7691,32233}, {8541,31857}, {10519,15051}, {10721,18440}, {11008,25320}, {11411,16003}, {11412,12429}, {11413,16010}, {11414,32254}, {11417,32291}, {11418,32292}, {11420,32301}, {11421,32302}, {11477,15044}, {12272,13201}, {13171,19588}, {13417,14913}, {14683,32114}, {15116,23293}, {15303,21356}, {15534,30744}, {16266,20379}, {19406,32293}, {19407,32294}, {19510,22151}

X(32244) = midpoint of X(i) and X(j) for these lines: {i,j}: {3448, 20080}, {11412, 32249}, {12272, 13201}
X(32244) = reflection of X(i) in X(j) for these (i,j): (4, 32275), (110, 69), (193, 125), (895, 67), (3146, 32250), (5095, 32257), (9140, 13169), (10721, 18440), (10752, 1352), (11061, 5181), (11477, 32274), (13417, 14913), (14683, 32114), (15054, 32247), (16176, 6593), (25329, 3631), (32234, 3)
X(32244) = anticomplement of X(5095)
X(32244) = X(1156)-of-1st-anti-circumperp-triangle if ABC is acute
X(32244) = anticomplementary conjugate of the anticomplement of X(15398)
X(32244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (67, 895, 9140), (895, 13169, 67), (5095, 32257, 2)

X(32245) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-CONWAY TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32245) lies on these lines: {6,110}, {54,67}, {159,1112}, {182,32257}, {184,1177}, {389,12584}, {511,12227}, {542,578}, {567,32272}, {569,32275}, {1147,5181}, {1181,2781}, {1353,19138}, {1503,15472}, {1614,2904}, {1899,15116}, {2892,6776}, {3043,14912}, {3047,25321}, {3564,12228}, {5012,32244}, {6467,13248}, {8537,9971}, {9306,32300}, {11402,32240}, {11423,32249}, {11424,32250}, {11425,16010}, {11426,32254}, {11427,32255}, {11428,32277}, {11429,32286}, {11430,32305}, {11536,32284}, {12161,14984}, {13366,32260}, {15471,18374}, {17809,32276}, {18388,32273}, {19128,32113}, {19365,32259}, {19408,32293}, {19409,32294}, {19459,19504}, {23292,25328}

X(32245) = midpoint of X(i) and X(j) for these lines: {i,j}: {19459, 19504}, {32240, 32251}
X(32245) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 2930, 32246), (54, 32234, 5622)
X(32245) = X(1156)-of-anti-Conway-triangle if ABC is acute

X(32246) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-CONWAY TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32246) lies on these lines: {4,67}, {5,5181}, {6,110}, {24,5622}, {25,1177}, {51,5095}, {52,32275}, {125,1205}, {159,13198}, {185,32250}, {389,542}, {427,15116}, {468,2393}, {511,7687}, {568,32272}, {578,12584}, {599,11444}, {858,6698}, {974,1503}, {1112,9969}, {1192,5621}, {3060,32244}, {3313,13416}, {3564,12236}, {3567,32234}, {3575,31978}, {3867,23315}, {5663,19161}, {5943,14763}, {5972,9822}, {6217,32281}, {6218,32280}, {6403,14644}, {6642,15462}, {6723,11574}, {7716,10117}, {9777,32240}, {9781,32249}, {9786,16010}, {9792,32258}, {9967,23515}, {10821,12367}, {11061,12824}, {11433,32255}, {11435,32277}, {11436,32286}, {11438,32305}, {11579,12412}, {11585,16789}, {11800,14913}, {12061,20303}, {12167,13248}, {12220,15059}, {13567,25328}, {15128,23327}, {15647,20987}, {17810,32276}, {18390,32273}, {19039,32252}, {19040,32253}, {19366,32259}, {19410,32293}, {19411,32294}, {22968,23047}, {23292,25488}, {32239,32285}

X(32246) = midpoint of X(i) and X(j) for these lines: {i,j}: {52, 32275}, {125, 1843}, {185, 32250}, {5095, 32260}, {11800, 14913}, {32239, 32285}
X(32246) = reflection of X(i) in X(j) for these (i,j): (6, 11746), (1112, 9969), (3313, 13416), (5972, 9822), (11574, 6723), (15738, 32274)
X(32246) = polar-circle-inverse of X(34163)
X(32246) = X(1156)-of-2nd-anti-Conway-triangle if ABC is acute
X(32246) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 32241, 2892), (2892, 32241, 67)

X(32247) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EULER TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32247) lies on these lines: {2,9970}, {3,11061}, {4,67}, {20,542}, {24,32262}, {30,32306}, {66,11564}, {69,5663}, {74,5486}, {104,32270}, {110,10519}, {125,10752}, {146,1352}, {182,25321}, {193,11579}, {376,32233}, {388,32307}, {468,15106}, {497,32308}, {511,3448}, {515,32261}, {524,7464}, {541,11180}, {578,5095}, {631,6593}, {842,13574}, {895,16003}, {1205,15073}, {1350,12383}, {1351,10264}, {1503,12244}, {1992,20126}, {2393,32249}, {2777,32250}, {2854,12317}, {3085,32289}, {3086,32290}, {3090,6698}, {3091,32271}, {3520,5621}, {3523,15462}, {3541,11431}, {3547,16534}, {3564,10620}, {3618,15061}, {3619,14643}, {4293,32243}, {4294,32297}, {5085,25329}, {5181,14094}, {5480,15081}, {5603,32238}, {5655,21356}, {5657,32278}, {5900,22336}, {6103,10766}, {7487,32239}, {7492,9143}, {7581,32253}, {7582,32252}, {7731,19161}, {7967,32298}, {9140,31099}, {9862,32268}, {10753,15357}, {10783,32280}, {10784,32281}, {10785,32287}, {10786,32288}, {10788,32242}, {10805,32309}, {10806,32310}, {11411,14984}, {11477,25328}, {11491,32256}, {11843,32265}, {11844,32266}, {11845,32279}, {11846,32295}, {11847,32296}, {12041,25406}, {12112,32113}, {12164,23296}, {13886,32303}, {13939,32304}, {14927,20127}, {15063,32257}, {15122,22151}, {20301,20423}, {25336,31884}

X(32247) = midpoint of X(15054) and X(32244)
X(32247) = reflection of X(i) in X(j) for these (i,j): (4, 67), (146, 1352), (193, 11579), (895, 16003), (1351, 10264), (1992, 20126), (5095, 20417), (6776, 74), (7731, 19161), (10752, 125), (10753, 15357), (11061, 3), (11180, 13169), (11477, 25328), (12112, 32113), (12164, 23296), (12383, 1350), (14094, 5181), (14927, 20127), (15063, 32257), (15073, 1205), (16176, 8550)
X(32247) = anticomplement of X(9970)
X(32247) = X(67)-of-anti-Euler-triangle
X(32247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (125, 10752, 14853), (5095, 20417, 5622)

X(32248) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-EULER TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32248) lies on these lines: {2,32260}, {3,32249}, {6,110}, {22,32276}, {511,12270}, {542,12111}, {1177,26881}, {1843,25321}, {1993,32240}, {2393,11061}, {2781,12279}, {2979,32244}, {3060,5095}, {3448,6467}, {3564,12273}, {5012,32251}, {5486,11442}, {5663,12283}, {5889,13148}, {7998,32257}, {9019,16176}, {9973,25329}, {11416,15141}, {11439,32250}, {11440,16010}, {11441,32254}, {11444,32275}, {11445,32277}, {11446,32286}, {11449,12584}, {11451,32300}, {11454,32305}, {11459,32272}, {12220,13201}, {12281,18438}, {15074,32306}, {18392,32273}, {18911,32241}, {19167,32258}, {19367,32259}, {19412,32293}, {19413,32294}, {23293,25328}

X(32248) = reflection of X(i) in X(j) for these (i,j): (3448, 6467), (5889, 32234), (9973, 25329), (12272, 110), (12281, 18438), (13201, 12220), (32249, 3), (32306, 15074)
X(32248) = anticomplement of X(32260)
X(32248) = X(1156)-of-3rd-anti-Euler-triangle if ABC is acute
X(32248) = {X(12272), X(15531)}-harmonic conjugate of X(11443)

X(32249) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-EULER TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32249) lies on these lines: {3,32248}, {4,32260}, {24,32276}, {54,32251}, {67,15073}, {74,1296}, {110,19123}, {511,12281}, {542,6241}, {895,11458}, {1177,26882}, {1205,11457}, {1614,2930}, {2393,32247}, {2781,12290}, {3564,12284}, {3567,5095}, {5663,12272}, {5890,32234}, {6403,7731}, {7592,32240}, {7999,32257}, {8537,15141}, {9781,32246}, {9970,11188}, {11412,12429}, {11423,32245}, {11455,32250}, {11456,32254}, {11459,32275}, {11460,32277}, {11461,32286}, {11462,32291}, {11463,32292}, {11464,12584}, {11465,32300}, {11466,32301}, {11467,32302}, {11468,32305}, {11898,12273}, {12111,32272}, {15106,23061}, {18394,32273}, {18912,32241}, {19168,32258}, {19368,32259}, {19414,32293}, {19415,32294}, {23294,25328}

X(32249) = reflection of X(i) in X(j) for these (i,j): (4, 32260), (7731, 6403), (11412, 32244), (12111, 32272), (12273, 11898), (12283, 74), (15073, 67), (32248, 3)
X(32249) = X(1156)-of-4th-anti-Euler-triangle if ABC is acute

X(32250) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EXCENTERS-REFLECTIONS TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32250) lies on these lines: {4,542}, {20,32257}, {24,32305}, {25,16010}, {30,32275}, {33,32259}, {34,32286}, {64,67}, {110,15431}, {113,15432}, {125,468}, {185,32246}, {235,25328}, {378,12584}, {382,32272}, {403,20301}, {511,12292}, {541,32306}, {1177,26883}, {1205,15738}, {1352,16163}, {1498,32251}, {1593,2930}, {1597,32254}, {1843,5663}, {1902,2836}, {1974,11579}, {2777,32247}, {2781,11381}, {2854,12133}, {3091,32300}, {3146,32244}, {3515,5621}, {3564,12295}, {4232,9140}, {5094,5642}, {5622,6759}, {5921,10733}, {6103,11646}, {6723,25406}, {6776,7687}, {10151,15471}, {10295,11645}, {10301,12828}, {11403,32240}, {11424,32245}, {11439,32248}, {11455,32249}, {11471,32277}, {11472,17702}, {11473,32291}, {11474,32292}, {11475,32301}, {11476,32302}, {12134,18488}, {12162,14984}, {12324,32241}, {14216,20417}, {14982,24981}, {15118,19153}, {15133,16534}, {15811,32276}, {19169,32258}, {19416,32293}, {19417,32294}

X(32250) = midpoint of X(i) and X(j) for these lines: {i,j}: {382, 32272}, {3146, 32244}, {5921, 10733}, {11381, 32260}
X(32250) = reflection of X(i) in X(j) for these (i,j): (20, 32257), (185, 32246), (1205, 15738), (5095, 4), (6776, 7687), (10990, 67), (12294, 12133), (16163, 1352), (24981, 14982)
X(32250) = X(1156)-of-anti-excenters-reflections-triangle if ABC is acute

X(32251) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-EXTOUCH TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32251) lies on these lines: {2,32241}, {3,895}, {5,9512}, {6,67}, {25,1177}, {54,32249}, {69,23296}, {110,19125}, {155,32275}, {184,2930}, {185,16010}, {371,19385}, {372,19384}, {394,32257}, {427,2892}, {511,19457}, {542,1181}, {974,11579}, {1204,1205}, {1498,32250}, {1593,2781}, {1843,10117}, {1899,25328}, {1992,18281}, {1993,32244}, {2393,21284}, {2854,13198}, {2931,19131}, {2935,19124}, {3448,26926}, {3564,19456}, {3594,19399}, {5012,32248}, {5050,12228}, {5159,22151}, {6593,11284}, {6776,32255}, {7592,32234}, {9970,15738}, {10510,21639}, {10601,32300}, {10605,32305}, {11402,32240}, {12167,13171}, {12584,19357}, {14683,19119}, {14853,18933}, {15059,26206}, {15122,19348}, {16063,18919}, {18396,32273}, {18445,32272}, {19170,32258}, {19347,32254}, {19349,32259}, {19350,32277}, {19354,32286}, {19355,32291}, {19356,32292}, {19358,32293}, {19359,32294}, {19363,32301}, {19364,32302}, {32239,32264}

X(32251) = midpoint of X(12167) and X(13171)
X(32251) = reflection of X(i) in X(j) for these (i,j): (19459, 13198), (19504, 6), (32240, 32245)
X(32251) = X(1156)-of-2nd-anti-extouch-triangle if ABC is acute
X(32251) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 67, 15141), (6, 32276, 5095), (125, 15118, 15128)

X(32252) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GREBE TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32252) lies on these lines: {2,32304}, {6,67}, {141,19111}, {372,32233}, {511,19051}, {542,3312}, {1503,19059}, {1587,32274}, {1588,2781}, {3068,6698}, {3069,6593}, {3299,32307}, {3301,32308}, {3763,8998}, {5085,13969}, {5411,32239}, {5648,32291}, {6418,32306}, {7582,32247}, {7584,9970}, {7585,32303}, {7586,11061}, {7968,32298}, {9971,19043}, {12367,19001}, {13785,32271}, {13910,15059}, {13936,32278}, {13966,15462}, {13979,14561}, {14984,19061}, {18991,32238}, {18993,32242}, {18995,32243}, {18999,32256}, {19003,32261}, {19005,32262}, {19007,32265}, {19009,32266}, {19011,32268}, {19013,32270}, {19017,32279}, {19023,32287}, {19025,32288}, {19027,32289}, {19029,32290}, {19031,32295}, {19033,32296}, {19037,32297}, {19039,32246}, {19047,32309}, {19049,32310}

X(32252) = X(67)-of-anti-inner-Grebe-triangle
X(32252) = {X(6), X(67)}-harmonic conjugate of X(32253)

X(32253) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-GREBE TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32253) lies on these lines: {2,32303}, {6,67}, {141,19110}, {371,32233}, {511,19052}, {542,3311}, {1503,19060}, {1587,2781}, {1588,32274}, {3068,6593}, {3069,6698}, {3299,32308}, {3301,32307}, {3763,13990}, {5085,8994}, {5410,32239}, {5648,32292}, {6417,32306}, {7581,32247}, {7583,9970}, {7585,11061}, {7586,32304}, {7969,32298}, {8981,15462}, {9971,19044}, {12367,19002}, {13665,32271}, {13883,32278}, {13915,14561}, {13972,15059}, {14984,19062}, {18992,32238}, {18994,32242}, {18996,32243}, {19000,32256}, {19004,32261}, {19006,32262}, {19008,32265}, {19010,32266}, {19012,32268}, {19014,32270}, {19018,32279}, {19024,32287}, {19026,32288}, {19028,32289}, {19030,32290}, {19032,32295}, {19034,32296}, {19038,32297}, {19040,32246}, {19048,32309}, {19050,32310}

X(32253) = X(67)-of-anti-outer-Grebe-triangle
X(32253) = {X(6), X(67)}-harmonic conjugate of X(32252)

X(32254) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INCIRCLE-CIRCLES TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32254) lies on these lines: {3,67}, {4,32240}, {5,32255}, {23,3564}, {25,32234}, {110,5050}, {399,1351}, {511,12308}, {575,18350}, {895,3527}, {999,32259}, {1177,14530}, {1181,32260}, {1352,8546}, {1482,2836}, {1597,32250}, {1598,5095}, {1656,25328}, {1995,9143}, {2781,12315}, {3295,32286}, {3311,32291}, {3312,32292}, {3843,32273}, {5055,20301}, {5093,19140}, {5655,16510}, {5663,11820}, {5921,12168}, {5965,25336}, {6403,12165}, {6759,32276}, {7530,11061}, {9920,15581}, {9924,10628}, {10272,25320}, {10306,32277}, {10510,19377}, {11414,32244}, {11426,32245}, {11432,32246}, {11441,32248}, {11456,32249}, {11477,12316}, {11484,32300}, {11485,32301}, {11486,32302}, {11579,12017}, {12106,18951}, {12164,12271}, {12902,14982}, {15039,15462}, {17702,19588}, {18440,31861}, {18583,20125}, {18914,32241}, {19173,32258}, {19347,32251}, {19418,32293}, {19419,32294}, {24206,25330}

X(32254) = reflection of X(i) in X(j) for these (i,j): (3, 2930), (895, 5609), (1351, 399), (12902, 14982), (16010, 12584), (32255, 5), (32262, 15581), (32276, 6759)
X(32254) = inverse of X(8724) in the Stammler circle
X(32254) = X(1156)-of-anti-incircle-circles-triangle if ABC is acute
X(32254) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2930, 16010, 12584), (12584, 16010, 3)

X(32255) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INVERSE-IN-INCIRCLE TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32255) lies on these lines: {2,2930}, {4,542}, {5,32254}, {6,7533}, {8,2836}, {20,16010}, {67,69}, {110,3618}, {125,3619}, {141,25330}, {193,16176}, {265,18489}, {376,32305}, {388,32259}, {399,14853}, {427,32240}, {497,32286}, {511,12317}, {524,5189}, {631,12584}, {1177,11206}, {1205,11457}, {1370,32244}, {1503,17812}, {1843,18947}, {1899,32241}, {2407,5984}, {2550,32277}, {2781,12324}, {2892,32064}, {3068,32291}, {3069,32292}, {3090,20301}, {3522,5621}, {3564,7574}, {3629,25336}, {4558,10991}, {5181,9140}, {5486,11442}, {5622,13336}, {5648,6698}, {5987,7735}, {6593,9143}, {6643,32275}, {6776,32251}, {7386,32257}, {7392,32300}, {8550,14516}, {9976,14912}, {10264,10519}, {11008,13203}, {11411,14984}, {11427,32245}, {11433,32246}, {11488,32301}, {11489,32302}, {11579,12383}, {12308,21850}, {14561,20125}, {14791,32306}, {14927,17702}, {15583,17847}, {18531,32272}, {19174,32258}, {19420,32293}, {19421,32294}

X(32255) = reflection of X(i) in X(j) for these (i,j): (20, 16010), (69, 3448), (2930, 25328), (11061, 895), (12308, 21850), (12383, 11579), (14683, 6), (17847, 15583), (25336, 3629), (32254, 5)
X(32255) = anticomplementary conjugate of the anticomplement of X(13574)
X(32255) = anticomplement of X(2930)
X(32255) = inverse of X(671) in the anticomplementary circle
X(32255) = X(1156)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(32255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (895, 11061, 1992), (2930, 25328, 2)

X(32256) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32256) lies on these lines: {3,32270}, {35,32261}, {55,67}, {56,32298}, {100,11061}, {197,32262}, {511,12334}, {542,11248}, {1001,6698}, {1376,6593}, {1503,12327}, {2781,11500}, {2836,3811}, {2930,4062}, {3295,32238}, {5687,32278}, {5846,22586}, {9970,11499}, {10310,32233}, {11383,32239}, {11490,32242}, {11491,32247}, {11492,32265}, {11493,32266}, {11494,32268}, {11496,32274}, {11497,32280}, {11498,32281}, {11501,32289}, {11502,32290}, {11503,32295}, {11504,32296}, {11507,32307}, {11508,32308}, {11509,32243}, {11510,32310}, {11848,32279}, {11849,32306}, {12328,14984}, {13887,32303}, {13940,32304}, {15622,16010}, {18491,32271}, {18999,32252}, {19000,32253}

X(32256) = reflection of X(i) in X(j) for these (i,j): (32270, 3), (32287, 6593)
X(32256) = X(67)-of-anti-Mandart-incircle-triangle

X(32257) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32257) lies on these lines: {2,5095}, {3,67}, {6,6723}, {20,32250}, {23,32239}, {69,125}, {95,32258}, {110,3620}, {141,5972}, {182,32245}, {193,15059}, {394,32251}, {511,7687}, {524,5159}, {631,32234}, {1038,32259}, {1040,32286}, {1092,5622}, {1112,9822}, {1177,9306}, {1216,14984}, {1270,13774}, {1271,13654}, {1351,23515}, {1352,2777}, {1368,22165}, {2781,5893}, {2854,3631}, {3284,15993}, {3292,32285}, {3448,15812}, {3564,6699}, {3917,32260}, {5642,11061}, {5847,11735}, {5894,8263}, {5921,15055}, {7386,32255}, {7484,32240}, {7998,32248}, {7999,32249}, {8542,15116}, {9970,11487}, {9972,14076}, {10319,32277}, {10510,19378}, {10519,16163}, {11178,32271}, {11284,12828}, {11513,32291}, {11514,32292}, {11515,32301}, {11516,32302}, {11585,20301}, {11850,15027}, {11898,15061}, {12359,15115}, {12363,15605}, {14645,15359}, {15063,32247}, {15303,16176}, {15533,30771}, {16111,18440}, {17811,32276}, {18323,19924}, {18531,32273}, {19422,32293}, {19423,32294}, {29012,32113}

X(32257) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32275}, {20, 32250}, {67, 5181}, {69, 125}, {3448, 32114}, {5095, 32244}, {5642, 13169}, {15063, 32247}, {16111, 18440}, {30714, 32306}
X(32257) = reflection of X(i) in X(j) for these (i,j): (6, 6723), (1112, 9822), (5095, 32300), (5972, 141), (11574, 13416), (15118, 6698)
X(32257) = anticomplement of X(32300)
X(32257) = complement of X(5095)
X(32257) = inverse of X(9876) in the circumcircle
X(32257) = X(1156)-of-6th-anti-mixtilinear-triangle if ABC is acute
X(32257) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5095, 32300), (2, 32244, 5095)

X(32258) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-SHARYGIN TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32258) lies on these lines: {54,67}, {95,32257}, {97,32244}, {110,19171}, {275,5095}, {511,19195}, {542,8884}, {895,8795}, {1177,26887}, {2781,19206}, {2854,19197}, {2930,19189}, {3564,19193}, {9792,32246}, {12584,19185}, {14984,19194}, {16010,19172}, {16030,32240}, {19166,32241}, {19167,32248}, {19168,32249}, {19169,32250}, {19170,32251}, {19173,32254}, {19174,32255}, {19175,32259}, {19176,32272}, {19177,32273}, {19179,32275}, {19180,32276}, {19181,32277}, {19182,32286}, {19183,32291}, {19184,32292}, {19186,32293}, {19187,32294}, {19188,32300}, {19190,32301}, {19191,32302}, {19192,32305}, {21638,32260}, {23295,25328}

X(32258) = X(1156)-of-1st-anti-Sharygin-triangle if ABC is acute

X(32259) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-TANGENTIAL-MIDARC TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32259) lies on these lines: {1,542}, {12,25328}, {33,32250}, {34,5095}, {35,32305}, {36,12584}, {55,16010}, {56,2930}, {65,651}, {67,73}, {110,1428}, {221,32276}, {388,32255}, {399,613}, {511,19470}, {524,7286}, {999,32254}, {1038,32257}, {1060,32275}, {1177,26888}, {1398,32240}, {1425,32260}, {1431,2842}, {1442,12739}, {1469,2854}, {1503,5160}, {1870,32234}, {2067,32291}, {2330,10088}, {2781,7355}, {3056,5663}, {3448,12588}, {3564,19469}, {3585,32273}, {4296,32244}, {4551,5018}, {5217,5621}, {5297,9140}, {6126,9976}, {6502,32292}, {7051,32301}, {7352,14984}, {7951,20301}, {8540,9970}, {12904,14982}, {14094,32290}, {18447,32272}, {18915,32241}, {19175,32258}, {19349,32251}, {19365,32245}, {19366,32246}, {19367,32248}, {19368,32249}, {19370,32293}, {19371,32294}, {19372,32300}, {19373,32302}

X(32259) = reflection of X(i) in X(j) for these (i,j): (1469, 3028), (32286, 1)
X(32259) = X(1156)-of-anti-tangential-midarc-triangle if ABC is acute
X(32259) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (895, 32289, 19369), (10088, 11579, 2330)

X(32260) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-WASAT TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32260) lies on these lines: {2,32248}, {4,32249}, {6,32240}, {25,32276}, {51,5095}, {67,1205}, {69,18125}, {110,14913}, {125,126}, {182,17701}, {184,2930}, {185,542}, {193,11800}, {373,32300}, {389,32234}, {511,10296}, {895,3292}, {1147,19361}, {1177,1495}, {1181,32254}, {1204,16010}, {1216,15133}, {1425,32259}, {1843,13417}, {1899,32241}, {2781,11381}, {2888,11444}, {2892,11550}, {3270,32286}, {3448,12272}, {3564,21649}, {3611,32277}, {3917,32257}, {5562,14984}, {5622,12584}, {6403,10628}, {6593,29959}, {7722,21851}, {8541,15141}, {9924,13171}, {9971,16176}, {11061,11188}, {12167,17847}, {13366,32245}, {13754,32272}, {13851,32273}, {16270,30714}, {21638,32258}, {21640,32291}, {21641,32292}, {21642,32293}, {21643,32294}, {21647,32301}, {21648,32302}, {21663,32305}

X(32260) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32249}, {3448, 12272}
X(32260) = reflection of X(i) in X(j) for these (i,j): (110, 14913), (193, 11800), (1205, 67), (5095, 32246), (5562, 32275), (6467, 125), (7722, 21851), (11381, 32250), (13417, 1843), (32234, 389)
X(32260) = complement of X(32248)
X(32260) = X(1156)-of-anti-Wasat-triangle if ABC is acute
X(32260) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2930, 32251, 184), (5095, 32246, 51)

X(32261) = ORTHOLOGIC CENTER OF THESE TRIANGLES: AQUILA TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32261) lies on these lines: {1,67}, {10,11061}, {35,32256}, {36,32270}, {40,542}, {57,32243}, {125,16475}, {165,32233}, {511,12407}, {515,32247}, {517,32306}, {1503,9904}, {1697,32297}, {1698,6593}, {1699,32274}, {2781,5691}, {2836,5904}, {2948,3416}, {3099,32268}, {3448,5847}, {3624,6698}, {3679,32278}, {3751,13211}, {4663,16176}, {5587,9970}, {5588,32281}, {5589,32280}, {7713,32239}, {8185,32262}, {8186,32265}, {8187,32266}, {8188,32295}, {8189,32296}, {9578,32289}, {9581,32290}, {9896,14984}, {10789,32242}, {10826,32287}, {10827,32288}, {11852,32279}, {13888,32303}, {13942,32304}, {15462,31423}, {18492,32271}, {19003,32252}, {19004,32253}

X(32261) = reflection of X(i) in X(j) for these (i,j): (1, 67), (2948, 3416), (3751, 13211), (11061, 10), (16176, 4663), (32298, 32238)
X(32261) = X(67)-of-Aquila-triangle
X(32261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (67, 32298, 32238), (32238, 32298, 1)

X(32262) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARA TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32262) lies on these lines: {3,1177}, {6,1205}, {22,11061}, {24,32247}, {25,67}, {159,2930}, {197,32256}, {206,17847}, {382,25328}, {511,12412}, {542,7387}, {597,14130}, {1204,19136}, {1503,9919}, {1593,5621}, {1598,32274}, {1995,2892}, {2393,32276}, {2777,23049}, {2916,25331}, {2937,15582}, {3556,5904}, {5020,6698}, {5594,32281}, {5595,32280}, {6293,9968}, {7517,32306}, {8185,32261}, {8190,32265}, {8191,32266}, {8192,32298}, {8193,32278}, {8194,32295}, {8195,32296}, {9818,32271}, {9908,14984}, {9914,16010}, {9920,15581}, {10037,32307}, {10046,32308}, {10628,19149}, {10790,32242}, {10828,32268}, {10829,32287}, {10830,32288}, {10831,32289}, {10832,32290}, {10833,32297}, {10834,32309}, {10835,32310}, {11284,15116}, {11365,32238}, {11414,32233}, {11853,32279}, {13201,20806}, {13203,23300}, {13889,32303}, {13943,32304}, {15579,20427}, {16176,32240}, {18954,32243}, {19005,32252}, {19006,32253}, {22654,32270}

X(32262) = reflection of X(i) in X(j) for these (i,j): (159, 10117), (13203, 23300), (15141, 1177), (17847, 206), (32254, 15581)
X(32262) = X(67)-of-Ara-triangle
X(32262) = {X(1177), X(15141)}-harmonic conjugate of X(19153)

X(32263) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH TO ARIES

The reciprocal orthologic center of these triangles is X(32264).

X(32263) lies on these lines: {6,5181}, {20,68}, {52,113}, {110,6353}, {125,343}, {161,542}, {511,32125}, {569,5504}, {1209,10170}, {1495,3564}, {1511,13292}, {2777,17834}, {2931,3515}, {3569,14391}, {5448,11002}, {5449,7999}, {5642,32226}, {6053,12164}, {6146,16163}, {8057,32112}, {8673,32120}, {8681,32113}, {9517,32121}, {11472,12295}, {12893,15078}, {13198,19131}, {13399,20725}, {13754,32111}

X(32263) = reflection of X(i) in X(j) for these (i,j): (12164, 6053), (30714, 2931)

X(32264) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARIES TO WALSMITH

The reciprocal orthologic center of these triangles is X(32263).

X(32264) lies on these lines: {20,2781}, {25,32285}, {67,468}, {69,15647}, {125,19118}, {154,5181}, {159,2930}, {382,17813}, {542,1498}, {895,1503}, {1853,15118}, {2854,5596}, {2892,6593}, {3564,9934}, {5095,5895}, {5622,6247}, {5648,31166}, {5972,19132}, {9833,14984}, {11598,25406}, {13203,25321}, {14982,19149}, {15116,19153}, {15126,15128}, {15141,31152}, {15462,16196}, {20079,25320}, {32239,32251}

X(32264) = reflection of X(i) in X(j) for these (i,j): (67, 1177), (69, 15647), (2892, 6593), (5648, 31166), (14982, 19149)
X(32264) = {X(2892), X(6593)}-harmonic conjugate of X(15131)

X(32265) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st AURIGA TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32265) lies on these lines: {55,32266}, {67,5597}, {542,11252}, {2781,9834}, {5598,32298}, {5599,6593}, {5601,11061}, {5846,13209}, {8186,32261}, {8190,32262}, {8196,32274}, {8197,32278}, {8198,32280}, {8199,32281}, {8200,9970}, {11366,32238}, {11384,32239}, {11492,32256}, {11493,32270}, {11822,32233}, {11837,32242}, {11843,32247}, {11861,32268}, {11865,32287}, {11867,32288}, {11869,32289}, {11871,32290}, {11873,32297}, {11875,32306}, {11877,32307}, {11879,32308}, {11881,32309}, {11883,32310}, {13890,32303}, {13944,32304}, {18495,32271}, {18955,32243}, {19007,32252}, {19008,32253}

X(32265) = reflection of X(32266) in X(55)
X(32265) = X(67)-of-1st-Auriga-triangle

X(32266) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd AURIGA TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32266) lies on these lines: {55,32265}, {67,5598}, {542,11253}, {2781,9835}, {5597,32298}, {5600,6593}, {5602,11061}, {5846,13208}, {8187,32261}, {8191,32262}, {8203,32274}, {8204,32278}, {8205,32280}, {8206,32281}, {8207,9970}, {11367,32238}, {11385,32239}, {11492,32270}, {11493,32256}, {11823,32233}, {11838,32242}, {11844,32247}, {11862,32268}, {11866,32287}, {11868,32288}, {11870,32289}, {11872,32290}, {11874,32297}, {11876,32306}, {11878,32307}, {11880,32308}, {11882,32309}, {11884,32310}, {13891,32303}, {13945,32304}, {18497,32271}, {18956,32243}, {19009,32252}, {19010,32253}

X(32266) = reflection of X(32265) in X(55)
X(32266) = X(67)-of-2nd-Auriga-triangle

X(32267) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: WALSMITH TO 4th BROCARD

See preamble just before X(31353).

X(32267) lies on these lines: {2,6030}, {23,5642}, {25,5476}, {30,5972}, {154,11225}, {182,26255}, {376,1533}, {468,11645}, {541,7575}, {542,1495}, {575,20192}, {1995,10168}, {2070,5655}, {3524,16187}, {4232,11179}, {5646,15706}, {5965,15360}, {7493,11178}, {12100,15082}, {12105,16534}, {13857,29317}, {14002,25555}, {14848,31860}, {14915,18579}, {15303,18374}

X(32267) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 5642}, {376, 1533}, {1495, 7426}
X(32267) = reflection of X(32223) in X(7426)
X(32267) = {X(15448), X(32237)}-harmonic conjugate of X(5972)

X(32268) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th BROCARD TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32268) lies on these lines: {32,67}, {511,12501}, {542,7826}, {1503,9984}, {2781,9873}, {2896,11061}, {3096,6593}, {3098,32233}, {3099,32261}, {6698,7846}, {9301,32306}, {9857,32278}, {9862,32247}, {9923,14984}, {9970,9996}, {9993,32274}, {9994,32280}, {9995,32281}, {9997,32298}, {10038,32307}, {10047,32308}, {10828,32262}, {10871,32287}, {10872,32288}, {10873,32289}, {10874,32290}, {10875,32295}, {10876,32296}, {10877,32297}, {10878,32309}, {10879,32310}, {11368,32238}, {11386,32239}, {11494,32256}, {11861,32265}, {11862,32266}, {11885,32279}, {13892,32303}, {13946,32304}, {18500,32271}, {18957,32243}, {19011,32252}, {19012,32253}, {22744,32270}

X(32268) = X(67)-of-5th-Brocard-triangle

X(32269) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: WALSMITH TO CIRCUMORTHIC

See preamble just before X(31353).

X(32269) lies on these lines: {2,1350}, {3,16657}, {6,7493}, {22,13567}, {23,1503}, {25,343}, {26,6146}, {30,125}, {51,6676}, {52,13383}, {68,9714}, {69,4232}, {107,297}, {110,524}, {140,373}, {141,1995}, {154,6515}, {184,1353}, {187,6388}, {193,15585}, {230,3124}, {237,23181}, {381,4549}, {394,6353}, {428,21243}, {460,13449}, {462,20429}, {463,20428}, {468,511}, {542,32237}, {549,22112}, {599,26255}, {858,15059}, {1211,4228}, {1213,7474}, {1330,4248}, {1370,26958}, {1495,3564}, {1514,3581}, {1620,30552}, {1624,5201}, {1648,4226}, {1853,7500}, {1899,9909}, {1993,10192}, {2070,12310}, {3060,23292}, {3098,30739}, {3146,6696}, {3542,17834}, {3589,5640}, {3631,10546}, {3658,15447}, {3796,10565}, {3818,10301}, {3917,6677}, {4239,26543}, {5054,5544}, {5094,31670}, {5104,24855}, {5446,7542}, {5449,7553}, {5562,21841}, {5663,16619}, {5889,16252}, {5943,7499}, {5946,25337}, {6243,9820}, {6329,15019}, {6723,19924}, {6800,8550}, {7391,23332}, {7465,25964}, {7488,12241}, {7494,10601}, {7503,15873}, {7517,12359}, {7530,16654}, {7556,12022}, {7568,10095}, {7570,7693}, {7706,15760}, {9019,11746}, {9730,16618}, {9970,32227}, {10020,10263}, {10516,31860}, {10625,16238}, {11002,14389}, {11003,12007}, {11594,32311}, {11649,11800}, {11745,13160}, {12088,26879}, {12107,12370}, {12828,16165}, {13142,13367}, {14449,18282}, {14693,15366}, {15993,20998}, {16195,19467}, {16789,19136}, {17522,26579}, {20850,31383}

X(32269) = midpoint of X(i) and X(j) for these lines: {i,j}: {23, 3580}, {858, 15107}, {3581, 11799}, {7426, 15360}
X(32269) = reflection of X(i) in X(j) for these (i,j): (110, 15448), (468, 32223), (1514, 11799), (11064, 468)
X(32269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 7493, 13394), (5640, 7495, 3589)

X(32270) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd CIRCUMPERP TANGENTIAL TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32270) lies on these lines: {1,15141}, {3,32256}, {36,32261}, {55,32298}, {56,67}, {104,32247}, {511,19478}, {542,11249}, {956,32278}, {958,6593}, {999,32238}, {1503,22583}, {2781,12114}, {2930,23361}, {2975,11061}, {3428,32233}, {5846,13204}, {6698,25524}, {9970,22758}, {10966,32297}, {11492,32266}, {11493,32265}, {14984,22659}, {18761,32271}, {19013,32252}, {19014,32253}, {22479,32239}, {22520,32242}, {22654,32262}, {22744,32268}, {22753,32274}, {22755,32279}, {22756,32280}, {22757,32281}, {22759,32289}, {22760,32290}, {22761,32295}, {22762,32296}, {22763,32303}, {22764,32304}, {22765,32306}, {22766,32307}, {22767,32308}, {22768,32309}

X(32270) = reflection of X(i) in X(j) for these (i,j): (32256, 3), (32288, 6593)
X(32270) = X(67)-of-2nd-circumperp-tangential-triangle

X(32271) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-MID TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32271) lies on these lines: {4,542}, {5,2781}, {6,7728}, {20,15462}, {23,5642}, {30,6593}, {67,381}, {74,14561}, {110,7519}, {113,511}, {125,5169}, {146,11579}, {182,1177}, {265,25335}, {382,15140}, {389,16003}, {541,5476}, {546,32274}, {611,12374}, {613,12373}, {858,12824}, {1350,14643}, {1351,14982}, {1352,10752}, {1478,32290}, {1479,32289}, {1503,1539}, {1511,29181}, {2854,21850}, {2930,5655}, {3091,32247}, {3098,5972}, {3583,32297}, {3585,32243}, {3589,12041}, {3618,12244}, {3843,32306}, {5085,20127}, {5092,16111}, {5480,5663}, {7527,10990}, {7530,12584}, {7540,30714}, {9818,32262}, {9955,32238}, {10296,13202}, {10510,18325}, {10605,15128}, {10895,32307}, {10896,32308}, {11178,32257}, {11444,18504}, {11645,15303}, {12061,14984}, {12699,32278}, {13665,32253}, {13785,32252}, {14483,18125}, {16163,29317}, {16176,32272}, {17702,19139}, {18491,32256}, {18492,32261}, {18495,32265}, {18497,32266}, {18500,32268}, {18502,32242}, {18507,32279}, {18509,32280}, {18511,32281}, {18516,32287}, {18517,32288}, {18520,32295}, {18522,32296}, {18525,32298}, {18538,32303}, {18542,32309}, {18544,32310}, {18553,32275}, {18761,32270}, {18762,32304}

X(32271) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 9970}, {6, 7728}, {110, 31670}, {146, 11579}, {382, 32233}, {1351, 14982}, {1352, 10752}, {10510, 18325}, {10706, 20423}, {12699, 32278}, {16176, 32272}, {18507, 32279}, {18525, 32298}
X(32271) = reflection of X(i) in X(j) for these (i,j): (125, 19130), (3098, 5972), (5642, 25566), (12041, 3589), (12584, 16534), (16003, 20301), (16111, 5092), (32238, 9955), (32274, 546), (32275, 18553), (32305, 15118)
X(32271) = X(67)-of-Ehrmann-mid-triangle
X(32271) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (146, 14853, 11579), (5476, 32305, 15118)

X(32272) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-SIDE TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32272) lies on these lines: {3,67}, {5,32234}, {30,32244}, {49,5622}, {69,12121}, {110,19129}, {193,10113}, {265,895}, {381,5095}, {382,32250}, {511,22584}, {524,18323}, {567,32245}, {568,32246}, {1177,10540}, {1352,6593}, {1353,14644}, {1503,20127}, {2072,25328}, {2781,18439}, {2854,7723}, {3448,16051}, {3545,10294}, {5055,32300}, {5093,7687}, {5159,9140}, {5655,11061}, {5663,5921}, {6288,9970}, {6698,11179}, {6776,15061}, {7728,18440}, {9818,32240}, {10255,20301}, {10510,18441}, {11459,32248}, {11562,14913}, {11898,17702}, {12111,32249}, {12272,12281}, {13754,32260}, {14516,15054}, {14912,20304}, {14984,18436}, {15027,15128}, {16176,32271}, {18403,32273}, {18445,32251}, {18447,32259}, {18451,32276}, {18453,32277}, {18455,32286}, {18457,32291}, {18459,32292}, {18462,32293}, {18463,32294}, {18468,32301}, {18470,32302}, {18531,32255}, {18917,32241}, {19176,32258}, {20397,26944}

X(32272) = midpoint of X(i) and X(j) for these lines: {i,j}: {12111, 32249}, {12272, 12281}
X(32272) = reflection of X(i) in X(j) for these (i,j): (3, 32275), (193, 10113), (382, 32250), (5655, 11180), (7728, 18440), (11562, 14913), (12121, 69), (16176, 32271), (18438, 7723), (32234, 5)
X(32272) = X(1156)-of-Ehrmann-side-triangle if ABC is acute
X(32272) = Stammler-circle-inverse of X(9876)

X(32273) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-VERTEX TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32273) lies on these lines: {3,20301}, {4,542}, {5,12584}, {6,12902}, {30,25328}, {67,265}, {74,29317}, {110,7533}, {125,3098}, {141,11801}, {182,15118}, {381,2930}, {382,16010}, {524,18572}, {575,32233}, {578,30714}, {1177,18400}, {1351,16176}, {1352,18387}, {1503,9976}, {1657,5621}, {2781,10263}, {2836,18480}, {2854,3818}, {3153,32244}, {3448,16981}, {3564,19479}, {3583,32286}, {3585,32259}, {3843,32254}, {3845,16510}, {5092,12121}, {5181,11178}, {5189,9140}, {5476,6593}, {5480,19140}, {5622,21659}, {5648,25561}, {5987,9993}, {6288,18553}, {6564,32291}, {6565,32292}, {9143,25566}, {9927,11591}, {10264,29181}, {10620,25330}, {10733,11579}, {11477,32306}, {11564,18125}, {11645,18325}, {12370,18428}, {12383,14561}, {13293,23300}, {13434,15462}, {13851,32260}, {14644,24206}, {14810,15061}, {14853,25556}, {15116,23325}, {15141,23049}, {16163,17508}, {16808,32301}, {16809,32302}, {18382,19506}, {18386,32240}, {18388,32245}, {18390,32246}, {18392,32248}, {18394,32249}, {18396,32251}, {18403,32272}, {18404,32275}, {18405,32276}, {18406,32277}, {18414,32293}, {18415,32294}, {18420,32300}, {18531,32257}, {18918,32241}, {19177,32258}

X(32273) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 12902}, {382, 16010}, {3448, 31670}, {10733, 11579}, {11477, 32306}
X(32273) = reflection of X(i) in X(j) for these (i,j): (3, 20301), (110, 19130), (141, 11801), (3098, 125), (3818, 10113), (5648, 25561), (9143, 25566), (12121, 5092), (12584, 5), (13293, 23300), (19140, 5480), (19506, 18382), (32233, 575), (32305, 25328)
X(32273) = X(1156)-of-Ehrmann-vertex-triangle if ABC is acute

X(32274) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EULER TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32274) lies on these lines: {2,32233}, {3,6698}, {4,67}, {5,542}, {6,7699}, {11,32243}, {12,32297}, {24,5621}, {30,8262}, {66,10293}, {98,32242}, {110,10516}, {113,25488}, {125,468}, {141,17702}, {182,20304}, {235,32239}, {265,1352}, {371,32303}, {372,32304}, {381,9970}, {511,10113}, {515,32238}, {524,10297}, {546,32271}, {895,15069}, {1350,10733}, {1478,32308}, {1479,32307}, {1511,24206}, {1587,32252}, {1588,32253}, {1598,32262}, {1614,5622}, {1656,15462}, {1699,32261}, {1986,32191}, {1995,9140}, {2493,11005}, {2836,5777}, {3091,11061}, {3448,14982}, {3564,11801}, {3574,5095}, {3575,10990}, {3589,23515}, {3763,15035}, {3818,5663}, {5085,15059}, {5480,7687}, {5587,32278}, {5603,32298}, {5921,25320}, {6103,28343}, {6201,32281}, {6202,32280}, {6247,13419}, {6776,15081}, {7495,16165}, {7533,12824}, {7547,16176}, {7574,9019}, {7575,11645}, {8196,32265}, {8203,32266}, {8212,32295}, {8213,32296}, {9517,18312}, {9815,25711}, {9927,11591}, {9969,10628}, {9993,32268}, {10531,32309}, {10532,32310}, {10893,32287}, {10894,32288}, {10895,32289}, {10896,32290}, {11178,12584}, {11477,15044}, {11496,32256}, {11579,18440}, {11897,32279}, {12041,29012}, {12061,18383}, {12106,20379}, {12295,29181}, {12588,12904}, {12589,12903}, {14094,25335}, {14787,23236}, {15577,19457}, {19161,21650}, {22753,32270}

X(32274) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 67}, {265, 1352}, {895, 15069}, {1350, 10733}, {3448, 14982}, {9970, 32306}, {11005, 11646}, {11477, 32244}, {11579, 18440}, {14094, 25335}, {15738, 32246}, {19161, 21650}
X(32274) = reflection of X(i) in X(j) for these (i,j): (3, 6698), (182, 20304), (1511, 24206), (1986, 32191), (5480, 7687), (6593, 5), (8550, 15118), (32271, 546), (32305, 20379)
X(32274) = complement of X(32233)
X(32274) = X(67)-of-Euler-triangle
X(32274) = {X(381), X(32306)}-harmonic conjugate of X(9970)

X(32275) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd EULER TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32275) lies on these lines: {2,32234}, {3,67}, {4,32244}, {5,5095}, {6,23515}, {30,32250}, {52,32246}, {68,895}, {69,4549}, {74,5921}, {110,19131}, {113,1352}, {125,3292}, {155,32251}, {193,14644}, {265,11898}, {511,7723}, {524,10297}, {541,11180}, {569,32245}, {575,24572}, {1060,32259}, {1062,32286}, {1147,5622}, {1177,10539}, {1209,6593}, {1351,7687}, {1353,20304}, {1503,16111}, {1656,32300}, {1995,12828}, {2072,20301}, {2777,18440}, {2781,12162}, {2854,9967}, {3620,15035}, {5050,6723}, {5562,14984}, {5609,31831}, {5965,18449}, {6334,9003}, {6403,12219}, {6643,32255}, {6698,8550}, {6699,6776}, {7395,32240}, {7530,32239}, {8251,32277}, {9140,16051}, {9822,16222}, {10510,19380}, {10628,14913}, {10634,32301}, {10635,32302}, {10897,32291}, {10898,32292}, {11061,16534}, {11178,15303}, {11411,32241}, {11444,32248}, {11459,32249}, {11585,25328}, {14912,15059}, {17814,32276}, {18404,32273}, {18553,32271}, {19179,32258}, {19428,32293}, {19429,32294}

X(32275) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32272}, {4, 32244}, {67, 15069}, {74, 5921}, {265, 11898}, {5562, 32260}, {6403, 12219}, {11180, 13169}
X(32275) = reflection of X(i) in X(j) for these (i,j): (3, 32257), (52, 32246), (113, 1352), (1351, 7687), (1353, 20304), (5095, 5), (6776, 6699), (8550, 6698), (9967, 12358), (11061, 16534), (15303, 11178), (16003, 67), (30714, 5181), (32271, 18553)
X(32275) = complement of X(32234)
X(32275) = X(1156)-of-2nd-Euler-triangle if ABC is acute

X(32276) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st EXCOSINE TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32276) lies on these lines: {6,67}, {22,32248}, {24,32249}, {25,32260}, {64,895}, {66,25330}, {110,19132}, {154,1177}, {184,32240}, {221,32259}, {394,32244}, {511,15138}, {542,1498}, {1181,32234}, {1205,10602}, {1351,10628}, {1503,17812}, {1853,2892}, {1992,17823}, {2192,32286}, {2393,32262}, {2854,9924}, {2888,11061}, {2935,11579}, {3197,32277}, {3564,17838}, {5505,31860}, {5621,8567}, {5622,11425}, {6467,13171}, {6759,32254}, {10606,32305}, {10982,15738}, {12167,13417}, {12584,17821}, {13203,15583}, {13567,32241}, {14984,17834}, {15811,32250}, {16003,17822}, {17809,32245}, {17810,32246}, {17811,32257}, {17814,32275}, {17819,32291}, {17820,32292}, {17825,32300}, {17826,32301}, {17827,32302}, {18405,32273}, {18451,32272}, {19180,32258}, {19430,32293}, {19431,32294}, {23315,25320}

X(32276) = reflection of X(i) in X(j) for these (i,j): (64, 16010), (2892, 25328), (2930, 1177), (2935, 11579), (9924, 10117), (13203, 15583), (17847, 6), (32254, 6759)
X(32276) = X(1156)-of-1st-excosine-triangle if ABC is acute
X(32276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1177, 2930, 154), (5095, 32251, 6)

X(32277) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EXTANGENTS TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32277) lies on these lines: {19,5095}, {40,542}, {55,2930}, {65,651}, {67,71}, {110,1963}, {511,7724}, {1177,10536}, {2550,32255}, {2781,6254}, {2854,3779}, {3101,32244}, {3197,32276}, {3564,12661}, {3611,32260}, {3925,25328}, {5415,32291}, {5416,32292}, {5584,16010}, {6197,32234}, {6237,14984}, {7067,16563}, {7688,32305}, {8251,32275}, {9816,32300}, {10306,32254}, {10319,32257}, {10636,32301}, {10637,32302}, {10902,12584}, {11406,32240}, {11428,32245}, {11435,32246}, {11445,32248}, {11460,32249}, {11471,32250}, {18406,32273}, {18453,32272}, {18921,32241}, {19181,32258}, {19350,32251}, {19432,32293}, {19433,32294}

X(32277) = reflection of X(32286) in X(2930)
X(32277) = X(1156)-of-extangents-triangle if ABC is acute

X(32278) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-GARCIA TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32278) lies on these lines: {1,6593}, {2,32238}, {8,11061}, {10,67}, {40,2781}, {65,651}, {72,692}, {110,518}, {355,542}, {511,12778}, {515,32233}, {517,9970}, {519,32298}, {956,32270}, {1385,15462}, {1386,7984}, {1503,12368}, {1698,6698}, {1737,32308}, {1837,32297}, {2771,11579}, {2854,2948}, {3057,32290}, {3242,11720}, {3679,32261}, {3827,13248}, {5085,11709}, {5090,32239}, {5252,32243}, {5587,32274}, {5657,32247}, {5687,32256}, {5688,32281}, {5689,32280}, {5790,32306}, {5846,25329}, {8193,32262}, {8197,32265}, {8204,32266}, {8214,32295}, {8215,32296}, {9857,32268}, {9928,14984}, {10039,32307}, {10791,32242}, {10914,32287}, {10915,32309}, {10916,32310}, {11900,32279}, {12261,14561}, {12699,32271}, {13883,32253}, {13893,32303}, {13936,32252}, {13947,32304}

X(32278) = midpoint of X(i) and X(j) for these lines: {i,j}: {8, 11061}, {2948, 3751}
X(32278) = reflection of X(i) in X(j) for these (i,j): (1, 6593), (67, 10), (895, 4663), (3242, 11720), (7984, 1386), (12699, 32271)
X(32278) = anticomplement of X(32238)
X(32278) = X(67)-of-outer-Garcia-triangle

X(32279) = ORTHOLOGIC CENTER OF THESE TRIANGLES: GOSSARD TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32279) lies on these lines: {30,9970}, {67,402}, {511,12790}, {542,11251}, {1503,12369}, {1650,6593}, {2781,12113}, {4240,11061}, {6698,15183}, {11831,32238}, {11832,32239}, {11839,32242}, {11845,32247}, {11848,32256}, {11852,32261}, {11853,32262}, {11885,32268}, {11897,32274}, {11900,32278}, {11901,32280}, {11902,32281}, {11903,32287}, {11904,32288}, {11905,32289}, {11906,32290}, {11907,32295}, {11908,32296}, {11909,32297}, {11910,32298}, {11911,32306}, {11912,32307}, {11913,32308}, {11914,32309}, {11915,32310}, {12418,14984}, {13894,32303}, {13948,32304}, {18507,32271}, {18958,32243}, {19017,32252}, {19018,32253}, {22755,32270}

X(32279) = midpoint of X(4240) and X(11061)
X(32279) = reflection of X(i) in X(j) for these (i,j): (67, 402), (1650, 6593), (18507, 32271)
X(32279) = X(67)-of-Gossard-triangle

X(32280) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-GREBE TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32280) lies on these lines: {6,67}, {511,12803}, {542,1161}, {1271,11061}, {1503,7725}, {2781,5871}, {2930,8903}, {5589,32261}, {5591,6593}, {5595,32262}, {5605,32298}, {5689,32278}, {6202,32274}, {6215,9970}, {6218,32246}, {7720,9971}, {8198,32265}, {8205,32266}, {8216,32295}, {8217,32296}, {8974,32303}, {9929,14984}, {9994,32268}, {10040,32307}, {10048,32308}, {10783,32247}, {10792,32242}, {10814,12367}, {10919,32287}, {10921,32288}, {10923,32289}, {10925,32290}, {10927,32297}, {10929,32309}, {10931,32310}, {11370,32238}, {11388,32239}, {11497,32256}, {11824,32233}, {11901,32279}, {11916,32306}, {13949,32304}, {18509,32271}, {18959,32243}, {22756,32270}

X(32280) = reflection of X(32281) in X(67)
X(32280) = X(67)-of-inner-Grebe-triangle

X(32281) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-GREBE TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32281) lies on these lines: {6,67}, {511,12804}, {542,1160}, {1270,11061}, {1503,7726}, {2781,5870}, {2930,8904}, {5588,32261}, {5590,6593}, {5594,32262}, {5604,32298}, {5688,32278}, {6201,32274}, {6214,9970}, {6217,32246}, {7721,9971}, {8199,32265}, {8206,32266}, {8218,32295}, {8219,32296}, {8975,32303}, {9930,14984}, {9995,32268}, {10041,32307}, {10049,32308}, {10784,32247}, {10793,32242}, {10815,12367}, {10920,32287}, {10922,32288}, {10924,32289}, {10926,32290}, {10928,32297}, {10930,32309}, {10932,32310}, {11371,32238}, {11389,32239}, {11498,32256}, {11825,32233}, {11902,32279}, {11917,32306}, {13950,32304}, {18511,32271}, {18960,32243}, {22757,32270}

X(32281) = reflection of X(32280) in X(67)
X(32281) = X(67)-of-outer-Grebe-triangle

X(32282) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH TO 3rd HATZIPOLAKIS

The reciprocal orthologic center of these triangles is X(32283).

X(32282) lies on these lines: {74,5894}, {110,13567}, {113,389}, {370,18604}, {1112,32125}, {1899,10117}, {2929,2931}, {11444,23308}, {11472,11801}, {15059,22830}, {15739,22530}

X(32283) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd HATZIPOLAKIS TO WALSMITH

The reciprocal orthologic center of these triangles is X(32282).

X(32283) lies on these lines: {6,67}, {542,13630}, {5012,5181}

X(32283) = midpoint of X(15118) and X(32285)

X(32284) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HYACINTH TO WALSMITH

The reciprocal orthologic center of these triangles is X(3580).

X(32284) lies on these lines: {4,15531}, {5,8681}, {6,1147}, {51,8780}, {52,1992}, {67,15134}, {143,15471}, {182,22829}, {193,9967}, {195,18449}, {389,14984}, {511,550}, {524,1216}, {542,12370}, {567,32127}, {575,5892}, {576,2393}, {578,8548}, {1181,1351}, {1493,6153}, {1503,12897}, {1843,5093}, {1993,8538}, {1994,8537}, {2854,16534}, {2883,21850}, {3564,5907}, {3567,5032}, {5097,9969}, {5447,18951}, {5965,12899}, {6403,21852}, {6776,10575}, {7999,11160}, {9027,10170}, {9306,9925}, {10574,14912}, {10627,11574}, {11426,21651}, {11470,18445}, {11511,16266}, {11536,32245}, {12007,22952}, {12242,14913}, {12294,18439}, {15116,15129}, {15118,15120}

X(32284) = midpoint of X(i) and X(j) for these lines: {i,j}: {52, 15073}, {193, 9967}, {1351, 6467}
X(32284) = reflection of X(i) in X(j) for these (i,j): (182, 22829), (5446, 576), (6403, 21852), (9969, 5097), (12585, 13292), (14913, 18583)
X(32284) = {X(1992), X(15073)}-harmonic conjugate of X(52)

X(32285) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HYACINTH TO WALSMITH

The reciprocal orthologic center of these triangles is X(32263).

X(32285) lies on these lines: {6,67}, {25,32264}, {69,13198}, {184,5181}, {185,542}, {858,21639}, {895,1899}, {974,3564}, {1885,2781}, {2854,26926}, {3091,9970}, {3292,32257}, {5622,15057}, {5972,21637}, {6146,14984}, {6699,15136}, {9825,25711}, {10938,17702}, {11061,32241}, {15063,32306}, {17818,32233}, {32239,32246}

X(32285) = reflection of X(i) in X(j) for these (i,j): (15118, 32283), (32239, 32246)
X(32285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 67, 15116), (67, 32251, 125)

X(32286) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INTANGENTS TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32286) lies on these lines: {1,542}, {11,25328}, {33,5095}, {34,32250}, {35,12584}, {36,32305}, {55,2930}, {56,16010}, {110,2330}, {399,611}, {497,32255}, {511,7727}, {524,5160}, {895,8540}, {1040,32257}, {1062,32275}, {1177,10535}, {1250,32302}, {1428,10091}, {1469,5663}, {1503,7286}, {2066,32291}, {2192,32276}, {2781,6285}, {2836,3057}, {2854,3024}, {3100,32244}, {3270,32260}, {3295,32254}, {3448,12589}, {3564,12888}, {3583,32273}, {5204,5621}, {5414,32292}, {6198,32234}, {6238,14984}, {7071,32240}, {7281,7312}, {7292,9140}, {7343,9976}, {7741,20301}, {9817,32300}, {9970,19369}, {10638,32301}, {11429,32245}, {11436,32246}, {11446,32248}, {11461,32249}, {11670,24471}, {12903,14982}, {14094,32289}, {18455,32272}, {18922,32241}, {19182,32258}, {19354,32251}, {19434,32293}, {19435,32294}

X(32286) = reflection of X(i) in X(j) for these (i,j): (11670, 24471), (32259, 1), (32277, 2930)
X(32286) = X(1156)-of-intangents-triangle if ABC is acute
X(32286) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (895, 32290, 8540), (10091, 11579, 1428)

X(32287) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-JOHNSON TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32287) lies on these lines: {11,67}, {12,32309}, {355,9970}, {511,12889}, {542,10525}, {1376,6593}, {1503,12371}, {2781,12114}, {3434,11061}, {10523,32307}, {10785,32247}, {10794,32242}, {10826,32261}, {10829,32262}, {10871,32268}, {10893,32274}, {10914,32278}, {10919,32280}, {10920,32281}, {10944,32289}, {10945,32295}, {10946,32296}, {10947,32297}, {10948,32308}, {10949,32310}, {11373,32238}, {11390,32239}, {11826,32233}, {11865,32265}, {11866,32266}, {11903,32279}, {11928,32306}, {12422,14984}, {13895,32303}, {13952,32304}, {18516,32271}, {18961,32243}, {19023,32252}, {19024,32253}

X(32287) = reflection of X(i) in X(j) for these (i,j): (32256, 6593), (32288, 9970)
X(32287) = X(67)-of-inner-Johnson-triangle
X(32287) = X(32309)-of-outer-Johnson-triangle

X(32288) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-JOHNSON TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32288) lies on these lines: {11,32310}, {12,67}, {72,692}, {355,9970}, {511,12890}, {542,10526}, {895,15232}, {958,6593}, {1503,12372}, {2781,11500}, {3436,11061}, {10523,32308}, {10786,32247}, {10795,32242}, {10827,32261}, {10830,32262}, {10872,32268}, {10894,32274}, {10921,32280}, {10922,32281}, {10950,32290}, {10951,32295}, {10952,32296}, {10953,32297}, {10954,32307}, {10955,32309}, {11374,32238}, {11391,32239}, {11827,32233}, {11867,32265}, {11868,32266}, {11904,32279}, {11929,32306}, {12423,14984}, {13896,32303}, {13953,32304}, {18517,32271}, {18962,32243}, {19025,32252}, {19026,32253}

X(32288) = reflection of X(i) in X(j) for these (i,j): (32270, 6593), (32287, 9970)
X(32288) = X(67)-of-outer-Johnson-triangle
X(32288) = X(32310)-of-inner-Johnson-triangle

X(32289) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JOHNSON-YFF TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32289) lies on these lines: {1,9970}, {4,32297}, {5,32308}, {6,3028}, {12,67}, {36,15462}, {55,2781}, {56,6593}, {65,651}, {73,1177}, {74,2330}, {110,1469}, {113,12589}, {182,10081}, {388,11061}, {495,32307}, {511,10088}, {542,1478}, {1479,32271}, {1503,12373}, {1870,8540}, {3056,10752}, {3085,32247}, {3157,14984}, {5480,12904}, {7286,10510}, {7354,32233}, {9578,32261}, {9654,32306}, {10091,19140}, {10797,32242}, {10831,32262}, {10873,32268}, {10895,32274}, {10923,32280}, {10924,32281}, {10944,32287}, {10956,32309}, {10957,32310}, {11375,32238}, {11392,32239}, {11501,32256}, {11579,19470}, {11869,32265}, {11870,32266}, {11905,32279}, {11930,32295}, {11931,32296}, {12896,31670}, {13897,32303}, {13954,32304}, {14094,32286}, {15128,26955}, {19027,32252}, {19028,32253}, {22759,32270}

X(32289) = reflection of X(32307) in X(495)
X(32289) = X(67)-of-1st-Johnson-Yff-triangle
X(32289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 9970, 32290), (19369, 32259, 895)

X(32290) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd JOHNSON-YFF TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32290) lies on these lines: {1,9970}, {4,32243}, {5,32307}, {6,3024}, {11,67}, {35,15462}, {55,6593}, {56,2781}, {74,1428}, {110,3056}, {113,12588}, {182,10065}, {496,32308}, {497,11061}, {511,10091}, {542,1479}, {613,5663}, {895,8540}, {1069,14984}, {1469,10752}, {1478,32271}, {1503,12374}, {3057,32278}, {3086,32247}, {5160,10510}, {5480,12903}, {6198,19369}, {6284,32233}, {7727,11579}, {9581,32261}, {9669,32306}, {10088,19140}, {10798,32242}, {10832,32262}, {10874,32268}, {10896,32274}, {10925,32280}, {10926,32281}, {10950,32288}, {10958,32309}, {10959,32310}, {11376,32238}, {11393,32239}, {11502,32256}, {11871,32265}, {11872,32266}, {11906,32279}, {11932,32295}, {11933,32296}, {13898,32303}, {13955,32304}, {14094,32259}, {15128,26956}, {18968,31670}, {19029,32252}, {19030,32253}, {22760,32270}

X(32290) = reflection of X(32308) in X(496)
X(32290) = X(67)-of-2nd-Johnson-Yff-triangle
X(32290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 9970, 32289), (497, 11061, 32297)

X(32291) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU DIAGONALS TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32291) lies on these lines: {6,110}, {67,6413}, {159,13288}, {371,542}, {372,12584}, {511,12375}, {590,25328}, {1151,16010}, {1177,10533}, {2066,32286}, {2067,32259}, {2781,12964}, {2836,7969}, {3068,32255}, {3311,32254}, {3564,12891}, {5095,5412}, {5181,10960}, {5410,32240}, {5415,32277}, {5621,6409}, {5648,32252}, {6200,32305}, {6564,32273}, {8253,13774}, {10576,20301}, {10665,14984}, {10819,11579}, {10880,32234}, {10897,32275}, {10961,32300}, {11417,32244}, {11462,32249}, {11473,32250}, {11513,32257}, {17819,32276}, {18457,32272}, {18923,32241}, {19183,32258}, {19355,32251}, {19436,32293}, {19438,32294}, {21640,32260}

X(32291) = X(1156)-of-1st-Kenmotu-diagonals-triangle if ABC is acute
X(32291) = {X(6), X(2930)}-harmonic conjugate of X(32292)

X(32292) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU DIAGONALS TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32292) lies on these lines: {6,110}, {67,6414}, {159,13287}, {371,12584}, {372,542}, {511,12376}, {615,25328}, {1152,16010}, {1177,10534}, {2781,12970}, {2836,7968}, {3069,32255}, {3312,32254}, {3564,12892}, {5095,5413}, {5181,10962}, {5411,32240}, {5414,32286}, {5416,32277}, {5621,6410}, {5648,32253}, {6396,32305}, {6502,32259}, {6565,32273}, {8252,13654}, {10577,20301}, {10666,14984}, {10820,11579}, {10881,32234}, {10898,32275}, {10963,32300}, {11418,32244}, {11463,32249}, {11474,32250}, {11514,32257}, {17820,32276}, {18459,32272}, {18924,32241}, {19184,32258}, {19356,32251}, {19437,32294}, {19439,32293}, {21641,32260}

X(32292) = {X(6), X(2930)}-harmonic conjugate of X(32291)
X(32292) = X(1156)-of-2nd-Kenmotu-diagonals-triangle if ABC is acute

X(32293) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS ANTIPODAL TANGENTIAL TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32293) lies on these lines: {110,19134}, {511,19484}, {542,18980}, {895,19426}, {2781,19500}, {2854,12590}, {2930,8939}, {3564,19482}, {5095,19446}, {9723,32294}, {12584,19440}, {13021,16010}, {14984,18939}, {18414,32273}, {18462,32272}, {18926,32241}, {19186,32258}, {19358,32251}, {19370,32259}, {19404,32240}, {19406,32244}, {19408,32245}, {19410,32246}, {19412,32248}, {19414,32249}, {19416,32250}, {19418,32254}, {19420,32255}, {19422,32257}, {19424,32234}, {19428,32275}, {19430,32276}, {19432,32277}, {19434,32286}, {19436,32291}, {19439,32292}, {19448,32300}, {19450,32301}, {19452,32302}, {19454,32305}, {21642,32260}, {23298,25328}

X(32293) = X(1156)-of-Lucas-antipodal-tangents-triangle if ABC is acute

X(32294) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) ANTIPODAL TANGENTIAL TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32294) lies on these lines: {110,19135}, {511,19485}, {542,18981}, {895,19427}, {2781,19501}, {2854,12591}, {2930,8943}, {3564,19483}, {5095,19447}, {9723,32293}, {12584,19441}, {13022,16010}, {14984,18940}, {18415,32273}, {18463,32272}, {18927,32241}, {19187,32258}, {19359,32251}, {19371,32259}, {19405,32240}, {19407,32244}, {19409,32245}, {19411,32246}, {19413,32248}, {19415,32249}, {19417,32250}, {19419,32254}, {19421,32255}, {19423,32257}, {19425,32234}, {19429,32275}, {19431,32276}, {19433,32277}, {19435,32286}, {19437,32292}, {19438,32291}, {19449,32300}, {19451,32301}, {19453,32302}, {19455,32305}, {21643,32260}, {23299,25328}

X(32294) = X(1156)-of-Lucas(-1)-antipodal-tangents-triangle if ABC is acute

X(32295) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS HOMOTHETIC TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32295) lies on these lines: {67,493}, {511,12894}, {542,10669}, {1503,12377}, {2781,9838}, {6461,32296}, {6462,11061}, {6593,8222}, {8188,32261}, {8194,32262}, {8210,32298}, {8212,32274}, {8214,32278}, {8218,32281}, {8220,9970}, {8408,19398}, {10875,32268}, {10945,32287}, {10951,32288}, {11377,32238}, {11394,32239}, {11503,32256}, {11828,32233}, {11840,32242}, {11846,32247}, {11907,32279}, {11930,32289}, {11932,32290}, {11947,32297}, {11949,32306}, {11951,32307}, {11953,32308}, {11955,32309}, {11957,32310}, {12426,14984}, {13899,32303}, {13956,32304}, {18520,32271}, {18963,32243}, {19031,32252}, {19032,32253}, {22761,32270}

X(32295) = X(67)-of-Lucas-homothetic-triangle

X(32296) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) HOMOTHETIC TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32296) lies on these lines: {67,494}, {511,12895}, {542,10673}, {1503,12378}, {2781,9839}, {6461,32295}, {6463,11061}, {6593,8223}, {8189,32261}, {8195,32262}, {8211,32298}, {8213,32274}, {8215,32278}, {8217,32280}, {8219,32281}, {8221,9970}, {8420,19399}, {10876,32268}, {10946,32287}, {10952,32288}, {11378,32238}, {11395,32239}, {11504,32256}, {11829,32233}, {11841,32242}, {11847,32247}, {11908,32279}, {11931,32289}, {11933,32290}, {11948,32297}, {11950,32306}, {11952,32307}, {11954,32308}, {11956,32309}, {11958,32310}, {12427,14984}, {13900,32303}, {13957,32304}, {18522,32271}, {18964,32243}, {19033,32252}, {19034,32253}, {22762,32270}

X(32296) = X(67)-of-Lucas(-1)-homothetic-triangle

X(32297) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MANDART-INCIRCLE TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32297) lies on these lines: {1,542}, {3,32308}, {4,32289}, {6,12904}, {11,6593}, {12,32274}, {33,32239}, {55,67}, {56,32233}, {110,12589}, {125,2330}, {265,611}, {497,11061}, {499,15462}, {511,12896}, {1352,10088}, {1479,9970}, {1503,3028}, {1697,32261}, {1837,32278}, {1858,2836}, {2098,32298}, {2646,32238}, {2781,6284}, {3295,32306}, {3583,32271}, {4294,32247}, {5095,8540}, {5432,6698}, {5621,9659}, {10833,32262}, {10877,32268}, {10927,32280}, {10928,32281}, {10947,32287}, {10953,32288}, {10965,32309}, {10966,32270}, {11873,32265}, {11874,32266}, {11909,32279}, {11947,32295}, {11948,32296}, {12428,14984}, {13901,32303}, {13958,32304}, {19037,32252}, {19038,32253}

X(32297) = reflection of X(32243) in X(1)
X(32297) = X(67)-of-Mandart-incircle-triangle
X(32297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497, 11061, 32290), (3295, 32306, 32307)

X(32298) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th MIXTILINEAR TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32298) lies on these lines: {1,67}, {8,6593}, {55,32270}, {56,32256}, {110,5846}, {145,11061}, {511,12898}, {517,32233}, {519,32278}, {542,1482}, {944,2781}, {952,9970}, {1386,13211}, {1503,7978}, {2098,32297}, {2099,32243}, {2836,3555}, {3416,11720}, {5603,32274}, {5648,28538}, {8192,32262}, {8211,32296}, {9053,25329}, {9933,14984}, {10516,11723}, {10944,32287}, {11396,32239}, {11910,32279}, {13959,32304}, {18525,32271}

X(32298) = midpoint of X(145) and X(11061)
X(32298) = reflection of X(i) in X(j) for these (i,j): (8, 6593), (67, 1), (3416, 11720), (13211, 1386), (18525, 32271), (32261, 32238)
X(32298) = X(67)-of-5th-mixtilinear-triangle
X(32298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32261, 32238), (32238, 32261, 67), (32309, 32310, 67)

X(32299) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: REFLECTION TO WALSMITH

See preamble just before X(31353).

X(32299) lies on these lines: {6,110}, {67,5189}, {125,17710}, {382,2781}, {524,32260}, {542,6102}, {1205,8705}, {2393,8262}, {3060,16176}, {3448,9973}, {3629,11800}, {9927,11591}, {9969,25329}, {9971,11061}, {10095,11536}, {11412,15738}, {11477,32249}, {15074,20301}, {19127,32251}

X(32299) = midpoint of X(i) and X(j) for these lines: {i,j}: {3448, 9973}, {11477, 32249}
X(32299) = reflection of X(i) in X(j) for these (i,j): (3629, 11800), (6593, 32246), (15074, 20301), (17710, 125), (25329, 9969)
X(32299) = {X(6593), X(32246)}-harmonic conjugate of X(16776)

X(32300) = ORTHOLOGIC CENTER OF THESE TRIANGLES: SUBMEDIAL TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32300) lies on these lines: {2,5095}, {5,542}, {6,5181}, {67,15303}, {110,19137}, {113,5050}, {125,3618}, {182,1177}, {373,32260}, {511,9826}, {578,9815}, {895,5642}, {1112,11574}, {1205,12824}, {1656,32275}, {1974,7519}, {2781,9729}, {2854,6329}, {2930,5020}, {3090,32234}, {3091,32250}, {3564,12900}, {3589,6698}, {5055,32272}, {5159,15471}, {5169,32239}, {5182,16278}, {5462,14984}, {5622,15063}, {5943,14763}, {6053,11579}, {6642,12584}, {6721,24975}, {7392,32255}, {7493,11511}, {7687,14561}, {9306,32245}, {9816,32277}, {9817,32286}, {9818,32305}, {9967,16222}, {9970,20417}, {10168,18580}, {10601,32251}, {10643,32301}, {10644,32302}, {10961,32291}, {10963,32292}, {11284,32240}, {11451,32248}, {11465,32249}, {11479,16010}, {11484,32254}, {12017,16111}, {13202,25406}, {14853,16163}, {15059,25321}, {15119,19510}, {15141,15805}, {15473,19128}, {16238,22330}, {17702,18583}, {17825,32276}, {18420,32273}, {18928,32241}, {19188,32258}, {19372,32259}, {19448,32293}, {19449,32294}, {22973,32163}, {24981,25320}

X(32300) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 5972}, {1112, 11574}, {5095, 32257}, {5159, 15471}, {6053, 11579}, {6593, 15118}, {9970, 20417}
X(32300) = reflection of X(6723) in X(3589)
X(32300) = complement of X(32257)
X(32300) = X(1156)-of-submedial-triangle if ABC is acute
X(32300) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5095, 32257), (597, 6593, 15118)

X(32301) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER TRI-EQUILATERAL TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32301) lies on these lines: {6,110}, {15,542}, {16,12584}, {159,10682}, {187,13859}, {511,10657}, {599,11130}, {1177,30402}, {2781,10675}, {3564,10663}, {5095,10641}, {5181,10639}, {5191,14173}, {5648,11081}, {7051,32259}, {9142,14179}, {10632,32234}, {10634,32275}, {10636,32277}, {10638,32286}, {10643,32300}, {10645,32305}, {10661,14984}, {11408,32240}, {11420,32244}, {11466,32249}, {11475,32250}, {11480,16010}, {11488,32255}, {11515,32257}, {16808,32273}, {16966,20301}, {17826,32276}, {18468,32272}, {18929,32241}, {19190,32258}, {19363,32251}, {19450,32293}, {19451,32294}, {21647,32260}, {23302,25328}

X(32301) = X(1156)-of-inner-tri-equilateral-triangle if ABC is acute
X(32301) = {X(6), X(2930)}-harmonic conjugate of X(32302)

X(32302) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER TRI-EQUILATERAL TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32302) lies on these lines: {6,110}, {15,12584}, {16,542}, {159,10681}, {187,13858}, {511,10658}, {574,13859}, {599,11131}, {1177,30403}, {1250,32286}, {2781,10676}, {3564,10664}, {5095,10642}, {5181,10640}, {5191,14179}, {5648,11086}, {9142,14173}, {10633,32234}, {10635,32275}, {10637,32277}, {10644,32300}, {10646,32305}, {10662,14984}, {11409,32240}, {11421,32244}, {11467,32249}, {11476,32250}, {11481,16010}, {11486,32254}, {11489,32255}, {11516,32257}, {16809,32273}, {16967,20301}, {17827,32276}, {18470,32272}, {18930,32241}, {19191,32258}, {19364,32251}, {19373,32259}, {19452,32293}, {19453,32294}, {21648,32260}, {23303,25328}

X(32302) = X(1156)-of-outer-tri-equilateral-triangle if ABC is acute
X(32302) = {X(6), X(2930)}-harmonic conjugate of X(32301)

X(32303) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd TRI-SQUARES-CENTRAL TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32303) lies on these lines: {2,32253}, {6,6698}, {67,3068}, {371,32274}, {485,2781}, {511,13915}, {542,8981}, {590,6593}, {1503,8994}, {3763,19110}, {6723,13972}, {7585,32252}, {8972,11061}, {8974,32280}, {8975,32281}, {8976,9970}, {9540,32233}, {10516,19060}, {13883,32238}, {13884,32239}, {13886,32247}, {13887,32256}, {13888,32261}, {13889,32262}, {13890,32265}, {13891,32266}, {13892,32268}, {13893,32278}, {13895,32287}, {13896,32288}, {13897,32289}, {13898,32290}, {13899,32295}, {13900,32296}, {13901,32297}, {13902,32298}, {13903,32306}, {13904,32307}, {13905,32308}, {13906,32309}, {13907,32310}, {13909,14984}, {18538,32271}, {18965,32243}, {22763,32270}

X(32303) = X(67)-of-3rd-tri-squares-central-triangle
X(32303) = {X(6), X(6698)}-harmonic conjugate of X(32304)

X(32304) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th TRI-SQUARES-CENTRAL TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32304) lies on these lines: {2,32252}, {6,6698}, {67,3069}, {372,32274}, {486,2781}, {511,13979}, {542,13966}, {615,6593}, {1503,13969}, {3763,19111}, {6723,13910}, {7586,32253}, {9970,13951}, {10516,19059}, {11061,13941}, {13935,32233}, {13936,32238}, {13937,32239}, {13938,32242}, {13939,32247}, {13940,32256}, {13942,32261}, {13943,32262}, {13944,32265}, {13945,32266}, {13946,32268}, {13947,32278}, {13948,32279}, {13949,32280}, {13950,32281}, {13952,32287}, {13953,32288}, {13954,32289}, {13955,32290}, {13956,32295}, {13957,32296}, {13958,32297}, {13959,32298}, {13961,32306}, {13962,32307}, {13963,32308}, {13964,32309}, {13965,32310}, {13970,14984}, {18762,32271}, {18966,32243}, {22764,32270}

X(32304) = X(67)-of-4th-tri-squares-central-triangle
X(32304) = {X(6), X(6698)}-harmonic conjugate of X(32303)

X(32305) = ORTHOLOGIC CENTER OF THESE TRIANGLES: TRINH TO WALSMITH

The reciprocal orthologic center of these triangles is X(110).

X(32305) lies on these lines: {3,67}, {4,20301}, {6,10620}, {23,9140}, {24,32250}, {30,25328}, {35,32259}, {36,32286}, {74,511}, {98,20404}, {110,5092}, {125,1995}, {146,14561}, {182,4550}, {185,575}, {265,29012}, {376,32255}, {378,5095}, {399,5085}, {541,5476}, {576,2781}, {690,13233}, {1177,6000}, {1350,15041}, {1428,7727}, {1503,7575}, {1511,17508}, {1691,14901}, {1974,12292}, {1986,19124}, {2071,32244}, {2330,19470}, {2393,16219}, {2777,23049}, {2836,3579}, {2854,3098}, {3448,7492}, {3520,32234}, {3564,12901}, {5050,25556}, {5097,10752}, {5655,10168}, {5907,7550}, {6200,32291}, {6396,32292}, {6698,11178}, {6800,32315}, {7530,18381}, {7545,15027}, {7555,12359}, {7556,11457}, {7688,32277}, {7689,14984}, {7691,15021}, {7728,19130}, {8546,16510}, {9517,13247}, {9818,32300}, {10249,15141}, {10510,19402}, {10605,32251}, {10606,32276}, {10628,19150}, {10645,32301}, {10646,32302}, {10733,29323}, {11061,11179}, {11410,32240}, {11430,32245}, {11438,32246}, {11454,32248}, {11468,32249}, {11572,15044}, {11643,19905}, {12017,12308}, {12106,20379}, {12244,25320}, {12317,25406}, {12902,25330}, {14677,29181}, {14810,15055}, {14865,22330}, {14982,15061}, {15116,23329}, {16042,25561}, {18931,32241}, {19192,32258}, {19454,32293}, {19455,32294}, {19506,23300}, {20127,29317}, {21663,32260}

X(32305) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 16010}, {6, 10620}, {74, 11579}, {9970, 15054}, {12244, 31670}
X(32305) = reflection of X(i) in X(j) for these (i,j): (4, 20301), (110, 5092), (3098, 12041), (3818, 125), (5655, 10168), (7728, 19130), (9970, 575), (9976, 11579), (10752, 5097), (12584, 3), (14982, 24206), (16510, 8546), (19140, 182), (19506, 23300), (32271, 15118), (32273, 25328), (32274, 20379)
X(32305) = circumperp conjugate of X(8724)
X(32305) = circumtangential isogonal conjugate of X(23)
X(32305) = inverse of X(14830) in the circumcircle
X(32305) = X(1156)-of-Trinh-triangle if ABC is acute
X(32305) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5621, 16010, 3), (5622, 9970, 575), (5622, 15054, 9970)

X(32306) = ORTHOLOGIC CENTER OF THESE TRIANGLES: X3-ABC REFLECTIONS TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32306) lies on these lines: {3,67}, {5,9512}, {6,7579}, {30,32247}, {125,5050}, {182,11597}, {195,15141}, {265,1351}, {323,858}, {381,9970}, {382,2781}, {399,1352}, {511,12902}, {517,32261}, {524,7574}, {541,32250}, {576,16176}, {895,11255}, {999,32243}, {1353,25320}, {1503,10620}, {1598,32239}, {1656,6593}, {2070,8262}, {2854,11898}, {3295,32297}, {3526,6698}, {3843,32271}, {5094,9140}, {5095,11482}, {5169,15135}, {5622,15132}, {5663,11188}, {5790,32278}, {5921,12317}, {6193,23296}, {6403,15100}, {6417,32253}, {6418,32252}, {6776,10264}, {7495,9143}, {7517,32262}, {9301,32268}, {9654,32289}, {9669,32290}, {9976,25330}, {10113,10752}, {10246,32238}, {10247,32298}, {10516,19140}, {11412,12429}, {11477,32273}, {11579,11935}, {11801,14853}, {11842,32242}, {11849,32256}, {11875,32265}, {11876,32266}, {11911,32279}, {11916,32280}, {11917,32281}, {11928,32287}, {11929,32288}, {11949,32295}, {11950,32296}, {12000,32309}, {12001,32310}, {12017,15061}, {12308,14982}, {13903,32303}, {13961,32304}, {14561,25329}, {14677,14927}, {14791,32255}, {15027,15118}, {15063,32285}, {15074,32248}, {15081,18583}, {19510,22115}, {22765,32270}, {25331,25556}

X(32306) = midpoint of X(i) and X(j) for these lines: {i,j}: {5921, 12317}, {6403, 15100}, {15069, 25335}
X(32306) = reflection of X(i) in X(j) for these (i,j): (3, 67), (399, 1352), (1351, 265), (6776, 10264), (9970, 32274), (10752, 10113), (11061, 5), (11477, 32273), (12308, 14982), (14927, 14677), (16176, 576), (23236, 5181), (25336, 19140), (30714, 32257), (32248, 15074)
X(32306) = X(67)-of-X3-ABC-reflections-triangle
X(32306) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (9970, 32274, 381), (32243, 32308, 999)

X(32307) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-YFF TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32307) lies on these lines: {1,67}, {3,32243}, {5,32290}, {12,9970}, {35,32233}, {55,542}, {125,613}, {141,10091}, {265,3056}, {388,32247}, {495,32289}, {498,6593}, {499,6698}, {511,12903}, {1350,18968}, {1352,3024}, {1428,15061}, {1478,2781}, {1479,32274}, {1503,10065}, {3085,11061}, {3295,32297}, {3299,32252}, {3301,32253}, {3818,12374}, {5432,15462}, {5622,26956}, {5663,12588}, {7727,14982}, {10037,32262}, {10038,32268}, {10039,32278}, {10041,32281}, {10055,14984}, {10387,12896}, {10523,32287}, {10801,32242}, {10895,32271}, {10954,32288}, {11398,32239}, {11507,32256}, {11877,32265}, {11878,32266}, {11912,32279}, {11951,32295}, {11952,32296}, {13904,32303}, {13962,32304}, {22766,32270}

X(32307) = midpoint of X(67) and X(32309)
X(32307) = reflection of X(32289) in X(495)
X(32307) = X(67)-of-inner-Yff-triangle
X(32307) = X(32309)-of-outer-Yff-triangle
X(32307) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 67, 32308), (3295, 32306, 32297)

X(32308) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-YFF TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32308) lies on these lines: {1,67}, {3,32297}, {5,32289}, {11,9970}, {36,32233}, {56,542}, {125,611}, {141,10088}, {265,1469}, {496,32290}, {497,32247}, {498,6698}, {499,6593}, {511,12904}, {999,32243}, {1350,12896}, {1352,3028}, {1478,32274}, {1479,2781}, {1503,10081}, {1737,32278}, {2330,15061}, {3086,11061}, {3299,32253}, {3301,32252}, {3818,12373}, {5433,15462}, {5622,26955}, {5663,12589}, {10046,32262}, {10047,32268}, {10048,32280}, {10049,32281}, {10071,14984}, {10523,32288}, {10802,32242}, {10896,32271}, {11399,32239}, {11508,32256}, {11879,32265}, {11880,32266}, {11913,32279}, {11953,32295}, {11954,32296}, {13905,32303}, {13963,32304}, {14982,19470}, {22767,32270}

X(32308) = midpoint of X(67) and X(32310)
X(32308) = reflection of X(32290) in X(496)
X(32308) = X(67)-of-outer-Yff-triangle
X(32308) = X(32310)-of-inner-Yff-triangle
X(32308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 67, 32307), (999, 32306, 32243)

X(32309) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-YFF TANGENTS TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32309) lies on these lines: {1,67}, {12,32287}, {511,12905}, {542,10679}, {1503,12381}, {2781,12115}, {5552,6593}, {9970,10942}, {10528,11061}, {10531,32274}, {10803,32242}, {10805,32247}, {10834,32262}, {10878,32268}, {10915,32278}, {10929,32280}, {10930,32281}, {10955,32288}, {10956,32289}, {10958,32290}, {10965,32297}, {11248,32233}, {11400,32239}, {11509,32243}, {11881,32265}, {11882,32266}, {11914,32279}, {11955,32295}, {11956,32296}, {12430,14984}, {13906,32303}, {13964,32304}, {18542,32271}, {19047,32252}, {19048,32253}, {22768,32270}

X(32309) = reflection of X(67) in X(32307)
X(32309) = X(67)-of-inner-Yff-tangents-triangle
X(32309) = {X(67), X(32298)}-harmonic conjugate of X(32310)

X(32310) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-YFF TANGENTS TO WALSMITH

The reciprocal orthologic center of these triangles is X(125).

X(32310) lies on these lines: {1,67}, {11,32288}, {511,12906}, {542,10680}, {1503,12382}, {2781,12116}, {6593,10527}, {9970,10943}, {10529,11061}, {10532,32274}, {10804,32242}, {10806,32247}, {10835,32262}, {10879,32268}, {10916,32278}, {10931,32280}, {10932,32281}, {10949,32287}, {10957,32289}, {10959,32290}, {10966,32270}, {11249,32233}, {11401,32239}, {11510,32256}, {11883,32265}, {11884,32266}, {11915,32279}, {11957,32295}, {11958,32296}, {12001,32306}, {12431,14984}, {13907,32303}, {13965,32304}, {18544,32271}, {18967,32243}, {19049,32252}, {19050,32253}

X(32310) = reflection of X(67) in X(32308)
X(32310) = X(67)-of-outer-Yff-tangents-triangle
X(32310) = {X(67), X(32298)}-harmonic conjugate of X(32309)

X(32311) = CENTER OF THE ORTHOLOGIC TANGENTIAL-CONIC OF THESE TRIANGLES: REFLECTION TO WALSMITH

See preamble just before X(31353).

X(32311) lies on these lines: {74,12505}, {110,599}, {113,31606}, {125,3849}, {2777,14866}, {3448,6031}, {5663,31744}, {5972,10163}, {6032,15059}, {6699,12506}, {6723,10162}, {11594,32269}, {17702,31729}, {23515,31749}

X(32311) = midpoint of X(74) and X(12505)
X(32311) = reflection of X(i) in X(j) for these (i,j): (113, 31606), (12506, 6699)

X(32312) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st PARRY TO WALSMITH

The reciprocal parallelogic center of these triangles is X(125).

X(32312) lies on these lines: {351,690}, {512,13290}, {525,9138}, {3566,15139}, {9131,9517}, {9208,13291}

X(32312) = reflection of X(i) in X(j) for these (i,j): (13291, 9208), (32313, 351)
X(32312) = X(67)-of-1st-Parry-triangle
X(32312) = X(32233)-of-2nd-Parry-triangle

X(32313) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd PARRY TO WALSMITH

The reciprocal parallelogic center of these triangles is X(125).

X(32313) lies on these lines: {67,18310}, {110,525}, {113,1560}, {351,690}, {512,13291}, {542,1640}, {1499,1551}, {1648,14114}, {2780,14698}, {3288,19140}, {3566,5653}, {5027,13290}, {5095,9033}, {6593,18311}, {8429,18332}, {9209,9759}, {9517,9979}, {11061,14977}, {22105,22255}

X(32313) = midpoint of X(11061) and X(14977)
X(32313) = reflection of X(i) in X(j) for these (i,j): (67, 18310), (3569, 14697), (13290, 5027), (18311, 6593), (32312, 351)
X(32313) = X(67)-of-2nd-Parry-triangle
X(32313) = X(32233)-of-1st-Parry-triangle

X(32314) = CENTER OF INVERSE SIMILITUDE OF THESE TRIANGLES: CIRCUMMEDIAL AND WALSMITH

X(32314) lies on these lines: {1316,14682}, {5642,9463}, {9140,15080}, {9745,15484}

X(32315) = CENTER OF INVERSE SIMILITUDE OF THESE TRIANGLES: 1st EHRMANN AND WALSMITH

X(32315) lies on these lines: {1511,5651}, {1995,5476}, {6800,32305}, {9125,14270}, {16510,32225}

X(32316) = ORTHOLOGIC CENTER OF THESE TRIANGLES: WALSMITH TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(32317).

X(32316) lies on these lines: {68,1658}, {74,6145}, {110,343}, {113,1209}, {161,3448}, {973,11746}, {1154,32123}, {6293,12281}, {7703,23315}, {7730,26917}, {10117,31383}, {15068,17824}, {18400,32110}

X(32317) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO WALSMITH

The reciprocal orthologic center of these triangles is X(32316).

X(32317) lies on these lines: {6,67}, {542,6102}, {1511,5965}, {2781,13403}, {3564,11561}, {9925,9932}, {11061,19136}, {16511,32244}, {32154,32257}

X(32317) = reflection of X(67) in X(32283)
X(32317) = {X(125), X(5095)}-harmonic conjugate of X(15140)

X(32318) = X(1)X(389)∩X(3)X(2262)

See Tran Quang Hung and César Lozada, Hyacinthos 28999.

X(32318) lies on these lines: {1, 389}, {3, 2262}

X(32319) = X(4)X(19209)∩X(20)X(2979)

See Angel Montesdeoca, Hyacinthos 29000 and HG020519

X(32319) lies on these lines: {4,19209}, {20,2979}, {51,3087}, {97,6759}, {154,160}, {217,3172}, {512,23613}, {3198,11190}

X(32319) = isogonal conjugate of X(20477)
X(32319) = isogonal of the anticomplement of X(53)
X(32319) = isogonal of the isotomic of X(15318)
X(32319) = polar conjugate of the isotomic of X(18890)
X(32319) = X(i)-Ceva conjugate of X(j) for these (i,j): {14371, 6}, {15318, 18890}
X(32319) = X(3199)-cross conjugate of X(6)
X(32319) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20477}, {75, 6759}, {799, 30442}
X(32319) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 18890}, {6, 15318}, {53, 14371}, {512, 30441}
X(32319) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6, 20477}, {32, 6759}, {669, 30442}, {3199, 14363}, {15318, 76}, {18890, 69}, {30441, 670}

X(32320) = REFLECTION OF X(17434) IN X(647)

See Angel Montesdeoca, Hyacinthos 29000 and HG020519

X(32320) lies on these lines: {6,2430}, {112,6080}, {323,401}, {394,3265}, {416,23090}, {418,23613}, {450,2451}, {520,647}, {651,2639}, {1640,23128}, {3569,6753}, {9033,12077}

X(32320) = reflection of X(17434) and X(647)
X(32320) = isogonal conjugate of X(15352)
X(32320) = isogonal of the polar conjugate of X(520)
X(32320) = X(i)-Ceva conjugate of X(j) for these (i,j): {110, 418}, {394, 2972}, {648, 3}, {651, 408}, {1625, 22052}, {2430, 1636}, {2986, 1650}, {4558, 417}, {4563, 426}, {15316, 20975}
X(32320) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15352}, {4, 823}, {19, 6528}, {75, 6529}, {92, 107}, {99, 6520}, {110, 6521}, {158, 648}, {162, 2052}, {264, 24019}, {393, 811}, {525, 24021}, {653, 1896}, {662, 1093}, {799, 6524}, {1096, 6331}, {1577, 32230}, {1784, 15459}, {2501, 23999}, {2617, 8794}, {3267, 24022}, {6330, 24024}, {6335, 8747}, {8748, 18026}, {14208, 23590}, {14618, 24000}, {17926, 24032}, {23582, 24006}
X(32320) = crosspoint of X(i) and X(j) for these (i,j): {3, 648}, {97, 110}
X(32320) = crosssum of X(i) and X(j) for these (i,j): {4, 647}, {53, 523}, {107, 6529}, {133, 1637}, {235, 2501}, {1896, 17926}, {2052, 14618}, {6750, 12077}
X(32320) = crosssum of Jerabek-hyperbola-intercepts of orthic axis
X(32320) = crossdifference of every pair of points on line {4, 51}
X(32320) = pole of Euler line wrt MacBeath circumconic
X(32320) = perspector of hyperbola {{A,B,C,X(3),X(95)}}
X(32320) = barycentric product X(i) X(j) for these lines: {i,j}: {3, 520}, {32, 4143}, {48, 24018}, {63, 822}, {71, 4091}, {72, 23224}, {97, 17434}, {110, 2972}, {184, 3265}, {217, 15414}, {228, 4131}, {255, 656}, {326, 810}, {394, 647}, {512, 3964}, {521, 22341}, {523, 1092}, {525, 577}, {661, 6507}, {669, 4176}, {684, 17974}, {798, 1102}, {850, 23606}, {905, 3990}, {924, 16391}, {1364, 23067}, {1459, 3682}, {1577, 4100}, {1636, 14919}, {1783, 16730}, {2200, 30805}, {2584, 2585}, {2632, 4575}, {3049, 3926}, {3267, 14585}, {3269, 4558}, {3733, 4158}, {3998, 22383}, {4025, 4055}, {4557, 7215}, {5562, 23286}, {6056, 17094}, {6368, 19210}, {7066, 23189}, {7125, 8611}, {8057, 14379}, {14642, 20580}, {23103, 32230}, {23107, 23963}, {23357, 23616}
X(32320) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {3, 6528}, {6, 15352}, {32, 6529}, {48, 823}, {184, 107}, {255, 811}, {394, 6331}, {512, 1093}, {520, 264}, {525, 18027}, {577, 648}, {647, 2052}, {661, 6521}, {669, 6524}, {798, 6520}, {810, 158}, {822, 92}, {1092, 99}, {1102, 4602}, {1363, 17094}, {1576, 32230}, {1946, 1896}, {2623, 8794}, {2972, 850}, {3049, 393}, {3265, 18022}, {3269, 14618}, {3964, 670}, {3990, 6335}, {4055, 1897}, {4100, 662}, {4143, 1502}, {4158, 27808}, {4176, 4609}, {4575, 23999}, {6507, 799}, {9247, 24019}, {14533, 16813}, {14585, 112}, {14600, 20031}, {15451, 13450}, {16730, 15413}, {17434, 324}, {17974, 22456}, {18877, 15459}, {19210, 18831}, {22341, 18026}, {23224, 286}, {23286, 8795}, {23606, 110}, {23613, 2972}, {23616, 23962}, {24018, 1969}, {30451, 11547}
X(32320) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 6587, 30442}, {647, 30451, 3049}, {1636, 17434, 647}

X(32321) = MIDPOINT OF X(9914) AND X(12085)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29002

X(32321) lies on these lines: {3, 64}, {4, 18532}, {22, 9833}, {24, 14216}, {25, 13419}, {26, 1503}, {30, 9938}, {159, 2918}, {161, 2937}, {186, 12324}, {265, 7517}, {378, 5878}, {511, 9908}, {542, 9937}, {1216, 1660}, {1593, 18388}, {1598, 18383}, {1853, 7506}, {2071, 12250}, {2777, 9914}, {2781, 16266}, {2883, 7526}, {3515, 13171}, {3517, 14864}, {3518, 32064}, {3520, 6225}, {3818, 6642}, {5073, 9919}, {5198, 18376}, {5656, 14118}, {5893, 31861}, {6053, 13293}, {6247, 6644}, {6293, 18445}, {6640, 32125}, {7387, 12293}, {7512, 11206}, {7514, 16252}, {7516, 10192}, {7525, 15577}, {7529, 23325}, {7555, 15581}, {9934, 12292}, {10249, 15805}, {10628, 12164}, {11413, 20427}, {12083, 17845}, {12084, 15311}, {22658, 22978}

X(32321) = midpoint of X(9914) and X(12085)
X(32321) = crosspoint of X(1288) and X(15384)
X(32321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1619, 6759}, {64, 1498, 18439}, {3357, 6759, 5907}

Centers related to the Hatzipolakis-Moses triangle: X(32322)-X(32413)

X(32322) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND 2nd ANTI-EXTOUCH

X(32322) lies on these lines: {26,1181}, {182,32251}, {184,2931}, {389,10274}, {567,19361}, {568,19362}, {1533,18534}, {1593,13403}, {1899,10264}, {6146,32345}, {8479,21331}, {9932,19357}, {10620,10938}, {12022,22533}, {12168,21243}, {14805,19348}, {19468,32358}

X(32323) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND ANTI-INNER-GREBE

X(32323) lies on these lines: {389,19095}, {1588,13403}, {3312,6102}, {6146,32342}, {6241,19087}

X(32324) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND ANTI-OUTER-GREBE

X(32324) lies on these lines: {389,19096}, {1587,13403}, {3311,6102}, {6146,32343}, {6241,19088}

X(32325) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND ANTI-ORTHOCENTROIDAL

X(32325) lies on these lines: {74,13403}, {389,2914}, {399,6102}, {1986,32349}, {6241,17812}, {10114,12380}

X(32326) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND 1st EXCOSINE

X(32326) lies on these lines: {3,32276}, {64,13403}, {389,15139}, {1498,6102}, {6759,17837}, {9932,17821}, {14677,17835}, {17846,32358}

X(32327) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND INNER-GREBE

X(32327) lies on these lines: {389,6277}, {1161,6102}, {5871,13403}, {6146,32373}, {6241,6267}

X(32328) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND OUTER-GREBE

X(32328) lies on these lines: {389,6276}, {1160,6102}, {5870,13403}, {6146,32374}, {6241,6266}

X(32329) = PERSPECTOR OF THESE TRIANGLES: HATZIPOLAKIS-MOSES AND ORTHOCENTROIDAL

X(32329) lies on these lines: {74,19361}, {195,1511}, {381,3567}, {389,6143}, {1986,32395}, {2777,22949}, {5890,13403}, {7730,10114}, {11561,12280}, {15033,32210}, {25739,32392}

X(32330) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ABC-X3 REFLECTIONS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32330) lies on these lines: {2,32369}, {3,161}, {4,32391}, {20,32354}, {30,32372}, {35,32403}, {36,32404}, {54,6240}, {55,32336}, {56,32390}, {110,12225}, {154,5448}, {165,32356}, {182,32335}, {371,32343}, {372,32342}, {376,32337}, {382,32364}, {515,32371}, {517,32394}, {973,18533}, {1154,12118}, {1593,32332}, {3098,32362}, {3428,32363}, {3574,11425}, {3576,32331}, {4549,5876}, {5925,11820}, {6000,18442}, {6242,6776}, {6284,32383}, {6689,32395}, {7354,32382}, {7487,11743}, {7507,17821}, {7691,15138}, {9540,32399}, {9630,32350}, {10274,13352}, {10282,31724}, {10310,32347}, {10619,32341}, {10625,10628}, {11248,32405}, {11249,32406}, {11414,32357}, {11824,32373}, {11825,32374}, {11826,32380}, {11827,32381}, {11828,32388}, {11829,32389}, {13160,32351}, {13935,32400}, {17818,17846}, {18405,32393}, {18569,32171}

X(32330) = midpoint of X(i) and X(j) for these lines: {i,j}: {20, 32354}, {17845, 32345}
X(32330) = reflection of X(i) in X(j) for these (i,j): (4, 32391), (382, 32364), (6145, 3), (6288, 23358), (32359, 32354)
X(32330) = anticomplement of X(32369)
X(32330) = X(6145)-of-ABC-X3-reflections-triangle

X(32331) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-AQUILA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32331) lies on these lines: {1,6145}, {2,32371}, {515,32369}, {960,1209}, {999,32363}, {1125,32391}, {1154,12259}, {1319,32336}, {1385,18400}, {2646,32390}, {3295,32347}, {3576,32330}, {3616,32354}, {5603,32337}, {5886,32379}, {9624,32359}, {9955,32364}, {10246,32402}, {10628,12261}, {11363,32332}, {11364,32335}, {11365,32357}, {11368,32362}, {11370,32373}, {11371,32374}, {11373,32380}, {11374,32381}, {11375,32382}, {11376,32383}, {11377,32388}, {11378,32389}, {11831,32372}, {13883,32399}, {13936,32400}, {18991,32342}, {18992,32343}

X(32331) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 6145}, {32356, 32394}
X(32331) = reflection of X(i) in X(j) for these (i,j): (32364, 9955), (32391, 1125)
X(32331) = complement of X(32371)
X(32331) = X(6145)-of-anti-Aquila-triangle
X(32331) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32356, 32394), (6145, 32394, 32356)

X(32332) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ARA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32332) lies on these lines: {4,54}, {25,6145}, {26,1209}, {33,32390}, {34,32336}, {66,1204}, {159,32333}, {235,32369}, {427,32391}, {428,11743}, {539,7540}, {973,6756}, {1154,11819}, {1352,7691}, {1593,32330}, {1598,32402}, {1843,32352}, {5090,32371}, {5410,32343}, {5411,32342}, {5576,6689}, {5965,12272}, {6288,7517}, {7487,32337}, {7488,32348}, {7564,11750}, {7713,32356}, {10628,12140}, {11363,32331}, {11380,32335}, {11383,32347}, {11386,32362}, {11388,32373}, {11389,32374}, {11390,32380}, {11391,32381}, {11392,32382}, {11393,32383}, {11394,32388}, {11395,32389}, {11396,32394}, {11398,32403}, {11399,32404}, {11400,32405}, {11401,32406}, {11572,32393}, {11832,32372}, {12133,16621}, {13884,32399}, {13937,32400}, {15761,22804}, {18563,32062}, {22479,32363}, {32341,32359}

X(32332) = reflection of X(i) in X(j) for these (i,j): (973, 6756), (32377, 973)
X(32332) = X(6145)-of-anti-Ara-triangle
X(32332) = {X(4), X(32379)}-harmonic conjugate of X(3574)

X(32333) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ASCELLA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32333) lies on these lines: {3,54}, {4,9920}, {6,32352}, {25,2917}, {26,20424}, {159,32332}, {184,6293}, {378,12254}, {427,32346}, {539,12166}, {578,12175}, {973,9777}, {1181,10628}, {1209,7395}, {1398,32350}, {1593,18400}, {1658,22051}, {2888,7503}, {2937,31815}, {3515,12242}, {3516,10619}, {3520,31804}, {5094,32351}, {5410,32384}, {5411,32385}, {6242,11426}, {6288,9818}, {6644,8254}, {7071,32378}, {7484,32348}, {7488,31802}, {7509,26869}, {7514,21230}, {7526,12168}, {9704,12412}, {10274,19357}, {10831,13079}, {10832,18984}, {10982,11808}, {11245,32334}, {11284,32396}, {11403,32340}, {11405,32368}, {11406,32370}, {11408,32397}, {11409,32398}, {11410,32401}, {11424,17846}, {11425,21660}, {12233,21284}, {13423,15033}, {14528,32226}, {15739,26864}, {18386,32365}, {19118,32344}, {19404,32386}, {19405,32387}

X(32333) = reflection of X(i) in X(j) for these (i,j): (12160, 195), (32341, 54)
X(32333) = X(21)-of-anti-Ascella-triangle if ABC is acute
X(32333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 32339, 7592), (54, 32341, 11402)

X(32334) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ATIK TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32334) lies on these lines: {2,32341}, {4,973}, {54,69}, {68,11802}, {195,3548}, {539,18934}, {1154,6643}, {1199,6143}, {1209,11411}, {1658,27552}, {1899,32346}, {2888,6815}, {2917,6776}, {3541,32251}, {3574,11433}, {6288,18917}, {6353,32379}, {6515,7691}, {7730,11457}, {9920,18914}, {10628,18933}, {11245,32333}, {11808,14216}, {12254,18910}, {12324,32340}, {13418,14528}, {13567,17824}, {15801,16051}, {18400,18909}, {18911,32338}, {18912,32339}, {18913,32345}, {18915,32350}, {18918,32365}, {18919,32368}, {18921,32370}, {18922,32378}, {18923,32384}, {18924,32385}, {18925,23358}, {18926,32386}, {18927,32387}, {18928,32396}, {18929,32397}, {18930,32398}, {18931,32401}, {19119,32344}, {19468,21844}, {22051,31283}, {23291,32351}, {32354,32377}

X(32334) = X(21)-of-anti-Atik-triangle if ABC is acute
X(32334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (973, 32337, 4), (1899, 32352, 32346)

X(32335) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th ANTI-BROCARD TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32335) lies on these lines: {32,6145}, {83,32391}, {98,32369}, {182,32330}, {1154,12193}, {3398,18400}, {7787,32354}, {10628,12201}, {10788,32337}, {10789,32356}, {10790,32357}, {10791,32371}, {10792,32373}, {10793,32374}, {10794,32380}, {10795,32381}, {10796,32379}, {10797,32382}, {10798,32383}, {10799,32390}, {10800,32394}, {10801,32403}, {10802,32404}, {10803,32405}, {10804,32406}, {11364,32331}, {11380,32332}, {11490,32347}, {11839,32372}, {11840,32388}, {11841,32389}, {11842,32402}, {12835,32336}, {13885,32399}, {13938,32400}, {18502,32364}, {18993,32342}, {18994,32343}, {22520,32363}

X(32335) = X(6145)-of-5th-anti-Brocard-triangle

X(32336) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-CIRCUMPERP-TANGENTIAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32336) lies on these lines: {1,18400}, {3,32403}, {4,32383}, {11,32369}, {12,32391}, {34,32332}, {55,32330}, {56,6145}, {57,32356}, {388,32354}, {999,32402}, {1154,18970}, {1319,32331}, {1478,32379}, {2099,32394}, {2917,9659}, {3574,19365}, {3585,32364}, {4293,32337}, {5252,32371}, {9657,32359}, {9672,32345}, {10628,18968}, {11509,32347}, {12835,32335}, {18954,32357}, {18957,32362}, {18958,32372}, {18959,32373}, {18960,32374}, {18961,32380}, {18962,32381}, {18963,32388}, {18964,32389}, {18965,32399}, {18966,32400}, {18967,32406}, {18995,32342}, {18996,32343}

X(32336) = reflection of X(32390) in X(1)
X(32336) = X(6145)-of-2nd-anti-circumperp-tangential-triangle
X(32336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 32354, 32382), (999, 32402, 32404)

X(32337) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EULER TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32337) lies on these lines: {2,32379}, {3,32354}, {4,973}, {20,2888}, {24,32357}, {30,32402}, {54,66}, {64,12244}, {70,18533}, {104,32363}, {376,32330}, {388,32403}, {427,32341}, {497,32404}, {515,32356}, {631,32359}, {1154,11411}, {1209,3547}, {1352,32348}, {1503,2916}, {1853,7592}, {1899,3574}, {2892,8549}, {3085,32382}, {3086,32383}, {3088,32377}, {3091,32364}, {3410,9833}, {3448,5889}, {3520,6247}, {4293,32336}, {4294,32390}, {5012,10274}, {5189,14864}, {5596,32344}, {5603,32331}, {5657,32371}, {6143,15139}, {6146,30100}, {6225,22804}, {6288,12324}, {6759,14076}, {7487,32332}, {7581,32343}, {7582,32342}, {7967,32394}, {9862,32362}, {9920,21230}, {10783,32373}, {10784,32374}, {10785,32380}, {10786,32381}, {10788,32335}, {10805,32405}, {10806,32406}, {11431,18912}, {11491,32347}, {11550,32352}, {11845,32372}, {11846,32388}, {11847,32389}, {12300,18910}, {13423,32247}, {13886,32399}, {13939,32400}, {15033,32412}, {15801,31099}, {22533,25739}

X(32337) = reflection of X(i) in X(j) for these (i,j): (4, 6145), (5596, 32344), (6759, 14076), (9833, 23358), (9920, 21230), (10274, 20299), (12254, 32345), (17824, 32351), (32345, 6247), (32354, 3), (32359, 32391)
X(32337) = anticomplement of X(32379)
X(32337) = X(6145)-of-anti-Euler-triangle
X(32337) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 32334, 973), (7691, 11442, 2888)

X(32338) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-EULER TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32338) lies on these lines: {2,32352}, {3,54}, {5,7730}, {20,10628}, {22,17824}, {30,15103}, {68,12319}, {110,2917}, {381,32196}, {539,12271}, {568,8254}, {631,11802}, {973,5640}, {1209,6242}, {1216,6143}, {1658,11597}, {2888,3153}, {2937,7731}, {3060,3574}, {3091,11808}, {3519,16000}, {5055,13365}, {5891,6153}, {5925,12279}, {5965,15073}, {6152,7547}, {6243,20424}, {6288,11459}, {6689,15043}, {7488,10274}, {7998,32348}, {9920,11441}, {10224,21230}, {10625,13619}, {11439,32340}, {11440,32345}, {11442,32346}, {11443,32368}, {11445,32370}, {11446,32378}, {11447,32384}, {11448,32385}, {11449,23358}, {11451,32396}, {11452,32397}, {11453,32398}, {11454,32401}, {11464,15091}, {11576,18386}, {11591,13368}, {11750,15100}, {12111,12226}, {12254,13754}, {12272,15069}, {12273,12281}, {12380,15068}, {13340,15332}, {15058,22804}, {18392,32365}, {18911,32334}, {19122,32344}, {19367,32350}, {19412,32386}, {19413,32387}, {19467,21660}, {23293,32351}, {26881,32379}

X(32338) = reflection of X(i) in X(j) for these (i,j): (54, 12606), (2888, 5562), (5889, 54), (6242, 1209), (6243, 20424), (12280, 2888), (12307, 6101), (13368, 11591), (13423, 6288), (32339, 3), (32341, 31807)
X(32338) = anticomplement of X(32352)
X(32338) = X(21)-of-3rd-anti-Euler-triangle if ABC is acute
X(32338) = {X(11459), X(13423)}-harmonic conjugate of X(6288)

X(32339) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-EULER TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32339) lies on these lines: {2,11802}, {3,54}, {4,7730}, {24,17824}, {52,3153}, {74,6799}, {143,14644}, {185,12254}, {186,10274}, {382,32196}, {389,6143}, {539,12282}, {568,10224}, {973,7547}, {1204,16013}, {1209,5448}, {1614,2917}, {1986,2929}, {2888,13754}, {2914,11438}, {3060,18377}, {3432,14979}, {3567,3574}, {3851,13365}, {5498,22051}, {5663,13368}, {5895,6152}, {6145,16000}, {6153,12162}, {6241,6242}, {6288,12111}, {6689,15045}, {7999,32348}, {9905,31728}, {9920,11456}, {11271,22647}, {11455,32340}, {11457,32346}, {11458,32368}, {11460,32370}, {11461,32378}, {11462,32384}, {11463,32385}, {11464,23358}, {11465,32396}, {11466,32397}, {11467,32398}, {11468,32401}, {11557,21451}, {12270,12278}, {13565,15056}, {15305,22804}, {17855,22949}, {18394,32365}, {18436,21230}, {18912,32334}, {19123,32344}, {19368,32350}, {19414,32386}, {19415,32387}, {21357,31834}, {23294,32351}, {26882,32379}

X(32339) = midpoint of X(6241) and X(13423)
X(32339) = reflection of X(i) in X(j) for these (i,j): (4, 32352), (195, 6102), (382, 32196), (9905, 31728), (11412, 7691), (12111, 6288), (12162, 6153), (12254, 185), (12291, 12254), (12300, 973), (13423, 6242), (18436, 21230), (22815, 10610), (32338, 3)
X(32339) = anticomplement of the anticomplement of X(11802)
X(32339) = X(21)-of-4th-anti-Euler-triangle if ABC is acute
X(32339) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 32352, 7730), (7592, 32333, 54)

X(32340) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EXCENTERS-REFLECTIONS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32340) lies on these lines: {4,54}, {5,15432}, {20,15431}, {24,32401}, {25,32345}, {30,1209}, {33,32350}, {34,32378}, {51,11743}, {64,6145}, {125,3575}, {185,973}, {195,5076}, {235,32351}, {378,23358}, {381,6689}, {382,6288}, {468,20376}, {539,3830}, {546,10610}, {548,20584}, {550,13565}, {1112,11262}, {1154,3627}, {1493,12102}, {1495,23047}, {1498,32341}, {1539,3853}, {1568,18350}, {1593,2917}, {1597,9920}, {2888,3543}, {3091,32396}, {3146,7691}, {3527,18396}, {3861,8254}, {5921,5965}, {6000,11808}, {6152,10628}, {6564,8995}, {6565,13986}, {6756,13851}, {7507,17821}, {7576,18383}, {7730,12290}, {10594,18376}, {11381,11576}, {11403,32333}, {11439,32338}, {11455,32339}, {11470,32368}, {11471,32370}, {11473,32384}, {11474,32385}, {11475,32397}, {11476,32398}, {11802,14915}, {12060,16337}, {12063,13423}, {12101,22051}, {12266,18483}, {12315,32377}, {12324,32334}, {12606,18323}, {12943,12956}, {12946,12953}, {13473,16656}, {15004,18945}, {15687,20424}, {15739,21660}, {15811,17824}, {18559,20299}, {19095,23259}, {19096,23249}, {19124,32344}, {19416,32386}, {19417,32387}

X(32340) = midpoint of X(i) and X(j) for these lines: {i,j}: {382, 6288}, {3146, 7691}, {11381, 32352}
X(32340) = reflection of X(i) in X(j) for these (i,j): (20, 32348), (185, 973), (548, 20584), (550, 13565), (1209, 22804), (3574, 4), (8254, 3861), (10610, 546), (10619, 3574), (12254, 12242), (12266, 18483), (21660, 15739), (32345, 32393), (32352, 11576)
X(32340) = X(21)-of-anti-excenters-reflections-triangle if ABC is acute
X(32340) = {X(3575), X(11572)}-harmonic conjugate of X(125)

X(32341) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-EXTOUCH TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32341) lies on these lines: {2,32334}, {3,54}, {4,19362}, {6,3574}, {25,973}, {155,1209}, {184,2917}, {185,32345}, {389,10274}, {394,32348}, {427,32337}, {539,19458}, {578,10628}, {1147,11802}, {1181,12173}, {1199,1594}, {1498,32340}, {1614,7730}, {1899,32351}, {1994,12225}, {2888,3564}, {2904,11426}, {2914,15106}, {3515,32391}, {3575,32354}, {5094,12242}, {5198,11743}, {6152,9920}, {6240,12254}, {6276,19352}, {6277,19351}, {6288,18445}, {6759,11808}, {6776,32346}, {7558,12325}, {8254,18916}, {9905,31811}, {10224,27552}, {10601,32396}, {10602,32368}, {10605,32401}, {10619,32330}, {10982,18376}, {11576,12167}, {11702,15132}, {11803,14791}, {12022,14627}, {12175,19459}, {13371,22051}, {13565,15068}, {15037,26879}, {15047,26917}, {18386,32369}, {18396,32365}, {18569,20424}, {18997,19095}, {18998,19096}, {19125,32344}, {19349,32350}, {19350,32370}, {19354,32378}, {19355,32384}, {19356,32385}, {19357,23358}, {19358,32386}, {19359,32387}, {19363,32397}, {19364,32398}, {19468,21284}, {20376,26937}, {22804,32139}, {32332,32359}

X(32341) = reflection of X(i) in X(j) for these (i,j): (195, 12161), (9905, 31811), (12254, 31804), (32333, 54), (32338, 31807)
X(32341) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7592, 12161, 11402), (11402, 32333, 54)
X(32341) = X(21)-of-2nd-anti-extouch-triangle if ABC is acute

X(32342) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GREBE TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32342) lies on these lines: {2,32400}, {6,3574}, {372,32330}, {973,19039}, {1154,19061}, {1587,32369}, {3069,32391}, {3299,32403}, {3301,32404}, {3312,18400}, {5411,32332}, {6146,32323}, {6293,19045}, {6418,32402}, {7582,32337}, {7584,32379}, {7585,32399}, {7586,32354}, {7968,32394}, {10628,19051}, {13785,32364}, {13936,32371}, {18991,32331}, {18993,32335}, {18995,32336}, {18997,32345}, {18999,32347}, {19003,32356}, {19005,32357}, {19011,32362}, {19013,32363}, {19017,32372}, {19023,32380}, {19025,32381}, {19027,32382}, {19029,32383}, {19031,32388}, {19033,32389}, {19037,32390}, {19047,32405}, {19049,32406}, {19096,32351}

X(32342) = X(6145)-of-anti-inner-Grebe-triangle
X(32342) = {X(6), X(6145)}-harmonic conjugate of X(32343)

X(32343) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-GREBE TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32343) lies on these lines: {2,32399}, {6,3574}, {371,32330}, {973,19040}, {1154,19062}, {1588,32369}, {3068,32391}, {3299,32404}, {3301,32403}, {3311,18400}, {5410,32332}, {6146,32324}, {6293,19046}, {6417,32402}, {7581,32337}, {7583,32379}, {7585,32354}, {7586,32400}, {7969,32394}, {10628,19052}, {13665,32364}, {13883,32371}, {18992,32331}, {18994,32335}, {18996,32336}, {18998,32345}, {19000,32347}, {19004,32356}, {19006,32357}, {19012,32362}, {19014,32363}, {19018,32372}, {19024,32380}, {19026,32381}, {19028,32382}, {19030,32383}, {19032,32388}, {19034,32389}, {19038,32390}, {19048,32405}, {19050,32406}, {19095,32351}

X(32343) = X(6145)-of-anti-outer-Grebe-triangle
X(32343) = {X(6), X(6145)}-harmonic conjugate of X(32342)

X(32344) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-HONSBERGER TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32344) lies on these lines: {6,24}, {110,343}, {159,9827}, {161,5012}, {182,18400}, {206,1209}, {511,23358}, {539,19141}, {569,9815}, {1154,19139}, {1176,1503}, {1177,10628}, {1428,32350}, {1974,3574}, {2330,32378}, {3589,32351}, {3618,32346}, {5050,9920}, {5085,32345}, {5092,32401}, {5596,32337}, {5965,10274}, {6288,19129}, {7691,19121}, {9967,15462}, {9972,32367}, {9977,10282}, {17824,19132}, {19118,32333}, {19119,32334}, {19122,32338}, {19123,32339}, {19124,32340}, {19125,32341}, {19126,32348}, {19127,19149}, {19130,32365}, {19133,32370}, {19134,32386}, {19135,32387}, {19137,32396}, {21637,32352}

X(32344) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 2917}, {5596, 32337}
X(32344) = reflection of X(i) in X(j) for these (i,j): (32351, 3589), (32365, 19130), (32368, 6), (32379, 206), (32401, 5092)
X(32344) = X(21)-of-anti-Honsberger-triangle if ABC is acute

X(32345) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-HUTSON INTOUCH TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32345) lies on these lines: {2,20376}, {3,161}, {4,10117}, {20,32346}, {24,11704}, {25,32340}, {26,18379}, {40,12341}, {54,64}, {55,32350}, {56,32378}, {74,6799}, {125,2929}, {154,7503}, {185,32341}, {195,2935}, {221,32382}, {382,32365}, {389,19361}, {539,12301}, {578,6293}, {973,9786}, {1147,19376}, {1151,32384}, {1152,32385}, {1154,10606}, {1192,11576}, {1204,1205}, {1350,7691}, {1498,7526}, {1503,32354}, {1593,3574}, {2070,18383}, {2071,2888}, {2192,32383}, {2883,7527}, {3060,11262}, {3516,10619}, {3518,23324}, {3520,6247}, {3522,15578}, {5085,32344}, {5448,12412}, {5584,32370}, {5646,7509}, {5878,8254}, {5894,12086}, {5898,25564}, {6000,10274}, {6102,17835}, {6146,32322}, {6644,22804}, {6689,9818}, {7514,17821}, {7730,17823}, {7973,12266}, {9659,32390}, {9672,32336}, {9905,12262}, {9934,32137}, {10282,14926}, {10625,12307}, {11250,12118}, {11438,11808}, {11440,32338}, {11456,32349}, {11468,13423}, {11477,32368}, {11479,32396}, {11480,32397}, {11481,32398}, {11597,18439}, {11743,17810}, {12041,13368}, {13021,32386}, {13022,32387}, {13366,32392}, {13367,15139}, {14216,18570}, {14864,18364}, {14865,15311}, {15100,17847}, {15579,16010}, {15622,32347}, {17822,17846}, {18376,18378}, {18382,31304}, {18431,20424}, {18913,32334}, {18997,32342}, {18998,32343}, {19351,32373}, {19352,32374}, {19460,31978}, {22467,23332}, {23292,30100}, {26937,32316}

X(32345) = midpoint of X(i) and X(j) for these lines: {i,j}: {20, 32346}, {64, 17824}, {12254, 32337}
X(32345) = reflection of X(i) in X(j) for these (i,j): (3, 32401), (4, 32351), (382, 32365), (1498, 32379), (2917, 3), (9920, 23358), (11477, 32368), (17824, 54), (17845, 32330), (32337, 6247), (32340, 32393), (32379, 10610), (32402, 18381)
X(32345) = anticomplement of the anticomplement of X(20376)
X(32345) = X(21)-of-anti-Hutson-intouch-triangle if ABC is acute
X(32345) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 9920, 23358), (9920, 23358, 2917)

X(32346) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INVERSE-IN-INCIRCLE TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32346) lies on these lines: {2,2917}, {4,54}, {5,9920}, {20,32345}, {69,1225}, {159,7566}, {195,31723}, {376,32401}, {388,32350}, {427,32333}, {497,32378}, {539,12318}, {631,23358}, {973,11433}, {1154,11411}, {1209,6643}, {1370,7691}, {1503,17824}, {1899,32334}, {1992,32368}, {2550,32370}, {3068,32384}, {3069,32385}, {3091,15582}, {3153,14516}, {3523,20376}, {3618,32344}, {5189,6247}, {6193,12319}, {6288,11487}, {6689,7401}, {6776,32341}, {6816,15435}, {7386,32348}, {7391,12324}, {7392,32396}, {7544,32391}, {7730,18912}, {8254,11818}, {10610,18420}, {10628,12284}, {11382,11576}, {11412,12325}, {11442,32338}, {11457,32339}, {11488,32397}, {11489,32398}, {13423,25739}, {14791,21230}, {18489,22804}, {19420,32386}, {19421,32387}

X(32346) = reflection of X(i) in X(j) for these (i,j): (20, 32345), (2888, 6145), (2917, 32351), (9833, 10274), (9920, 5), (32354, 54)
X(32346) = anticomplement of X(2917)
X(32346) = X(21)-of-anti-inverse-in-incircle-triangle if ABC is acute
X(32346) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 12254, 18925), (2917, 32351, 2)

X(32347) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32347) lies on these lines: {3,32363}, {35,32356}, {55,6145}, {56,32394}, {100,32354}, {197,32357}, {1154,12328}, {1376,32380}, {3295,32331}, {5687,32371}, {10310,32330}, {10628,12334}, {11248,18400}, {11383,32332}, {11490,32335}, {11491,32337}, {11494,32362}, {11496,32369}, {11497,32373}, {11498,32374}, {11499,32379}, {11500,32381}, {11501,32382}, {11502,32383}, {11503,32388}, {11504,32389}, {11507,32403}, {11508,32404}, {11509,32336}, {11510,32406}, {11848,32372}, {11849,32402}, {13887,32399}, {13940,32400}, {15622,32345}, {18491,32364}, {18999,32342}, {19000,32343}

X(32347) = reflection of X(i) in X(j) for these (i,j): (32363, 3), (32380, 32391)
X(32347) = X(6145)-of-anti-Mandart-incircle-triangle

X(32348) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32348) lies on these lines: {2,3574}, {3,161}, {5,32223}, {20,15431}, {24,24206}, {30,13565}, {54,69}, {140,389}, {141,32391}, {185,7495}, {195,5054}, {343,10112}, {394,32341}, {511,973}, {539,549}, {550,22804}, {569,11225}, {632,20424}, {1038,32350}, {1040,32378}, {1352,32337}, {1368,32351}, {1493,14869}, {1899,2888}, {3098,3541}, {3153,18428}, {3519,14528}, {3524,12254}, {3526,5646}, {3530,6699}, {3547,5878}, {3549,32364}, {3567,25555}, {3576,12785}, {3628,13566}, {3818,9715}, {3917,32352}, {5204,12946}, {5217,12956}, {5418,8995}, {5420,13986}, {5432,18984}, {5433,13079}, {5657,7979}, {5894,6823}, {5907,6676}, {5972,7542}, {6153,23336}, {6745,9940}, {7386,32346}, {7484,32333}, {7488,32332}, {7494,12324}, {7499,9729}, {7502,13419}, {7512,29012}, {7516,9932}, {7568,13754}, {7998,32338}, {7999,32339}, {9306,11487}, {9540,19096}, {9827,11808}, {10018,12300}, {10020,10170}, {10165,12266}, {10257,12363}, {10303,15801}, {10319,32370}, {10516,16195}, {11017,25338}, {11438,14542}, {11511,32368}, {11513,32384}, {11514,32385}, {11515,32397}, {11516,32398}, {11548,11745}, {11574,16196}, {11576,13348}, {11743,13598}, {12108,20585}, {12362,32393}, {13347,26937}, {13365,13391}, {13367,32377}, {13474,16618}, {13564,18488}, {13935,19095}, {14389,14531}, {14862,18435}, {15559,29317}, {15712,21357}, {16976,22581}, {17811,17824}, {17821,32359}, {18531,32365}, {19126,32344}, {19422,32386}, {19423,32387}, {21167,23300}

X(32348) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 1209}, {20, 32340}, {550, 22804}, {1216, 11802}, {2888, 10619}, {3574, 7691}, {10610, 21230}, {11808, 15644}, {13564, 18488}
X(32348) = reflection of X(i) in X(j) for these (i,j): (3574, 32396), (6689, 140), (12242, 6689), (13598, 11743), (15605, 21230)
X(32348) = anticomplement of X(32396)
X(32348) = complement of X(3574)
X(32348) = X(21)-of-6th-anti-Mixtilinear-triangle if ABC is acute
X(32348) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 3574, 32396), (2, 7691, 3574)

X(32349) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ORTHOCENTROIDAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(1986).

X(32349) lies on these lines: {6,3574}, {64,32401}, {195,18405}, {399,15091}, {1986,32325}, {2917,15068}, {3581,10628}, {6000,11597}, {10274,14805}, {11441,12226}, {11456,32345}, {11750,32359}, {15032,32351}

X(32350) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-TANGENTIAL-MIDARC TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32350) lies on these lines: {1,18400}, {12,32351}, {33,32340}, {34,3574}, {35,32401}, {36,23358}, {54,65}, {55,32345}, {56,2917}, {73,6145}, {221,17824}, {388,32346}, {539,19471}, {973,19366}, {999,9920}, {1038,32348}, {1060,1209}, {1154,7352}, {1398,32333}, {1425,32352}, {1428,32344}, {1469,18984}, {2067,32384}, {3468,4551}, {3585,32365}, {4296,7691}, {5432,20376}, {6284,10118}, {6286,10628}, {6288,18447}, {6502,32385}, {7051,32397}, {7355,13079}, {9630,32330}, {10082,26888}, {10535,32383}, {10895,32395}, {18915,32334}, {18970,19469}, {19349,32341}, {19367,32338}, {19368,32339}, {19369,32368}, {19370,32386}, {19371,32387}, {19372,32396}, {19373,32398}

X(32350) = reflection of X(32378) in X(1)
X(32350) = X(21)-of-anti-tangential-midarc-triangle if ABC is acute

X(32351) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-URSA MINOR TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32351) lies on these lines: {2,2917}, {3,20376}, {4,10117}, {5,5944}, {11,32378}, {12,32350}, {30,32365}, {52,11262}, {54,1594}, {125,6746}, {140,23358}, {141,1209}, {161,7569}, {185,427}, {195,15141}, {235,32340}, {394,2888}, {524,32368}, {539,23307}, {590,32384}, {615,32385}, {858,7691}, {973,13567}, {1147,10224}, {1154,12359}, {1216,14076}, {1368,32348}, {1498,5169}, {1503,5576}, {1656,9920}, {1853,7592}, {1899,32341}, {2072,6288}, {2883,32137}, {3549,18382}, {3589,32344}, {3925,32370}, {5094,32333}, {5133,16252}, {5965,23326}, {6102,10115}, {7577,12254}, {7730,26917}, {8254,10274}, {8550,12242}, {10066,32404}, {10082,32403}, {11743,15873}, {13160,32330}, {13406,18376}, {15032,32349}, {15311,15559}, {19095,32343}, {19096,32342}, {19176,32181}, {21243,31807}, {23291,32334}, {23293,32338}, {23294,32339}, {23298,32386}, {23299,32387}, {23302,32397}, {23303,32398}, {23328,23335}

X(32351) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32345}, {54, 6145}, {2917, 32346}, {10274, 18381}, {17824, 32337}, {32365, 32401}
X(32351) = reflection of X(i) in X(j) for these (i,j): (3, 20376), (52, 11262), (2883, 32364), (10274, 8254), (21230, 14076), (23358, 140), (32344, 3589), (32369, 32393), (32391, 6689)
X(32351) = complement of X(2917)
X(32351) = X(21)-of-anti-Ursa-minor-triangle if ABC is acute
X(32351) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 32346, 2917), (32345, 32395, 4)

X(32352) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-WASAT TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

Let H_AH_BH_C be as described in Anapolis #2471 (March 19, 2015, Antreas Hatzipolakis). X(32352) is the intersection of the Euler lines of the orthic triangle and H_AH_BH_C. (Randy Hutson, June 7, 2019)

X(32352) lies on these lines: {2,32338}, {3,11802}, {4,7730}, {5,51}, {6,32333}, {24,10274}, {25,17824}, {30,32196}, {54,186}, {125,6746}, {184,2917}, {185,6152}, {195,568}, {373,32396}, {511,7691}, {539,14831}, {1181,9920}, {1204,1205}, {1425,32350}, {1495,32379}, {1594,14076}, {1843,32332}, {1899,32334}, {2888,5889}, {3270,32378}, {3292,15801}, {3567,14940}, {3611,32370}, {3917,32348}, {5446,18403}, {5462,22815}, {5890,12254}, {5946,8254}, {6101,15426}, {6102,11562}, {6145,11572}, {6153,6288}, {6243,11424}, {6403,32354}, {6467,8550}, {6689,12606}, {9729,12226}, {9730,10610}, {9786,12175}, {10018,12242}, {10296,13598}, {11262,13567}, {11381,11576}, {11550,32337}, {11561,14049}, {12162,22804}, {12280,32248}, {12380,15032}, {12897,18563}, {13382,13433}, {13451,25402}, {13568,21652}, {13851,32365}, {14449,16657}, {15060,20584}, {16227,22249}, {16881,22051}, {21637,32344}, {21639,32368}, {21640,32384}, {21641,32385}, {21642,32386}, {21643,32387}, {21647,32397}, {21648,32398}, {21663,32401}

X(32352) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32339}, {54, 6242}, {2888, 5889}, {6102, 13368}, {6243, 12307}, {12254, 13423}
X(32352) = reflection of X(i) in X(j) for these (i,j): (3, 11802), (4, 11808), (54, 389), (195, 10115), (3574, 973), (5562, 1209), (6288, 6153), (11381, 32340), (12162, 22804), (12606, 6689), (20424, 143), (21660, 54), (22051, 16881), (32340, 11576)
X(32352) = complement of X(32338)
X(32352) = X(21)-of-anti-Wasat-triangle if ABC is acute
X(32352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 7730, 11808), (7730, 32339, 4)

X(32353) = ORTHOLOGIC CENTER OF THESE TRIANGLES: antiAOA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(10114)

X(32353) lies on these lines: {3,161}, {265,19402}, {1154,15133}, {5094,32355}, {6143,32391}, {7574,10628}, {10115,15134}, {10224,32379}, {11202,18432}, {15131,19381}

X(32353) = X(11604)-of-AAOA-triangle if ABC is acute

X(32354) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32354) lies on these lines: {2,6145}, {3,32337}, {4,54}, {5,32402}, {8,32371}, {10,32356}, {20,32330}, {22,32357}, {26,9920}, {69,7691}, {70,21844}, {100,32347}, {145,32394}, {146,1498}, {193,31304}, {195,31802}, {343,1601}, {388,32336}, {497,32383}, {973,7487}, {1154,6193}, {1270,32374}, {1271,32373}, {1503,32345}, {1853,20376}, {1993,17824}, {2892,11413}, {2896,32362}, {2975,32363}, {3085,32403}, {3086,32404}, {3091,32369}, {3434,32380}, {3436,32381}, {3549,6288}, {3575,32341}, {3616,32331}, {4240,32372}, {6403,32352}, {6462,32388}, {6463,32389}, {6995,11743}, {7564,8254}, {7585,32343}, {7586,32342}, {7787,32335}, {8972,32399}, {10528,32405}, {10529,32406}, {10628,11412}, {11202,14076}, {11271,14531}, {12363,18439}, {13941,32400}, {14216,32401}, {14389,32395}, {32334,32377}

X(32354) = midpoint of X(i) and X(j) for these lines: {i,j}: {17824, 17845}, {32330, 32359}
X(32354) = reflection of X(i) in X(j) for these (i,j): (4, 32379), (8, 32371), (20, 32330), (145, 32394), (2888, 2917), (4240, 32372), (6145, 32391), (14216, 32401), (32337, 3), (32346, 54), (32356, 10), (32402, 5)
X(32354) = anticomplementary conjugate of the anticomplement of X(7488)
X(32354) = anticomplement of X(6145)
X(32354) = X(6145)-of-anticomplementary-triangle
X(32354) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 3574, 11427), (6145, 32391, 2)

X(32355) = ORTHOLOGIC CENTER OF THESE TRIANGLES: AOA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(10114).

X(32355) lies on these lines: {5,5944}, {1154,15115}, {5094,32353}, {5965,23296}, {10115,15120}, {10274,18281}, {10628,15122}, {11597,15116}

X(32355) = X(11604)-of-AOA-triangle if ABC is acute

X(32356) = ORTHOLOGIC CENTER OF THESE TRIANGLES: AQUILA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32356) lies on these lines: {1,6145}, {10,32354}, {35,32347}, {36,32363}, {40,12785}, {57,32336}, {165,32330}, {515,32337}, {517,32402}, {1154,9896}, {1697,32390}, {1698,32391}, {1699,32369}, {3099,32362}, {3679,32371}, {5587,32379}, {5588,32374}, {5589,32373}, {7713,32332}, {8185,32357}, {8188,32388}, {8189,32389}, {9578,32382}, {9581,32383}, {10628,12407}, {10789,32335}, {10826,32380}, {10827,32381}, {11852,32372}, {13888,32399}, {13942,32400}, {16473,17824}, {18492,32364}, {19003,32342}, {19004,32343}

X(32356) = reflection of X(i) in X(j) for these (i,j): (1, 6145), (32354, 10), (32394, 32331)
X(32356) = X(6145)-of-Aquilla-triangle
X(32356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6145, 32394, 32331), (32331, 32394, 1)

X(32357) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32357) lies on these lines: {3,32379}, {22,32354}, {24,32337}, {25,6145}, {64,13171}, {155,10628}, {159,2917}, {184,6293}, {197,32347}, {382,9919}, {1154,9908}, {1593,3574}, {1598,32369}, {2937,9833}, {3556,5693}, {5562,22658}, {5594,32374}, {5595,32373}, {7387,12293}, {7517,32402}, {8185,32356}, {8192,32394}, {8193,32371}, {8194,32388}, {8195,32389}, {9818,32364}, {10037,32403}, {10046,32404}, {10790,32335}, {10828,32362}, {10829,32380}, {10830,32381}, {10831,32382}, {10832,32383}, {10833,32390}, {10834,32405}, {10835,32406}, {11365,32331}, {11414,32330}, {11477,32262}, {11853,32372}, {13889,32399}, {13943,32400}, {14130,15311}, {18954,32336}, {19005,32342}, {19006,32343}, {22654,32363}

X(32357) = X(6145)-of-Ara-triangle

X(32358) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO ARIES

The reciprocal orthologic center of these triangles is X(32359).

Let A'B'C' be the reflection triangle. Let A_B and A_C be the orthogonal projections of A' on CA and AB, resp. Let A" = C_AA_C∩A_BB_A, and define B" and C" cyclically. Triangle A"B"C" is homothetic to ABC at X(6). X(32358) = X(5)-of-A"B"C". (Randy Hutson, March 29, 2020)

X(32358) lies on these lines: {5,6}, {26,6515}, {30,5889}, {49,3580}, {52,11819}, {54,140}, {69,7516}, {70,1993}, {143,12134}, {193,14790}, {195,1594}, {323,11271}, {343,7568}, {389,539}, {394,18952}, {427,18356}, {511,10116}, {524,6101}, {542,5446}, {550,10605}, {568,14516}, {1154,6146}, {1199,2888}, {1209,13366}, {1216,5965}, {1493,23292}, {1503,10263}, {1899,16266}, {1986,3575}, {1994,5576}, {3627,13142}, {3628,11422}, {3853,7728}, {5133,14627}, {5462,11225}, {5876,12241}, {6102,13568}, {6193,6644}, {6759,16619}, {7393,11898}, {7502,31804}, {7526,11411}, {7553,14449}, {7574,12316}, {8537,16198}, {8681,12585}, {9703,10018}, {10112,12370}, {10255,25740}, {10602,14791}, {11449,16531}, {11750,14531}, {12022,18436}, {12084,18917}, {12160,18569}, {12359,32166}, {13160,15087}, {13413,22051}, {15073,26926}, {15083,18390}, {15644,18128}, {15761,18445}, {15801,25739}, {17846,32326}, {18400,32392}, {19468,32322}, {22660,23323}

X(32358) = midpoint of X(6243) and X(34224)
X(32358) = midpoint of X(11750) and X(14531)
X(32358) = reflection of X(i) in X(j) for these (i,j): (5, 13292), (68, 22663), (140, 32165), (550, 18914), (3627, 13142), (5876, 12241), (6146, 11264), (7553, 14449), (11819, 52), (12134, 143), (12359, 32166), (12370, 10112), (14516, 31830), (15644, 18128)
X(32358) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (49, 3580, 10020), (68, 12161, 5)

X(32359) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARIES TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(32358).

X(32359) lies on these lines: {5,6145}, {20,32330}, {25,32377}, {54,1503}, {154,1209}, {159,2917}, {195,382}, {539,7387}, {548,15138}, {631,32337}, {973,9971}, {1154,6293}, {1593,10619}, {1619,9920}, {1853,6689}, {2888,11206}, {2937,3519}, {3574,11402}, {3832,32369}, {3843,32364}, {5596,11271}, {5965,9924}, {6152,9973}, {6278,32374}, {6281,32373}, {6288,6759}, {9624,32331}, {9657,32336}, {9670,32390}, {10535,12956}, {10610,14216}, {10628,23236}, {11362,32371}, {11576,31383}, {11750,32349}, {12234,13419}, {12242,17809}, {12254,15739}, {12946,26888}, {15774,32372}, {15888,32382}, {17821,32348}, {32332,32341}

X(32359) = reflection of X(i) in X(j) for these (i,j): (6145, 32379), (6288, 6759), (14216, 10610), (32330, 32354), (32337, 32391), (32402, 32364)

X(32360) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st AURIGA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32360) lies on these lines: {}

X(32360) = X(6145)-of-1st-Auriga-triangle

X(32361) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd AURIGA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146)

X(32361) lies on these lines: {}

X(32361) = X(6145)-of-2nd-Auriga-triangle

X(32362) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th BROCARD TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32362) lies on these lines: {32,6145}, {1154,9923}, {2896,32354}, {3096,32391}, {3098,32330}, {3099,32356}, {9301,32402}, {9821,18400}, {9857,32371}, {9862,32337}, {9993,32369}, {9994,32373}, {9995,32374}, {9996,32379}, {9997,32394}, {10038,32403}, {10047,32404}, {10628,12501}, {10828,32357}, {10871,32380}, {10872,32381}, {10873,32382}, {10874,32383}, {10875,32388}, {10876,32389}, {10877,32390}, {10878,32405}, {10879,32406}, {11368,32331}, {11386,32332}, {11494,32347}, {11885,32372}, {13892,32399}, {13946,32400}, {18500,32364}, {18957,32336}, {19011,32342}, {19012,32343}, {22744,32363}

X(32362) = X(6145)-of-5th-Brocard-triangle

X(32363) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd CIRCUMPERP TANGENTIAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32363) lies on these lines: {3,32347}, {36,32356}, {55,32394}, {56,6145}, {104,32337}, {956,32371}, {958,32381}, {999,32331}, {1154,22659}, {2917,23361}, {2975,32354}, {3428,32330}, {10628,19478}, {10966,32390}, {11249,18400}, {12114,32380}, {18761,32364}, {19013,32342}, {19014,32343}, {22479,32332}, {22520,32335}, {22654,32357}, {22744,32362}, {22753,32369}, {22755,32372}, {22756,32373}, {22757,32374}, {22758,32379}, {22759,32382}, {22760,32383}, {22761,32388}, {22762,32389}, {22763,32399}, {22764,32400}, {22765,32402}, {22766,32403}, {22767,32404}, {22768,32405}

X(32363) = reflection of X(i) in X(j) for these (i,j): (32347, 3), (32381, 32391)
X(32363) = X(6145)-of-2nd-circumperp-tangential-triangle

X(32364) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-MID TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32364) lies on these lines: {4,54}, {26,5448}, {30,32391}, {113,1209}, {235,973}, {381,6145}, {382,32330}, {546,32369}, {1154,15761}, {1478,32383}, {1479,32382}, {1498,32395}, {1539,5893}, {1568,7488}, {1596,11743}, {2883,32137}, {2917,7517}, {3091,32337}, {3357,4846}, {3549,32348}, {3583,32390}, {3585,32336}, {3818,9977}, {3843,32359}, {5576,6000}, {6288,17824}, {6689,7526}, {7564,18128}, {7703,10574}, {9818,32357}, {9955,32331}, {10895,32403}, {10896,32404}, {11802,22800}, {11819,16252}, {12699,32371}, {13665,32343}, {13785,32342}, {14076,18504}, {15311,20376}, {18491,32347}, {18492,32356}, {18500,32362}, {18502,32335}, {18507,32372}, {18509,32373}, {18511,32374}, {18516,32380}, {18517,32381}, {18520,32388}, {18522,32389}, {18525,32394}, {18538,32399}, {18542,32405}, {18544,32406}, {18761,32363}, {18762,32400}, {20424,21850}

X(32364) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32379}, {382, 32330}, {2883, 32351}, {6288, 17824}, {6759, 32365}, {12699, 32371}, {18507, 32372}, {18525, 32394}, {22802, 32401}, {32359, 32402}
X(32364) = reflection of X(i) in X(j) for these (i,j): (18381, 32393), (32331, 9955), (32369, 546), (32401, 6689)
X(32364) = X(6145)-of-Ehrmann-mid-triangle

X(32365) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-VERTEX TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32365) lies on these lines: {3,32395}, {4,54}, {5,18428}, {30,32351}, {52,265}, {381,2917}, {382,32345}, {539,18568}, {542,32368}, {550,20376}, {576,18382}, {973,18390}, {1154,9927}, {1209,18404}, {2888,18387}, {3153,7691}, {3357,31723}, {3583,32378}, {3585,32350}, {3627,11804}, {3818,22804}, {3843,9920}, {5449,18569}, {5907,6288}, {6102,11262}, {6564,32384}, {6565,32385}, {10113,32196}, {11204,14790}, {11576,18385}, {12370,20424}, {12893,13371}, {13851,32352}, {16808,32397}, {16809,32398}, {17824,18405}, {18386,32333}, {18392,32338}, {18394,32339}, {18396,32341}, {18406,32370}, {18414,32386}, {18415,32387}, {18420,32396}, {18531,32348}, {18567,19479}, {18572,21230}, {18918,32334}, {19130,32344}

X(32365) = midpoint of X(i) and X(j) for these lines: {i,j}: {382, 32345}, {17824, 32402}
X(32365) = reflection of X(i) in X(j) for these (i,j): (550, 20376), (6102, 11262), (6145, 18383), (6759, 32364), (7691, 14076), (10274, 3574), (23358, 5), (32344, 19130), (32401, 32351)
X(32365) = X(21)-of-Ehrmann-vertex-triangle if ABC is acute
X(32365) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3574, 21659, 54), (18383, 31724, 19506)

X(32366) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO 1st EHRMANN

The reciprocal orthologic center of these triangles is X(32367).

X(32366) lies on these lines: {6,25}, {66,17040}, {69,3266}, {141,8681}, {157,5065}, {160,800}, {182,8548}, {193,3313}, {389,12007}, {511,550}, {524,6665}, {570,20975}, {597,9822}, {1216,5965}, {1503,13403}, {1511,5892}, {1992,12220}, {2386,15048}, {2854,3589}, {2929,13367}, {2979,11008}, {3003,20775}, {3564,11264}, {3618,12272}, {3631,3819}, {5097,5446}, {5140,5254}, {5181,26156}, {5421,23635}, {5943,6329}, {6146,15739}, {6241,6776}, {7668,14767}, {10574,27082}, {12235,32046}, {12283,14853}, {14778,23642}, {14912,15073}, {15126,23300}, {15140,32226}, {18583,18874}, {20583,21849}, {25320,32248}

X(32366) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 6467}, {193, 3313}, {1353, 15074}, {3629, 17710}, {15073, 19161}
X(32366) = reflection of X(i) in X(j) for these (i,j): (6, 22829), (389, 12007), (5446, 5097), (9969, 6), (14913, 3589), (21849, 20583)
X(32366) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 159, 19136), (6, 19459, 206), (6467, 22829, 9969)

X(32367) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st EHRMANN TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(32366).

X(32367) lies on these lines: {54,2393}, {159,3574}, {206,576}, {5965,9925}, {8542,32391}, {9970,32379}, {9972,32344}, {12584,23358}, {15579,32401}, {15581,18400}

X(32368) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd EHRMANN TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32368) lies on these lines: {6,24}, {68,5965}, {161,11422}, {511,32401}, {524,32351}, {539,9926}, {542,32365}, {575,23358}, {576,18400}, {895,6145}, {1154,8548}, {1209,8538}, {1992,32346}, {2393,32379}, {3574,8541}, {5486,12242}, {6288,18449}, {7691,11416}, {8539,32370}, {8540,32378}, {9813,32396}, {9920,11482}, {9976,10628}, {10602,32341}, {11405,32333}, {11443,32338}, {11458,32339}, {11470,32340}, {11477,32345}, {11511,32348}, {15069,32395}, {17813,17824}, {18919,32334}, {19369,32350}, {19426,32386}, {19427,32387}, {21639,32352}, {23049,32369}

X(32368) = midpoint of X(11477) and X(32345)
X(32368) = reflection of X(i) in X(j) for these (i,j): (23358, 575), (32344, 6)
X(32368) = X(21)-of-2nd-Ehrmann-triangle if ABC is acute

X(32369) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EULER TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32369) lies on these lines: {2,32330}, {4,973}, {5,5944}, {11,32336}, {12,32390}, {24,11704}, {54,7547}, {98,32335}, {125,3575}, {235,32332}, {265,11262}, {371,32399}, {372,32400}, {381,32379}, {515,32331}, {546,32364}, {1154,9927}, {1209,12605}, {1352,6288}, {1478,32404}, {1479,32403}, {1587,32342}, {1588,32343}, {1598,32357}, {1658,23325}, {1699,32356}, {2917,7503}, {3091,32354}, {3574,12241}, {3832,32359}, {3861,27552}, {5446,10113}, {5587,32371}, {5603,32394}, {6152,15738}, {6201,32374}, {6202,32373}, {7542,20376}, {7569,17845}, {7691,18392}, {7706,13630}, {8212,32388}, {8213,32389}, {9993,32362}, {10531,32405}, {10532,32406}, {10893,32380}, {10894,32381}, {10895,32382}, {10896,32383}, {10982,17824}, {11496,32347}, {11897,32372}, {13565,23358}, {18386,32341}, {20191,23332}, {22753,32363}, {23049,32368}

X(32369) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 6145}, {32379, 32402}
X(32369) = reflection of X(i) in X(j) for these (i,j): (23358, 13565), (32351, 32393), (32364, 546), (32391, 5)
X(32369) = complement of X(32330)
X(32369) = X(6145)-of-Euler-triangle
X(32369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 32402, 32379), (23324, 32351, 32393)

X(32370) = ORTHOLOGIC CENTER OF THESE TRIANGLES: EXTANGENTS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32370) lies on these lines: {19,3574}, {40,12785}, {54,65}, {55,2917}, {71,6145}, {539,12417}, {973,11435}, {1154,6237}, {1209,8251}, {2550,32346}, {2888,9537}, {3101,7691}, {3197,17824}, {3611,32352}, {3925,32351}, {5415,32384}, {5416,32385}, {5584,32345}, {6288,18453}, {7688,32401}, {7724,10119}, {8274,9572}, {8539,32368}, {9816,32396}, {9920,10306}, {10319,32348}, {10536,32379}, {10636,32397}, {10637,32398}, {10901,12946}, {10902,23358}, {11406,32333}, {11445,32338}, {11460,32339}, {11471,32340}, {18406,32365}, {18921,32334}, {19133,32344}, {19350,32341}, {19432,32386}, {19433,32387}

X(32370) = reflection of X(32378) in X(2917)
X(32370) = X(21)-of-extangents-triangle if ABC is acute

X(32371) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-GARCIA TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32371) lies on these lines: {1,32391}, {2,32331}, {8,32354}, {10,6145}, {54,65}, {72,32381}, {355,18400}, {515,32330}, {517,32379}, {519,32394}, {956,32363}, {1154,9928}, {1737,32404}, {1837,32390}, {3057,32383}, {3679,32356}, {3751,9905}, {5090,32332}, {5252,32336}, {5587,32369}, {5657,32337}, {5687,32347}, {5688,32374}, {5689,32373}, {5790,32402}, {7713,11743}, {8193,32357}, {8214,32388}, {8215,32389}, {9857,32362}, {10039,32403}, {10628,12778}, {10791,32335}, {10914,32380}, {10915,32405}, {10916,32406}, {11362,32359}, {11900,32372}, {12699,32364}, {13883,32343}, {13893,32399}, {13936,32342}, {13947,32400}

X(32371) = midpoint of X(8) and X(32354)
X(32371) = reflection of X(i) in X(j) for these (i,j): (1, 32391), (6145, 10), (12699, 32364)
X(32371) = anticomplement of X(32331)
X(32371) = X(6145)-of-outer-Garcia-triangle

X(32372) = ORTHOLOGIC CENTER OF THESE TRIANGLES: GOSSARD TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32372) lies on these lines: {30,32330}, {402,6145}, {1154,12418}, {1650,32391}, {4240,32354}, {10628,12790}, {11251,18400}, {11831,32331}, {11832,32332}, {11839,32335}, {11845,32337}, {11848,32347}, {11852,32356}, {11853,32357}, {11885,32362}, {11897,32369}, {11900,32371}, {11901,32373}, {11902,32374}, {11903,32380}, {11904,32381}, {11905,32382}, {11906,32383}, {11907,32388}, {11908,32389}, {11909,32390}, {11910,32394}, {11911,32402}, {11912,32403}, {11913,32404}, {11914,32405}, {11915,32406}, {13894,32399}, {13948,32400}, {15774,32359}, {18507,32364}, {18958,32336}, {19017,32342}, {19018,32343}, {22755,32363}

X(32372) = midpoint of X(4240) and X(32354)
X(32372) = reflection of X(i) in X(j) for these (i,j): (1650, 32391), (6145, 402), (18507, 32364)
X(32372) = X(6145)-of-Gossard-triangle

X(32373) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-GREBE TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32373) lies on these lines: {6,3574}, {973,6218}, {1154,9929}, {1161,18400}, {1271,32354}, {2917,8903}, {5589,32356}, {5591,32391}, {5595,32357}, {5605,32394}, {5689,32371}, {6146,32327}, {6202,32369}, {6215,32379}, {6220,6293}, {6281,32359}, {8216,32388}, {8217,32389}, {8974,32399}, {9994,32362}, {10040,32403}, {10048,32404}, {10628,12803}, {10783,32337}, {10792,32335}, {10919,32380}, {10921,32381}, {10923,32382}, {10925,32383}, {10927,32390}, {10929,32405}, {10931,32406}, {11370,32331}, {11388,32332}, {11497,32347}, {11824,32330}, {11901,32372}, {11916,32402}, {13949,32400}, {18509,32364}, {18959,32336}, {19351,32345}, {22756,32363}

X(32373) = X(6145)-of-inner-Grebe-triangle

X(32374) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-GREBE TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32374) lies on these lines: {6,3574}, {973,6217}, {1154,9930}, {1160,18400}, {1270,32354}, {2917,8904}, {5588,32356}, {5590,32391}, {5594,32357}, {5604,32394}, {5688,32371}, {6146,32328}, {6201,32369}, {6214,32379}, {6219,6293}, {6278,32359}, {8218,32388}, {8219,32389}, {8975,32399}, {9995,32362}, {10041,32403}, {10049,32404}, {10628,12804}, {10784,32337}, {10793,32335}, {10920,32380}, {10922,32381}, {10924,32382}, {10926,32383}, {10928,32390}, {10930,32405}, {10932,32406}, {11371,32331}, {11389,32332}, {11498,32347}, {11825,32330}, {11902,32372}, {11917,32402}, {13950,32400}, {18511,32364}, {18960,32336}, {19352,32345}, {22757,32363}

X(32374) = X(6145)-of-outer-Grebe-triangle

X(32375) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO 3rd HATZIPOLAKIS

The reciprocal orthologic center of these triangles is X(32376).

X(32375) lies on these lines: {6,17837}, {54,22533}, {3521,22979}, {9932,22962}, {19511,22834}

X(32375) = reflection of X(22466) in X(31985)

X(32376) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd HATZIPOLAKIS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(32375).

X(32376) lies on these lines: {6,3574}, {54,22533}, {368,20917}, {539,14076}, {13630,18128}

X(32376) = midpoint of X(i) and X(j) for these lines: {i,j}: {6145, 32412}, {32377, 32393}

X(32377) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HYACINTH TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(32358).

X(32377) lies on these lines: {3,539}, {6,3574}, {25,32359}, {54,70}, {125,6689}, {184,1209}, {185,6152}, {542,13160}, {973,6756}, {974,18914}, {1154,6146}, {1181,6288}, {1493,13371}, {1503,11576}, {1594,12242}, {2888,6776}, {3088,32337}, {3542,32379}, {5965,6467}, {6243,10938}, {7691,19467}, {9827,12134}, {10112,12225}, {11271,18946}, {11416,15801}, {12022,12300}, {12234,18381}, {12254,18909}, {12315,32340}, {12946,19349}, {12956,19354}, {13367,32348}, {13431,14791}, {17818,17846}, {21230,31804}, {32334,32354}

X(32377) = reflection of X(i) in X(j) for these (i,j): (32332, 973), (32393, 32376)
X(32377) = {X(6145), X(32341)}-harmonic conjugate of X(3574)

X(32378) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INTANGENTS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32378) lies on these lines: {1,18400}, {11,32351}, {33,3574}, {34,32340}, {35,23358}, {36,32401}, {54,6198}, {55,2917}, {56,32345}, {195,9642}, {497,32346}, {539,9931}, {973,11436}, {1040,32348}, {1062,1209}, {1154,6238}, {1250,32398}, {2066,32384}, {2192,17824}, {2330,32344}, {2888,9538}, {3056,13079}, {3057,7979}, {3100,7691}, {3270,32352}, {3295,9920}, {3583,32365}, {5414,32385}, {5433,20376}, {6145,9630}, {6285,18984}, {6288,18455}, {7071,32333}, {7354,19505}, {7356,7727}, {8540,32368}, {9577,9905}, {9627,12946}, {9641,12307}, {9817,32396}, {10066,10535}, {10149,22954}, {10638,32397}, {10896,32395}, {11446,32338}, {11461,32339}, {12428,12888}, {18922,32334}, {19354,32341}, {19434,32386}, {19435,32387}, {26888,32382}

X(32378) = reflection of X(i) in X(j) for these (i,j): (32350, 1), (32370, 2917)
X(32378) = X(21)-of-intangents-triangle if ABC is acute

X(32379) = ORTHOLOGIC CENTER OF THESE TRIANGLES: JOHNSON TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32379) lies on these lines: {1,32382}, {2,32337}, {3,32357}, {4,54}, {5,6145}, {11,32404}, {12,32403}, {23,15801}, {25,973}, {26,154}, {30,32330}, {110,5562}, {140,15139}, {159,195}, {161,12161}, {182,32396}, {206,1209}, {355,32380}, {381,32369}, {517,32371}, {569,32393}, {952,32394}, {1177,3519}, {1478,32336}, {1479,32390}, {1493,7530}, {1495,32352}, {1498,7526}, {1503,5576}, {1598,11743}, {1843,11808}, {2393,32368}, {2777,8718}, {2781,13564}, {2883,7728}, {2918,10117}, {3542,32377}, {5012,18381}, {5587,32356}, {5886,32331}, {5887,24301}, {6000,15062}, {6214,32374}, {6215,32373}, {6247,20376}, {6288,10024}, {6293,7502}, {6353,32334}, {6689,14216}, {7529,19153}, {7552,10203}, {7564,32046}, {7583,32343}, {7584,32342}, {8220,32388}, {8221,32389}, {8976,32399}, {9306,11487}, {9544,31304}, {9652,13079}, {9667,18984}, {9707,12300}, {9970,32367}, {9996,32362}, {10066,10535}, {10082,26888}, {10192,18350}, {10224,32353}, {10533,32384}, {10534,32385}, {10536,32370}, {10627,17847}, {10796,32335}, {10942,32405}, {10943,32406}, {11262,15087}, {11499,32347}, {11585,15462}, {11819,20424}, {12363,19149}, {13434,18383}, {13951,32400}, {15132,15331}, {15647,22815}, {15739,26864}, {18374,21841}, {21230,31831}, {22758,32363}, {26881,32338}, {26882,32339}, {30402,32397}, {30403,32398}

X(32379) = midpoint of X(i) and X(j) for these lines: {i,j}: {4, 32354}, {195, 9920}, {1498, 32345}, {2917, 17824}, {6145, 32359}, {6759, 10274}, {32380, 32381}
X(32379) = reflection of X(i) in X(j) for these (i,j): (3, 32391), (4, 32364), (54, 10274), (6145, 5), (6247, 20376), (7691, 23358), (9935, 9920), (23358, 10282), (32344, 206), (32345, 10610), (32402, 32369)
X(32379) = complement of X(32337)
X(32379) = X(6145)-of-Johnson-triangle
X(32379) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (184, 3574, 54), (184, 6759, 9833), (32382, 32383, 1)

X(32380) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-JOHNSON TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32380) lies on these lines: {11,6145}, {12,32405}, {355,32379}, {1154,12422}, {1376,32347}, {3434,32354}, {10523,32403}, {10525,18400}, {10628,12889}, {10785,32337}, {10794,32335}, {10826,32356}, {10829,32357}, {10871,32362}, {10893,32369}, {10914,32371}, {10919,32373}, {10920,32374}, {10944,32382}, {10945,32388}, {10946,32389}, {10947,32390}, {10948,32404}, {10949,32406}, {11373,32331}, {11390,32332}, {11826,32330}, {11903,32372}, {11928,32402}, {12114,32363}, {13895,32399}, {13952,32400}, {18516,32364}, {18961,32336}, {19023,32342}, {19024,32343}

X(32380) = reflection of X(i) in X(j) for these (i,j): (32347, 32391), (32381, 32379)
X(32380) = X(6145)-of-inner-Johnson-triangle

X(32381) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-JOHNSON TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32381) lies on these lines: {11,32406}, {12,6145}, {54,15232}, {72,32371}, {355,32379}, {958,32363}, {1154,12423}, {3436,32354}, {10523,32404}, {10526,18400}, {10628,12890}, {10786,32337}, {10795,32335}, {10827,32356}, {10830,32357}, {10872,32362}, {10894,32369}, {10921,32373}, {10922,32374}, {10950,32383}, {10951,32388}, {10952,32389}, {10953,32390}, {10954,32403}, {10955,32405}, {11374,32331}, {11391,32332}, {11500,32347}, {11827,32330}, {11904,32372}, {11929,32402}, {13896,32399}, {13953,32400}, {18517,32364}, {18962,32336}, {19025,32342}, {19026,32343}

X(32381) = reflection of X(i) in X(j) for these (i,j): (32363, 32391), (32380, 32379)
X(32381) = X(6145)-of-outer-Johnson-triangle

X(32382) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JOHNSON-YFF TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32382) lies on these lines: {1,32379}, {4,32390}, {5,32404}, {12,6145}, {54,65}, {56,32391}, {221,32345}, {388,32336}, {495,32403}, {973,11398}, {1154,3157}, {1478,10066}, {1479,32364}, {2917,18984}, {3085,32337}, {3574,11393}, {7354,32330}, {9578,32356}, {9654,32402}, {10082,10274}, {10088,10628}, {10797,32335}, {10831,32357}, {10873,32362}, {10895,32369}, {10923,32373}, {10924,32374}, {10944,32380}, {10956,32405}, {10957,32406}, {11375,32331}, {11392,32332}, {11501,32347}, {11905,32372}, {11930,32388}, {11931,32389}, {13079,17824}, {13897,32399}, {13954,32400}, {15888,32359}, {19027,32342}, {19028,32343}, {22759,32363}, {26888,32378}

X(32382) = reflection of X(32403) in X(495)
X(32382) = X(6145)-of-1st-Johnson-Yff-triangle
X(32382) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32379, 32383), (388, 32354, 32336)

X(32383) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd JOHNSON-YFF TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32383) lies on these lines: {1,32379}, {4,32336}, {5,32403}, {11,6145}, {54,6198}, {55,32391}, {496,32404}, {497,32354}, {973,11399}, {1069,1154}, {1478,32364}, {1479,10082}, {2192,32345}, {2917,13079}, {3057,32371}, {3086,32337}, {3574,11392}, {6284,32330}, {9581,32356}, {9669,32402}, {10066,10274}, {10091,10628}, {10535,32350}, {10798,32335}, {10832,32357}, {10874,32362}, {10896,32369}, {10925,32373}, {10926,32374}, {10950,32381}, {10958,32405}, {10959,32406}, {11376,32331}, {11393,32332}, {11502,32347}, {11906,32372}, {11932,32388}, {11933,32389}, {13898,32399}, {13955,32400}, {17824,18984}, {19029,32342}, {19030,32343}, {22760,32363}

X(32383) = reflection of X(32404) in X(496)
X(32383) = X(6145)-of-2nd-Johnson-Yff-triangle
X(32383) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32379, 32382), (497, 32354, 32390)

X(32384) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU DIAGONALS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32384) lies on these lines: {6,24}, {371,18400}, {372,23358}, {539,12424}, {590,32351}, {1151,32345}, {1154,10665}, {1209,10897}, {2066,32378}, {2067,32350}, {3068,32346}, {3311,9920}, {3574,5412}, {5410,32333}, {5415,32370}, {6145,6413}, {6200,32401}, {6288,18457}, {6564,32365}, {7691,11417}, {10274,12971}, {10533,32379}, {10628,12375}, {10961,32396}, {11447,32338}, {11462,32339}, {11473,32340}, {11513,32348}, {17819,17824}, {18923,32334}, {19355,32341}, {19436,32386}, {19438,32387}, {21640,32352}

X(32384) = X(21)-of-1st-Kenmotu-diagonals-triangle if ABC is acute
X(32384) = {X(6), X(2917)}-harmonic conjugate of X(32385)

X(32385) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU DIAGONALS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32385) lies on these lines: {6,24}, {371,23358}, {372,18400}, {539,12425}, {615,32351}, {1152,32345}, {1154,10666}, {1209,10898}, {3069,32346}, {3312,9920}, {3574,5413}, {5411,32333}, {5414,32378}, {5416,32370}, {6145,6414}, {6288,18459}, {6396,32401}, {6502,32350}, {6565,32365}, {7691,11418}, {10274,12965}, {10534,32379}, {10628,12376}, {10963,32396}, {11448,32338}, {11463,32339}, {11474,32340}, {11514,32348}, {17820,17824}, {18924,32334}, {19356,32341}, {19437,32387}, {19439,32386}, {21641,32352}

X(32385) = X(21)-of-2nd-Kenmotu-diagonals-triangle if ABC is acute
X(32385) = {X(6), X(2917)}-harmonic conjugate of X(32384)

X(32386) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS ANTIPODAL TANGENTIAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32386) lies on these lines: {54,19186}, {539,19486}, {973,19410}, {1154,18939}, {1209,19428}, {2917,8939}, {3574,19446}, {6288,18462}, {7691,19406}, {9723,32387}, {9920,19418}, {10628,19484}, {12590,12998}, {13021,32345}, {17824,19430}, {18400,18980}, {18414,32365}, {18926,32334}, {19134,32344}, {19358,32341}, {19370,32350}, {19404,32333}, {19412,32338}, {19414,32339}, {19416,32340}, {19420,32346}, {19422,32348}, {19426,32368}, {19432,32370}, {19434,32378}, {19436,32384}, {19439,32385}, {19440,23358}, {19448,32396}, {19450,32397}, {19452,32398}, {19454,32401}, {21642,32352}, {23298,32351}

X(32386) = X(21)-of-Lucas-antipodal-tangents-triangle if ABC is acute

X(32387) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) ANTIPODAL TANGENTIAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32387) lies on these lines: {54,19187}, {539,19487}, {973,19411}, {1154,18940}, {1209,19429}, {2917,8943}, {3574,19447}, {6288,18463}, {7691,19407}, {9723,32386}, {9920,19419}, {10628,19485}, {12591,12999}, {13022,32345}, {17824,19431}, {18400,18981}, {18415,32365}, {18927,32334}, {19135,32344}, {19359,32341}, {19371,32350}, {19405,32333}, {19413,32338}, {19415,32339}, {19417,32340}, {19421,32346}, {19423,32348}, {19427,32368}, {19433,32370}, {19435,32378}, {19437,32385}, {19438,32384}, {19441,23358}, {19449,32396}, {19451,32397}, {19453,32398}, {19455,32401}, {21643,32352}, {23299,32351}

X(32387) = X(21)-of-Lucas(-1)-antipodal-tangents-triangle if ABC is acute

X(32388) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS HOMOTHETIC TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32388) lies on these lines: {493,6145}, {1154,12426}, {6461,32389}, {6462,32354}, {8188,32356}, {8194,32357}, {8210,32394}, {8212,32369}, {8214,32371}, {8216,32373}, {8218,32374}, {8220,32379}, {8222,32391}, {10628,12894}, {10669,18400}, {10875,32362}, {10945,32380}, {10951,32381}, {11377,32331}, {11394,32332}, {11503,32347}, {11828,32330}, {11840,32335}, {11846,32337}, {11907,32372}, {11930,32382}, {11932,32383}, {11947,32390}, {11949,32402}, {11951,32403}, {11953,32404}, {11955,32405}, {11957,32406}, {13899,32399}, {13956,32400}, {18520,32364}, {18963,32336}, {19031,32342}, {19032,32343}, {22761,32363}

X(32388) = X(6145)-of-Lucas-homothetic-triangle

X(32389) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) HOMOTHETIC TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32389) lies on these lines: {494,6145}, {1154,12427}, {6461,32388}, {6463,32354}, {8189,32356}, {8195,32357}, {8211,32394}, {8213,32369}, {8215,32371}, {8217,32373}, {8219,32374}, {8221,32379}, {8223,32391}, {10628,12895}, {10673,18400}, {10876,32362}, {10946,32380}, {10952,32381}, {11378,32331}, {11395,32332}, {11504,32347}, {11829,32330}, {11841,32335}, {11847,32337}, {11908,32372}, {11931,32382}, {11933,32383}, {11948,32390}, {11950,32402}, {11952,32403}, {11954,32404}, {11956,32405}, {11958,32406}, {13900,32399}, {13957,32400}, {18522,32364}, {18964,32336}, {19033,32342}, {19034,32343}, {22762,32363}

X(32389) = X(6145)-of-Lucas(-1)-homothetic-triangle

X(32390) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MANDART-INCIRCLE TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32390) lies on these lines: {1,18400}, {3,32404}, {4,32382}, {11,32391}, {12,32369}, {33,32332}, {55,6145}, {56,32330}, {497,32354}, {1154,12428}, {1479,32379}, {1697,32356}, {1837,32371}, {1858,6152}, {2098,32394}, {2646,32331}, {2917,9672}, {3295,32402}, {3574,11429}, {3583,32364}, {4294,32337}, {9659,32345}, {9670,32359}, {10628,12896}, {10799,32335}, {10833,32357}, {10877,32362}, {10927,32373}, {10928,32374}, {10947,32380}, {10953,32381}, {10965,32405}, {10966,32363}, {11909,32372}, {11947,32388}, {11948,32389}, {13901,32399}, {13958,32400}, {19037,32342}, {19038,32343}

X(32390) = reflection of X(32336) in X(1)
X(32390) = X(6145)-of-Mandart-incircle-triangle
X(32390) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497, 32354, 32383), (3295, 32402, 32403)

X(32391) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MEDIAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32391) lies on these lines: {1,32371}, {2,6145}, {3,32357}, {4,32330}, {5,5944}, {6,24}, {8,32394}, {11,32390}, {12,32336}, {25,11743}, {30,32364}, {55,32383}, {56,32382}, {64,15080}, {83,32335}, {113,12605}, {141,32348}, {154,7503}, {389,15872}, {394,7691}, {427,32332}, {468,10619}, {498,32403}, {499,32404}, {590,32399}, {615,32400}, {631,32337}, {942,12266}, {958,32363}, {1125,32331}, {1147,1154}, {1209,7542}, {1216,1511}, {1376,32347}, {1493,7575}, {1495,23047}, {1503,20376}, {1650,32372}, {1656,32402}, {1698,32356}, {2781,7512}, {3068,32343}, {3069,32342}, {3096,32362}, {3515,32341}, {3574,3575}, {4550,6759}, {5552,32405}, {5590,32374}, {5591,32373}, {6143,32353}, {6288,6639}, {6696,22352}, {6750,8146}, {7505,12254}, {7506,9920}, {7544,32346}, {7547,26882}, {8222,32388}, {8223,32389}, {8254,31830}, {8542,32367}, {10182,14076}, {10527,32406}, {11597,12606}, {15116,16196}, {16195,19153}, {17845,32395}, {22249,27552}

X(32391) = midpoint of X(i) and X(j) for these lines: {i,j}: {1, 32371}, {3, 32379}, {4, 32330}, {8, 32394}, {54, 2917}, {1650, 32372}, {6145, 32354}, {6759, 32401}, {7691, 17824}, {10274, 23358}, {32337, 32359}, {32347, 32380}, {32363, 32381}
X(32391) = reflection of X(i) in X(j) for these (i,j): (32331, 1125), (32351, 6689), (32369, 5), (32393, 32396)
X(32391) = complement of X(6145)
X(32391) = complementary conjugate of X(1594)
X(32391) = X(6145)-of-medial-triangle
X(32391) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 32354, 6145), (6689, 18475, 10610)

X(32392) = ORTHOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO MIDHEIGHT

The reciprocal orthologic center of these triangles is X(32393).

X(32392) lies on these lines: {6,64}, {26,6759}, {369,11761}, {389,32393}, {1216,1511}, {1660,12164}, {2393,5889}, {2929,15139}, {3627,5446}, {5562,17821}, {5878,18917}, {5892,32396}, {5895,16879}, {6053,16252}, {6144,14531}, {6241,18945}, {6247,13382}, {12315,18534}, {13366,32345}, {13367,17824}, {13403,15311}, {15012,23332}, {18400,32358}, {22802,32140}, {25739,32329}

X(32392) = midpoint of X(i) and X(j) for these lines: {i,j}: {185, 6293}, {14531, 17845}
X(32392) = reflection of X(i) in X(j) for these (i,j): (64, 22967), (6247, 13382), (31978, 185)
X(32392) = X(6145)-of-5th-mixtilinear-triangle
X(32392) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (64, 185, 22967), (64, 22967, 31978)

X(32393) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MIDHEIGHT TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(32392).

X(32393) lies on these lines: {4,11747}, {5,5944}, {6,3574}, {25,32340}, {26,18376}, {54,18945}, {206,3091}, {389,32392}, {569,32379}, {1154,12235}, {1209,18531}, {2917,7395}, {5449,18569}, {6676,20376}, {6756,7687}, {6816,15435}, {7514,23358}, {7564,18128}, {9969,11743}, {10628,12236}, {11431,18912}, {11572,32332}, {11576,32246}, {12362,32348}, {15077,15801}, {18405,32330}

X(32393) = midpoint of X(i) and X(j) for these lines: {i,j}: {3574, 6145}, {18381, 32364}, {32340, 32345}, {32351, 32369}
X(32393) = reflection of X(i) in X(j) for these (i,j): (32377, 32376), (32391, 32396)
X(32393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6145, 32395, 3574), (23324, 32351, 32369)

X(32394) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th MIXTILINEAR TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32394) lies on these lines: {1,6145}, {8,32391}, {55,32363}, {56,32347}, {145,32354}, {517,32330}, {519,32371}, {952,32379}, {1154,9933}, {1482,18400}, {2098,32390}, {2099,32336}, {5603,32369}, {5604,32374}, {5605,32373}, {7718,11743}, {7967,32337}, {7968,32342}, {7969,32343}, {8192,32357}, {8210,32388}, {8211,32389}, {9997,32362}, {10247,32402}, {10628,12898}, {10800,32335}, {10944,32380}, {10950,32381}, {11396,32332}, {11910,32372}, {13902,32399}, {13959,32400}, {18525,32364}

X(32394) = midpoint of X(145) and X(32354)
X(32394) = reflection of X(i) in X(j) for these (i,j): (8, 32391), (6145, 1), (18525, 32364), (32356, 32331)
X(32394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 32356, 32331), (32331, 32356, 6145), (32405, 32406, 6145)

X(32395) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ORTHOCENTROIDAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(1986).

X(32395) lies on these lines: {3,32365}, {4,10117}, {5,2917}, {6,3574}, {20,20376}, {54,7547}, {154,381}, {195,265}, {382,32401}, {567,10274}, {568,10628}, {1154,14852}, {1498,32364}, {1503,7565}, {1656,23358}, {1853,5890}, {1986,32329}, {2931,10224}, {3091,15582}, {3851,9920}, {5889,11262}, {6288,17814}, {6689,32330}, {7564,32046}, {7730,14644}, {10516,11188}, {10539,11597}, {10895,32350}, {10896,32378}, {12022,23324}, {12307,14076}, {14389,32354}, {15069,32368}, {17835,20299}, {17845,32391}

X(32395) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 32351, 32345), (3574, 6145, 17824), (3574, 32393, 6145)

X(32396) = ORTHOLOGIC CENTER OF THESE TRIANGLES: SUBMEDIAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32396) lies on these lines: {2,3574}, {5,5944}, {6,17}, {54,3090}, {182,32379}, {373,32352}, {485,13986}, {486,8995}, {539,547}, {973,5943}, {1154,3628}, {1493,16254}, {2888,7486}, {2917,5020}, {3091,32340}, {3357,4846}, {3549,19130}, {3818,14530}, {5055,6288}, {5056,10619}, {5071,12254}, {5449,32068}, {5576,29012}, {5892,32392}, {5893,20376}, {5972,14788}, {6642,23358}, {6723,9826}, {7392,32346}, {7569,7592}, {8889,13347}, {9813,32368}, {9816,32370}, {9817,32378}, {9818,32401}, {9920,11484}, {10109,20584}, {10112,14389}, {10115,10170}, {10175,12266}, {10601,32341}, {10643,32397}, {10644,32398}, {10961,32384}, {10963,32385}, {11284,32333}, {11451,32338}, {11465,32339}, {11479,32345}, {11597,23515}, {11808,12363}, {12046,15350}, {12900,15088}, {13469,25339}, {15699,21230}, {17824,17825}, {18420,32365}, {18928,32334}, {19137,32344}, {19372,32350}, {19448,32386}, {19449,32387}

X(32396) = midpoint of X(i) and X(j) for these lines: {i,j}: {5, 6689}, {195, 15605}, {1209, 12242}, {3574, 32348}, {8254, 13565}, {11808, 12363}, {32391, 32393}
X(32396) = complement of X(32348)
X(32396) = X(21)-of-submedial-triangle if ABC is acute
X(32396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 3574, 32348), (195, 1209, 15605), (12242, 15605, 195)

X(32397) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER TRI-EQUILATERAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32397) lies on these lines: {6,24}, {15,18400}, {16,23358}, {539,10659}, {1154,10661}, {1209,8837}, {3166,10635}, {3574,10641}, {6288,18468}, {7051,32350}, {7691,11420}, {9920,11485}, {10274,10678}, {10628,10657}, {10636,32370}, {10638,32378}, {10643,32396}, {10645,32401}, {11408,32333}, {11452,32338}, {11466,32339}, {11475,32340}, {11480,32345}, {11488,32346}, {11515,32348}, {16808,32365}, {17824,17826}, {18929,32334}, {19363,32341}, {19450,32386}, {19451,32387}, {21647,32352}, {23302,32351}, {30402,32379}

X(32397) = X(21)-of-inner-tri-equilateral-triangle if ABC is acute
X(32397) = {X(6), X(2917)}-harmonic conjugate of X(32398)

X(32398) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER TRI-EQUILATERAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32398) lies on these lines: {6,24}, {15,23358}, {16,18400}, {539,10660}, {1154,10662}, {1209,8839}, {1250,32378}, {3165,10634}, {3574,10642}, {6288,18470}, {7691,11421}, {9920,11486}, {10274,10677}, {10628,10658}, {10637,32370}, {10644,32396}, {10646,32401}, {11409,32333}, {11453,32338}, {11467,32339}, {11476,32340}, {11481,32345}, {11489,32346}, {11516,32348}, {16809,32365}, {17824,17827}, {18930,32334}, {19364,32341}, {19373,32350}, {19452,32386}, {19453,32387}, {21648,32352}, {23303,32351}, {30403,32379}

X(32398) = X(21)-of-outer-tri-equilateral-triangle if ABC is acute
X(32398) = {X(6), X(2917)}-harmonic conjugate of X(32397)

X(32399) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd TRI-SQUARES-CENTRAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32399) lies on these lines: {2,32343}, {6,32400}, {371,32369}, {590,32391}, {1154,13909}, {3068,6145}, {7585,32342}, {8972,32354}, {8974,32373}, {8976,32379}, {8981,18400}, {9540,32330}, {10628,13915}, {13883,32331}, {13884,32332}, {13885,32335}, {13886,32337}, {13887,32347}, {13888,32356}, {13889,32357}, {13893,32371}, {13894,32372}, {13895,32380}, {13897,32382}, {13898,32383}, {13899,32388}, {13900,32389}, {13901,32390}, {13902,32394}, {13903,32402}, {13904,32403}, {13905,32404}, {13906,32405}, {13907,32406}, {18538,32364}, {18965,32336}, {22763,32363}

X(32399) = X(6145)-of-3rd-tri-squares-central-triangle

X(32400) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th TRI-SQUARES-CENTRAL TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32400) lies on these lines: {2,32342}, {6,32399}, {372,32369}, {615,32391}, {1154,13970}, {3069,6145}, {7586,32343}, {10628,13979}, {13935,32330}, {13936,32331}, {13937,32332}, {13938,32335}, {13939,32337}, {13940,32347}, {13941,32354}, {13942,32356}, {13943,32357}, {13946,32362}, {13947,32371}, {13948,32372}, {13949,32373}, {13950,32374}, {13951,32379}, {13952,32380}, {13953,32381}, {13954,32382}, {13955,32383}, {13956,32388}, {13957,32389}, {13958,32390}, {13959,32394}, {13961,32402}, {13962,32403}, {13963,32404}, {13964,32405}, {13965,32406}, {13966,18400}, {18762,32364}, {18966,32336}, {22764,32363}

X(32400) = X(6145)-of-4th-tri-squares-central-triangle

X(32401) = ORTHOLOGIC CENTER OF THESE TRIANGLES: TRINH TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(389).

X(32401) lies on these lines: {3,161}, {5,13289}, {24,32340}, {26,18376}, {30,32351}, {35,32350}, {36,32378}, {49,19402}, {54,74}, {64,32349}, {186,11572}, {195,8567}, {376,32346}, {378,3574}, {382,32395}, {511,32368}, {539,9938}, {973,11438}, {1154,7689}, {1204,12234}, {1658,23325}, {2071,7691}, {2777,3521}, {3098,15578}, {3357,10274}, {3516,12242}, {4550,6759}, {5092,32344}, {5894,8254}, {6000,15062}, {6200,32384}, {6293,14805}, {6396,32385}, {6689,7526}, {6699,22962}, {7488,18383}, {7688,32370}, {9818,32396}, {9977,11802}, {10226,12901}, {10263,11262}, {10605,32341}, {10606,17824}, {10645,32397}, {10646,32398}, {11410,32333}, {11454,32338}, {11457,12254}, {11468,32339}, {11793,22955}, {12038,15132}, {12107,23324}, {12893,13561}, {13403,19457}, {14216,32354}, {15331,23332}, {15579,32367}, {16003,25564}, {18128,32412}, {18931,32334}, {19454,32386}, {19455,32387}, {21230,22978}, {21663,32352}, {32184,32196}

X(32401) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32345}, {3357, 10274}, {14216, 32354}
X(32401) = reflection of X(i) in X(j) for these (i,j): (5, 20376), (6145, 20299), (6288, 14076), (6759, 32391), (10263, 11262), (10274, 10610), (14076, 25563), (22802, 32364), (23358, 3), (32344, 5092), (32364, 6689), (32365, 32351), (32412, 18128)
X(32401) = circumtangential-isogonal conjugate of X(7488)
X(32401) = X(21)-of-Trinh-triangle if ABC is acute
X(32401) = {X(11750), X(20299)}-harmonic conjugate of X(18381)

X(32402) = ORTHOLOGIC CENTER OF THESE TRIANGLES: X3-ABC REFLECTIONS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32402) lies on these lines: {3,161}, {4,19362}, {5,32354}, {30,32337}, {54,7507}, {195,31724}, {381,32369}, {517,32356}, {567,10274}, {973,18494}, {999,32336}, {1154,12429}, {1594,12254}, {1598,32332}, {1656,32391}, {2888,12225}, {3295,32390}, {3574,11426}, {3843,32359}, {5790,32371}, {6193,12319}, {6241,7730}, {6243,10628}, {6417,32343}, {6418,32342}, {7517,32357}, {9301,32362}, {9654,32382}, {9669,32383}, {10246,32331}, {10247,32394}, {10620,14216}, {11842,32335}, {11849,32347}, {11911,32372}, {11916,32373}, {11917,32374}, {11928,32380}, {11929,32381}, {11949,32388}, {11950,32389}, {12000,32405}, {12001,32406}, {12315,32340}, {13903,32399}, {13961,32400}, {17824,18405}, {22765,32363}

X(32402) = reflection of X(i) in X(j) for these (i,j): (3, 6145), (9920, 6288), (10274, 18383), (17824, 32365), (17845, 23358), (32345, 18381), (32354, 5), (32359, 32364), (32379, 32369)
X(32402) = X(6145)-of-X3-ABC-reflections-triangle
X(32402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (10274, 18383, 32395), (32369, 32379, 381)

X(32403) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-YFF TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32403) lies on these lines: {1,6145}, {3,32336}, {5,32383}, {12,32379}, {35,32330}, {55,12946}, {388,32337}, {495,32382}, {498,32391}, {973,11392}, {1154,10055}, {1479,32369}, {3295,32390}, {3299,32342}, {3301,32343}, {6288,18455}, {10037,32357}, {10038,32362}, {10039,32371}, {10040,32373}, {10041,32374}, {10082,32351}, {10523,32380}, {10628,12903}, {10801,32335}, {10895,32364}, {10954,32381}, {11398,32332}, {11507,32347}, {11912,32372}, {11951,32388}, {11952,32389}, {13904,32399}, {13962,32400}, {22766,32363}

X(32403) = midpoint of X(6145) and X(32405)
X(32403) = reflection of X(32382) in X(495)
X(32403) = X(6145)-of-inner-Yff-triangle
X(32403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6145, 32404), (3295, 32402, 32390)

X(32404) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-YFF TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32404) lies on these lines: {1,6145}, {3,32390}, {5,32382}, {11,32379}, {36,32330}, {56,12956}, {496,32383}, {497,32337}, {499,32391}, {973,11393}, {999,32336}, {1154,10071}, {1478,32369}, {1737,32371}, {3086,32354}, {3299,32343}, {3301,32342}, {6288,18447}, {10046,32357}, {10047,32362}, {10048,32373}, {10049,32374}, {10066,32351}, {10523,32381}, {10628,12904}, {10802,32335}, {10896,32364}, {10948,32380}, {11399,32332}, {11508,32347}, {11913,32372}, {11953,32388}, {11954,32389}, {13905,32399}, {13963,32400}, {22767,32363}

X(32404) = midpoint of X(6145) and X(32406)
X(32404) = reflection of X(32383) in X(496)
X(32404) = X(6145)-of-outer-Yff-triangle
X(32404) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6145, 32403), (999, 32402, 32336)

X(32405) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-YFF TANGENTS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32405) lies on these lines: {1,6145}, {12,32380}, {1154,12430}, {5552,32391}, {10528,32354}, {10531,32369}, {10628,12905}, {10679,18400}, {10803,32335}, {10805,32337}, {10834,32357}, {10878,32362}, {10915,32371}, {10929,32373}, {10930,32374}, {10942,32379}, {10955,32381}, {10956,32382}, {10958,32383}, {10965,32390}, {11248,32330}, {11400,32332}, {11509,32336}, {11914,32372}, {11955,32388}, {11956,32389}, {12000,32402}, {13906,32399}, {13964,32400}, {18542,32364}, {19047,32342}, {19048,32343}, {22768,32363}

X(32405) = reflection of X(6145) in X(32403)
X(32405) = X(6145)-of-inner-Yff-tangents-triangle
X(32405) = {X(6145), X(32394)}-harmonic conjugate of X(32406)

X(32406) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-YFF TANGENTS TO HATZIPOLAKIS-MOSES

The reciprocal orthologic center of these triangles is X(6146).

X(32406) lies on these lines: {1,6145}, {11,32381}, {1154,12431}, {10527,32391}, {10529,32354}, {10532,32369}, {10628,12906}, {10680,18400}, {10804,32335}, {10806,32337}, {10835,32357}, {10879,32362}, {10916,32371}, {10931,32373}, {10932,32374}, {10943,32379}, {10949,32380}, {10957,32382}, {10959,32383}, {10966,32363}, {11249,32330}, {11401,32332}, {11510,32347}, {11915,32372}, {11957,32388}, {11958,32389}, {12001,32402}, {13907,32399}, {13965,32400}, {18544,32364}, {18967,32336}, {19049,32342}, {19050,32343}

X(32406) = reflection of X(6145) in X(32404)
X(32406) = X(6145)-of-outer-Yff-tangents-triangle
X(32406) = {X(6145), X(32394)}-harmonic conjugate of X(32405)

X(32407) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st PARRY TO HATZIPOLAKIS-MOSES

The reciprocal parallelogic center of these triangles is X(6146).

X(32407) lies on these lines: {351,6368}, {1510,13223}

X(32407) = reflection of X(32408) in X(351)
X(32407) = X(6145)-of-1st-Parry-triangle

X(32408) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd PARRY TO HATZIPOLAKIS-MOSES

The reciprocal parallelogic center of these triangles is X(6146).

X(32408) lies on these lines: {110,16039}, {351,6368}, {1510,13224}

X(32408) = reflection of X(32407) in X(351)
X(32408) = X(6145)-of-2nd-Parry-triangle

X(32409) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-CONWAY TO HATZIPOLAKIS-MOSES

The reciprocal cyclologic center of these triangles is X(389).

X(32409) lies on these lines: {5,51}, {54,3432}, {568,19552}, {1157,3567}, {5462,10615}, {5946,6150}, {11077,15401}, {18400,32410}

X(32409) = midpoint of X(52) and X(16336)
X(32409) = reflection of X(10615) in X(5462)
X(32409) = complement of X(16337) wrt orthic triangle
X(32409) = X(1325)-of-2nd-anti-Conway-triangle if ABC is acute

X(32410) = CYCLOLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO ORTHIC

The reciprocal cyclologic center of these triangles is X(1986).

X(32410) lies on these lines: {5,49}, {137,12241}, {12370,25150}, {15959,19467}, {18400,32409}

X(32410) = reflection of X(137) in X(12241)

X(32411) = EULEROLOGIC CENTER OF THESE TRIANGLES: HATZIPOLAKIS-MOSES TO 2nd ANTI-CONWAY

X(32411) lies on these lines: {6,2070}, {30,143}, {51,403}, {52,2072}, {186,578}, {468,973}, {511,10257}, {568,18390}, {1112,6000}, {1154,11746}, {1986,13851}, {2071,3060}, {5899,11432}, {5946,11430}, {6746,10110}, {7687,12236}, {7722,23043}, {9786,18859}, {10114,11557}, {10297,13376}, {10540,12227}, {11262,11745}, {11431,20063}, {11563,12233}, {11807,15311}, {15473,18400}, {15644,16976}

X(32411) = midpoint of X(i) and X(j) for these lines: {i,j}: {52, 2072}, {1986, 13851}, {13376, 16625}
X(32411) = reflection of X(i) in X(j) for these (i,j): (10151, 10110), (10297, 13376), (15644, 16976)
X(32411) = {X(12241), X(16881)}-harmonic conjugate of X(389)

X(32412) = ORTHOCENTER OF THE HATZIPOLAKIS-MOSES TRIANGLE

X(32412) lies on these lines: {6,3574}, {539,9932}, {1511,21230}, {5449,10274}, {6102,10116}, {6689,14076}, {11225,11262}, {15033,32337}, {18128,32401}

X(32412) = reflection of X(i) in X(j) for these (i,j): (6145, 32376), (11262, 32413), (32401, 18128)
X(32412) = {X(11262), X(32413)}-harmonic conjugate of X(11225)

X(32413) = X(5)-OF-HATZIPOLAKIS-MOSES TRIANGLE

X(32413) lies on these lines: {11225,11262}, {11245,20376}, {12242,15118}, {18400,32165}

X(32413) = midpoint of X(11262) and X(32412)
X(32413) = {X(11225), X(32412)}-harmonic conjugate of X(11262)

X(32414) = X(2)X(1495)∩X(5)X(26614)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004.

X(32414) lies on these lines: {2, 1495}, {5, 26614}, {30, 1153}, {381, 5215}, {511, 7610}, {542, 9771}, {575, 6055}, {3830, 8588}, {6054, 10486}, {7603, 14830}, {13355, 21358}, {15597, 19924}, {23053, 31670}

X(32415) = X(2)X(32401)∩X(140)X(6000)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004

X(32415) lies on these lines: {2, 32401}, {140, 6000}, {2777, 5498}, {6143, 13289}, {6288, 11202}, {10018, 18383}, {10125, 18400}, {10182, 14076}, {13363, 15426}, {15694, 32321}, {16532, 32351}

X(32416) = X(511)X(25488)∩X(3589)X(5066)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004.

X(32416) lies on these lines: {511, 25488}, {3589, 5066}, {3818, 5012}, {6676, 10219}, {7605, 32305}, {14389, 25561}

X(32417) = X(3)X(31378)∩X(4)X(5627)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004.

X(32417) lies on these lines: {3, 31378}, {4, 5627}, {20, 14480}, {30, 511}, {74, 3258}, {107, 18809}, {113, 22104}, {133, 1552}, {146, 476}, {381, 18279}, {477, 1138}, {550, 18285}, {1304, 5667}, {3154, 20417}, {3233, 6053}, {5502, 20128}, {7471, 15063}, {7687, 12079}, {7728, 14993}, {10096, 16244}, {10620, 20957}, {10745, 16177}, {12041, 31379}, {13382, 14895}, {14508, 14731}, {14611, 16163}, {14934, 16111}, {15054, 17511}, {16978, 21649}

X(32418) = X(107)X(12121)∩X(476)X(16163)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29004.

X(32418) lies on the circumcircle and these lines: {107, 12121}, {476, 16163}, {1304, 1511}, {2132, 15035}

X(32419) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES, 4th TRI-SQUARES, AND INNER-VECTEN

Centers X(32419) to X(32441) were contributed by César Lozada, May 5, 2019.

X(32419) lies on these lines: {2,371}, {3,591}, {4,5861}, {6,13644}, {13,22607}, {14,22608}, {20,26288}, {30,511}, {69,6561}, {187,13989}, {193,6560}, {298,22601}, {299,22603}, {323,12376}, {372,489}, {376,5860}, {381,1991}, {395,6307}, {396,6306}, {428,12147}, {485,12322}, {488,13712}, {491,6565}, {492,6200}, {551,12268}, {615,9675}, {640,3071}, {641,1151}, {1161,13748}, {1270,9541}, {1271,23259}, {1327,2996}, {1328,5491}, {1504,5309}, {1651,12799}, {2462,5182}, {2858,32422}, {3058,13081}, {3068,13650}, {3069,13770}, {3102,8356}, {3241,7980}, {3543,12296}, {3592,11313}, {3679,9906}, {3830,22809}, {3845,22596}, {4421,12343}, {5434,18989}, {5591,23273}, {5875,14230}, {6118,8981}, {6231,9892}, {6278,13710}, {6289,12313}, {6337,13701}, {6419,7389}, {6420,11293}, {6425,11315}, {6459,26619}, {6463,13798}, {7811,9986}, {7833,9991}, {7837,22613}, {7840,22501}, {9732,9766}, {9742,13681}, {9758,9770}, {9909,9921}, {10008,13684}, {10056,10067}, {10072,10083}, {10653,22612}, {10654,22611}, {11194,22595}, {11207,12484}, {11208,12485}, {11235,12928}, {11236,12938}, {11237,12948}, {11238,12958}, {11239,13132}, {11240,13133}, {12150,12210}, {12152,13002}, {12153,13003}, {12222,22644}, {12237,21849}, {12323,22615}, {12962,13846}, {12963,13821}, {12972,14070}, {13926,13927}, {16267,22602}, {16268,22604}, {19053,19104}, {19054,19105}, {19493,32060}, {21653,21969}, {23267,26339}

X(32419) = isogonal conjugate of X(32420)

X(32420) = ISOGONAL CONJUGATE OF X(32419)

X(32420) lies on the circumcircle and these lines: {99,491}, {110,372}, {112,5412}, {485,925}, {691,2460}, {1307,6396}, {2858,32421}, {2872,9142}, {3565,6200}

X(32420) = isogonal conjugate of X(32419)
X(32420) = reflection of X(98) in the line X(3)X(9892)

X(32421) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES, 3rd TRI-SQUARES, AND OUTER-VECTEN

X(32421) lies on these lines: {2,372}, {3,1991}, {4,5860}, {6,13763}, {13,22636}, {14,22637}, {20,26289}, {30,511}, {69,6560}, {187,8997}, {193,6561}, {298,22630}, {299,22632}, {323,12375}, {371,490}, {376,5861}, {381,591}, {395,6303}, {396,6302}, {428,12148}, {486,12323}, {487,13835}, {491,6396}, {492,6564}, {551,12269}, {639,3070}, {642,1152}, {1160,13749}, {1270,23249}, {1327,5490}, {1328,2996}, {1505,5309}, {1651,12800}, {2461,5182}, {2858,32420}, {3058,13082}, {3068,13651}, {3069,13771}, {3103,8356}, {3241,7981}, {3543,12297}, {3594,11314}, {3679,9907}, {3830,22810}, {3845,22625}, {4421,12344}, {5434,18988}, {5590,23267}, {5874,14233}, {6119,13966}, {6230,9894}, {6281,13830}, {6290,12314}, {6337,13821}, {6419,11294}, {6420,7388}, {6426,11316}, {6460,26620}, {6462,13678}, {7811,9987}, {7833,9992}, {7837,22642}, {7840,22502}, {8989,12973}, {8996,9909}, {9733,9766}, {9742,13801}, {9757,9770}, {10008,13804}, {10056,10068}, {10072,10084}, {10653,22641}, {10654,22640}, {11194,22624}, {11207,12486}, {11208,12487}, {11235,12929}, {11236,12939}, {11237,12949}, {11238,12959}, {11239,13134}, {11240,13135}, {12150,12211}, {12152,13004}, {12153,13005}, {12221,22615}, {12238,21849}, {12322,22644}, {12968,13701}, {12969,13847}, {13873,13874}, {16267,22631}, {16268,22633}, {19053,19102}, {19054,19103}, {19492,32059}, {21654,21969}, {23273,26340}

X(32421) = isogonal conjugate of X(32422)

X(32422) = ISOGONAL CONJUGATE OF X(32421)

X(32422) lies on the circumcircle and these lines: {99,492}, {110,371}, {112,5413}, {486,925}, {691,2459}, {1306,6200}, {2858,32419}, {2872,9142}, {3565,6396}

X(32422) = isogonal conjugate of X(32421)
X(32422) = reflection of X(98) in the line X(3)X(9894)

X(32423) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: AOA, AAOA, AND 1st HYACINTH

X(32423) lies on the cubic K466, the curve Q110 and these lines: {2,11694}, {3,2888}, {4,195}, {5,49}, {20,10620}, {26,9920}, {30,511}, {52,32196}, {68,1658}, {69,32306}, {74,550}, {99,15545}, {113,137}, {125,128}, {141,12584}, {143,10112}, {146,382}, {155,18377}, {156,9927}, {182,25328}, {252,19268}, {323,7574}, {343,22109}, {355,2948}, {376,15041}, {381,9143}, {389,6153}, {427,15463}, {495,10066}, {496,10082}, {547,5642}, {548,12041}, {549,9140}, {568,7730}, {576,25329}, {631,15040}, {632,15027}, {895,1353}, {946,11699}, {973,12236}, {974,18914}, {1112,6756}, {1147,10224}, {1216,13470}, {1350,25335}, {1351,11061}, {1352,2930}, {1385,13605}, {1483,7979}, {1484,10778}, {1495,25338}, {1513,5987}, {1539,3853}, {1594,3043}, {1595,15472}, {1656,15081}, {1657,12244}, {1770,11670}, {1885,12292}, {1986,3575}, {2935,14216}, {3028,3327}, {3047,10024}, {3070,12375}, {3071,12376}, {3090,15039}, {3091,20125}, {3530,6699}, {3545,15046}, {3580,7575}, {3581,12380}, {3585,14101}, {3589,20301}, {3627,7728}, {3628,5972}, {3845,5655}, {3850,7687}, {3857,15044}, {3861,6053}, {4857,7343}, {5050,25320}, {5066,23516}, {5073,13432}, {5085,25330}, {5093,25321}, {5102,25331}, {5254,14901}, {5270,6126}, {5318,10657}, {5321,10658}, {5448,18379}, {5449,10125}, {5462,13365}, {5480,19140}, {5498,12038}, {5501,25340}, {5504,6145}, {5654,32395}, {5690,12778}, {5874,6276}, {5875,6277}, {5876,15532}, {5889,13423}, {5901,11720}, {5946,16223}, {6101,11750}, {6102,11562}, {6193,12319}, {6240,6242}, {6243,7731}, {6247,13293}, {6253,6255}, {6284,6286}, {6321,15342}, {6593,18583}, {6644,26869}, {6696,25564}, {6723,16239}, {6776,32251}, {6794,22146}, {7354,7356}, {7487,18947}, {7526,12168}, {7577,9703}, {7579,11935}, {7689,15332}, {7723,12605}, {8550,9976}, {8703,15055}, {8981,10819}, {8995,8998}, {9544,10254}, {9825,9826}, {9833,10117}, {9934,32359}, {9970,21850}, {9985,12501}, {10020,32391}, {10021,16164}, {10095,13163}, {10111,14708}, {10116,11802}, {10126,18016}, {10127,12099}, {10205,30484}, {10226,12901}, {10263,13417}, {10282,18282}, {10299,15042}, {10540,11563}, {10663,32397}, {10664,32398}, {10706,15687}, {10721,16659}, {10820,13966}, {10942,12890}, {10943,12889}, {11064,32235}, {11202,15330}, {11250,12118}, {11412,15100}, {11442,18570}, {11477,25336}, {11536,18428}, {11559,13418}, {11565,32142}, {11577,15738}, {11579,32233}, {11807,13419}, {11818,14853}, {11819,14449}, {12079,15468}, {12084,32337}, {12103,16111}, {12105,32269}, {12107,13289}, {12108,20397}, {12112,18325}, {12133,13488}, {12165,12173}, {12201,12208}, {12219,12225}, {12227,12233}, {12270,12278}, {12273,12281}, {12293,17824}, {12334,12341}, {12358,12362}, {12359,12893}, {12364,32349}, {12428,12888}, {12596,32368}, {12661,32370}, {12790,12797}, {12824,13451}, {12891,32384}, {12892,32385}, {12894,12998}, {12895,12999}, {12897,32137}, {12900,15088}, {12905,13121}, {12906,13122}, {13142,32332}, {13188,18331}, {13198,31804}, {13202,13431}, {13353,27866}, {13383,20773}, {13393,15605}, {13413,23292}, {13979,13986}, {14480,20957}, {14791,15106}, {14869,15020}, {14912,18420}, {14934,16340}, {15036,15057}, {15051,15712}, {15054,15704}, {15068,18396}, {15085,17835}, {15091,18572}, {15093,22265}, {15113,15114}, {15122,15124}, {15123,32355}, {15136,32353}, {15345,27868}, {15465,23411}, {15761,32379}, {16165,25337}, {16266,17847}, {16337,24385}, {18358,32274}, {18381,23315}, {18440,31861}, {18563,22584}, {18567,19479}, {18874,23409}, {18932,32334}, {18933,18945}, {18970,19469}, {19051,19095}, {19052,19096}, {19138,32344}, {19139,23049}, {19195,19205}, {19456,32341}, {19457,19467}, {19478,22586}, {19482,32386}, {19483,32387}, {19484,19498}, {19485,19499}, {19552,24144}, {20030,20414}, {22115,25739}, {32114,32275}

X(32423) = isogonal conjugate of X(14979)

X(32424) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: 4th BROCARD, CIRCUMMEDIAL, AND 5th EULER

X(32424) lies on these lines: {2,10748}, {3,9829}, {4,31824}, {5,9172}, {30,511}, {110,11159}, {111,381}, {113,13994}, {125,11569}, {126,549}, {140,31606}, {143,31763}, {376,6031}, {546,31749}, {547,6719}, {550,31729}, {1296,3534}, {1316,32222}, {1385,31747}, {3543,20099}, {3579,31746}, {3830,10734}, {3845,5512}, {5077,9140}, {5476,28662}, {5694,31823}, {5946,31743}, {5987,9855}, {6101,31736}, {6102,31745}, {6232,9129}, {9940,31818}, {9955,31755}, {9956,31758}, {11591,31753}, {12041,32311}, {12161,31809}, {13643,13644}, {13762,13763}, {14657,18324}, {15303,18907}, {31727,31748}, {31761,32161}, {32219,32225}

X(32424) = isogonal conjugate of X(32425)

X(32425) = ISOGONAL CONJUGATE OF X(32424)

X(32425) lies on the circumcircle and these lines: {476,11159}, {523,11568}, {524,6236}, {1296,8705}, {1499,6325}

X(32425) = isogonal conjugate of X(32424)
X(32425) = (circumsymmedial)-isogonal conjugate of-X(2780)
X(32425) = X(2696) of circumsymmedial triangle
X(32425) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (74, 3, 352), (111, 3, 11663), (477, 3, 11628), (1296, 3, 17414), (11568, 2, 3)

X(32426) = INTERSECTION OF THE EULER LINES OF THESE TRIANGLES: EXCENTERS-MIDPOINTS, GARCIA-REFLECTION, AND 2nd SCHIFFLER

X(32426) lies on these lines: {8,1997}, {30,511}, {145,1376}, {497,3621}, {1699,3680}, {2886,12648}, {3338,3633}, {3476,5221}, {3632,15829}, {3813,5790}, {3913,7967}, {4969,16561}, {5506,13606}, {5603,10912}, {6667,6735}, {8256,17728}, {10164,11260}, {10915,11230}, {11219,11256}, {11246,14923}, {12645,26333}, {17784,20014}

X(32426) = isogonal conjugate of X(32427)

X(32427) = ISOGONAL CONJUGATE OF X(32426)

X(32427) lies on the circumcircle and these lines: {100,20323}, {30236,31798}

X(32427) = isogonal conjugate of X(32426)
X(32427) = X(110)-of-3rd mixtilinear triangle

X(32428) = POINT AT INFINITY OF THE BROCARD AXIS OF THE CIRCUMORTHIC TRIANGLE

X(32428) lies on these lines: {2,10184}, {3,95}, {4,3164}, {5,53}, {20,31388}, {26,157}, {30,511}, {52,6751}, {68,8612}, {110,32439}, {140,6709}, {143,15912}, {155,17849}, {324,418}, {381,14635}, {1209,15780}, {1316,19128}, {1513,12131}, {2052,6638}, {2070,30716}, {2980,17714}, {5872,8175}, {5873,8174}, {6662,10627}, {6663,10095}, {9747,9909}, {10125,13467}, {13371,23333}, {13599,17039}, {17041,31505}, {18377,18380}, {18951,18953}, {19154,19156}, {19210,19212}, {27352,27361}

X(32428) = complementary conjugate of X(129)
X(32428) = isogonal conjugate of X(1298)
X(32428) = point at infinity of Brocard axis of any triangle homothetic to circumorthic triangle

X(32429) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 6th ANTI-BROCARD, ANTI-EULER, AND 1st NEUBERG

X(32429) lies on these lines: {6,18501}, {20,185}, {39,3818}, {76,5092}, {182,2782}, {542,1569}, {732,3098}, {1352,7709}, {3095,29012}, {5085,13108}, {5116,12188}, {5476,7739}, {6248,7803}, {7757,11645}, {7765,13331}, {7795,13334}, {8149,14880}, {10007,11178}, {11171,14981}, {11179,18906}

X(32429) = reflection of X(i) in X(j) for these (i,j): (76, 5092), (3818, 39), (11261, 7709), (32430, 14712)
X(32429) = (1st Neuberg)-isogonal conjugate of-X(6194)
X(32429) = (1st Ehrmann)-anticomplement of-X(24256)
X(32429) = X(9821)-of-1st Brocard triangle

X(32430) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: ANTI-EULER, 1st BROCARD-REFLECTED, AND 2nd NEUBERG

X(32430) lies on these lines: {20,185}, {8150,14881}, {10796,11261}

X(32430) = reflection of X(32429) in X(14712)

X(32431) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: ANTI-ORTHOCENTROIDAL, EXCENTRAL, AND FEUERBACH

X(32431) lies on these lines: {2,17190}, {3,31872}, {4,9}, {5,572}, {6,13}, {7,24224}, {8,24048}, {30,1213}, {37,18480}, {80,2171}, {191,21014}, {219,24045}, {284,6841}, {355,4053}, {391,3839}, {403,1474}, {429,15946}, {430,2328}, {517,21873}, {594,18357}, {604,7741}, {941,5560}, {1030,13743}, {1100,9955}, {1400,3585}, {1568,22133}, {1765,6839}, {1781,21044}, {1999,10478}, {2160,22798}, {2173,7110}, {2178,18761}, {2268,7951}, {2269,3583}, {2285,10826}, {3686,18483}, {3723,28204}, {3845,17330}, {4034,31162}, {4253,6849}, {4909,5712}, {5080,21061}, {5086,21078}, {5257,31673}, {5443,17440}, {5747,6866}, {6894,18865}, {6996,17307}, {7377,17352}, {7384,17300}, {8287,24884}, {9355,13610}, {9665,21785}, {10446,17343}, {10883,19642}, {12699,17275}, {13478,14534}, {15971,26079}, {16777,18525}, {16884,18493}, {17205,28091}, {17258,29069}, {17362,22791}, {17748,27871}, {20546,24267}, {21773,26321}, {24271,27688}

X(32431) = (2nd Fuhrmann)-isotomic conjugate of-X(22791)
X(32431) = intersection of the Brocard axes of these triangles: anti-orthocentroidal, 2nd extouch and Feuerbach
X(32431) = intersection of the Brocard axes of these triangles: anti-orthocentroidal, Feuerbach and 2nd Zaniah
X(32431) = inverse-in-Kiepert-hyperbola of X(3017)
X(32431) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 5816, 573), (13, 14, 3017)

X(32432) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES, EULER, AND OUTER-VECTEN

X(32432) lies on these lines: {2,2459}, {5,141}, {316,2460}, {371,7773}, {372,7887}, {487,23259}, {641,3070}, {642,13449}, {1691,11314}, {2456,6290}, {3102,7752}, {3103,5025}, {6567,31173}, {7825,9738}, {7862,9739}, {13665,22623}

X(32432) = midpoint of X(316) and X(2460)
X(32432) = reflection of X(32435) in X(625)
X(32432) = complement of X(2459)
X(32432) = (outer-Vecten)-isogonal conjugate of-X(13926)
X(32432) = (1st Brocard)-complement of-X(2459)
X(32432) = inverse of X(639) in the nine-point circle
X(32432) = X(6567)-of-outer-Vecten triangle
X(32432) = intersection of the Brocard axes of these triangles: 3rd anti-tri-squares, medial and outer-Vecten
X(32432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 5031, 32435), (2039, 2040, 639)

X(32433) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES, 4th TRI-SQUARES, AND INNER-VECTEN

X(32433) lies on these lines: {30,511}, {371,7851}, {486,489}, {487,23259}, {642,3071}, {2459,12221}, {3103,7921}, {6119,18762}, {6316,12601}

X(32433) = isogonal conjugate of X(32434)

X(32434) = ISOGONAL CONJUGATE OF X(32433)

X(32434) lies on the circumcircle and the line {110,32074}

X(32434) = isogonal conjugate of X(32433)

X(32435) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES, EULER, AND INNER-VECTEN

X(32435) lies on these lines: {2,2460}, {5,141}, {316,2459}, {371,7887}, {372,7773}, {488,23249}, {641,13449}, {642,3071}, {1691,11313}, {2456,6289}, {3102,5025}, {3103,7752}, {6566,31173}, {7825,9739}, {7862,9738}, {13785,22594}

X(32435) = midpoint of X(316) and X(2459)
X(32435) = reflection of X(32432) in X(625)
X(32435) = (inner-Vecten)-isogonal conjugate of-X(13873)
X(32435) = (1st Brocard)-complement of-X(2460)
X(32435) = complement of X(2460)
X(32435) = inverse of X(640) in the nine-point circle
X(32435) = intersection of the Brocard axes of these triangles: 4th anti-tri-squares, medial and inner-Vecten
X(32435) = X(6567)-of-inner-Vecten triangle
X(32435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 5031, 32432), (2039, 2040, 640)

X(32436) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES, 3rd TRI-SQUARES, AND OUTER-VECTEN

X(32436) lies on these lines: {30,511}, {187,13879}, {372,7851}, {485,490}, {488,23249}, {641,3070}, {2460,12222}, {3102,7921}, {6118,18538}, {6312,12602}

X(32436) = isogonal conjugate of X(32437)

X(32437) = ISOGONAL CONJUGATE OF X(32436)

X(32437) lies on the circumcircle and the line {110,11199}

X(32437) = isogonal conjugate of X(32436)

X(32438) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: AAOA, AOA, AND 1st HYACINTH

X(32438) lies on these lines: {30,511}, {74,1303}, {97,110}, {113,130}, {125,129}, {265,6528}, {1511,22052}, {5504,8612}, {12310,22551}, {17838,22552}, {21649,21661}

X(32438) = isogonal conjugate of X(32439)

X(32439) = ISOGONAL CONJUGATE OF X(32438)

X(32439) lies on the circumcircle and these lines: {30,1303}, {418,476}, {436,1304}, {523,1298}, {2713,12022}, {8613,10420}

X(32439) = isogonal conjugate of X(32438)

X(32440) = INTERSECTION OF THE BROCARD AXES OF THESE TRIANGLES: EXCENTERS-MIDPOINTS, GARCIA-REFLECTION AND 2nd SCHIFFLER

X(32440) lies on these lines: {8,18811}, {30,511}

X(32440) = isogonal conjugate of X(32441)

X(32441) = ISOGONAL CONJUGATE OF X(32440)

X(32441) lies on the circumcircle and these lines: {}

X(32441) = isogonal conjugate of X(32440)
X(32441) = X(99)-of-3rd mixtilinear triangle

X(32442) = REFLECTION OF X(6786) IN X(27088)

X(32442) lies on the cubic K1099 and these lines: {30, 6784}, {187, 237}, {376, 511}, {1691, 19136}, {2080, 8717}, {3111, 3849}, {6179, 14135}, {6786, 27088}, {6787, 26613}, {14830, 14915}

X(32442) = reflection of X(6786) in X(27088)

X(32443) = WALSMITH-LEMOINE POINT

See the preamble just before X(32215). The connection with the Lemoine point (X(6), the symmedian point) is that X(32443)-of-Walsmith-Lemoine-triangle = X(6); see the preamble just before X(32217). Contributed by Peter Moses, May 6, 2019.

X(32443) lies on the circumcircle and on no lines X(i)X(j) for 0 < i < j < 32444.

X(32444) = X(2)X(3)∩X(39)X(6000)

As a point on the Euler line, X(32444) has Shinagawa coefficients (EF+F²+S²,2E²+EF-F² -S²).

X(32444) lies on these lines: {2, 3}, {39, 6000}, {217, 9605}, {3095, 13754}, {3331, 3426}, {4550, 5167}, {9155, 16261}, {11171, 14915}, {12294, 30258}, {18440, 20794}

X(32444) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 381, 11328}, {3, 12083, 21512}, {376, 14096, 3}, {378, 3148, 3}

X(32445) = X(3)X(1625)∩X(4)X(6)

X(32445) lies on the cubics K622 and K1100 and also on these lines: {3, 1625}, {4, 6}, {20, 3289}, {32, 1971}, {39, 6000}, {64, 5013}, {112, 1614}, {154, 237}, {159, 3499}, {172, 10535}, {184, 1968}, {185, 232}, {187, 10282}, {206, 1691}, {216, 5907}, {221, 16781}, {230, 16252}, {389, 3199}, {394, 7750}, {512, 3202}, {574, 3357}, {1384, 14530}, {1506, 20299}, {1660, 2056}, {1914, 26888}, {1993, 7823}, {2052, 27359}, {2076, 11674}, {2174, 8761}, {2176, 10537}, {2275, 7355}, {2276, 6285}, {2393, 13330}, {2548, 14216}, {2549, 5878}, {2777, 7756}, {3016, 7746}, {3051, 11206}, {3094, 12502}, {3224, 14601}, {3269, 6241}, {3566, 10685}, {3815, 6247}, {5023, 17821}, {5024, 13093}, {5033, 23042}, {5038, 12202}, {5206, 11202}, {5301, 7113}, {5475, 18381}, {6225, 7738}, {7736, 12324}, {7737, 9833}, {7747, 18400}, {7748, 22802}, {7755, 14862}, {7904, 15066}, {8571, 13406}, {8778, 9412}, {9291, 9308}, {9418, 11325}, {9419, 11257}, {9574, 9899}, {9597, 12940}, {9598, 12950}, {9605, 12315}, {9863, 11441}, {9985, 13236}, {10060, 31448}, {10192, 21001}, {10311, 26883}, {10312, 14157}, {10533, 12963}, {10534, 12968}, {10574, 15355}, {10575, 14961}, {10606, 15815}, {10790, 27374}, {11204, 15515}, {12111, 22240}, {14264, 18573}, {15068, 32151}, {15305, 26216}, {18388, 27371}, {18621, 21788}, {19780, 30403}, {19781, 30402}, {20775, 31382}, {20965, 32064}, {23128, 32139}, {23329, 31455}, {30435, 32063}

X(32445) = isogonal conjugate of the isotomic conjugate of X(3164)
X(32445) = isogonal conjugate of the polar conjugate of X(3168)
X(32445) = polar conjugate of the isotomic conjugate of X(6638)
X(32445) = X(i)-Ceva conjugate of X(j) for these (i,j): {184, 6}, {1968, 3053}, {3164, 6638}
X(32445) = X(3168)-cross conjugate of X(6)
X(32445) = X(75)-isoconjugate of X(1988)
X(32445) = crosspoint of X(3164) and X(3168)
X(32445) = crossdifference of every pair of points on line {520, 6130}
X(32445) = tangential-isotomic conjugate of X(159)
X(32445) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 3168}, {4, 6638}, {5, 26887}, {6, 3164}
X(32445) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {32, 1988}, {3164, 76}, {3168, 264}, {6638, 69}, {26887, 95}
X(32445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 217, 6}, {32, 6759, 1971}, {112, 1614, 14585}, {184, 1968, 1970}, {217, 3331, 4}, {1181, 2207, 6}, {2211, 6776, 6}, {12111, 22240, 22416}, {12964, 12970, 19149}

X(32446) = X(2)X(2124)∩X(10)X(971)

See Angel Montesdeoca, Hyacinthos 29006.

X(32446) lies on these lines: {2,2124}, {10,971}, {142,10004}, {279,19605}, {2391,3452}, {6706,20205}

X(32446) = complement of X(2124)
X(32446) = X(i)-complementary conjugate of X(j) for these (i,j): {55, 17113}, {2125, 10}, {8917, 142}

X(32447) = MIDPOINT OF X(262) AND X(7757)

Let X be a point on the 2nd Brocard circle. As X varies, the locus of X(381) of triangle XPU(1) is a circle with center X(32447). (Randy Hutson, June 7, 2019)

Let (O1) and (O2) be the circles that are the loci of the 1st and 2nd Isogonic Centers, respectively, in a Brocard porism (triangles sharing circumcircle and Brocard inellipse with ABC). The center of (O1) is X(3107). The center of (O2) is X(3106). The insimilicenter of (O1) and (O2) is X(6), and the exsimilicenter is X(32447). (Randy Hutson, June 7, 2019)

X(32447) lies on these lines: {2, 8179}, {3, 6}, {5, 194}, {30, 7709}, {76, 1656}, {99, 10796}, {140, 7806}, {237, 11002}, {262, 381}, {382, 11257}, {517, 3097}, {538, 5055}, {549, 6194}, {597, 31958}, {599, 11261}, {698, 14561}, {726, 5886}, {730, 5790}, {732, 13085}, {736, 9766}, {999, 12837}, {1482, 12782}, {1569, 5475}, {1916, 11170}, {3090, 20081}, {3202, 9704}, {3295, 12836}, {3399, 7754}, {3526, 7786}, {3534, 12156}, {3552, 32134}, {3628, 31276}, {3851, 6248}, {3934, 5070}, {5054, 22712}, {5056, 20105}, {5191, 11422}, {5355, 6036}, {5476, 8724}, {5640, 9155}, {5663, 32444}, {5969, 11165}, {6234, 18872}, {6390, 18583}, {6660, 6800}, {7753, 23698}, {7760, 10104}, {7781, 10358}, {7783, 18501}, {7813, 24206}, {7820, 25555}, {7838, 32152}, {7976, 12645}, {8704, 9178}, {9466, 15703}, {9654, 18982}, {9669, 13077}, {9902, 9956}, {10063, 31479}, {10247, 14839}, {10567, 30209}, {11152, 11317}, {11188, 20794}, {12150, 21166}, {12188, 13860}, {13586, 22521}, {14269, 22682}, {14981, 19130}, {15048, 15980}, {15072, 31952}, {15531, 23635}, {15688, 22676}, {15694, 15819}, {22650, 28204}

X(32447) = midpoint of X(262) and X(7757)
X(32447) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 11171}, {381, 262}, {599, 11261}, {6194, 549}, {31958, 597}
X(32447) = midpoint of centers of circles {{X(1340),X(3557),PU(1)}} and {{X(1341),X(3558),PU(1)}}
X(32447) = harmonic center of circumcircle and circle (X(6), |OK|/2)
X(32447) = Brocard-circle-inverse of X(11842)
X(32447) = 2nd-Brocard-circle-inverse of X(575)
X(32447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 11842}, {3, 1351, 9301}, {5, 194, 13108}, {39, 3094, 5024}, {39, 3095, 3}, {76, 11272, 1656}, {574, 576, 2080}, {574, 2080, 3}, {575, 18860, 26316}, {576, 8586, 1351}, {1351, 5024, 3}, {1670, 1671, 575}, {1689, 1690, 187}, {2021, 13330, 1384}, {3102, 3103, 13330}, {3106, 3107, 6}, {3398, 9737, 3}, {5640, 9155, 11328}, {7772, 9737, 3398}, {9605, 10983, 3}, {9734, 15520, 32}, {9821, 13334, 3}, {11257, 14881, 382}, {11482, 12313, 3311}, {11482, 12314, 3312}, {12054, 30270, 3}, {13343, 13344, 2076}, {14961, 30258, 3}, {18860, 26316, 3}

X(32448) = MIDPOINT OF X(3) AND X(194)

X(32448) lies on these lines: {2, 13108}, {3, 194}, {4, 32447}, {5, 39}, {6, 32134}, {30, 3095}, {54, 15093}, {76, 140}, {83, 23235}, {99, 3398}, {182, 698}, {262, 546}, {355, 3097}, {384, 10353}, {397, 3107}, {398, 3106}, {495, 18982}, {496, 13077}, {511, 550}, {538, 549}, {548, 9821}, {574, 10104}, {575, 5026}, {631, 20081}, {632, 3934}, {726, 1385}, {730, 5690}, {952, 12782}, {1483, 14839}, {1503, 32429}, {1595, 12143}, {2080, 7760}, {3094, 3564}, {3146, 22728}, {3523, 20105}, {3526, 31276}, {3530, 22712}, {3552, 11842}, {3627, 14881}, {3628, 7697}, {3857, 22681}, {5050, 18906}, {5171, 7798}, {5188, 8703}, {5844, 7976}, {5965, 7830}, {6287, 14692}, {7755, 14693}, {7772, 10796}, {7827, 8724}, {7828, 15561}, {7839, 11676}, {8370, 11152}, {9466, 11539}, {9737, 14880}, {9902, 26446}, {10079, 15325}, {11055, 12100}, {12836, 15171}, {12837, 18990}, {13331, 18583}, {14711, 15713}, {14869, 15819}, {15712, 21163}, {19522, 31036}

X(32448) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 194}, {3095, 11257}
X(32448) = reflection of X(i) in X(j) for these lines: {i,j}: {5, 39}, {76, 140}, {3627, 14881}, {6248, 11272}, {9821, 548}
X(32448) = complement of X(13108)
X(32448) = inverse-in-circle-{{X(3102),X(3103),PU(1)}} of X(115)
X(32448) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 6248, 11272}, {76, 11171, 140}, {194, 7709, 3}, {3102, 3103, 115}, {6248, 11272, 5}, {7697, 7786, 3628}, {7757, 11257, 3095}, {32470, 32471, 6}

X(32449) = MIDPOINT OF X(6) AND X(194)

X(32449) lies on these lines: {6, 194}, {30, 32429}, {39, 141}, {76, 3589}, {99, 12212}, {182, 7798}, {385, 5116}, {427, 17949}, {511, 550}, {524, 3094}, {538, 597}, {726, 1386}, {736, 15048}, {1078, 12055}, {1100, 17760}, {1350, 7709}, {1352, 32447}, {1503, 3095}, {1569, 5052}, {1691, 7760}, {1916, 12830}, {2076, 7783}, {2782, 5480}, {3051, 4576}, {3097, 3416}, {3106, 23000}, {3107, 23009}, {3231, 31088}, {3329, 24273}, {3618, 20081}, {3867, 12143}, {4074, 19568}, {5017, 31859}, {5031, 7764}, {5039, 7781}, {5085, 12251}, {5092, 7805}, {5103, 5254}, {5207, 13571}, {5305, 8149}, {5306, 5976}, {5846, 12782}, {6309, 7789}, {7754, 8177}, {7766, 10335}, {7792, 9865}, {7838, 29012}, {7976, 9053}, {8024, 11205}, {8267, 20965}, {8891, 10191}, {9605, 31981}, {11257, 29181}, {13108, 14561}, {13334, 21167}, {20583, 22486}, {31406, 32189}

X(32449) = midpoint of X(6) and X(194)
X(32449) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 3589}, {141, 39}, {14994, 10007}, {22486, 20583}
X(32449) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 14994, 10007}, {76, 13331, 3589}, {7839, 12215, 6}, {10007, 14994, 141}
X(32449) = X(14617)-Ceva conjugate of X(141)
X(32449) = crossdifference of every pair of points on line {3221, 18105}
X(32449) = barycentric product X(i)*X(j) for these lines: {i,j}: {141, 7766}, {3051, 10010}, {4576, 25423}, {10335, 14617}
X(32449) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {1634, 25424}, {7766, 83}

X(32450) = MIDPOINT OF X(39) AND X(194)

X(32450) lies on these lines: {2, 39}, {3, 7798}, {6, 7781}, {30, 7838}, {32, 31859}, {99, 5007}, {148, 7858}, {187, 7760}, {262, 3855}, {316, 13571}, {325, 7765}, {382, 3095}, {384, 5041}, {511, 550}, {524, 7830}, {543, 7745}, {546, 2782}, {574, 7754}, {620, 5305}, {625, 5254}, {626, 15048}, {698, 6329}, {726, 3636}, {730, 3626}, {732, 3631}, {736, 8357}, {1015, 25264}, {1078, 31652}, {1500, 25303}, {1569, 19687}, {1916, 14042}, {1975, 7772}, {2482, 5368}, {2549, 7759}, {2996, 31415}, {3244, 14839}, {3528, 5188}, {3529, 11257}, {3530, 13334}, {3552, 5008}, {3632, 12782}, {3734, 9605}, {3849, 7756}, {3851, 6248}, {3933, 4045}, {5013, 7751}, {5024, 7815}, {5079, 13108}, {5206, 14614}, {5319, 6337}, {5346, 16925}, {5355, 7807}, {5969, 20583}, {6179, 15513}, {6390, 6680}, {6459, 26340}, {6460, 26339}, {6655, 7845}, {6656, 7813}, {7738, 7758}, {7748, 7774}, {7750, 7890}, {7766, 7782}, {7773, 11648}, {7776, 7872}, {7778, 7902}, {7779, 7847}, {7784, 7916}, {7788, 7935}, {7789, 7829}, {7790, 7821}, {7791, 7848}, {7792, 7863}, {7793, 8589}, {7796, 7853}, {7802, 7837}, {7825, 9766}, {7826, 8356}, {7833, 7877}, {7835, 7920}, {7840, 7911}, {7841, 7903}, {7851, 7888}, {7856, 7891}, {7866, 7908}, {7871, 7933}, {7881, 7913}, {7896, 11287}, {7897, 7918}, {7898, 7949}, {7909, 7923}, {7910, 7946}, {7917, 7924}, {7919, 7947}, {7921, 14537}, {7941, 31173}, {7976, 20050}, {8716, 30435}, {9821, 15688}, {10299, 12251}, {11171, 15720}, {11174, 17130}, {11285, 17131}, {12263, 15808}, {14482, 18841}, {14881, 15687}, {15482, 22332}, {22330, 32134}

X(32450) = midpoint of X(i) and X(j) for these lines: {i,j}: {39, 194}, {7750, 7890}, {7756, 7762}, {9466, 11055}
X(32450) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 6683}, {3934, 39}
X(32450) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7798, 7805}, {6, 7781, 7816}, {39, 76, 6683}, {39, 9466, 7786}, {76, 6683, 3934}, {99, 7839, 5007}, {194, 7757, 39}, {194, 20081, 11055}, {325, 7765, 7861}, {574, 7754, 7780}, {1975, 7772, 7804}, {2549, 7759, 7842}, {3552, 7894, 5008}, {3788, 5286, 7817}, {3926, 7739, 7834}, {3926, 7834, 7880}, {3933, 4045, 7849}, {3933, 9607, 4045}, {5013, 22253, 7751}, {5254, 7764, 625}, {5309, 7763, 7886}, {6655, 7905, 7845}, {6656, 7813, 7895}, {7738, 7758, 7761}, {7748, 7774, 7843}, {7758, 7761, 7882}, {7760, 7783, 187}, {7779, 7847, 7873}, {7781, 7816, 15301}, {7786, 11055, 20081}, {7786, 20081, 9466}, {7790, 7906, 7821}, {7791, 7855, 7848}, {7796, 7864, 7853}, {7797, 7799, 7874}, {7801, 7803, 7915}, {7827, 7836, 7852}, {7829, 14148, 7789}

X(32451) = MIDPOINT OF X(193) AND X(194)

X(32451) lies on these lines: {2, 11175}, {6, 76}, {20, 185}, {32, 6309}, {39, 69}, {99, 5017}, {141, 7786}, {182, 385}, {262, 1352}, {287, 1993}, {305, 3051}, {384, 5039}, {518, 7976}, {524, 3094}, {538, 1992}, {542, 1916}, {599, 10007}, {698, 3629}, {730, 3751}, {736, 5028}, {1350, 31859}, {1351, 2782}, {1503, 7762}, {1569, 14645}, {1691, 6179}, {1692, 7805}, {2023, 9766}, {2024, 7763}, {2025, 3767}, {2076, 7782}, {3056, 25264}, {3060, 8267}, {3095, 3564}, {3098, 7783}, {3104, 23000}, {3105, 23009}, {3231, 11059}, {3266, 9463}, {3589, 7856}, {3618, 3934}, {3619, 6683}, {3763, 7909}, {3818, 7785}, {3926, 13357}, {3972, 4048}, {5031, 7814}, {5034, 7751}, {5038, 8177}, {5092, 7793}, {5093, 13108}, {5116, 7771}, {5182, 5976}, {5188, 25406}, {5207, 7759}, {5476, 19570}, {5847, 12782}, {5969, 8593}, {6248, 6392}, {7697, 18583}, {7766, 9865}, {7777, 24206}, {7823, 29012}, {7839, 9983}, {7926, 11646}, {7998, 31088}, {8878, 11550}, {9917, 19459}, {10519, 13334}, {11008, 32450}, {11898, 32447}, {12143, 12167}, {12251, 13354}, {12263, 16475}, {13877, 19103}, {13930, 19104}, {14467, 30739}, {14881, 18440}

X(32451) = midpoint of X(193) and X(194)
X(32451) = reflection of X(i) in X(j) for these lines: {i,j}: {69, 39}, {76, 6}, {3094, 32449}, {12251, 13354}, {13330, 3629}, {18440, 14881}, {18906, 5052}, {22486, 1992}
X(32451) = anticomplement of X(14994)
X(32451) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {263, 21289}, {2186, 1369}, {3402, 2896}
X(32451) = crosssum of X(1084) and X(3288)
X(32451) = crossdifference of every pair of points on line {688, 2451}
X(32451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 13331, 7786}, {1992, 18906, 5052}, {3094, 32449, 7757}, {4048, 12212, 3972}, {5052, 18906, 22486}, {6272, 19090, 76}, {6273, 19089, 76}, {12251, 14912, 13354}

X(32452) = MIDPOINT OF X(194) and X(315)

X(32452) lies on these lines: {2, 18806}, {3, 6}, {69, 31981}, {76, 115}, {99, 10350}, {183, 32189}, {194, 315}, {262, 1506}, {298, 6294}, {299, 6581}, {325, 8149}, {538, 7788}, {698, 3933}, {730, 4769}, {732, 7855}, {754, 7757}, {760, 12782}, {1015, 12836}, {1500, 12837}, {1569, 2794}, {1571, 3097}, {2023, 7746}, {2782, 7748}, {2979, 8623}, {3117, 20859}, {3202, 9696}, {3229, 3981}, {3735, 3865}, {3767, 12251}, {3788, 5976}, {3934, 7867}, {5149, 10349}, {5475, 14881}, {5969, 7801}, {6309, 7813}, {6680, 7786}, {7749, 22712}, {7768, 9983}, {7782, 10351}, {7795, 18906}, {7796, 9865}, {7810, 13085}, {7822, 24256}, {7836, 8782}, {7906, 10335}, {9466, 11318}, {9651, 18982}, {9664, 13077}, {9753, 31401}, {10000, 10333}, {11272, 31455}

X(32452) = midpoint of X(194) and X(315)
X(32452) = reflection of X(i) in X(j) for these lines: {i,j}: {32, 39}, {76, 626}
X(32452) = reflection of X(32) in line PU(1)
X(32452) = anticomplement of X(18806)
X(32452) = 2nd-Brocard-Circle-inverse of X(1691)
X(32452) = X(30254)-Ceva conjugate of X(512)
X(32452) = circle-{{X(3102),X(3103),PU(1)}}-inverse of X(182)
X(32452) = X(163)-isoconjugate of X(30492)
X(32452) = barycentric quotient X(523)/X(30492)
X(32452) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 30270, 5162}, {39, 5041, 13331}, {39, 5188, 2021}, {1569, 7756, 11257}, {1670, 1671, 1691}, {1689, 1690, 3398}, {2021, 5188, 5206}, {2458, 5028, 6}, {2562, 2563, 11171}, {3094, 3095, 39}, {3102, 3103, 182}, {5013, 32447, 39}, {5028, 30270, 32}, {13325, 13326, 3094}

X(32453) = MIDPOINT OF X(192) and X(194)

X(32453) lies on these lines: {1, 87}, {2, 21443}, {37, 76}, {39, 75}, {42, 17486}, {511, 30273}, {518, 7976}, {536, 7757}, {538, 4664}, {561, 21814}, {579, 17034}, {700, 24696}, {716, 3774}, {730, 984}, {740, 12782}, {742, 3094}, {1045, 19566}, {1278, 26801}, {1575, 10009}, {1655, 9902}, {1921, 27091}, {2350, 17027}, {2782, 20430}, {3095, 29010}, {3097, 17759}, {3210, 17026}, {3550, 30661}, {3644, 32450}, {3739, 7786}, {3875, 24727}, {3934, 4687}, {3995, 17032}, {4660, 17493}, {4704, 20081}, {4751, 6683}, {6376, 21830}, {6382, 21877}, {8620, 30964}, {9055, 32449}, {16468, 30667}, {17028, 17495}, {17033, 17489}, {17262, 21788}, {24621, 27478}, {27268, 31276}, {27481, 31036}

X(32453) = midpoint of X(192) and X(194)
X(32453) = reflection of X(i) in X(j) for these lines: {i,j}: {75, 39}, {76, 37}
X(32453) = anticomplement of X(21443)
X(32453) = {X(192),X(19565)}-harmonic conjugate of X(1)

X(32454) = MIDPOINT OF X(149) and X(194)

X(32454) lies on these lines: {3, 12199}, {6, 13194}, {11, 76}, {39, 100}, {80, 730}, {104, 511}, {106, 24516}, {119, 262}, {149, 194}, {528, 7757}, {538, 10707}, {726, 21630}, {952, 3095}, {1317, 12837}, {1320, 14839}, {1916, 2787}, {2530, 31129}, {2782, 10738}, {2802, 12782}, {3035, 7786}, {3045, 3202}, {3094, 9024}, {3097, 5541}, {3934, 31272}, {5533, 10079}, {5840, 11257}, {6713, 22712}, {7709, 13199}, {8068, 10063}, {9263, 23646}, {10742, 14881}, {12263, 16173}, {12331, 32447}, {13077, 13274}, {13273, 18982}

X(32454) = midpoint of X(149) and X(194)
X(32454) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 11}, {100, 39}, {10742, 14881}
X(32454) = {X(12836),X(12923)}-harmonic conjugate of X(76)

X(32455) = MIDPOINT OF X(6) and X(3629)

X(32455) lies on these lines: {2, 6}, {5, 15520}, {39, 3793}, {44, 17390}, {66, 23326}, {140, 15516}, {182, 15712}, {239, 7277}, {487, 6432}, {488, 6431}, {511, 548}, {518, 3635}, {536, 4856}, {542, 14893}, {545, 4852}, {575, 12108}, {576, 1353}, {594, 17120}, {625, 5305}, {648, 6748}, {698, 5052}, {742, 4726}, {894, 4399}, {895, 25329}, {1086, 17121}, {1100, 17332}, {1285, 8716}, {1350, 21735}, {1351, 1657}, {1352, 5072}, {1449, 4364}, {1743, 17243}, {1974, 15471}, {1990, 27377}, {2321, 28337}, {2325, 4889}, {2393, 21847}, {2854, 9969}, {3124, 10552}, {3564, 3850}, {3625, 4663}, {3633, 3751}, {3663, 28333}, {3686, 4472}, {3707, 28639}, {3729, 28309}, {3739, 4700}, {3758, 7227}, {3759, 4395}, {3818, 23046}, {3843, 5093}, {3875, 28297}, {3879, 4422}, {3912, 16671}, {3946, 4715}, {4357, 16668}, {4361, 7222}, {4363, 4371}, {4370, 17315}, {4393, 17334}, {4402, 4644}, {4405, 17118}, {4416, 16666}, {4478, 17363}, {4643, 16667}, {4665, 5839}, {4667, 17348}, {4691, 5847}, {4718, 9055}, {4725, 17355}, {4755, 4909}, {4851, 16670}, {4946, 9024}, {4966, 16477}, {4971, 17351}, {4991, 17771}, {5007, 7789}, {5008, 6390}, {5041, 7767}, {5092, 14891}, {5102, 6776}, {5111, 19695}, {5368, 8361}, {5596, 17813}, {5965, 12812}, {6467, 8705}, {6593, 32114}, {6664, 31506}, {6749, 9308}, {7238, 17364}, {7745, 7760}, {7762, 7790}, {7798, 18907}, {7801, 14075}, {7819, 7890}, {7839, 14712}, {7877, 7937}, {7882, 8364}, {7949, 8363}, {8787, 14928}, {9019, 32366}, {9027, 9822}, {9607, 20065}, {9973, 15531}, {10022, 28634}, {10115, 32284}, {10168, 14890}, {10192, 21970}, {11179, 15689}, {11216, 15583}, {11422, 32269}, {11477, 14912}, {12017, 15706}, {12161, 16252}, {12212, 13196}, {13330, 32449}, {14032, 18906}, {14892, 18358}, {15492, 29574}, {15585, 32218}, {15684, 31670}, {15826, 32220}, {16176, 25320}, {17014, 17255}, {17246, 20072}, {17340, 17377}, {17347, 17395}, {17350, 17388}, {21639, 26926}, {25331, 32255}, {25488, 32127}

X(32455) = midpoint of X(i) and X(j) for these lines: {i,j}: {6, 3629}, {141, 193}, {576, 1353}, {597, 15534}, {895, 25329}, {1351, 8550}, {1992, 8584}, {3630, 6144}, {7798, 18907}, {13330, 32449}, {15826, 32220}
X(32455) = reflection of X(i) in X(j) for these lines: {i,j}: {140, 15516}, {141, 6329}, {3589, 6}, {3631, 3589}, {18583, 22330}, {20583, 8584}
X(32455) = complement of X(3630)
X(32455) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6144, 3630}, {6, 69, 597}, {6, 141, 6329}, {6, 193, 141}, {6, 1992, 3629}, {6, 6144, 2}, {6, 15534, 69}, {69, 5032, 6}, {141, 3629, 193}, {141, 6329, 3589}, {597, 8584, 5032}, {894, 4969, 4399}, {1992, 5032, 15534}, {3589, 3631, 20582}, {3589, 20583, 6}, {3629, 8584, 6}, {3629, 20583, 3631}, {3758, 17362, 7227}, {3759, 17365, 4395}, {3763, 20080, 22165}, {3879, 16669, 4422}, {4416, 16666, 17045}, {5032, 15534, 597}, {7585, 26340, 591}, {7586, 26339, 1991}, {17330, 17379, 6707}, {17363, 17369, 4478}, {17364, 17366, 7238}
X(32455) = crosssum of X(6) and X(15513)
X(32455) = crossdifference of every pair of points on line {512, 15514}

X(32456) = MIDPOINT OF X(99) and X(187)

X(32456) lies on these lines: {2, 8589}, {3, 3734}, {20, 3788}, {30, 620}, {32, 31859}, {39, 3552}, {76, 15513}, {83, 31652}, {99, 187}, {126, 7426}, {141, 8703}, {183, 8588}, {230, 543}, {232, 4235}, {325, 2482}, {376, 7761}, {382, 7862}, {384, 6683}, {439, 3767}, {511, 5026}, {524, 14148}, {548, 7789}, {550, 626}, {574, 1003}, {671, 5215}, {754, 6390}, {1153, 11164}, {1384, 7798}, {1495, 5108}, {1506, 19687}, {1657, 7825}, {1692, 10754}, {1975, 5206}, {2030, 5969}, {2549, 7817}, {3053, 7781}, {3363, 7619}, {3522, 7795}, {3528, 7800}, {3534, 7778}, {3926, 7882}, {4027, 10631}, {4045, 8369}, {4048, 14810}, {4226, 11052}, {5007, 7783}, {5008, 7757}, {5023, 7751}, {5031, 29323}, {5107, 5182}, {5118, 9418}, {5148, 15452}, {5149, 11676}, {6337, 7759}, {6636, 15822}, {6655, 7874}, {6658, 7769}, {6704, 19697}, {7492, 30749}, {7603, 11361}, {7618, 7736}, {7622, 11159}, {7748, 7886}, {7750, 7863}, {7756, 7807}, {7763, 7843}, {7770, 15515}, {7771, 9466}, {7777, 14537}, {7784, 15696}, {7791, 7915}, {7799, 7845}, {7801, 7848}, {7802, 7821}, {7808, 15815}, {7820, 8356}, {7833, 7835}, {7836, 7873}, {7844, 11288}, {7847, 7852}, {7865, 15688}, {7870, 7898}, {7897, 11057}, {7910, 7945}, {7925, 9855}, {8176, 11147}, {8182, 15589}, {8352, 9167}, {8591, 26613}, {8667, 15655}, {9341, 25264}, {10150, 22247}, {11286, 15482}, {13349, 22689}, {13350, 22687}, {13449, 15561}, {14035, 31455}, {14041, 31275}, {14568, 20094}, {14762, 15491}, {14767, 18570}, {14928, 15993}, {15031, 16923}, {15300, 22329}, {15810, 16986}, {16589, 17693}, {21445, 23235}, {21937, 24275}, {26276, 31128}

X(32456) = midpoint of X(i) and X(j) for these lines: {i,j}: {99, 187}, {325, 6781}, {2482, 8598}, {7845, 14712}, {9855, 31173}, {11676, 18860}, {14928, 15993}, {15300, 22329}
X(32456) = reflection of X(i) in X(j) for these lines: {i,j}: {625, 620}, {15301, 99}
X(32456) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7816, 3934}, {20, 3788, 7842}, {99, 13586, 187}, {325, 8598, 6781}, {548, 7789, 7830}, {574, 1003, 7804}, {1384, 8716, 7798}, {1975, 5206, 7780}, {2482, 6781, 325}, {3053, 7781, 7805}, {3552, 7782, 39}, {7748, 16925, 7886}, {7750, 7863, 7895}, {7756, 7807, 7861}, {7789, 7830, 7849}, {7799, 14712, 7845}, {7801, 14907, 7848}, {7802, 7891, 7821}, {7833, 7835, 7853}, {11676, 21166, 18860}

X(32457) = MIDPOINT OF X(148) and X(187)

X(32457) lies on these lines: {4, 7805}, {5, 32450}, {6, 18546}, {39, 16921}, {76, 7849}, {115, 325}, {148, 187}, {183, 11648}, {230, 543}, {316, 19570}, {381, 7798}, {385, 671}, {546, 7838}, {620, 15301}, {754, 15480}, {1975, 7886}, {2996, 3767}, {3314, 14711}, {3629, 3845}, {3734, 7817}, {3934, 4045}, {5008, 11361}, {5025, 7895}, {5041, 16044}, {5215, 8591}, {5304, 7620}, {5309, 7804}, {5346, 14035}, {5355, 8370}, {5461, 10150}, {6390, 6722}, {6392, 7759}, {6683, 7765}, {6781, 22329}, {7603, 7757}, {7615, 7736}, {7617, 31489}, {7748, 7780}, {7751, 7842}, {7754, 7843}, {7761, 15589}, {7766, 14537}, {7774, 18424}, {7775, 22253}, {7779, 11054}, {7781, 13881}, {7790, 9466}, {7799, 31275}, {7814, 20105}, {7821, 20081}, {7825, 7882}, {7839, 15031}, {7841, 7848}, {7844, 7880}, {7845, 14041}, {7851, 7915}, {7852, 17128}, {7855, 14063}, {7864, 31239}, {7873, 17129}, {7877, 14062}, {7908, 11318}, {7917, 14045}, {7925, 9166}, {8589, 17004}, {8596, 26613}, {11174, 14762}, {14651, 18860}, {15048, 15491}

X(32457) = midpoint of X(i) and X(j) for these lines: {i,j}: {148, 187}, {11054, 31173}
X(32457) = reflection of X(i) in X(j) for these lines: {i,j}: {625, 115}, {6390, 6722}, {15301, 620}
X(32457) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 7861, 7849}, {148, 14568, 187}, {5309, 11185, 7804}, {7841, 17131, 7848}, {7851, 17130, 7915}

X(32458) = MIDPOINT OF X(99) and X(315)

X(32458) lies on these lines: {2, 2987}, {20, 99}, {32, 620}, {69, 98}, {76, 115}, {114, 325}, {132, 877}, {141, 2023}, {183, 6036}, {305, 1972}, {439, 20065}, {524, 12829}, {542, 5989}, {543, 7818}, {670, 15526}, {736, 1569}, {754, 2482}, {1007, 9753}, {1506, 18806}, {1975, 23698}, {2458, 4027}, {2782, 3933}, {2967, 23098}, {3266, 23965}, {3329, 6680}, {3425, 9723}, {4558, 11610}, {5017, 9766}, {5026, 12830}, {5149, 7759}, {5152, 7768}, {5181, 23342}, {5503, 21356}, {5984, 10513}, {6033, 7776}, {6337, 21166}, {6722, 7867}, {7767, 12042}, {7836, 10350}, {7896, 8178}, {7897, 8782}, {8024, 23962}, {9146, 30789}, {10722, 32006}

X(32458) = midpoint of X(99) and X(315)
X(32458) = reflection of X(i) in X(j) for these lines: {i,j}: {32, 620}, {115, 626}
X(32458) = isotomic conjugate of isogonal conjugate of X(36790)
X(32458) = complement of X(36849)
X(32458) = X(i)-isoconjugate of X(j) for these (i,j): {1821, 14601}, {1910, 1976}
X(32458) = crosspoint of X(2396) and X(4590)
X(32458) = crosssum of X(i) and X(j) for these (i,j): {1501, 14601}, {2422, 3124}
X(32458) = crossdifference of every pair of points on line {2422, 14601}
X(32458) = barycentric product X(i)*X(j)for these lines: {i,j}: {297, 6393}, {305, 2967}, {325, 325}, {561, 23996}, {850, 15631}, {877, 6333}, {1502, 11672}, {2396, 2799}, {16725, 27801}, {18024, 23098}
X(32458) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {237, 14601}, {297, 6531}, {325, 98}, {511, 1976}, {684, 878}, {877, 685}, {1355, 1397}, {1959, 1910}, {2396, 2966}, {2421, 2715}, {2799, 2395}, {2967, 25}, {3289, 14600}, {3569, 2422}, {6333, 879}, {6393, 287}, {7062, 2175}, {9419, 1501}, {11672, 32}, {15631, 110}, {16725, 1333}, {18829, 18858}, {23098, 237}, {23611, 9418}, {23996, 31}
X(32458) = X(325),X(5976)}-harmonic conjugate of X(114),is on K778,X(i)-Ceva conjugate of X(j) for these (i,j): {670, 6333}, {4590, 2396}

X(32459) = MIDPOINT OF X(99) and X(230)

X(32459) lies on these lines: {2, 11147}, {3, 66}, {5, 9734}, {30, 620}, {39, 6329}, {69, 5210}, {99, 230}, {126, 468}, {140, 7816}, {187, 524}, {193, 439}, {316, 8598}, {325, 13586}, {376, 7778}, {548, 626}, {549, 3734}, {550, 3788}, {574, 3589}, {597, 5024}, {599, 5585}, {698, 2021}, {1003, 3815}, {1213, 21937}, {1384, 3629}, {1513, 21166}, {1975, 17008}, {2080, 13196}, {2549, 11288}, {3054, 11185}, {3055, 8370}, {3522, 7784}, {3524, 15271}, {3530, 3934}, {3552, 7745}, {3566, 3798}, {3580, 5866}, {3618, 5013}, {3627, 7862}, {3630, 15655}, {3631, 7801}, {3712, 7267}, {3926, 5023}, {3933, 5206}, {3972, 9300}, {4045, 8368}, {4760, 7181}, {5215, 15300}, {5241, 21511}, {5254, 16925}, {5306, 31859}, {5467, 15471}, {5743, 16436}, {6683, 19697}, {7472, 16320}, {7664, 24855}, {7735, 8716}, {7750, 7891}, {7756, 8361}, {7761, 8703}, {7767, 7863}, {7769, 19687}, {7782, 7790}, {7815, 15712}, {7820, 8359}, {7825, 15704}, {7835, 7937}, {7842, 12103}, {7853, 8354}, {7874, 8357}, {7899, 19695}, {7908, 14929}, {7934, 8353}, {8182, 22165}, {8355, 22247}, {8362, 15515}, {8584, 11165}, {9167, 31275}, {9737, 21850}, {9771, 11159}, {10011, 23698}, {10256, 15980}, {11149, 11151}, {11286, 15491}, {13468, 21843}, {14001, 15815}, {14033, 31489}, {17005, 19686}, {18860, 29181}, {19661, 20583}, {21163, 24256}

X(32459) = midpoint of X(i) and X(j) for these lines: {i,j}: {99, 230}, {187, 6390}, {2482, 27088}, {3793, 7813}, {7472, 16320}, {8598, 22110}
X(32459) = reflection of X(8355) in X(22247)
X(32459) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {187, 2482, 6390}, {187, 7813, 3793}, {439, 6337, 3053}, {574, 8369, 3589}, {3793, 6390, 7813}, {6390, 27088, 187}, {7820, 8589, 8359}, {7863, 15513, 7767}
X(32459) = X(468)-Ceva conjugate of X(524)
X(32459) = X(i)-isoconjugate of X(j) for these (i,j): {111, 8769}, {897, 8770}, {923, 2996}, {3565, 23894}
X(32459) = crossdifference of every pair of points on line {2485, 8770}
X(32459) = barycentric product X(i)*X(j)for these lines: {i,j}: {193, 524}, {468, 6337}, {896, 18156}, {1707, 14210}, {3053, 3266}, {3566, 5468}, {3712, 17081}, {4028, 6629}, {6353, 6390}, {16741, 21874}
X(32459) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {187, 8770}, {193, 671}, {524, 2996}, {896, 8769}, {1707, 897}, {3053, 111}, {3167, 895}, {3292, 6391}, {3566, 5466}, {5095, 5203}, {5467, 3565}, {6091, 15398}, {6337, 30786}, {6353, 17983}, {6390, 6340}, {8651, 9178}, {19118, 8753}

X(32460) = EULER LINE INTERCEPT OF TRILINEAR POLAR OF X(14)

As a point on the Euler line, X(32460) has Shinagawa coefficients (-3*F+sqrt(3)*S/3, E+F-sqrt(3)*S).

See Konstantin Knop, Vladimir Dubrovsky and César Lozada, Hyacinthos 29009.

X(32460) lies on these lines: {2, 3}, {13, 11657}, {14, 3166}, {15, 16319}, {110, 11092}, {396, 523}, {398, 8015}, {476, 8838}, {530, 32225}, {531, 5642}, {533, 3292}, {627, 15794}, {635, 15785}, {1525, 2777}, {2453, 16644}, {3163, 23713}, {3284, 23715}, {3642, 5651}, {5318, 30468}, {6105, 6107}, {8836, 20253}, {14704, 22510}, {18487, 23712}

X(32461) = EULER LINE INTERCEPT OF TRILINEAR POLAR OF X(13)

As a point on the Euler line, X(32461) has Shinagawa coefficients (-3*F-sqrt(3)*S/3, E+F+sqrt(3)*S).

See Konstantin Knop, Vladimir Dubrovsky and César Lozada, Hyacinthos 29009.

X(32461) lies on these lines: {2, 3}, {13, 3165}, {14, 11657}, {16, 16319}, {62, 8919}, {110, 11078}, {395, 523}, {397, 8014}, {476, 8836}, {530, 5642}, {531, 32225}, {532, 3292}, {628, 15793}, {636, 15784}, {1524, 2777}, {2453, 16645}, {3163, 23712}, {3284, 23714}, {3643, 5651}, {5321, 30465}, {6104, 6106}, {8838, 20252}, {14705, 22511}, {18487, 23713}

X(32461) = midpoint of X(i) and X(j) for these lines: {i,j}: {110, 11078}, {16180, 16182}
X(32461) = reflection of X(32460) in X(468)
X(32461) = isogonal conjugate of the antigonal conjugate of X(2992)
X(32461) = circumcircle-inverse-of X(3129)
X(32461) = outer-Napoleon circle-inverse-of X(4)
X(32461) = orthoptic circle of Steiner inellipse-inverse-of X(1080)
X(32461) = polar circle-inverse-of X(470)
X(32461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1316, 32460), (3, 4, 23721), (1113, 1114, 3129)

Points associated with the inscribed triply bilogic triangle: X(32462)-X(32480)

X(32462) = X(1)X(85)∩X(3)X(238)

X(32462) lies on these lines: {1, 85}, {3, 238}, {10, 26068}, {43, 170}, {78, 32117}, {497, 20731}, {954, 4335}, {1045, 1047}, {1053, 2082}, {2808, 12782}, {3010, 3212}, {15726, 24696}, {19545, 20368}, {21778, 21882}

X(32462) = excentral-isogonal conjugate of X(1759)
X(32462) = excentral-isotomic conjugate of X(1766)
X(32462) = X(41)-Ceva conjugate of X(1)
X(32462) = X(21882)-cross conjugate of X(21218)
X(32462) = crosspoint of X(21218) and X(31604)
X(32462) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 21218}, {9, 31604}, {75, 21778}, {86, 21882}, {92, 23078}
X(32462) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {21218, 75}, {21778, 1}, {21882, 10}, {23078, 63}, {31604, 85}

X(32463) = X(3)X(3231)∩X(30)X(1351)

X(32463) lies on these lines: {3, 3231}, {30, 1351}, {182, 30229}, {2080, 8717}, {3095, 14915}, {3426, 10983}, {6321, 7706}, {11472, 32444}

X(32464) = X(576)X(3146)∩X(1176)X(30496)

X(32464) lies on these lines: {576, 3146}, {1176, 30496}, {5206, 6030}, {7802, 23061}

X(32465) = REFLECTION OF X(13) IN X(3107)

X(32465) lies on these lines: {6, 1569}, {13, 2782}, {14, 32447}, {16, 7709}, {17, 13108}, {18, 39}, {61, 194}, {62, 32448}, {262, 11602}, {511, 5473}, {538, 16962}, {3095, 16964}, {3105, 11257}, {3106, 5463}, {5238, 12251}, {5469, 9762}, {6194, 10645}, {6777, 22695}, {7697, 16966}, {8594, 9114}, {9112, 22701}, {11171, 16242}, {19107, 22728}

X(32465) = reflection of X(13) in X(3107)
X(32465) = reflection of X(32466) in X(1569)

X(32466) = REFLECTION OF X(14) IN X(3106)

X(32466) lies on these lines: {6, 1569}, {13, 32447}, {14, 2782}, {15, 7709}, {17, 39}, {18, 13108}, {61, 32448}, {62, 194}, {262, 11603}, {511, 5474}, {538, 16963}, {3095, 16965}, {3104, 11257}, {3107, 5464}, {5237, 12251}, {5470, 9760}, {6194, 10646}, {6778, 22696}, {7697, 16967}, {8595, 9116}, {9113, 22702}, {11171, 16241}, {19106, 22728}

X(32466) = reflection of X(14) in X(3106)
X(32466) = reflection of X(32465) in X(1569)

X(32467) = REFLECTION OF X(3399) IN X(39)

X(32467) lies on these lines: {3, 6179}, {4, 7739}, {5, 6054}, {6, 11257}, {20, 576}, {30, 12156}, {32, 7709}, {39, 98}, {54, 826}, {83, 2782}, {99, 3398}, {114, 7797}, {140, 7799}, {182, 194}, {262, 9605}, {384, 575}, {385, 13334}, {401, 13366}, {511, 7839}, {572, 12197}, {631, 7622}, {1078, 11171}, {1353, 7750}, {1506, 14651}, {1569, 12176}, {1656, 7884}, {1975, 5050}, {2896, 5965}, {3095, 12203}, {3329, 6248}, {3413, 14630}, {3414, 14631}, {3526, 7607}, {3734, 10359}, {5007, 11676}, {5013, 9755}, {5028, 7738}, {5111, 12007}, {5171, 7766}, {5254, 14639}, {5286, 9744}, {6776, 9873}, {7608, 9302}, {7754, 22712}, {7783, 13335}, {7798, 12251}, {7805, 21163}, {7817, 23234}, {7829, 14981}, {7858, 15980}, {8550, 9607}, {8721, 9993}, {9751, 12054}, {10722, 15048}, {11272, 12188}, {14880, 32447}, {15819, 17129}

X(32467) = reflection of X(3399) in X(39)
X(32467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 11257, 12110}, {3398, 32448, 99}, {7783, 13335, 21166}

X(32468) = X(31)-CEVA CONJUGATE OF X(9)

X(32468) lies on these lines: {6, 979}, {8, 23640}, {9, 341}, {40, 740}, {55, 2053}, {200, 4531}, {1018, 7031}, {1043, 4050}, {2136, 24578}, {3503, 3875}, {3729, 24579}, {3880, 17448}, {5710, 17754}, {14829, 17144}, {17752, 19591}

X(32468) = X(31)-Ceva conjugate of X(9)
X(32468) = barycentric product X(318)*X(23159)
X(32468) = barycentric quotient X(23159)/X(77)
X(32468) = {X(2319),X(3208)}-harmonic conjugate of X(2329)

X(32469) = REFLECTION OF X(98) IN X(7709)

X(32469) lies on these lines: {39, 7608}, {98, 574}, {99, 2080}, {194, 576}, {262, 381}, {511, 8593}, {538, 19911}, {5182, 31958}, {6194, 21166}, {7617, 23234}, {7697, 8179}, {8586, 10753}, {8724, 11054}, {9166, 14159}, {10723, 22728}, {12191, 15520}

X(32469) = reflection of X(i) in X(j) for these lines: {i,j}: {98, 7709}, {671, 32447}, {7709, 1569}, {10723, 22728}

X(32470) = X(6)X(32134)∩X(39)X(486)

X(32470) lies on these lines: {6, 32134}, {39, 486}, {76, 5418}, {194, 371}, {372, 7709}, {485, 2782}, {511, 12124}, {590, 13108}, {698, 19145}, {1504, 1569}, {3071, 32447}, {3095, 6561}, {3102, 7757}, {3103, 6560}, {5420, 11171}, {6200, 12251}, {9540, 20081}, {9683, 9917}, {11152, 13669}, {14881, 22615}

X(32470) = {X(6),X(32448)}-harmonic conjugate of X(32471)
X(32470) = {X(3103),X(11257)}-harmonic conjugate of X(6560)

X(32471) = X(6)X(32134)∩X(39)X(485)

X(32471) lies on these lines: {6, 32134}, {39, 485}, {76, 5420}, {194, 372}, {371, 7709}, {486, 2782}, {511, 12123}, {615, 13108}, {698, 19146}, {1505, 1569}, {3070, 32447}, {3095, 6560}, {3102, 6561}, {3103, 7757}, {5418, 11171}, {11152, 13789}, {13935, 20081}, {14881, 22644}

X(32471) = {X(6),X(32448)}-harmonic conjugate of X(32470)
X(32471) = {X(3103),X(11257)}-harmonic conjugate of X(6561)

X(32472) = X(2)X(8644)∩X(3)X(9489)

X(32472) lies on these lines: {2, 8644}, {3, 9489}, {4, 2489}, {30, 511}, {98, 5970}, {114, 9152}, {182, 9426}, {351, 31176}, {381, 9175}, {647, 5996}, {669, 9148}, {850, 3804}, {887, 11616}, {2485, 11620}, {3818, 11182}, {3830, 9178}, {3835, 8653}, {4108, 31174}, {4140, 4761}, {4170, 7212}, {5466, 14458}, {5926, 16235}, {8430, 10722}, {8651, 11176}, {9123, 13306}, {9137, 10989}, {9185, 13307}, {24782, 26148}, {25084, 25299}

X(32472) = Thomson-isogonal conjugate of X(729)
X(32472) = Lucas-isogonal conjugate of X(729)
X(32472) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {850, 31299, 3804}, {5996, 9147, 647}

X(32473) = X(3)X(18105)∩X(30)X(511)

X(32473) lies on these lines: {3, 18105}, {30, 511}, {1637, 5996}, {1649, 11633}, {3005, 14420}, {3098, 14318}, {3804, 6563}, {4108, 14417}, {5466, 14492}, {9123, 13308}, {9125, 15724}, {9134, 31176}, {9180, 9302}, {9185, 13309}, {11616, 21006}, {21732, 32467}

X(32473) = Lucas-isogonal conjugate of X(755)
X(32473) = Thomson-isogonal conjugate of X(755)

X(32474) = REFLECTION OF X(4) IN X(9764)

X(32474) lies on these lines: {4, 9764}, {39, 18841}, {194, 1003}, {376, 538}, {511, 15428}, {698, 5085}, {2782, 3424}, {5485, 9466}, {7757, 9741}, {8782, 11148}

X(32474) = reflection of X(4) in X(9764)

X(32475) = X(3)X(1459)∩X(4)X(20293)

X(32475) lies on these lines: {3, 1459}, {4, 20293}, {5, 20316}, {30, 511}, {40, 21173}, {573, 6586}, {1293, 15403}, {3261, 10446}, {4791, 15488}

X(32475) = isogonal conjugate of X(32704)
X(32475) = Lucas-isogonal conjugate of X(2370)
X(32475) = Thomson-isogonal conjugate of X(2370)
X(32475) = crossdifference of every pair of points on line {6, 8756}

X(32476) = MIDPOINT OF X(194) AND X(2896)

X(194) and X(2896) are the centers of the 1st and 2nd Neuberg radical circles, resp.

X(32476) lies on these lines: {5, 9772}, {6, 10131}, {20, 3095}, {39, 83}, {69, 194}, {76, 4045}, {115, 32190}, {262, 6249}, {385, 6308}, {511, 7839}, {538, 31168}, {574, 8150}, {730, 12783}, {736, 7847}, {754, 7757}, {1975, 24273}, {2549, 31982}, {2782, 3399}, {3097, 9903}, {3314, 6309}, {3663, 17760}, {3934, 7923}, {4048, 10345}, {5254, 9478}, {5976, 7797}, {6296, 6775}, {6297, 6772}, {6337, 16898}, {6655, 9866}, {6656, 9865}, {6683, 16896}, {6704, 7786}, {7750, 32449}, {7766, 9821}, {7787, 13331}, {7790, 8149}, {7827, 18806}, {7977, 14839}, {9751, 13334}, {9765, 14041}, {9855, 12156}, {9873, 32429}, {10329, 16985}, {10333, 12215}, {10350, 12216}, {11257, 29012}, {12836, 13078}, {12837, 18983}, {12944, 18982}, {12954, 13077}, {13111, 32447}, {13357, 13586}

X(32476) = midpoint of X(194) and X(2896)
X(32476) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 6292}, {83, 39}
X(32476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {194, 7791, 9983}, {7864, 10335, 76}

X(32477) = REFLECTION OF X(76) IN X(6337)

X(32477) lies on these lines: {39, 2996}, {76, 631}, {99, 3053}, {194, 5052}, {1975, 5050}, {2782, 8781}, {3564, 7750}, {5033, 10131}, {5395, 32450}, {7757, 8370}, {7786, 13881}, {11152, 14645}

X(32477) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 6337}, {2996, 39}

X(32478) = X(2)X(18308)∩X(3)X(18336)

X(32478) lies on these lines: {2, 18308}, {3, 18336}, {4, 18335}, {30, 511}, {381, 1116}, {669, 14417}, {879, 16835}, {1637, 31176}, {2519, 7651}, {2525, 8664}, {3569, 22889}, {3830, 15475}, {3845, 15543}, {4807, 18004}, {5027, 13315}, {5466, 33698}, {5652, 6030}, {8718, 8723}, {9135, 22888}, {9208, 13318}, {9218, 15342}, {9494, 14824}, {9979, 12075}, {10097, 15321}, {11550, 14582}, {12077, 13412}, {18310, 18313}

X(32478) = Lucas-isogonal conjugate of X(5966)
X(32478) = Thomson-isogonal conjugate of X(5966)
X(32478) = crossdifference of every pair of points on line {6, 11451}

X(32479) = X(2)X(8589)∩X(3)X(1153)

X(32479) lies on these lines: {2, 8589}, {3, 1153}, {4, 7618}, {5, 7619}, {20, 7620}, {21, 7621}, {30, 511}, {39, 598}, {99, 8597}, {115, 8598}, {187, 671}, {316, 8591}, {325, 15300}, {376, 5569}, {381, 7622}, {382, 7775}, {549, 20112}, {550, 16509}, {574, 11317}, {625, 2482}, {1657, 7780}, {2080, 12355}, {3146, 7843}, {3529, 5485}, {3534, 7610}, {3734, 5077}, {3830, 11184}, {3845, 9771}, {3934, 7833}, {5007, 19696}, {5008, 33687}, {5032, 7737}, {5073, 7781}, {5092, 7606}, {5107, 8593}, {5140, 12132}, {5148, 12354}, {5184, 9875}, {5194, 18969}, {5215, 9166}, {5254, 19661}, {5309, 33193}, {5461, 27088}, {5999, 9877}, {6658, 7827}, {6683, 7756}, {6781, 22329}, {7746, 33208}, {7748, 7817}, {7751, 17800}, {7758, 11541}, {7759, 33703}, {7761, 21356}, {7801, 7842}, {7804, 11159}, {7810, 32819}, {7812, 32450}, {7816, 7841}, {7845, 20094}, {7848, 32815}, {7849, 19695}, {7854, 33271}, {7861, 8369}, {7870, 33019}, {7872, 33237}, {7873, 19691}, {7880, 33017}, {7883, 33256}, {7886, 32985}, {7915, 33190}, {8355, 22247}, {8586, 10488}, {8588, 8860}, {8596, 11054}, {8667, 15685}, {8703, 15597}, {8716, 15684}, {8724, 13449}, {9167, 10150}, {9466, 33264}, {9770, 15682}, {10302, 17128}, {11055, 19569}, {11057, 14711}, {11147, 32984}, {12040, 15687}, {12117, 18860}, {13330, 33683}, {13468, 19710}, {14042, 31652}, {26613, 33265}, {31709, 33476}, {31710, 33477}

X(32479) = Lucas-isogonal conjugate of X(8600)
X(32479) = Thomson-isogonal conjugate of X(8600)
X(32479) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7617, 1153}, {4, 7618, 8176}, {20, 7620, 8182}, {99, 8597, 31173}, {376, 7615, 5569}, {671, 9855, 187}, {2482, 8352, 625}, {8596, 14712, 11054}, {9166, 13586, 5215}

X(32480) = REFLECTION OF X(76) IN X(15810)

X(32480) lies on these lines: {2, 99}, {3, 8859}, {4, 10484}, {6, 9855}, {20, 576}, {30, 7709}, {39, 598}, {76, 15810}, {182, 12117}, {194, 524}, {376, 2080}, {384, 11164}, {1975, 21358}, {1992, 8586}, {2896, 11148}, {3091, 7608}, {3094, 9830}, {3329, 11159}, {3543, 9744}, {3552, 7827}, {3849, 7757}, {5024, 11317}, {5038, 7738}, {5077, 7840}, {5116, 7606}, {5309, 26613}, {5569, 14568}, {7748, 8176}, {7756, 7812}, {7777, 8352}, {7781, 7883}, {7782, 7817}, {7783, 7841}, {7785, 23334}, {7786, 14762}, {7791, 21356}, {7793, 8182}, {7801, 7847}, {7806, 27088}, {7810, 20081}, {7830, 20105}, {7837, 8353}, {7864, 8369}, {7870, 7933}, {7891, 8360}, {7923, 8366}, {7924, 8716}, {7937, 15301}, {8359, 31276}, {8597, 11163}, {8598, 15048}, {9606, 14066}, {10168, 10992}, {11147, 16925}, {11178, 23235}, {11184, 14041}, {11257, 11645}, {14042, 22332}

X(32480) = reflection of X(i) in X(j) for these lines: {i,j}: {76, 15810}, {598, 39}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8596, 11185}, {194, 7833, 9939}, {574, 671, 2}, {2482, 7790, 2}, {5077, 7840, 7898}, {5077, 31859, 7840}, {7622, 9166, 2}, {7622, 11648, 9166}, {7837, 8353, 14976}

X(32481) = X(3)X(76)∩X(114)X(2567)

X(32481) lies on the the 2nd Brocard circle, the cubics K019 and K1103, and on these lines: {3, 76}, {114, 2567}, {115, 2566}, {1663, 12215}, {1664, 6776}, {1665, 18906}, {1670, 3414}, {1671, 3413}, {2564, 3023}, {2565, 3027}, {2572, 9860}, {2573, 13174}

X(32481) = reflection of X(32482) in X(3)
X(32481) = antipode in 2nd Brocard circle of X(32482)
X(32481) = {X(76),X(99)}-harmonic conjugate of X(32482)
X(32481) = {X(98),X(11257)}-harmonic conjugate of X(32482)
X(32481) = X(1663)-of-6th-Brocard-triangle
X(32481) = X(1665)-of-1st-anti-Brocard-triangle

X(32482) = X(3)X(76)∩X(114)X(2566)

X(32482) lies on the the 2nd Brocard circle, the cubics K019 and K1103, and on these lines: {3, 76}, {114, 2566}, {115, 2567}, {1662, 12215}, {1664, 18906}, {1665, 6776}, {1670, 3413}, {1671, 3414}, {2564, 3027}, {2565, 3023}, {2572, 13174}, {2573, 9860}

X(32482) = reflection of X(32481) in X(3)
X(32482) = antipode in 2nd Brocard circle of X(32481)
X(32482) = {X(76),X(99)}-harmonic conjugate of X(32481)
X(32482) = {X(98),X(11257)}-harmonic conjugate of X(32481)
X(32482) = X(1662)-of-6th-Brocard-triangle
X(32482) = X(1664)-of-1st-anti-Brocard-triangle

X(32483) = X(98)X(385)∩X(880)X(2782)

X(32483) lies on the cubic K1103 and these lines: {98, 385}, {880, 2782}

X(32484) = X(39)X(512)∩X(99)X(511)

X(32484) lies on the cubic K1103 and these lines: {39, 512}, {99, 511}, {1916, 14509}, {2023, 6071}, {2679, 2782}, {8870, 13137}

X(32484) = midpoint of X(1916) and X(14509)
X(32484) = reflection of X(i) in X(j) for these lines: {i,j}: {6071, 2023}, {16068, 39}
X(32484) = reflection of X(16068) in the Brocard axis
X(32484) = orthogonal projection of X(99) on line PU(1)

X(32485) = (name pending)

X(32485) lies on this line: {3,6}

X(32486) = MIDPOINT OF X(1) AND X(5400)

See Angel Montesdeoca, Hyacinthos 29011 and HG130519

X(32486) lies on these lines: {1,5}, {3,23404}, {40,1054}, {43,16200}, {56,1777}, {57,1361}, {102,105}, {104,106}, {117,614}, {244,2800}, {386,10595}, {392,25939}, {484,23153}, {515,1149}, {517,1739}, {551,1064}, {581,3622}, {759,953}, {899,28234}, {912,4694}, {946,1201}, {962,28370}, {978,7982}, {995,4000}, {999,6180}, {1086,1537}, {1125,26095}, {1193,13464}, {1318,14511}, {1331,13279}, {1482,3216}, {1616,3149}, {1647,10265}, {1724,10680}, {1742,3576}, {1772,12758}, {2718,28219}, {3073,5563}, {3293,10222}, {3953,5887}, {3976,5693}, {3987,23340}, {4202,19861}, {4657,17044}, {5844,31855}, {6261,28011}, {6684,28352}, {6788,12247}, {8583,25882}, {8686,28233}, {10090,23703}, {11362,27627}, {12245,17749}, {12608,23675}, {12616,28018}, {14217,24715}, {15558,24028}, {16483,22753}, {17154,30196}

X(32486) = midpoint of X(i) and X(j), for these lines: {i, j}: {1, 5400}, {17154, 30196}

X(32487) = X(2292)X(3754)∩X(4535)X(18697)

See Angel Montesdeoca, Hyacinthos 29011 and HG130519

X(32487) lies on these lines: {2292,3754}, {4535,18697}

2nd and 3rd Vecten triangles: X(32488)-X(32513)

X(32488) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-VECTEN AND ANTICOMPLEMENTARY

As a point on the Euler line, X(32488) has Shinagawa coefficients (E+F-S, -2*S).

X(32488) lies on these lines: {2,3}, {193,9975}, {486,638}, {487,23259}, {489,23261}, {490,615}, {491,3071}, {637,640}, {1132,1271}, {1587,7797}, {1588,7785}, {3069,12323}, {3070,7851}, {5591,12322}, {6776,26469}, {13758,13881}

X(32488) = anticomplement of the anticomplement of X(32490)
X(32488) = inverse of X(11293) in the orthocentroidal circle
X(32488) = X(12963)-of-3rd anti-tri-squares triangle, when ABC is obtuse
X(32488) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4, 11293), (4, 5025, 32489), (4, 11292, 14035)

X(32489) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-VECTEN AND ANTICOMPLEMENTARY

As a point on the Euler line, X(32489) has Shinagawa coefficients (E+F+S, 2*S).

X(32489) lies on these lines: {2,3}, {69,31412}, {193,9974}, {485,637}, {488,23249}, {489,590}, {490,23251}, {492,3070}, {638,639}, {1131,1270}, {1587,7785}, {1588,7797}, {3068,12322}, {3071,7851}, {3594,13757}, {5590,12323}, {5860,31414}, {6118,6200}, {6250,11825}, {6425,13663}, {6776,26468}, {7581,7921}, {7582,7920}, {7585,12221}, {7745,13758}, {8376,13941}, {8960,32419}, {13638,13881}

X(32489) = anticomplement of the anticomplement of X(32491)
X(32489) = inverse of X(11294) in the orthocentroidal circle
X(32489) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4, 11294), (4, 5025, 32488), (4, 11291, 14035)

X(32490) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-VECTEN AND MEDIAL

As a point on the Euler line, X(32490) has Shinagawa coefficients (2*E+2*F-3*S, -S).

X(32490) lies on these lines: {2,3}, {69,13951}, {115,32494}, {141,10577}, {372,23312}, {487,13785}, {491,7584}, {590,1506}, {597,8960}, {615,640}, {637,18762}, {638,13966}, {639,7867}, {642,3071}, {1270,3317}, {1271,13939}, {1588,26362}, {3589,10576}, {3595,7582}, {3618,8976}, {6318,22725}, {6395,12222}, {6398,12323}, {10195,13663}, {31455,32497}

X(32490) = complement of the complement of X(32488)
X(32490) = inverse of X(11316) in the orthocentroidal circle
X(32490) = X(371)-of-inner-Vecten triangle, when ABC is obtuse
X(32490) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4, 11316), (5, 8361, 32491), (3090, 6811, 5)

X(32491) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-VECTEN AND MEDIAL

As a point on the Euler line, X(32491) has Shinagawa coefficients (2*E+2*F+3*S, S).

X(32491) lies on these lines: {2,3}, {69,8976}, {115,32497}, {141,10576}, {371,23311}, {488,13665}, {492,7583}, {524,8960}, {590,639}, {615,1506}, {637,8981}, {638,18538}, {640,7867}, {641,3070}, {1270,13886}, {1271,3316}, {1587,26361}, {3589,10577}, {3593,7581}, {3618,13951}, {6199,12221}, {6221,12322}, {6314,22724}, {10194,13783}, {26288,31414}, {31454,32419}, {31455,32494}

X(32491) = complement of the complement of X(32489)
X(32491) = inverse of X(11315) in the orthocentroidal circle
X(32491) = X(371)-of-outer-Vecten triangle
X(32491) = X(6213)-of-3rd outer-Vecten triangle
X(32491) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4, 11315), (5, 8361, 32490), (3090, 6813, 5)

X(32492) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES TO 2nd INNER-VECTEN

The reciprocal orthologic center of these triangles is X(486).

X(32492) lies on these lines: {3,486}, {30,12969}, {315,32419}, {371,6251}, {487,23259}, {489,642}, {616,22601}, {617,22603}, {1322,13036}, {1503,9975}, {1588,12296}, {2782,22501}, {6290,23261}, {12221,20081}, {12509,23275}, {20423,32495}, {22484,22591}, {32506,32508}

X(32492) = reflection of X(i) in X(j) for these (i,j): (486, 3071), (489, 642), (32506, 32508)
X(32492) = (3rd anti-tri-squares)-isogonal conjugate of-X(486)
X(32492) = X(372)-of-3rd anti-tri-squares triangle, when ABC is obtuse
X(32492) = X(8982)-of-inner-Vecten triangle, when ABC is obtuse
X(32492) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6561, 22617, 486), (13785, 13934, 486)

X(32493) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) REFLECTION TO 2nd INNER-VECTEN

The reciprocal orthologic center of these triangles is X(3071).

X(32493) lies on these lines: {32,6402}, {184,3071}

X(32493) = X(1)-of-Lucas(-1) reflection triangle
X(32493) = (Lucas(-1) reflection)-isogonal conjugate of-X(32493)

X(32494) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th TRI-SQUARES TO 2nd INNER-VECTEN

The reciprocal orthologic center of these triangles is X(486).

X(32494) lies on these lines: {2,1975}, {3,486}, {4,19493}, {6,487}, {32,32419}, {37,31535}, {39,590}, {69,6463}, {115,32490}, {372,3564}, {489,3053}, {494,11091}, {524,12969}, {574,6119}, {591,3785}, {597,12962}, {1152,1503}, {1322,13020}, {1352,15884}, {1384,13770}, {1588,12509}, {2548,9767}, {2549,11314}, {2782,13926}, {3070,6290}, {3767,11316}, {3815,7389}, {3926,5491}, {5023,13798}, {5024,13711}, {5206,32209}, {5210,13941}, {6414,8420}, {6776,8406}, {7375,31400}, {7745,11293}, {8252,11292}, {8253,22332}, {8576,13046}, {8855,8964}, {9605,19105}, {9906,13973}, {10991,13989}, {11313,31401}, {12169,19005}, {12296,23261}, {12963,13972}, {13036,13429}, {13880,13968}, {18937,19411}, {19104,30435}, {31455,32491}

X(32494) = midpoint of X(489) and X(12221)
X(32494) = reflection of X(3071) in X(486)
X(32494) = (4th tri-squares)-isogonal conjugate of-X(486)
X(32494) = X(371)-of-4th tri-squares triangle, when ABC is acute
X(32494) = X(372)-of-4th tri-squares triangle, when ABC is obtuse
X(32494) = X(489)-of-4th tri-squares-central triangle
X(32494) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5013, 32497), (5254, 7789, 32497), (6337, 13881, 32497)

X(32495) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES TO 2nd OUTER-VECTEN

The reciprocal orthologic center of these triangles is X(485).

X(32495) lies on these lines: {3,485}, {30,12962}, {315,32421}, {372,6250}, {488,23249}, {490,641}, {616,22630}, {617,22632}, {1321,13035}, {1503,9974}, {1587,12297}, {2782,22502}, {5254,19102}, {6118,6396}, {6200,13879}, {6228,7389}, {6289,23251}, {6561,19103}, {8352,12159}, {8376,13834}, {12222,20081}, {12510,23269}, {20423,32492}, {22485,22592}, {32507,32509}

X(32495) = reflection of X(i) in X(j) for these (i,j): (485, 3070), (490, 641), (32507, 32509)
X(32495) = (4th anti-tri-squares)-isogonal conjugate of-X(485)
X(32495) = X(8982)-of-outer-Vecten triangle
X(32495) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6560, 22646, 485), (13665, 13882, 485)

X(32496) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS REFLECTION TO 2nd OUTER-VECTEN

The reciprocal orthologic center of these triangles is X(3070).

X(32496) lies on these lines: {32,6401}, {184,3070}

X(32496) = (Lucas reflection)-isogonal conjugate of-X(32496)
X(32496) = X(1)-of-Lucas reflection triangle

X(32497) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd TRI-SQUARES TO 2nd OUTER-VECTEN

The reciprocal orthologic center of these triangles is X(485).

X(32497) lies on these lines: {2,1975}, {3,485}, {4,19492}, {6,488}, {32,32421}, {39,615}, {69,6462}, {115,32491}, {187,13879}, {371,3564}, {490,3053}, {493,11090}, {524,12962}, {574,6118}, {597,12969}, {1144,6529}, {1151,1503}, {1321,13019}, {1352,15883}, {1384,13651}, {1587,12510}, {1991,3785}, {2548,9768}, {2549,11313}, {2782,13873}, {3071,6289}, {3767,11315}, {3815,7388}, {3926,5490}, {5023,13678}, {5024,13834}, {5206,13924}, {5210,8972}, {6413,8408}, {6776,8414}, {7376,31400}, {7745,11294}, {8252,22332}, {8253,11291}, {8577,13047}, {8997,10991}, {9605,19102}, {9907,13911}, {11314,31401}, {12170,19006}, {12297,23251}, {12968,13910}, {13035,13440}, {13908,13921}, {18938,19410}, {19103,30435}, {31455,32490}

X(32497) = midpoint of X(490) and X(12222)
X(32497) = reflection of X(3070) in X(485)
X(32497) = (3rd tri-squares)-isogonal conjugate of-X(485)
X(32497) = X(372)-of-3rd tri-squares triangle
X(32497) = X(490)-of-3rd tri-squares-central triangle
X(32497) = X(31559)-of-3rd outer-Vecten triangle
X(32497) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5013, 32494), (5254, 7789, 32494), (6337, 13881, 32494)

X(32498) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES TO 3rd INNER-VECTEN

The reciprocal orthologic center of these triangles is X(486).

X(32498) lies on these lines: {4,372}, {6,22596}, {30,13934}, {487,23259}, {642,6561}, {1161,12601}, {1328,5491}, {3071,6290}, {3564,9975}, {6119,11291}, {6229,12322}, {6564,19105}, {7000,13926}, {7900,12221}, {8184,11293}, {12296,23263}, {12306,23261}, {13881,22625}, {19130,32499}

X(32498) = (3rd anti-tri-squares)-isogonal conjugate of-X(22617)
X(32498) = (3rd anti-tri-squares)-complement of-X(22617)
X(32498) = X(3)-of-3rd anti-tri-squares triangle

X(32499) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES TO 3rd OUTER-VECTEN

The reciprocal orthologic center of these triangles is X(485).

X(32499) lies on these lines: {4,371}, {6,22625}, {30,13882}, {488,23249}, {641,6560}, {1160,12602}, {1327,5490}, {3070,6289}, {3564,9974}, {6118,11292}, {6228,12323}, {6565,19102}, {7374,13873}, {7900,12222}, {8180,11294}, {12297,23253}, {12305,23251}, {13881,22596}, {19130,32498}

X(32499) = (4th anti-tri-squares)-isogonal conjugate of-X(22646)
X(32499) = (4th anti-tri-squares)-complement of-X(22646)
X(32499) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (488, 23249, 32495), (12257, 31412, 485)

X(32500) = EULEROLOGIC CENTER OF THESE TRIANGLES: INNER-VECTEN TO 3rd INNER-VECTEN

There is not reciprocal eulerologic center for these triangles

X(32500) lies on these lines: {2,7599}, {136,641}, {369,20799}

X(32500) = complement of X(13520)
X(32500) = X(125)-of-inner-Vecten triangle
X(32500) = orthoptic-circle-of-Steiner-inellipse-inverse of X(33340)

X(32501) = EULEROLOGIC CENTER OF THESE TRIANGLES: OUTER-VECTEN TO 3rd INNER-VECTEN

There is not reciprocal eulerologic center for these triangles

X(32501) lies on these lines: {2,7598}, {136,642}

X(32501) = complement of X(13521)
X(32501) = X(100)-of-3rd outer-Vecten triangle
X(32501) = X(125)-of-outer-Vecten triangle
X(32501) = orthoptic-circle-of-Steiner-inellipse-inverse of X(33341)

X(32502) = CENTROID OF THE 2nd INNER-VECTEN TRIANGLE

X(32502) lies on these lines: {2,32433}, {486,32508}, {642,32512}, {3071,32506}

X(32502) = reflection of X(2) in X(32504)
X(32502) = {X(3071), X(32510)}-harmonic conjugate of X(32506)
X(32502) = X(3060)-of-inner-Vecten triangle

X(32503) = CENTROID OF THE 2nd OUTER-VECTEN TRIANGLE

X(32503) lies on these lines: {2,32436}, {485,32509}, {641,32513}, {3070,32507}

X(32503) = reflection of X(2) in X(32505)
X(32503) = X(1699)-of-3rd outer-Vecten triangle
X(32503) = X(3060)-of-outer-Vecten triangle
X(32503) = {X(3070), X(32511)}-harmonic conjugate of X(32507)

X(32504) = CENTROID OF THE 3rd INNER-VECTEN TRIANGLE

X(32504) lies on these lines: {2,32433}, {6119,32508}

X(32504) = midpoint of X(2) and X(32502)
X(32504) = X(51)-of-inner-Vecten triangle
X(32504) = {X(6119), X(32512)}-harmonic conjugate of X(32508)

X(32505) = CENTROID OF THE 3rd OUTER-VECTEN TRIANGLE

X(32505) lies on these lines: {2,32436}, {6118,32509}

X(32505) = midpoint of X(2) and X(32503)
X(32505) = X(51)-of-outer-Vecten triangle
X(32505) = {X(6118), X(32513)}-harmonic conjugate of X(32509)

X(32506) = ORTHOCENTER OF THE 2nd INNER-VECTEN TRIANGLE

X(32506) lies on these lines: {486,489}, {3071,32502}, {32492,32508}

X(32506) = reflection of X(i) in X(j) for these (i,j): (3071, 32510), (32492, 32508)
X(32506) = {X(3071), X(32510)}-harmonic conjugate of X(32502)

X(32507) = ORTHOCENTER OF THE 2nd OUTER-VECTEN TRIANGLE

X(32507) lies on these lines: {485,490}, {3070,32503}, {32495,32509}

X(32507) = reflection of X(i) in X(j) for these (i,j): (3070, 32511), (32495, 32509)
X(32507) = {X(3070), X(32511)}-harmonic conjugate of X(32503)

X(32508) = ORTHOCENTER OF THE 3rd INNER-VECTEN TRIANGLE

X(32508) lies on these lines: {486,32502}, {642,3071}, {6119,32504}, {32492,32506}

X(32508) = midpoint of X(32492) and X(32506)
X(32508) = reflection of X(6119) in X(32512)
X(32508) = X(52)-of-inner-Vecten triangle
X(32508) = {X(6119), X(32512)}-harmonic conjugate of X(32504)

X(32509) = ORTHOCENTER OF THE 3rd OUTER-VECTEN TRIANGLE

X(32509) lies on these lines: {485,32503}, {641,3070}, {6118,32505}, {32495,32507}

X(32509) = midpoint of X(32495) and X(32507)
X(32509) = reflection of X(6118) in X(32513)
X(32509) = X(52)-of-outer-Vecten triangle
X(32509) = {X(6118), X(32513)}-harmonic conjugate of X(32505)

X(32510) = X(5)-OF-2nd INNER-VECTEN TRIANGLE

X(32510) lies on these lines: {3071,32502}, {6119,18762}

X(32510) = midpoint of X(3071) and X(32506)
X(32510) = {X(32502), X(32506)}-harmonic conjugate of X(3071)

X(32511) = X(5)-OF-2nd OUTER-VECTEN TRIANGLE

X(32511) lies on these lines: {3070,32503}, {6118,18538}

X(32511) = midpoint of X(3070) and X(32507)
X(32511) = {X(32503), X(32507)}-harmonic conjugate of X(3070)

X(32512) = X(5)-OF-3rd INNER-VECTEN TRIANGLE

X(32512) lies on these lines: {642,32502}, {6119,32504}

X(32512) = midpoint of X(6119) and X(32508)
X(32512) = X(143)-of-inner-Vecten triangle
X(32512) = {X(32504), X(32508)}-harmonic conjugate of X(6119)

X(32513) = X(5)-OF-3rd OUTER-VECTEN TRIANGLE

X(32513) lies on these lines: {641,32503}, {6118,32505}

X(32513) = midpoint of X(6118) and X(32509)
X(32513) = X(143)-of-outer-Vecten triangle
X(32513) = {X(32505), X(32509)}-harmonic conjugate of X(6118)

X(32514) = X(3)X(194)∩X(699)X(1384)

X(32514) = X(25)-of-inscribed-triply-bilogic-triangle; see the preamble just before X(32562)

X(32514) lies on these lines: {3, 194}, {699, 1384}, {2076, 32442}, {3552, 19597}, {5017, 9431}

X(32515) = X(3)X(194)∩X(5)X(76)

X(32515) lies on these lines: {2, 8179}, {3, 194}, {4, 7779}, {5, 76}, {6, 22525}, {15, 32465}, {16, 32466}, {20, 20105}, {26, 9917}, {30, 511}, {39, 140}, {98, 10290}, {99, 2080}, {114, 7813}, {141, 11261}, {182, 7798}, {187, 1569}, {298, 20426}, {299, 20425}, {316, 6321}, {323, 1316}, {355, 9902}, {381, 7840}, {384, 22521}, {395, 3106}, {396, 3107}, {397, 3105}, {398, 3104}, {495, 10063}, {496, 10079}, {546, 6248}, {547, 9466}, {548, 5188}, {549, 7757}, {550, 9821}, {576, 3734}, {620, 14693}, {632, 7786}, {1151, 32470}, {1152, 32471}, {1351, 18906}, {1353, 32451}, {1483, 7976}, {1484, 32454}, {1513, 9772}, {1656, 7881}, {1916, 15980}, {3094, 15048}, {3097, 26446}, {3102, 7584}, {3103, 7583}, {3186, 22152}, {3398, 7760}, {3530, 13334}, {3580, 11007}, {3589, 32149}, {3628, 3934}, {3926, 9752}, {4385, 15973}, {5054, 8859}, {5066, 14711}, {5093, 11286}, {5097, 7804}, {5149, 13196}, {5171, 7781}, {5254, 32452}, {5690, 12782}, {5874, 6272}, {5875, 6273}, {5901, 12263}, {5976, 6390}, {5999, 12188}, {6234, 18829}, {6683, 16239}, {6756, 12143}, {6781, 10992}, {6795, 32599}, {7467, 8267}, {7617, 14159}, {7694, 7758}, {7751, 9737}, {7763, 9754}, {7766, 11842}, {7789, 18806}, {7799, 15561}, {7805, 13335}, {7809, 14639}, {7826, 32152}, {7845, 13449}, {8597, 12355}, {8598, 11152}, {8703, 11055}, {8782, 9301}, {8992, 13925}, {9743, 9764}, {9748, 32830}, {9751, 12054}, {9753, 32833}, {9756, 31981}, {9983, 22678}, {10263, 16983}, {10358, 17130}, {10942, 12933}, {10943, 12923}, {11054, 11632}, {12042, 18860}, {12100, 21163}, {12338, 22556}, {12474, 22668}, {12475, 22672}, {12794, 22698}, {12992, 22709}, {12993, 22710}, {13077, 15171}, {13109, 22731}, {13110, 22732}, {13172, 14712}, {13330, 18907}, {13983, 13993}, {14651, 19570}, {14853, 32836}, {14880, 30270}, {15122, 16315}, {16266, 23128}, {16316, 16619}, {16320, 25338}, {18583, 24256}, {18971, 18982}, {19063, 19089}, {19064, 19090}, {22680, 22779}, {22735, 33873}

X(32515) = Lucas-isogonal conjugate of X(25424)
X(32515) = Thomson-isogonal conjugate of X(25424)
X(32515) = X(30)-of-inscribed-triply-bilogic-triangle

X(32515) = X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 194, 32448}, {4, 20081, 13108}, {76, 262, 7697}, {76, 3095, 5}, {194, 6194, 7709}, {194, 12251, 3}, {262, 7697, 5}, {576, 3734, 10796}, {3095, 7697, 262}, {3934, 11272, 3628}, {6194, 7709, 3}, {6248, 14881, 546}, {6248, 22682, 22681}, {7709, 12251, 6194}, {7751, 9737, 10104}, {7757, 22712, 11171}, {9301, 13188, 11676}, {9821, 11257, 550}, {10063, 12837, 495}, {10063, 22729, 22705}, {10079, 12836, 496}, {10079, 22730, 22706}, {11152, 22564, 8598}, {11171, 22712, 549}, {12836, 22706, 22730}, {12837, 22705, 22729}, {14881, 22681, 22682}, {22681, 22682, 546}, {22705, 22729, 495}, {22706, 22730, 496}

X(32516) = X(3)X(194)∩X(30)X(39)

X(32516) lies on these lines: {3, 194}, {5, 7786}, {20, 32447}, {30, 39}, {76, 549}, {99, 12054}, {140, 620}, {141, 32429}, {262, 3627}, {511, 548}, {538, 12100}, {546, 11272}, {547, 6683}, {550, 3095}, {574, 14880}, {631, 13108}, {632, 7697}, {698, 5092}, {726, 13624}, {1151, 32471}, {1152, 32470}, {1569, 12042}, {2021, 5305}, {2080, 32467}, {3097, 18481}, {3098, 32449}, {3524, 20081}, {3529, 22728}, {3530, 21163}, {3628, 6248}, {5054, 31276}, {5237, 32465}, {5238, 32466}, {6033, 7847}, {7467, 31088}, {7618, 18768}, {7757, 8703}, {7782, 26316}, {7824, 12188}, {7832, 8724}, {7839, 9301}, {8356, 32151}, {8716, 31981}, {9466, 11812}, {10007, 18358}, {10124, 31239}, {10541, 31958}, {11055, 15711}, {11676, 32134}, {12017, 18906}, {12102, 22682}, {12108, 15819}, {12811, 22681}, {13077, 15325}, {13331, 21850}, {15692, 20105}, {15712, 22712}, {18806, 32459}

X(32516) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 32448}, {5, 11257}, {141, 32429}, {550, 3095}, {1569, 12042}, {3098, 32449}, {7757, 8703}
X(32516) = reflection of X(i) in X(j) for these lines: {i,j}: {140, 13334}, {546, 11272}, {6248, 3628}, {9466, 11812}, {18358, 10007}
X(32516) = X(140)-of-inscribed-triply-bilogic-triangle
X(32516) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7709, 32448}, {11171, 11257, 5}

X(32517) = X(3)X(194)∩X(187)X(699)

X(32517) lies on these lines: {3, 194}, {187, 699}, {9491, 13586}

X(32517) = circumcircle-inverse of X(194)
X(32517) = X(186)-of-inscribed-triply-bilogic-triangle

X(32518) = X(3)X(194)∩X(32)X(9490)

X(32518) lies on these lines: {3, 194}, {32, 9490}, {187, 237}, {805, 2080}, {865, 5913}, {1613, 23221}, {3053, 3224}, {3360, 5023}, {3511, 13586}, {7771, 14096}, {11332, 11580}, {16514, 22386}

X(32518) = {X(187),X(21444)}-harmonic conjugate of X(237)
X(32518) = X(237)-of-inscribed-triply-bilogic-triangle

X(32519) = X(3)X(194)∩X(6)X(15690)

X(32519) lies on these lines: {3, 194}, {6, 1569}, {39, 1656}, {76, 3526}, {99, 11842}, {140, 20081}, {262, 381}, {382, 3095}, {511, 3534}, {538, 1153}, {631, 20105}, {698, 5050}, {726, 10246}, {732, 22677}, {1351, 32449}, {1499, 32463}, {1657, 11257}, {2070, 22655}, {2080, 7798}, {3094, 11898}, {3097, 5790}, {3311, 32470}, {3312, 32471}, {3398, 7781}, {3818, 14692}, {3906, 8723}, {5072, 6248}, {5076, 14881}, {5079, 11272}, {5309, 15561}, {7748, 10242}, {7839, 22521}, {9466, 15723}, {9756, 12188}, {9917, 13564}, {10256, 18768}, {10796, 23235}, {11055, 15693}, {11152, 11159}, {12645, 12782}, {13077, 22730}, {15696, 22676}, {15700, 21163}, {18525, 22650}, {18982, 22729}

X(32519) = midpoint of X(i) and X(j) for these lines: {i,j}: {194, 7709}, {11055, 22712}
X(32519) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 7709}, {381, 32447}, {382, 22728}, {5790, 3097}, {7697, 39}, {7709, 32448}, {13108, 7697}, {18525, 22650}, {22728, 3095}, {32447, 7757}
X(32519) = X(381)-of-inscribed-triply-bilogic-triangle
X(32519) ={X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 13108, 1656}, {194, 32448, 3}, {32465, 32466, 6}

X(32520) = X(3)X(194)∩X(4)X(20105)

X(32520) lies on these lines: {3, 194}, {4, 20105}, {5, 7906}, {39, 3526}, {76, 1656}, {262, 5072}, {381, 538}, {382, 2782}, {511, 1657}, {576, 18501}, {698, 1351}, {726, 1482}, {730, 12645}, {732, 11898}, {1569, 3053}, {2080, 7781}, {2937, 9917}, {3102, 18510}, {3103, 18512}, {3398, 7798}, {3534, 11055}, {5050, 32449}, {5054, 7757}, {5070, 31276}, {5076, 22728}, {5079, 7697}, {5093, 18906}, {5188, 15688}, {5790, 9902}, {6221, 32470}, {6321, 7759}, {6398, 32471}, {7760, 11842}, {7890, 23698}, {9821, 15696}, {10983, 31981}, {11171, 15720}, {13334, 15693}, {15069, 18503}, {22236, 32465}, {22238, 32466}

X(32520) = midpoint of X(4) and X(20105)
X(32520) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 194}, {12251, 32448}, {13108, 3095}, {20081, 5}
X(32520) = X(382)-of-inscribed-triply-bilogic-triangle
X(32520) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 32447, 1656}, {194, 12251, 32448}, {3095, 13108, 381}, {12251, 32448, 3}

X(32521) = X(3)X(194)∩X(5)X(141)

X(32521) lies on these lines: {3, 194}, {4, 7929}, {5, 141}, {20, 13108}, {30, 76}, {39, 549}, {140, 3095}, {230, 32452}, {262, 3628}, {343, 21536}, {376, 20081}, {381, 7879}, {384, 9301}, {395, 3104}, {396, 3105}, {524, 8149}, {538, 8703}, {546, 7697}, {548, 11257}, {550, 2782}, {631, 32447}, {632, 11272}, {698, 3098}, {726, 3579}, {1353, 13354}, {1569, 15513}, {2979, 21531}, {3091, 22728}, {3094, 5305}, {3102, 13966}, {3103, 8981}, {3106, 16773}, {3107, 16772}, {3530, 11171}, {3627, 6248}, {3845, 9466}, {3857, 22682}, {3933, 5976}, {5092, 7805}, {5351, 32466}, {5352, 32465}, {6033, 7768}, {6179, 26316}, {6409, 32470}, {6410, 32471}, {6644, 9917}, {6683, 11539}, {7470, 8782}, {7757, 12100}, {7760, 12054}, {7780, 12042}, {7797, 10357}, {7842, 22515}, {7854, 9996}, {8367, 22486}, {8370, 22564}, {8667, 31981}, {9902, 18481}, {10063, 18990}, {10079, 15171}, {10104, 30270}, {10304, 20105}, {11055, 15759}, {11477, 31958}, {12103, 22676}, {12263, 22791}, {12836, 15325}, {13334, 15712}, {13468, 32189}, {14711, 19710}, {15699, 31239}, {17504, 32450}

X(32521) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 12251}, {20, 13108}, {76, 9821}, {8782, 12188}, {9902, 18481}
X(32521) = reflection of X(i) in X(j) for these lines: {i,j}: {550, 5188}, {1353, 13354}, {3095, 140}, {3627, 6248}, {3845, 9466}, {7757, 12100}, {11257, 548}, {14881, 3934}, {21850, 24256}, {22791, 12263}, {32151, 7767}, {32448, 3}, {32449, 5092}
X(32521) = X(550)-of-inscribed-triply-bilogic-triangle
X(32521) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3095, 22712, 140}, {3098, 7751, 14880}, {3934, 14881, 5}, {6194, 12251, 3}, {7470, 17129, 12188}, {11272, 15819, 632}

X(32522) = X(3)X(194)∩X(20)X(39)

X(32522) lies on these lines: {2, 6248}, {3, 194}, {4, 11171}, {20, 39}, {76, 3523}, {114, 7933}, {147, 7791}, {182, 3552}, {262, 3146}, {376, 3095}, {511, 3522}, {538, 15692}, {549, 13108}, {550, 32447}, {574, 12203}, {631, 2782}, {726, 7987}, {1513, 7864}, {1569, 15515}, {2021, 5286}, {3091, 7786}, {3094, 25406}, {3096, 14981}, {3097, 4297}, {3102, 9541}, {3525, 7697}, {3528, 9821}, {3529, 14881}, {3564, 7904}, {3934, 10303}, {5013, 5999}, {5056, 6683}, {5085, 18906}, {5171, 7766}, {5188, 7757}, {5218, 18982}, {5351, 32465}, {5352, 32466}, {5731, 12782}, {6200, 32471}, {6396, 32470}, {6655, 9744}, {7288, 13077}, {7760, 8722}, {7787, 11676}, {7815, 15483}, {8356, 9863}, {8782, 21166}, {9466, 15708}, {9902, 10164}, {15704, 22728}, {15717, 20081}, {20190, 31958}, {31884, 32449}

X(32522) = reflection of X(i) in X(j) for these lines: {i,j}: {3091, 7786}, {31276, 631}
X(32522) = X(631)-of-inscribed-triply-bilogic-triangle
X(32522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 194, 6194}, {3, 7709, 194}, {3, 32448, 12251}, {76, 21163, 3523}, {5171, 32467, 7766}, {7709, 12251, 32448}, {11257, 13334, 2}, {12251, 32448, 194}, {15717, 20081, 22712}

X(32523) = X(3)X(194)∩X(39)X(3627)

X(32523) lies on these lines: {3, 194}, {39, 3627}, {76, 12108}, {262, 12102}, {538, 15712}, {546, 11257}, {548, 7757}, {549, 14711}, {632, 2782}, {726, 31666}, {3095, 12103}, {3529, 32447}, {3628, 11171}, {3857, 11272}, {6425, 32471}, {6426, 32470}, {7786, 12812}, {10303, 13108}, {11055, 14891}, {13334, 14869}

X(32523) = X(632)-of-inscribed-triply-bilogic-triangle

X(32524) = X(3)X(194)∩X(39)X(3224)

X(32524) lies on these s {3, 194}, {39, 3224}, {99, 11328}, {574, 3229}, {1975, 14937}, {3225, 7757}, {3360, 5013}, {3511, 8716}, {8841, 9737}, {9490, 9605}

X(32524) = Thomson-isogonal conjugate of X(6194)

X(32525) = MIDPOINT OF X(2) AND X(9169)

X(32525) lies on the cubic K249 and these s {2, 6}, {5, 1499}, {126, 5969}, {373, 2679}, {542, 6719}, {3090, 15098}, {4045, 11007}, {5026, 10418}, {5055, 18346}, {6034, 30786}, {6082, 14658}, {7603, 9151}, {7804, 22104}, {9152, 31654}, {9172, 9830}, {10160, 10168}, {10278, 22260}, {20382, 23297}

X(32525) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 9169}, {126, 6791}, {5108, 6792}
X(32525) = complement of X(5108)
X(32525) = nine-point-circle-inverse of X(23301)
X(32525) = orthoptic-circle-of-Steiner-inellipe-inverse of X(385)
X(32525) = circumcircle-of-inner-Napoleon-triangle-inverse of X(3180)
X(32525) = circumcircle-of-outer-Napoleon-triangle inverse of X(3181)
X(32525) = complement of the isogonal conjugate of X(14948)
X(32525) = psi-transform of X(148)
X(32525) = X(14948)-complementary conjugate of X(10)
X(32525) = crossdifference of every pair of points lies on these lines: {512, 9225}
X(32525) = orthogonal projection of X(5) on line X(2)X(6)
X(32525) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 11053}, {2, 1648, 141}, {2, 6792, 5108}, {5108, 9169, 6792}

X(32526) = X(2)X(39)∩X(23)X(5106)

X(32526) lies on the Parry circle, the cubic K794, and on these lines: {2, 39}, {23, 5106}, {110, 1691}, {187, 9999}, {237, 9157}, {353, 5092}, {511, 9998}, {647, 5996}, {694, 20977}, {698, 13518}, {1084, 7840}, {3292, 9463}, {3796, 21001}, {7711, 11580}, {7931, 8265}, {8620, 9978}, {9138, 9210}, {9156, 17414}, {9208, 9212}, {14684, 20481}

X(32526) = reflection of X(9998) in the Lemoine axis
X(32526) = orthoptic-circle-of-Steiner-inellipse-inverse of X(39)
X(32526) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(194)
X(32526) = psi-transform of X(3094)
X(32526) = crossdifference of every pair of points lies on these lines: {669, 11182}
X(32526) = X(5970)-of-2nd-Parry-triangle

X(32527) = X(4)X(147)∩X(25)X(5152)

X(32527) lies on these lines: {4, 147}, {25, 5152}, {804, 2489}

X(32527) = polar circle inverse of X(194)
X(32527) = {X(5186),X(12131)}-harmonic conjugate of X(12143)

X(32528) = X(2)X(4159)∩X(4)X(147)

X(32528) lies on these lines: {2, 4159}, {4, 147}, {83, 115}, {99, 626}, {315, 8782}, {316, 9865}, {542, 19570}, {543, 7809}, {620, 7944}, {671, 7753}, {804, 2514}, {2794, 14712}, {2896, 5976}, {3926, 20094}, {5025, 5989}, {5103, 12215}, {5939, 7932}, {5987, 19577}, {6034, 9830}, {6656, 8290}, {7752, 8178}, {7790, 10334}, {7791, 7945}, {7793, 9862}, {7803, 10353}, {7839, 12830}, {7889, 14061}, {9880, 14492}, {11646, 24256}, {12177, 14639}

X(32528) = anticomplement of X(5152)
X(32528) = polar circle inverse of X(12143)
X(32528) = circumcircle-of-anticomplementary-triangle-inverse of X(194)
X(32528) = X(30530)-anticomplementary conjugate of X(17217)
X(32528) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {115, 4027, 7797}, {147, 148, 194}, {148, 7785, 1916}, {1916, 6033, 7785}, {6033, 6321, 14881}, {11606, 16044, 115}

X(32529) = X(20)X(185)∩X(22)X(1613)

X(32529) lies on these lines: {20, 185}, {22, 1613}, {401, 19585}, {512, 16084}, {805, 1297}, {858, 5103}, {1691, 19121}, {1843, 6658}, {2456, 2698}, {2882, 12215}, {5104, 32464}, {5111, 11416}, {11634, 14965}

X(32529) = crosssum of X(3229) and X(6467)
X(32529) = de Longchamps-circle-inverse of X(194)
X(32529) = anticomplement of the isogonal conjugate of X(8858)
X(32529) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {699, 21216}, {3225, 5905}, {8858, 8}

X(32530) = X(2)X(39)∩X(8651)X(11176)

X(32530) lies on these lines: {2, 39}, {8651, 11176}

X(32530) = orthoptic-circle-of-Steiner-inellipse-inverse of X(194)
X(32530) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(20105)

X(32531) = X(2)X(669)∩X(3)X(194)

X(32531) lies on these lines: {2, 669}, {3, 194}, {182, 805}, {353, 3231}, {574, 5970}, {3407, 14870}, {5092, 15920}, {5108, 7496}, {8289, 21444}

X(32531) = circumcircle-inverse of X(385)
X(32531) = Brocard-circle-inverse of X(805)
X(32531) = orthoptic-circle-of-Steiner-inellipse-inverse of X(23301)
X(32531) = 2nd-Brocard-circle-inverse of X(194)
X(32531) = psi-transform of X(5027)

X(32532) = ISOGONAL CONJUGATE OF X(15655)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32532) lies on the Kiepert hyperbola and these lines: {4, 8584}, {98, 15682}, {115, 10153}, {376, 7607}, {631, 10185}, {1992, 17503}, {2996, 8352}, {3424, 3830}, {3545, 7608}, {3845, 14484}, {5254, 18843}, {5286, 18844}, {5395, 11317}, {5485, 15533}, {7612, 11001}, {11668, 15719}

X(32532) = reflection of X(10153) in X(115)
X(32532) = isogonal conjugate of X(15655)
X(32532) = antigonal conjugate of X(10153)
X(32532) = antitomic conjugate of X(10153)
X(32532) = isotomic conjugate of the anticomplement of X(15534)
X(32532) = antipode of X(10153) in the Kiepert hyperbola

X(32533) = X(5)X(14528)∩X(6)X(546)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32533) lies on the Jerabek hyperbola and these lines: {5, 14528}, {6, 546}, {30, 3532}, {54, 3091}, {64, 3627}, {66, 18383}, {67, 18569}, {68, 13851}, {69, 9927}, {70, 18394}, {74, 3146}, {895, 15083}, {1352, 13622}, {1899, 3521}, {3090, 3431}, {3426, 5076}, {3519, 18404}, {3529, 11270}, {3839, 10116}, {5486, 18553}, {10113, 11744}, {10293, 31725}, {10297, 15316}, {10594, 18532}, {12102, 22334}, {13754, 15077}, {14542, 18390}, {15740, 18918}, {16625, 18376}, {17538, 20421}, {21400, 25738}

X(32533) = isogonal conjugate of X(32534)
X(32533) = anticomplement of X(33556)

X(32534) = ISOGONAL CONJUGATE OF X(32533)

As a point on the Euler line, X(32534) has Shinagawa coefficients (-6*F, E+6*F).

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32534) lies on these lines: {2, 3}, {54, 9786}, {64, 11468}, {74, 1498}, {110, 12163}, {112, 5023}, {154, 6241}, {155, 11449}, {184, 13382}, {185, 9707}, {187, 8743}, {232, 5206}, {340, 9723}, {1151, 10881}, {1152, 10880}, {1181, 11464}, {1192, 5890}, {1199, 3431}, {1204, 10282}, {1350, 19128}, {1495, 3357}, {1511, 13148}, {1614, 1620}, {1829, 17502}, {1843, 17508}, {1870, 5204}, {1968, 15513}, {1974, 14810}, {1986, 11412}, {1990, 8553}, {1993, 12038}, {2207, 5210}, {2351, 5963}, {2904, 16879}, {2931, 9938}, {3043, 15040}, {3092, 6411}, {3093, 6412}, {3567, 11425}, {3580, 12118}, {3581, 16266}, {5013, 10312}, {5085, 6403}, {5217, 6198}, {5237, 8740}, {5238, 8739}, {5410, 6450}, {5411, 6449}, {5621, 15581}, {5702, 8573}, {6030, 15086}, {6759, 21663}, {7592, 11438}, {7689, 11441}, {8541, 20190}, {8744, 8778}, {8907, 12893}, {8960, 9682}, {10193, 13419}, {10606, 12290}, {10619, 23358}, {10632, 11481}, {10633, 11480}, {10990, 13289}, {11204, 11381}, {11270, 12315}, {11363, 31663}, {11440, 18451}, {11550, 25563}, {12112, 13093}, {12278, 14852}, {12279, 12292}, {12383, 12429}, {13481, 19189}, {13558, 16080}, {15036, 15472}, {15578, 20987}, {16655, 23328}, {17845, 25739}, {18396, 26917}, {18445, 32171}, {18474, 20191}, {19467, 26879}, {20427, 32111}

X(32534) = reflection of X(3) in X(23323)
X(32534) = isogonal conjugate of X(32533)
X(32534) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,4,35477), (3, 7387, 2071), (4, 3515, 24), (14865, 23040, 11410)

X(32535) = X(3)X(1487)∩X(4)X(1493)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32535) lies on these lines: {3, 1487}, {4, 1493}, {20, 3459}, {3853, 15619}, {17507, 20424}

X(32536) = X(4)X(137)∩X(5)X(27684)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32536) lies on these lines: {4, 137}, {5, 27684}, {30, 13856}, {128, 24573}, {381, 30484}, {539, 23337}, {546, 20413}, {3853, 5893}, {8146, 28341}, {15307, 31376}, {15619, 17507}, {18807, 28237}, {20120, 25150}

X(32536) = reflection of X(i) in X(j) for these (i,j): (13856, 31879), (18016, 23338)

X(32537) = X(5)X(519)∩X(7)X(8)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32537) lies on these lines: {1, 5123}, {5, 519}, {7, 8}, {10, 6691}, {145, 11376}, {355, 3880}, {474, 3679}, {517, 32159}, {528, 12640}, {529, 11362}, {946, 5854}, {952, 10915}, {960, 12647}, {1012, 3913}, {1210, 3036}, {1317, 27385}, {1319, 17566}, {1387, 3244}, {1482, 22835}, {1837, 12648}, {2098, 5087}, {2802, 18480}, {3057, 5046}, {3241, 6931}, {3337, 4668}, {3621, 25568}, {3625, 5855}, {3632, 10827}, {3633, 23708}, {3742, 5554}, {3811, 12645}, {3838, 9578}, {3893, 5086}, {4134, 15862}, {4297, 32157}, {4669, 24391}, {4677, 11523}, {4678, 24477}, {4861, 7504}, {5048, 11681}, {5258, 19525}, {5587, 10912}, {5795, 15254}, {5837, 15481}, {5844, 21077}, {6735, 10944}, {6738, 15570}, {6871, 31145}, {7483, 10039}, {7982, 11236}, {7991, 28534}, {8256, 10106}, {8715, 28204}, {9037, 31785}, {9956, 22837}, {11567, 22836}, {12641, 13271}, {12672, 12751}, {13463, 19925}, {15888, 25962}, {20323, 25005}, {21627, 32426}

X(32537) = midpoint of X(i) and X(j) for these lines: {i,j}: {8, 32049}, {3632, 12635}, {3811, 12645}, {3913, 5881}, {12641, 13271}
X(32537) = reflection of X(i) in X(j) for these (i,j): (4297, 32157), (11260, 10), (13463, 19925), (22837, 9956)
X(32537) = {X(8), X(5252)}-harmonic conjugate of X(5836)

X(32538) = X(381)X(7620)∩X(3734)X(16509)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32538) lies on these lines: {381, 7620}, {3734, 16509}, {5485, 18907}

X(32539) = X(4)X(52)∩X(125)X(1147)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29016.

X(32539) lies on these lines: {4, 52}, {5, 32166}, {125, 1147}, {155, 10255}, {539, 18281}, {1899, 12038}, {3357, 17702}, {3448, 12118}, {3564, 10224}, {5449, 9306}, {5504, 23294}, {6696, 11250}, {12163, 18565}, {13383, 32145}, {15316, 19477}

X(32539) = reflection of X(32145) in X(13383)
X(32539) = {X(68), X(11442)}-harmonic conjugate of X(9927)

X(32540) = X(3)X(76)∩X(6)X(14251)

X(32540) lies on the cubic K1104 and these on lines {3, 76}, {6, 14251}, {32, 512}, {39, 15630}, {248, 30496}, {446, 1503}, {1634, 19120}, {1910, 2053}, {3095, 13137}, {3224, 14601}, {5025, 10342}, {17932, 19597}

X(32540) = X(i)-isoconjugate of X(j) for these (i,j): {240, 8858}, {1959, 3225}
X(32540) = crosssum of X(i) and X(j) for these (i,j): {511, 5976}, {2679, 2799}
X(32540) = crossdifference of every pair of points on line {325, 2491}
X(32540) = barycentric product X(i)*X(j) for these lines: {i,j}: {98, 3229}, {698, 1976}, {1910, 2227}
X(32540) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {248, 8858}, {1976, 3225}, {3229, 325}, {9429, 3569}, {14601, 699}
X(32540) = {X(98),X(8870)}-harmonic conjugate of X(14382)

X(32541) = X(3)X(3224)∩X(3360)X(18829)

X(32541) lies on the cubic K1104 and these lines: {3, 3224}, {3360, 18829}, {8789, 10131}

X(32541) = barycentric product X(9468)*X(9493)
X(32541) = barycentric quotient X(9493) / X(14603)

X(32542) = X(3)X(1625)∩X(24)X(2698)

X(32542) lies on the cubics K389 and K1104, and on these lines: {3, 1625}, {24, 2698}, {3148, 14251}, {3406, 8743}

X(32542) = isogonal conjugate of the anticomplement of X(14382)
X(32542) = X(i)-isoconjugate of X(j) for these (i,j): {401, 1581}, {1916, 1955}, {1934, 1971}
X(32542) = barycentric product X(i)*X(j) for these lines: {i,j}: {385, 1987}, {419, 14941}, {1580, 1956}, {1691, 1972}
X(32542) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {419, 16089}, {1691, 401}, {1933, 1955}, {1956, 1934}, {1972, 18896}, {1987, 1916}, {5027, 6130}, {14602, 1971}

X(32543) = (name pending)

X(32543) lies on the cubic K1104 and this line: {3360, 32514}

X(32543) = isogonal conjugate of X(32548)

X(32544) = X(32)X(99)∩X(880)X(1691)

X(32544) lies on the cubics K444 and K1013, and on these lines: {32, 99}, {880, 1691}, {14602, 17941}

X(32544) = X(1691)-cross conjugate of X(699)
X(32544) = X(i)-isoconjugate of X(j) for these (i,j): {694, 2227}, {698, 1967}, {1581, 3229}
X(32544) = cevapoint of X(1691) and X(4027)
X(32544) = barycentric product X(i)*X(j) for these lines: {i,j}: {385, 3225}, {419, 8858}, {699, 3978}
X(32544) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {385, 698}, {699, 694}, {1580, 2227}, {1691, 3229}, {3225, 1916}

X(32545) = X(3)X(2966)∩X(4)X(32)

X(32545) lies on the cubics K444, K629, K790, and on these lines: {3, 2966}, {4, 32}, {20, 9218}, {54, 826}, {194, 17974}, {1316, 14265}, {1975, 17932}, {2065, 9307}, {2715, 11257}, {3398, 14382}, {14251, 18858}

X(32545) = X(i)-isoconjugate of X(j) for these (i,j): {240, 14941}, {511, 1956}, {1755, 1972}, {1959, 1987}
X(32545) = trilinear pole of line {1971, 6130}
X(32545) = barycentric product X(i)*X(j) for these lines: {i,j}: {98, 401}, {248, 16089}, {290, 1971}, {1821, 1955}, {2966, 6130}
X(32545) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {98, 1972}, {248, 14941}, {401, 325}, {1910, 1956}, {1955, 1959}, {1971, 511}, {1976, 1987}, {6130, 2799}

X(32546) = (name pending)

X(32546) lies on the cubic K444 and on no line X(i)X(j) for 0 < i < j < 32546.

X(32547) = X(2)X(9292)∩X(69)X(32529)

X(32547) lies on these lines: {2, 9292}, {69, 32529}, {76, 512}, {110, 32445}, {699, 3224}, {1297, 11440}, {1503, 12272}, {1968, 2001}, {2387, 7802}, {2698, 10104}, {2979, 7750}, {3060, 7823}, {3111, 7940}, {3491, 3552}, {3852, 12220}, {4173, 7833}, {5167, 7793}, {5640, 7745}, {6787, 7746}, {7860, 14962}, {7904, 7998}, {9863, 12111}, {11459, 32151}, {15270, 26881}, {19597, 32464}

X(32547) = reflection of X(12111) in X(9863)
X(32547) = crosspoint of X(3224) and X(30496)
X(32547) = crosssum of X(194) and X(3552)

X(32548) = X(2)X(3224)∩X(69)X(698)

X(32548) lies on these lines: {2, 3224}, {69, 698}, {76, 9493}, {315, 1899}, {5207, 32529}, {6337, 22089}, {6374, 9492}, {7785, 13518}, {10453, 17137}, {17138, 21281}

X(32548) = isogonal conjugate of X(32543)
X(32548) = anticomplement of X(3224)
X(32548) = X(6374)-Ceva conjugate of X(2)
X(32548) = isotomic conjugate of cyclocevian conjugate of X(38262)
X(32548) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 20081}, {2, 21299}, {6, 21223}, {31, 2998}, {81, 17157}, {88, 23633}, {100, 20979}, {162, 2451}, {190, 20983}, {194, 8}, {651, 23655}, {660, 23656}, {662, 669}, {673, 20863}, {799, 3221}, {897, 20977}, {1424, 145}, {1613, 192}, {1740, 2}, {3186, 5905}, {3221, 21220}, {4598, 23464}, {6374, 6327}, {7075, 144}, {11325, 21216}, {17082, 7}, {17149, 69}, {18837, 315}, {20332, 20464}, {20794, 6360}, {20910, 3448}, {21080, 2895}, {21191, 149}, {21877, 1654}, {22028, 1330}, {23301, 21221}, {23503, 25054}, {23572, 9263}, {23807, 150}, {27644, 3223}

X(32549) = X(5)X(2883)∩X(546)X(14374)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29027.

X(32549) lies on these lines: {5, 2883}, {546, 14374}, {1113, 32110}, {1312, 13754}, {1313, 14915}, {1346, 9730}, {1347, 16194}, {1531, 10751}, {2575, 6699}

X(32550) = X(5)X(2883)∩X(546)X(14375)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29027.

X(32550) lies on these lines: {5, 2883}, {546, 14375}, {1114, 32110}, {1312, 14915}, {1313, 13754}, {1346, 16194}, {1347, 9730}, {1531, 10750}, {2574, 6699}

X(32551) = COMPLEMENT OF X(15345)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29027.

X(32551) lies on these lines: {2, 3459}, {5, 51}, {140, 6592}, {252, 6150}, {1493, 19553}, {1510, 20327}, {3628, 13856}, {5501, 20414}, {8254, 24385}, {10285, 14143}, {14051, 24306}, {14142, 18400}, {15957, 31879}, {18282, 32428}

X(32551) = midpoint of X(i) and X(j) for these lines: {i,j}: {10285, 14143}, {15345, 25043}
X(32551) = reflection of X(i) in X(j) for these (i,j): (13856, 3628), (18016, 140), (20414, 5501), (31879, 15957)
X(32551) = complement of X(15345)
X(32551) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 25043, 15345), (5, 21230, 16336)

X(32552) = COMPLEMENT OF X(6777)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29029.

X(32552) lies onthese lines: {2, 6777}, {3, 22509}, {6, 6299}, {13, 148}, {14, 6669}, {69, 6582}, {98, 635}, {99, 299}, {114, 630}, {115, 396}, {140, 25560}, {141, 542}, {385, 533}, {532, 7813}, {621, 25236}, {623, 6771}, {624, 5613}, {633, 5982}, {2782, 25559}, {3412, 20394}, {3642, 12188}, {3643, 9862}, {5460, 6722}, {5478, 22515}, {5859, 22570}, {5981, 6115}, {6114, 7792}, {6295, 11646}, {6672, 6782}, {6770, 22687}, {6773, 21156}, {6780, 31710}, {8594, 8597}, {9113, 9760}, {9114, 20094}, {10645, 14904}, {11602, 20377}, {14136, 16529}, {15561, 22507}

X(32552) = reflection of X(i) in X(j) for these (i,j): (14, 6669), (618, 619), (6782, 6672), (11602, 20377), (25560, 140)
X(32552) = complement of X(6777)
X(32552) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5464, 6778, 99), (5613, 22689, 624)

X(32553) = COMPLEMENT OF X(6778)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29029.

X(32553) lies these lines: {2, 6778}, {3, 22507}, {6, 6298}, {13, 6670}, {14, 148}, {69, 6295}, {98, 636}, {99, 298}, {114, 629}, {115, 395}, {140, 25559}, {141, 542}, {385, 532}, {533, 7813}, {622, 25235}, {623, 5617}, {624, 6774}, {634, 5983}, {2782, 25560}, {3411, 20395}, {3642, 9862}, {3643, 12188}, {5459, 6722}, {5479, 22515}, {5858, 22568}, {5980, 6114}, {6115, 7792}, {6582, 11646}, {6671, 6783}, {6770, 21157}, {6773, 22689}, {6779, 31709}, {8595, 8597}, {9112, 9762}, {9116, 20094}, {10646, 14905}, {11603, 20378}, {14137, 16530}, {15561, 22509}

X(32553) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 22507}, {14, 616}, {99, 6777}, {622, 25235}, {5858, 22568}, {5979, 22998}
X(32553) = reflection of X(i) in X(j) for these (i,j): (13, 6670), (619, 618), (6783, 6671), (11603, 20378), (25559, 140)
X(32553) = complement of X(6778)
X(32553) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5463, 6777, 99), (5617, 22687, 623)

X(32554) = MIDPOINT OF X(104) AND X(3436)

See Antreas Hatzipolakis and César Lozada, Hyacinthos 29029.

X(32554) lies these lines: {3, 119}, {11, 517}, {12, 21154}, {46, 8068}, {56, 6713}, {78, 952}, {100, 6827}, {104, 3436}, {153, 6926}, {1385, 10956}, {1537, 4187}, {2478, 12775}, {2800, 21616}, {3826, 6980}, {4413, 6923}, {5533, 30323}, {5690, 18802}, {5840, 6928}, {5854, 19914}, {6174, 28459}, {6667, 7680}, {6842, 11231}, {6863, 31246}, {6948, 10728}, {6961, 11681}, {6963, 10698}, {6971, 7681}, {6978, 31272}, {7491, 24466}, {8256, 26470}, {10265, 24391}, {10955, 26287}, {10958, 26285}, {12611, 31788}, {12616, 18254}, {15017, 30503}, {15528, 21077}, {22799, 31775}

X(32554) = midpoint of X(i) and X(j) for these lines: {i,j}: {104, 3436}, {10310, 12764}
X(32554) = reflection of X(i) in X(j) for these (i,j): (56, 6713), (119, 1329), (18802, 5690)

X(32555) = X(1)X(372)∩X(3)X(9)

See Vu Thanh Tung and César Lozada, Hyacinthos 29031.

In the configuration at X(6212), the lines I_AJ_A, I_BJ_B, I_CJ_C concur in X(32555), which is also the perspector of A'B'C' and the excentral triangle. (Randy Hutson, June 7, 2019)

X(32555) lies on the cubic K414 and these lines: {1, 372}, {2, 31540}, {3, 9}, {7, 31541}, {20, 30412}, {37, 1152}, {40, 30556}, {41, 30400}, {43, 1685}, {44, 1151}, {45, 6410}, {48, 19067}, {57, 16432}, {63, 16440}, {101, 31564}, {165, 6212}, {169, 31563}, {223, 13388}, {371, 1743}, {487, 4416}, {488, 3912}, {515, 7090}, {573, 31438}, {1100, 3594}, {1123, 31533}, {1124, 7074}, {1449, 3312}, {1587, 5393}, {2183, 19068}, {2951, 31545}, {3218, 21568}, {3219, 21567}, {3247, 6398}, {3305, 16441}, {3306, 21492}, {3311, 16670}, {3523, 30413}, {3576, 30557}, {3592, 16669}, {3723, 6438}, {3731, 6396}, {3911, 8957}, {3928, 21561}, {3929, 21560}, {3973, 6200}, {4292, 30324}, {4297, 31595}, {4357, 11291}, {5405, 13935}, {5437, 21548}, {6204, 15803}, {6351, 6460}, {6409, 16885}, {6411, 15492}, {6412, 16814}, {6420, 16667}, {6426, 16777}, {6430, 16672}, {6431, 16671}, {6432, 16666}, {6434, 16677}, {6450, 16676}, {6454, 16673}, {6469, 16674}, {6684, 14121}, {7308, 16433}, {9583, 13332}, {10164, 31594}, {11292, 17353}, {13411, 30325}, {21566, 27065}, {21569, 27003}

X(32555) = (excentral)-isogonal conjugate of-X(6213)
X(32555) = X(485)-of-excentral triangle
X(32555) = X(488)-of-1st circumperp triangle
X(32555) = X(641)-of-6th mixtilinear triangle
X(32555) = X(6289)-of-hexyl triangle
X(32555) = X(12257)-of-2nd circumperp triangle
X(32555) = X(40)-Ceva conjugate of X(32556)
X(32555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 9, 32556), (20, 30412, 31562), (84, 198, 32556), (610, 1490, 32556), (6502, 7133, 1)

X(32556) = X(1)X(371)∩X(3)X(9)

X(32556) lies on the cubic K414, the Kiepert circumhyperbola of the excentral triangle, and on these lines: {1, 371}, {2, 31541}, {3, 9}, {7, 31540}, {20, 30413}, {37, 1151}, {40, 30557}, {41, 30401}, {43, 1686}, {44, 1152}, {45, 6409}, {48, 19068}, {57, 16433}, {63, 16441}, {101, 31563}, {165, 6213}, {169, 31564}, {223, 13389}, {372, 1743}, {487, 3912}, {488, 4416}, {505, 3645}, {515, 14121}, {572, 31438}, {846, 9582}, {950, 8957}, {1100, 3592}, {1335, 7074}, {1336, 31532}, {1449, 3311}, {1588, 5405}, {2183, 19067}, {2951, 31544}, {3218, 21565}, {3219, 21566}, {3247, 6221}, {3305, 16440}, {3306, 21553}, {3312, 16670}, {3523, 30412}, {3576, 30556}, {3594, 16669}, {3723, 6437}, {3731, 6200}, {3928, 21558}, {3929, 21559}, {3973, 6396}, {4292, 30325}, {4297, 31594}, {4357, 11292}, {5393, 9540}, {5437, 21547}, {6203, 15803}, {6352, 6459}, {6410, 16885}, {6411, 16814}, {6412, 15492}, {6419, 16667}, {6425, 16777}, {6429, 16672}, {6431, 16666}, {6432, 16671}, {6433, 16677}, {6449, 16676}, {6453, 16673}, {6468, 16674}, {6684, 7090}, {7308, 16432}, {10164, 31595}, {10436, 21909}, {11291, 17353}, {13411, 30324}, {21564, 27003}, {21567, 27065}

X(32556) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9, 32555}, {20, 30413, 31561}, {84, 198, 32555}, {610, 1490, 32555}
X(32556) = excentral-isogonal conjugate of X(6212)
X(32556) = X(485)-of-excentral-triangle
X(32556) = X(487)-of-1st-circumperp-triangle
X(32556) = X(12257)-of-2nd-circumperp-triangle
X(32556) = X(642)-of-6th-mixtilinear-triangle
X(32556) = X(6290)-of-hexyl-triangle
X(32556) = X(i)-Ceva conjugate of X(j) for these (i,j): {40, 32555}, {30557, 1}

X(32557) = X(1)X(6702)∩X(2)X(2802)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29037.

X(32557) lies these lines: {1, 6702}, {2, 2802}, {3, 16174}, {5, 11715}, {10, 1387}, {11, 214}, {80, 3616}, {100, 3624}, {104, 8227}, {124, 29008}, {149, 5550}, {499, 3878}, {515, 23513}, {516, 21154}, {528, 19883}, {547, 551}, {631, 14217}, {758, 3582}, {946, 6713}, {1145, 3634}, {1317, 3636}, {1320, 1698}, {1385, 6246}, {1656, 12737}, {2771, 3742}, {2800, 5883}, {2801, 5817}, {2829, 3817}, {3035, 14150}, {3036, 3244}, {3057, 20107}, {3086, 3874}, {3090, 12751}, {3617, 26726}, {3622, 7972}, {3626, 25416}, {3698, 17652}, {3754, 12758}, {3825, 8068}, {3892, 10072}, {4973, 11813}, {4996, 5259}, {5083, 11375}, {5248, 10090}, {5439, 17638}, {5443, 11570}, {5840, 10165}, {5901, 12619}, {6265, 30143}, {6681, 30384}, {7968, 8988}, {7969, 13976}, {7987, 10724}, {9624, 10698}, {10057, 10584}, {10058, 23708}, {10265, 11729}, {10527, 14740}, {10707, 15015}, {11108, 22560}, {11263, 12611}, {11376, 15558}, {11717, 24222}, {12019, 15808}, {12515, 18493}, {12532, 18398}, {12740, 30147}, {13205, 16408}, {13624, 22938}, {13902, 19077}, {13959, 19078}, {13996, 31253}, {15528, 31803}, {15950, 20118}, {17636, 20104}, {17724, 23869}, {18857, 24042}, {19878, 31235}, {20418, 21635}

X(32557) = midpoint of X(i) and X(j) for these lines: {i,j}: {2, 16173}, {10707, 15015}
X(32557) = centroid of X(1)X(10)X(11)
X(32557) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 6702, 15863}, {1, 31272, 6702}, {11, 1125, 214}, {1387, 6667, 10}, {5886, 10199, 5883}, {5901, 12619, 25485}, {11813, 15325, 4973}, {18240, 18254, 3874}, {19862, 21630, 3035}

X(32558) = X(2)X(2802)∩X(8)X(1387)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29037.

X(32558) lies these lines: {2, 2802}, {8, 1387}, {11, 2476}, {20, 16174}, {80, 3622}, {100, 5550}, {145, 6702}, {149, 1125}, {153, 8227}, {214, 31418}, {952, 5055}, {962, 6713}, {1145, 19877}, {1320, 6667}, {2771, 5886}, {2829, 9779}, {3035, 9802}, {3036, 20050}, {3090, 12737}, {3091, 11715}, {3523, 14217}, {3623, 15863}, {3624, 21630}, {3634, 12653}, {3636, 9897}, {3890, 6797}, {4323, 12832}, {4678, 26726}, {5047, 22560}, {5056, 12751}, {5180, 15325}, {5541, 19862}, {5901, 12247}, {9624, 10265}, {9778, 21154}, {9803, 11729}, {9809, 20418}, {9955, 12248}, {10588, 20586}, {10595, 12619}, {11373, 27529}, {11376, 25414}, {12531, 20057}, {12532, 18240}, {13205, 17531}, {15558, 18220}

X(32558) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 3616, 6224}, {1320, 6667, 9780}, {1387, 31272, 8}

Mutual polar conics: X(32559)-X(32588)

X(32559) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND ANDROMEDA

X(32559) lies on these lines: {1,738}, {2,3677}, {37,32560}, {3666,21446}

X(32560) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND ANTLIA

X(32560) lies on these lines: {1,728}, {2,479}, {37,32559}, {10582,21450}

X(32561) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND APUS

X(32561) lies on these lines: {3,169}, {6,255}, {9,35}, {21,6554}, {32,16588}, {37,8573}, {41,55}, {56,17451}, {71,11434}, {101,10267}, {198,23843}, {218,11507}, {219,584}, {384,26068}, {411,5819}, {672,11509}, {958,1146}, {1376,26036}, {1466,5022}, {2082,26357}, {2170,10966}, {2178,7742}, {2183,15592}, {2225,7085}, {2246,5217}, {2478,6506}, {2911,15830}, {3208,8668}, {3295,6603}, {3560,5179}, {3730,11248}, {5251,23058}, {7367,8606}, {8069,16601}, {9310,11510}, {10306,21872}, {11496,17747}, {12329,23851}, {16367,30854}, {16865,27541}

X(32561) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 15288, 1212), (1802, 8012, 220)

X(32562) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS BROCARD

X(32562) lies on these lines: {574,8373}, {1151,1584}

X(32563) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS INNER

X(32563) lies on these lines: {2,6568}, {110,32072}, {574,32570}, {6221,8854}, {6407,32564}

X(32564) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS INNER TANGENTIAL

X(32564) lies on the line {6407,32563}

X(32565) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS SECONDARY CENTRAL

X(32565) lies on these lines: {1152,32568}, {8407,10133}, {22112,32572}

X(32566) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS 1st SECONDARY TANGENTS

X(32566) lies on the line {1151,10133}

X(32567) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS 2nd SECONDARY TANGENTS

X(32567) lies on these lines: {22,6480}, {372,1600}, {3156,6431}

X(32568) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS TANGENTS

X(32568) lies on these lines: {2,7598}, {3,493}, {6,6216}, {22,6200}, {110,11199}, {154,1151}, {371,1599}, {574,20859}, {1152,32565}, {1501,9675}, {1583,15883}, {3167,6221}, {6413,8939}, {6560,11209}, {7484,9600}, {8216,21642}, {8414,10133}, {13882,32588}, {19358,26347}

X(32568) = isogonal conjugate of X(18819)
X(32568) = {X(3), X(493)}-harmonic conjugate of X(8577)

X(32569) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) BROCARD

X(32569) lies on these lines: {574,8374}, {1152,1583}

X(32570) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) INNER

X(32570) lies on these lines: {2,6569}, {110,32073}, {574,32563}, {6398,8855}, {6408,32571}

X(32571) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) INNER TANGENTIAL

X(32571) lies on the line {6408,32570}

X(32572) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) SECONDARY CENTRAL

X(32572) lies on these lines: {1151,32575}, {8400,10132}, {22112,32565}

X(32573) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) 1st SECONDARY TANGENTS

X(32573) lies on the line {1152,10132}

X(32574) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) 2nd SECONDARY TANGENTS

X(32574) lies on these lines: {22,6481}, {371,1599}, {3155,6432}

X(32575) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND LUCAS(-1) TANGENTS

X(32575) lies on these lines: {2,7599}, {3,494}, {6,6397}, {22,6396}, {110,32074}, {154,1152}, {372,1600}, {574,20859}, {1151,32572}, {1584,15884}, {3167,6398}, {6414,8943}, {6561,11210}, {8219,21643}, {8406,10132}, {13934,32587}

X(32575) = isogonal conjugate of X(18820)
X(32575) = {X(3), X(494)}-harmonic conjugate of X(8576)

X(32576) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND MALFATTI

X(32576) lies on this line: {258,483}

X(32576) = X(289)-isoconjugate of X(557)
X(32576) = barycentric product X(236)*X(483)
X(32576) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {7010, 21456}, {7014, 1488}

X(32577) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 3rd MIXTILINEAR

X(32577) lies on these lines: {1,88}, {3,1149}, {8,9350}, {25,8278}, {31,56}, {36,3915}, {38,19861}, {41,1015}, {42,3304}, {57,15839}, {200,7963}, {220,23649}, {227,1319}, {238,28370}, {355,28096}, {515,28018}, {551,16393}, {602,22765}, {604,17053}, {614,1420}, {748,2975}, {756,8583}, {899,12513}, {944,28074}, {956,27627}, {958,8688}, {976,17614}, {995,1203}, {999,1066}, {1064,16203}, {1125,5192}, {1253,10966}, {1357,16945}, {1385,19548}, {1388,17054}, {1450,26437}, {1458,15287}, {1477,9439}, {1496,22767}, {1647,1837}, {1739,22837}, {2209,20470}, {2267,8610}, {2275,9259}, {2650,3333}, {3086,21935}, {3120,11376}, {3303,17782}, {3576,28011}, {3616,4195}, {3720,16405}, {3752,20323}, {3756,10950}, {3890,17596}, {3953,30144}, {3976,4511}, {4251,9336}, {4298,24725}, {4310,24558}, {4694,22836}, {4861,24174}, {5193,10571}, {5288,17749}, {5303,8616}, {5450,32486}, {5484,25960}, {5731,28016}, {6762,21805}, {9619,21808}, {9708,28257}, {10165,28027}, {10459,17124}, {11260,16610}, {11682,18193}, {12635,17449}, {14986,26050}, {16466,23070}, {21842,30117}, {22437,23057}, {26561,30816}

X(32577) = isogonal conjugate of the isotomic conjugate of X(4862)
X(32577) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 1054, 14923), (1, 4855, 3722), (1, 5253, 750)

X(32578) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 4th MIXTILINEAR

X(32578) lies on these lines: {9,100}, {31,15263}, {41,55}, {57,17451}, {165,169}, {200,15838}, {672,1405}, {899,6181}, {1155,1212}, {1253,14936}, {2078,9310}, {2280,2323}, {3730,5537}, {5745,24596}

X(32578) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (55, 8012, 6602), (1212, 15855, 1155)

X(32579) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND MONTESDEOCA-HUNG

X(32579) lies on these lines: {}

X(32580) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND MOSES-HUNG

X(32580) lies on these lines: {4,6}, {37,115}, {3553,8818}, {6354,8736}

X(32581) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 2nd ORTHOSYMMEDIAL

X(32581) lies on these lines: {4,83}, {5,26224}, {25,14535}, {66,8801}, {112,251}, {406,27005}, {475,27067}, {1594,28724}, {1799,8889}, {5094,10130}, {5523,10549}, {7507,10547}, {7770,12220}

X(32581) = polar conjugate of X(23297)

X(32582) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 1st PAMFILOS-ZHOU

X(32582) lies on these lines: {2,31546}, {165,16441}, {1621,5314}

X(32583) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 3rd PARRY

X(32583) lies on these lines: {2,10558}, {110,249}, {111,352}, {323,895}, {647,9216}, {892,5466}, {1296,15406}, {2421,9186}, {2434,2444}, {3292,15899}, {3906,9146}, {5968,15066}, {6137,9202}, {6138,9203}, {9124,9178}, {9145,17414}, {9872,10510}, {10989,14833}, {11215,13241}, {15398,23061}

X(32583) = midpoint of X(9872) and X(10510)
X(32583) = isogonal conjugate of X(23287)
X(32583) = trilinear pole of the line {574, 8542}
X(32583) = homothetic center of ABC and 3rd Parry of 3rd Parry triangle
X(32583) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 10559, 10558), (2, 10560, 21460), (10560, 21460, 10558)

X(32584) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND SCHROETER

X(32584) lies on the line {115,523}

X(32585) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND INNER TRI-EQUILATERAL

X(32585) lies on the Jerabek hyperbola and these lines: {2,10639}, {3,10661}, {4,15}, {6,3132}, {16,54}, {61,1173}, {62,13472}, {64,10675}, {65,7051}, {67,32301}, {68,10634}, {69,11515}, {74,3166}, {110,10640}, {184,10979}, {216,21648}, {290,32036}, {1176,11516}, {2963,3458}, {2992,19779}, {3131,30402}, {3431,10646}, {3527,11485}, {5238,16835}, {5352,13452}, {6145,32397}, {8795,19190}, {11081,11139}, {11144,11420}, {11421,14170}, {11481,14528}, {21647,22052}, {22466,22974}

X(32585) = isogonal conjugate of X(473)
X(32585) = isotomic conjugate of the polar conjugate of X(21461)
X(32585) = anticomplement of the complementary conjugate of X(465)
X(32585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (15, 8837, 10632), (184, 10979, 32586)

X(32586) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND OUTER TRI-EQUILATERAL

X(32586) lies on the Jerabek hyperbola and these lines: {2,10640}, {3,10662}, {4,16}, {6,3131}, {15,54}, {61,13472}, {62,1173}, {64,10676}, {65,10637}, {67,32302}, {68,10635}, {69,11516}, {74,3165}, {110,10639}, {184,10979}, {216,21647}, {290,32037}, {1176,11515}, {2963,3457}, {2992,11131}, {3132,30403}, {3431,10645}, {3527,11486}, {5237,16835}, {5351,13452}, {6145,32398}, {8795,19191}, {11143,11421}, {11420,14169}, {11480,14528}, {21648,22052}, {22466,22975}

X(32586) = isogonal conjugate of X(472)
X(32586) = isotomic conjugate of the polar conjugate of X(21462)
X(32586) = anticomplement of the complementary conjugate of X(466)
X(32586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (16, 8839, 10633), (184, 10979, 32585)

X(32587) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 2nd INNER-VECTEN

As a point on the Euler line, X(32587) has Shinagawa coefficients (F, E+F-2*S).

X(32587) lies on these lines: {2,3}, {51,12299}, {69,24243}, {136,5408}, {184,13749}, {275,14238}, {486,494}, {488,11395}, {490,12172}, {591,8754}, {615,8564}, {640,8946}, {1249,19041}, {1322,1899}, {1351,13439}, {1588,11245}, {1853,23261}, {2052,14231}, {2969,13387}, {2979,6400}, {3070,12232}, {3917,6406}, {5409,6290}, {5591,26376}, {6414,13960}, {6561,8940}, {6747,11474}, {7140,13386}, {11090,14593}, {11550,13748}, {12601,13428}, {13429,13951}, {13934,32575}, {14230,23292}

X(32587) = polar conjugate of the isogonal conjugate of X(1505)
X(32587) = anticomplement of X(8964)
X(32587) = X(22553)-of-4th tri-squares triangle, when ABC is obtuse
X(32587) = X(22554)-of-4th tri-squares triangle, when ABC is acute
X(32587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 427, 32588), (4, 1586, 25), (4, 3128, 427), (4, 5200, 428)

X(32588) = CENTER OF THE MUTUAL POLAR CONIC OF THESE TRIANGLES: ABC AND 2nd OUTER-VECTEN

As a point on the Euler line, X(32587) has Shinagawa coefficients (F, E+F+2*S).

X(32588) lies on these lines: {2,3}, {51,12298}, {69,24244}, {136,5409}, {184,13748}, {275,14234}, {485,493}, {487,11394}, {489,12171}, {590,8563}, {639,8948}, {1249,19042}, {1321,1899}, {1351,13428}, {1587,11245}, {1853,23251}, {1991,8754}, {2052,14245}, {2969,13386}, {2979,6239}, {3071,12231}, {3917,6291}, {5408,6289}, {5590,26375}, {6413,8966}, {6560,8944}, {6564,8956}, {6747,11473}, {7140,13387}, {8976,13440}, {11091,14593}, {11550,13749}, {12602,13439}, {13882,32568}, {14233,23292}

X(32588) = polar conjugate of the isogonal conjugate of X(1504)
X(32588) = X(15891)-of-3rd outer-Vecten triangle
X(32588) = X(22553)-of-3rd tri-squares triangle
X(32588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 427, 32587), (4, 1585, 25), (4, 3535, 5200)

X(32589) = SS( S → -S) of X(8954)

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32589) lies on these lines: {1, 32591}, {3, 6}, {24, 6414}, {155, 10960}, {485, 6810}, {486, 1586}, {590, 8955}, {1075, 3069}, {1600, 26922}, {5562, 8963}, {6413, 7592}, {6565, 8887}, {6642, 10962}, {8855, 15199}, {10880, 26920}

X(32590) = X(1)X(372)∩X(4)X(48)

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32590) lies on these lines: {1, 372}, {4, 48}, {41, 1588}, {101, 31562}, {572, 31561}, {604, 1587}, {610, 6212}, {637, 20769}, {1745, 2067}, {2066, 3362}, {2174, 3071}, {2286, 3093}, {3070, 7113}, {3092, 7124}, {5709, 19215}, {7330, 19216}

X(32591) = ISOGONAL CONJUGATE OF X(32590)

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32591) lies on these lines: {1, 32589}, {1745, 6212}

X(32592) = X(1)X(371)∩X(4)X(48)

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32592) lies on these lines: {1, 371}, {4, 48}, {41, 1587}, {101, 31561}, {572, 31562}, {604, 1588}, {610, 6213}, {638, 20769}, {1745, 6502}, {2174, 3070}, {2286, 3092}, {3071, 7113}, {3093, 7124}, {3362, 5414}, {5709, 19216}, {7330, 19215}

X(32593) = ISOGONAL CONJUGATE OF X(32592)

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32593) lies on these lines: {1, 8954}, {1745, 6213}

X(32594) = X(3)X(8287)∩X(5)X(6)

See Vu Thanh Tung, Vu Quoc My and César Lozada, Hyacinthos 29049.

X(32594) lies on these lines: {3, 8287}, {5, 6}, {368, 18453}, {1736, 1893}, {2478, 25000}, {5221, 5729}, {5706, 14873}, {5740, 6835}

X(32595) = X(3)X(25424)∩X(6)X(1569)

X(32595) lies on the Stammler circle, the cubic K1105, and on these lines: {3,25424}, {6,1569}

X(32596) = X(4)X(3104)∩X(16)X(7709)

X(32596) lies on the cubic K1105 and on these lines: {4, 3104}, {16, 7709}, {98, 3098}, {511, 3180}, {616, 2782}, {3094, 16941}, {5980, 18906}, {9821, 22532}, {11257, 22531}, {12251, 14540}, {16940, 22707}, {31683, 31701}

X(32597) = X(4)X(3105)∩X(15)X(7709)

X(32597) lies on the cubic K1105 and these lines: {4, 3105}, {15, 7709}, {98, 3098}, {511, 3181}, {617, 2782}, {3094, 16940}, {5981, 18906}, {9821, 22531}, {11257, 22532}, {12251, 14541}, {16941, 22708}, {31684, 31702}

X(32598) = X(54)X(511)∩X(2916)X(2931)

X(32598) lies on the cubic K1107 and these lines: {54, 511}, {2916, 2931}, {7488, 29012}, {9019, 19129}, {13564, 32351}\

X(32599) = X(3)X(524)∩X(23)X(542)

X(32599) lies on the cubic K1107 and these lines: {3, 524}, {23, 542}, {30, 16010}, {54, 20190}, {68, 7530}, {74, 511}, {110, 32315}, {182, 323}, {186, 12584}, {399, 32217}, {575, 1199}, {576, 5889}, {1154, 10510}, {1204, 15073}, {1352, 1995}, {1503, 9919}, {2070, 32254}, {2854, 3581}, {2930, 2931}, {3098, 15531}, {3292, 15462}, {5609, 18374}, {5622, 23061}, {5648, 15361}, {5965, 14049}, {6776, 7492}, {6795, 32515}, {7574, 25328}, {8537, 14865}, {8548, 11477}, {9027, 32110}, {9970, 13754}, {9972, 32352}, {10296, 32273}, {10990, 19924}, {11178, 16042}, {11180, 14002}, {12105, 19596}, {12106, 15069}, {15534, 18570}, {20423, 31861}

X(32599) = reflection of X(i) in X(j) for these lines: {i,j}: {323, 182}, {399, 32217}, {1352, 3580}, {2930, 7575}, {5648, 15361}, {7464, 32305}, {7574, 25328}, {10296, 32273}

X(32600) = X(3)X(2916)∩X(74)X(827)

X(32600) lies on the cubic K1107 and on these lines: {3, 2916}, {74, 827}, {141, 12901}, {182, 7689}, {206, 3357}, {511, 7691}, {549, 13289}, {1352, 16013}, {1495, 5888}, {1503, 32401}, {1531, 7550}, {1843, 3520}, {3098, 9019}, {5085, 11999}, {7512, 29323}, {8718, 15030}, {10226, 21167}, {14130, 29317}, {20190, 21637}

X(32600) = reflection of X(1176) in X(5092)

X(32601) = X(4)X(64)∩X(20)X(12164)

X(32601) lies on the cubic K1108 and on these lines: {4, 64}, {20, 12164}, {74, 3090}, {376, 1092}, {511, 3529}, {546, 15431}, {578, 20427}, {631, 11468}, {1204, 6622}, {1620, 2883}, {2777, 18909}, {3357, 8889}, {5878, 6353}, {5925, 6776}, {6225, 22750}, {6240, 20079}, {9825, 11469}, {11456, 17538}, {11457, 15682}, {12244, 15463}, {13347, 15740}, {18931, 22802}, {25712, 32139}

X(32601) = {X(5895),X(18913)}-harmonic conjugate of X(4)

X(32602) = X(20)X(154)∩X(25)X(64)

X(32602) lies on the cubic K1108 and these lines: {20, 154}, {25, 64}, {511, 1498}, {1181, 16105}, {1853, 16656}, {5085, 5893}, {8567, 10117}, {11744, 14528}, {13598, 17813}, {17812, 17818}, {17822, 18535}

X(32602) = reflection of X(64) in X(1192)
X(32602) = {X(9914),X(15811)}-harmonic conjugate of X(64)

X(32603) = X(3)X(3620)∩X(125)X(6353)

X(32603) lies on the cubic K1108 and on these lines: {3, 3620}, {125, 6353}, {185, 14912}, {376, 12283}, {5907, 25406}, {6776, 10606}

X(32604) = X(185)X(14914)∩X(511)X(6391)

X(32604) lies on the cubic K1108) and on these lines: {185, 14914}, {511, 6391}, {11820, 19458}

X(32605) = X(2)X(185)∩X(4)X(3167)

X(32605) lies on the cubics K182, K329, K1108, the Thomson-Gibert-Moses hyperbola, the Feuerbach circumhyperbola of the orthic triangle, and on these lines: {2, 185}, {4, 3167}, {5, 5644}, {6, 3091}, {20, 154}, {25, 15741}, {30, 25712}, {52, 3089}, {110, 3146}, {113, 6193}, {155, 6623}, {193, 235}, {354, 1858}, {648, 6526}, {1498, 7396}, {1986, 3542}, {3090, 5544}, {3522, 6030}, {3523, 3532}, {3541, 22948}, {3546, 13491}, {3574, 3832}, {3839, 14516}, {5056, 18928}, {5068, 11442}, {5643, 15022}, {5646, 10303}, {5888, 11440}, {5889, 16879}, {6053, 14216}, {6225, 11064}, {6247, 30769}, {6622, 12164}, {6816, 19125}, {7398, 12233}, {7400, 7999}, {7487, 22660}, {7712, 11449}, {10151, 15751}, {10565, 16252}, {12174, 16051}, {12250, 15063}\

X(32605) = reflection of X(i) in X(j) for these lines: {i,j}: {20, 27082}, {5889, 16879}
X(32605) = {X(3091),X(11441)}-harmonic conjugate of X(5921)
X(32605) = Thomson-isogonal conjugate of X(9909)
X(32605) = orthic-isogonal conjugate of X(20)
X(32605) = X(4)-Ceva conjugate of X(20)
X(32605) = crosspoint of X(4) and X(6622)
X(32605) = barycentric product X(12164)*X(15466)
X(32605) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6622, 459}, {12164, 1073}

X(32606) = (name pending)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29052.

X(32606) lies on this line: {1, 23279}

X(32607) = X(3)X(125)∩X(4)X(13289)

X(32607) lies on the cubic K1107 and these lines: {3, 125}, {4, 13289}, {24, 7687}, {26, 12295}, {49, 22584}, {54, 74}, {64, 17856}, {110, 5907}, {113, 7526}, {159, 32250}, {184, 5663}, {186, 13851}, {378, 2777}, {399, 19357}, {511, 2071}, {550, 11804}, {569, 14708}, {578, 1986}, {631, 18933}, {974, 1204}, {1092, 12358}, {1112, 11424}, {1147, 7723}, {1177, 12294}, {1181, 10620}, {1350, 32251}, {1425, 10081}, {1511, 15738}, {1593, 10117}, {1594, 19506}, {1658, 10113}, {2935, 3516}, {3043, 12281}, {3047, 12111}, {3270, 10065}, {3357, 17854}, {3448, 19467}, {5504, 5562}, {5621, 11410}, {5650, 15035}, {5890, 16219}, {5972, 7503}, {6146, 10264}, {6240, 32365}, {6467, 11579}, {6644, 23515}, {6723, 17928}, {6759, 12292}, {6776, 32305}, {7488, 10733}, {7728, 14130}, {9934, 11381}, {9970, 21637}, {9976, 15073}, {10114, 20417}, {10605, 15041}, {10606, 17853}, {10619, 18364}, {10681, 11476}, {10682, 11475}, {10721, 14865}, {11473, 13288}, {11474, 13287}, {11562, 12228}, {11801, 15331}, {12084, 16111}, {12133, 15647}, {12163, 19456}, {12168, 24981}, {12317, 18925}, {12412, 15063}, {12605, 23306}, {13358, 16270}, {13417, 15472}, {14049, 32333}, {14448, 17835}, {14585, 14901}, {15059, 22467}, {15081, 21844}, {15089, 22815}, {16010, 19459}, {18379, 20304}, {18563, 19479}

X(32607) = midpoint of X(74) and X(15463)
X(32607) = reflection of X(i) in X(j) for these lines: {i,j}: {15463, 11430}, {22109, 3}}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {{3, 265, 12893}, {3, 12302, 16163}, {3, 19457, 125}, {54, 74, 7722}, {54, 7722, 12227}, {74, 3520, 13293}, {74, 13198, 185}, {125, 21659, 265}, {974, 12041, 1204}, {1593, 10117, 13202}, {2935, 13171, 10990}, {3516, 13171, 2935}, {11425, 17835, 19504}, {12133, 15647, 26883}, {13367, 21650, 110}, {17835, 19504, 14448}

X(32608) = X(3)X(54)∩X(30)X(3448)

X(32608) lies on the cubic K1107 and these lines: {3, 54}, {30, 3448}, {52, 14130}, {74, 13391}, {185, 13564}, {323, 15646}, {381, 17810}, {382, 9927}, {389, 15047}, {399, 1495}, {511, 5621}, {539, 15085}, {567, 14831}, {568, 15004}, {1350, 15688}, {1568, 1656}, {1657, 11750}, {1658, 9544}, {3526, 9786}, {3534, 10605}, {3580, 18403}, {3830, 18392}, {5054, 14156}, {5055, 7699}, {5663, 5899}, {5876, 13621}, {5907, 18369}, {6241, 15086}, {6243, 7689}, {7545, 18435}, {7666, 32534}, {9306, 18436}, {9703, 18324}, {9818, 13321}, {10263, 11440}, {11438, 23039}, {12111, 18378}, {12308, 14157}, {12359, 31724}, {13403, 18442}, {13414, 28447}, {13415, 28448}, {14118, 14627}, {14128, 22462}, {14449, 14865}, {15040, 22115}, {15053, 15067}, {15060, 21308}, {15707, 21766}, {17835, 18400}

X(32608) = reflection of X(i) in X(j) for these lines: {i,j}: {323, 15646}, {399, 2070}, {2070, 3581}, {12308, 14157}, {18403, 3580}, {22115, 32110}
X(32608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5889, 195}, {7691, 13630, 3}

X(32609) = X(2)X(11694)∩X(3)X(74)

X(32609) lies on the cubic K1107 and these lines: {2, 11694}, {3, 74}, {4, 7666}, {5, 12383}, {6, 11935}, {20, 20125}, {24, 3043}, {25, 15463}, {40, 11699}, {49, 9730}, {54, 5898}, {64, 25564}, {113, 382}, {125, 3526}, {140, 3448}, {141, 32306}, {146, 550}, {154, 2777}, {155, 12893}, {182, 2930}, {184, 17701}, {195, 568}, {265, 1656}, {323, 7575}, {373, 567}, {381, 5642}, {394, 22109}, {511, 2070}, {541, 15688}, {542, 5054}, {548, 12244}, {549, 9143}, {569, 15089}, {620, 15545}, {631, 10264}, {974, 19347}, {999, 10088}, {1092, 2937}, {1112, 3517}, {1151, 12376}, {1152, 12375}, {1350, 19140}, {1351, 6593}, {1385, 2948}, {1482, 11720}, {1498, 13293}, {1539, 5073}, {1598, 15472}, {1657, 7728}, {1658, 12307}, {1986, 3515}, {2079, 9696}, {2574, 28447}, {2575, 28448}, {2771, 3576}, {2778, 28450}, {2842, 22586}, {2854, 5050}, {2888, 10125}, {2935, 6759}, {3090, 11801}, {3200, 30439}, {3201, 30440}, {3233, 14934}, {3292, 3581}, {3295, 10091}, {3311, 10819}, {3312, 10820}, {3431, 14926}, {3516, 12292}, {3522, 14677}, {3523, 12317}, {3527, 5504}, {3628, 15081}, {3796, 15693}, {3843, 10733}, {3851, 10113}, {5013, 14901}, {5055, 14644}, {5070, 20304}, {5072, 7687}, {5079, 12900}, {5092, 16010}, {5093, 13321}, {5181, 11898}, {5204, 19470}, {5217, 7727}, {5465, 12355}, {5621, 17508}, {5640, 15038}, {5650, 18475}, {5651, 14805}, {5889, 11561}, {5907, 18364}, {6053, 16111}, {6101, 7731}, {6102, 12273}, {6243, 11557}, {6417, 19110}, {6418, 19111}, {6642, 12228}, {6644, 9703}, {6699, 15720}, {6723, 15027}, {7387, 20773}, {7517, 20771}, {7545, 13352}, {7574, 11064}, {7722, 32534}, {8909, 12892}, {8998, 19052}, {9129, 11258}, {9140, 15694}, {9545, 13472}, {9654, 18968}, {9669, 12896}, {9704, 17928}, {9705, 12284}, {9706, 12006}, {9786, 12227}, {9833, 23315}, {9904, 31663}, {9919, 15647}, {9934, 14530}, {9956, 12407}, {10117, 10282}, {10170, 13367}, {10540, 14915}, {10627, 13201}, {10628, 11202}, {10657, 11481}, {10658, 11480}, {10706, 15681}, {10721, 17800}, {11002, 12106}, {11426, 11746}, {11477, 25556}, {11562, 18436}, {11579, 12017}, {11598, 13093}, {11702, 12316}, {11999, 15748}, {12038, 12302}, {12083, 16165}, {12085, 25487}, {12165, 15750}, {12645, 12898}, {12903, 31479}, {13188, 18332}, {13289, 17821}, {13358, 15043}, {13434, 22462}, {13743, 16164}, {13990, 19051}, {14695, 32204}, {15033, 21308}, {15063, 15696}, {15141, 15577}, {17845, 19506}, {18440, 32233}, {18534, 20772}, {19145, 32292}, {19146, 32291}, {27866, 32046}

X(32609) = midpoint of X(i) and X(j) for these lines: {i,j}: {110, 15035}, {399, 15041}, {23515, 30714}
X(32609) = reflection of X(i) in X(j) for these lines: {i,j}: {3, 15035}, {265, 23515}, {381, 14643}, {568, 16223}, {5050, 15462}, {5621, 17508}, {10620, 15041}, {14643, 5642}, {15035, 1511}, {15041, 3}, {23515, 5972}
X(32609) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 110, 399}, {3, 399, 10620}, {3, 1511, 15040}, {3, 12308, 74}, {5, 12383, 12902}, {24, 3043, 19504}, {74, 110, 5609}, {74, 5609, 12308}, {110, 1511, 3}, {110, 15020, 74}, {110, 15034, 1511}, {110, 15040, 10620}, {110, 15051, 14094}, {113, 12121, 382}, {265, 5972, 1656}, {381, 14643, 15046}, {399, 15039, 110}, {399, 15040, 3}, {399, 15042, 74}, {631, 14683, 10264}, {1511, 15039, 10620}, {5609, 12308, 399}, {5609, 15020, 3}, {5609, 15042, 10620}, {5972, 30714, 265}, {6644, 9703, 15087}, {7728, 16163, 1657}, {11720, 12778, 1482}, {12017, 32254, 11579}, {12038, 18350, 14130}, {12041, 15051, 3}, {12308, 15020, 15042}, {14094, 15051, 12041}, {15039, 15040, 399}, {16163, 16534, 7728}, {17821, 17847, 13289}

X(32609) = circumcircle- inverse of X(5609)
X(32609) = crosssum of X(523) and X(6070)
X(32609) = pole of line X(526)X(5607) wrt circumcircle

X(32610) = X(35)X(79)∩X(5010)X(20277)

See Ercole Suppa, Antreas Hatzipolakis and César Lozada, Hyacinthos 29057.

X(32610) lies on these lines: {35, 79}, {5010, 20277}

X(32611) = ISOGONAL CONJUGATE OF X(32610)

See Ercole Suppa, Antreas Hatzipolakis and César Lozada, Hyacinthos 29057.

X(32611) lies on this line: {500, 9642}

X(32612) = MIDPOINT OF X(3) AND X(56)

See Ercole Suppa, Antreas Hatzipolakis and César Lozada, Hyacinthos 29059 and Hyacinthos 29062.

X(32612) lies these lines: {1, 3}, {4, 10584}, {5, 2829}, {10, 32153}, {12, 21154}, {24, 1828}, {30, 7681}, {84, 31828}, {104, 355}, {119, 13747}, {140, 993}, {182, 8679}, {214, 5884}, {388, 6961}, {474, 9956}, {496, 5840}, {499, 6923}, {515, 6924}, {528, 32214}, {529, 549}, {631, 3436}, {944, 4188}, {952, 8256}, {958, 11231}, {971, 15297}, {997, 5694}, {1006, 5303}, {1012, 9955}, {1125, 6914}, {1158, 22775}, {1478, 6958}, {1483, 5854}, {1656, 18515}, {1766, 21773}, {1837, 10090}, {2390, 11202}, {2975, 6940}, {3035, 10942}, {3086, 6948}, {3149, 28160}, {3523, 20076}, {3526, 5251}, {3560, 3824}, {3585, 6971}, {3616, 6950}, {3624, 7489}, {3653, 17549}, {3655, 11491}, {4190, 10785}, {4293, 6891}, {4299, 6928}, {4511, 26877}, {4640, 31838}, {4881, 21740}, {4973, 31806}, {5054, 31141}, {5229, 6978}, {5253, 5886}, {5267, 10165}, {5298, 15908}, {5322, 16434}, {5428, 17768}, {5433, 6842}, {5587, 26321}, {5690, 8666}, {5731, 6942}, {5818, 17572}, {5881, 12773}, {5882, 32141}, {5887, 17614}, {6256, 6959}, {6265, 18861}, {6850, 7288}, {6875, 11415}, {6882, 7354}, {6885, 18517}, {6905, 18481}, {6909, 12699}, {6911, 12114}, {6918, 18761}, {6921, 12115}, {6929, 10200}, {6944, 18516}, {6955, 10527}, {6966, 10532}, {6970, 12667}, {6980, 15446}, {7491, 15326}, {7741, 12764}, {8227, 13743}, {8583, 22936}, {8703, 12511}, {9657, 11929}, {10058, 11376}, {10943, 20418}, {11112, 26470}, {11263, 17009}, {11499, 16371}, {12737, 14923}, {13731, 27657}, {14988, 30144}, {15325, 15866}, {18446, 26201}, {19525, 19861}, {19548, 28096}, {22753, 22793}, {22836, 24475}, {28459, 30264}

X(32612) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 56}, {4299, 6928}, {10310, 10680}
X(32612) = reflection of X(i) in X(j) for these (i,j): (5, 6691), (1329, 140)
X(32612) = complement of complement of X(37002)
X(32612) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1,3,26285}, {3,36,26286}, {3,55,26086}, {3, 1385, 32613}, {3,999,11248}, {3,1482,2077}, {3,3428,31663}, {3,10246,35}, {3,10269,1385}, {3,10680,10310}, {3,11249,3579}, {3,16202,5217}, {3,16203,55}, {3,22765,40}, {36,14800,1}, {55,16203,15178}, {56,8069,24928}, {56,10310,10680}, {104,404,355}, {474,22758,9956}, {997,24467,5694}, {999,1466,31794}, {999,11248,10222}, {1319,25414,1}, {1385,23961,3}, {1470,22766,942}, {2077,5563,1482}, {2975,6940,26446}, {3086,6948,10525}, {3560,25524,11230}, {3576,7280,3}, {4293,6891,10526}, {5253,6906,5886}, {5885,13624,26287}, {5885,26287,1}, {6911,12114,18480}, {8071,22768,24929}, {9940,13624,1385}, {13528,20323,23340}, {15178,26086,55}, {31663,31797,3579}

X(32613) = MIDPOINT OF X(3) AND X(55)

See Ercole Suppa, Antreas Hatzipolakis and César Lozada, Hyacinthos 29059 and Hyacinthos 29062.

X(32613) lies these lines: {1, 3}, {4, 10585}, {5, 5248}, {8, 6875}, {10, 32141}, {11, 21155}, {12, 7491}, {21, 355}, {24, 1824}, {30, 7680}, {31, 5396}, {42, 5398}, {47, 2594}, {100, 1006}, {104, 3655}, {119, 11113}, {140, 2886}, {153, 15677}, {182, 674}, {255, 5399}, {405, 9956}, {411, 12699}, {497, 6954}, {498, 6928}, {500, 601}, {515, 6914}, {528, 549}, {529, 32213}, {631, 3434}, {902, 1064}, {912, 4640}, {943, 5812}, {944, 4189}, {952, 993}, {962, 6876}, {971, 15296}, {991, 19624}, {997, 22935}, {1001, 6911}, {1012, 28160}, {1030, 2079}, {1125, 6924}, {1283, 14663}, {1324, 3185}, {1376, 6883}, {1479, 6863}, {1483, 5855}, {1490, 31828}, {1621, 5886}, {1656, 5259}, {1871, 14017}, {2771, 18446}, {2875, 18475}, {3085, 6868}, {3145, 9959}, {3149, 9955}, {3523, 20075}, {3526, 31245}, {3560, 11500}, {3583, 6980}, {3584, 15175}, {3616, 6942}, {3651, 16159}, {3652, 12528}, {3653, 13587}, {3654, 21161}, {3679, 12331}, {3811, 22937}, {3870, 21165}, {3877, 6265}, {4192, 29678}, {4220, 29665}, {4294, 6825}, {4302, 6923}, {4420, 26878}, {4421, 28466}, {4428, 22753}, {4512, 5720}, {4995, 28459}, {4996, 12737}, {4999, 10943}, {5054, 31140}, {5070, 25542}, {5218, 6827}, {5251, 5790}, {5258, 12645}, {5267, 5882}, {5281, 6987}, {5284, 6946}, {5310, 19544}, {5428, 5690}, {5432, 6882}, {5534, 31424}, {5552, 6936}, {5587, 7489}, {5691, 13743}, {5694, 12514}, {5731, 6950}, {5762, 8255}, {5818, 16865}, {5840, 6907}, {5844, 25439}, {5887, 20846}, {6097, 13754}, {6253, 6841}, {6284, 6842}, {6824, 18517}, {6872, 10786}, {6902, 27529}, {6906, 18481}, {6910, 12116}, {6913, 18491}, {6917, 10198}, {6930, 18516}, {6962, 10531}, {6970, 26105}, {6985, 11496}, {7301, 7609}, {7330, 22936}, {7483, 26470}, {7488, 20243}, {7580, 28146}, {8053, 14723}, {9670, 11928}, {10282, 10537}, {11604, 13199}, {13323, 22276}, {15623, 17524}, {15733, 31658}, {15865, 31789}, {15888, 30264}, {16139, 31660}, {16370, 22758}, {19524, 19861}, {19649, 29680}, {20999, 23206}, {24309, 29243}, {24466, 28458}, {28208, 28444}

X(32613) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 55}, {3428, 10679}, {4302, 6923}
X(32613) = reflection of X(i) in X(j) for these (i,j): (5, 6690), (993, 7508), (2886, 140), (5173, 13373), (10537, 10282), (18407, 5)
X(32613) = complement of complement of X(37000)
X(32613) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1,3,26286}, {1,165,5535}, {1,1454,942} ,{3,35,26285}, {3, 1385, 32612}, {3,1482,11012}, {3,3295,11249}, {3,5217,26086}, {3,10246,36}, {3,10267,1385}, {3,10269,23961}, {3,10310,31663}, {3,10679,3428}, {3,11248,3579}, {3,11849,40}, {3,16202,56}, {3,16203,5204}, {21,11491,355}, {35,10902,3}, {35,14795,1}, {35,14799,5010}, {35,15931,2077}, {55,3428,10679}, {55,5172,1}, {55,8069,24929}, {56,16202,15178}, {100,1006,26446}, {405,11499,9956}, {1001,6911,11230}, {1376,6883,11231}, {1385,17502,18857}, {1385,23961,10269}, {1621,6905,5886}, {2077,10902,15931}, {2077,15931,3}, {3085,6868,10526}, {3295,11249,10222}, {3560,11500,18480}, {3576,5010,3}, {3746,11012,1482}, {3746,14804,1}, {4294,6825,10525}, {5248,6796,5}, {5267,5882,32153}, {6985,11496,22793}, {7489,18524,5587}, {8071,11510,24928}, {11508,26357,9957}, {13624,26086,3}, {26398,26422,1}

X(32613) = center of circle that is inverse-in-circumcircle of antiorthic axis

X(32614) = X(4)X(13414)∩X(20)X(13415)

X(32614) lies on the cubic K1108 and these lines: {4, 13414}, {20, 13415}, {64, 2574}, {110, 3146}, {185, 24651}, {511, 15156}, {1114, 21663}, {1495, 15157}, {2575, 12164}, {5907, 25407}, {13598, 24650}, {15155, 32608}

X(32614) = reflection of X(32615) in X(13346)
X(32614) = {X(110),X(3146)}-harmonic conjugate of X(32615)

X(32615) = X(4)X(13415)∩X(20)X(13414)

X(32615) lies on the cubic K1108 and these lines: {4, 13415}, {20, 13414}, {64, 2575}, {110, 3146}, {185, 24650}, {511, 15157}, {1113, 21663}, {1495, 15156}, {2574, 12164}, {5907, 25408}, {13598, 24651}, {15154, 32608}

X(32615) = reflection of X(32614) in X(13346)
X(32615) = {X(110),X(3146)}-harmonic conjugate of X(32614)

X(32616) = X(3)X(74)∩X(4)X(2575)

X(32616) lies on the cubic K1108 and these lines: {3, 74}, {4, 2575}, {20, 2574}, {64, 15461}, {185, 13415}, {511, 15156}, {1113, 6000}, {1114, 13754}, {1154, 15155}, {1344, 15305}, {1345, 5890}, {1347, 18388}, {5562, 25407}, {5889, 24651}, {5907, 13414}, {10751, 25739}, {12162, 14709}, {14915, 15157}, {18439, 20478}

X(32616) = reflection of X(i) in X(j) for these lines: {i,j}: {24650, 31955}, {31954, 13415}
X(32616) = reflection of X(32617) in X(3)
X(32616) = {X(74),X(6241)}-harmonic conjugate of X(32617)
X(32616) = {X(110),X(12111)}-harmonic conjugate of X(32617)

X(32617) = X(3)X(74)∩X(4)X(2574)

X(32617) lies on the cubic K1108 and these lines: {3, 74}, {4, 2574}, {20, 2575}, {64, 15460}, {185, 13414}, {511, 15157}, {1113, 13754}, {1114, 6000}, {1154, 15154}, {1344, 5890}, {1345, 15305}, {1346, 18388}, {5562, 25408}, {5889, 24650}, {5907, 13415}, {10750, 25739}, {12162, 14710}, {14915, 15156}, {18439, 20479}

X(32617) = reflection of X(i) in X(j) for these lines: {i,j}: {24651, 31954}, {31955, 13414}
X(32617) = reflection of X(32616) in X(3)
X(32617) = {X(74),X(6241)}-harmonic conjugate of X(32616)
X(32617) = {X(110),X(12111)}-harmonic conjugate of X(32616)

X(32618) = ISOGONAL CONJUGATE OF X(5000)

X(32618) lies on the following curves: Jerabek circumhyperbola, K018, K270, K305, K336, K337, K1096, Q021, Q030, Q044, Q094, and on these lines: {2, 98}, {10264, 31665}

X(32618) = reflection of X(32619) in X(125)
X(32618) = isogonal conjugate of X(5000)
X(32618) = isogonal conjugate of the complement of X(5002)
X(32618) = Brocard-circle inverse of X(32619)
X(32618) = antigonal image of X(32619)
X(32618) = psi-transform of X(5001)
X(32618) = X(511)-cross conjugate of X(32619)
X(32618) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5000}, {240,32619}
X(32618) = barycentric product X(287)*X(5001)
X(32618) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6, 5000}, {248, 32619}, {5001, 297}
X(32618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6776, 32619}, {98, 287, 32619}, {110, 5622, 32619}, {182, 184, 32619}, {1352, 1899, 32619}, {1976, 17974, 32619}, {5921, 23291, 32619}, {13198, 15462, 32619}, {13414, 13415, 32619}

X(32619) = ISOGONAL CONJUGATE OF X(5001)

X(32619) lies on the following curves: Jerabek circumhyperbola, K018, K270, K305, K336, K337, K1096, Q021, Q030, Q044, Q094, and on these lines: {2, 98}, {10264, 31664}

X(32619) = reflection of X(32618) in X(125)
X(32619) = Brocard-circle inverse of X(32618)
X(32619) = isogonal conjugate of X(5001)
X(32619) = isogonal conjugate of the complement of X(5003)
X(32619) = antigonal image of X(32618)
X(32619) = psi-transform of X(5000)
X(32619) = X(511)-cross conjugate of X(32618)
X(32619) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5001}, {240, 32618}
X(32619) = barycentric product X(287)*X(5000)
X(32619) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {6, 5001}, {248, 32618}, {5000, 297}
X(32619 = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6776, 32618}, {98, 287, 32618}, {110, 5622, 32618}, {182, 184, 32618}, {1352, 1899, 32618}, {1976, 17974, 32618}, {5921, 23291, 32618}, {13198, 15462, 32618}, {13414, 13415, 32618}

X(32620) = X(3)X(1495)∩X(5)X(4549)

X(32620) lies on the cubic K1107 and on these lines: {3, 1495}, {5, 4549}, {6, 32599}, {22, 16261}, {30, 10516}, {54, 155}, {64, 7516}, {140, 3532}, {154, 15060}, {378, 7998}, {511, 9813}, {541, 5054}, {549, 10606}, {1154, 5102}, {1192, 3628}, {1350, 31861}, {1656, 7706}, {3066, 3581}, {3336, 7986}, {3796, 18435}, {5050, 13754}, {5085, 5621}, {5646, 12041}, {5891, 6090}, {6000, 17508}, {6800, 18451}, {7393, 16836}, {7395, 9730}, {7464, 21766}, {7509, 15072}, {7525, 15811}, {7526, 15067}, {9786, 13363}, {9827, 17834}, {10938, 19357}, {10982, 32352}, {11248, 15625}, {11284, 32110}, {11387, 11817}, {13154, 32138}, {16072, 23515}, {17811, 18570}, {18377, 20584}, {32607, 32609}

X(32620) = reflection of X(5085) in X(7514)
X(32620) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3426, 8717}, {3, 4550, 11472}, {7395, 12163, 15805}

X(32621) = X(3)X(524)∩X(6)X(25)

Let A'B'C' be the reflection of ABC in X(6). Let A_B = BC∩C'A', A_C = BC∩A'B', and define B_C, B_A, C_A, C_B cyclically. A_B, A_C, B_C, B_A, C_A, C_B lie on the 2nd Lemoine circle. Let A" be the intersection of the tangents to the 2nd Lemoine circle at B_A and C_A, and define B" and C" cyclically. X(32621) = X(4)-of-A"B"C". (see also X(5050)) (Randy Hutson, June 7, 2019)

X(32621) lies on the cubic K1107 and on these lines: {3, 524}, {6, 25}, {22, 1992}, {23, 5032}, {24, 11431}, {67, 32240}, {69, 7485}, {140, 9925}, {141, 16419}, {160, 8573}, {182, 8681}, {186, 14912}, {193, 6636}, {378, 6776}, {542, 9818}, {575, 6642}, {576, 7387}, {578, 8549}, {597, 5020}, {599, 7484}, {1181, 9914}, {1351, 8547}, {1353, 7502}, {1449, 1486}, {1503, 1597}, {1598, 15581}, {1609, 20775}, {2854, 5050}, {2930, 5642}, {2936, 18800}, {3158, 12329}, {3455, 5477}, {3517, 15582}, {3564, 7514}, {3576, 9004}, {4663, 9798}, {5012, 15531}, {5024, 9142}, {5085, 9027}, {5093, 5899}, {5095, 32262}, {5422, 11188}, {5480, 18535}, {5621, 11410}, {6515, 16789}, {7395, 15069}, {7517, 11482}, {7592, 15073}, {7666, 32154}, {8537, 11423}, {8540, 10833}, {8548, 9937}, {8584, 9909}, {8787, 9876}, {8889, 18935}, {10169, 18919}, {10249, 11430}, {10541, 14528}, {10601, 29959}, {11160, 15246}, {11255, 32136}, {11414, 11477}, {11416, 11422}, {12007, 15577}, {12161, 15074}, {15141, 32245}, {16010, 16510}, {18388, 23049}, {18534, 20423}, {18954, 19369}, {20583, 20850}, {23292, 23327}, {32254, 32274}

X(32621) = reflection of X(9813) in X(575)
X(32621) = X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 154, 19136}, {6, 184, 19153}, {6, 9924, 9969}, {6, 9971, 9777}, {6, 10602, 11216}, {6, 19459, 159}, {206, 22829, 6}, {6467, 13366, 8541}, {8541, 13366, 6}, {10602, 11402, 6}

X(32622) = 1st MOSES-STEVANOVIC POINT

"Tripolars" abbreviates "homogeneous tripolar coordinates"; i.e., to say that x : y : z are tripolars for a point X means that x, y, z, are respectively proportional to |AX|, |BX|, |CX|.

X(32622) is one of two points (X(32623) is the other) whose pedal antipodal perspector is X(7). Also, X(32622) is the perspector of the excentral triangles of ABC and the circumcevian triangle of X(3513). (Randy Hutson, June 5, 2019 )

X(32622) lies on the Stevanovic circle, the curves K352 and Q037, and on this line: {1, 3}

X(32622) = reflection of X(32623) in X(1155)
X(32622) = X(513)-vertex conjugate of X(32623)
X(32622) = X(972)-Ceva conjugate of X(32623)
X(32622) = circumcircle-inverse of X(32623)
X(32622) = Bevan-circle-inverse of X(32623)
X(32622) = isogonal conjugate of X(39144)
X(32622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 165, 32623}, {3, 55, 32623}, {35, 15931, 32623}, {36, 5537, 32623}, {40, 57, 32623}, {55, 3514, 1}, {56, 6244, 32623}, {354, 3579, 32623}, {484, 5536, 32623}, {942, 7964, 32623}, {1155, 3514, 36}, {1381, 1382, 32623}, {1617, 10310, 32623}, {2077, 2078, 32623}, {2448, 2449, 32623}, {3256, 11012, 32623}, {3660, 13528, 32623}, {3748, 31663, 32623}, {7987, 31508, 32623}, {7994, 15803, 32623}, {8186, 8187, 32623}, {10268, 10383, 32623}, {10270, 10388, 32623}

X(32623) = 2nd MOSES-STEVANOVIC POINT

X(32623) is one of two points (X(32622) is the other) whose pedal antipodal perspector is X(7). Also, X(32623) is the perspector of the excentral triangles of ABC and the circumcevian triangle of X(3514). (Randy Hutson, June 5, 2019 )

p> X(32623) lies on the Stevanovic circle, the curves K352 and Q037, and on this line: {1, 3}

X(32623) = reflection of X(32622) in X(1155)
X(32623) = isogonal conjugate of X(39145)
X(32623) = X(513)-vertex conjugate of X(32622)
X(32623) = X(972)-Ceva conjugate of X(32622)
X(32623) = circumcircle-inverse of X(32622)
X(32623) = Bevan-circle-inverse of X(32622)
X(32623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 165, 32622}, {3, 55, 32622}, {35, 15931, 32622}, {36, 5537, 32622}, {40, 57, 32622}, {55, 3513, 1}, {56, 6244, 32622}, {354, 3579, 32622}, {484, 5536, 32622}, {942, 7964, 32622}, {1155, 3513, 36}, {1381, 1382, 32622}, {1617, 10310, 32622}, {2077, 2078, 32622}, {2448, 2449, 32622}, {3256, 11012, 32622}, {3660, 13528, 32622}, {3748, 31663, 32622}, {7987, 31508, 32622}, {7994, 15803, 32622}, {8186, 8187, 32622}, {10268, 10383, 32622}, {10270, 10388, 32622}

X(32624) = CIRCUMCIRCLE-INVERSE OF X(7)

X(32624) lies on these lines: {3,7}, {1358,5172}, {4367,8638}, {5543,26357}, {7742,14878}, {9436,27086}, {23839,32613}

X(32624) = circumcircle-inverse of X(7)

X(32625) = CIRCUMCIRCLE-INVERSE OF X(9)

X(32625) lies on these lines: {3, 9}, {35, 3207}, {36, 910}, {48, 4262}, {101, 2077}, {104, 8074}, {404, 8568}, {667, 3900}, {934, 2391}, {1055, 2078}, {1108, 7297}, {1615, 15931}, {2170, 5193}, {2178, 18594}, {2183, 5030}, {2317, 4251}, {3911, 11349}, {4394, 4730}, {5537, 6603}, {7987, 32561}, {12114, 23058}

X(32625) = circumcircle-inverse of X(9)
X(32625) = crosspoint of X(2291) and X(3451)
X(32625) = crosssum of X(i) and X(j) for these (i,j): {527, 3452}, {5514, 6366}
X(32625) = crossdifference of every pair of points on line {3752, 6129}
X(32625) = {X(1436),X(1604)}-harmonic conjugate of X(9)

X(32626) = CIRCUMCIRCLE-INVERSE OF X(12)

X(32626) lies on these lines: {3, 12}, {2915, 14882}

X(32626) = circumcircle-inverse of X(12)

X(32627) = CIRCUMCIRCLE-INVERSE OF X(17)

X(32627) lies on the cubic K937 and these lines: {3, 13}, {16, 16806}, {61, 1337}, {3130, 16530}, {3439, 11602}, {3442, 15444}, {5012, 21461}, {10677, 16257}, {11087, 22511}

X(32627) = isogonal conjugate of X(34219)
X(32627) = circumcircle-inverse of X(17)
X(32627) = {X(6104),X(31939)}-harmonic conjugate of X(3)

X(32628) = CIRCUMCIRCLE-INVERSE OF X(18)

X(32628) lies on the cubic K937 and these lines: {3, 14}, {15, 16807}, {62, 1338}, {3129, 16529}, {3438, 11603}, {3443, 15445}, {5012, 21462}, {10678, 16258}, {11082, 22510}

X(32628) = isogonal conjugate of X(34220)
X(32628) = circumcircle-inverse of X(18)
X(32628) = {X(6105),X(31940)}-harmonic conjugate of X(3)

X(32629) = X(13624)X(28185)∩X(15178)X(28173)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29066.

X(32629) lies on the circumcircle and these lines: {13624, 28185}, {15178, 28173}

X(32630) = X(1)X(28535)∩X(101)X(14422)

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29068.

X(32630) lies on the circumcircle and these lines: {1,28535}, {101,14422}, {103,10246}, {244,28317}, {2291,4860}, {3576,28159}, {5425,28471}, {14413,2899}

X(32631) = ISOGONAL CONJUGATE OF X(19654)

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29068.

X(32631) lies on these lines: {2,1155}, {4671,27756}, {4870,27761}, {4945,27741}, {4956,27753}, {5219,27737}, {5235,27740}, {5603,28537}, {9093,28899}

X(32631) = isogonal conjugate of X(19654)
X(32631) = barycentric quotient of X(i) and X(j) for these lines: {i,j}: {6,19654}, {45,5220}, {3679,17294}, {4777,28898}, {28899,4588}
X(32631) = trilinear product of X(i) and X(j) for these lines: {i,j}: {4791,28899}
X(32631) = trilinear quotient of X(i) and X(j) for these lines: {i,j}: {1,19654}, {3679,5220}, {4671,17294}

X(32632) = X(1)X(4127)∩X(9)X(19872)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32632) lies on the Jerabek circumhyperbola of the excentral triangle and these lines: {1, 4127}, {9, 19872}, {40, 3627}, {191, 9780}, {2136, 4816}, {3219, 3337}, {3626, 5541}, {3646, 6763}, {3647, 13146}, {6326, 13624}

X(32632) = excentral isogonal conjugate of X(31663)
X(32632) = X(3634)-Ceva conjugate of X(1)

X(32633) = X(1)X(4757)∩X(3)X(5260)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32633) lies on these lines: {1, 4757}, {3, 5260}, {8, 19704}, {21, 19862}, {100, 3626}, {404, 19872}, {1001, 4189}, {1621, 19535}, {2975, 3621}, {3634, 13587}, {3736, 16477}, {4816, 5010}, {5251, 22266}, {5284, 7280}, {5550, 16370}, {6265, 13624}, {7173, 15680}, {19705, 19877}, {21161, 22936}, {22355, 27026}

X(32633) = {X(7280),X(17574)}-harmonic conjugate of X(5284)

X(32634) = X(1)X(3968)∩X(8)X(381)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32634) lies on these lines: {1, 3968}, {8, 381}, {10, 13606}, {100, 13624}, {2550, 3621}, {3617, 3813}, {3626, 21630}, {4420, 10222}, {4853, 5303}, {5178, 12751}, {5223, 14923}, {10914, 11684}, {11024, 20050}

X(32634) = reflection of X(13606) in X(10)

X(32635) = X(1)X(748)∩X(2)X(3296)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32635) lies on Feuerbach circumhyperbola and these lines: {1, 748}, {2, 3296}, {4, 3617}, {7, 12}, {8, 3058}, {9, 3871}, {10, 79}, {21, 210}, {44, 2298}, {45, 941}, {80, 3626}, {84, 1796}, {100, 3065}, {104, 6986}, {191, 3956}, {256, 3214}, {314, 3701}, {354, 17546}, {404, 7284}, {484, 4540}, {517, 16615}, {518, 17536}, {519, 13606}, {943, 3935}, {958, 2320}, {960, 1320}, {1000, 3621}, {1171, 5297}, {1389, 11278}, {1392, 5330}, {2346, 15254}, {2478, 5686}, {2481, 6540}, {2891, 25479}, {3062, 7997}, {3219, 3579}, {3254, 6734}, {3475, 5550}, {3625, 5559}, {3634, 5557}, {3679, 5560}, {3680, 3877}, {3691, 4876}, {3740, 17531}, {3811, 16858}, {3869, 17098}, {3873, 17534}, {3885, 4900}, {3889, 7308}, {3983, 15481}, {4096, 27368}, {4430, 16842}, {4532, 16126}, {4537, 5425}, {4647, 4756}, {4661, 11108}, {4866, 5250}, {4943, 23836}, {5044, 15179}, {5251, 5424}, {5551, 5708}, {5665, 15556}, {5719, 17552}, {6595, 18259}, {6684, 13243}, {6763, 9342}, {7320, 20050}, {10266, 21031}, {11544, 17484}, {11604, 13272}, {11698, 16006}, {12019, 24298}, {17420, 23838}, {18483, 25006}, {21077, 31254}, {26792, 31419}, {27549, 30479}

X(32635) = isogonal conjugate of X(32636)
X(32635) = X(1268)-Ceva conjugate of X(1255)
X(32635) = X(i)-cross conjugate of X(j) for these (i,j): {3737, 3699}, {4041, 644}, {4662, 8}
X(32635) = X(i)-isoconjugate of X(j) for these (i,j): {6, 553}, {7, 2308}, {34, 3916}, {56, 1125}, {57, 1100}, {58, 3649}, {73, 31900}, {77, 2355}, {101, 30724}, {106, 5298}, {109, 4977}, {181, 30593}, {222, 1839}, {269, 3683}, {273, 23201}, {278, 22054}, {604, 4359}, {608, 4001}, {651, 4979}, {1014, 1962}, {1106, 3702}, {1213, 1412}, {1230, 16947}, {1269, 1397}, {1396, 3958}, {1400, 8025}, {1402, 16709}, {1407, 3686}, {1408, 4647}, {1411, 4973}, {1414, 4983}, {1415, 4978}, {1416, 4966}, {1417, 4975}, {1431, 4697}, {1434, 20970}, {1461, 4976}, {2163, 4870}, {2171, 30581}, {4565, 4988}, {4990, 6614}, {7341, 8013}
X(32635) = cevapoint of X(i) and X(j) for these (i,j): {1, 3579}, {9, 210}
X(32635) = crosspoint of X(1268) and X(4102)
X(32635) = trilinear pole of line {650, 4501}
X(32635) = barycentric product X(i) X(j) for these lines: {i,j}: {1, 4102}, {8, 1255}, {9, 1268}, {21, 6539}, {55, 32018}, {210, 32014}, {312, 1126}, {318, 1796}, {643, 31010}, {644, 4608}, {650, 6540}, {1171, 3701}, {1320, 31011}, {2185, 6538}, {3596, 28615}, {3700, 4596}, {4041, 4632}, {4086, 4629}, {4391, 8701}
X(32635) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {1, 553}, {8, 4359}, {9, 1125}, {21, 8025}, {33, 1839}, {37, 3649}, {41, 2308}, {44, 5298}, {45, 4870}, {55, 1100}, {60, 30581}, {78, 4001}, {200, 3686}, {210, 1213}, {212, 22054}, {219, 3916}, {220, 3683}, {312, 1269}, {333, 16709}, {346, 3702}, {513, 30724}, {522, 4978}, {607, 2355}, {644, 4427}, {650, 4977}, {663, 4979}, {1126, 57}, {1171, 1014}, {1172, 31900}, {1255, 7}, {1268, 85}, {1334, 1962}, {1796, 77}, {2185, 30593}, {2318, 3958}, {2321, 4647}, {2323, 4973}, {2325, 4975}, {2329, 4697}, {3158, 4856}, {3208, 4970}, {3239, 4985}, {3684, 4974}, {3686, 6533}, {3689, 4969}, {3693, 4966}, {3700, 30591}, {3701, 1230}, {3709, 4983}, {3900, 4976}, {4041, 4988}, {4069, 4115}, {4102, 75}, {4130, 4990}, {4420, 3578}, {4515, 4046}, {4526, 30592}, {4578, 30729}, {4596, 4573}, {4608, 24002}, {4629, 1414}, {4632, 4625}, {4873, 4717}, {4895, 4984}, {6538, 6358}, {6539, 1441}, {6540, 4554}, {7064, 21816}, {8701, 651}, {28615, 56}, {31010, 4077}, {32018, 6063}
X(32635) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {210, 5302, 4420}, {4420, 5302, 21}

X(32636) = MIDPOINT OF X(3336) AND X(5563)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29070.

X(32636) lies on these lines: {1, 3}, {2, 5302}, {4, 17728}, {7, 5550}, {10, 5434}, {11, 1354}, {12, 3634}, {21, 3742}, {34, 17523}, {44, 583}, {45, 2285}, {58, 14158}, {60, 757}, {63, 25524}, {79, 3582}, {81, 4719}, {88, 961}, {89, 959}, {104, 7686}, {108, 1887}, {140, 13407}, {142, 24953}, {145, 9352}, {210, 474}, {226, 5433}, {229, 4228}, {244, 1104}, {329, 24954}, {355, 4317}, {388, 5435}, {404, 518}, {496, 1770}, {499, 17605}, {501, 1412}, {529, 24982}, {553, 1125}, {584, 604}, {595, 18360}, {603, 1418}, {614, 4252}, {631, 17718}, {749, 1469}, {758, 17614}, {896, 28352}, {908, 6691}, {910, 1475}, {936, 4005}, {946, 11246}, {950, 15326}, {956, 3698}, {958, 3306}, {960, 3218}, {976, 21342}, {978, 4641}, {993, 5439}, {997, 3962}, {1001, 4652}, {1042, 1450}, {1100, 17454}, {1106, 1427}, {1193, 1464}, {1203, 8614}, {1210, 7354}, {1357, 2842}, {1358, 10521}, {1386, 17092}, {1393, 1455}, {1398, 1452}, {1406, 16466}, {1434, 1447}, {1445, 5220}, {1458, 2594}, {1468, 3752}, {1478, 17606}, {1698, 11237}, {1708, 15650}, {1737, 18357}, {1768, 9856}, {1788, 3600}, {1836, 3086}, {1837, 4293}, {2096, 12679}, {2173, 2260}, {2306, 19373}, {2348, 4253}, {2975, 3812}, {3052, 28011}, {3058, 31730}, {3149, 12680}, {3296, 3524}, {3474, 12701}, {3475, 3523}, {3476, 3621}, {3485, 5265}, {3555, 3689}, {3556, 26866}, {3584, 5442}, {3585, 31776}, {3598, 24796}, {3616, 4640}, {3624, 4654}, {3625, 4315}, {3626, 10106}, {3669, 4782}, {3671, 4031}, {3674, 7181}, {3681, 17572}, {3720, 11553}, {3740, 17531}, {3753, 8666}, {3811, 16371}, {3848, 5047}, {3869, 23958}, {3873, 4188}, {3874, 5440}, {3925, 12436}, {3928, 8583}, {3983, 4413}, {4018, 30144}, {4295, 11376}, {4299, 5722}, {4301, 17613}, {4308, 20050}, {4311, 10950}, {4324, 31795}, {4325, 28160}, {4333, 9668}, {4340, 17723}, {4355, 5219}, {4383, 11512}, {4423, 31424}, {4650, 21214}, {4676, 26093}, {4857, 28146}, {4861, 10107}, {4999, 5249}, {5030, 16601}, {5044, 6763}, {5057, 20084}, {5083, 12432}, {5123, 20060}, {5218, 11037}, {5225, 10431}, {5229, 5704}, {5247, 16610}, {5267, 5427}, {5270, 9956}, {5290, 19872}, {5294, 25914}, {5393, 10910}, {5405, 10911}, {5432, 21620}, {5542, 15837}, {5586, 14150}, {5587, 9657}, {5714, 6832}, {5880, 10527}, {5905, 25681}, {6001, 26877}, {6284, 11019}, {6684, 15888}, {6692, 12527}, {6848, 12678}, {6904, 24477}, {6905, 12675}, {6906, 13374}, {6911, 14872}, {7173, 8226}, {7175, 16477}, {7198, 9436}, {7248, 27655}, {7989, 9656}, {8686, 8698}, {9579, 10896}, {9581, 12943}, {9655, 10826}, {9776, 30478}, {9965, 28647}, {10072, 12699}, {10074, 17636}, {10085, 19541}, {10090, 12738}, {10091, 11670}, {10308, 16141}, {10916, 11112}, {11038, 15717}, {11194, 19860}, {11544, 12047}, {12019, 20118}, {12688, 22753}, {12832, 18976}, {13369, 17637}, {13747, 21077}, {14027, 31524}, {15299, 31391}, {16736, 27660}, {17351, 25591}, {17736, 25066}, {17751, 24593}, {17863, 18661}, {18253, 24564}, {19861, 31165}, {20470, 22345}, {22344, 23383}, {22836, 24473}, {24628, 30038}, {31190, 31246}

X(32636) = isogonal conjugate of X(32635)
X(32636) = midpoint of X(3336) and X(5563)
X(32636) = reflection of X(20323) in X(5563)
X(32636) = X(i)-Ceva conjugate of X(j) for these (i,j): {553, 1100}, {1414, 3669}, {26700, 513}
X(32636) = X(2308)-cross conjugate of X(1100)
X(32636) = X(i)-isoconjugate of X(j) for these (i,j): {6, 4102}, {8, 1126}, {9, 1255}, {41, 32018}, {55, 1268}, {60, 6538}, {281, 1796}, {284, 6539}, {312, 28615}, {522, 8701}, {663, 6540}, {1171, 2321}, {1334, 32014}, {2316, 31011}, {3700, 4629}, {3709, 4632}, {3939, 4608}, {4041, 4596}, {5546, 31010}, {5547, 31013}
X(32636) = crosspoint of X(i) and X(j) for these (i,j): {1, 10308}, {57, 1014}
X(32636) = crosssum of X(i) and X(j) for these (i,j): {1, 3579}, {9, 210}
X(32636) = crossdifference of every pair of points on line {650, 4501}
X(32636) = barycentric product X(i) X(j) for these lines: {i,j}: {1, 553}, {7, 1100}, {12, 30581}, {34, 4001}, {56, 4359}, {57, 1125}, {65, 8025}, {77, 1839}, {81, 3649}, {85, 2308}, {88, 5298}, {89, 4870}, {100, 30724}, {109, 4978}, {269, 3686}, {273, 22054}, {278, 3916}, {279, 3683}, {331, 23201}, {348, 2355}, {552, 21816}, {604, 1269}, {651, 4977}, {664, 4979}, {934, 4976}, {1014, 1213}, {1214, 31900}, {1230, 1408}, {1400, 16709}, {1407, 3702}, {1412, 4647}, {1414, 4988}, {1432, 4697}, {1434, 1962}, {1461, 4985}, {1462, 4966}, {2006, 4973}, {2171, 30593}, {3669, 4427}, {4115, 7203}, {4565, 30591}, {4573, 4983}, {4617, 4990}, {4856, 19604}, {4970, 7153}, {4989, 21446}
X(32636) = barycentric quotient X(i) / X(j) for these lines: {i,j}: {1, 4102}, {7, 32018}, {56, 1255}, {57, 1268}, {65, 6539}, {553, 75}, {603, 1796}, {604, 1126}, {651, 6540}, {1014, 32014}, {1100, 8}, {1125, 312}, {1213, 3701}, {1269, 28659}, {1319, 31011}, {1397, 28615}, {1408, 1171}, {1414, 4632}, {1415, 8701}, {1839, 318}, {1962, 2321}, {2171, 6538}, {2308, 9}, {2355, 281}, {3649, 321}, {3669, 4608}, {3683, 346}, {3686, 341}, {3916, 345}, {3958, 3710}, {4001, 3718}, {4017, 31010}, {4359, 3596}, {4427, 646}, {4565, 4596}, {4647, 30713}, {4697, 17787}, {4870, 4671}, {4969, 4723}, {4970, 4110}, {4974, 3975}, {4976, 4397}, {4977, 4391}, {4979, 522}, {4983, 3700}, {4984, 4768}, {4988, 4086}, {4989, 30854}, {5298, 4358}, {8025, 314}, {16709, 28660}, {17454, 4420}, {20970, 210}, {21816, 6057}, {22054, 78}, {22080, 3694}, {23201, 219}, {30581, 261}, {30724, 693}, {31900, 31623}
X(32636) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 36, 13624}, {1, 46, 12702}, {1, 57, 5221}, {1, 5221, 65}, {1, 5903, 11278}, {1, 11278, 5048}, {1, 12702, 3057}, {1, 13624, 2646}, {3, 3338, 354}, {3, 12704, 7957}, {7, 7288, 11375}, {35, 5045, 3748}, {36, 942, 2646}, {36, 3337, 942}, {40, 3304, 5919}, {46, 999, 3057}, {46, 3057, 5183}, {55, 3333, 17609}, {56, 57, 65}, {56, 65, 1319}, {56, 1388, 13462}, {56, 2099, 1420}, {56, 5221, 1}, {56, 11509, 1617}, {57, 1420, 3339}, {57, 3361, 56}, {63, 25524, 25917}, {65, 1319, 11011}, {79, 3582, 9955}, {388, 5435, 24914}, {553, 1125, 3649}, {553, 5298, 4870}, {942, 13624, 1}, {999, 12702, 1}, {1125, 3649, 4870}, {1125, 3916, 3683}, {1125, 4973, 3916}, {1418, 1471, 1456}, {1420, 3339, 2099}, {1434, 1447, 4059}, {1447, 4059, 24805}, {1788, 3600, 5252}, {2099, 3339, 65}, {2975, 27003, 3812}, {3218, 5253, 960}, {3333, 15803, 55}, {3340, 13462, 1388}, {3361, 15932, 13370}, {3474, 14986, 12701}, {3513, 3514, 3748}, {3555, 25440, 3689}, {3649, 5298, 1125}, {3746, 5131, 31663}, {3911, 4298, 12}, {4315, 4848, 10944}, {4860, 5204, 1}, {5045, 5122, 35}, {5049, 31663, 3746}, {5126, 31794, 1}, {5265, 21454, 3485}, {5903, 24928, 5048}, {7280, 18398, 24929}, {11278, 24928, 1}, {12009, 31794, 942}, {13388, 13389, 20182}, {15325, 24470, 12047}

X(32637) = ISOGONAL CONJUGATE OF X(27357)

See Antreas Hatzipolakis, Ercole Suppa and Peter Moses, Hyacinthos 29077 and Hyacinthos 29079.

X(32637) lies on these lines: {3,252}, {137,1487}, {1157,6592}, {3519,14072}, {19268,19552}, {27868,31392}

X(32638) = X(5)X(49)∩X(1263)X(15038)

See Antreas Hatzipolakis, Ercole Suppa and Peter Moses, Hyacinthos 29077 and Hyacinthos 29079.

X(32638) lies on these lines: {5,49}, {1263,15038}, {6343,13621}, {6592,11584}, {10096,14071}, {14627,31674}, {14857,24306}

X(32639) = X(30)X(1141)∩X(140)X(10277)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29079.

X(32639) lies on these lines: {30, 1141}, {140, 10277}

X(32639) = barycentric product X(8254)*X(13582)

Centers associated with barycentric products of circumcircle-P-antipodes: X(32640)-X(32741)

X(32640) = BARYCENTRIC PRODUCT X(74)*X(110)

As the barycentric product of circumcircle antipodes, X(32640) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32640) lies on these lines: {32, 14385}, {74, 187}, {110, 32681}, {112, 647}, {115, 14989}, {186, 3003}, {237, 14908}, {249, 4558}, {1384, 9717}, {1576, 32715}, {23357, 32320} et al

X(32640) = isogonal conjugate of polar conjugate of X(1304)
X(32640) = isotomic conjugate of polar conjugate of X(32715)
X(32640) = trilinear pole of line X(184)X(1576)
X(32640) = center of bianticevian conic of X(15) and X(16)
X(32640) = barycentric product X(i)*X(j) for these lines: {i,j}: {69, 32715}, {74, 110}, {112, 14919}, {163, 2349}, {249, 2433}, {476, 14385}, {691, 9717}, {4558, 8749}, {15066, 32681}
X(32640) = barycentric quotient X(i)/X(j) for these (i,j): (32, 1637), (74, 850), (110, 3260), (163, 14206), (2159, 32671), (2349, 20948), (2433, 338), (8749, 14618), (14385, 3268), (14919, 3267), (32715, 4)

X(32641) = BARYCENTRIC PRODUCT X(100)*X(104)

As the barycentric product of circumcircle antipodes, X(32641) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32641) lies on these lines: {36, 909}, {44, 14578}, {100, 32685}, {101, 652}, {104, 294}, {112, 1309}, {248, 5291}, {644, 906}, {645, 4558}, {650, 1415}, {651, 905}, {654, 32675}, {666, 2401}, {692, 32723}, {1110, 3939}, {1576, 14776}, {1795, 2338}, {1983, 23703}, {2250, 2341}, {2323, 15629}, {2342, 4845}, {5546, 32661}, {8609, 15500}, {15627, 18877}, {23987, 32647} et al

X(32641) = isogonal conjugate of X(10015)
X(32641) = trilinear pole of line X(55)X(184)
X(32641) = crossdifference of every pair of points on line X(3259)X(3326)
X(32641) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 1309}, {6, 13136}, {69, 14776}, {100, 104}, {108, 1809}, {190, 909}, {662, 2250}, {664, 2342}, {692, 18816}, {906, 16082}, {1252, 2401}, {1795, 1897}, {6335, 14578}
X(32641) = barycentric quotient X(i)/X(j) for these (i,j): (6, 10015), (100, 3262), (101, 908), (104, 693), (109, 22464), (692, 517), (909, 514), (1252, 2397), (1309, 264), (1415, 1465), (1576, 859), (1795, 4025), (1983, 16586), (2250, 1577), (2342, 522), (2401, 23989), (3939, 6735), (13136, 76), (14578, 905), (14776, 4)

X(32642) = BARYCENTRIC PRODUCT X(101)*X(103)

As the barycentric product of circumcircle antipodes, X(32642) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32642) lies on these lines: {101, 32684}, {103, 32682}, {112, 21789}, {248, 17735}, {677, 4558}, {692, 24027}, {906, 1110}, {911, 2223}, {1415, 1946}, {6586, 8750}, {8608, 32699}, {23990, 32656}, {32659, 32719}, {32721, 32739} et al

X(32642) = isogonal conjugate of isotomic conjugate of X(677)
X(32642) = trilinear pole of line X(184)X(14827)
X(32642) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 677}, {100, 911}, {101, 103}, {109, 2338}, {18025, 32739}
X(32642) = barycentric quotient X(i)/X(j) for these (i,j): (32, 676), (103, 3261), (677, 76), (911, 693), (24027, 24015), (32656, 26006), (32739, 516)

X(32643) = BARYCENTRIC PRODUCT X(102)*X(109)

As the barycentric product of circumcircle antipodes, X(32643) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32643) lies on these lines: {102, 32689}, {109, 32683}, {248, 17966}, {906, 2149}, {1415, 32667}, {1946, 32652}, {2425, 2432}, {5053, 15629}, {6589, 32653}, {7113, 14578}, {8607, 32707}, {23979, 32660}

X(32643) = isogonal conjugate of polar conjugate of X(36067)
X(32643) = barycentric product X(i)*X(j) for these lines: {i,j}: {63, 32667}, {102, 109}, {1262, 2432}, {1461, 15629}, {2399, 23979}
X(32643) = barycentric quotient X(i)/X(j) for these (i,j): (2432, 23978), (23979, 2406), (32667, 92)

X(32644) = BARYCENTRIC PRODUCT X(105)*X(1292)

As the barycentric product of circumcircle antipodes, X(32644) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32644) lies on these lines: {666, 2414}, {906, 919}, {2428, 2440}, {3290, 8751}, {32656, 32666}

X(32644) = barycentric product X(i)*X(j) for these lines: {i,j}: {105, 1292}, {277, 919}, {2428, 6185}
X(32644) = barycentric quotient X(i)/X(j) for these (i,j): (919, 344), (1292, 3263), (2428, 4437)

X(32645) = BARYCENTRIC PRODUCT X(106)*X(1293)

As the barycentric product of circumcircle antipodes, X(32645) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32645) lies on these lines: {1293, 32686}, {2429, 2441}, {4558, 4591}, {8610, 8752}, {32656, 32719}

X(32645) = barycentric product X(i)*X(j) for these lines: {i,j}: {106, 1293}, {2226, 2429}, {4373, 32719}
X(32645) = barycentric quotient X(i)/X(j) for these (i,j): (1293, 3264), (32719, 145)

X(32646) = BARYCENTRIC PRODUCT X(107)*X(1294)

As the barycentric product of circumcircle antipodes, X(32646) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32646) lies on these lines: {112, 23590}, {1990, 15311}, {2404, 16077}, {2430, 2442}, {4558, 23582}, {6529, 6587}, {23964, 32661}

X(32646) = trilinear pole of line X(184)X(6525)
X(32646) = barycentric product X(i)*X(j) for these lines: {i,j}: {107, 1294}, {2416, 23590}
X(32646) = barycentric quotient X(i)/X(j) for these (i,j): (1294, 3265), (2416, 23974), (23590, 2404)

X(32647) = BARYCENTRIC PRODUCT X(108)*X(1295)

As the barycentric product of circumcircle antipodes, X(32647) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32647) lies on these lines: {906, 7115}, {1295, 32688}, {1415, 23985}, {1455, 14571}, {1457, 32667}, {2431, 2443}, {23987, 32641}

X(32647) = trilinear pole of line X(184)X(3195)
X(32647) = barycentric product X(i)*X(j) for these lines: {i,j}: {108, 1295}, {2417, 23985}, {2431, 23984}
X(32647) = barycentric quotient X(23985)/X(2405)

X(32648) = BARYCENTRIC PRODUCT X(111)*X(1296)

As the barycentric product of circumcircle antipodes, X(32648) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32648) lies on these lines: {691, 1296}, {892, 2418}, {2434, 2444}, {3291, 8753}, {10422, 15899}, {32661, 32729}

X(32648) = barycentric product X(i)*X(j) for these lines: {i,j}: {111, 1296}, {691, 21448}, {2434, 10630}, {5485, 32729}
X(32648) = barycentric quotient X(i)/X(j) for these (i,j): (691, 11059), (1296, 3266), (32729, 1992)

X(32649) = BARYCENTRIC PRODUCT X(112)*X(1297)

As the barycentric product of circumcircle antipodes, X(32649) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32649) lies on these lines: {112, 32687}, {186, 1297}, {232, 248}, {250, 4558}, {2409, 2966}, {2435, 2445}, {2485, 32713}, {18374, 18877}

X(32649) = trilinear pole of line X(184)X(17409)
X(32649) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 32687}, {112, 1297}, {2435, 23964}
X(32649) = barycentric quotient X(i)/X(j) for these (i,j): (112, 30737), (1297, 3267), (32687, 264)

X(32650) = BARYCENTRIC PRODUCT X(476)*X(477)

As the barycentric product of circumcircle antipodes, X(32650) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32650) lies on these lines: {476, 32690}, {1637, 32640}, {1989, 18320}, {2436, 2437}, {3018, 32711}, {4558, 30528}, {14401, 32661}, {14560, 32733}, {23588, 32662}

X(32650) = trilinear pole of line X(184)X(14560)
X(32650) = barycentric product X(i)*X(j) for these lines: {i,j}: {476, 477}, {1989, 30528}
X(32650) = barycentric quotient X(i)/X(j) for these (i,j): (477, 3268), (30528, 7799)

X(32651) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(7)

As the barycentric product of circumcircle antipodes, X(32651) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32651) lies on these lines: {109, 15439}, {651, 906}, {943, 9372}, {1415, 32714}, {1461, 32660}, {1462, 32658}, {2259, 32657}, {2982, 14578}, {4558, 4573}, {4565, 32661} et al

X(32651) = trilinear pole of line X(56)X(184)
X(32651) = barycentric product X(i)*X(j) for these lines: {i,j}: {7, 15439}, {651, 2982}, {934, 943}
X(32651) = barycentric quotient X(i)/X(j) for these (i,j): (109, 6734), (943, 4397), (1576, 8021), (2982, 4391), (15439, 8)

X(32652) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(9)

As the barycentric product of circumcircle antipodes, X(32652) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32652) lies on these lines: {31, 2188}, {32, 7367}, {109, 8059}, {248, 1903}, {643, 4558}, {692, 32660}, {906, 3939}, {1415, 8750}, {1436, 2195}, {1946, 32643}, {2192, 2342}, {2208, 2352}, {6129, 32714}, {7151, 32655}, {21059, 32657} et al

X(32652) = isogonal conjugate of X(17896)
X(32652) = trilinear pole of line X(41)X(184)
X(32652) = crossdifference of every pair of points on line X(5514)X(16596)
X(32652) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 13138}, {9, 8059}, {84, 101}, {100, 1436}, {108, 268}, {109, 282}, {110, 1903}, {189, 692}, {190, 2208}, {280, 1415}, {644, 1413}, {651, 2192}, {653, 2188}, {934, 7367}, {1422, 3939}, {1332, 7151}, {7020, 32660}
X(32652) = barycentric quotient X(i)/X(j) for these (i,j): (6, 17896), (31, 14837), (32, 6129), (84, 3261), (101, 322), (692, 329), (1413, 24002), (1415, 347), (1436, 693), (1903, 850), (2188, 6332), (2192, 4391), (2208, 514), (7151, 17924), (7367, 4397), (8059, 85), (13138, 76), (32660, 7013)

X(32653) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(10)

As the barycentric product of circumcircle antipodes, X(32653) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32653) lies on these lines: {32, 1146}, {101, 32661}, {112, 26704}, {190, 4558}, {248, 15232}, {577, 23986}, {906, 1018}, {1576, 8750}, {2178, 32659}, {2217, 16968}, {2250, 14578}, {2425, 4559}, {4557, 32656}, {5301, 32655}, {6589, 32643} et al

X(32653) = trilinear pole of line X(42)X(184)
X(32653) = crossdifference of every pair of points on line X(124)X(2968)
X(32653) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 26704}, {100, 2217}, {101, 13478}, {109, 10570}, {110, 15232}, {692, 2995}, {4559, 19607}, {8687, 19608}
X(32653) = barycentric quotient X(i)/X(j) for these (i,j): (32, 6589), (101, 4417), (692, 3869), (2217, 693), (13478, 3261), (15232, 850), (26704, 264)

X(32654) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(512)

As the barycentric product of circumcircle antipodes, X(32654) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184), and as the barycentric product of circumcircle-X(512)-antipodes, X(32654) also lies on conic {{A,B,C,X(6),X(32),X(83),X(213),X(729)}} with perspector X(669).

Let A'B'C' be the circumcevian triangle of X(511). Let A" be the barycentric product B'*C', and define B" and C" cyclically. A", B", C" are collinear on line X(2491)X(3289). The lines AA", BB", CC" concur in X(32654). (Randy Hutson, August 19, 2019)

X(32654) lies on these lines: {6, 2987}, {24, 112}, {32, 1147}, {50, 32740}, {83, 3815}, {187, 5961}, {213, 906}, {230, 297}, {237, 14601}, {248, 2422}, {571, 1576}, {577, 1084}, {729, 10425}, {1691, 2065}, {1918, 32656} et al

X(32654) = isogonal conjugate of isotomic conjugate of X(2987)
X(32654) = isogonal conjugate of anticomplement of X(36212)
X(32654) = trilinear pole of line X(184)X(669)
X(32654) = crossdifference of every pair of points on line X(114)X(2974)
X(32654) = X(92)-isoconjugate of X(3564)
X(32654) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 3563}, {6, 2987}, {31, 8773}, {32, 8781}
X(32654) = barycentric quotient X(i)/X(j) for these (i,j): (31, 1733), (32, 230), (184, 3564), (237, 114), (1576, 4226), (2987, 76), (3563, 264), (8773, 561), (8781, 1502)

X(32655) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(3)X(513)

As the barycentric product of circumcircle antipodes, X(32655) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

Let A'B'C' be the circumcevian triangle of X(517). Let A" be the barycentric product B'*C', and define B" and C" cyclically. A", B", C" are collinear with X(3310). The lines AA", BB", CC" concur in X(32655). (Randy Hutson, August 19, 2019)

X(32655) lies on these lines: {6, 906}, {31, 32656}, {32, 23980}, {81, 2990}, {112, 915}, {248, 3657}, {563, 604}, {571, 608}, {577, 1015}, {654, 2423}, {739, 6099}, {1333, 32661}, {1576, 2203}, {5301, 32653}, {7151, 32652}, {8609, 15500} et al

X(32655) = isogonal conjugate of polar conjugate of X(915)
X(32655) = isogonal conjugate of isotomic conjugate of X(2990)
X(32655) = trilinear pole of line X(184)X(667)
X(32655) = X(92)-isoconjugate of X(912)
X(32655) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 915}, {6, 2990}, {110, 3657}, {905, 32698}
X(32655) = barycentric quotient X(i)/X(j) for these (i,j): (31, 1737), (32, 8609), (184, 912), (915, 264), (2990, 76), (3657, 850), (32698, 6335)

X(32656) = BARYCENTRIC PRODUCT X(3)*X(101)

X(32656) is the barycentric product of the circumcircle intercepts of line X(3)X(71). As the barycentric product of circumcircle antipodes, X(32656) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32656) lies on these lines: {31, 32655}, {42, 14910}, {48, 23203}, {71, 248}, {100, 15440}, {101, 112}, {109, 15439}, {110, 28624}, {184, 32659}, {190, 2966}, {212, 2638}, {560, 21059}, {577, 20776}, {692, 1415}, {1110, 3939}, {1331, 4558}, {1459, 1813}, {1576, 32739}, {1897, 16813}, {1918, 32654}, {4557, 32653}, {7649, 32699}, {23990, 32642}, {32644, 32666}, {32645, 32719} et al

X(32656) = isogonal conjugate of polar conjugate of X(101)
X(32656) = isotomic conjugate of polar conjugate of X(32739)
X(32656) = X(92)-isoconjugate of X(514)
X(32656) = trilinear pole of line X(184)X(2200)
X(32656) = crossdifference of every pair of points on X(116)X(2973)
X(32656) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 906}, {3, 101}, {6, 1331}, {8, 32660}, {10, 32661}, {31, 1332}, {32, 4561}, {41, 6516}, {42, 4558}, {48, 100}, {55, 1813}, {56, 4587}, {58, 4574}, {63, 692}, {69, 32739}, {71, 110}, {72, 163}, {108, 2289}, {109, 219}, {112, 3682}, {162, 3990}, {184, 190}, {212, 651}, {577, 1897}, {905, 1110}, {1252, 1459}, {1790, 4557}, {1918, 4563}, {3977, 32719}, {17780, 32659}, {25083, 32666}, {26006, 32642}
X(32656) = barycentric quotient X(i)/X(j) for these (i,j): (3, 3261), (31, 17924), (32, 7649), (42, 14618), (48, 693), (71, 850), (72, 20948), (100, 1969), (101, 264), (109, 331), (163, 286), (184, 514), (190, 18022), (212, 4391), (560, 6591), (577, 4025), (649, 2973), (692, 92), (906, 75), (1110, 6335), (1331, 76), (1332, 561), (1459, 23989), (1813, 6063), (1897, 18027), (1918, 2501), (3682, 3267), (3990, 14208), (4558, 310), (4561, 1502), (4574, 313), (4587, 3596), (6516, 20567), (32659, 6548), (32660, 7), (32661, 86), (32719, 6336), (32739, 4)

X(32657) = BARYCENTRIC PRODUCT X(3)*X(103)

X(32657) is the barycentric product of the circumcircle intercepts of line X(3)X(4091). As the barycentric product of circumcircle antipodes, X(32657) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32657) lies on these lines: {41, 603}, {58, 103}, {255, 906}, {577, 20776}, {1795, 2338}, {1815, 2327}, {1886, 32701}, {2259, 32651}, {7335, 32660}, {21059, 32652} et al

X(32657) = isogonal conjugate of polar conjugate of X(103)
X(32657) = X(92)-isoconjugate of X(516)
X(32657) = crossdifference of every pair of points on line X(118)X(20622)
X(32657) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 103}, {6, 1815}, {63, 911}, {184, 18025}, {222, 2338}, {677, 1459}, {916, 15380}
X(32657) = barycentric quotient X(i)/X(j) for these (i,j): (32, 1886), (103, 264), (184, 516), (577, 26006), (911, 92), (1815, 76), (2338, 7017), (18025, 18022)

X(32658) = BARYCENTRIC PRODUCT X(3)*X(105)

X(32658) is the barycentric product of the circumcircle intercepts of line X(3)X(905). As the barycentric product of circumcircle antipodes, X(32658) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32658) lies on these lines: {3, 906}, {6, 3433}, {28, 105}, {32, 56}, {48, 23203}, {104, 294}, {248, 10099}, {448, 2481}, {603, 9247}, {665, 2440}, {911, 2223}, {1333, 1576}, {1384, 3420}, {1436, 2195}, {1437, 32661}, {1444, 1814}, {1462, 32651}, {2217, 16968}, {3053, 3435}, {5089, 32703} et al

X(32658) = isogonal conjugate of polar conjugate of X(105)
X(32658) = X(92)-isoconjugate of X(518)
X(32658) = crossdifference of every pair of points on line X(120)X(20621)
X(32658) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 105}, {6, 1814}, {31, 31637}, {48, 673}, {63, 1438}, {77, 2195}, {78, 1416}, {109, 23696}, {110, 10099}, {184, 2481}, {219, 1462}, {222, 294}, {603, 14942}, {905, 919}, {1437, 13576}, {6185, 20752}, {9247, 18031}
X(32658) = barycentric quotient X(i)/X(j) for these (i,j): (3, 3263), (31, 1861), (32, 5089), (48, 3912), (105, 264), (184, 518), (222, 27818), (294, 7017), (577, 25083), (603, 9436), (604, 5236), (673, 1969), (919, 6335), (1333, 15149), (1416, 273), (1437, 30941), (1438, 92), (1462, 331), (1576, 4238), (1814, 76), (2195, 318), (2481, 18022), (9247, 672), (10099, 850), (20752, 4437), (31637, 561)

X(32659) = BARYCENTRIC PRODUCT X(3)*X(106)

X(32659) is the barycentric product of the circumcircle intercepts of line X(3)X(1459). As the barycentric product of circumcircle antipodes, X(32659) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32659) lies on these lines: {36, 909}, {48, 906}, {106, 112}, {184, 32656}, {604, 1415}, {903, 2966}, {1576, 2206}, {1790, 1797}, {2178, 32653}, {2208, 2352}, {2359, 22054}, {8756, 32705}, {32642, 32719} et al

X(32659) = isogonal conjugate of polar conjugate of X(106)
X(32659) = X(92)-isoconjugate of X(519)
X(32659) = crossdifference of every pair of points on line X(121)X(4768)
X(32659) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 106}, {6, 1797}, {48, 88}, {63, 9456}, {78, 1417}, {184, 903}, {222, 2316}, {577, 6336}, {603, 1320}, {901, 1459}, {905, 32665}, {906, 1022}, {4025, 32719}, {4049, 32661}, {6548, 32656}, {9247, 20568}
X(32659) = barycentric quotient X(i)/X(j) for these (i,j): (3, 3264), (32, 8756), (48, 4358), (88, 1969), (106, 264), (184, 519), (577, 3977), (903, 18022), (906, 24004), (1417, 273), (1797, 76), (2316, 7017), (6336, 18027), (9247, 44), (9456, 92), (32656, 17780), (32665, 6335), (32719, 1897)

X(32660) = BARYCENTRIC PRODUCT X(3)*X(109)

X(32660) is the barycentric product of the circumcircle intercepts of line X(3)X(73). As the barycentric product of circumcircle antipodes, X(32660) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

The trilinear polar of X(32660) passes through X(184).

X(32660) lies on these lines: {48, 14578}, {73, 248}, {101, 652}, {109, 112}, {563, 604}, {603, 9247}, {653, 16813}, {664, 2966}, {692, 32652}, {1400, 14910}, {1404, 2252}, {1415, 32739}, {1461, 32651}, {1813, 4558}, {2425, 4559}, {3064, 32707}, {7335, 32657}, {23979, 32643} et al

X(32660) = isogonal conjugate of polar conjugate of X(109)
X(32660) = X(92)-isoconjugate of X(522)
X(32660) = crossdifference of every pair of points on line X(124)X(20620)
X(32660) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 109}, {6, 1813}, {7, 32656}, {31, 6516}, {48, 651}, {63, 1415}, {65, 4575}, {71, 4565}, {73, 110}, {77, 692}, {100, 603}, {101, 222}, {108, 255}, {162, 22341}, {163, 1214}, {184, 664}, {212, 4397}, {219, 1461}, {226, 32661}, {228, 1414}, {307, 1576}, {348, 32739}, {577, 653}, {604, 1332}, {652, 1262}, {1400, 4558}, {1790, 4559}, {1897, 7335}, {4554, 9247}, {6332, 23979}, {7013, 32652}, {14578, 24029}
X(32660) = barycentric quotient X(i)/X(j) for these (i,j): (32, 3064), (48, 4391), (73, 850), (101, 7017), (109, 264), (163, 31623), (184, 522), (212, 934), (222, 3261), (228, 4086), (577, 6332), (603, 693), (604, 17924), (651, 1969), (652, 23978), (653, 18027), (664, 18022), (692, 318), (1214, 20948), (1332, 28659), (1400, 14618), (1415, 92), (1459, 59), (1461, 331), (1576, 29), (1813, 76), (4558, 28660), (4575, 314), (6516, 561), (7335, 4025), (9247, 650), (22341, 14208), (23979, 653), (32656, 8), (32661, 333), (32739, 281), (32652, 7020)

X(32661) = BARYCENTRIC PRODUCT X(3)*X(110)

X(32661) is the barycentric product of the circumcircle intercepts of line X(3)X(49). As the barycentric product of circumcircle antipodes, X(32661) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32661) lies on these lines: {3, 248}, {5, 1970}, {6, 1511}, {30, 1971}, {32, 1147}, {39, 12038}, {49, 217}, {50, 15136}, {99, 249}, {101, 32653}, {110, 112}, {115, 17702}, {155, 3053}, {163, 1415}, {184, 14908}, {187, 13754}, {206, 2882}, {216, 5961}, {394, 18876}, {520, 9145}, {577, 18877}, {647, 32662}, {648, 16813}, {686, 23181}, {827, 26714}, {906, 4575}, {912, 5006}, {916, 1326}, {925, 32692}, {933, 6570}, {1092, 10316}, {1333, 32655}, {1384, 1501}, {1437, 32658}, {1562, 16163}, {1576, 14270}, {1691, 3564}, {1915, 18907}, {1968, 10539}, {2030, 8681}, {2071, 13509}, {2193, 14578}, {2421, 4611}, {2501, 32708}, {3060, 10986}, {3124, 12310}, {3202, 15257}, {3284, 32663}, {3289, 10317}, {3331, 10540}, {3767, 12118}, {4558, 8552}, {4565, 32651}, {5023, 12163}, {5206, 7689}, {5448, 7747}, {5449, 7749}, {5546, 32641}, {14401, 32650}, {23357, 32640}, {23964, 32646}, {32648, 32729} et al

X(32661) = isogonal conjugate of X(14618)
X(32661) = isotomic conjugate of polar conjugate of X(1576)
X(32661) = crosssum of X(i) and X(j) for these {i,j}: {6, 13558}, {523, 2501}, {647, 924}
X(32661) = crosspoint of X(i) and X(j) for these {i,j}: {110, 4558}, {648, 925}
X(32661) = X(i)-isoconjugate of X(j) for these lines: {i,j}: {1, 14618}, {4, 1577}, {92, 523}, {107, 20902}
X(32661) = trilinear pole of line X(184)X(418) (the tangent at X(577) to the inellipse that is the barycentric square of the Brocard axis)
X(32661) = crossdifference of every pair of points on line X(125)X(136)
X(32661) = crosspoint of X(371)-isoconjugate-of-X(1577) and X(372)-isoconjugate-of-X(1577)
X(32661) = crosssum of polar circle intercepts of Brocard axis
X(32661) = trilinear product of vertices of circumanticevian triangle of X(3)
X(32661) = barycentric product of MacBeath circumconic intercepts of Brocard axis
X(32661) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 4575}, {3, 110}, {5, 15958}, {6, 4558}, {31, 4592}, {32, 4563}, {48, 662}, {49, 930}, {54, 23181}, {58, 1331}, {63, 163}, {69, 1576}, {81, 906}, {86, 32656}, {99, 184}, {100, 1437}, {101, 1790}, {107, 1092}, {109, 283}, {112, 394}, {155, 13398}, {162, 255}, {216, 18315}, {219, 4565}, {222, 5546}, {248, 2421}, {249, 647}, {250, 520}, {284, 1813}, {287, 14966}, {323, 32662}, {476, 22115}, {577, 648}, {651, 2193}, {686, 18879}, {691, 3292}, {692, 1444}, {827, 3917}, {907, 3796}, {925, 1147}, {933, 5562}, {1332, 1333}, {1415, 1812}, {1511, 2425}, {2396, 14600}, {2407, 18877}, {2966, 3289}, {3167, 3565}, {3267, 23963}, {4230, 17974), {5468, 14908}, {6390, 32729}, {10317, 17708}, {10420, 13754}, {11064, 32640}, {15136, 16167}
X(32661) = barycentric quotient X(i)/X(j) for these (i,j): (3, 850), (6, 14618), (31, 24006), (32, 2501), (48, 1577), (63, 20948), (99, 18022), (110, 264), (112, 2052), (163, 92), (184, 523), (216, 18314), (217, 12077), (249, 6331), (250, 6528), (255, 14208), (394, 3267), (476, 18817), (520, 339), (577, 525), (647, 338), (648, 18027), (662, 1969), (906, 321), (930, 20572), (933, 8795), (1092, 3265), (1147, 6563), (1331, 313), (1332, 27801), (1333, 17924), (1437, 693), (1501, 2489), (1576, 4), (1790, 3261), (1813, 349), (2193, 4391), (3289, 2799), (3917, 23285), (4558, 76), (4563, 1502), (4565, 331), (4575, 75), (4592, 561), (5546, 7017), (10317, 9979), (14600, 2395), (14908, 5466), (14966, 297), (15958, 95), (18315, 276), (18877, 2394), (20975, 23105), (22115, 3268), (23181, 311), (23963, 112), (23964, 15352), (32640, 16080), (32656, 10), (32662, 94), (32729, 17983)

X(32662) = BARYCENTRIC PRODUCT X(3)*X(476)

X(32662) is the barycentric product of the circumcircle intercepts of line X(3)X(125). As the barycentric product of circumcircle antipodes, X(32662) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32662) lies on these lines: {30, 50}, {32, 23967}, {94, 401}, {112, 476}, {187, 5961}, {248, 265}, {297, 18883}, {328, 15013}, {441, 18876}, {512, 1576}, {525, 4558}, {577, 32663}, {647, 32661}, {691, 23969}, {1415, 32678}, {1625, 2623}, {2420, 2433}, {2966, 14592}, {3284, 13754}, {14590, 16077}, {14591, 30510}, {14966, 23968}, {16813, 23582}, {23588, 32650}, {32708, 32711} et al

X(32662) = isogonal conjugate of polar conjugate of X(476)
X(32662) = isotomic conjugate of polar conjugate of X(14560)
X(32662) = X(92)-isoconjugate of X(526)
X(32662) = trilinear pole of line X(184)X(5158)
X(32662) = crossdifference of every pair of points on line X(3258)X(16186)
X(32662) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 476}, {63, 32678}, {69, 14560}, {94, 32661}, {110, 265}, {249, 14582}, {328, 1576}, {925, 5961}, {1141, 23181}, {1989, 4558}, {2166, 4575}, {2410, 32663}, {8552, 23588}, {14592, 23357}
X(32662) = barycentric quotient X(i)/X(j) for these (i,j): (3, 3268), (48, 32679), (110, 340), (112, 14165), (184, 526), (265, 850), (476, 264), (577, 8552), (1576, 186), (1625, 14918), (1989, 14618), (2420, 14920), (3049, 2088), (3284, 5664), (4558, 7799), (5961, 6563), (8552, 23965), (14560, 4), (14582, 338), (14592, 23962), (14908, 9213), (23181, 1273), (23357, 14590), (32661, 323), (32663, 2411), (32678, 92)

X(32663) = BARYCENTRIC PRODUCT X(3)*X(477)

X(32663) is the barycentric product of the circumcircle intercepts of line X(3)X(9033). As the barycentric product of circumcircle antipodes, X(32663) lies on the conic {{A,B,C,X(112),X(248)}} with center X(22391) and perspector X(184).

X(32663) lies on these lines: {6, 32640}, {50, 112}, {248, 14220}, {577, 32662}, {647, 18877}, {841, 32690}, {1495, 1576}, {2966, 30528}, {3284, 32661}, {4558, 11064}, {6587, 14910}, {14586, 18365}

X(32663) = isogonal conjugate of polar conjugate of X(477)
X(32663) = X(92)-isoconjugate of X(5663)
X(32663) = trilinear pole of line X(184)X(9409)
X(32663) = crossdifference of every pair of points on line X(11251)X(18809)
X(32663) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 477}, {110, 14220}, {647, 30528}, {2411, 32662}
X(32663) = barycentric quotient X(i)/X(j) for these (i,j): (477, 264), (14220, 850), (30528, 6331), (32662, 2410)

X(32664) = CENTER OF LOCUS OF BARYCENTRIC PRODUCT OF CIRCUMCIRCLE-X(1)-ANTIPODES

The locus of the barycentric product of circumcircle-X(1)-antipodes is a circumconic that is also the locus of the trilinear product of circumcircle-X(6)-antipodes, and the locus of trilinear poles of lines passing through X(31). The conic is the isogonal conjugate of line X(514)X(661), and passes through X(101), X(163), X(662), X(693), X(909), X(913), X(923), X(1415), X(1438), X(1461), X(1910), X(2159), X(2576), X(2577), X(4586), X(4593), X(8632), X(9456), X(18268), X(24019), X(32665), X(32666), X(32667), X(32668), X(32669), X(32670), X(32671), X(32672), X(32673), X(32674), X(32675), X(32676), X(32677), X(32678). The perspector of this conic is X(31).

X(32664) lies on these lines: {2, 7357}, {31, 1501}, {41, 6186}, {48, 354}, {101, 3681}, {184, 2225}, {379, 2140}, {561, 4586}, {572, 11220}, {604, 1401}, {748, 2112}, {1495, 16588}, {3185, 32739} et al

X(32664) = complement of X(7357)
X(32664) = perspector of circumconic centered at X(31)
X(32664) = X(2)-Ceva conjugate of X(31)

X(32665) = BARYCENTRIC PRODUCT X(100)*X(106)

As the barycentric product of circumcircle-X(1)-antipodes, X(32665) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32665) lies on these lines: {36, 909}, {41, 16944}, {88, 2224}, {100, 32686}, {101, 649}, {106, 919}, {662, 1019}, {667, 692}, {813, 6551}, {859, 3285}, {913, 8752}, {1262, 1461}, {1320, 5011}, {1415, 2149}, {1783, 32705}, {7115, 32674}, {23981, 32675} et al

X(32665) = isogonal conjugate of X(3762)
X(32665) = trilinear pole of line X(31)X(692)
X(32665) = complement of anticomplementary conjugate of X(21222)
X(32665) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 901}, {6, 3257}, {31, 4555}, {75, 32719}, {88, 101}, {100, 106}, {109, 1320}, {110, 4674}, {163, 4080}, {244, 6551}, {649, 5376}, {692, 903}, {1332, 8752}, {1415, 4997}, {6335, 32659}
X(32665) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3762), (31, 900), (32, 1635), (41, 1639), (88, 3261), (100, 3264), (101, 4358), (106, 693), (163, 16704), (667, 1647), (692, 519), (901, 75), (1415, 3911), (3257, 76), (4080, 20948), (4555, 561), (4674, 850), (5376, 1978), (6551, 7035), (8752, 17924), (16944, 4453), (32659, 905), (32719, 1)

X(32666) = BARYCENTRIC PRODUCT X(101)*X(105)

As the barycentric product of circumcircle-X(1)-antipodes, X(32666) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32666) lies on these lines: {101, 663}, {105, 2224}, {662, 3737}, {666, 4586}, {667, 1415}, {692, 3063}, {884, 32675}, {909, 2195}, {911, 2223}, {1416, 1457}, {1438, 2210}, {1461, 24027}, {8750, 32703}, {8751, 32699}, {9456, 32719}, {32644, 32656}, {32724, 32739}

X(32666) = trilinear pole of line X(31)X(9447)
X(32666) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 919}, {31, 666}, {100, 1438}, {101, 105}, {109, 294}, {110, 18785}, {163, 13576}, {644, 1416}, {649, 5377}, {651, 2195}, {673, 692}, {884, 4564}, {1415, 14942}, {1461, 28071}, {2481, 32739}, {24027, 28132}
X(32666) = barycentric quotient X(i)/X(j) for these (i,j): (31, 918), (101, 3263), (105, 3261), (109, 27818), (110, 18157), (163, 30941), (663, 693), (666, 561), (692, 3912), (884, 4858), (919, 75), (1415, 9436), (1416, 24002), (2195, 4391), (5377, 1978), (13576, 20948), (18785, 850), (32656, 25083), (32739, 518)

X(32667) = BARYCENTRIC PRODUCT X(102)*X(108)

As the barycentric product of circumcircle-X(1)-antipodes, X(32667) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32667) lies on these lines: {101, 7115}, {102, 32688}, {108, 32683}, {909, 32702}, {1415, 32643}, {1457, 32647}, {2432, 2443}, {23985, 32674}

X(32667) = barycentric product X(i)*X(j) for these lines: {i,j}: {92, 32643}, {102, 108}, {2432, 7128}
X(32667) = barycentric quotient X(i)/X(j) for these (i,j): (32643, 63)

X(32668) = BARYCENTRIC PRODUCT X(103)*X(934)

As the barycentric product of circumcircle-X(1)-antipodes, X(32668) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32668) lies on these lines: {101, 1262}, {692, 24027}, {934, 32684}, {1019, 24019}, {1461, 23971}, {6614, 32674)}, {32701, 32714}

X(32668) = trilinear pole of line X(31)X(7099)
X(32668) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 24016}, {103, 934}, {1815, 32714}, {2400, 24027}
X(32668) = barycentric quotient X(i)/X(j) for these (i,j): (103, 4397), (1815, 15416), (23971, 24015), (24016, 75), (24027, 2398)

X(32669) = BARYCENTRIC PRODUCT X(104)*X(109)

As the barycentric product of circumcircle-X(1)-antipodes, X(32669) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32669) lies on these lines: {101, 652}, {109, 32685}, {649, 32674}, {692, 1946}, {909, 1404}, {1415, 23979}, {2423, 2425}, {7113, 14578}

X(32669) = isogonal conjugate of isotomic conjugate of X(37136)
X(32669) = isogonal conjugate of polar conjugate of X(36110)
X(32669) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 2720}, {63, 32702}, {104, 109}, {108, 1795}, {651, 909}, {653, 14578}, {2423, 4564}
X(32669) = barycentric quotient X(i)/X(j) for these (i,j): (109, 3262), (692, 6735), (909, 4391), (1415, 908), (2423, 4858), (2720, 75), (14578, 6332), (23979, 24029), (32702, 92)

X(32670) = BARYCENTRIC PRODUCT X(107)*X(26701)

As the barycentric product of circumcircle-X(1)-antipodes, X(32670) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32670) lies on these lines: {163, 23964}, {662, 23582}, {2159, 32695}, {23590, 24019}, {26701, 32687}

X(32670) = barycentric product X(i)*X(j) for these lines: {i,j}: {107, 26701}
X(32670) = barycentric quotient X(i)/X(j) for these (i,j): (26701, 3265)

X(32671) = BARYCENTRIC PRODUCT X(110)*X(759)

As the barycentric product of circumcircle-X(1)-antipodes, X(32671) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32671) lies on these lines: {163, 23357}, {249, 662}, {759, 1910}, {923, 32729}, {2159, 32640}, {9274, 99500}, {23964,24019}

X(32671) = trilinear pole of line X(31)X(1576)
X(32671) = isogonal conjugate of isotomic conjugate of X(37140)
X(32671) = barycentric product X(i)*X(j) for these lines: {i,j}: {110, 759}, {163, 24624}, {1576, 14616}
X(32671) = barycentric quotient X(i)/X(j) for these (i,j): (163, 3936), (759, 850), (1576, 758), (23357, 4585), (24624, 20948)

X(32672) = BARYCENTRIC PRODUCT X(111)*X(8691)

As the barycentric product of circumcircle-X(1)-antipodes, X(32672) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32672) lies on these lines: {163, 32729}, {662, 691}

X(32673) = BARYCENTRIC PRODUCT X(112)*X(26702)

As the barycentric product of circumcircle-X(1)-antipodes, X(32673) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32673) lies on these lines: {250, 662}, {1910, 32696}, {2159, 32715}, {10423, 26702}

X(32674) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(1)X(4)

As the barycentric product of circumcircle-X(1)-antipodes, X(32674) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31), and as the barycentric product of circumcircle-X(4)-antipodes, X(32674) also lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32674) lies on these lines: {1, 20613}, {6, 3209}, {19, 604}, {34, 1438}, {41, 208}, {48, 2331}, {56, 607}, {65, 2332}, {101, 108}, {109, 112}, {196, 2301}, {204, 2187}, {207, 7114}, {221, 3172}, {225, 1910}, {232, 17966}, {278, 2224}, {281, 3476}, {478, 21148}, {608, 8752}, {648, 653}, {649, 32669}, {692, 2498}, {906, 23981}, {923, 8753}, {1033, 3197}, {1249, 1630}, {1319, 5089}, {1400, 2159}, {1402, 1945}, {1411, 1474}, {1415, 2425}, {1420, 7719}, {1429, 5236}, {1461, 32714}, {1767, 7125}, {1826, 7120}, {1877, 2201}, {1886, 2202}, {2172, 21147}, {3192, 17408}, {6589, 32643}, {6591, 32675}, {6614, 32668}, {7115, 32665}, {8687, 32691}, {23985, 32667} et al

X(32674) = isogonal conjugate of X(6332)
X(32674) = polar conjugate of isotomic conjugate of X(109)
X(32674) = crossdifference of every pair of points on line X(2968)X(4082)
X(32674) = trilinear pole of line X(25)X(31) (the isogonal conjugate of the isotomic conjugate of line X(1)X(4))
X(32674) = barycentric product of PU(100)
X(32674) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 108}, {4, 109}, {6, 653}, {7, 8750}, {9, 32714}, {19, 651}, {25, 664}, {27, 4559}, {28, 4551}, {31, 18026}, {33, 934}, {34, 100}, {41, 13149}, {56, 1897}, {57, 1783}, {65, 162}, {73, 107}, {92, 1415}, {101, 278}, {102, 23987}, {104, 23706}, {110, 225}, {112, 226}, {190, 608}, {208, 13138}, {273, 692}, {281, 1461}, {388, 32691}, {514, 7115}, {521, 24033}, {604, 6335}, {607, 658}, {648, 1400}, {811, 1402}, {901, 1877}, {919, 5236}, {1411, 4242}, {1474, 4552}, {1826, 4565}, {1945, 1981}, {1973, 4554}, {3476, 9088}, {4564, 6591}, {6332, 23985}, {6614, 7046}, {17923, 32675}, {23979, 32707}
X(32674) = barycentric quotient X(i)/X(j) for these (i,j): (6, 6332), (19, 4391), (25, 522), (28, 18155), (31, 521), (33, 4397), (34, 693), (56, 4025), (57, 15413), (65, 14208), (73, 3265), (100, 3718), (101, 345), (108, 75), (109, 69), (110, 332), (112, 333), (162, 314), (163, 1812), (208, 17896), (225, 850), (226, 3267), (278, 3261), (604, 905), (607, 3239), (608, 514), (648, 28660), (649, 26932), (651, 304), (653, 76), (664, 305), (692, 78), (906, 3719), (934, 7182), (1400, 525), (1402, 656), (1415, 63), (1461, 348), (1474, 4560), (1783, 312), (1897, 3596), (1973, 650), (3172, 14331), (3209, 14837), (4551, 20336), (4559, 306), (6335, 28659), (6591, 4858), (6614, 7056), (7115, 190), (7120, 17899), (8750, 8), (13149, 20567), (18026, 561), (23706, 3262), (23979, 1813), (23985, 653), (24027, 6516), (24033, 18026), (32676, 21), (32691, 30479), (32714, 85)

X(32675) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(1)X(5)

As the barycentric product of circumcircle-X(1)-antipodes, X(32675) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31), and as the barycentric product of circumcircle-X(5)-antipodes, X(32675) also lies on conic {{A,B,C,X(112),X(1987)}} with perspector X(51).

X(32675) lies on these lines: {101, 650}, {163, 1625}, {649, 1415}, {654, 32641}, {655, 662}, {663, 692}, {884, 32666}, {909, 1319}, {911, 1055}, {913, 14571}, {1404, 1457}, {1411, 1438}, {1429, 2006}, {1461, 3669}, {2159, 19297}, {2183, 32677}, {2423, 2425}, {17923, 32674}, {23981, 32665} et al

X(32675) = isogonal conjugate of X(3904)
X(32675) = trilinear pole of line X(31)X(51) (the isogonal conjugate of the isotomic conjugate of line X(1)X(5))
X(32675) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 2222}, {6, 655}, {80, 109}, {100, 1411}, {101, 2006}, {108, 1807}, {654, 23592}, {692, 18815}, {1415, 18359}, {14628, 32665}
X(32675) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3904), (109, 320), (655, 76), (692, 4511), (1411, 693), (1415, 3218), (2006, 3261), (2222, 75), (32674, 17923)

X(32676) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(1)X(19)

As the barycentric product of circumcircle-X(1)-antipodes, X(32676) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31), and as the barycentric product of circumcircle-X(19)-antipodes, X(32676) also lies on conic {{A,B,C,X(162),X(8750)}} with perspector X(1973).

X(32676) lies on these lines: {19, 560}, {28, 2224}, {31, 2159}, {101, 112}, {107, 15440}, {110, 32691}, {162, 662}, {648, 4586}, {692, 2873}, {811, 4593}, {823, 24000}, {909, 2206}, {911, 1333}, {923, 1973}, {1086, 14119}, {1415, 1576}, {1438, 1474}, {1582, 20883}, {1974, 18268}, {2194, 2288}, {2203, 9456} et al

X(32676) = isogonal conjugate of X(14208)
X(32676) = polar conjugate of X(20948)
X(32676) = X(i)-isoconjugate of X(j) for these lines: {i,j}: {1, 14208}, {2, 525}, {4, 3265}, {6, 3267}, {48, 20948}, {690, 30786}, {3566, 6340}
X(32676) = trilinear pole of line X(31)X(1932)
X(32676) = crossdifference of every pair of points on line X(3708)X(4466)
X(32676) = barycentric product of PU(108)
X(32676) = trilinear product of circumcircle intercepts of Moses radical circle
X(32676) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 112}, {3, 24019}, {4, 163}, {6, 162}, {19, 110}, {21, 32674}, {25, 662}, {27, 692}, {28, 101}, {29, 1415}, {31, 648}, {32, 811}, {33, 4565}, {34, 5546}, {48, 107}, {58, 1783}, {63, 32713}, {92, 1576}, {99, 1973}, {100, 1474}, {108, 284}, {109, 1172}, {184, 823}, {190, 2203}, {240, 2715}, {286, 32739}, {560, 6331}, {647, 24000}, {649, 5379}, {651, 2299}, {653, 2194}, {799, 1974}, {909, 4246}, {911, 4241}, {923, 4235}, {1333, 1897}, {1461, 4183}, {1969, 14574}, {2159, 4240}, {2206, 6335}, {2224, 4249}, {2303, 32691}, {4593, 27369}, {4630, 20883}
X(32676) = barycentric quotient X(i)/X(j) for these (i,j): (1, 3267), (4, 20948), (6, 14208), (19, 850), (25, 1577), (28, 3261), (31, 525), (32, 656), (48, 3265), (58, 15413), (101, 20336), (107, 1969), (108, 349), (109, 1231), (110, 304), (112, 75), (162, 76), (163, 69), (184, 24018), (560, 647), (648, 561), (662, 305), (669, 3708), (692, 306), (811, 1502), (823, 18022), (923, 14977), (1333, 4025), (1415, 307), (1474, 693), (1576, 63), (1783, 313), (1897, 27801), (1973, 523), (1974, 661), (2194, 6332), (2203, 514), (2206, 905), (2299, 4391), (2715, 336), (4565, 7182), (5379, 1978), (5546, 3718), (6331, 1928), (8750, 321), (9780, 4466), (14574, 48), (24000, 6331), (24019, 264), (27369, 8061), (32674, 1441), (32713, 92), (32739, 72)

X(32677) = BARYCENTRIC PRODUCT X(1)*X(102)

X(32677) is the barycentric product of the circumcircle intercepts of line X(1)X(521). As the barycentric product of circumcircle-X(1)-antipodes, X(32677) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32677) lies on these lines: {6, 3209}, {25, 2192}, {48, 1415}, {101, 102}, {163, 2193}, {197, 2875}, {212, 692}, {222, 1461}, {654, 909}, {662, 1812}, {1172, 1905}, {2182, 6001}, {2183, 32675}, {2194, 2288}, {2431, 8677}, {7113, 14578}

X(32677) = isogonal conjugate of isotomic conjugate of X(36100)
X(32677) = polar conjugate of isotomic conjugate of X(36055)
X(32677) = X(2)-isoconjugate of X(515)
X(32677) = trilinear pole of line X(31)X(1946)
X(32677) = trilinear product X(6)*X(102)
X(32677) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 102}, {57, 15629}, {651, 2432}, {1415, 2399}
X(32677) = barycentric quotient X(i)/X(j) for these (i,j): (31, 515), (102, 75), (1415, 2406), (2432, 4391), (15629, 312)

X(32678) = BARYCENTRIC PRODUCT X(1)*X(476)

X(32678) is the barycentric product of the circumcircle intercepts of line X(1)X(564). As the barycentric product of circumcircle-X(1)-antipodes, X(32678) lies on conic {{A,B,C,X(101),X(163)}} with center X(32664) and perspector X(31).

X(32678) lies on these lines: {101, 476}, {163, 661}, {662, 1577}, {923, 8772}, {1415, 32662}, {1725, 2159}, {1910, 2166}, {9455, 11076}, {11060, 18268}

X(32678) = isogonal conjugate of X(32679)
X(32678) = trilinear pole of line X(31)X(2153)
X(32678) = polar conjugate of isotomic conjugate of X(36061)
X(32678) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 476}, {6, 32680}, {75, 14560}, {92, 32662}, {94, 163}, {110, 2166}, {162, 265}, {328, 32676}, {662, 1989}, {799, 11060}
X(32678) = barycentric quotient X(i)/X(j) for these (i,j): (1, 3268), (6, 32679), (48, 8552), (94, 20948), (162, 340), (163, 323), (265, 14208), (476, 75), (662, 7799), (923, 9213), (1989, 1577), (2166, 850), (11060, 661), (14560, 1), (32680, 76), (32662, 63), (32676, 186)

X(32679) = ISOGONAL CONJUGATE OF X(32678)

X(32679) lies on these lines: {163, 662}, {323, 14838}, {442, 6366}, {514, 661}, {2349, 2631}, {2573, 19178}, {2610, 3960}, {4707, 5664}, {7202, 8287}, {8773, 23894}, {10015, 17056}, {16559, 16563}

X(32679) = isogonal conjugate of X(32678)
X(32679) = isotomic conjugate of X(32680)
X(32679) = crossdifference of every pair of points on line X(31)X(2153)
X(32679) = polar conjugate of X(36129)
X(32679) = pole wrt polar circle of trilinear polar of X(36129) (line X(19)X(23894))
X(32679) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 3268}, {50, 20948}, {75, 526}, {92, 8552}, {186, 14208}, {323, 1577}, {340, 656}, {561, 14270}, {661, 7799}, {799, 2088}, {850, 6149}, {2349, 5664}, {3219, 4707}, {3936, 14838}, {3960, 3969}, {4585, 8287}, {14590, 20902}
X(32679) = barycentric quotient X(i)/X(j) for these (i,j): (1, 476), (6, 32678), (31, 14560), (48, 32662), (50, 163), (186, 162), (323, 662), (340, 811), (526, 1), (656, 265), (661, 1989), (1577, 94), (2088, 661), (2610, 8818), (3268, 75), (3936, 15455), (4707, 30690), (5664, 14206), (6149, 110), (7799, 799), (8552, 63), (14208, 328), (14270, 31), (14838, 24624), (20902, 14592), (20948, 20573), (21828, 2160)

X(32680) = TRILINEAR PRODUCT X(2)*X(476)

X(32680) is the trilinear product of the circumcircle intercepts of line X(2)X(94) (the isotomic conjugate of the isogonal conjugate of the Fermat axis). As the trilinear product of circumcircle-X(2)-antipodes, X(32680) lies on conic {{A,B,C,X(100),X(162)}} with center X(9) and perspector X(1). X(32680) is also the barycentric product of the circumcircle intercepts of line X(75)X(2166).

Let H be the rectangular hyperbola passing through X(1), X(5), X(30) and the excenters (centered at X(476)); then X(32680) is the perspector of ABC and the tangential triangle, wrt excentral triangle, of H.

X(32680) lies on these lines: {94, 24624}, {100, 476}, {162, 24006}, {662, 1577}, {799, 20948}, {897, 1733}, {1101, 2618}, {1492, 14560}, {1821, 16568}, {2349, 14206}, {5802, 10991}

X(32680) = isogonal conjugate of X(2624)
X(32680) = isotomic conjugate of X(32679)
X(32680) = X(6)-isoconjugate of X(526)
X(32680) = trilinear pole of line X(1)X(564)
X(32680) = polar conjugate of isogonal conjugate of X(36061)
X(32680) = trilinear product X(i)*X(j) for these lines: {i,j}: {2, 476}, {75, 32678}, {76, 14560}, {94, 110}, {99, 1989}, {112, 328}, {250, 14592}, {662, 2166}, {759, 15455}, {1576, 20573}, {3268, 23588}, {6742, 24624}
X(32680) = trilinear quotient X(i)/X(j) for these (i,j): (2, 526), (6, 14270), (75, 32679), (76, 3268), (94, 523), (99, 323), (110, 50), (250, 14591), (329, 3267), (476, 6), (526, 18334), (662, 6149), (1989, 512), (2166, 661), (6742, 2245), (14560, 32), (14592, 125), (15455, 758), (20573, 850), (23588, 14560), (24624, 2605), (32678, 31)
X(32680) = barycentric product X(i)*X(j) for these lines: {i,j}: {75, 476}, {76, 32678}, {94, 662}, {99, 2166}, {162, 328}, {163, 20573}, {561, 14560}, {799, 1989}, {6742, 14616}, {15455, 24624}
X(32680) = barycentric quotient X(i)/X(j) for these (i,j): (1, 526), (31, 14270), (63, 8552), (75, 3268), (94, 1577), (110, 6149), (162, 186), (328, 14208), (476, 1), (662, 323), (759, 2605), (799, 7799), (897, 9213), (1989, 661), (2166, 523), (3268, 32679), (6742, 758), (14206, 5664), (14560, 31), (14616, 4467), (15455, 3936), (20573, 20948), (24624, 14838), (32678, 6)

X(32681) = BARYCENTRIC PRODUCT X(74)*X(1302)

As the barycentric product of circumcircle-X(2)-antipodes, X(32681) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(30) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32681).

X(32681) lies on the circumcircle and these lines: {6, 841}, {74, 3003}, {110, 32640}, {1300, 1990}, {1302, 9209}, {2420, 10420}, {2433, 9060} et al

X(32681) = Λ(PU(168))
X(32681) = Λ(X(1637), X(5664))
X(32681) = Λ(X(8552), X(14566))
X(32681) = Ψ(X(2), X(74))
X(32681) = barycentric product X(74)*X(1302)
X(32681) = barycentric quotient X(i)/X(j) for these (i,j): (74, 30474), (1302, 3260), (32640, 15066)

X(32682) = BARYCENTRIC PRODUCT X(101)*X(675)

As the barycentric product of circumcircle-X(2)-antipodes, X(32682) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(31) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32682).

X(32682) lies on the circumcircle and these lines: {98, 17734}, {99, 4570}, {100, 1110}, {101, 6586}, {102, 13329}, {103, 32642}, {105, 2224}, {106, 32719}, {675, 3011}, {759, 5009}, {789, 5384}, {813, 1983}, {840, 4257}, {917, 32699}, {934, 24027}, {953, 995}, {1311, 1737} et al

X(32682) = isogonal conjugate of ideal point of 1st and 2nd isobarycs of X(101)
X(32682) = Ψ(X(2), X(101))
X(32682) = barycentric product X(i)*X(j) for these lines: {i,j}: {100, 2224}, {101, 675}
X(32682) = barycentric quotient X(i)/X(j) for these (i,j): (101, 3006), (2224, 693), (675, 3261)

X(32683) = BARYCENTRIC PRODUCT X(102)*X(9056)

As the barycentric product of circumcircle-X(2)-antipodes, X(32683) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(652) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32683).

X(32683) lies on the circumcircle and these lines: {102, 8607}, {108, 32667}, {109, 32643}, {8755, 32706}, {26704, 32700}, {26715, 32720}

X(32683) = Ψ(X(2), X(102))

X(32684) = BARYCENTRIC PRODUCT X(103)*X(9057)

As the barycentric product of circumcircle-X(2)-antipodes, X(32684) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(657) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32684).

X(32684) lies on the circumcircle and these lines: {101, 32642}, {103, 8608}, {917, 1886}, {934, 32668}, {26705, 32701}, {26716, 32721}

X(32684) = Ψ(X(2), X(103))

X(32685) = BARYCENTRIC PRODUCT X(104)*X(9058)

As the barycentric product of circumcircle-X(2)-antipodes, X(32685) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(650) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32685).

X(32685) lies on the circumcircle and these lines: {100, 32641}, {102, 5053}, {104, 8609}, {108, 32702}, {109, 32669}, {915, 14571}, {998, 2717}, {1983, 2743}, {2427, 6099}, {32722, 32723}

X(32685) = Ψ(X(2), X(104))

X(32686) = BARYCENTRIC PRODUCT X(106)*X(9059)

As the barycentric product of circumcircle-X(2)-antipodes, X(32686) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(649) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32686).

X(32686) lies on the circumcircle and these lines: {99, 4582}, {100, 32665}, {101, 32719}, {106, 5053}, {110, 5548}, {996, 2726}, {1293, 32645}, {3257, 13396}, {32704, 32705}

X(32686) = Ψ(X(2), X(106))
X(32686) = barycentric product X(i)*X(j) for these lines: {i,j}: {106, 9059}, {901, 996}
X(32686) = barycentric quotient X(i)/X(j) for these (i,j): (901, 4389), (9059, 3264), (32719, 995)

X(32687) = BARYCENTRIC PRODUCT X(107)*X(1297)

As the barycentric product of circumcircle-X(2)-antipodes, X(32687) lies on the circumcircle.

Let A', B', C' be the intersections of the van Aubel line and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32687).

X(32687) lies on the circumcircle and these lines: {74, 8744}, {98, 6530}, {99, 20580}, {107, 6587}, {110, 23964}, {112, 32649}, {232, 1297}, {393, 2697}, {647, 1301}, {1289, 6529}, {26701, 32670}, {26717, 32725} et al

X(32687) = Λ(X(i), X(j)) for these lines: {i,j}: {2, 14345}, {287, 2419}, {648, 2404}, {3269, 15526}
X(32687) = Ψ(X(2), X(107))
X(32687) = Moses-radical-circle-inverse of X(1301)
X(32687) = polar-circle-inverse of X(33504)
X(32687) = barycentric product X(i)*X(j) for these lines: {i,j}: {107, 1297}, {264, 32649}
X(32687) = barycentric quotient X(i)/X(j) for these (i,j): (1297, 3265), (32649, 3)

X(32688) = BARYCENTRIC PRODUCT X(108)*X(26703)

As the barycentric product of circumcircle-X(2)-antipodes, X(32688) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(19) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32688).

X(32688) lies on the circumcircle and these lines: {100, 7115}, {102, 32667}, {104, 32702}, {108, 6588}, {1295, 32647}, {1415, 26706}, {5089, 26703}, {32726, 32727}

X(32688) = Ψ(X(2), X(108))
X(32688) = polar-circle-inverse of X(38972)

X(32689) = BARYCENTRIC PRODUCT X(109)*X(1311)

As the barycentric product of circumcircle-X(2)-antipodes, X(32689) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(41) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32689).

X(32689) lies on the circumcircle and these lines: {100, 2149}, {102, 32643}, {104, 32669}, {109, 6589}, {2291, 32728}, {3064, 26704}, {8558, 26703}, {32706, 32707}

X(32689) = Ψ(X(2), X(109))

X(32690) = BARYCENTRIC PRODUCT X(477)*X(9060)

As the barycentric product of circumcircle-X(2)-antipodes, X(32690) lies on the circumcircle.

Let A', B', C' be the intersections of line X(6)X(1637) and lines BC, CA, AB, resp. The circumcircles of triangles AB'C', BC'A', CA'B' concur in X(32690).

X(32690) lies on the circumcircle and these lines: {99, 30528}, {476, 32650}, {477, 3018}, {841, 32663}, {1304, 32712}, {32732, 32733}

X(32690) = Ψ(X(2), X(477))

X(32691) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(2)X(19)

As the barycentric product of circumcircle-X(2)-antipodes, X(32691) lies on the circumcircle, and as the barycentric product of circumcircle-X(19)-antipodes, X(32691) also lies on conic {{A,B,C,X(162),X(8750)}} with perspector X(1973).

Let P be a point of the line X(2)X(19), other than X(2). Let A'B'C' be the cevian triangle of P. Let A" be the {B,C}-harmonic conjugate of A' (i.e., A" = BC∩B'C'), and define B" and C" cyclically. The circumcircles of AB"C", BC"A", CA"B" concur in X(32691).

X(32691) lies on the circumcircle and these lines: {4, 5515}, {25, 28476}, {74, 1245}, {99, 162}, {100, 8750}, {102, 1036}, {103, 2221}, {104, 1039}, {105, 5338}, {110, 32676}, {595, 11383}, {689, 32691}, {759, 17520}, {833, 4242}, {1897, 8707}, {2249, 2281}, {2339, 26703}, {2370, 11319}, {8687, 32674}.

X(32691) = isogonal conjugate of X(23874)
X(32691) = trilinear pole of line X(6)X(1245)
X(32691) = inverse-in-polar-circle of X(5515)
X(32691) = cevapoint of X(8646) and X(21750)
X(32691) = Ψ(X(i), X(j)) for these (i,j): (1, 25), (2, 19), (3, 31), (6, 1245), (63, 6), (69, 1), (75, 4), (1010, 2)
X(32691) = X(834)-cross conjugate of X(4)
X(32691) = trilinear product of circumcircle intercepts of line X(1)X(25)
X(32691) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23874}, {2, 2522}, {3, 2517}, {63, 6590}, {69, 8678}, {100, 26933}, {304, 2484}, {305, 8646}, {388, 521}, {514, 5227}, {522, 1038}, {525, 2303}, {612, 4025}, {649, 19799}, {656, 1010}, {693, 7085}, {905, 2345}, {1019, 3610}, {1459, 4385}, {2285, 6332}, {2286, 4391}, {3265, 4206}, {4131, 7102}, {7004, 14594}, {8898, 15411}
X(32691) = barycentric product X(i)*X(j) for these lines: {i,j}: {19, 1310}, {108, 2339}, {648, 1245}, {651, 1039}, {653, 1036}, {811, 2281}, {1897, 2221}, {30479, 32674}
X(32691) = barycentric quotient X(i)/X(j) for these (i,j): (19, 2517), (25, 6590), (31, 2522), (100, 19799), (112, 1010), (1036, 6332), (1039, 4391), (1245, 525), (1310, 304), (1415, 1038), (2221, 4025), (2281, 656), (8750, 2345), (32674, 388), (32676, 2303)

X(32692) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(2)X(54)

As the barycentric product of circumcircle-X(2)-antipodes, X(32692) lies on the circumcircle.

Let P be a point of the line X(2)X(54), other than X(2). Let A'B'C' be the cevian triangle of P. Let A" be the {B,C}-harmonic conjugate of A' (i.e., A" = BC∩B'C'), and define B" and C" cyclically. The circumcircles of AB"C", BC"A", CA"B" concur in X(32692).

X(32692) lies on the circumcircle and these lines: {4, 139}, {6, 2383}, {54, 3563}, {74, 15664}, {96, 98}, {99, 18315}, {110, 14586}, {112, 32734}, {759, 2168}, {847, 14585}, {925, 32661}, {1141, 2165}, {1297, 10625}, {1299, 8882}, {1300, 14533}, {1971, 5962}, {2623, 10420} et al

X(32692) = trilinear pole of line X(6)X(2351) (the tangent to hyperbola {A,B,C,X(5),X(6)} at X(6))
X(32692) = inverse-in-polar-circle of X(139)
X(32692) = Ψ(X(i), X(j)) for these (i,j): (2, 54), (5, 6), (6, 2351), (51, 31), (76, 95), (317, 2)
X(32692) = Λ(trilinear polar of isotomic conjugate of X(96))
X(32692) = X(52)-isoconjugate of X(1577)
X(32692) = barycentric product X(i)*X(j) for these lines: {i,j}: {54, 925}, {68, 933}, {95, 32692}, {96, 110}, {662, 2168}, {847, 15958}, {2165, 18315}, {2351, 18831}, {5392, 14586}, {14533, 30450}
X(32692) = barycentric quotient X(i)/X(j) for these (i,j): (54, 6563), (96, 850), (925, 311), (933, 317), (1576, 52), (2165, 18314), (2168, 1577), (2351, 6368), (5392, 15415), (14586, 1993), (15958, 9723), (18315, 7763), (32692, 5)

X(32693) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(2)X(65)

As the barycentric product of circumcircle-X(2)-antipodes, X(32693) lies on the circumcircle, and as the barycentric product of circumcircle-X(65)-antipodes, X(32693) also lies on conic {{A,B,C,X(651),X(1415)}} with perspector X(1402).

Let P be a point of the line X(2)X(65), other than X(2). Let A'B'C' be the cevian triangle of P. Let A" be the {B,C}-harmonic conjugate of A' (i.e., A" = BC∩B'C'), and define B" and C" cyclically. The circumcircles of AB"C", BC"A", CA"B" concur in X(32693).

X(32693) lies on the circumcircle and these lines: {99, 651}, {100, 4559}, {104, 941}, {105, 959}, {110, 1415}, {644, 8707}, {692, 8687}, {1311, 31359}, {1783, 26704}, {2258, 2291}, {2284, 6574} et al

X(32693) = trilinear pole of line X(6)X(1402)
X(32693) = Ψ(X(i), X(j)) for these (i,j): (2, 65), (6, 1402), (21, 6), (314, 2)
X(32693) = Λ(X(i), X(j)) for these lines: {i,j}: {650, 3975}, {693, 3669}, {905, 1577}
X(32693) = Λ(polar of X(10435) wrt Conway circle)
X(32693) = barycentric product X(i)*X(j) for these lines: {i,j}: {65, 931}, {100, 959}, {109, 31359}, {651, 941}, {664, 2258}
X(32693) = barycentric quotient X(i)/X(j) for these (i,j): (101, 11679), (109, 10436), (931, 314), (941, 4391), (959, 693), (1415, 940), (2258, 522)

X(32694) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(2)X(353)

As the barycentric product of circumcircle-X(2)-antipodes, X(32694) lies on the circumcircle.

X(32694) lies on the circumcircle and these lines: {6, 9831}, {32, 843}, {74, 2080}, {98, 8859}, {99, 3906}, {110, 17414}, {111, 1691}, {182, 842}, {187, 6323}, {249, 12074}, {511, 14388}, {512, 11636}, {805, 5467}, {1296, 9218}, {1297, 11416}, {2698, 11842}, {2710, 8722}, {2770, 9169} et al

X(32694) = trilinear pole, wrt circumsymmedial triangle, of line X(6)X(9208)
X(32694) = inverse-in-Schoute-circle of X(6323)
X(32694) = inverse-in-circle-{{X(1687),X(1688),PU(1),PU(2)}} of X(111)
X(32694) = Ψ(X(2), X(353))
X(32694) = Λ(X(i), X(j)) for these lines: {i,j}: {76, 9180}, {98, 14388}, {99, 5467}, {115, 17416}, {262, 14223}
X(32694) = barycentric quotient X(i)/X(j) for these (i,j): (32, 9208), (110, 7840)

X(32695) = BARYCENTRIC PRODUCT X(74)*X(107)

As the barycentric product of circumcircle-X(4)-antipodes, X(32695) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32695) lies on these lines: {74, 8744}, {112, 647}, {512, 32713}, {525, 648}, {878, 32696}, {1552, 16318}, {1990, 15311}, {2159, 32670}, {2433, 2442}, {2501, 6529} et al

X(32695) = polar conjugate of isotomic conjugate of X(1304)
X(32695) = trilinear pole of line X(25)X(8749) (the isogonal conjugate of the isotomic conjugate of line X(4)X(74))
X(32695) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 1304}, {6, 15459}, {25, 16077}, {74, 107}, {112, 16080}, {264, 32715}, {648, 8749}, {823, 2159}, {1494, 32713}, {2433, 23582}, {6529, 14919}
X(32695) = barycentric quotient X(i)/X(j) for these (i,j): (25, 9033), (32, 1636), (74, 3265), (107, 3260), (112, 11064), (512, 1650), (1304, 69), (2159, 24018), (2433, 15526), (8749, 525), (14919, 4143), (15459, 76), (16077, 305), (16080, 3267), (32713, 30), (32715, 3)

X(32696) = BARYCENTRIC PRODUCT X(98)*X(112)

As the barycentric product of circumcircle-X(4)-antipodes, X(32696) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32696) lies on these lines: {98, 403}, {112, 512}, {232, 248}, {250, 523}, {351, 1304}, {378, 14355}, {460, 6531}, {669, 23964}, {827, 22456}, {878, 32695}, {933, 6037}, {1783, 4705}, {1910, 32673}, {1976, 8749}, {2386, 11610}, {2422, 2445}, {2489, 32713}, {4079, 8750}, {4230, 32697}, {6529, 20031} et al

X(32696) = isogonal conjugate of X(6333)
X(32696) = polar conjugate of isotomic conjugate of X(2715)
X(32696) = trilinear pole of line X(25)X(1501) (the isogonal conjugate of the isotomic conjugate of line X(4)X(32))
X(32696) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 20031}, {4, 2715}, {6, 685}, {25, 2966}, {32, 22456}, {98, 112}, {107, 248}, {110, 6531}, {162, 1910}, {250, 2395}, {287, 32713}, {648, 1976}, {878, 23582}, {879, 23964}, {1289, 11610}, {2207, 17932}, {2422, 18020}, {2445, 9476}, {6037, 10311}, {6331, 14601}, {6528, 14600}, {6529, 17974}
X(32696) = barycentric quotient X(i)/X(j) for these (i,j): (6, 6333), (25, 2799), (32, 684), (98, 3267), (112, 325), (248, 3265), (250, 2396), (685, 76), (878, 15526), (1910, 14208), (1974, 3569), (1976, 525), (2207, 16230), (2395, 339), (2422, 125), (2445, 15595), (2489, 868), (2715, 69), (2966, 305), (6531, 850), (14600, 520), (14601, 647), (17974, 4143), (20031, 264), (22456, 1502), (23964, 877), (32713, 297)

X(32697) = BARYCENTRIC PRODUCT X(99)*X(3563)

As the barycentric product of circumcircle-X(4)-antipodes, X(32697) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32697) lies on these lines: {112, 249}, {186, 691}, {230, 297}, {250, 7468}, {648, 4590}, {1783, 4567}, {2489, 4558}, {4230, 32696}, {18879, 32708} et al

X(32697) = polar conjugate of isotomic conjugate of X(10425)
X(32697) = trilinear pole of line X(25)X(110) (the isogonal conjugate of the isotomic conjugate of line X(4)X(99))
X(32697) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 10425}, {99, 3563}, {112, 8781}, {162, 8773}, {648, 2987}
X(32697) = barycentric quotient X(i)/X(j) for these (i,j): (110, 3564), (112, 230), (162, 1733), (250, 4226), (2987, 525), (3563, 523), (4230, 114), (8773, 14208), (8781, 3267), (10425, 69)

X(32698) = BARYCENTRIC PRODUCT X(100)*X(915)

As the barycentric product of circumcircle-X(4)-antipodes, X(32698) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32698) lies on these lines: {112, 6099}, {648, 4567}, {906, 6591}, {913, 8752}, {915, 919}, {1110, 8750}, {1252, 1783}, {1262, 32714}, {2149, 32674}, {8609, 15500} et al

X(32698) = polar conjugate of isotomic conjugate of X(6099)
X(32698) = trilinear pole of line X(25)X(692) (the isogonal conjugate of the isotomic conjugate of line X(4)X(100))
X(32698) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 6099}, {100, 915}, {190, 913}, {1783, 2990}, {6335, 32655}
X(32698) = barycentric quotient X(i)/X(j) for these (i,j): (101, 914), (913, 514), (915, 693), (2990, 15413), (6099, 69), (8750, 1737), (32655, 905)

X(32699) = BARYCENTRIC PRODUCT X(101)*X(917)

As the barycentric product of circumcircle-X(4)-antipodes, X(32699) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32699) lies on these lines: {648, 4570}, {917, 32682}, {1110, 1783}, {7649, 32656}, {8608, 32642}, {8750, 23990}, {8751, 32666}, {8752, 32719}, {24027, 32714}

X(32699) = barycentric product X(i)*X(j) for these lines: {i,j}: {101, 917}, {2989, 8750}
X(32699) = barycentric quotient X(i)/X(j) for these (i,j): (917, 3261)

X(32700) = BARYCENTRIC PRODUCT X(102)*X(26704)

As the barycentric product of circumcircle-X(4)-antipodes, X(32700) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32700) lies on these lines: {6589, 32643}, {26704, 32683}

X(32701) = BARYCENTRIC PRODUCT X(103)*X(26705)

As the barycentric product of circumcircle-X(4)-antipodes, X(32701) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32701) lies on these lines: {1734, 1783}, {1886, 32657}, {6586, 8750}, {6589, 32643}, {26705, 32684}, {32668, 32714}

X(32702) = BARYCENTRIC PRODUCT X(104)*X(108)

As the barycentric product of circumcircle-X(4)-antipodes, X(32702) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32702) lies on these lines: {104, 32688}, {108, 32685}, {112, 2720}, {648, 4560}, {649, 32669}, {650, 1415}, {663, 8750}, {909, 32667}, {1309, 8687}, {1455, 14571}, {2423, 2443}, {3669, 32714}, {6591, 23985}

X(32702) = polar conjugate of isotomic conjugate of X(2720)
X(32702) = trilinear pole of line X(25)X(1397)
X(32702) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 2720}, {7, 14776}, {56, 1309}, {92, 32669}, {104, 108}, {653, 909}, {1415, 16082}
X(32702) = barycentric quotient X(i)/X(j) for these (i,j): (108, 3262), (909, 6332), (1309, 3596), (2720, 69), (8750, 6735), (14776, 8), (32669, 63)

X(32703) = BARYCENTRIC PRODUCT X(105)*X(26706)

As the barycentric product of circumcircle-X(4)-antipodes, X(32703) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32703) lies on these lines: {919, 1783}, {5089, 32658}, {8750, 32666}

X(32704) = CIRCUMCIRCLE-X(4)-ANTIPODE OF X(106)

X(32704) lies on the circumcircle and these lines: {3, 2370}, {4, 106}, {25, 9083}, {186, 2758}, {901, 1897}, {972, 30273}, {1311, 15626}, {32686, 32705}

X(32704) = reflection of X(i) in X(j) for these (i,j): (4, 20619), (2370, 3)
X(32704) = isogonal conjugate of X(32475)
X(32704) = circumcircle antipode of X(2370)
X(32704) = trilinear pole of line X(6)X(8756)
X(32704) = inverse-in-polar-circle of X(5510)
X(32704) = Λ(X(3), X(1459))
X(32704) = Ψ(X(i), X(j)) for these (i,j): (3, 519), (6, 8756), (106, 4), (1797, 2)
X(32704) = barycentric product X(3264)*X(32705)
X(32704) = 2nd-circumperp-isogonal conjugate of X(2390)
X(32704) = circumorthic-isogonal conjugate of X(2390) if ABC is acute

X(32705) = BARYCENTRIC PRODUCT X(106)*X(32704)

As the barycentric product of circumcircle-X(4)-antipodes, X(32705) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32705) lies on these lines: {648, 4591}, {1783, 32665}, {8756, 32659}, {32686, 32704}

X(32705) = barycentric quotient X(32704)/X(3264)

X(32706) = CIRCUMCIRCLE-X(4)-ANTIPODE OF X(109)

X(32706) lies on the circumcircle and these lines: {3, 21666}, {4, 109}, {24, 26704}, {25, 9056}, {29, 110}, {99, 7436}, {100, 318}, {101, 281}, {108, 158}, {112, 8748}, {186, 2689}, {242, 2728}, {273, 934}, {411, 13397}, {476, 2075}, {925, 4225}, {944, 7040}, {1294, 7454}, {1295, 7456}, {1297, 7441}, {1305, 7420}, {1766, 29014}, {2370, 7457}, {2373, 7439}, {3518, 26709}, {3565, 7415}, {5176, 6099}, {7424, 10420}, {7443, 26703}, {8750, 32719}, {8755, 32683}, {32689, 32707}

X(32706) = reflection of X(4) in X(20620)
X(32706) = trilinear pole of line X(6)X(3064)
X(32706) = inverse-in-polar-circle of X(117)
X(32706) = X(63)-isoconjugate of X(8607)
X(32706) = Λ(X(3), X(73))
X(32706) = Ψ(X(i), X(j)) for these (i,j): (3, 522), (6, 3064), (109, 4), (1813, 2)

X(32707) = BARYCENTRIC PRODUCT X(109)*X(32706)

As the barycentric product of circumcircle-X(4)-antipodes, X(32707) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32707) lies on these lines: {1783, 2149}, {3064, 32660}, {8607, 32643}, {23979, 32674}, {32689, 32706}

X(32708) = BARYCENTRIC PRODUCT X(110)*X(1300)

As the barycentric product of circumcircle-X(4)-antipodes, X(32708) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32708) lies on these lines: {112, 6753}, {186, 3003}, {249, 648}, {297, 2986}, {1300, 2715}, {2501, 32661}, {4240, 14591}, {6529, 23964}, {8753, 32729}, {18879, 32697}, {32662, 32711}

X(32708) = isogonal conjugate of X(6334)
X(32708) = polar conjugate of isotomic conjugate of X(10420)
X(32708) = trilinear pole of line X(25)X(1576)
X(32708) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 10420}, {6, 687}, {25, 18878}, {107, 5504}, {110, 1300}, {112, 2986}, {250, 15328}, {648, 14910}, {2501, 18879}, {4240, 10419}, {15421, 23964}
X(32708) = barycentric quotient X(i)/X(j) for these (i,j): (6, 6334), (32, 686), (112, 3580), (687, 76), (1300, 850), (2986, 3267), (5504, 3265), (10420, 69), (14910, 525), (15328, 339), (18878, 305), (18879, 4563), (23964, 16237), (32713, 403)

X(32709) = BARYCENTRIC PRODUCT X(111)*X(30247)

As the barycentric product of circumcircle-X(4)-antipodes, X(32709) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32709) lies on these lines: {112, 32729}, {468, 10422}, {648, 691}, {8753, 14580}

X(32710) = CIRCUMCIRCLE-X(4)-ANTIPODE OF X(476)

X(32710) lies on the circumcircle and these lines: {2, 16167}, {3, 10420}, {4, 476}, {24, 1304}, {25, 9060}, {30, 925}, {74, 924}, {99, 340}, {107, 403}, {110, 186}, {112, 3003}, {250, 1986}, {378, 691}, {468, 1302}, {523, 1300}, {562, 930}, {935, 18533}, {1287, 7576}, {1290, 7414}, {1291, 3520}, {1825, 2222}, {1835, 26700}, {2071, 13398}, {23969, 32711} et al

X(32710) = reflection of X(i) in X(j) for these (i,j): (4, 16221), (10420, 3)
X(32710) = isogonal conjugate of X(17702)
X(32710) = inverse-in-polar-circle of X(25641)
X(32710) = circumcircle antipode of X(10420)
X(32710) = X(63)-isoconjugate of X(3018)
X(32710) = trilinear pole of line X(6)X(686)
X(32710) = Λ(X(3), X(125))
X(32710) = Λ(X(4), X(110))
X(32710) = Ψ(X(i), X(j)) for these (i,j): (3, 526), (6, 686), (476, 4), (687, 2)
X(32710) = barycentric quotient X(i)/X(j) for these (i,j): (25, 3018), (112, 7471)

X(32711) = BARYCENTRIC PRODUCT X(476)*X(32710)

As the barycentric product of circumcircle-X(4)-antipodes, X(32711) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32711) lies on these lines: {3018, 32650}, {23969, 32710}, {32662, 32708}

X(32711) = trilinear pole of line X(25)X(14560)

X(32712) = BARYCENTRIC PRODUCT X(477)*X(1304)

As the barycentric product of circumcircle-X(4)-antipodes, X(32712) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25).

X(32712) lies on these lines: {648, 5664}, {1304, 32690}, {1637, 32640}, {2088, 8749}, {32715, 32733}

X(32713) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF VAN AUBEL LINE

As the barycentric product of circumcircle-X(4)-antipodes, X(32713) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25), and as the barycentric product of circumcircle-X(6)-antipodes, X(32713) also lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32713) lies on these lines: {4, 1177}, {25, 8749}, {107, 110}, {112, 1576}, {132, 23583}, {133, 9934}, {159, 15259}, {162, 1633}, {182, 10002}, {184, 6525}, {206, 1249}, {250, 7468}, {393, 1974}, {512, 32695}, {520, 15384}, {685, 15352}, {692, 1783}, {823, 1492}, {1304, 9064}, {1632, 2409}, {1660, 3079}, {1990, 18374}, {2207, 8753}, {2393, 15262}, {2445, 14398}, {2485, 32649}, {2489, 32696}, {4230, 4558}, {4577, 6528}, {5317, 8751}, {6523, 6759}, {6526, 26883}, {6529, 23977}, {8743, 20410}, {8745, 19118}, {10561, 23964}, {14569, 18384}, {20031, 32716}, {23590, 32725}

X(32713) = isogonal conjugate of X(3265)
X(32713) = polar conjugate of X(3267)
X(32713) = pole wrt polar circle of trilinear polar of X(3267) (line X(125)X(339))
X(32713) = trilinear pole of line X(25)X(32) (the isogonal conjugate of the isotomic conjugate of the van Aubel line)
X(32713) = center of bianticevian conic of X(6) and X(25)
X(32713) = X(i)-isoconjugate of X(j) for these lines: {i,j}: {1, 3265}, {2, 24018}, {3, 14208}, {48, 3267}
X(32713) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 24019}, {3, 6529}, {4, 112}, {6, 107}, {19, 162}, {25, 648}, {27, 8750}, {28, 1783}, {30, 32695}, {31, 823}, {32, 6528}, {51, 16813}, {53, 933}, {92, 32676}, {99, 2207}, {100, 5317}, {101, 8747}, {108, 1172}, {109, 8748}, {110, 393}, {158, 163}, {184, 15352}, {232, 685}, {250, 2501}, {297, 32696}, {403, 32708}, {511, 20031}, {512, 23582}, {520, 23590}, {523, 23964}, {662, 1096}, {811, 1973}, {925, 8745}, {1249, 1301}, {1289, 8743}, {1297, 23977}, {1304, 1990}, {1474, 1897}, {1576, 2052}, {1974, 6331}, {2445, 6330}, {2489, 18020}, {4230, 6531}, {4235, 8753}, {4238, 8751}, {4240, 8749}, {4558, 6524}, {6587, 15384}, {14569, 18315}, {14590, 18384}, {15262, 22239}
X(32713) = barycentric quotient X(i)/X(j) for these (i,j): (3, 4143), (4, 3267), (6, 3265), (19, 14208), (25, 525), (28, 15413), (31, 24018), (32, 520), (107, 76), (108, 1231), (110, 3926), (112, 69), (158, 20948), (162, 304), (163, 326), (232, 6333), (250, 4563), (393, 850), (512, 15526), (520, 23974), (648, 305), (692, 3998), (823, 561), (1096, 1577), (1474, 4025), (1576, 394), (1783, 20336), (1973, 656), (1974, 647), (2207, 523), (2445, 441), (2489, 125), (2501, 339), (4230, 6393), (4558, 4176), (5317, 693), (6524, 14618), (6528, 1502), (6529, 264), (8745, 6563), (8747, 3261), (8750, 306), (14398, 1650), (14569, 18314), (15352, 18022), (18384, 14592), (20031, 290), (23582, 670), (23590, 6528), (23964, 99), (23977, 30737), (24019, 75), (32676, 63), (32695, 1494), (32696, 287)

X(32714) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(4)X(7)

As the barycentric product of circumcircle-X(4)-antipodes, X(32713) lies on conic {{A,B,C,X(112),X(648)}} with center X(3162) and perspector X(25), and as the barycentric product of circumcircle-X(7)-antipodes, X(32713) also lies on conic {{A,B,C,X(109),X(651)}} with center X(478) and perspector X(56).

X(32714) lies on these lines: {4, 9372}, {19, 269}, {28, 1042}, {108, 109}, {112, 934}, {196, 222}, {207, 1394}, {223, 1767}, {240, 5018}, {278, 1086}, {281, 6180}, {513, 24033}, {608, 1119}, {648, 4569}, {651, 653}, {1118, 1406}, {1172, 3668}, {1262, 32698}, {1415, 32651}, {1419, 2331}, {1426, 7316}, {1427, 8749}, {1435, 8752}, {1461, 32674}, {1712, 2956}, {3669, 32702}, {6129, 32652}, {24027, 32699}, {32668, 32701}

X(32714) = isogonal conjugate of complement of X(17896)
X(32714) = isotomic conjugate of X(15416)
X(32714) = trilinear pole of line X(25)X(34)
X(32714) = barycentric product X(i)*X(j) for these lines: {i,j}: {4, 934}, {6, 13149}, {7, 108}, {19, 658}, {25, 4569}, {28, 4566}, {56, 18026}, {57, 653}, {85, 32674}, {92, 1461}, {99, 1426}, {100, 1119}, {101, 1847}, {107, 1439}, {109, 273}, {112, 1446}, {162, 3668}, {190, 1435}, {269, 1897}, {278, 651}, {281, 4617}, {331, 1415}, {608, 4554}, {648, 1427}, {811, 1042}, {1118, 6516}, {1262, 17924}, {4025, 24033}
X(32714) = barycentric quotient X(i)/X(j) for these (i,j): (4, 4397), (19, 3239), (25, 3900), (28, 7253), (56, 521), (57, 6332), (100, 1265), (101, 3692), (108, 8), (109, 78), (110, 1792), (112, 2287), (162, 1043), (269, 4025), (278, 4391), (513, 2968), (608, 650), (651, 345), (653, 312), (658, 304), (934, 69), (1042, 656), (1119, 693), (1262, 1332), (1415, 219), (1426, 523), (1427, 525), (1435, 514), (1439, 3265), (1446, 3267), (1461, 63), (1847, 3261), (1897, 341), (3668, 14208), (3669, 26932), (4566, 20336), (4569, 305), (4617, 348), (6516, 1264), (8059, 271), (13149, 76), (17924, 23978), (18026, 3596), (24027, 1331), (24033, 1897), (32668, 1815), (32674, 9)

X(32715) = BARYCENTRIC PRODUCT X(74)*X(112)

As the barycentric product of circumcircle-X(6)-antipodes, X(32715) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

The trilinear polar of X(32715) passes through X(32) and the barycentric square of X(647).

X(32715) lies on these lines: {74, 1177}, {110, 250}, {112, 32738}, {512, 32695}, {685, 879}, {687, 4240}, {1576, 32640}, {1976, 8749}, {2159, 32673}, {2211, 32740}, {2393, 15291}, {2433, 2445}, {18374, 18877}, {32712, 32733} et al

X(32715) = polar conjugate of isotomic conjugate of X(32640)
X(32715) = barycentric product X(i)*X(j) for these lines: {i,j}: {3, 32695}, {4, 32640}, {6, 1304}, {32, 16077}, {74, 112}, {110, 8749}, {162, 2159}, {250, 2433}, {1301, 15291}, {1576, 16080}
X(32715) = barycentric quotient X(i)/X(j) for these (i,j): (32, 9033), (74, 3267), (112, 3260), (1304, 76), (1576, 11064), (2159, 14208), (2433, 339), (8749, 850), (16077, 1502), (32695, 264), (32640, 69)

X(32716) = BARYCENTRIC PRODUCT X(98)*X(26714)

As the barycentric product of circumcircle-X(6)-antipodes, X(32716) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32716) lies on these lines: {110, 2966}, {262, 14355}, {1177, 11653}, {1576, 2715}, {1976, 9418}, {4577, 17932}, {20031, 32713}

X(32716) = trilinear pole of line X(32)X(263)
X(32716) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 6037}, {98, 26714}, {262, 2715}, {263, 2966}
X(32716) = barycentric quotient X(i)/X(j) for these (i,j): (263, 2799), (2715, 183), (2966, 20023), (6037, 76), (26714, 325)

X(32717) = BARYCENTRIC PRODUCT X(99)*X(729)

As the barycentric product of circumcircle-X(6)-antipodes, X(32717) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32717) lies on these lines: {110, 4590}, {249, 1576}, {691, 729}, {692, 4567}, {886, 4577}, {892, 5027}, {1976, 2966}, {5467, 17938} et al

X(32717) = isogonal conjugate of X(9148)
X(32717) = trilinear pole of line X(32)X(110)
X(32717) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 9150}, {32, 886}, {99, 729}, {110, 3228}, {691, 14608}
X(32717) = barycentric quotient X(i)/X(j) for these (i,j): (6, 9148), (32, 888), (99, 30736), (110, 538), (729, 523), (886, 1502), (1576, 3231), (3228, 850), (9150, 76)

X(32718) = BARYCENTRIC PRODUCT X(100)*X(739)

As the barycentric product of circumcircle-X(6)-antipodes, X(32718) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32718) lies on these lines: {110, 898}, {692, 1252}, {739, 919}, {889, 4577}, {1110, 32739}, {1492, 4607}, {2210, 32665}

X(32718) = trilinear pole of line X(32)X(692)
X(32718) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 898}, {31, 4607}, {32, 889}, {100, 739}, {692, 3227}, {31002, 32739}
X(32718) = barycentric quotient X(i)/X(j) for these (i,j): (31, 4728), (32, 891), (101, 6381), (692, 536), (739, 693), (889, 1502), (898, 76), (4607, 561), (32739, 899)

X(32719) = BARYCENTRIC PRODUCT X(101)*X(106)

As the barycentric product of circumcircle-X(6)-antipodes, X(32719) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32719) lies on these lines: {59, 4057}, {101, 32686}, {106, 32682}, {110, 901}, {667, 692}, {898, 6551}, {900, 13136}, {1492, 3257}, {1919, 23990}, {2426, 2441}, {5548, 32736}, {8750, 32705}, {8752, 32699}, {9456, 32666}, {32642, 32659}, {32645, 32656} et al

X(32719) = isogonal conjugate of isotomic conjugate of X(901)
X(32719) = isogonal conjugate of complement of polar conjugate of isogonal conjugate of X(23184)
X(32719) = isogonal conjugate of anticomplement of X(3310)
X(32719) = trilinear pole of line X(32)X(1977)
X(32719) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 32665}, {6, 901}, {31, 3257}, {32, 4555}, {88, 692}, {100, 9456}, {101, 106}, {145, 32645}, {649, 9268}, {667, 5376}, {902, 4638}, {903, 32739}, {995, 32686}, {1015, 6551}, {1331, 8752}, {1797, 8750}, {1897, 32659}, {6336, 32656}, {6635, 23990}
X(32719) = barycentric quotient X(i)/X(j) for these (i,j): (31, 3762), (32, 900), (101, 3264), (106, 3261), (692, 4358), (901, 76), (1919, 1647), (3257, 561), (4555, 1502), (5376, 6386), (6551, 31625), (9268, 1978), (9456, 693), (23990, 6550), (32645, 4373), (32656, 3977), (32659, 4025), (32665, 75), (32739, 519)

X(32720) = BARYCENTRIC PRODUCT X(102)*X(26715)

As the barycentric product of circumcircle-X(6)-antipodes, X(32720) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32720) lies on the line {26715, 32683}

X(32721) = BARYCENTRIC PRODUCT X(103)*X(26716)

As the barycentric product of circumcircle-X(6)-antipodes, X(32721) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32721) lies on these lines: {26716, 32684}, {32642, 32739}

X(32722) = CIRCUMCIRCLE-X(6)-ANTIPODE OF X(104)

X(32722) lies on the circumcircle and these lines: {6, 104}, {100, 2427}, {103, 4256}, {105, 957}, {187, 2699}, {644, 9059}, {739, 1384}, {1309, 1783}, {1415, 2720}, {2726, 3230}, {2751, 5526}, {32685, 32723} et al

X(32722) = Λ(X(2), X(905))
X(32722) = trilinear pole, wrt circumsymmedial triangle, of line X(6)X(650)
X(32722) = circumcircle intercept, other than X(104), of circle {{X(15),X(16),X(104)}} (or V(X(104))
X(32722) = inverse-in-Schoute-circle of X(2699)
X(32722) = barycentric product X(100)*X(957)
X(32722) = barycentric quotient X(957)/X(693)

X(32723) = BARYCENTRIC PRODUCT X(104)*X(32722)

As the barycentric product of circumcircle-X(6)-antipodes, X(32723) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32723) lies on these lines: {692, 32641}, {32685, 32722}

X(32724) = BARYCENTRIC PRODUCT X(105)*X(8693)

As the barycentric product of circumcircle-X(6)-antipodes, X(32724) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32724) lies on these lines: {692, 919}, {32666, 32739}

X(32724) = barycentric product X(i)*X(j) for these lines: {i,j}: {105, 8693}, {919, 1002}
X(32724) = barycentric quotient X(i)/X(j) for these (i,j): (919, 4441), (8693, 3263)

X(32725) = BARYCENTRIC PRODUCT X(107)*X(26717)

As the barycentric product of circumcircle-X(6)-antipodes, X(32725) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32725) lies on these lines: {110, 23582}, {1576, 23964}, {1976, 20031}, {23590, 32713}, {26717, 32687}

X(32725) = trilinear pole of line X(32)X(32713)
X(32725) = barycentric product X(i)*X(j) for these lines: {i,j}: {107, 26717}
X(32725) = barycentric quotient X(i)/X(j) for these (i,j): (26717, 3265)

X(32726) = CIRCUMCIRCLE-X(6)-ANTIPODE OF X(108)

X(32726) lies on the circumcircle and these lines: {6, 108}, {48, 109}, {99, 1812}, {100, 219}, {101, 212}, {107, 1172}, {110, 2193}, {112, 2194}, {187, 2714}, {222, 934}, {927, 1814}, {1055, 1949}, {1295, 2431}, {1951, 14733}, {2720, 14578}, {2722, 13509}, {2730, 5526}, {32688, 32727} et al

X(32726) = trilinear pole of line X(6)X(1946)
X(32726) = Ψ(X(i), X(j)) for these (i,j): (4, 650), (6, 1946), (651, 3), (18026, 2)
X(32726) = trilinear pole, wrt circumsymmedial triangle, of line X(6)X(19)
X(32726) = circumcircle intercept, other than X(108), of circle {{X(15),X(16),X(108)}} (or V(X(108))
X(32726) = inverse-in-Schoute-circle of X(2714)
X(32726) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 23707}
X(32726) = barycentric quotient X(i)/X(j) for these (i,j): (23707, 75), (32727, 108)

X(32727) = BARYCENTRIC PRODUCT X(108)*X(32726)

As the barycentric product of circumcircle-X(6)-antipodes, X(32727) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32727) lies on these lines: {692, 7115}, {32688, 32726}

X(32728) = BARYCENTRIC PRODUCT X(109)*X(2291)

As the barycentric product of circumcircle-X(6)-antipodes, X(32728) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32728) lies on these lines: {110, 14733}, {692, 2149}, {884, 32735}, {2291, 32689}

X(32728) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 14733}, {109, 2291}
X(32728) = barycentric quotient X(i)/X(j) for these (i,j): (14733, 76)

X(32729) = BARYCENTRIC PRODUCT X(110)*X(111)

As the barycentric product of circumcircle-X(6)-antipodes, X(32729) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

Let A₁B₁C₁ and A₂B₂C₂ be the 1st and 2nd Parry triangles. Let A' be the barycentric product A₁*A₂, and define B', C' cyclically. The lines AA', BB', CC' concur in X(32729).

X(32729) lies on these lines: {6, 32741}, {23, 895}, {110, 249}, {111, 1495}, {112, 32709}, {163, 32672}, {184, 10558}, {187, 9215}, {237, 14908}, {669, 1576}, {685, 4240}, {690, 17708}, {881, 17938}, {892, 4577}, {923, 32671}, {2420, 2444}, {2966, 9147}, {5968, 6800}, {8753, 32708}, {9178, 9206}, {9544, 10559}, {10561, 23964}, {11003, 21460}, {14567, 18374}, {14602, 19626}, {32648, 32661}

X(32729) = isogonal conjugate of X(35522)
X(32729) = trilinear pole of line X(32)X(1084)
X(32729) = X(92)-isoconjugate of X(14417)
X(32729) = barycentric product of PU(62)
X(32729) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 691}, {15, 9206}, {16, 9207}, {32, 892}, {110, 111}, {112, 895}, {163, 897}, {249, 9178}, {250, 10097}, {648, 14908}, {662, 923}, {670, 19626}, {671, 1576}, {1992, 32648}, {2420, 9139}, {2715, 5968}, {4558, 8753}, {11634, 15387}, {14574, 18023}, {17983, 32661}
X(32729) = barycentric quotient X(i)/X(j) for these (i,j): (32, 690), (110, 3266), (111, 850), (163, 14210), (184, 14417), (691, 76), (892, 1502), (895, 3267), (897, 20948), (923, 1577), (1576, 524), (8753, 14618), (9178, 338), (9206, 300), (9207, 301), (10097, 339), (14567, 1649), (14574, 187), (14602, 11183), (14908, 525), (19626, 512), (32648, 5485), (32661, 6390)

X(32730) = CIRCUMCIRCLE-X(6)-ANTIPODE OF X(476)

X(32730) lies on the circumcircle and these lines: {6, 476}, {50, 110}, {98, 5996}, {99, 323}, {187, 9160}, {325, 9066}, {477, 2436}, {691, 10560}, {805, 15080}, {1141, 2623}, {1384, 32732}, {2222, 21741}, {2715, 9463}, {23969, 32731}

X(32730) = trilinear pole of line X(6)X(14270)
X(32730) = Ψ(X(6), X(14270))
X(32730) = Λ(X(2), X(94))
X(32730) = trilinear pole, wrt circumsymmedial triangle, of Fermat axis
X(32730) = circumcircle intercept, other than X(476), of circle {X(15),X(16),X(476)} (or V(X(476))
X(32730) = barycentric product X(3268)*X(32731)
X(32730) = barycentric quotient X(32731)/X(476)

X(32731) = BARYCENTRIC PRODUCT X(476)*X(32730)

As the barycentric product of circumcircle-X(6)-antipodes, X(32731) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32731) lies on these lines: {14560, 23588}, {23969, 32730}

X(32731) = trilinear pole of line X(32)X(14560)
X(32731) = barycentric quotient X(32730)/X(3268)

X(32732) = CIRCUMCIRCLE-X(6)-ANTIPODE OF X(477)

X(32732) lies on the circumcircle and these lines: {6, 477}, {98, 12112}, {187, 9161}, {476, 2437}, {1297, 3581}, {1384, 32730}, {32690, 32733}

X(32732) = Λ(X(2), X(2411))
X(32732) = trilinear pole, wrt circumsymmedial triangle, of line X(6)X(1637)
X(32732) = circumcircle intercept, other than X(477), of circle {X(15),X(16),X(477)} (or V(X(477))

X(32733) = BARYCENTRIC PRODUCT X(477)*X(32732)

As the barycentric product of circumcircle-X(6)-antipodes, X(32733) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32733) lies on these lines: {110, 30528}, {14560, 32650}, {32690, 32732}, {32712, 32715}

X(32734) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(5)X(6)

As the barycentric product of circumcircle-X(5)-antipodes, X(32734) lies on conic {{A,B,C,X(112),X(1987)}} with perspector X(51), and as the barycentric product of circumcircle-X(6)-antipodes, X(32734) also lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32734) lies on these lines: {68, 542}, {110, 925}, {112, 32692}, {154, 2351}, {159, 2871}, {184, 8754}, {206, 1976}, {485, 30427}, {486, 30428}, {685, 30450}, {847, 1614}, {924, 4558}, {1498, 16391}, {1576, 1625} et al

X(32734) = isogonal conjugate of X(6563)
X(32734) = trilinear pole of line X(32)X(51) (the isogonal conjugate of the isotomic conjugate of line X(5)X(6))
X(32734) = barycentric product X(i)*X(j) for these lines: {i,j}: {5, 32692}, {6, 925}, {68, 112}, {96, 1625}, {184, 30450}, {648, 2351}, {847, 32661}, {1576, 5392}, {4558, 14593}, {6529, 16391}
X(32734) = barycentric quotient X(i)/X(j) for these (i,j): (6, 6563), (68, 3267), (112, 317), (847, 32661), (925, 76), (1576, 1993), (2351, 525), (14593, 14618), (16391, 4143), (30450, 18022), (32692, 95), (32661, 9723)

X(32735) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(7)

As the barycentric product of circumcircle-X(6)-antipodes, X(32735) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(7)-antipodes, X(32735) also lies on conic {{A,B,C,X(109),X(651)}} with center X(478) and perspector X(56).

X(32735) lies on these lines: {59, 513}, {100, 30626}, {105, 2720}, {109, 649}, {110, 927}, {294, 2182}, {666, 4581}, {667, 1262}, {677, 926}, {883, 3573}, {884, 32728}, {885, 14776}, {971, 28071}, {1404, 1438}, {1428, 1456}, {1458, 2195}, {1461, 24027}, {1576, 3733}, {1814, 3827}, {1876, 15382}, {1960, 14733}, {4617, 7339}, {7316, 32740} et al

X(32735) = trilinear pole of line X(32)X(56) (the isogonal conjugate of the isotomic conjugate of line X(6)X(7))
X(32735) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 927}, {7, 919}, {56, 666}, {100, 1462}, {105, 651}, {108, 1814}, {109, 673}, {294, 934}, {658, 2195}, {664, 1438}, {884, 1275}, {885, 1262}, {1461, 14942}, {4617, 28071}, {7339, 28132}
X(32735) = barycentric quotient X(i)/X(j) for these (i,j): (56, 918), (105, 4391), (109, 3912), (294, 4397), (651, 3263), (666, 3596), (667, 17435), (884, 1146), (885, 23978), (919, 8), (927, 76), (934, 27818), (1262, 883), (1438, 522), (1461, 9436), (1462, 693), (2195, 3239)

X(32736) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(8)

As the barycentric product of circumcircle-X(6)-antipodes, X(32736) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(8)-antipodes, X(32736) also lies on conic {{A,B,C,X(101),X(651)}} with center X(5452) and perspector X(55).

X(32736) lies on these lines: {101, 8687}, {110, 645}, {294, 2264}, {644, 692}, {666, 4581}, {1169, 2311}, {1576, 4557}, {1976, 14624}, {2308, 2316}, {2338, 2359}, {3939, 32739}, {5547, 32740}, {5548, 32719} et al

X(32736) = isogonal conjugate of X(3004)
X(32736) = trilinear pole of line X(32)X(55) (the isogonal conjugate of the isotomic conjugate of line X(6)X(8))
X(32736) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 8707}, {8, 8687}, {55, 6648}, {100, 2298}, {101, 1220}, {110, 14624}, {644, 961}, {692, 30710}, {1169, 3952}, {1240, 32739}, {1252, 4581}, {1897, 2359}, {4557, 14534}
X(32736) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3004), (55, 3910), (100, 20911), (101, 4357), (110, 16705), (692, 3666), (961, 24002), (1169, 7192), (1220, 3261), (2298, 693), (2359, 4025), (3952, 1228), (4557, 1211), (4581, 23989), (6648, 6063), (8687, 7), (8707, 76), (14624, 850), (32739, 1193)

X(32737) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF NAPOLEON AXIS

As the barycentric product of circumcircle-X(6)-antipodes, X(32737) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32).

X(32737) lies on these lines: {110, 930}, {156, 25043}, {184, 11082}, {252, 1614}, {1177, 3519}, {1510, 18315}, {1576, 6140}, {1976, 2963} et al

X(32737) = isogonal conjugate of isotomic conjugate of X(930)
X(32737) = trilinear pole of line X(32)X(8565)
X(32737) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 930}, {17, 16807}, {18, 16806}, {110, 2963}, {112, 3519}, {163, 2962}, {252, 1625}, {1576, 11140}, {14586, 25043}
X(32737) = barycentric quotient X(i)/X(j) for these (i,j): (110, 7769), (930, 76), (1576, 1994), (2962, 20948), (2963, 850), (3519, 3267), (16806, 303), (16807, 302), (25043, 15415)

X(32738) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(30)

As the barycentric product of circumcircle-X(6)-antipodes, X(32738) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(30)-antipodes, X(32738) also lies on conic {{A,B,C,X(6),X(112)}} with perspector X(1495).

X(32738) lies on these lines: {110, 1302}, {112, 32715}, {182, 1177}, {1576, 2420}, {1974, 16240}

X(32738) = isogonal conjugate of X(30474)
X(32738) = trilinear pole of line X(32)X(1495) (the isogonal conjugate of the isotomic conjugate of line X(6)X(30))
X(32738) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 1302}, {112, 4846}
X(32738) = barycentric quotient X(i)/X(j) for these (i,j): (6, 30474), (1302, 76), (1576, 15066), (4846, 3267)

X(32739) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(31)

As the barycentric product of circumcircle-X(6)-antipodes, X(32739) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(31)-antipodes, X(32739) also lies on conic {{A,B,C,X(163),X(825)}} with perspector X(560).

X(32739) lies on these lines: {31, 9447}, {32, 1977}, {41, 9247}, {42, 1976}, {71, 1177}, {99, 769}, {100, 825}, {101, 110}, {109, 649}, {112, 28624}, {184, 14827}, {190, 4577}, {514, 15378}, {657, 14776}, {685, 1897}, {692, 2874}, {1110, 32718}, {1415, 32660}, {1576, 32656}, {1918, 32740}, {1919, 23990}, {1922, 2205}, {2225, 2361}, {3185, 32664}, {3234, 9057}, {3939, 32736}, {23989, 24279}, {32666, 32724}, {32642, 32721} et al

X(32739) = isogonal conjugate of X(3261)
X(32739) = polar conjugate of isotomic conjugate of X(32656)
X(32739) = trilinear pole of line X(32)X(560) (the isogonal conjugate of the isotomic conjugate of line X(6)X(31))
X(32739) = crossdifference of every pair of points on line X(1111)X(3120)
X(32739) = barycentric product of vertices of 1st circumperp triangle
X(32739) = complement of anticomplementary conjugate of X(21225)
X(32739) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 692}, {4, 32656}, {6, 101}, {9, 1415}, {10, 1576}, {19, 906}, {31, 100}, {32, 190}, {37, 163}, {41, 651}, {42, 110}, {48, 1783}, {55, 109}, {56, 3939}, {71, 112}, {72, 32676}, {99, 1918}, {103, 2426}, {106, 23344}, {107, 4055}, {108, 212}, {162, 228}, {184, 1897}, {281, 32660}, {513, 1110}, {514, 23990}, {516, 32642}, {518, 32666}, {519, 32719}, {648, 2200}, {649, 1252}, {657, 1262}, {658, 14827}, {799, 2205}, {825, 2276}, {899, 32718}, {1011, 28624}, {1016, 1919}, {1193, 32736}, {1292, 21059}, {1501, 1978}, {1922, 3570}, {1977, 6632}, {2222, 2361}, {4554, 9447}, {6335, 9247}, {6586, 15378}, {14776, 22350}
X(32739) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3261), (31, 693), (32, 514), (37, 20948), (41, 4391), (42, 850), (48, 15413), (71, 3267), (100, 561), (101, 76), (109, 6063), (110, 310), (163, 274), (184, 4025), (190, 1502), (228, 14208), (649, 23989), (651, 20567), (657, 23978), (692, 75), (906, 304), (1110, 668), (1252, 1978), (1415, 85), (1501, 649), (1576, 86), (1783, 1969), (1897, 18022), (1918, 523), (1919, 1086), (1922, 4444), (1977, 6545), (2200, 525), (2205, 661), (3939, 3596), (4055, 3265), (9247, 905), (9447, 650), (14827, 3239), (15378, 31624), (23344, 3264), (23990, 190), (32642, 18025), (32656, 69), (32660, 348), (32666, 2481), (32718, 31002), (32719, 903), (32736, 1240), (32676, 286)

X(32740) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(512)

As the barycentric product of circumcircle-X(6)-antipodes, X(32740) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(512)-antipodes, X(32740) also lies on conic {{A,B,C,X(6),X(32),X(83),X(213),X(729)}} with perspector X(669).

X(32740) lies on these lines: {2, 9516}, {3, 15268}, {6, 110}, {23, 5166}, {32, 1084}, {50, 32654}, {67, 1648}, {83, 597}, {115, 15118}, {182, 14609}, {187, 13493}, {213, 692}, {512, 32741}, {524, 9225}, {575, 9966}, {685, 1990}, {691, 729}, {892, 3225}, {897, 1492}, {1177, 2492}, {1613, 10559}, {1692, 11060}, {1918, 32739}, {1976, 2422}, {2030, 9192}, {2056, 8584}, {2207, 8753}, {2211, 32715}, {3051, 10558}, {3114, 18023}, {3228, 17941}, {3589, 30786}, {5023, 6091}, {5095, 6791}, {5104, 11643}, {5106, 9145}, {5181, 10418}, {5380, 27810}, {5547, 32736}, {5618, 10036}, {6792, 11061}, {7316, 32735}, {9084, 15638}, {9407, 14601}, {9463, 10560}, {9468, 17938}, {11646, 25328}, {14567, 18374}, {16092, 16306}

X(32740) = isogonal conjugate of X(3266)
X(32740) = trilinear pole of line X(32)X(669) (the isogonal conjugate of the isotomic conjugate of line X(6)X(512))
X(32740) = crossdifference of every pair of points on line X(690)X(5181)
X(32740) = barycentric product of circumcircle-intercepts of Schoute circle
X(32740) = isotomic conjugate of isogonal conjugate of X(19626)
X(32740) = barycentric product X(i)*X(j) for these lines: {i,j}: {1, 923}, {3, 8753}, {4, 14908}, {6, 111}, {25, 895}, {31, 897}, {32, 671}, {55, 7316}, {56, 5547}, {76, 19626}, {110, 9178}, {163, 23894}, {184, 17983}, {187, 10630}, {237, 9154}, {669, 892}, {729, 14609}, {1501, 18023}, {1974, 30786}, {1976, 5968}, {3455, 14246}, {5380, 9780}, {6091, 14248}, {10415, 18374}
X(32740) = barycentric quotient X(i)/X(j) for these (i,j): (6, 3266), (31, 14210), (32, 524), (111, 76), (163, 24039), (184, 6390), (669, 690), (671, 1502), (892, 4609), (895, 305), (897, 561), (923, 75), (1084, 1648), (1501, 187), (1974, 468), (5380, 28626), (5547, 3596), (7316, 6063), (8753, 264), (9154, 18024), (9178, 850), (9407, 5642), (9426, 351), (10630, 18023), (14567, 2482), (14601, 5967), (14609, 30736), (14908, 69), (17983, 18022), (18374, 7664), (19626, 6), (23894, 20948)

X(32741) = BARYCENTRIC PRODUCT OF CIRCUMCIRCLE INTERCEPTS OF LINE X(6)X(690)

As the barycentric product of circumcircle-X(6)-antipodes, X(32741) lies on conic {{A,B,C,X(110),X(685)}} with center X(206) and perspector X(32), and as the barycentric product of circumcircle-X(690)-antipodes, X(32741) also lies on hyperbola {{A,B,C,X(6),X(187),X(249),X(512),X(524),X(598),X(843)}} with perspector X(351).

X(32741) lies on these lines: {6, 32729}, {110, 524}, {182, 9192}, {187, 1576}, {249, 6593}, {512, 32740}, {692, 21839}, {1177, 3566}, {10630, 28662}, {10765, 12367}, {17938, 18872}

X(32741) = trilinear pole of line X(32)X(351) (the isogonal conjugate of the isotomic conjugate of line X(6)X(690))
X(32741) = barycentric product X(6)*X(2770)
X(32741) = barycentric quotient X(i)/X(j) for these (i,j): (32, 2854), (2770, 76)

X(32742) = (name pending)

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29086.

X(32742) lies on this line: {597,6055}

X(32743) = COMPLEMENT OF X(13289)

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29086.

X(32743) lies on these lines: {2,13289}, {3,19506}, {4,13293}, {5,1539}, {30,15090}, {66,19140}, {74,7577}, {110,18381}, {113,2072}, {125,389}, {265,13352}, {381,2935}, {399,1853}, {403,13202}, {427,7687}, {511,15116}, {542,23300}, {858,16163}, {974,18388}, {1503,10272}, {1511,14156}, {1568,12825}, {1656,10117}, {1899,12227}, {2778,9955}, {2781,6697}, {2892,14561}, {3043,25739}, {3090,13203}, {3357,7728}, {5055,9919}, {5092,12900}, {5094,19457}, {5097,20300}, {5448,5663}, {5576,23515}, {5972,10282}, {6759,14643}, {7579,17835}, {7722,23294}, {7741,10118}, {7951,19505}, {8889,18933}, {9976,23327}, {10024,16111}, {10113,12897}, {10254,11204}, {10264,23332}, {10576,13287}, {10577,13288}, {10606,23043}, {10721,16868}, {10733,18376}, {11572,17701}, {11597,15139}, {12219,23293}, {12358,21243}, {12893,18569}, {12901,18281}, {13371,17702}, {14864,16534}, {15040,17845}, {15051,31101}, {15472,18390}, {20125,32064}

X(32744) = X(3)X(14140)∩X(5)X(252)

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29089.

X(32744) lies on these lines: {3, 14140}, {5, 252}, {12, 14102}, {30, 511}, {137, 24147}, {140, 6150}, {546, 16337}, {550, 14141}, {930, 6345}, {1263, 19553}, {3628, 10615}, {5501, 20414}, {10096, 10227}, {10126, 13856}, {10205, 14095}, {13372, 27090}, {16881, 32409}, {20030, 32536}, {22051, 27246}, {25043, 28237}, {27868, 30484}, {30480, 32638}

X(32745) = (name pending)

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29086.

X(32745) lies on this line: {541,597}

X(32746) = X(2)-CEVA CONJUGATE OF X(194)

X(32746) lies on these lines: {69, 25319}, {126, 7897}, {141, 5025}, {160, 9491}, {194, 6374}, {670, 2998}, {1368, 3314}, {3662, 3741}, {3739, 17448}, {6383, 24621}, {6389, 7836}

X(32746) = complement of X(38262)
X(32746) = complement of the isogonal conjugate of X(21001)
X(32746) = complement of the isotomic conjugate of X(20081)
X(32746) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 194}, {21001, 20081}
X(32746) = crosspoint of X(2) and X(20081)
X(32746) = barycentric product X(i)*X(j) for these lines: {i,j}: {194, 20081}, {1740, 20945}, {6374, 21001}, {16571, 17149}
X(32746) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {16571, 3223}, {20081, 2998}, {20945, 18832}, {21001, 3224}, {22152, 3504}
X(32746) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 194}, {16571, 141}, {17091, 17046}, {20081, 2887}, {20945, 626}, {21001, 10}, {21095, 21245}, {21206, 21252}, {22152, 18589}

X(32747) = X(194)-CEVA CONJUGATE OF X(2)

X(32747) lies on these lines: {2, 2998}, {69, 698}, {75, 330}, {192, 17149}, {193, 25332}, {194, 15968}, {670, 8264}, {1278, 17135}, {1370, 7779}, {3186, 8782}, {3797, 18750}, {7774, 19583}, {9865, 14615}, {20245, 20535}, {21080, 21219}

X(32747) = anticomplement of X(2998)
X(32747) = reflection of X(2998) and X(6374)
X(32747) = anticomplement of the isogonal conjugate of X(1613)
X(32747) = anticomplement of the isotomic conjugate of X(194)
X(32747) = isotomic conjugate of the isogonal conjugate of X(3360)
X(32747) = X(194)-Ceva conjugate of X(2)
X(32747) = crosspoint of X(3360) and X(15965)
X(32747) = {X(2998),X(6374)}-harmonic conjugate of X(2)
X(32747) = trilinear pole, wrt anticomplementary triangle, of Lemoine axis
X(32747) = barycentric product X(i)*X(j) for these lines: {i,j}: {76, 3360}, {6374, 15965}
X(32747) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {194, 15968}, {3360, 6}, {15965, 3224}
X(32747) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {6, 21299}, {31, 20081}, {32, 21223}, {101, 20983}, {163, 669}, {194, 6327}, {560, 2998}, {662, 3221}, {692, 20979}, {923, 20977}, {1333, 17157}, {1415, 23655}, {1424, 3434}, {1438, 20863}, {1613, 8}, {1740, 69}, {3186, 21270}, {3221, 21221}, {6374, 21275}, {7075, 3436}, {9456, 23633}, {9491, 21220}, {11325, 5905}, {17082, 21285}, {17149, 315}, {20794, 4329}, {21080, 21287}, {21191, 21293}, {21877, 1330}, {23301, 21294}, {23503, 148}, {23572, 149}, {24037, 4609}

X(32748) = X(1)X(6)∩X(31)X(7104)

X(32748) lies on the cubic K789 and these lines: {2, 6}, {31, 7104}, {32, 9490}, {187, 9427}, {237, 9468}, {669, 688}, {699, 805}, {1186, 7772}, {1197, 23576}, {1501, 15389}, {1576, 18902}, {1692, 9419}, {1914, 21762}, {1922, 19554}, {3224, 3552}, {3499, 7839}, {4173, 14820}, {6380, 9150}, {8023, 23200}, {9431, 13586}

X(32748) = isogonal conjugate of the isotomic conjugate of X(3229)
X(32748) = crosspoint of X(6) and X(9468)
X(32748) = crosssum of X(i) and X(j) for these (i,j): {2, 3978}, {3225, 8858}, {3766, 6377}, {3948, 6382}
X(32748) = crossdifference of every pair of points on line {76, 512}
X(32748) = X(i)-Ceva conjugate of X(j) for these (i,j): {805, 669}, {1691, 237}, {8789, 3051}
X(32748) = X(i)-isoconjugate of X(j) for these (i,j): {75, 3225}, {92, 8858}, {561, 699}, {1934, 32544}
X(32748) = barycentric product X(i)*X(j) for these lines: {i,j}: {6, 3229}, {31, 2227}, {32, 698}, {99, 9429}, {511, 32540}
X(32748) = barycentric quotient X(i)/X(j) for these lines: {i,j}: {32, 3225}, {184, 8858}, {698, 1502}, {1501, 699}, {2227, 561}, {3229, 76}, {9429, 523}, {14602, 32544}, {32540, 290}
X(32748) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1613, 7766}, {6, 3329, 20965}, {6, 18899, 3051}

X(32749) = ISOGONAL CONJUGATE OF X(32744)

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 29089.

X(32749) lies on the circumcircle and these lines: {110,15345}, {930,10205}, {1510,6345}

X(32750) = X(2)X(15351)∩X(14401)X(15183)

See Tran Quang Hung and César Lozada, Hyacinthos 29090.

X(32750) lies on these lines: {2, 15351}, {14401, 15183}

X(32750) = medial-isotomic conjugate of-X(15184)
X(32750) = complement of the isotomic conjugate of X(402)
X(32750) = barycentric product X(402)*X(15184)

Points Selected for Their Tripolar Coordinates: X(32751)-X(32766)

X(32751) = X(3)X(76)∩X(83)X(1688)

X(32751) lies on these lines: {3,76}, {83,1688}, {1690,7760}

X(32751) = circumcircle-inverse of X(32752)
X(32751) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {3, 1078, 32752}, {76, 12203, 32752}, {98, 99, 32752}

X(32752) = X(3)X(76)∩X(83)X(1687)

X(32752) lies on these lines: {3,76}, {83,1687}, {1689,7760}

X(32752) = circumcircle-inverse of X(32751)
X(32752) = {X(i),X(j)}-harmonic conjugate of X(k) for these lines: {i,j,k}: {3, 1078, 32751}, {76, 12203, 32751}, {98, 99, 32751}

X(32753) = (name pending)

X(32753) lies on the Stevanovic circle and this line: {3,142}

X(32753) = reflection of X(32754) in the Gergonne line
X(32753) = circumcircle-inverse of X(32754)
X(32753) = {X(3),X(1486)}-harmonic conjugate of X(32754)

X(32754) = (name pending)

X(32754) lies on the Stevanovic circle and this line: {3,142}

X(32754) = reflection of X(32753) in the Gergonne line
X(32754) = circumcircle-inverse of X(32753)
X(32754) = {X(3),X(1486)}-harmonic conjugate of X(32753)

X(32755) = (name pending)

X(32755) lies on this line: {3, 8}

X(32755) = {X(100),X(104)}-harmonic conjugate of X(32770)
X(32755) = circumcircle-inverse of X(32770)

X(32756) = CIRCUMCIRCLE-INVERSE OF X(19)

X(32756) lies on these lines: {3, 19}, {650, 1946}, {5089, 5172}

X(32756) = circumcircle-inverse of X(19)

X(32757) = CIRCUMCIRCLE-INVERSE OF X(34)

X(32757) lies on these lines: {3, 34}, {1785, 10058}, {1870, 18861}, {1946, 6129}

X(32757) = circumcircle-inverse of X(34)
X(32757) = circumperp conjugate of X(36986)

X(32758) = CIRCUMCIRCLE-INVERSE OF X(37)

X(32758) lies on these 3, 37}, {36, 3290}, {172, 2915}, {187, 20872}, {502, 3444}, {650, 667}, {1325, 17737}, {3230, 5078}, {5251, 19309}, {18447, 21861}

X(32758) = circumcircle-inverse of X(37)
X(32758) = Stevanovic circle inverse of X(20989)

X(32759) = CIRCUMCIRCLE-INVERSE OF X(42)

X(32759) lies on these lines: {3, 42}, {649, 4079}, {3011, 17729}, {5196, 17734}, {5264, 17019}

X(32759) = circumcircle-inverse of X(42)

X(32760) = CIRCUMCIRCLE-INVERSE OF X(46)

X(32760) lies on these lines: {1, 3}, {21, 5176}, {90, 17857}, {100, 1737}, {186, 15500}, {405, 5123}, {497, 6880}, {498, 2478}, {499, 3434}, {515, 10057}, {519, 10087}, {528, 3582}, {535, 10056}, {611, 9037}, {855, 1283}, {902, 22350}, {906, 8608}, {912, 1727}, {915, 1785}, {920, 3811}, {954, 28534}, {993, 12647}, {1399, 5399}, {1478, 6938}, {1479, 6796}, {1532, 3583}, {1698, 25875}, {1725, 5497}, {1728, 2900}, {1772, 30117}, {1837, 32141}, {1878, 11398}, {1914, 13006}, {2886, 13747}, {3085, 5080}, {3086, 20075}, {3149, 22835}, {3419, 18395}, {3476, 6950}, {3488, 10051}, {3560, 10827}, {3584, 11113}, {3585, 7680}, {3651, 16153}, {4187, 5259}, {4294, 6838}, {4302, 6925}, {4309, 6962}, {4881, 17100}, {5180, 5703}, {5218, 6947}, {5252, 6914}, {5281, 6992}, {5312, 16472}, {5433, 10948}, {6149, 19624}, {6284, 10523}, {6905, 30384}, {6909, 21578}, {6911, 23708}, {6924, 11376}, {6929, 7951}, {6936, 31452}, {6959, 7741}, {8715, 10573}, {10090, 21630}, {10572, 11491}, {10826, 11499}, {10896, 18499}, {11813, 13411}, {12739, 14988}, {13405, 16152}

X(32760) = midpoint of X(55) and X(5172)
X(32760) = reflection of X(36) and X(5172)
X(32760) = circumcircle-inverse of X(46)
X(32760) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5010, 14793}, {3, 55, 5119}, {3, 1319, 36}, {3, 3295, 10966}, {3, 11508, 1}, {35, 36, 2077}, {35, 14795, 10902}, {35, 14798, 3}, {35, 15931, 5010}, {36, 5537, 484}, {55, 56, 10679}, {55, 8069, 1}, {55, 24929, 3746}, {55, 32613, 35}, {56, 10679, 25415}, {56, 23961, 36}, {1381, 1382, 46}, {2077, 2078, 36}, {3295, 22765, 5048}, {3295, 22766, 1}, {3560, 11501, 10827}, {11249, 26358, 30323}, {14796, 14797, 5697}, {23961, 25405, 56}

X(32761) = CIRCUMCIRCLE-INVERSE OF X(50)

X(32761) lies on these lines: {2, 249}, {3, 6}, {4, 14591}, {30, 19627}, {49, 18321}, {110, 3016}, {112, 9161}, {115, 17702}, {184, 512}, {246, 20976}, {477, 2549}, {691, 10560}, {842, 3431}, {868, 5475}, {1147, 31848}, {1511, 2493}, {1625, 9696}, {1915, 14537}, {2871, 3455}, {3269, 32607}, {5012, 9218}, {5477, 15357}, {6785, 15033}, {6792, 21843}, {7748, 14585}, {7749, 10413}, {14355, 18333}, {18334, 32662}

X(32761) = circumcircle-inverse of X(50)
X(32761) = Brocard-circle-inverse of X(2088)
X(32761) = second-Lemoine-circle-inverse of X(18449)
X(32761) = Moses-circle-inverse of X(3284)
X(32761) = X(1577)-isoconjugate of X(9160)
X(32761) = crosssum of X(31862) and X(31863)
X(32761) = crossdifference of every pair of points on line {523, 3580}
X(32761) = barycentric quotient X(1576)/X(9160)
X(32761) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 2088}, {6, 2420, 32}, {371, 372, 18114}, {1379, 1380, 50}, {1666, 1667, 18449}, {2028, 2029, 3284}

X(32762) = CIRCUMCIRCLE-INVERSE OF X(52)

X(32762) lies on these lines: {3, 6}, {5, 2934}, {24, 5963}, {26, 14693}, {249, 14587}, {316, 7509}, {625, 7393}, {691, 2383}, {7395, 13449}, {16188, 21284}

X(32762) = circumcircle-inverse of X(52)
X(32762) = {X(1379),X(1380)}-harmonic conjugate of X(52)

X(32763) = (name pending)

The barycentrics are real-valued only when ABC is acute.

X(32763) lies on this line: {3, 142}

X(32763) = circumcircle-inverse of X(32764)

X(32764) = (name pending)

The barycentrics are real-valued only when ABC is acute.

X(32764) lies on this line: {3, 142}

X(32764) = circumcircle-inverse of X(32763)

X(32765) = (name pending)

The barycentrics are real-valued only when ABC is acute.

X(32765) lies on this line: {3, 10}

X(32765) = circumcircle-inverse of X(32766)

X(32766) = (name pending)

The barycentrics are real-valued only when ABC is acute.

X(32766) lies on this line: {3, 10}

X(32766) = circumcircle-inverse of X(32765)

X(32767) = COMPLEMENT OF X(10282)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29094.

X(32767) lies on these lines: {2, 9833}, {3, 18383}, {4, 11270}, {5, 2883}, {20, 18376}, {30, 20191}, {51, 26917}, {64, 3851}, {125, 389}, {140, 13470}, {154, 5070}, {185, 7577}, {186, 11572}, {343, 15606}, {381, 3357}, {382, 11204}, {403, 13474}, {427, 10110}, {468, 13419}, {511, 5449}, {542, 9820}, {546, 2777}, {547, 16252}, {550, 10193}, {575, 18952}, {578, 5094}, {632, 10182}, {858, 15644}, {1092, 30744}, {1147, 31283}, {1204, 7547}, {1209, 3819}, {1216, 14076}, {1493, 11232}, {1495, 14940}, {1498, 5055}, {1503, 3628}, {1531, 11440}, {1656, 1853}, {1885, 7687}, {2072, 5907}, {2781, 10095}, {3090, 14216}, {3091, 7703}, {3520, 13851}, {3526, 11202}, {3541, 18390}, {3545, 5878}, {3581, 32395}, {3627, 23328}, {3830, 8567}, {3832, 20427}, {3843, 10606}, {3845, 5894}, {3850, 15311}, {5020, 32321}, {5054, 17845}, {5066, 5893}, {5067, 32064}, {5071, 12324}, {5498, 30522}, {5562, 23293}, {5576, 5943}, {5651, 31282}, {5656, 15022}, {5663, 32184}, {5972, 12134}, {6143, 12254}, {6640, 18474}, {6723, 16238}, {7505, 11550}, {7507, 11438}, {7553, 32223}, {7574, 32365}, {7603, 32445}, {8549, 11178}, {8681, 23307}, {9927, 15123}, {10113, 25564}, {10117, 18369}, {10224, 13561}, {10226, 18379}, {10250, 15069}, {10254, 10575}, {10255, 12162}, {10274, 13353}, {11245, 12242}, {11264, 32376}, {11381, 16868}, {11585, 11793}, {12006, 13413}, {12370, 15113}, {13093, 19709}, {13154, 15577}, {13160, 16836}, {13289, 15059}, {13293, 14644}, {13346, 14852}, {13382, 18388}, {13383, 29012}, {13406, 14915}, {14530, 15703}, {14627, 17847}, {14810, 18382}, {15027, 15131}, {15037, 17824}, {15057, 16219}, {15061, 19506}, {15116, 20301}, {15578, 17714}, {17702, 23336}, {17712, 25337}, {18488, 23515}, {18567, 32210}, {23300, 24206}, {31724, 32110}

X(32767) = complement of X(10282)
X(32767) = complement of the isogonal of X(15319)
X(32767) = X(15319)-complementary conjugate of X(10)
X(32767) = midpoint of X(i) and X(j) for these lines: {i,j}: {3, 18383}, {5, 20299}, {125, 32743}, {546, 6696}, {5449, 13371}, {6697, 20300}, {6759, 14864}, {10113, 25564}, {10193, 23324}, {10224, 13561}, {10226, 18379}, {10282, 18381}, {14076, 32351}, {14810, 18382}, {15116, 20301}, {18567, 32210}, {23300, 24206}
X(32767) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 18381, 10282}, {3, 23325, 18383}, {5, 23332, 20299}, {125, 1594, 389}, {125, 3574, 26879}, {1594, 26879, 3574}, {1656, 1853, 6759}, {1853, 6759, 14864}, {3574, 26879, 389}, {6143, 25739, 13367}, {7577, 23294, 185}, {11585, 21243, 11793}, {13353, 15139, 10274}

X(32768) = COMPLEMENT OF X(32769)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29097.

X(32768) lies on this line: {2, 32769}

X(32769) = ANTICOMPLEMENT OF X(32768)

See Antreas Hatzipolakis and Peter Moses, Hyacinthos 29097.

X(32769) lies on these lines: {2, 32768}, {10625, 15331}

X(32770) = (name pending)

X(32770) lies on this line: {3, 8}

X(32770) = {X(100),X(104)}-harmonic conjugate of X(32755)
X(32770) = circumcircle inverse of X(32755)

Centers of degree 3 with coefficients in {-1,0,1}: X(32771)-X(32784)

X(32771) = X(1)X(321)∩X(2)X(38)

X(32771) lies on these lines: {1, 321}, {2, 38}, {7, 26034}, {8, 2650}, {10, 3681}, {31, 894}, {37, 17157}, {42, 75}, {43, 4359}, {51, 17049}, {55, 4363}, {56, 7211}, {57, 29828}, {72, 31339}, {81, 4362}, {86, 5311}, {100, 3980}, {142, 25961}, {171, 26227}, {192, 1962}, {200, 25590}, {210, 3739}, {226, 25760}, {238, 26223}, {274, 869}, {312, 3720}, {354, 30942}, {518, 30969}, {551, 4135}, {561, 1909}, {611, 26000}, {612, 3263}, {726, 28606}, {740, 17018}, {748, 16823}, {750, 7081}, {870, 3112}, {873, 7033}, {899, 19804}, {908, 25960}, {940, 17763}, {968, 3729}, {976, 1010}, {977, 1220}, {986, 26115}, {1125, 3971}, {1278, 21806}, {1621, 3923}, {1757, 5278}, {1911, 18895}, {2177, 17116}, {2308, 3758}, {2345, 3475}, {2887, 29667}, {3009, 31997}, {3120, 29685}, {3159, 27785}, {3175, 15569}, {3187, 4649}, {3190, 18698}, {3293, 28612}, {3315, 29668}, {3474, 7222}, {3589, 29852}, {3616, 3994}, {3666, 17155}, {3677, 29826}, {3683, 17351}, {3703, 17056}, {3705, 31120}, {3715, 17259}, {3736, 30599}, {3741, 3873}, {3742, 30818}, {3745, 4670}, {3751, 5271}, {3772, 29631}, {3782, 4026}, {3797, 17032}, {3836, 27186}, {3846, 31053}, {3869, 30076}, {3874, 10479}, {3896, 4980}, {3932, 29854}, {3938, 5263}, {3961, 24342}, {3974, 4648}, {4011, 5284}, {4037, 16777}, {4046, 4665}, {4054, 24210}, {4082, 29571}, {4088, 24353}, {4358, 26102}, {4388, 24725}, {4446, 20966}, {4519, 4891}, {4655, 17483}, {4660, 20292}, {4661, 27798}, {4671, 29814}, {4672, 17127}, {4683, 5905}, {4688, 4849}, {4692, 30116}, {4697, 17126}, {4699, 21805}, {4703, 17484}, {4739, 21870}, {4850, 6685}, {4892, 25958}, {4972, 17889}, {5205, 17124}, {5220, 19732}, {5293, 16454}, {5550, 25079}, {5718, 29849}, {5750, 21101}, {5835, 15888}, {6057, 17243}, {6382, 18059}, {6533, 17749}, {6535, 17233}, {6679, 29681}, {6703, 17602}, {7191, 25496}, {7229, 10578}, {10434, 29069}, {11680, 25385}, {12263, 17397}, {13476, 14973}, {13740, 28082}, {15523, 18134}, {16569, 24589}, {16706, 29663}, {16720, 21010}, {16915, 18266}, {17030, 20456}, {17061, 29636}, {17122, 26627}, {17135, 31025}, {17147, 17592}, {17150, 19717}, {17163, 20011}, {17234, 29687}, {17279, 29851}, {17289, 24943}, {17369, 29638}, {17449, 31241}, {17591, 29825}, {17716, 20045}, {17718, 29846}, {17720, 29845}, {17724, 29848}, {17874, 20237}, {18139, 29674}, {18743, 30950}, {19784, 24159}, {19786, 29647}, {19869, 26728}, {20711, 26107}, {20909, 23655}, {21350, 24674}, {24174, 26030}, {24295, 29672}, {24321, 24333}, {24330, 24357}, {24456, 26976}, {24709, 26105}, {24789, 29850}, {24924, 30584}, {25525, 29857}, {25526, 30142}, {25959, 28595}, {27475, 30821}

X(32771) =

X(32772) = X(1)X(321)∩X(2)X(31)

X(32772) lies on these lines: {1, 321}, {2, 31}, {6, 4042}, {10, 1203}, {11, 6703}, {21, 36}, {38, 894}, {42, 3996}, {55, 16405}, {57, 29826}, {58, 19863}, {75, 17017}, {81, 3741}, {86, 310}, {100, 6685}, {142, 4224}, {190, 3989}, {239, 21020}, {244, 1281}, {274, 21415}, {312, 5311}, {333, 2308}, {354, 4670}, {474, 27639}, {497, 2268}, {561, 870}, {614, 10436}, {740, 17011}, {756, 16830}, {940, 30942}, {975, 25591}, {978, 16454}, {984, 26223}, {1001, 1011}, {1010, 1193}, {1100, 3706}, {1215, 3920}, {1220, 10459}, {1386, 31993}, {1449, 17156}, {1471, 27339}, {1621, 4203}, {1699, 19645}, {1724, 19858}, {1757, 4981}, {1836, 4657}, {1848, 4206}, {1909, 18064}, {1961, 4358}, {1962, 3685}, {2049, 16466}, {2298, 4071}, {2344, 32664}, {2886, 29631}, {2895, 3775}, {2975, 30076}, {3112, 18091}, {3120, 14012}, {3218, 4697}, {3219, 4672}, {3550, 29825}, {3589, 3925}, {3616, 4195}, {3624, 16342}, {3666, 4418}, {3703, 17369}, {3745, 17763}, {3750, 29822}, {3757, 17469}, {3772, 29636}, {3821, 20292}, {3842, 27065}, {3873, 29652}, {3914, 17023}, {3923, 28606}, {3966, 17303}, {3980, 4850}, {4038, 8025}, {4046, 14459}, {4357, 4683}, {4359, 24342}, {4360, 4365}, {4363, 17155}, {4383, 26037}, {4387, 16777}, {4423, 15668}, {4429, 29663}, {4432, 10180}, {4438, 29664}, {4514, 29685}, {4649, 17135}, {4682, 30818}, {4693, 27804}, {4716, 17163}, {4722, 17120}, {4854, 17045}, {4865, 29667}, {4886, 8013}, {4972, 29633}, {4974, 27798}, {5014, 29659}, {5248, 16452}, {5255, 26115}, {5269, 29828}, {5271, 16475}, {5278, 16468}, {5695, 20182}, {5718, 29846}, {6536, 17322}, {6686, 9342}, {7081, 31264}, {7083, 16352}, {7191, 24325}, {8053, 19339}, {8692, 19749}, {9313, 30909}, {9347, 29649}, {10453, 17379}, {10582, 24179}, {10886, 13478}, {11680, 29635}, {13733, 28628}, {14006, 17923}, {14829, 31241}, {15523, 17289}, {15988, 24997}, {16445, 25498}, {16477, 19742}, {16480, 29576}, {16484, 19740}, {16706, 29684}, {16827, 16926}, {17056, 29632}, {17061, 29834}, {17063, 26627}, {17140, 17598}, {17147, 17600}, {17150, 31025}, {17234, 29677}, {17279, 29854}, {17368, 26061}, {17381, 29647}, {17686, 23682}, {17716, 26227}, {17718, 29848}, {17720, 29847}, {17723, 29849}, {17889, 19271}, {18134, 24943}, {18139, 29637}, {19738, 28650}, {20132, 31027}, {20148, 27035}, {24295, 29653}, {24725, 27184}, {24789, 29852}, {25385, 29645}, {25441, 25639}, {25524, 28348}, {25525, 29855}, {26102, 31005}, {26105, 30943}, {26128, 29648}, {27186, 29666}, {29860, 30588}

X(32772) = complement of X(33083)

X(32773) = X(1)X(977)∩X(2)X(11)

X(32773) lies on these lines: {1, 977}, {2, 11}, {4, 1220}, {6, 4388}, {8, 1211}, {10, 312}, {31, 29631}, {33, 5174}, {37, 29641}, {38, 1227}, {42, 4417}, {43, 3846}, {56, 4201}, {63, 24723}, {75, 305}, {76, 18057}, {81, 6327}, {141, 10453}, {171, 4660}, {192, 3703}, {209, 3869}, {238, 25453}, {239, 3966}, {319, 17156}, {321, 29667}, {350, 5224}, {354, 3662}, {495, 16052}, {518, 27184}, {595, 20083}, {614, 16706}, {748, 17352}, {750, 29845}, {846, 4438}, {894, 1836}, {899, 25960}, {902, 29863}, {940, 4645}, {958, 26117}, {962, 5799}, {968, 29857}, {982, 3821}, {984, 4425}, {999, 11359}, {1213, 23918}, {1215, 3944}, {1233, 3673}, {1478, 17677}, {1479, 13740}, {1486, 25494}, {1654, 4042}, {1738, 19804}, {1757, 4703}, {1818, 24550}, {1848, 1869}, {1962, 29643}, {1999, 3416}, {2049, 19865}, {2177, 29846}, {2345, 21956}, {2476, 26115}, {2975, 17676}, {3006, 28606}, {3120, 29685}, {3136, 27042}, {3175, 3790}, {3240, 5741}, {3314, 17302}, {3475, 26132}, {3616, 4202}, {3617, 3974}, {3661, 3706}, {3666, 3705}, {3677, 17304}, {3681, 26580}, {3687, 3755}, {3717, 4656}, {3720, 17234}, {3722, 29848}, {3739, 21949}, {3743, 30172}, {3744, 29634}, {3745, 29841}, {3750, 3771}, {3757, 3772}, {3782, 24349}, {3836, 26102}, {3840, 24217}, {3873, 17184}, {3886, 19815}, {3920, 5014}, {3936, 17018}, {3959, 21954}, {3980, 24715}, {3995, 31079}, {3996, 30832}, {4030, 17602}, {4073, 4357}, {4193, 26030}, {4195, 6284}, {4205, 19853}, {4234, 4302}, {4358, 29679}, {4387, 17280}, {4398, 17155}, {4442, 28605}, {4450, 17126}, {4657, 20541}, {4676, 5294}, {4683, 17347}, {4872, 10436}, {4884, 17246}, {4891, 17231}, {4999, 19278}, {5016, 17016}, {5057, 26223}, {5241, 26038}, {5259, 19846}, {5264, 25441}, {5484, 12513}, {5550, 17674}, {5698, 26065}, {5749, 9812}, {6679, 8616}, {6682, 17774}, {6685, 17717}, {7069, 25024}, {7081, 17720}, {8543, 28776}, {9664, 24275}, {9668, 11354}, {10582, 17282}, {11109, 11393}, {11110, 19854}, {11269, 14829}, {13725, 19843}, {13728, 24390}, {15171, 17698}, {15523, 17233}, {15985, 21299}, {16060, 27309}, {16484, 29642}, {16823, 24789}, {17017, 17380}, {17063, 24169}, {17127, 29868}, {17235, 21342}, {17306, 24392}, {17354, 26061}, {17378, 31134}, {17381, 29647}, {17469, 29636}, {17522, 20988}, {17550, 26965}, {17592, 29671}, {17598, 29844}, {17671, 30107}, {17715, 29656}, {17716, 17766}, {17719, 29670}, {17722, 29650}, {17792, 21334}, {17889, 24325}, {18139, 25959}, {19270, 26363}, {19273, 31493}, {19823, 19993}, {20011, 31037}, {20173, 25006}, {21020, 23928}, {21026, 29854}, {22267, 26686}, {23682, 31997}, {24357, 25345}, {24551, 24678}, {24703, 27064}, {24752, 25978}, {25496, 29633}, {25914, 26093}, {25961, 30950}, {27047, 27313}, {28595, 29674}, {29632, 31237}, {29839, 30811}

X(32773) =

X(32774) = X(1)X(4202)∩X(2)X(37)

X(32774) lies on these lines: {1, 4202}, {2, 37}, {6, 17184}, {10, 3891}, {31, 3821}, {38, 25453}, {42, 26128}, {55, 26230}, {57, 21376}, {63, 17304}, {81, 3662}, {86, 17173}, {100, 29634}, {141, 3187}, {142, 20268}, {171, 29636}, {226, 7225}, {238, 29852}, {244, 29635}, {306, 3946}, {333, 17305}, {354, 29829}, {379, 2140}, {443, 1058}, {693, 25603}, {726, 26061}, {740, 24943}, {748, 4425}, {750, 24169}, {940, 17290}, {942, 4463}, {964, 23537}, {968, 24542}, {975, 17674}, {982, 29631}, {984, 29850}, {1104, 17676}, {1125, 3914}, {1211, 17366}, {1215, 29663}, {1255, 17244}, {1386, 6327}, {1824, 5439}, {1961, 25961}, {1962, 29642}, {1999, 17291}, {2177, 29656}, {2275, 16717}, {2308, 4655}, {2887, 17017}, {2895, 3759}, {2999, 5741}, {3006, 17599}, {3120, 25496}, {3219, 4389}, {3315, 29843}, {3416, 17150}, {3578, 17272}, {3589, 3782}, {3618, 5905}, {3624, 4442}, {3663, 5294}, {3670, 20083}, {3702, 19836}, {3744, 29831}, {3750, 29638}, {3758, 17483}, {3765, 26965}, {3836, 5311}, {3875, 3969}, {3920, 4429}, {3936, 5256}, {3938, 4085}, {3948, 30107}, {4357, 5278}, {4383, 26580}, {4392, 29868}, {4414, 6679}, {4417, 17012}, {4438, 29867}, {4514, 17024}, {4641, 17235}, {4643, 19742}, {4656, 31191}, {4660, 17469}, {4675, 8025}, {4683, 16468}, {4852, 20017}, {4865, 29819}, {4968, 19784}, {5016, 5262}, {5222, 5739}, {5233, 17020}, {5263, 29648}, {5268, 24988}, {5271, 17306}, {5287, 17282}, {5333, 17397}, {5745, 31229}, {5826, 14557}, {6682, 24892}, {6703, 26627}, {7490, 9776}, {10453, 26150}, {12610, 19645}, {16484, 29853}, {17011, 17380}, {17019, 17234}, {17025, 25958}, {17027, 30965}, {17061, 26227}, {17063, 29845}, {17064, 29826}, {17122, 29847}, {17127, 24723}, {17253, 19723}, {17325, 19732}, {17352, 27065}, {17361, 20086}, {17367, 27184}, {17372, 20046}, {17394, 20553}, {17591, 29856}, {17592, 29632}, {17594, 29855}, {17596, 29859}, {17597, 29835}, {17600, 29643}, {17715, 29836}, {17716, 29834}, {17750, 18098}, {17861, 20886}, {17889, 19271}, {18044, 28654}, {23292, 26651}, {23681, 29598}, {24046, 25441}, {24175, 24594}, {24325, 29647}, {25581, 25598}, {25760, 29821}, {27064, 29630}, {29671, 31237}

X(32774) =

X(32775) = X(1)X(3454)∩X(2)X(38)

X(32775) lies on these lines: {1, 3454}, {2, 38}, {6, 29636}, {9, 29855}, {31, 4683}, {37, 29632}, {42, 19786}, {55, 29848}, {81, 29645}, {100, 3821}, {141, 17602}, {171, 17184}, {210, 29850}, {238, 26230}, {312, 24943}, {321, 23689}, {354, 29845}, {518, 29631}, {612, 25527}, {614, 25960}, {750, 3662}, {896, 6646}, {899, 16706}, {902, 24723}, {908, 1125}, {940, 29847}, {976, 16062}, {1001, 20999}, {1150, 29658}, {1155, 17235}, {1211, 17061}, {1279, 29836}, {1283, 1621}, {1386, 29834}, {1757, 29859}, {1961, 18139}, {1962, 29839}, {2239, 31004}, {2887, 3920}, {2895, 3791}, {3011, 4357}, {3120, 5263}, {3219, 6679}, {3616, 5484}, {3666, 29846}, {3681, 25453}, {3712, 17246}, {3717, 30768}, {3771, 28606}, {3772, 31330}, {3782, 4418}, {3836, 5297}, {3846, 7191}, {3873, 29635}, {3874, 25441}, {3935, 4085}, {3944, 24552}, {3961, 4972}, {3989, 29865}, {3994, 17280}, {4009, 17357}, {4023, 17366}, {4026, 17724}, {4062, 4360}, {4104, 26723}, {4202, 5293}, {4204, 30961}, {4358, 29637}, {4364, 9318}, {4383, 29852}, {4388, 17469}, {4389, 4414}, {4413, 17290}, {4417, 17017}, {4423, 29853}, {4430, 29864}, {4649, 29833}, {4655, 17126}, {4657, 17718}, {4661, 29868}, {4672, 17484}, {4696, 19879}, {4697, 17483}, {4703, 17127}, {4766, 16826}, {4852, 14459}, {4865, 25958}, {5205, 17291}, {5219, 29826}, {5268, 25961}, {5284, 29672}, {5311, 18134}, {5363, 31019}, {5741, 29821}, {5904, 20083}, {6327, 17716}, {6536, 29689}, {6693, 6763}, {7018, 18064}, {7174, 29857}, {11375, 28386}, {11680, 29652}, {14829, 29683}, {17150, 31037}, {17305, 25374}, {17306, 29828}, {17599, 29849}, {17720, 30942}, {17722, 29823}, {17725, 26227}, {18743, 29677}, {19812, 29647}, {19836, 25591}, {19863, 24160}, {21093, 24295}, {24412, 24450}, {24542, 29860}, {24709, 29660}, {24789, 26037}, {25466, 27687}, {25496, 29648}, {27065, 29871}, {27131, 29666}, {29641, 31237}, {29643, 30811}, {29657, 30834}, {29671, 30831}

X(32775) =

X(32776) = X(1)X(6327)∩X(2)X(846)

X(32776) lies on these lines: {1, 6327}, {2, 846}, {6, 4683}, {9, 29850}, {10, 28605}, {31, 19786}, {37, 25957}, {38, 1227}, {42, 27184}, {43, 26580}, {55, 29848}, {57, 29845}, {63, 29631}, {81, 4655}, {141, 4854}, {149, 29652}, {171, 29847}, {190, 26061}, {191, 20083}, {192, 15523}, {238, 29852}, {354, 17235}, {614, 17304}, {726, 29667}, {748, 16706}, {756, 4429}, {894, 29647}, {902, 29634}, {964, 24851}, {968, 25527}, {984, 4972}, {986, 5051}, {1001, 16064}, {1125, 1770}, {1621, 26128}, {1699, 29826}, {1738, 26037}, {1836, 4657}, {1962, 18134}, {2292, 16062}, {2887, 28606}, {3175, 3844}, {3218, 29635}, {3219, 25453}, {3661, 4365}, {3662, 3720}, {3663, 17155}, {3666, 25760}, {3681, 4085}, {3685, 24943}, {3703, 17246}, {3706, 17237}, {3735, 20859}, {3752, 25960}, {3763, 4387}, {3782, 4026}, {3816, 25378}, {3846, 4850}, {3914, 4357}, {3920, 4660}, {3924, 26117}, {3925, 4364}, {3936, 17592}, {3966, 17301}, {3971, 29679}, {3989, 17247}, {3995, 29674}, {4042, 17253}, {4388, 17017}, {4392, 29655}, {4423, 17290}, {4450, 17716}, {4512, 29855}, {4645, 5311}, {4722, 17347}, {5057, 25496}, {5224, 21020}, {5249, 16778}, {5278, 24697}, {6682, 11680}, {6685, 31053}, {6703, 11246}, {7018, 30964}, {7226, 29673}, {8616, 26230}, {10453, 17236}, {12514, 27661}, {12579, 16865}, {16342, 24161}, {16705, 16891}, {17126, 29645}, {17127, 29654}, {17156, 17272}, {17165, 29659}, {17187, 17202}, {17291, 29677}, {17320, 31134}, {17323, 17599}, {17383, 29684}, {17449, 29843}, {17491, 19717}, {17594, 29846}, {17763, 26034}, {17766, 29815}, {21241, 29664}, {23537, 31339}, {24210, 30942}, {24349, 29685}, {24551, 26573}, {24627, 29662}, {25058, 30984}, {25958, 29671}, {25959, 29653}, {26223, 29633}, {26840, 29837}, {27064, 29663}, {27804, 31017}, {30632, 31008}

X(32776) =

X(32777) = X(1)X(3695)∩X(2)X(37)

X(32777) lies on these lines: {1, 3695}, {2, 37}, {3, 23847}, {6, 306}, {8, 1104}, {9, 440}, {10, 55}, {25, 1376}, {31, 3416}, {38, 24943}, {42, 26061}, {44, 5739}, {57, 7198}, {63, 141}, {69, 4641}, {81, 4851}, {100, 9078}, {171, 29674}, {190, 27184}, {209, 10477}, {226, 17355}, {238, 3966}, {239, 16974}, {244, 29677}, {318, 18679}, {333, 3661}, {355, 1746}, {406, 9371}, {429, 1329}, {474, 27802}, {553, 21255}, {594, 5271}, {599, 4001}, {612, 3932}, {726, 26128}, {740, 25453}, {750, 29687}, {894, 18134}, {936, 1040}, {940, 3912}, {958, 8192}, {968, 4026}, {982, 29637}, {1009, 2352}, {1125, 17599}, {1214, 14376}, {1215, 3771}, {1403, 3831}, {1427, 28739}, {1441, 28776}, {1621, 29667}, {1698, 3712}, {1708, 26942}, {1714, 5295}, {1722, 25992}, {1724, 5814}, {1766, 19542}, {1836, 2887}, {1914, 5278}, {1962, 29647}, {1999, 17233}, {2161, 2339}, {2325, 4656}, {2886, 29857}, {2901, 20083}, {2915, 25440}, {3006, 24552}, {3120, 31237}, {3187, 3969}, {3219, 4376}, {3452, 21062}, {3501, 24310}, {3589, 5256}, {3679, 3749}, {3686, 19723}, {3687, 3713}, {3705, 17721}, {3714, 5230}, {3715, 4104}, {3719, 26543}, {3729, 3782}, {3741, 4438}, {3750, 29659}, {3758, 17778}, {3763, 3977}, {3773, 4362}, {3790, 29634}, {3836, 3980}, {3840, 17728}, {3844, 4640}, {3846, 4011}, {3891, 26230}, {3914, 5695}, {3929, 17272}, {3931, 19784}, {3936, 26223}, {3961, 30615}, {3965, 23600}, {4024, 25684}, {4195, 7270}, {4204, 26037}, {4361, 26723}, {4363, 5249}, {4365, 29867}, {4387, 24210}, {4388, 4676}, {4415, 17340}, {4417, 17354}, {4418, 5880}, {4647, 19846}, {4659, 23681}, {4660, 28595}, {4675, 18139}, {4689, 9780}, {4760, 21221}, {4798, 5333}, {4863, 29673}, {4886, 17349}, {5014, 31079}, {5016, 11319}, {5057, 25958}, {5090, 17520}, {5226, 30823}, {5241, 7308}, {5247, 10371}, {5263, 29641}, {5273, 14021}, {5287, 6703}, {5328, 28656}, {5332, 19742}, {5336, 11679}, {5712, 5749}, {5737, 17293}, {5745, 21483}, {5750, 19701}, {5772, 10578}, {5791, 10479}, {5793, 24987}, {5794, 13733}, {5835, 19860}, {5905, 17351}, {6057, 17602}, {6541, 29645}, {6690, 29828}, {7283, 16062}, {7580, 12618}, {7795, 25083}, {8299, 31330}, {11374, 25645}, {11680, 29872}, {14555, 26685}, {14829, 17285}, {15985, 22370}, {16577, 25078}, {16594, 20196}, {16844, 19857}, {17023, 20182}, {17056, 17369}, {17061, 29855}, {17080, 28780}, {17184, 17276}, {17227, 26840}, {17229, 24597}, {17242, 29841}, {17334, 25734}, {17339, 30832}, {17345, 20078}, {17592, 29633}, {17595, 29596}, {17598, 29660}, {17600, 29646}, {17723, 24295}, {18141, 29579}, {18235, 26066}, {19744, 31477}, {20292, 25959}, {21245, 27052}, {21376, 24335}, {24325, 29642}, {24330, 30985}, {24691, 30965}, {24703, 25760}, {24954, 25079}, {25019, 26958}, {25591, 25681}, {27272, 31997}, {29678, 31264}, {30831, 31053}

X(32777) =

X(32778) = X(1)X(2)∩X(57)X(12588)

X(32778) lies on these lines: {1, 2}, {57, 12588}, {75, 2887}, {141, 982}, {171, 3416}, {190, 4703}, {192, 4425}, {238, 3966}, {305, 1930}, {312, 3773}, {321, 3944}, {333, 4438}, {345, 846}, {573, 5282}, {584, 3684}, {594, 2886}, {726, 27184}, {984, 1211}, {1215, 4417}, {1376, 5096}, {1757, 5739}, {2321, 24210}, {2345, 4071}, {3120, 25958}, {3210, 3821}, {3509, 5227}, {3596, 6382}, {3662, 24165}, {3686, 5037}, {3690, 5692}, {3717, 4104}, {3742, 17231}, {3744, 4914}, {3752, 3844}, {3790, 3971}, {3836, 19804}, {3883, 8616}, {3923, 4388}, {3932, 5743}, {3980, 4645}, {4011, 17280}, {4026, 17592}, {4038, 4851}, {4358, 25960}, {4359, 25957}, {4418, 6327}, {4429, 28595}, {4657, 17600}, {4671, 6535}, {4680, 14012}, {4865, 5263}, {5247, 5814}, {5278, 8300}, {5294, 16468}, {5300, 19271}, {5515, 20551}, {5846, 17716}, {5904, 10974}, {7281, 27542}, {8167, 17267}, {10009, 30631}, {16478, 17698}, {17123, 17279}, {17140, 31017}, {17155, 17184}, {17165, 31037}, {17229, 24217}, {17281, 24703}, {17289, 25496}, {17293, 17722}, {17490, 24169}, {17596, 17740}, {18134, 24325}, {18203, 20911}, {18788, 26118}, {19822, 24342}, {20292, 31134}, {21024, 23918}, {21241, 21829}, {21726, 31003}, {21920, 31245}, {21962, 25666}, {24589, 25961}, {26590, 27474}, {30599, 30984}, {31327, 31419}

X(32778) =

X(32779) = X(2)X(37)∩X(8)X(5266)

X(32779) lies on these lines: {2, 37}, {8, 5266}, {9, 21368}, {10, 21}, {22, 1376}, {43, 26061}, {55, 29667}, {63, 17272}, {81, 306}, {88, 24170}, {141, 3218}, {171, 15523}, {190, 26580}, {226, 30831}, {244, 29637}, {319, 16704}, {320, 31017}, {333, 32025}, {464, 5273}, {740, 29631}, {750, 29674}, {894, 3936}, {908, 17355}, {940, 17311}, {982, 24943}, {1150, 3661}, {1155, 3844}, {1211, 3219}, {1214, 18632}, {1215, 29846}, {1332, 26637}, {1465, 28780}, {1698, 21935}, {1738, 30768}, {1836, 25958}, {1861, 7466}, {1999, 3969}, {2064, 20896}, {2177, 29659}, {2886, 29872}, {2887, 4418}, {2895, 4641}, {2901, 25441}, {3006, 5263}, {3306, 5525}, {3416, 17126}, {3589, 17012}, {3687, 5294}, {3703, 3920}, {3704, 17016}, {3705, 24552}, {3712, 4026}, {3750, 29685}, {3758, 31034}, {3763, 17595}, {3773, 17763}, {3891, 29634}, {3912, 16785}, {3923, 5057}, {3925, 29873}, {3932, 5297}, {3966, 17127}, {3977, 4357}, {3980, 25957}, {4011, 25960}, {4062, 4649}, {4195, 5016}, {4256, 19867}, {4360, 29833}, {4363, 30811}, {4365, 29863}, {4370, 27776}, {4416, 31143}, {4417, 26223}, {4422, 5241}, {4427, 24723}, {4438, 31330}, {4642, 19879}, {4851, 14996}, {4886, 19742}, {4933, 21806}, {5051, 7283}, {5233, 17354}, {5247, 20653}, {5249, 20106}, {5262, 17698}, {5295, 24883}, {5333, 17189}, {5718, 17369}, {5739, 26065}, {5741, 27064}, {5743, 27065}, {5744, 29611}, {5791, 13726}, {5880, 25959}, {5955, 9780}, {6292, 17292}, {6350, 24635}, {6535, 29683}, {6703, 17019}, {7270, 11115}, {9709, 13730}, {16729, 25280}, {16823, 24542}, {17021, 17243}, {17061, 29874}, {17063, 29677}, {17122, 29687}, {17155, 26128}, {17234, 26627}, {17256, 27081}, {17293, 21488}, {17351, 17484}, {17360, 31303}, {17367, 24277}, {17521, 19842}, {17557, 19857}, {17592, 29647}, {17598, 29686}, {17599, 29648}, {17889, 31237}, {19262, 26446}, {19846, 28612}, {21857, 27320}, {24160, 25669}, {24325, 29632}, {24342, 29862}, {24593, 29587}, {24594, 29629}, {25496, 29849}, {26064, 31445}, {26070, 29591}, {26685, 30479}, {26738, 30828}, {30566, 30867}

X(32779) =

X(32780) = X(1)X(3695)∩X(2)X(38)

X(32780) lies on these lines: {1, 3695}, {2, 38}, {8, 3791}, {10, 58}, {12, 57}, {31, 29667}, {36, 19867}, {55, 29659}, {65, 19879}, {75, 25453}, {81, 15523}, {86, 29653}, {190, 4425}, {238, 5294}, {292, 16587}, {306, 4649}, {312, 29635}, {321, 29631}, {334, 8033}, {345, 17592}, {354, 29637}, {409, 5260}, {583, 17303}, {726, 19786}, {750, 29679}, {846, 4026}, {894, 2887}, {940, 29674}, {958, 5329}, {985, 5278}, {986, 19784}, {1089, 25441}, {1125, 17598}, {1126, 21081}, {1211, 1757}, {1213, 3509}, {1376, 4265}, {1460, 9708}, {1621, 29685}, {1723, 5831}, {1762, 3925}, {1961, 3932}, {1999, 3773}, {2161, 2886}, {2895, 4722}, {3219, 24697}, {3329, 3705}, {3339, 19880}, {3589, 29821}, {3624, 3677}, {3634, 18201}, {3666, 29633}, {3678, 24931}, {3679, 5269}, {3741, 17289}, {3742, 17357}, {3757, 6679}, {3772, 29856}, {3790, 29841}, {3846, 27064}, {3873, 24943}, {3891, 29636}, {3912, 4038}, {3953, 19881}, {3966, 16468}, {3976, 19836}, {3980, 4429}, {4011, 17354}, {4284, 5750}, {4358, 29845}, {4359, 29850}, {4363, 17889}, {4385, 19806}, {4388, 4672}, {4418, 4972}, {4645, 4697}, {4650, 26034}, {4671, 29864}, {4703, 17350}, {4850, 29663}, {5143, 18235}, {5249, 30768}, {5251, 5285}, {5263, 29673}, {5749, 26098}, {5955, 6048}, {7186, 17792}, {7262, 26065}, {16706, 24165}, {17023, 17600}, {17056, 29862}, {17061, 29859}, {17123, 17353}, {17263, 25501}, {17279, 26102}, {17280, 29837}, {17355, 24210}, {17381, 29644}, {17597, 29660}, {17599, 29646}, {18165, 22279}, {19684, 29643}, {19792, 20083}, {20368, 26446}, {24295, 29655}, {24586, 29576}, {24725, 25958}, {24746, 28653}, {25760, 26223}, {25961, 26627}, {26040, 26929}, {27798, 28604}, {28605, 29868}, {28606, 29647}, {31019, 31237}

X(32780) =

X(32781) = X(2)X(31)∩X(6)X(29663)

X(32781) lies on these lines: {2, 31}, {6, 29663}, {10, 38}, {37, 29687}, {42, 141}, {55, 3763}, {63, 1698}, {81, 29633}, {210, 17237}, {226, 31264}, {321, 3821}, {333, 29850}, {354, 29685}, {536, 6535}, {595, 19881}, {612, 17306}, {672, 1213}, {756, 3263}, {758, 19867}, {896, 3634}, {899, 1211}, {940, 29647}, {968, 17284}, {982, 29667}, {984, 29679}, {1001, 29677}, {1125, 17469}, {1150, 25453}, {1215, 17184}, {1386, 29684}, {1468, 19784}, {1621, 29637}, {1737, 11031}, {1738, 21020}, {1962, 3912}, {2177, 3619}, {2223, 6292}, {2228, 20966}, {2308, 3589}, {2886, 31241}, {2975, 19879}, {3006, 6682}, {3416, 17017}, {3666, 3844}, {3683, 17357}, {3715, 17253}, {3720, 4026}, {3741, 4972}, {3744, 29686}, {3745, 17384}, {3757, 17291}, {3769, 29636}, {3773, 17147}, {3775, 4651}, {3812, 27714}, {3831, 5051}, {3873, 29659}, {3915, 19836}, {3925, 30970}, {3932, 3989}, {3936, 6685}, {3969, 4970}, {4001, 4722}, {4085, 17135}, {4358, 4425}, {4413, 7085}, {4418, 17289}, {4429, 31330}, {4655, 26223}, {4657, 5311}, {4660, 24552}, {4683, 27064}, {4698, 8040}, {4987, 5750}, {5014, 29652}, {5224, 26037}, {5251, 7293}, {5282, 17303}, {5314, 24931}, {5372, 29868}, {5745, 30768}, {5846, 29819}, {6057, 17246}, {6690, 29865}, {8013, 17239}, {8620, 16587}, {8728, 28274}, {9342, 31247}, {9345, 18141}, {11246, 17369}, {11680, 29827}, {14829, 29631}, {16062, 19810}, {16570, 19876}, {16707, 16887}, {16818, 20985}, {17283, 29851}, {17370, 29852}, {17398, 21764}, {17674, 28269}, {17716, 25539}, {17763, 19786}, {19812, 29847}, {19877, 26065}, {24697, 27065}, {25351, 27798}, {25527, 29828}, {25914, 28352}, {26128, 26227}, {28599, 29823}, {28606, 29674}, {29678, 30811}

X(32781) =

X(32782) = X(2)X(6)∩X(7)X(19822)

X(32782) lies on these lines: {2, 6}, {7, 19822}, {8, 3891}, {9, 21367}, {10, 3681}, {63, 17272}, {75, 17184}, {76, 321}, {100, 26034}, {192, 3969}, {210, 3844}, {238, 24943}, {305, 16703}, {306, 4357}, {308, 18096}, {312, 17228}, {319, 3187}, {320, 19808}, {329, 29611}, {405, 26064}, {464, 18642}, {518, 29667}, {594, 3782}, {748, 29637}, {756, 29674}, {956, 19258}, {961, 10372}, {964, 1330}, {980, 7794}, {984, 15523}, {986, 20653}, {997, 6505}, {1008, 4388}, {1043, 17676}, {1255, 17316}, {1257, 15474}, {1352, 4220}, {1386, 29648}, {1757, 26061}, {1999, 17287}, {2049, 26131}, {2345, 5905}, {2476, 3454}, {2886, 25958}, {2887, 3775}, {3175, 17229}, {3210, 17236}, {3219, 4376}, {3305, 17284}, {3416, 3920}, {3662, 4359}, {3666, 17237}, {3679, 23681}, {3686, 26723}, {3687, 4850}, {3703, 7226}, {3739, 27186}, {3741, 11680}, {3791, 29636}, {3821, 21085}, {3836, 26037}, {3840, 25960}, {3842, 29854}, {3846, 30942}, {3923, 4683}, {3925, 25959}, {3948, 17550}, {3966, 7191}, {3995, 17233}, {4026, 17018}, {4062, 17592}, {4193, 17182}, {4202, 9534}, {4360, 20017}, {4363, 17483}, {4384, 26724}, {4389, 17147}, {4415, 4671}, {4416, 5294}, {4418, 4655}, {4429, 4651}, {4469, 8024}, {4641, 17344}, {4649, 29647}, {4656, 29594}, {4657, 17011}, {4851, 17019}, {4886, 16706}, {4966, 29814}, {4974, 29852}, {4981, 29641}, {5044, 18732}, {5051, 10449}, {5256, 17306}, {5262, 5814}, {5263, 6327}, {5271, 17270}, {5273, 26932}, {5287, 17296}, {5337, 7854}, {5564, 19796}, {5793, 20060}, {5846, 29815}, {6682, 29849}, {6989, 12359}, {7232, 26842}, {7321, 19797}, {7465, 11442}, {7761, 24271}, {7789, 21508}, {7795, 21511}, {7800, 21495}, {10371, 17016}, {10519, 26118}, {13728, 19767}, {14907, 16046}, {16342, 25650}, {16585, 25078}, {16887, 18601}, {17123, 29677}, {17227, 19804}, {17239, 31019}, {17257, 17776}, {17275, 24789}, {17279, 27065}, {17289, 26223}, {17292, 27064}, {17293, 17484}, {17325, 20182}, {17355, 17781}, {17360, 19812}, {17361, 19827}, {17717, 31241}, {17889, 21020}, {18135, 26601}, {18200, 24921}, {18229, 31266}, {18747, 31018}, {19819, 32087}, {20173, 26593}, {20208, 21482}, {20929, 20955}, {21024, 31060}, {21240, 29576}, {24988, 26038}, {25539, 29684}, {25914, 27625}, {26747, 27641}, {27038, 27096}, {27047, 27263}, {27131, 30818}, {27476, 27495}, {28654, 30473}

X(32782) = complement of X(37685)

X(32783) = X(1)X(2)∩X(75)X(26128)

X(32783) lies on these lines: {1, 2}, {75, 26128}, {141, 171}, {238, 1211}, {242, 1848}, {261, 7305}, {319, 3791}, {320, 4697}, {321, 23689}, {333, 3775}, {350, 18697}, {594, 17061}, {740, 19786}, {846, 4357}, {1011, 23850}, {1213, 3684}, {1215, 17289}, {1283, 4199}, {1376, 3763}, {1707, 17272}, {1757, 5294}, {1891, 4212}, {2238, 16470}, {2308, 2895}, {2309, 27270}, {2345, 21101}, {2887, 5263}, {3416, 17716}, {3550, 26034}, {3662, 3980}, {3681, 26061}, {3683, 24697}, {3685, 4425}, {3740, 17357}, {3750, 4026}, {3769, 17228}, {3846, 30832}, {3923, 27184}, {3967, 17359}, {3971, 17280}, {3996, 4085}, {4038, 4966}, {4046, 4716}, {4104, 17353}, {4204, 5259}, {4279, 28242}, {4417, 25496}, {4418, 17184}, {4640, 17237}, {4643, 4797}, {4647, 19787}, {4657, 17592}, {4676, 4703}, {4682, 17231}, {4693, 4854}, {4734, 17383}, {4886, 4974}, {4970, 17302}, {5227, 17754}, {5247, 17698}, {5249, 24342}, {5284, 31247}, {5285, 16056}, {5329, 11358}, {5739, 16468}, {5743, 17123}, {5814, 16478}, {5955, 24174}, {7110, 14844}, {8300, 24542}, {10180, 17322}, {16800, 17277}, {17291, 24169}, {17293, 17725}, {17306, 17594}, {17358, 27538}, {17490, 26150}, {17591, 17740}, {17889, 25527}, {18491, 19540}, {19808, 24325}, {24259, 31004}, {24295, 27064}, {24552, 25760}

X(32783) =

X(32784) = X(1)X(141)∩X(2)X(31)

X(32784) lies on these lines: {1, 141}, {2, 31}, {3, 29020}, {5, 6210}, {6, 29633}, {8, 3775}, {9, 46}, {10, 75}, {11, 29827}, {12, 1423}, {37, 3844}, {38, 29667}, {43, 1211}, {69, 4649}, {81, 29647}, {165, 19542}, {192, 3773}, {242, 5117}, {256, 5051}, {306, 17592}, {312, 4425}, {333, 25453}, {405, 7295}, {451, 2212}, {516, 7377}, {518, 17237}, {519, 17399}, {524, 28650}, {545, 19875}, {740, 3661}, {756, 29679}, {894, 4655}, {958, 19879}, {960, 25144}, {982, 24163}, {1001, 3763}, {1125, 3883}, {1150, 29631}, {1215, 27184}, {1279, 29660}, {1386, 17384}, {1429, 12588}, {1621, 24943}, {1716, 4205}, {1757, 4643}, {1861, 24341}, {2209, 27270}, {2214, 16470}, {2345, 24248}, {2354, 5142}, {3097, 25349}, {3219, 26061}, {3220, 5251}, {3454, 27042}, {3589, 16468}, {3616, 17232}, {3618, 16477}, {3619, 16484}, {3624, 7290}, {3634, 17353}, {3662, 24325}, {3670, 4446}, {3679, 7174}, {3685, 17292}, {3696, 17239}, {3705, 6682}, {3751, 17272}, {3755, 4923}, {3757, 26128}, {3758, 17770}, {3769, 19812}, {3790, 17247}, {3823, 4708}, {3831, 21257}, {3842, 4019}, {3873, 29685}, {3915, 21289}, {3923, 17289}, {3925, 24310}, {3932, 4364}, {3966, 29821}, {3980, 19808}, {3993, 17233}, {4073, 6734}, {4197, 28287}, {4202, 31339}, {4356, 29594}, {4362, 19786}, {4393, 17772}, {4417, 6685}, {4432, 29613}, {4488, 7229}, {4514, 29652}, {4660, 5263}, {4663, 17344}, {4664, 6541}, {4672, 17368}, {4676, 17371}, {4683, 26223}, {4687, 25354}, {4693, 29611}, {4703, 27064}, {4710, 30473}, {4741, 17771}, {4972, 31330}, {4974, 17367}, {5047, 7301}, {5220, 17253}, {5234, 19880}, {5247, 19784}, {5271, 19834}, {5278, 29850}, {5284, 29677}, {5294, 7262}, {5361, 29868}, {5372, 29864}, {5625, 17391}, {5692, 19867}, {5695, 17293}, {5718, 29825}, {5743, 16569}, {5749, 24695}, {5847, 17023}, {5904, 22277}, {6211, 26446}, {6536, 29687}, {7083, 11108}, {8728, 27626}, {9791, 17280}, {11680, 31241}, {12587, 18162}, {14829, 29635}, {15254, 17357}, {15523, 28606}, {15569, 17231}, {15601, 19872}, {16475, 29598}, {16476, 16818}, {16706, 16825}, {16739, 18057}, {16823, 17291}, {16830, 17326}, {16927, 30174}, {17064, 18229}, {17236, 24349}, {17308, 17738}, {17327, 19856}, {17350, 26083}, {17469, 29648}, {17593, 17740}, {17719, 29828}, {17722, 29826}, {17725, 26227}, {17755, 25351}, {17889, 31993}, {19717, 20290}, {19804, 24169}, {19855, 27509}, {19877, 26685}, {20994, 24273}, {21912, 26040}, {24206, 31394}, {24217, 30942}, {24231, 31178}, {24693, 29610}, {24931, 25440}, {25005, 25024}, {26030, 26772}, {26064, 27320}, {26251, 26580}, {28595, 29641}, {29640, 30811}, {29678, 30831}, {29822, 31017}, {30940, 30966}, {31053, 31264}

X(32784) =

Points with first barycentric of type h f(a,b,c) + k S: X(32785)-X(32841)

X(32785) = (name pending)

X(32785) lies on these lines: {2, 6}, {3, 18538}, {4, 5418}, {5, 6221}, {10, 13902}, {20, 6411}, {30, 6451}, {125, 18923}, {140, 1587}, {187, 11292}, {239, 32795}, {371, 3090}, {372, 3525}, {376, 6564}, {381, 6445}, {485, 631}, {486, 5067}, {488, 8376}, {546, 6449}, {547, 13785}, {549, 6452}, {550, 23253}, {574, 11291}, {605, 17123}, {606, 17122}, {632, 3312}, {638, 33364}, {641, 13651}, {642, 7376}, {894, 32796}, {1030, 21565}, {1125, 13893}, {1131, 15717}, {1151, 3091}, {1267, 17117}, {1327, 19708}, {1588, 1656}, {1589, 22052}, {1590, 10979}, {1600, 8939}, {1698, 8983}, {2045, 5335}, {2046, 5334}, {2066, 10589}, {2067, 10588}, {3035, 31413}, {3070, 3523}, {3071, 5056}, {3085, 9661}, {3086, 9646}, {3146, 6409}, {3247, 5393}, {3311, 3628}, {3317, 6435}, {3366, 18581}, {3391, 18582}, {3522, 23251}, {3524, 6560}, {3526, 6395}, {3533, 5420}, {3545, 6480}, {3590, 6434}, {3616, 13911}, {3624, 13883}, {3627, 6455}, {3634, 18991}, {3731, 6351}, {3817, 9616}, {3832, 6433}, {3851, 9690}, {3855, 9680}, {4254, 21546}, {4294, 31499}, {4361, 32799}, {4363, 32800}, {4413, 13887}, {5054, 6446}, {5068, 6468}, {5070, 7584}, {5071, 6565}, {5072, 6407}, {5094, 13884}, {5120, 21549}, {5124, 21568}, {5326, 19037}, {5391, 17116}, {5412, 8889}, {5432, 13898}, {5433, 13897}, {5550, 7968}, {6118, 13834}, {6119, 13770}, {6419, 13939}, {6424, 31404}, {6425, 15022}, {6427, 13993}, {6439, 9543}, {6447, 12812}, {6450, 14869}, {6456, 12108}, {6481, 15702}, {6496, 15704}, {6519, 12811}, {6622, 11473}, {6667, 19113}, {6683, 19090}, {6721, 19056}, {6722, 19109}, {6723, 19111}, {7288, 31472}, {7294, 18995}, {7389, 9600}, {7484, 13889}, {7486, 31454}, {7509, 8276}, {7582, 10577}, {7749, 31411}, {7786, 8992}, {7808, 13885}, {7914, 13892}, {7969, 9780}, {8167, 18999}, {8227, 13912}, {8993, 31268}, {8997, 14061}, {8998, 15059}, {9582, 18483}, {9583, 10175}, {9602, 18584}, {9615, 19925}, {9675, 31415}, {9679, 31418}, {10299, 23269}, {10533, 32064}, {10819, 15081}, {11444, 12239}, {11513, 16051}, {12240, 15028}, {12257, 26951}, {12900, 19060}, {13888, 13936}, {13894, 15184}, {13896, 24953}, {13906, 26364}, {13907, 26363}, {13922, 31272}, {13924, 19102}, {13973, 19877}, {14241, 15719}, {15492, 30412}, {15694, 18512}, {15703, 18510}, {16239, 19117}, {16419, 19006}, {16814, 30413}, {17538, 22644}, {17819, 23332}, {18755, 21991}, {18992, 19862}, {19004, 19872}, {19058, 22247}, {19089, 31239}, {19108, 31274}, {19112, 31235}, {19116, 31487}, {19355, 23291}, {24842, 27191}}

X(32785) = {X(2),X(6)}-harmonic conjugate of X(32786)

X(32786) = (name pending)

X(32786) lies on these lines: {2, 6}, {3, 18762}, {4, 5420}, {5, 6398}, {10, 13959}, {20, 6412}, {30, 6452}, {125, 18924}, {140, 1588}, {187, 11291}, {239, 32796}, {371, 3525}, {372, 3090}, {376, 6565}, {381, 6446}, {485, 5067}, {486, 631}, {546, 6450}, {547, 13665}, {549, 6451}, {550, 23263}, {574, 11292}, {605, 17122}, {606, 17123}, {632, 3311}, {637, 9675}, {641, 7375}, {642, 13770}, {894, 32795}, {1030, 21568}, {1125, 13947}, {1132, 15717}, {1151, 10303}, {1152, 3091}, {1267, 17116}, {1328, 19708}, {1587, 1656}, {1589, 10979}, {1590, 22052}, {1599, 8943}, {1698, 13971}, {2045, 5334}, {2046, 5335}, {3070, 5056}, {3071, 3523}, {3146, 6410}, {3247, 5405}, {3312, 3628}, {3316, 6436}, {3367, 18581}, {3392, 18582}, {3522, 23261}, {3524, 6561}, {3526, 6199}, {3533, 5418}, {3545, 6481}, {3591, 6433}, {3616, 13973}, {3624, 13902}, {3627, 6456}, {3634, 18992}, {3731, 6352}, {3832, 6434}, {3851, 23253}, {4254, 21549}, {4361, 32800}, {4363, 32799}, {4413, 13940}, {5054, 6445}, {5068, 6469}, {5070, 7583}, {5071, 6564}, {5072, 6408}, {5094, 13937}, {5120, 21546}, {5124, 21565}, {5326, 19038}, {5391, 17117}, {5413, 8889}, {5414, 10589}, {5432, 13955}, {5433, 13954}, {5550, 7969}, {6118, 13651}, {6119, 13711}, {6420, 13886}, {6423, 31404}, {6426, 15022}, {6428, 13925}, {6448, 12812}, {6449, 14869}, {6455, 12108}, {6480, 15702}, {6490, 9692}, {6497, 15704}, {6502, 10588}, {6522, 12811}, {6622, 11474}, {6667, 19112}, {6683, 19089}, {6721, 19055}, {6722, 19108}, {6723, 19110}, {7294, 18996}, {7388, 13934}, {7484, 13943}, {7486, 31414}, {7509, 8277}, {7581, 10576}, {7786, 13983}, {7808, 13938}, {7914, 13946}, {7968, 9780}, {8167, 19000}, {8227, 13975}, {9602, 12221}, {10299, 23275}, {10534, 32064}, {10820, 15081}, {11444, 12240}, {11514, 16051}, {12239, 15028}, {12900, 19059}, {13883, 13942}, {13911, 19877}, {13948, 15184}, {13953, 24953}, {13964, 26364}, {13965, 26363}, {13989, 14061}, {13991, 31272}, {14226, 15719}, {15492, 30413}, {15694, 18510}, {15703, 18512}, {16239, 19116}, {16419, 19005}, {16814, 30412}, {17538, 22615}, {17820, 23332}, {17851, 19709}, {18966, 31408}, {18991, 19862}, {19003, 19872}, {19057, 22247}, {19090, 31239}, {19105, 32209}, {19109, 31274}, {19113, 31235}, {19356, 23291}, {24843, 27191}}

X(32786) = {X(2),X(6)}-harmonic conjugate of X(32785)

X(32787) = (name pending)

X(32787) lies on these lines: {2, 6}, {3, 9680}, {4, 3592}, {5, 6419}, {16, 15764}, {20, 6425}, {30, 371}, {32, 32421}, {39, 13821}, {44, 5393}, {61, 18585}, {62, 15765}, {99, 19058}, {115, 13703}, {140, 6420}, {239, 32801}, {372, 549}, {376, 1151}, {381, 485}, {397, 2043}, {398, 2044}, {428, 5412}, {486, 5055}, {519, 7969}, {547, 7584}, {550, 6453}, {551, 7968}, {588, 1989}, {589, 30537}, {631, 3594}, {671, 19109}, {894, 32802}, {903, 24819}, {1124, 10072}, {3524, 7581}, {1327, 3830}, {1335, 10056}, {1384, 13712}, {1503, 11241}, {1504, 5309}, {1506, 13921}, {1585, 1990}, {1586, 6749}, {1588, 3545}, {1656, 6427}, {1657, 6447}, {1702, 31162}, {2066, 3058}, {2067, 5434}, {2482, 8997}, {2549, 13644}, {2965, 26912}, {3003, 8962}, {3094, 22722}, {3146, 31414}, {3163, 8968}, {3167, 11209}, {3241, 19066}, {3299, 3582}, {3301, 3584}, {3304, 31475}, {3312, 5054}, {3365, 16962}, {3390, 16963}, {3523, 6426}, {3526, 6428}, {3530, 6454}, {3534, 6221}, {3543, 6459}, {3590, 15022}, {3679, 13911}, {3828, 13936}, {3839, 6470}, {3845, 6564}, {4254, 21558}, {4361, 32797}, {4363, 32798}, {4370, 24842}, {4428, 13887}, {4995, 5414}, {5058, 7753}, {5064, 5410}, {5066, 6565}, {5070, 10195}, {5071, 7582}, {5120, 21561}, {5254, 12962}, {5286, 26289}, {5298, 6502}, {5319, 11313}, {5405, 16666}, {5413, 13884}, {5415, 19024}, {5420, 6418}, {5421, 8963}, {5459, 13917}, {5460, 13916}, {5463, 19074}, {5464, 19076}, {5642, 8998}, {6054, 19056}, {6055, 8980}, {6174, 13922}, {6200, 8703}, {6351, 16885}, {6352, 16884}, {6395, 15701}, {6396, 12100}, {6398, 15693}, {6407, 15689}, {6408, 15718}, {6409, 6460}, {6410, 15692}, {6411, 19708}, {6412, 15698}, {6415, 10262}, {6422, 7739}, {6424, 31411}, {6432, 13935}, {6433, 9542}, {6435, 10109}, {6437, 9541}, {6438, 15719}, {6441, 23273}, {6445, 15695}, {6449, 15688}, {6450, 15700}, {6452, 15716}, {6455, 14093}, {6456, 15706}, {6468, 15697}, {6471, 15721}, {6480, 15690}, {6481, 19711}, {6500, 13951}, {6519, 15696}, {6772, 13646}, {6775, 13645}, {6811, 8550}, {7392, 20197}, {7576, 10880}, {7615, 12158}, {7737, 8375}, {7755, 32491}, {7757, 19090}, {7772, 31483}, {7865, 19012}, {7991, 31440}, {8376, 21843}, {8573, 8939}, {8909, 19062}, {8992, 9466}, {9140, 19111}, {9166, 19057}, {9167, 13989}, {9605, 19105}, {9607, 11293}, {9692, 10147}, {10128, 10961}, {10192, 11242}, {10577, 15699}, {10691, 11513}, {10706, 19060}, {10707, 19113}, {10711, 19082}, {10718, 19115}, {10819, 19052}, {11157, 12159}, {11179, 19145}, {11237, 18996}, {11238, 19038}, {11291, 31465}, {11539, 13966}, {11646, 13640}, {12239, 14831}, {12240, 16226}, {13651, 22485}, {13674, 13749}, {13701, 13720}, {13711, 13932}, {13785, 19709}, {13832, 33457}, {13833, 13835}, {13882, 19103}, {13888, 18992}, {13893, 13973}, {13947, 19876}, {13961, 15723}, {13968, 14971}, {15682, 23249}, {15684, 22644}, {16777, 30413}, {17120, 32792}, {17121, 32791}, {19064, 22712}, {19073, 22489}, {19075, 22490}, {19092, 31168}, {28198, 31439}}

X(32787) = complement of X(32808)
X(32787) = {X(2),X(6)}-harmonic conjugate of X(32788)

X(32788) = (name pending)

X(32788) lies on these lines: {2, 6}, {3, 9681}, {4, 3594}, {5, 6420}, {15, 15764}, {20, 6426}, {30, 372}, {32, 32419}, {39, 13701}, {44, 5405}, {61, 15765}, {62, 18585}, {99, 19057}, {115, 13823}, {140, 6419}, {239, 32802}, {371, 549}, {376, 1152}, {381, 486}, {397, 2044}, {398, 2043}, {428, 5413}, {485, 5055}, {519, 7968}, {547, 7583}, {550, 6454}, {551, 7969}, {588, 30537}, {589, 1989}, {631, 3592}, {671, 19108}, {894, 32801}, {903, 24818}, {1124, 10056}, {1151, 3524}, {1328, 3830}, {1335, 10072}, {1384, 13835}, {1503, 11242}, {1505, 5309}, {1506, 13880}, {1585, 6749}, {1586, 1990}, {1587, 3545}, {1656, 6428}, {1657, 6448}, {1703, 31162}, {2066, 4995}, {2067, 5298}, {2482, 13989}, {2549, 13763}, {3058, 5414}, {3094, 22723}, {3167, 11210}, {3241, 19065}, {3299, 3584}, {3301, 3582}, {3311, 5054}, {3364, 16962}, {3389, 16963}, {3523, 6425}, {3526, 6427}, {3530, 6453}, {3534, 6398}, {3543, 6460}, {3591, 15022}, {3628, 8960}, {3679, 13973}, {3828, 13883}, {3839, 6471}, {3845, 6565}, {4254, 21561}, {4361, 32798}, {4363, 32797}, {4370, 24843}, {4428, 13940}, {5062, 7753}, {5064, 5411}, {5066, 6564}, {5068, 31414}, {5070, 10194}, {5071, 7581}, {5120, 21558}, {5254, 12969}, {5286, 26288}, {5319, 11314}, {5393, 16666}, {5412, 13937}, {5416, 19023}, {5418, 6417}, {5434, 6502}, {5459, 13982}, {5460, 13981}, {5463, 19073}, {5464, 19075}, {5642, 13990}, {6054, 19055}, {6055, 13967}, {6174, 13991}, {6199, 15701}, {6200, 12100}, {6221, 15693}, {6351, 16884}, {6352, 16885}, {6396, 8703}, {6407, 15718}, {6408, 15689}, {6409, 15692}, {6410, 6459}, {6411, 15698}, {6412, 9541}, {6416, 10261}, {6421, 7739}, {6431, 9540}, {6436, 10109}, {6437, 15719}, {6438, 11001}, {6442, 23267}, {6446, 15695}, {6449, 15700}, {6450, 15688}, {6451, 15716}, {6455, 15706}, {6456, 14093}, {6469, 15697}, {6470, 15721}, {6480, 19711}, {6481, 15690}, {6488, 9693}, {6501, 8976}, {6522, 15696}, {6772, 13765}, {6775, 13764}, {6813, 8550}, {7494, 20197}, {7576, 10881}, {7615, 12159}, {7737, 8376}, {7755, 32490}, {7757, 19089}, {7865, 19011}, {8375, 21843}, {8573, 8943}, {8981, 11539}, {8983, 19883}, {8997, 9167}, {9140, 19110}, {9166, 19058}, {9466, 13983}, {9605, 19102}, {9607, 11294}, {9680, 15720}, {10128, 10963}, {10192, 11241}, {10576, 15699}, {10691, 11514}, {10706, 19059}, {10707, 19112}, {10711, 19081}, {10718, 19114}, {11158, 12158}, {11179, 19146}, {11237, 18995}, {11238, 19037}, {11646, 13760}, {12239, 16226}, {12240, 14831}, {13665, 19709}, {13712, 13769}, {13748, 13794}, {13821, 13843}, {13831, 33456}, {13834, 13850}, {13893, 19876}, {13903, 15723}, {13908, 14971}, {13911, 13947}, {13942, 18991}, {13954, 31472}, {15682, 23259}, {15684, 22615}, {16777, 30412}, {17120, 32791}, {17121, 32792}, {19063, 22712}, {19074, 22489}, {19076, 22490}, {19091, 31168}

X(32788) = complement of X(32809)
X(32788) = {X(2),X(6)}-harmonic conjugate of X(32787)

X(32789) = (name pending)

X(32789) lies on these lines: {2, 6}, {3, 22644}, {4, 6411}, {5, 6200}, {140, 3070}, {187, 32432}, {371, 3628}, {372, 632}, {381, 6451}, {485, 3526}, {486, 5070}, {547, 6480}, {549, 6564}, {574, 6118}, {631, 6412}, {641, 11614}, {642, 32491}, {1030, 21553}, {1151, 3090}, {3525, 23267}, {1327, 15701}, {1587, 3533}, {1656, 3071}, {2045, 5318}, {2046, 5321}, {3091, 6409}, {3316, 13935}, {3366, 33416}, {3391, 33417}, {3523, 23251}, {3594, 13886}, {3624, 13911}, {3634, 7969}, {3723, 5393}, {4361, 32795}, {4363, 32796}, {5024, 13711}, {5054, 6452}, {5055, 6445}, {5056, 6433}, {5067, 6437}, {5071, 9541}, {5072, 6455}, {5079, 6449}, {5124, 21492}, {5159, 11513}, {5210, 11292}, {5326, 5414}, {5420, 6395}, {6351, 16677}, {6352, 16674}, {6410, 10303}, {6420, 13925}, {6431, 13939}, {6434, 6460}, {6436, 19117}, {6440, 31414}, {6441, 7582}, {6446, 13665}, {6459, 6468}, {6481, 11539}, {6502, 7294}, {7583, 16239}, {7741, 31499}, {7968, 19862}, {8960, 13966}, {8981, 10577}, {9600, 11313}, {9675, 32490}, {9680, 9690}, {10299, 23253}, {10533, 23332}, {10645, 18585}, {10646, 15765}, {11314, 31415}, {13785, 15703}, {13834, 13882}, {13883, 19878}, {13902, 19877}, {13924, 31483}, {13936, 31253}, {14813, 16967}, {14814, 16966}, {15723, 18512}, {17116, 32792}, {17117, 32791}, {17118, 32800}, {17119, 32799}, {18991, 19872}

X(32789) = complement of X(32807)
X(32789) = {X(2),X(6)}-harmonic conjugate of X(32790)

X(32790) = (name pending)

X(32790) lies on these

X(32790) lies on these lines: {2, 6}, {3, 22615}, {4, 6412}, {5, 6396}, {140, 3071}, {187, 32435}, {371, 632}, {372, 3628}, {381, 6452}, {485, 5070}, {486, 3526}, {547, 6481}, {549, 6565}, {574, 6119}, {631, 6411}, {639, 9675}, {641, 32490}, {642, 11614}, {1030, 21492}, {1151, 3525}, {3090, 23249}, {1328, 15701}, {1588, 3533}, {1656, 3070}, {2045, 5321}, {2046, 5318}, {2066, 5326}, {2067, 7294}, {3091, 6410}, {3317, 9540}, {3367, 33416}, {3392, 33417}, {3523, 23261}, {3592, 13939}, {3624, 13973}, {3634, 7968}, {3723, 5405}, {4361, 32796}, {4363, 32795}, {5024, 13834}, {5054, 6451}, {5055, 6446}, {5056, 6434}, {5067, 6438}, {5072, 6456}, {5079, 6450}, {5124, 21553}, {5159, 11514}, {5210, 11291}, {5418, 6199}, {6351, 16674}, {6352, 16677}, {6409, 10303}, {6419, 13993}, {6426, 31412}, {6432, 13886}, {6433, 6459}, {6435, 19116}, {6436, 8960}, {6442, 7581}, {6445, 13785}, {6460, 6469}, {6480, 11539}, {7584, 16239}, {7969, 19862}, {9541, 15702}, {9600, 11315}, {10299, 23263}, {10534, 23332}, {10576, 13966}, {10645, 15765}, {10646, 18585}, {11313, 31415}, {13665, 15703}, {13883, 31253}, {13936, 19878}, {13959, 19877}, {14813, 16966}, {14814, 16967}, {15723, 18510}, {17116, 32791}, {17117, 32792}, {17118, 32799}, {17119, 32800}, {18992, 19872}

X(32790) = complement of isotomic conjugate of X(10194)
X(32790) = {X(2),X(6)}-harmonic conjugate of X(32789)

X(32791) = (name pending)

X(32791) lies on these

X(32791) = lines: {2, 37}, {7, 32805}, {8, 32806}, {86, 5405}, {239, 590}, {274, 3302}, {319, 491}, {320, 492}, {591, 17364}, {615, 894}, {1270, 17361}, {1271, 17360}, {1991, 17363}, {3068, 3759}, {3069, 3758}, {4360, 5393}, {4361, 8253}, {4363, 8252}, {5590, 17227}, {5591, 17228}, {7321, 32807}, {10436, 16513}, {17116, 32790}, {17117, 32789}, {17120, 32788}, {17121, 32787}, {17335, 30413}, {17336, 30412}, {21296, 32810}, {32099, 32811}

X(32791) = {X(2),X(75)}-harmonic conjugate of X(32792)

X(32792) = (name pending)

X(32792) lies on these

X(32792) = lines: {2, 37}, {7, 32806}, {8, 32805}, {86, 5393}, {239, 615}, {274, 3300}, {319, 492}, {320, 491}, {590, 894}, {591, 17363}, {1270, 17360}, {1271, 17361}, {1991, 17364}, {3068, 3758}, {3069, 3759}, {4360, 5405}, {4361, 8252}, {4363, 8253}, {5564, 32807}, {5590, 17228}, {5591, 17227}, {10436, 16512}, {17116, 32789}, {17117, 32790}, {17120, 32787}, {17121, 32788}, {17335, 30412}, {17336, 30413}, {21296, 32811}, {32099, 32810}

X(32792) = {X(2),X(75)}-harmonic conjugate of X(32791)

X(32793) = (name pending)

X(32793) lies on these

X(32793) = lines: {2, 37}, {7, 1270}, {8, 176}, {239, 7585}, {320, 32814}, {590, 17119}, {594, 5591}, {615, 17118}, {894, 7586}, {1086, 5590}, {1991, 4399}, {3068, 4361}, {3069, 4363}, {3593, 31995}, {3595, 32087}, {3729, 30412}, {4384, 30413}, {4969, 26339}, {5393, 17151}, {5405, 25590}, {5860, 17365}, {5861, 17362}, {7277, 26340}, {8972, 17117}, {13941, 17116}

X(32793) = anticomplement of X(6351)
X(32793) = {X(2),X(75)}-harmonic conjugate of X(32794)

X(32794) = (name pending)

X(32794) lies on these lines: {2, 37}, {7, 1271}, {8, 175}, {239, 7586}, {319, 32814}, {590, 17118}, {591, 4399}, {594, 5590}, {615, 17119}, {894, 7585}, {1086, 5591}, {3068, 4363}, {3069, 4361}, {3593, 32087}, {3595, 31995}, {3729, 30413}, {4384, 30412}, {4969, 26340}, {5393, 25590}, {5405, 17151}, {5860, 17362}, {5861, 17365}, {7277, 26339}, {8972, 17116}, {13941, 17117}

X(32794) = anticomplement of X(6352)
X(32794) = {X(2),X(75)}-harmonic conjugate of X(32793)

X(32795) = (name pending)

X(32795) lies on these lines: {2, 37}, {7, 32807}, {239, 32785}, {319, 3595}, {320, 3593}, {491, 32099}, {492, 21296}, {894, 32786}, {3068, 17121}, {3069, 17120}, {3661, 26362}, {3662, 26361}, {3758, 13941}, {3759, 8972}, {4361, 32789}, {4363, 32790}

X(32795) =

X(32796) = (name pending)

X(32796) lies on these

X(32796) = lines: {2, 37}, {8, 32807}, {239, 32786}, {319, 3593}, {320, 3595}, {491, 21296}, {492, 32099}, {894, 32785}, {3068, 17120}, {3069, 17121}, {3661, 26361}, {3662, 26362}, {3758, 8972}, {3759, 13941}, {4361, 32790}, {4363, 32789}

X(32797) = (name pending)

X(32797) lies on these

X(32797) = lines: {2, 37}, {7, 32808}, {8, 10910}, {239, 19054}, {491, 32087}, {492, 31995}, {894, 19053}, {1270, 7321}, {1271, 5564}, {3068, 17117}, {3069, 17116}, {4361, 32787}, {4363, 32788}, {5861, 29617}, {13846, 17119}

X(32798) = (name pending)

X(32798) lies on these lines: {2, 37}, {7, 32809}, {8, 10911}, {239, 19053}, {491, 31995}, {492, 32087}, {894, 19054}, {1270, 5564}, {1271, 7321}, {3068, 17116}, {3069, 17117}, {4361, 32788}, {4363, 32787}, {5860, 29617}, {13846, 17118}, {13847, 17119}

X(32798) =

X(32799) = (name pending)

X(32799) lies on these lines: {2, 37}, {7, 3593}, {8, 3595}, {239, 8972}, {594, 26362}, {894, 13941}, {1086, 26361}, {1270, 21296}, {1271, 32099}, {4361, 32785}, {4363, 32786}, {7585, 17121}, {7586, 17120}, {17118, 32790}, {17119, 32789}, {25728, 30412}

X(32799) =

X(32800) = (name pending)

X(32800) lies on these lines: {2, 37}, {7, 3595}, {8, 3593}, {239, 13941}, {594, 26361}, {894, 8972}, {1086, 26362}, {1270, 32099}, {1271, 21296}, {4361, 32786}, {4363, 32785}, {7585, 17120}, {7586, 17121}, {17118, 32789}, {17119, 32790}, {25728, 30413}

X(32800) =

X(32801) = (name pending)

X(32801) lies on these lines: {2, 37}, {7, 32810}, {8, 32811}, {239, 32787}, {319, 32809}, {320, 32808}, {491, 5564}, {492, 7321}, {590, 17117}, {615, 17116}, {894, 32788}, {1991, 29617}, {3758, 19053}, {3759, 19054}, {4361, 13846}, {4363, 13847}, {5393, 17160}, {31995, 32805}, {32087, 32806}

X(32801) =

X(32802) = (name pending)

X(32802) lies on these

X(32802) = lines: {2, 37}, {7, 32811}, {8, 32810}, {239, 32788}, {319, 32808}, {320, 32809}, {491, 7321}, {492, 5564}, {590, 17116}, {591, 29617}, {615, 17117}, {894, 32787}, {3758, 19054}, {3759, 19053