PART 1: | Introduction and Centers X(1) - X(1000) | PART 2: | Centers X(1001) - X(3000) | PART 3: | Centers X(3001) - X(5000) |
PART 4: | Centers X(5001) - X(7000) | PART 5: | Centers X(7001) - X(10000) | PART 6: | Centers X(10001) - X(12000) |
PART 7: | Centers X(12001) - X(14000) | PART 8: | Centers X(14001) - X(16000) | PART 9: | Centers X(16001) - X(18000) |
PART 10: | Centers X(18001) - X(20000) | PART 11: | Centers X(20001) - X(22000) | PART 12: | Centers X(22001) - X(24000) |
PART 13: | Centers X(24001) - X(26000) | PART 14: | Centers X(26001) - X(28000) | PART 15: | Centers X(28001) - X(30000) |
PART 16: | Centers X(30001) - X(32000) | PART 17: | Centers X(32001) - X(34000) | PART 18: | Centers X(34001) - X(36000) |
PART 19: | Centers X(36001) - X(38000) | PART 20: | Centers X(38001) - X(40000) | PART 21: | Centers X(40001) - X(42000) |
PART 22: | Centers X(42001) - X(44000) | PART 23: | Centers X(44001) - X(46000) | PART 24: | Centers X(46001) - X(48000) |
PART 25: | Centers X(48001) - X(50000) | PART 26: | Centers X(50001) - X(52000) | PART 27: | Centers X(52001) - X(54000) |
PART 28: | Centers X(54001) - X(56000) | PART 29: | Centers X(56001) - X(58000) | PART 30: | Centers X(58001) - X(60000) |
PART 31: | Centers X(60001) - X(62000) | PART 32: | Centers X(62001) - X(64000) | PART 33: | Centers X(64001) - X(66000) |
PART 34: | Centers X(66001) - X(68000) | PART 35: | Centers X(68001) - X(70000) | PART 36: | Centers X(70001) - X(72000) |
X(22001) lies on these lines: {9, 5307}, {10, 407}, {37, 226}, {40, 17860}, {63, 321}, {71, 6358}, {72, 515}, {92, 573}, {190, 2064}, {329, 21078}, {516, 1824}, {527, 3175}, {758, 2901}, {993, 13733}, {1868, 12572}, {2321, 8896}, {2328, 7009}, {3029, 6044}, {3191, 18446}, {3869, 10454}, {3970, 3995}, {3998, 22003}, {17862, 20367}, {22004, 22019}, {22009, 22033}
X(22002) lies on these lines: {37, 226}, {63, 22022}, {72, 5882}, {228, 22027}, {321, 20879}, {516, 21807}, {572, 2167}, {894, 18646}, {3218, 3995}, {18662, 21363}, {22013, 22033}
X(22003) lies on these lines: {10, 2652}, {37, 142}, {72, 2801}, {99, 101}, {100, 6011}, {307, 21069}, {320, 22047}, {321, 20879}, {514, 3882}, {522, 4436}, {527, 4053}, {1018, 1020}, {2295, 14750}, {3159, 8720}, {3998, 22001}, {4033, 4169}, {4791, 18740}, {5773, 21061}, {18698, 21811}
X(22004) lies on these lines: {10, 6058}, {37, 3452}, {72, 3244}, {321, 20879}, {1999, 3219}, {22001, 22019}
X(22005) lies on these lines: {3, 37}, {72, 4513}, {101, 1819}, {169, 1824}, {321, 857}, {346, 21078}, {1334, 4456}, {3159, 3950}, {3970, 3995}, {4043, 20926}, {4222, 5011}, {5074, 22011}, {21017, 21029}, {21070, 22022}
X(22006) lies on these lines: {37, 226}, {321, 1848}, {908, 20336}, {946, 12618}, {5279, 17171}
X(22007) lies on these lines: {37, 226}, {321, 20884}, {824, 22043}
X(22008) lies on these lines: {10, 872}, {37, 141}, {69, 21061}, {72, 3717}, {76, 4043}, {213, 17353}, {226, 306}, {312, 22000}, {344, 3294}, {495, 5295}, {1423, 17296}, {2901, 13161}, {3159, 6541}, {3588, 3882}, {3596, 4417}, {3687, 4967}, {3695, 10381}, {3932, 7064}, {3995, 17242}, {4150, 4153}, {15523, 21803}, {16574, 17137}, {20336, 21078}, {20496, 21076}, {21099, 22046}, {22009, 22015}, {22016, 22031}
X(22009) lies on these lines: {10, 7109}, {37, 744}, {306, 1230}, {321, 4766}, {2205, 17766}, {4109, 21085}, {4150, 4177}, {21093, 22039}, {22001, 22033}, {22008, 22015}
X(22010) lies on these lines: {37, 3782}, {72, 22791}, {190, 17167}, {226, 3995}, {306, 4043}, {321, 908}, {3159, 12047}, {17781, 21061}
X(22011) lies on these lines: {2, 22013}, {10, 762}, {37, 39}, {75, 2140}, {226, 4153}, {274, 4568}, {321, 1930}, {335, 16887}, {514, 1909}, {894, 17200}, {1018, 17164}, {1086, 6292}, {1089, 21808}, {1215, 16600}, {2321, 12609}, {3239, 21193}, {3294, 4115}, {3754, 4095}, {3822, 4136}, {3930, 4647}, {3934, 21208}, {3963, 17867}, {3992, 21921}, {3995, 16826}, {4043, 18157}, {4054, 21073}, {4066, 21071}, {4071, 11263}, {4075, 16589}, {4692, 17451}, {5074, 22005}, {5279, 10461}, {5299, 18098}, {16552, 17165}, {16720, 17205}, {21194, 22042}
X(22012) lies on these lines: {37, 3589}, {72, 3883}, {75, 2140}, {83, 4360}, {86, 4568}, {226, 306}, {313, 21067}, {350, 22013}, {732, 3879}, {2667, 3159}, {3663, 22035}, {3954, 4357}, {3970, 20336}, {3995, 17011}
X(22013) lies on these lines: {2, 22011}, {37, 714}, {42, 21067}, {306, 1230}, {310, 4568}, {321, 20433}, {350, 22012}, {726, 21814}, {3294, 3757}, {3741, 3954}, {3840, 22035}, {4103, 4651}, {18152, 18833}, {21093, 22026}, {21877, 22036}, {22002, 22033}
X(22014) lies on these lines: {37, 57}, {72, 4853}, {226, 21801}, {228, 5537}, {321, 908}, {517, 21361}, {2171, 4656}, {3175, 22021}, {3970, 3995}, {4043, 20928}, {4053, 22034}, {5850, 21328}
X(22015) lies on these lines: {37, 2886}, {226, 3970}, {312, 21070}, {321, 20431}, {497, 3294}, {22008, 22009}
X(22016) lies on these lines: {2, 37}, {76, 17242}, {213, 17121}, {313, 3943}, {314, 17261}, {726, 3953}, {740, 3214}, {872, 3896}, {984, 3702}, {1089, 3993}, {1269, 17243}, {2321, 3948}, {3121, 21895}, {3728, 3971}, {3760, 20435}, {3765, 17314}, {3770, 17315}, {3912, 22019}, {3932, 21927}, {3950, 3963}, {3970, 14210}, {3992, 4709}, {3994, 21080}, {6378, 7230}, {6381, 21070}, {17143, 17260}, {17144, 17349}, {17229, 18133}, {17240, 18144}, {17269, 18044}, {20706, 21071}, {21435, 21830}, {22008, 22031}
X(22017) lies on these lines: {37, 537}, {321, 1930}, {3753, 4169}, {3930, 4714}, {3992, 21067}, {4125, 21101}
X(22018) lies on these lines: {5, 37}, {29, 101}, {72, 5179}, {312, 21070}, {321, 857}, {469, 22000}, {1737, 2198}, {1826, 21077}, {2478, 3294}, {3159, 21090}, {3970, 22032}, {4043, 21579}, {4150, 4153}
X(22019) lies on these lines: {10, 7064}, {37, 142}, {72, 4301}, {76, 4043}, {144, 10446}, {226, 3175}, {321, 908}, {344, 2140}, {2321, 4377}, {2486, 21865}, {3294, 18230}, {3674, 3970}, {3912, 22016}, {4133, 21077}, {4924, 21627}, {5074, 22005}, {17197, 17351}, {17353, 17761}, {18698, 21809}, {20683, 21927}, {21065, 21091}, {21069, 21073}, {22001, 22004}
X(22020) lies on these lines: {2, 10468}, {8, 10478}, {10, 12}, {37, 3452}, {200, 10888}, {228, 6745}, {306, 21069}, {312, 21070}, {321, 908}, {329, 573}, {386, 3191}, {946, 5295}, {956, 19701}, {1764, 3588}, {1999, 17182}, {2064, 4568}, {2092, 4415}, {2901, 21616}, {3159, 17748}, {3294, 18228}, {3421, 5712}, {3596, 4417}, {3912, 22028}, {3998, 22001}, {5815, 19853}, {14973, 15281}, {22031, 22034}
X(22021) lies on these lines: {1, 6}, {4, 2901}, {10, 2294}, {19, 3811}, {35, 1761}, {42, 7237}, {48, 22836}, {57, 3998}, {65, 3694}, {69, 18726}, {71, 758}, {101, 1474}, {145, 5802}, {199, 228}, {226, 306}, {284, 5279}, {319, 18714}, {329, 3995}, {346, 5746}, {442, 594}, {519, 1953}, {527, 18650}, {579, 2198}, {912, 1765}, {950, 17452}, {965, 3940}, {1018, 21853}, {1400, 15556}, {1500, 10381}, {1751, 3187}, {1766, 18446}, {1824, 2900}, {1826, 21077}, {1848, 22000}, {1880, 4551}, {1897, 8748}, {1901, 3943}, {1959, 3879}, {2092, 3721}, {2178, 11517}, {2260, 3874}, {2345, 3487}, {2893, 6542}, {3125, 21857}, {3158, 3198}, {3159, 3950}, {3175, 22014}, {3219, 4877}, {3419, 17299}, {3586, 4898}, {3670, 4261}, {3684, 16547}, {3686, 17451}, {3726, 17053}, {3822, 21675}, {3870, 4463}, {3875, 19791}, {3912, 20336}, {3958, 4067}, {3962, 4047}, {3987, 21858}, {3991, 21871}, {4007, 5295}, {4016, 4424}, {4018, 21866}, {4029, 21809}, {4037, 22039}, {4043, 20444}, {4069, 20702}, {4086, 22041}, {4158, 10974}, {4659, 7201}, {4851, 18733}, {4876, 15314}, {5257, 21033}, {6356, 18642}, {7146, 17296}, {10445, 22035}, {16548, 18598}, {17315, 18720}, {17362, 17443}, {17377, 18041}, {17388, 17444}, {17757, 21933}, {21039, 22312}, {21068, 21096}, {22031, 22040}
X(22022) lies on these lines: {37, 5745}, {63, 22002}, {72, 519}, {321, 908}, {1999, 3219}, {4066, 21075}, {4133, 4135}, {4847, 21807}, {21062, 21069}, {21070, 22005}, {21273, 21363}
X(22023) lies on these lines: {37, 16582}, {321, 2172}, {3995, 17492}, {21079, 22000}
X(22024) lies on these lines: {1, 3159}, {10, 20966}, {37, 714}, {38, 321}, {537, 3175}, {596, 19863}, {740, 22275}, {758, 2901}, {835, 2206}, {4003, 6682}, {4362, 5282}, {10453, 20068}, {20671, 21877}, {21070, 22026}, {21093, 22000}
X(22025) lies on these lines: {37, 6292}, {321, 17873}, {3159, 6541}, {3912, 3995}, {4109, 4129}
X(22026) lies on these lines: {37, 744}, {321, 20898}, {672, 3741}, {3840, 22032}, {3912, 3995}, {17766, 18098}, {21070, 22024}, {21093, 22013}
X(22027) lies on these lines: {10, 201}, {37, 800}, {72, 519}, {228, 22002}, {321, 4712}, {516, 1824}, {522, 4640}, {756, 17874}, {1867, 19925}, {1897, 2328}, {3870, 3995}, {3930, 3950}, {4075, 21075}, {4362, 5282}, {5223, 17156}, {7211, 21804}, {21807, 22000}
X(22028) lies on these lines: {10, 3728}, {37, 2998}, {72, 19222}, {76, 321}, {194, 17149}, {213, 668}, {306, 3948}, {313, 21024}, {1575, 18148}, {3178, 20710}, {3264, 20255}, {3721, 21435}, {3912, 22020}, {4033, 20691}, {4043, 20943}, {6374, 18837}, {6381, 21070}, {9229, 9239}, {16589, 21827}, {20892, 21240}, {21257, 22189}
X(22029) lies on these lines: {37, 537}, {190, 18645}, {321, 3452}, {2321, 4103}, {3125, 5257}, {3971, 4029}, {3992, 21801}, {4035, 21062}, {21070, 22030}
X(22030) lies on these lines: {37, 519}, {321, 3262}, {2321, 21088}, {3943, 3971}, {4042, 16672}, {21070, 22029}
X(22031) lies on these lines: {10, 2486}, {37, 142}, {72, 21627}, {190, 17197}, {226, 3995}, {313, 2321}, {321, 3452}, {918, 22035}, {946, 3159}, {3175, 22000}, {3191, 12437}, {3294, 20257}, {3912, 18150}, {4010, 21093}, {4069, 13576}, {4422, 17761}, {4728, 22032}, {7064, 21927}, {21090, 21091}, {22008, 22016}, {22020, 22034}, {22021, 22040}
X(22032) lies on these lines: {11, 37}, {306, 20496}, {321, 20431}, {3840, 22026}, {3970, 22018}, {4043, 21580}, {4054, 21073}, {4120, 21090}, {4728, 22031}
X(22033) lies on these lines: {37, 16592}, {321, 20903}, {1023, 4115}, {2796, 21833}, {4024, 4427}, {22001, 22009}, {22002, 22013}
X(22034) lies on these lines: {1, 19747}, {2, 37}, {38, 4519}, {44, 19750}, {72, 3586}, {210, 3994}, {226, 3943}, {329, 17299}, {594, 4656}, {726, 21342}, {740, 3967}, {1089, 4646}, {1100, 19739}, {1279, 4387}, {1999, 17351}, {2321, 4415}, {2901, 3244}, {3159, 3626}, {3187, 16669}, {3198, 6154}, {3696, 3971}, {3701, 21896}, {3723, 19746}, {3751, 4942}, {3782, 17231}, {3914, 6057}, {3931, 4066}, {3932, 21949}, {3948, 21868}, {3950, 17056}, {4035, 4052}, {4044, 20691}, {4053, 22014}, {4096, 4709}, {4431, 5743}, {4654, 17311}, {5271, 16814}, {5905, 17374}, {7230, 16583}, {7308, 17119}, {11679, 17262}, {16676, 19744}, {17022, 17118}, {22020, 22031}
X(22035) lies on these lines: {10, 762}, {37, 537}, {321, 1111}, {335, 4568}, {918, 22031}, {3159, 3970}, {3663, 22012}, {3840, 22013}, {4013, 21044}, {4075, 21808}, {4120, 21090}, {4169, 21888}, {4958, 22045}, {9055, 17761}, {10445, 22021}, {21070, 22036}
X(22036) lies on these lines: {37, 39}, {72, 14839}, {76, 321}, {115, 4136}, {187, 8669}, {194, 3995}, {313, 21412}, {519, 14537}, {538, 3175}, {730, 2901}, {1089, 3721}, {1500, 21101}, {3125, 3701}, {3700, 3906}, {3727, 4692}, {3734, 3905}, {3735, 4385}, {3967, 16583}, {3970, 4037}, {3971, 16589}, {3992, 21951}, {3994, 21808}, {4066, 21024}, {4103, 21868}, {4109, 21093}, {4125, 21025}, {4135, 7230}, {4424, 21021}, {4721, 17489}, {4920, 7794}, {12699, 17299}, {15810, 17132}, {17165, 20963}, {20691, 21067}, {21070, 22035}, {21877, 22013}
X(22037) lies on these lines: {10, 690}, {37, 3960}, {72, 3887}, {74, 2372}, {99, 101}, {321, 3762}, {514, 4024}, {525, 4129}, {918, 22031}, {2785, 13181}, {3566, 4807}, {3667, 4064}, {3906, 4806}, {3947, 18006}, {3995, 21222}, {4049, 4080}, {4066, 18003}
X(22038) lies on these lines: {37, 4892}, {306, 1230}, {321, 20904}, {3006, 4115}, {3261, 3835}
X(22039) lies on these lines: {37, 714}, {76, 321}, {716, 3175}, {718, 2901}, {726, 21877}, {3701, 22171}, {3948, 22200}, {3995, 17486}, {4037, 22021}, {4135, 21070}, {21093, 22009}
X(22040) lies on these lines: {2, 37}, {72, 5809}, {726, 21346}, {1089, 4356}, {1441, 3950}, {1446, 21096}, {2901, 6765}, {3674, 3970}, {3701, 3755}, {3702, 7174}, {3896, 4878}, {3932, 21955}, {3971, 21039}, {4098, 18698}, {10889, 21061}, {22021, 22031}
X(22041) lies on these lines: {37, 4529}, {321, 4171}, {3239, 4064}, {3261, 3835}, {4024, 20294}, {4086, 22021}, {8045, 22044}
X(22042) lies on these lines: {10, 21960}, {37, 522}, {321, 20907}, {514, 4079}, {657, 3294}, {1577, 4171}, {2321, 4036}, {3239, 4024}, {3261, 4043}, {3686, 8702}, {3700, 7180}, {3709, 4151}, {3950, 4140}, {4791, 21070}, {8714, 21348}, {17233, 18158}, {21194, 22011}
X(22043) lies on these lines: {10, 4155}, {37, 812}, {321, 4728}, {335, 2786}, {514, 4079}, {523, 4129}, {804, 3993}, {824, 22007}, {918, 22031}, {1577, 21834}, {3835, 4024}, {3995, 21297}, {4033, 4103}, {4043, 20950}
X(22044) lies on these lines: {37, 523}, {321, 4374}, {514, 4079}, {522, 649}, {661, 4815}, {784, 21348}, {798, 4151}, {802, 4500}, {1577, 21099}, {3700, 8672}, {4043, 7199}, {4705, 21960}, {5214, 21061}, {6367, 17990}, {8045, 22041}
X(22045) lies on these lines: {37, 6377}, {42, 3952}, {244, 321}, {537, 3175}, {726, 17154}, {740, 22313}, {2802, 2901}, {3159, 3244}, {4010, 21093}, {4958, 22035}
X(22046) lies on these lines: {321, 20910}, {824, 22007}, {3261, 3835}, {21099, 22008}
X(22046) lies on these lines: {37, 524}, {226, 306}, {320, 22003}, {514, 4079}, {3912, 4053}, {4043, 20956}, {4062, 21829}, {4115, 17264}, {16704, 17019}
X(22048) lies on these lines: {1, 3159}, {10, 20703}, {37, 3589}, {321, 1930}, {538, 3175}, {3948, 21067}, {4044, 21101}, {4568, 16826}
See Kadir Altintas, Antreas Hatzipolakis, and Peter Moses, Hyacinthos 28137.
X(22049) lies on this line: {2,3}
See Kadir Altintas, Antreas Hatzipolakis, and Peter Moses, Hyacinthos 28137.
X(22050) lies on this line: {2,3}
See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28138.
X(22051) lies on these lines: {2, 12316}, {5, 195}, {30, 54}, {51, 13368}, {110, 13163}, {113, 137}, {140, 389}, {143, 10096}, {252, 10289}, {468, 6242}, {539, 5066}, {547, 1209}, {548, 10610}, {549, 12307}, {568, 10125}, {1157, 10126}, {1173, 14643}, {1263, 20030}, {1594, 2914}, {1656, 12325}, {3530, 7691}, {3542, 12175}, {3564, 19150}, {3580, 3628}, {3627, 12254}, {3850, 6288}, {3853, 5893}, {3881, 5901}, {4994, 15557}, {5056, 13432}, {5898, 18369}, {5965, 12812}, {6152, 21841}, {6153, 10095}, {6676, 12606}, {6696, 10628}, {7356, 15325}, {7583, 12971}, {7584, 12965}, {10066, 15172}, {10203, 13353}, {10224, 18912}, {10619, 20585}, {10677, 11543}, {10678, 11542}, {11805, 15089}, {11808, 13451}, {12161, 18356}, {12363, 16197}, {14216, 17824}, {18946, 19347}
X(22051) = X(22051) = midpoint of X(i) and X(j) for these {i,j}: {2914, 11804}, {10113, 14049}, {15801, 21230}
X(22051) = reflection of X(i) in X(j) for these {i,j}: {140, 8254}, {546, 3574}, {548, 10610}, {6153, 10095}, {6288, 3850}, {7691, 3530}, {8254, 12242}, {10619, 20585}, {21230, 3628}
X(22051) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {143, 15806, 10096}, {1656, 12325, 21357}, {11803, 12242, 140}
Let A'B'C' be the cevian triangle of X(3). X(22052) is the perspector, wrt A'B'C', of the circumconic of A'B'C' centered at X(140). (Randy Hutson, November 30, 2018)
X(22052) lies on these lines: {2, 10985}, {3, 6}, {53, 550}, {71, 22055}, {95, 401}, {97, 323}, {140, 233}, {230, 10691}, {232, 6636}, {393, 3522}, {418, 1495}, {631, 10986}, {940, 21503}, {1040, 10987}, {1196, 9609}, {1216, 14533}, {1249, 21735}, {1368, 3054}, {1971, 3819}, {2165, 7748}, {3055, 6676}, {3087, 3523}, {3131, 10642}, {3132, 10641}, {3289, 22352}, {3357, 17849}, {3481, 21354}, {3620, 6389}, {3631, 15526}, {6509, 15066}, {6640, 11614}, {6749, 15712}, {7484, 10314}, {7485, 10311}, {7492, 15355}, {7502, 14576}, {7749, 9722}, {8703, 18487}, {8908, 10133}, {9220, 18564}, {10313, 15246}, {10319, 10988}, {17277, 22359}, {18424, 18531}, {22062, 22085}
X(22052) = isogonal conjugate of polar conjugate of X(140)
X(22052) = complement of X(32002)
X(22052) = complement of polar conjugate of X(2963)
X(22052) = isotomic conjugate of polar conjugate of X(13366)
X(22052) = crosspoint of X(32585) and X(32586)
X(22052) = X(92)-isoconjugate of X(1173)
X(22052) = crosssum of X(472) and X(473)
X(22052) = inverse-in-Brocard-circle of X(10979)
X(22052) = Schoute-circle-inverse of X(389)
X(22052) = {X(15),X(16)}-harmonic conjugate of X(389)
X(22053) lies on these lines: {1, 376}, {2, 2635}, {3, 73}, {20, 2654}, {33, 5732}, {34, 8726}, {35, 1066}, {36, 1064}, {42, 1155}, {48, 1473}, {55, 1407}, {56, 4300}, {57, 955}, {63, 1818}, {71, 3917}, {77, 1040}, {109, 15931}, {142, 17194}, {184, 20780}, {201, 1071}, {216, 22410}, {221, 8273}, {223, 10857}, {228, 3937}, {241, 10391}, {269, 10383}, {278, 21151}, {354, 1418}, {497, 1742}, {577, 22054}, {581, 15803}, {601, 7742}, {631, 1745}, {971, 7069}, {1038, 10884}, {1042, 2646}, {1044, 3485}, {1193, 4252}, {1214, 7004}, {1333, 17187}, {1393, 9940}, {1401, 2223}, {1409, 22400}, {1427, 17603}, {1457, 3576}, {1465, 11227}, {1790, 4575}, {1836, 3000}, {1935, 6986}, {1936, 7411}, {2003, 13329}, {2183, 4191}, {2197, 22418}, {2267, 7484}, {3057, 4322}, {3075, 3651}, {3190, 3928}, {3475, 4334}, {3601, 4306}, {3682, 3916}, {3920, 18450}, {3942, 17441}, {4551, 10164}, {5122, 5396}, {5165, 20973}, {5287, 8544}, {7987, 10571}, {9371, 10178}, {11020, 17092}, {18591, 22064}, {20755, 20783}, {22066, 22449}, {22069, 22084}, {22070, 22088}, {22341, 22347}
X(22053) = isogonal conjugate of polar conjugate of X(142)
X(22053) = isotomic conjugate of polar conjugate of X(1475)
X(22053) = crosssum of X(4) and X(33)
X(22053) = crosspoint of X(3) and X(77)
X(22053) = {X(3),X(73)}-harmonic conjugate of X(22072)
X(22053) = X(19)-isoconjugate of X(32008)
X(22053) = X(92)-isoconjugate of X(1174)
X(22054) lies on these lines: {2, 20289}, {3, 48}, {6, 5204}, {9, 5267}, {19, 3576}, {36, 284}, {37, 1055}, {42, 4497}, {55, 37519}, {172, 5110}, {187, 2300}, {198, 2267}, {199, 14547}, {228, 20775}, {501, 2150}, {515, 21011}, {517, 17438}, {572, 2183}, {573, 2317}, {574, 2273}, {577, 22053}, {579, 7280}, {584, 1475}, {604, 1470}, {609, 5105}, {610, 7987}, {672, 2174}, {902, 16685}, {1030, 2269}, {1100, 17454}, {1125, 1839}, {1193, 1333}, {1201, 5301}, {1385, 1953}, {1400, 2278}, {1404, 4271}, {1436, 8273}, {1444, 20769}, {1449, 4262}, {1457, 1950}, {1630, 2272}, {1631, 2293}, {1761, 4511}, {1790, 4288}, {1826, 4297}, {1901, 15326}, {2173, 13624}, {2178, 2268}, {2193, 4303}, {2197, 22059}, {2245, 21748}, {2256, 5217}, {2287, 5303}, {2294, 2646}, {2302, 11012}, {2347, 4268}, {3916, 3958}, {3949, 5440}, {4299, 5747}, {4466, 18650}, {4471, 20978}, {4855, 5227}, {4860, 16884}, {5011, 16553}, {6511, 10607}, {6684, 21012}, {7117, 18591}, {11573, 22162}, {14597, 22056}, {15586, 17443}, {17647, 21675}, {20729, 22077}, {20750, 22096}, {20752, 22352}, {20756, 20784}, {20757, 22062}, {22073, 22447}, {22118, 22350}
X(22054) = isogonal conjugate of isotomic conjugate of X(4001)
X(22054) = isogonal conjugate of polar conjugate of X(1125)
X(22054) = isotomic conjugate of polar conjugate of X(2308)
X(22054) = X(19)-isoconjugate of X(1268)
X(22054) = X(92)-isoconjugate of X(1126)
X(22055) lies on these lines: {3, 906}, {71, 22052}, {187, 672}, {577, 22071}, {647, 22375}, {1951, 2077}, {1983, 13006}, {3284, 22059}, {5546, 17100}
X(22055) = isogonal conjugate of polar conjugate of X(3035)
X(22055) = isotomic conjugate of polar conjugate of X(20958)
X(22056) lies on these lines: on lines {3, 2197}, {71, 22052}, {187, 2269}, {577, 22070}, {1950, 11012}, {2193, 7117}, {3284, 22058}, {14597, 22054}, {22079, 22378}
X(22056) = isogonal conjugate of polar conjugate of X(4999)
X(22056) = isotomic conjugate of polar conjugate of X(20959)
X(22056) = X(92)-isoconjugate of X(18772)
X(22057) lies on these lines: {1, 6349}, {3, 31}, {42, 1214}, {43, 6350}, {71, 22069}, {73, 228}, {326, 4176}, {426, 22421}, {497, 614}, {577, 22053}, {1066, 20764}, {1458, 7011}, {1473, 7124}, {2193, 17187}, {3120, 18588}, {3682, 3998}, {3720, 17073}, {3917, 22074}, {21530, 21935}, {22060, 22070}, {22064, 22400}, {22399, 22418}, {22404, 22434}
X(22057) = isogonal conjugate of polar conjugate of X(18589)
X(22057) = isotomic conjugate of polar conjugate of X(23620)
X(22058) lies on these lines: {3, 22122}, {71, 216}, {570, 672}, {1100, 21798}, {2197, 22356}, {2260, 3002}, {2269, 3003}, {3284, 22056}, {4466, 18606}, {7117, 18591}, {20819, 22449}, {20821, 22062}, {20975, 22389}, {22065, 22073}
X(22058) = isogonal conjugate of polar conjugate of X(25639)
X(22058) = isotomic conjugate of polar conjugate of X(20961)
X(22058) = {X(71),X(216)}-harmonic conjugate of X(22059)
X(22059) lies on these lines: {3, 22123}, {71, 216}, {570, 2269}, {672, 3003}, {2183, 13006}, {2197, 22054}, {2252, 22350}, {3284, 22055}, {3917, 22429}, {7117, 22356}, {8607, 21801}, {20729, 22095}, {20731, 22084}, {20775, 22169}, {20777, 20975}, {20821, 22087}, {22410, 22435}, {22414, 22428}
X(22059) = isogonal conjugate of polar conjugate of X(3814)
X(22059) = isotomic conjugate of polar conjugate of X(20962)
X(22059) = {X(71),X(216)}-harmonic conjugate of X(22058)
X(22060) lies on these lines: {3, 63}, {9, 4191}, {36, 846}, {38, 2223}, {56, 968}, {57, 1011}, {71, 3917}, {199, 3220}, {295, 1796}, {354, 8053}, {527, 21319}, {614, 20992}, {851, 5745}, {896, 20967}, {942, 17524}, {993, 3980}, {1040, 18606}, {1402, 4414}, {1444, 22389}, {1790, 7193}, {1818, 3690}, {2300, 17187}, {3218, 4184}, {3219, 4210}, {3286, 3666}, {3305, 16059}, {3306, 16058}, {3677, 16688}, {3683, 20470}, {3706, 4436}, {3928, 19346}, {3937, 20730}, {3941, 17599}, {4303, 22076}, {4640, 16678}, {4641, 5132}, {5122, 16374}, {5249, 8731}, {5285, 16064}, {5303, 11688}, {5437, 16373}, {10436, 16343}, {16574, 19339}, {17194, 20367}, {18210, 18607}, {18591, 22420}, {20731, 22061}, {20735, 20756}, {20736, 22409}, {20780, 22352}, {20785, 22062}, {20821, 22077}, {22057, 22070}, {22074, 22400}, {22084, 22405}, {22128, 22139}
X(22060) = isogonal conjugate of polar conjugate of X(3739)
X(22060) = isotomic conjugate of polar conjugate of X(20963)
X(22060) = {X(3),X(63)}-harmonic conjugate of X(228)
X(22060) = X(19)-isoconjugate of X(32009)
X(22061) lies on these lines: {3, 295}, {48, 78}, {71, 73}, {72, 2200}, {101, 3678}, {172, 1691}, {228, 22364}, {419, 1215}, {756, 9310}, {813, 2698}, {1237, 14382}, {2295, 18905}, {2304, 3811}, {3690, 15377}, {4019, 12215}, {4303, 20729}, {9016, 16689}, {20731, 22060}, {20752, 22065}, {20785, 22345}, {22069, 22422}, {22342, 22375}, {22350, 22447}, {22367, 22373}
X(22061) = isogonal conjugate of polar conjugate of X(1215)
X(22061) = isotomic conjugate of polar conjugate of X(20964)
X(22061) = {X(71),X(73)}-harmonic conjugate of X(20727)
X(22061) = X(19)-isoconjugate of X(32010)
X(22061) = X(92)-isoconjugate of X(1178)
X(22062) lies on these lines: {3, 69}, {6, 11175}, {22, 16990}, {71, 20730}, {141, 237}, {160, 599}, {183, 7467}, {216, 3289}, {264, 22712}, {418, 6389}, {1078, 9230}, {1232, 2782}, {1634, 3631}, {1843, 5188}, {3231, 8265}, {3589, 5201}, {3619, 11328}, {7484, 7736}, {7485, 7774}, {7779, 15246}, {9407, 19121}, {9917, 16043}, {10790, 16045}, {11574, 20975}, {14575, 19126}, {20731, 22412}, {20757, 22054}, {20785, 22060}, {20821, 22058}, {20823, 22065}, {22052, 22085}, {22138, 22151}
X(22062) = isogonal conjugate of polar conjugate of X(3934)
X(22062) = isotomic conjugate of polar conjugate of X(20965)
X(22063) lies on these lines: {1, 281}, {3, 22124}, {6, 41}, {19, 1457}, {42, 21860}, {71, 216}, {102, 112}, {204, 3192}, {219, 22350}, {221, 1436}, {393, 2654}, {577, 22053}, {610, 10571}, {614, 3554}, {800, 2300}, {820, 836}, {995, 2257}, {1033, 21148}, {1108, 1201}, {1386, 8766}, {1409, 7117}, {1953, 14571}, {2272, 21767}, {2289, 22131}, {2293, 2638}, {2635, 3087}, {3284, 22357}, {3553, 7221}, {3666, 6508}, {4303, 15905}, {5105, 14482}, {5158, 22356}, {8608, 16685}, {14597, 22088}, {15851, 20818}
X(22063) = isogonal conjugate of polar conjugate of X(946)
X(22063) = X(92)-isoconjugate of X(947)
X(22064) lies on these lines: {3, 22125}, {71, 20728}, {216, 20731}, {3917, 22069}, {7004, 18589}, {18591, 22053}, {20727, 20819}, {20734, 20826}, {20821, 22413}, {22057, 22400}, {22065, 22401}, {22070, 22440}
X(22064) = isogonal conjugate of polar conjugate of X(17046)
X(22064) = isotomic conjugate of polar conjugate of X(23636)
X(22065) lies on these lines: {3, 48}, {19, 10476}, {72, 4020}, {172, 672}, {220, 20471}, {255, 20812}, {392, 2179}, {960, 1755}, {1125, 14964}, {1610, 2272}, {1613, 2275}, {1791, 2196}, {1812, 7116}, {2260, 2303}, {2269, 18755}, {3688, 18758}, {3690, 20777}, {3730, 5267}, {3917, 20727}, {4426, 20460}, {6626, 17209}, {7117, 20750}, {14547, 16372}, {16604, 20459}, {20735, 20827}, {20752, 22061}, {20757, 22409}, {20823, 22062}, {22058, 22073}, {22064, 22401}
X(22065) = isogonal conjugate of polar conjugate of X(3741)
X(22065) = isotomic conjugate of polar conjugate of X(2309)
X(22066) lies on these lines: {3, 48}, {78, 20785}, {1575, 20460}, {2179, 17614}, {2318, 20777}, {3056, 20996}, {3917, 20755}, {4020, 5440}, {7117, 20727}, {20729, 22070}, {20731, 22435}, {20732, 20824}, {20750, 22072}, {22053, 22449}, {22096, 22381}
X(22066) = isogonal conjugate of polar conjugate of X(3840)
X(22066) = isotomic conjugate of polar conjugate of X(22343)
X(22066) = X(19)-isoconjugate of X(32011)
X(22067) lies on these lines: {3, 22083}, {71, 3917}, {228, 3784}, {1473, 20818}, {1818, 3937}, {3292, 20780}, {17616, 21807}, {20731, 20757}, {20733, 22094}, {22082, 22350}, {22084, 22406}
X(22067) = isogonal conjugate of polar conjugate of X(3834)
X(22067) = isotomic conjugate of polar conjugate of isogonal conjugate of X(32012)
X(22067) = X(19)-isoconjugate of X(32012)
X(22068) lies on these lines: {3, 1331}, {71, 3917}, {3784, 22080}
X(22068) = isogonal conjugate of polar conjugate of X(34824)
X(22068) = isotomic conjugate of polar conjugate of isogonal conjugate of X(32013)
X(22068) = X(19)-isoconjugate of X(32013)
X(22069) lies on these lines: {3, 22130}, {31, 1779}, {43, 63}, {71, 22057}, {75, 18022}, {228, 22094}, {307, 3778}, {656, 21912}, {1737, 21935}, {3917, 22064}, {20727, 22404}, {20823, 22411}, {22053, 22084}, {22061, 22422}
X(22069) = isogonal conjugate of polar conjugate of X(20305)
X(22069) = isotomic conjugate of polar conjugate of X(23619)
X(22069) = crosssum of X(4) and X(31)
X(22069) = crosspoint of X(3) and X(75)
X(22070) lies on these lines: {1, 3002}, {3, 906}, {39, 213}, {48, 18591}, {71, 216}, {73, 20752}, {219, 2197}, {577, 22056}, {607, 3428}, {614, 1194}, {800, 2269}, {1107, 9284}, {1951, 11012}, {2193, 22122}, {2886, 16699}, {2968, 21915}, {3057, 8608}, {3730, 13006}, {3917, 20727}, {6467, 22389}, {8735, 15908}, {16588, 17451}, {18210, 18671}, {18589, 18606}, {20729, 22066}, {20734, 20755}, {20822, 22427}, {22053, 22088}, {22057, 22060}, {22064, 22440}, {22416, 22432}
X(22070) = isogonal conjugate of polar conjugate of X(2886)
X(22070) = isotomic conjugate of polar conjugate of X(21746)
X(22070) = {X(71),X(216)}-harmonic conjugate of X(22071)
X(22070) = X(92)-isoconjugate of X(3449)
X(22071) lies on these lines: {3, 2197}, {37, 5432}, {39, 2269}, {55, 4261}, {71, 216}, {212, 8606}, {219, 4587}, {573, 13006}, {577, 22055}, {608, 10310}, {672, 800}, {1409, 22350}, {1950, 2077}, {2092, 2268}, {2252, 3990}, {3270, 20753}, {3917, 22064}, {3949, 7004}, {6467, 20777}, {8607, 21871}, {10950, 21858}, {11998, 17362}, {14749, 17398}, {17053, 17452}, {20729, 20732}, {20730, 22413}, {20731, 22440}, {20819, 20820}
X(22071) = isogonal conjugate of polar conjugate of X(1329)
X(22071) = isotomic conjugate of polar conjugate of X(23638)
X(22071) = {X(71),X(216)}-harmonic conjugate of X(22070)
X(22071) = X(92)-isoconjugate of X(3450)
X(22072) lies on these lines: {1, 631}, {2, 2654}, {3, 73}, {20, 2635}, {33, 936}, {34, 6282}, {35, 1064}, {36, 1066}, {40, 1457}, {42, 2646}, {43, 3486}, {55, 1191}, {56, 7074}, {71, 216}, {72, 7004}, {78, 345}, {165, 10571}, {201, 17102}, {228, 22347}, {376, 1745}, {386, 1453}, {404, 1936}, {497, 978}, {517, 1393}, {602, 8069}, {899, 1837}, {950, 3216}, {960, 9371}, {995, 1697}, {1038, 20277}, {1042, 1155}, {1149, 2098}, {1201, 3057}, {1364, 22082}, {1458, 5204}, {1468, 22768}, {1470, 1496}, {1802, 7124}, {1818, 4855}, {1935, 6909}, {2269, 4261}, {3074, 6906}, {3075, 6940}, {3100, 17280}, {3214, 10950}, {3682, 5440}, {3937, 22376}, {4297, 4551}, {4300, 5217}, {4324, 6127}, {5044, 7069}, {5399, 13624}, {5438, 7070}, {9581, 17749}, {11376, 17278}, {20727, 20728}, {20750, 22066}, {20752, 22088}, {20781, 20786}, {22076, 22418}, {22079, 22369}, {22341, 22346}
X(22072) = isogonal conjugate of polar conjugate of X(3452)
X(22072) = isotomic conjugate of polar conjugate of X(2347)
X(22072) = crosssum of X(4) and X(34)
X(22072) = crosspoint of X(3) and X(78)
X(22072) = {X(3),X(73)}-harmonic conjugate of X(22053)
X(22072) = X(92)-isoconjugate of X(3451)
X(22073) lies on these lines: {3, 22133}, {9, 14963}, {71, 73}, {216, 3289}, {442, 1953}, {604, 2245}, {1474, 3430}, {1901, 21801}, {2092, 20228}, {2260, 10974}, {2294, 17056}, {3142, 21011}, {3269, 22428}, {20729, 22080}, {20730, 22084}, {20759, 20830}, {20820, 22433}, {22054, 22447}, {22058, 22065}
X(22073) = isogonal conjugate of polar conjugate of X(3454)
X(22073) = isotomic conjugate of polar conjugate of X(20966)
X(22073) = X(92)-isoconjugate of X(3453)
X(22074) lies on these lines: {3, 1409}, {6, 1732}, {48, 184}, {71, 216}, {78, 219}, {213, 2268}, {612, 2256}, {614, 21334}, {869, 1253}, {1193, 1682}, {1333, 2361}, {1880, 14110}, {2197, 22350}, {2286, 7078}, {3057, 16685}, {3100, 3786}, {3230, 17452}, {3917, 22057}, {3958, 7004}, {14597, 22054}, {17440, 20963}, {20732, 22099}, {22060, 22400}
X(22074) = isogonal conjugate of polar conjugate of X(960)
X(22074) = isotomic conjugate of polar conjugate of X(20967)
X(22074) = X(19)-isoconjugate of X(31643)
X(22074) = X(92)-isoconjugate of X(961)
X(22075) lies on these lines: {3, 22135}, {6, 21213}, {22, 11610}, {32, 184}, {154, 3162}, {206, 17409}, {216, 8779}, {394, 18876}, {418, 22391}, {1691, 1899}, {2351, 14600}, {14597, 22362}
X(22075) = isogonal conjugate of polar conjugate of X(206)
X(22075) = isotomic conjugate of polar conjugate of X(20968)
X(22076) lies on these lines: {1, 10974}, {2, 970}, {3, 49}, {10, 3142}, {12, 22299}, {21, 511}, {40, 851}, {42, 10822}, {51, 405}, {56, 2245}, {65, 17056}, {71, 73}, {72, 306}, {78, 3781}, {125, 21530}, {181, 10474}, {199, 2360}, {201, 18592}, {228, 3682}, {373, 11108}, {389, 1006}, {392, 4205}, {404, 3819}, {407, 14110}, {408, 2972}, {411, 5907}, {429, 960}, {442, 517}, {474, 5650}, {500, 17524}, {573, 13738}, {581, 1011}, {758, 3178}, {857, 3661}, {946, 3136}, {958, 16980}, {976, 3688}, {1154, 5428}, {1193, 1682}, {1201, 20966}, {1213, 2262}, {1214, 1425}, {1332, 1791}, {1364, 22361}, {1495, 2915}, {1818, 22369}, {1834, 3057}, {1901, 21871}, {1993, 13323}, {2082, 2238}, {2280, 20970}, {2328, 3145}, {2392, 3647}, {2476, 15488}, {2979, 4189}, {3060, 16865}, {3191, 21319}, {3269, 20728}, {3454, 3878}, {3649, 20718}, {3651, 6000}, {3730, 14963}, {3784, 4652}, {3869, 3936}, {3877, 5051}, {3916, 3937}, {3925, 22300}, {3948, 19582}, {3954, 21799}, {4188, 7998}, {4199, 5250}, {4259, 19765}, {4260, 19767}, {4303, 22060}, {5047, 5943}, {5164, 16589}, {5230, 10480}, {5320, 16471}, {5396, 16287}, {5446, 7489}, {5640, 16859}, {5754, 16286}, {5972, 12826}, {6044, 6737}, {6101, 7508}, {6675, 18180}, {6688, 17536}, {6875, 11412}, {6876, 11459}, {6905, 11793}, {6906, 15644}, {6909, 13348}, {6912, 13598}, {6914, 10625}, {6920, 10110}, {6942, 7999}, {6985, 15030}, {6986, 9729}, {7078, 7085}, {7117, 20750}, {7580, 11381}, {8582, 10440}, {9306, 11337}, {10219, 17546}, {11451, 17570}, {14915, 16117}, {15082, 17535}, {16418, 21969}, {16858, 21849}, {20738, 20787}, {20821, 22350}, {22072, 22418}, {22082, 22094}, {22097, 22345}
X(22076) = isogonal conjugate of polar conjugate of X(1211)
X(22076) = isotomic conjugate of polar conjugate of X(2092)
X(22076) = crosssum of X(4) and X(28)
X(22076) = crosspoint of X(3) and X(72)
X(22076) = X(19)-isoconjugate of X(14534)
X(22076) = X(92)-isoconjugate of X(1169)
X(22077) lies on these lines: {3, 22137}, {71, 22348}, {228, 20727}, {2525, 8611}, {20729, 22054}, {20821, 22060}, {22094, 22409}
X(22077) = isogonal conjugate of polar conjugate of X(21249)
X(22077) = isotomic conjugate of polar conjugate of X(20969)
X(22078) lies on these lines: {3, 1176}, {1818, 22345}, {3313, 14096}, {3618, 9821}, {3917, 20775}, {11574, 20975}, {20729, 22054}
X(22078) = isogonal conjugate of polar conjugate of X(6292)
X(22078) = isotomic conjugate of polar conjugate of X(11205)
X(22079) lies on these lines: {3, 77}, {31, 5065}, {48, 184}, {55, 1100}, {71, 3270}, {604, 1253}, {861, 20262}, {1011, 7070}, {1040, 18606}, {1212, 1827}, {1398, 5584}, {1475, 2293}, {4319, 20992}, {14557, 20853}, {15837, 20990}, {20775, 20780}, {22056, 22378}, {22072, 22369}
X(22079) = isogonal conjugate of polar conjugate of X(1212)
X(22079) = isotomic conjugate of polar conjugate of X(20229)
X(22079) = X(19)-isoconjugate of X(31618)
X(22079) = X(92)-isoconjugate of X(1170)
X(22080) lies on these lines: {3, 49}, {9, 15496}, {31, 2092}, {35, 10974}, {51, 573}, {55, 2245}, {71, 228}, {125, 440}, {165, 851}, {187, 2206}, {199, 1495}, {212, 8606}, {373, 16058}, {430, 1213}, {442, 3579}, {464, 1899}, {511, 4184}, {516, 3136}, {572, 13366}, {661, 11124}, {902, 20966}, {926, 2624}, {970, 16452}, {991, 19346}, {1030, 2194}, {1155, 17056}, {1195, 20967}, {1211, 4640}, {1230, 4427}, {1331, 1796}, {2308, 20970}, {2610, 6139}, {3142, 6684}, {3784, 22068}, {3819, 4210}, {3916, 4001}, {3937, 20730}, {3955, 20733}, {4191, 5650}, {4204, 4512}, {5651, 11350}, {6000, 7430}, {9306, 11340}, {20666, 21838}, {20729, 22073}, {20749, 20820}, {20975, 22371}, {22372, 22429}
X(22080) = crosssum of X(4) and X(27)
X(22080) = isogonal conjugate of polar conjugate of X(1213)
X(22080) = isotomic conjugate of polar conjugate of X(20970)
X(22080) = crosspoint of X(3) and X(71)
X(22080) = X(19)-isoconjugate of X(32014)
X(22080) = X(92)-isoconjugate of X(1171)
X(22081) lies on these lines: {3, 15373}, {63, 69}, {228, 20759}, {3784, 20736}, {3917, 20755}, {20729, 20732}, {20730, 22053}, {20820, 20826}
X(22081) = isogonal conjugate of polar conjugate of X(34832)
X(22081) = isotomic conjugate of polar conjugate of X(20971)
X(22082) lies on these lines: {3, 1331}, {71, 7117}, {1149, 6018}, {1332, 1811}, {1364, 22072}, {3917, 22083}, {3977, 5440}, {4587, 20818}, {5151, 16594}, {22067, 22350}, {22076, 22094}, {22369, 22373}
X(22082) = isogonal conjugate of polar conjugate of X(16594)
X(22082) = isotomic conjugate of polar conjugate of X(20972)
X(22083) lies on these lines: {3, 22067}, {71, 22134}, {3917, 22082}, {5440, 22370}
X(22083) = isogonal conjugate of polar conjugate of complement of X(89)
X(22083) = isogonal conjugate of polar conjugate of complementary conjugate of X(34824)
X(22083) = isotomic conjugate of polar conjugate of X(20973)
X(22084) lies on these lines: {3, 22145}, {11, 244}, {71, 20728}, {103, 8750}, {216, 22440}, {603, 2594}, {1459, 3270}, {1473, 4286}, {3269, 22433}, {3917, 22428}, {3937, 20975}, {7117, 22437}, {20730, 22073}, {20731, 22059}, {20819, 20830}, {22053, 22069}, {22060, 22405}, {22067, 22406}, {22418, 22435}
X(22084) = isogonal conjugate of polar conjugate of X(116)
X(22084) = isotomic conjugate of polar conjugate of X(20974)
X(22085) lies on these lines: {3, 895}, {99, 9512}, {577, 20819}, {648, 21166}, {1576, 9155}, {1634, 5191}, {3284, 22087}, {7669, 9145}, {9723, 14575}, {20756, 20784}, {22052, 22062}, {22093, 22399}
X(22085) = isogonal conjugate of polar conjugate of X(620)
X(22085) = isotomic conjugate of polar conjugate of X(20976)
X(22086) lies on these lines: {6, 654}, {31, 926}, {42, 6139}, {44, 1639}, {520, 647}, {649, 6363}, {665, 21742}, {906, 1331}, {918, 4641}, {1635, 20972}, {1769, 14399}, {2092, 2624}, {3937, 7117}, {21786, 22108}, {22144, 22148}
X(22086) = isogonal conjugate of polar conjugate of X(900)
X(22086) = isotomic conjugate of polar conjugate of X(1960)
X(22086) = X(19)-isoconjugate of X(4555)
X(22086) = X(92)-isoconjugate of X(901)
X(22087) lies on these lines: {3, 22151}, {216, 3289}, {237, 3001}, {566, 14096}, {2393, 9155}, {2524, 3049}, {3284, 22085}, {5024, 5166}, {8681, 20975}, {14570, 21531}, {20821, 22059}
X(22087) = isogonal conjugate of polar conjugate of X(625)
X(22087) = isotomic conjugate of polar conjugate of X(20977)
X(22088) lies on these lines: {1, 2272}, {3, 48}, {6, 1106}, {19, 3333}, {41, 1470}, {73, 7117}, {198, 5022}, {603, 7124}, {610, 2260}, {672, 3207}, {910, 1475}, {1202, 1615}, {1466, 2266}, {1953, 5045}, {2183, 4253}, {2253, 4020}, {2275, 20995}, {2317, 4251}, {4322, 8608}, {4860, 17474}, {7177, 7289}, {9310, 22768}, {14597, 22063}, {15656, 17558}, {20727, 22435}, {20752, 22072}, {22053, 22070}
X(22088) = isogonal conjugate of polar conjugate of X(11019)
X(22088) = isotomic conjugate of polar conjugate of X(20978)
X(22089) lies on these lines: {3, 525}, {74, 2706}, {99, 22456}, {512, 684}, {520, 11589}, {523, 2071}, {647, 22091}, {669, 3265}, {804, 3267}, {2524, 3049}, {2797, 14618}, {3357, 23103}, {4558, 9218}, {5664, 18570}, {7484, 9209}, {8673, 9409}, {9210, 14096}, {15143, 16229}, {15411, 16695}
X(22089) = isogonal conjugate of polar conjugate of X(30476)
X(22089) = isotomic conjugate of polar conjugate of X(2451)
X(22090) lies on these lines: {1, 17072}, {3, 22154}, {42, 2533}, {43, 4147}, {386, 514}, {521, 656}, {663, 1193}, {1946, 22384}, {2524, 3049}, {3835, 17921}, {4040, 5313}, {4885, 17478}, {16695, 20979}, {20731, 20757}, {20821, 22406}
X(22090) = isogonal conjugate of polar conjugate of X(3835)
X(22090) = isotomic conjugate of polar conjugate of X(20979)
X(22090) = X(19)-isoconjugate of X(4598)
X(22091) lies on these lines: {3, 905}, {36, 1734}, {56, 3900}, {404, 4391}, {521, 23087}, {647, 22089}, {663, 2821}, {667, 2254}, {3733, 7655}, {4188, 17496}, {4367, 9511}, {20731, 20757}
X(22091) = isogonal conjugate of polar conjugate of X(4885)
X(22091) = isotomic conjugate of polar conjugate of X(20980)
X(22091) = X(19)-isoconjugate of X(30610)
X(22092) lies on these lines: {3, 22155}, {39, 665}, {441, 525}, {1459, 22095}, {2275, 4435}, {3937, 7117}, {4526, 17053}, {5069, 22108}, {6373, 20663}, {20731, 20757}
X(22092) = isogonal conjugate of polar conjugate of X(3837)
X(22092) = isotomic conjugate of polar conjugate of X(6373)
X(22092) = X(19)-isoconjugate of X(8709)
X(22093) lies on these lines: {3, 810}, {58, 14838}, {171, 3907}, {419, 4369}, {741, 2698}, {750, 21052}, {905, 22384}, {940, 17478}, {1010, 21259}, {1459, 1946}, {1468, 4041}, {1691, 20981}, {3406, 4444}, {4252, 21789}, {14382, 17103}, {20731, 20757}, {22085, 22399}, {22403, 22444}, {22441, 22443}
X(22093) = isogonal conjugate of polar conjugate of X(4369)
X(22093) = isotomic conjugate of polar conjugate of X(20981)
X(22093) = X(19)-isoconjugate of X(27805)
X(22094) lies on these lines: {3, 4575}, {71, 22434}, {125, 656}, {228, 22069}, {1818, 22406}, {1834, 12832}, {2088, 2624}, {2605, 3024}, {2972, 3270}, {3269, 7117}, {3937, 20975}, {20729, 20825}, {20733, 22067}, {20738, 22420}, {20749, 20820}, {22076, 22082}, {22077, 22409}, {22097, 22405}, {22363, 22402}, {22404, 22439}
X(22094) = isogonal conjugate of polar conjugate of X(8287)
X(22094) = isotomic conjugate of polar conjugate of X(20982)
X(22095) lies on these lines: {3, 22157}, {39, 3063}, {513, 4261}, {1459, 22092}, {2092, 20980}, {2276, 21348}, {2524, 3049}, {17072, 21347}, {20729, 22059}, {20828, 22387}
X(22095) = isogonal conjugate of polar conjugate of X(21260)
X(22095) = isotomic conjugate of polar conjugate of X(20983)
X(22096) lies on these lines: {3, 1332}, {48, 2196}, {69, 23086}, {71, 20759}, {228, 22357}, {237, 7113}, {667, 3271}, {854, 5137}, {1086, 3733}, {1437, 17971}, {2643, 8639}, {3248, 8660}, {3937, 22379}, {7117, 20975}, {20750, 22054}, {20777, 22356}, {22066, 22381}
X(22096) = isogonal conjugate of polar conjugate of X(1015)
X(22096) = isotomic conjugate of polar conjugate of X(1977)
X(22096) = X(19)-isoconjugate of X(31625)
X(22096) = X(92)-isoconjugate of X(1016)
X(22097) lies on these lines: {1, 19262}, {2, 2183}, {3, 73}, {9, 20205}, {36, 1412}, {40, 388}, {42, 4259}, {48, 394}, {55, 1350}, {57, 573}, {63, 69}, {81, 2260}, {142, 1730}, {184, 22390}, {198, 17811}, {223, 10856}, {226, 1764}, {228, 1818}, {238, 5324}, {497, 6210}, {511, 14547}, {553, 20367}, {572, 2003}, {672, 4641}, {940, 1400}, {1193, 4267}, {1211, 19608}, {1284, 21334}, {1331, 5314}, {1368, 21912}, {1458, 16678}, {1762, 7291}, {1788, 9548}, {1790, 4288}, {1796, 1797}, {1804, 7099}, {1812, 7116}, {1848, 2354}, {1936, 4220}, {1993, 2317}, {2185, 17209}, {2269, 3666}, {2318, 3781}, {2328, 3220}, {2347, 4383}, {2635, 4192}, {2654, 9840}, {2999, 4266}, {3198, 5784}, {3218, 17778}, {3219, 17280}, {3452, 21361}, {3485, 10476}, {3687, 3882}, {3720, 18165}, {3730, 3929}, {3752, 4271}, {3911, 21363}, {3937, 20730}, {3942, 18607}, {4466, 18651}, {4643, 5928}, {5218, 20368}, {5307, 10444}, {7193, 22139}, {7293, 20780}, {10571, 10882}, {17147, 21271}, {18141, 21371}, {22076, 22345}, {22094, 22405}, {22369, 22412}
X(22097) = isogonal conjugate of polar conjugate of X(4357)
X(22097) = isotomic conjugate of polar conjugate of X(1193)
X(22097) = X(19)-isoconjugate of X(1220)
X(22098) lies on these lines: {3, 22162}, {71, 73}, {4303, 22447}, {8540, 8586}, {20729, 22350}, {20731, 20757}, {20752, 22414}
X(22098) = isogonal conjugate of polar conjugate of X(4892)
X(22098) = isotomic conjugate of polar conjugate of X(20984)
X(22099) lies on these lines: {3, 295}, {48, 63}, {71, 3917}, {73, 22447}, {228, 20775}, {572, 3509}, {1755, 16678}, {2200, 3916}, {4303, 20727}, {20732, 22074}
X(22099) = isogonal conjugate of polar conjugate of X(24325)
X(22099) = isotomic conjugate of polar conjugate of X(20985)
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 28146.
X(22100) lies on these lines: {5,524}, {7812,9487}, {8787,9966}, {11317,14262}
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 28146.
X(22101) lies on these lines: {2,195}, {6,3459}, {288,1157}, {1263,14627}, {1994,15345}
X(22102) lies on the nine-point circle of the medial triangle and on these lines: {1,14026}, {2,901}, {3,2222}, {36,19335}, {100,6075}, {104,6073}, {150,4998}, {165,3322}, {513,3035}, {517,1387}, {620,4369}, {631,953}, {1054,7336}, {1155,5988}, {2810,15632}, {3025,5432}, {5433,13756}, {6681,6715}
X(22102) = complement of X(3259)
X(22102) = midpoint of X(i) and X(j) for these {i,j}: {100, 6075}, {104, 6073}, {901, 3259}, {15632, 15635}
X(22102) = X(9268)-complementary conjugate of X(119)
X(22102) = {X(2),X(901)}-harmonic conjugate of X(3259)
X(22102) = center of rectangular bicevian hyperbola of X(2) and X(901)
X(22102) = centroid of ABCX(901)
X(22103) lies on the on the nine-point circle of the medial triangle and one these lines: on lines {2,805}, {51,16979}, {98,6072}, {99,6071}, {230,511}, {512,620}, {631,2698}, {5976,16068}, {6787,7835}, {15630,15631}
X(22103) = complement X(2679)
X(22103) = midpoint of X(i) and X(j) for these {i,j}: {98, 6072}, {99, 6071}, {805, 2679}, {5976, 16068}, {15630, 15631}
X(22103) = center of rectangular bicevian hyperbola of X(2) and X(805)
X(22103) = centroid of ABCX(805)
X(22103) = intersection of axes of parabolas {{A,B,C,X(511),X(805)}} and {{A,B,C,X(512),X(669)}}
X(22103) = {X(2),X(805)}-harmonic conjugate of X(2679)
X(22104) lies on these lines: {2,476}, {3,16177}, {30,6699}, {51,16978}, {74,1553}, {110,6070}, {125,7471}, {126,9179}, {140,16168}, {376,14989}, {468,6036}, {477,631}, {511,11657}, {523,5972}, {542,3233}, {549,18319}, {1656,20957}, {3154,6723}, {5627,12383}, {5642,14611}, {5943,12052}, {6720,14341}, {10113,21315}, {11539,11749}, {15059,17511}
X(22104) = midpoint of X(i) and X(j) for these {i,j}: {74, 1553}, {110, 6070}, {125, 7471}, {126, 9179}, {476, 3258}, {3233, 12079}
X(22104) = reflection of X(i) in X(j) for these {i,j}: {3154, 6723}, {5972, 12068}
X(22104) = reflection X(5972) in the Euler line
X(22104) = reflection of X(32223) in the orthic axis
X(22104) = complement X(3258)
X(22104) = X(15395)-complementary conjugate of X(10)
X(22104) = {X(2),X(476)}-harmonic conjugate of X(3258)
X(22104) = centroid of ABCX(476)
X(22104) = intersection of axes of parabolas {{A,B,C,X(30),X(476)}} and {{A,B,C,X(476),X(523)}}
X(22105) lies on these lines: {5,11620}, {23,385}, {83,9180}, {99,827}, {111,9076}, {115,804}, {141,5113}, {308,14606}, {351,7664}, {690,5026}, {3228,14970}, {3589,14428}, {9185,14277}, {9189,14278}, {9293,17997}
X(22105) = midpoint of X(4580) and X(18105)
X(22105) = reflection of X(i) in X(j) for these {i,j}: {5, 11620}, {141, 5113}
X(22105) = isogonal conjugate of X(36827)
X(22105) = X(i)-cross conjugate of X(j) for these (i,j): {18311, 523}, {21906, 524}
X(22105) = X(i)-isoconjugate of X(j) for these (i,j): {38, 691}, {892, 1964}, {897, 1634}, {923, 4576}, {5380, 17187}
X(22105) = cevapoint of X(351) and X(690)
X(22105) = trilinear pole of line {1648, 11183}
X(22105) = crossdifference of every pair of points on line {39, 1634}
X(22105) = barycentric product X(i)*X(j) for these {i,j}: {83, 690}, {308, 351}, {468, 4580}, {689, 21906}, {896, 18070}, {1648, 4577}, {1799, 14273}, {2642, 3112}, {3266, 18105}, {4062, 10566}, {4750, 18082}, {9076, 18311}, {11183, 14970}, {14432, 18097}, {19326, 20483}
X(22105) = barycentric quotient X(i)/X(j) for these {i,j}: {83, 892}, {187, 1634}, {251, 691}, {351, 39}, {524, 4576}, {690, 141}, {1648, 826}, {1649, 7813}, {2642, 38}, {4062, 4568}, {4750, 16887}, {11183, 732}, {14273, 427}, {14417, 3933}, {14419, 16696}, {14424, 7794}, {18098, 5380}, {18105, 111}, {21839, 4553}, {21906, 3005}
X(22105) = trilinear product X(i)*X(j) for these {i,j}: {82, 690}, {83, 2642}, {187, 18070}, {351, 3112}, {1648, 4599}, {4062, 18108}, {4593, 21906}, {4750, 18098}, {10566, 21839}, {14210, 18105}, {14273, 34055}, {14419, 18082}, {23889, 34294}
X(22106) lies on the incircle and these lines: {482,1360}, {918,1086}, {1335,13436}, {1361,8243}, {3321,5393}
X(22106) = X(13436)-Ceva conjugate of X(6365)
X(22106) = X(i)-isoconjugate of X(j) for these (i,j): {59, 13427}, {101, 6136}, {1110, 1336}, {2149, 13426}, {6065, 13460}
X(22106) = barycentric product X(i)*X(j) for these {i,j}: {11, 13436}, {693, 6365}, {1086, 5391}, {1111, 3084}, {1358, 13458}, {1565, 13387}
X(22106) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 13426}, {513, 6136}, {606, 1110}, {1086, 1336}, {1335, 1252}, {1358, 13459}, {1565, 13386}, {2170, 13427}, {3084, 765}, {3942, 6212}, {5391, 1016}, {6365, 100}, {13387, 15742}, {13436, 4998}, {13458, 4076}
X(22106) = {X(1086),X(1111)}-harmonic conjugate of X(22107)
X(22107) lies on the incircle and these lines: {481,1360}, {918,1086}, {1124,13453}, {3321,5405}
X(22107) = X(13453)-Ceva conjugate of X(6364)
X(22107) = X(i)-isoconjugate of X(j) for these (i,j): {59, 13456}, {101, 6135}, {1110, 1123}, {2149, 13454}, {6065, 13438}
X(22107) = barycentric product X(i)*X(j) for these {i,j}: {11, 13453}, {693, 6364}, {1086, 1267}, {1111, 3083}, {1358, 13425}, {1565, 13386}
X(22107) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 13454}, {513, 6135}, {605, 1110}, {1086, 1123}, {1124, 1252}, {1267, 1016}, {1358, 13437}, {1565, 13387}, {2170, 13456}, {3083, 765}, {3942, 6213}, {6364, 100}, {13386, 15742}, {13425, 4076}, {13453, 4998}
{X(1086),X(1111)}-harmonic conjugate of X(22106)
X(22108) lies on these lines: {6,665}, {9,900}, {37,4435}, {44,513}, {45,4526}, {101,692}, {523,21390}, {667,9029}, {909,911}, {1024,2161}, {2170,17463}, {2291,6139}, {2605,3063}, {2820,4869}, {3196,8658}, {3709,21007}, {3766,17277}, {3887,6594}, {4491,8659}, {5069,22092}, {5540,6084}, {8632,14407}, {8638,15624}, {21131,21832}, {21786,22086}
X(22108) = midpoint of X(2590) and X(2591)
X(22108) = isogonal conjugate of X(37143)
X(22108) = X(i)-zayin conjugate of X(j) for these (i,j): {9, 1308}, {650, 3254}, {1308, 1638}, {1638, 9}, {2826, 57}, {5527, 658}, {5536, 651}
X(22108) = X(2742)-Ceva conjugate of X(55)
X(22108) = X(i)-isoconjugate of X(j) for these (i,j): {2, 1308}, {651, 3254}
X(22108) = crosspoint of X(i) and X(j) for these (i,j): {1, 37143}, {57, 14733}, {101, 2291}
X(22108) = crossdifference of every pair of points on line {1, 528}
X(22108) = crosssum of X(i) and X(j) for these (i,j): {1, 22108}, {9, 6366}, {514, 527}, {522, 5199}, {650, 18839}
X(22108) = barycentric product X(i)*X(j) for these {i,j}: {1, 3887}, {75, 8645}, {513, 3935}, {514, 5526}, {522, 2078}, {649, 17264}, {693, 19624}
X(22108) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 1308}, {663, 3254}, {2078, 664}, {3887, 75}, {3935, 668}, {5526, 190}, {8645, 1}, {17264, 1978}, {19624, 100}
X(22108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1635, 2246, 659), (3063, 6586, 2605)
X(22109) lies on these lines: {3,125}, {20,13293}, {22,2777}, {23,1531}, {24,5972}, {26,113}, {52,12228}, {69,12584}, {74,7512}, {110,5562}, {143,9826}, {186,249}, {569,12236}, {974,10984}, {1092,1511}, {1350,15141}, {1539,17714}, {1568,2070}, {1594,18428}, {2935,11414}, {2937,7728}, {3043,11412}, {3047,12273}, {3917,17701}, {5181,15577}, {5504,13367}, {5642,14070}, {5663,7502}, {5889,12227}, {6636,15055}, {6723,7509}, {6759,12825}, {7387,13202}, {7503,7687}, {7506,12900}, {7525,12041}, {7526,12295}, {7575,11064}, {9626,12368}, {9715,10117}, {9967,19138}, {10024,19479}, {10272,12107}, {10539,20773}, {10634,10664}, {10635,10663}, {10721,12088}, {10733,14118}, {10897,12892}, {10898,12891}, {11430,13434}, {12225,19506}, {13198,21649}, {13564,20127}, {14984,19131}, {15085,19456}, {17834,19504}
X(22109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 2931, 125), (3, 12121, 12901), (3, 12310, 19457), (110, 7488, 13289), (110, 7691, 12219), (9715, 12168, 10117), (10117, 12168, 15063)
X(22110) lies on these lines: {2,6}, {5,7801}, {30,114}, {39,8360}, {98,12151}, {99,8352}, {115,8355}, {126,9193}, {140,7810}, {147,10488}, {187,9167}, {316,8598}, {338,3266}, {468,9164}, {523,7625}, {538,2023}, {543,625}, {546,7863}, {547,9466}, {549,7818}, {574,12040}, {598,7835}, {620,3849}, {626,8359}, {632,7854}, {671,7799}, {858,10717}, {1153,7848}, {1503,6054}, {1506,8367}, {2549,11165}, {3291,9165}, {3363,3734}, {3530,7873}, {3564,6055}, {3628,7794}, {3788,7745}, {3933,7862}, {5077,7618}, {5159,15526}, {5215,7845}, {5254,11318}, {5648,9759}, {5976,15814}, {6722,10150}, {7181,21057}, {7495,9829}, {7617,7908}, {7622,7761}, {7752,7789}, {7753,8368}, {7762,7940}, {7763,7841}, {7764,7817}, {7769,7883}, {7807,7812}, {7813,14971}, {7827,7899}, {7833,7912}, {7866,9606}, {7874,8365}, {7907,9939}, {8290,8786}, {8364,9698}, {8591,14041}, {8705,12093}, {8716,16041}, {8724,15980}, {8787,12830}, {9607,14064}, {9756,11180}, {11054,14061}, {11057,11149}, {11185,20112}, {12036,13857}, {15702,21445}
X(22110) = midpoint of X(i) and X(j) for these {i,j}: {2, 325}, {99, 8352}, {316, 8598}, {8724, 15980}
X(22110) = reflection of X(i) in X(j) for these {i,j}: {115, 8355}, {230, 2}
X(22110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 69, 7610), (2, 183, 15597), (2, 599, 11168), (2, 1007, 11184), (2, 7610, 3054), (2, 7779, 8859), (2, 7788, 13468), (2, 9766, 5306), (2, 9770, 6), (2, 9771, 3055), (2, 11163, 597), (2, 11184, 3815), (2, 21356, 15271), (141, 9771, 2), (597, 11163, 9300), (1007, 7778, 3815), (3734, 8176, 3363), (3788, 7775, 8369), (6189, 6190, 11160), (7752, 7870, 8370), (7775, 8369, 7745), (7778, 11184, 2), (7870, 8370, 7789)
X(22110) = orthoptic circle of the Steiner inellipe inverse of X(14916)
X(22110) = complement of X(22329)
X(22110) = isotomic of the isogonal of X(5107)
X(22110) = X(2)-daleth conjugate of X(599)
X(22110) = X(i)-complementary conjugate of X(j) for these (i,j): {2709, 4369}, {5503, 2887}
X(22110) = X(2)-Hirst inverse of X(11160)
X(22110) = crosspoint of X(2) and X(5503)
X(22110) = crossdifference of every pair of points on line {512, 1384}
X(22110) = crosssum of X(6) and X(2030)
X(22110) = barycentric product X(76)*X(5107)
X(22110) = barycentric quotient X(5107)/X(6)
X(22111) lies on these lines: {2,5503}, {6,373}, {51,11173}, {111,182}, {184,2502}, {187,3148}, {352,576}, {511,20481}, {574,3124}, {597,16317}, {647,9171}, {1383,10545}, {1384,3066}, {1995,2030}, {3098,13192}, {5166,9813}, {5354,11451}, {5476,5913}, {5640,11580}, {6032,11647}, {6792,11178}, {7606,10160}, {7617,9169}, {8288,18362}, {10485,20998}
X(22111) = crossdifference of every pair of points on line {1499, 8598}
X(22111) = crosssum of X(2) and X(9741)
X(22111) = psi-transform of X(13492)
X(22111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 8585, 5651), (111, 7708, 182)
X(22112) is the perspector of the Thomson-Gibert-Moses hyperbola wrt triangle X(2)X(3)X(6). (Randy Hutson, October 15, 2018)
X(22112) lies on these lines: {2,98}, {3,373}, {5,16654}, {6,5646}, {22,6688}, {23,17508}, {51,1350}, {52,13154}, {140,13142}, {381,8717}, {468,19124}, {511,21766}, {567,1092}, {569,632}, {574,3124}, {575,15066}, {576,7998}, {578,3525}, {582,16296}, {631,11424}, {868,7913}, {1204,7395}, {1351,3917}, {1397,17124}, {1437,16863}, {1495,5085}, {1656,10984}, {1790,16409}, {1974,5094}, {1993,15516}, {1995,5092}, {2175,17125}, {2972,5158}, {3091,13347}, {3098,5640}, {3231,5034}, {3292,5050}, {3628,13336}, {3819,5097}, {4550,10620}, {5056,15431}, {5067,6759}, {5118,15482}, {5159,19131}, {5398,19249}, {5562,15805}, {5643,11002}, {5645,5888}, {5943,7485}, {6784,9145}, {6800,12045}, {6803,21659}, {7392,14927}, {7492,10545}, {7509,11695}, {7550,11438}, {7570,7703}, {7889,14003}, {8371,8723}, {8541,12039}, {8585,20998}, {8722,14096}, {9275,17749}, {10303,13346}, {11451,15246}, {11935,15723}, {12100,20192}, {13323,17531}, {13329,16373}, {13366,17811}, {14805,15040}, {14926,18435}, {15033,15702}, {15080,16042}, {15720,21970}, {16051,19126}, {16063,19130}
X(22112) = crossdifference of every pair of points on line {3569, 9123}
X(22112) = trilinear product of vertices of Stammler triangle
X(22112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 110, 16187), (2, 182, 5651), (3, 5544, 3066), (110, 16187, 5651), (182, 5651, 184), (182, 9306, 11003), (182, 16187, 110), (575, 15082, 15066), (3066, 5544, 373), (3917, 10601, 15004), (5085, 11284, 1495), (5640, 7496, 3098), (7484, 17825, 51), (7998, 15018, 576), (10601, 16419, 3917)
X(22113) lies on the curves Q088 and K906, and on these lines: {2,17}, {4,3180}, {5,3181}, {13,633}, {20,6770}, {61,622}, {148,16001}, {193,576}, {299,397}, {530,5238}, {617,16965}, {628,10653}, {2896,16941}, {3105,5335}, {3600,18973}, {3622,11739}, {3926,11132}, {5340,5859}, {5613,13571}
X(22113) = anticomplement X(627)
X(22113) = reflection of X(i) in X(j) for these {i,j}: {4, 16629}, {627, 17}
X(22113) = anticomplement of the isotomic of X(19712)
X(22113) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3489, 8}, {19712, 6327}
X(22113) = X(19712)-Ceva conjugate of X(2)
X(22114) lies on the curves Q088 and K906, and on these lines: {2,18}, {4,3181}, {5,3180}, {14,634}, {20,6773}, {62,621}, {148,16002}, {193,576}, {298,398}, {531,5237}, {616,16964}, {627,10654}, {2896,16940}, {3104,5334}, {3600,18972}, {3622,11740}, {3926,11133}, {5339,5858}, {5617,13571}
X(22114) = anticomplement X(628)
X(22114) = reflection of X(i) in X(j) for these {i,j}: {4, 16628}, {628, 18}
X(22114) = anticomplement of the isotomic of X(19713)
X(22114) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3490, 8}, {19713, 6327}
X(22114) = X(19713)-Ceva conjugate of X(2)
X(22114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18, 628, 2), (193,3091,22113), (5872, 20426, 4)
X(22115) lies on these lines: {2,567}, {3,49}, {4,18350}, {5,15033}, {6,9676}, {15,3200}, {16,3201}, {20,156}, {22,13340}, {23,13391}, {24,6243}, {30,110}, {32,9603}, {35,2477}, {36,215}, {50,18334}, {54,140}, {60,5453}, {68,6640}, {69,19129}, {125,539}, {154,12083}, {165,9621}, {182,599}, {186,323}, {187,9696}, {195,389}, {265,2072}, {376,9544}, {378,15068}, {381,9306}, {382,10539}, {399,2935}, {403,14643}, {498,9653}, {499,9666}, {500,17104}, {511,2070}, {520,6760}, {524,15462}, {526,15470}, {548,9705}, {549,5012}, {550,1614}, {568,1993}, {569,3526}, {574,9604}, {576,13321}, {578,1656}, {631,9545}, {858,15132}, {974,10816}, {993,9702}, {1199,1493}, {1351,19136}, {1495,5899}, {1568,17702}, {1594,6288}, {1657,5895}, {1658,11412}, {1994,5946}, {2063,18466}, {2071,5663}, {2888,6143}, {2931,18127}, {2937,10282}, {2979,7502}, {3044,12042}, {3047,12041}, {3060,12106}, {3153,12383}, {3202,9821}, {3203,12054}, {3205,5238}, {3206,5237}, {3289,10317}, {3431,18882}, {3518,10263}, {3520,5876}, {3524,11003}, {3530,9706}, {3548,6193}, {3564,5622}, {3575,15800}, {3576,9586}, {3580,12228}, {3628,13434}, {3851,11424}, {4299,9652}, {4302,9667}, {5050,9027}, {5055,5651}, {5066,13482}, {5159,15027}, {5446,13621}, {5462,14627}, {5609,7464}, {5891,11430}, {5892,13366}, {5907,14130}, {5943,15038}, {5944,7512}, {6090,9818}, {6101,7488}, {6409,9677}, {6445,9687}, {6642,9777}, {7506,17810}, {7514,14805}, {7527,15060}, {7574,15139}, {7575,15034}, {7666,10274}, {7799,10411}, {7987,9622}, {8717,15689}, {8718,12103}, {8780,18534}, {9145,15365}, {9301,9418}, {9730,15087}, {9820,10024}, {9927,10255}, {10091,10149}, {10096,13392}, {10110,18369}, {10151,15472}, {10226,11440}, {10272,11563}, {10510,11649}, {11250,12111}, {11422,15045}, {11441,12084}, {11442,18281}, {11459,18570}, {11591,14118}, {11693,15303}, {11694,15360}, {11695,15047}, {12118,18404}, {12161,17928}, {12254,13470}, {12278,18377}, {12429,15123}, {12902,13851}, {13336,15720}, {13371,14516}, {13445,14094}, {13564,15644}, {13596,15052}, {14106,19552}, {14984,18449}, {15020,18571}, {15035,15646}, {15316,15317}, {16089,18831}, {16386,20127}, {16534,18325}, {18438,20806}
X(22115) = midpoint of X(i) and X(j) for these {i,j}: {186, 323}, {399, 18859}, {3153, 12383}, {13445, 14094}
X(22115) = reflection of X(i) in X(j) for these {i,j}: {125, 14156}, {186, 1511}, {265, 2072}, {2072, 11064}, {3581, 186}, {5899, 1495}, {10096, 13392}, {10540, 110}, {11563, 10272}, {12902, 13851}, {18403, 1568}, {18859, 10564}, {20127, 16386}
X(22115) = isogonal conjugate of X(6344)
X(22115) = isotomic conjugate of X(18817)
X(22115) = X(i)-Ceva conjugate of X(j) for these (i,j): {323, 50}, {5504, 3}, {10411, 8552}, {14919, 577}
X(22115) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6344}, {4, 2166}, {19, 94}, {31, 18817}, {75, 18384}, {92, 1989}, {158, 265}, {162, 10412}, {328, 1096}, {811, 15475}, {823, 14582}, {1784, 5627}, {1969, 11060}, {1973, 20573}
X(22115) = crosspoint of X(i) and X(j) for these (i,j): {95, 2986}, {328, 11140}
X(22115) = crossdifference of every pair of points on line {53, 2501}
X(22115) = crosssum of X(i) and X(j) for these (i,j): {51, 3003}, {1989, 18384}, {1990, 14583}
X(22115) = barycentric product X(i)*X(j) for these {i,j}: {3, 323}, {50, 69}, {63, 6149}, {97, 1154}, {110, 8552}, {184, 7799}, {186, 394}, {249, 16186}, {305, 19627}, {340, 577}, {520, 14590}, {526, 4558}, {647, 10411}, {1092, 14165}, {1273, 14533}, {1511, 14919}, {2624, 4592}, {3265, 14591}, {4563, 14270}, {6148, 18877}, {11064, 14385}, {14918, 19210}
X(22115) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 18817}, {3, 94}, {6, 6344}, {32, 18384}, {48, 2166}, {50, 4}, {69, 20573}, {184, 1989}, {186, 2052}, {323, 264}, {340, 18027}, {394, 328}, {520, 14592}, {526, 14618}, {577, 265}, {647, 10412}, {1147, 18883}, {1154, 324}, {2088, 2970}, {3043, 14165}, {3049, 15475}, {3284, 14254}, {3289, 14356}, {6149, 92}, {7799, 18022}, {8552, 850}, {10411, 6331}, {11062, 13450}, {11077, 14859}, {14270, 2501}, {14355, 16081}, {14385, 16080}, {14533, 1141}, {14575, 11060}, {14590, 6528}, {14591, 107}, {16186, 338}, {18877, 5627}, {19627, 25}
X(22115) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 1147, 49), (3, 3167, 18445), (3, 9703, 184), (15, 3200, 11137), (16, 3201, 11134), (24, 16266, 6243), (54, 140, 13353), (184, 1147, 9703), (184, 9703, 49), (323, 1511, 3581), (378, 15068, 18435), (549, 5012, 13339), (1092, 1147, 3), (1092, 3292, 15136), (1216, 13367, 3), (1493, 12006, 1199), (1511, 3043, 11597), (1993, 6644, 568), (2979, 11464, 7502), (3917, 18475, 3), (5562, 12038, 3), (5892, 13366, 15037), (5944, 10627, 7512), (9306, 13352, 381), (10282, 10625, 2937), (10539, 13346, 382), (11412, 11449, 1658), (11441, 12084, 18439)
X(22116) lies on the cubics K1038, K1068, K1069) and these lines: {1,39}, {2,19897}, {8,4562}, {9,9470}, {10,514}, {12,85}, {56,4564}, {76,4583}, {335,16593}, {518,3252}, {660,5220}, {813,1083}, {1026,4447}, {1376,9503}, {3573,17798}, {3675,3912}, {3932,18157}, {4075,17758}, {8256,9311}, {17169,18827}
X(22116) = X(i)-complementary conjugate of X(j) for these (i,j): {518, 20551}, {672, 20343}, {727, 518}, {2223, 20532}, {3226, 20544}, {20332, 20335}
X(22116) = X(i)-Ceva conjugate of X(j) for these (i,j): {291, 518}, {4583, 918}
X(22116) = X(i)-cross conjugate of X(j) for these (i,j): {3675, 876}, {4712, 518}
X(22116) = X(i)-Hirst inverse of X(j) for these (i,j): {291, 4876}, {518, 3252}
X(22116) = cevapoint of X(i) and X(j) for these (i,j): {3126, 3675}, {6184, 20683}
X(22116) = trilinear pole of line {2254, 3930}
X(22116) = crossdifference of every pair of points on line {659, 1914}
X(22116) = crosssum of X(238) and X(8300)
X(22116) = X(2254)-zayin conjugate of X(659)
X(22116) = barycentric product X(i)X(j) for these {i,j}: {75, 3252}, {241, 4518}, {291, 3912}, {292, 3263}, {334, 672}, {335, 518}, {337, 5089}, {660, 918}, {665, 4583}, {1026, 4444}, {1916, 4447}, {2223, 18895}, {2254, 4562}, {3693, 7233}, {3930, 18827}, {4088, 4584}, {4876, 9436}
X(22116) = X(i)-isoconjugate of X(j) for these (i,j): {6, 6654}, {105, 238}, {239, 1438}, {294, 1429}, {666, 8632}, {673, 1914}, {812, 919}, {1027, 3573}, {1416, 3685}, {1428, 14942}, {1447, 2195}, {1462, 3684}, {1814, 2201}, {2210, 2481}, {5009, 13576}, {8751, 20769}, {14599, 18031}
X(22116) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 6654}, {241, 1447}, {291, 673}, {292, 105}, {295, 1814}, {334, 18031}, {335, 2481}, {518, 239}, {660, 666}, {665, 659}, {672, 238}, {918, 3766}, {926, 4435}, {1026, 3570}, {1458, 1429}, {1818, 20769}, {1911, 1438}, {2223, 1914}, {2254, 812}, {2284, 3573}, {2340, 3684}, {2356, 2201}, {3252, 1}, {3263, 1921}, {3572, 1027}, {3693, 3685}, {3717, 3975}, {3912, 350}, {3930, 740}, {3932, 3948}, {4447, 385}, {4712, 17755}, {4876, 14942}, {5089, 242}, {6184, 8299}, {7077, 294}, {8299, 4366}, {9436, 10030}, {9454, 2210}, {9455, 14599}, {14439, 4432}, {17435, 4124}, {20683, 2238}, {20752, 7193}
X(22117) lies on these lines: {1, 3683}, {3, 73}, {6, 13404}, {33, 5779}, {55, 2003}, {81, 954}, {109, 6244}, {165, 1419}, {278, 5762}, {329, 15252}, {394, 1260}, {405, 3562}, {582, 1167}, {651, 7580}, {971, 7070}, {999, 5398}, {1074, 18541}, {1103, 3579}, {1407, 13329}, {1496, 16466}, {1617, 2361}, {1754, 6180}, {1771, 9709}, {1795, 22141}, {1936, 19541}, {3074, 11108}, {3075, 16408}, {3167, 20752}, {3745, 15298}, {3990, 15905}, {4667, 13405}, {5759, 18623}, {6056, 7011}, {6149, 8069}, {7193, 23089}, {7290, 12915}, {9654, 13408}, {20796, 20799}, {20797, 22149}, {22132, 22139}
X(22117) = isogonal conjugate of polar conjugate of X(144)
X(22117) = isotomic conjugate of polar conjugate of X(3207)
X(22117) = X(19)-isoconjugate of X(10405)
X(22117) = X(92)-isoconjugate of X(11051)
X(22118) lies on these lines: {1, 1333}, {3, 2197}, {6, 8071}, {48, 255}, {63, 18604}, {160, 692}, {216, 22123}, {218, 5065}, {219, 577}, {517, 1950}, {573, 1415}, {608, 11249}, {2169, 3990}, {2327, 22126}, {2911, 5063}, {3284, 22122}, {3562, 7054}, {4261, 14793}, {5124, 13006}, {5841, 8736}, {15905, 22131}, {20793, 23086}, {22054, 22350}
X(22118) = isogonal conjugate of polar conjugate of X(2975)
X(22118) = isotomic conjugate of polar conjugate of X(20986)
X(22118) = X(92)-isoconjugate of X(34434)
X(22119) lies on these lines: {3, 31}, {6, 1214}, {48, 222}, {63, 22131}, {81, 6349}, {219, 22130}, {380, 2999}, {394, 22134}, {608, 11347}, {857, 17902}, {940, 17073}, {997, 17811}, {1040, 7290}, {1073, 1260}, {3101, 8743}, {3157, 7016}, {3195, 7580}, {3772, 18588}, {4329, 17903}, {5230, 21530}, {5711, 18641}, {20967, 22341}
X(22119) = isogonal conjugate of polar conjugate of X(4329)
X(22119) = isotomic conjugate of polar conjugate of X(3556)
X(22119) = X(19)-isoconjugate of X(7219)
X(22119) = X(92)-isoconjugate of X(7169)
X(22120) lies on these lines: {3, 6}, {26, 10313}, {30, 8743}, {112, 12084}, {127, 7759}, {155, 22146}, {194, 15013}, {230, 6640}, {232, 7517}, {248, 15317}, {339, 7754}, {382, 2207}, {441, 1993}, {1060, 5280}, {1062, 5299}, {1147, 8779}, {1180, 15818}, {1368, 5359}, {1576, 2353}, {2072, 3767}, {2548, 10024}, {2549, 18563}, {3087, 7528}, {3146, 8744}, {3172, 12085}, {3546, 5304}, {3548, 7735}, {3549, 7736}, {3815, 6639}, {3926, 22151}, {3927, 22131}, {3933, 20806}, {5254, 18404}, {5286, 18531}, {5305, 11585}, {5354, 16051}, {5523, 18569}, {5938, 20993}, {6644, 10312}, {7400, 14930}, {7506, 10311}, {7553, 8745}, {7737, 15075}, {7758, 14376}, {7890, 15526}, {10255, 13881}, {12605, 15048}, {13861, 15355}, {15341, 22660}, {16502, 18455}, {19597, 22143}
X(22120) = isogonal conjugate of polar conjugate of X(7391)
X(22120) = isotomic conjugate of polar conjugate of X(20987)
X(22120) = X(92)-isoconjugate of X(34436)
X(22121) lies on these lines: {3, 6}, {30, 8744}, {112, 18859}, {232, 5899}, {323, 441}, {399, 13509}, {647, 22155}, {1368, 5354}, {1576, 5938}, {1657, 8743}, {2070, 10313}, {2207, 5073}, {2549, 18564}, {3289, 22146}, {5159, 11580}, {5523, 7574}, {6390, 22151}, {7545, 15355}, {8779, 22115}, {10985, 13621}, {15075, 18565}, {16784, 18455}, {16785, 18447}
X(22121) = isogonal conjugate of polar conjugate of X(5189)
X(22121) = isotomic conjugate of polar conjugate of X(19596)
X(22121) = X(92)-isoconjugate of X(34437)
X(22122) lies on these lines: {1, 6}, {3, 22058}, {48, 22144}, {69, 20808}, {216, 906}, {2193, 22070}, {2259, 5396}, {2286, 23073}, {3284, 22118}, {22126, 22133}, {22143, 23094}
X(22122) = isogonal conjugate of polar conjugate of isogonal conjugate of X(34441)
X(22122) = isogonal conjugate of polar conjugate of complement of X(20066)
X(22122) = isogonal conjugate of polar conjugate of anticomplement of X(35)
X(22122) = isotomic conjugate of polar conjugate of X(20988)
X(22122) = X(92)-isoconjugate of X(34441)
X(22123) lies on these lines: {1, 6}, {3, 22059}, {59, 7115}, {216, 22118}, {284, 2594}, {521, 2522}, {692, 2393}, {906, 3284}, {1332, 20808}, {1783, 7359}, {2193, 2197}, {2302, 5399}, {3157, 19350}, {4282, 5172}, {7124, 23073}, {20744, 22145}, {20796, 22143}, {22144, 22356}
X(22123) = isogonal conjugate of polar conjugate of X(5080)
X(22123) = isotomic conjugate of polar conjugate of X(20989)
X(22123) = X(92)-isoconjugate of X(34442)
X(22124) lies on these lines: {1, 6}, {3, 22063}, {48, 222}, {109, 1436}, {198, 10571}, {221, 610}, {517, 2331}, {602, 1622}, {1064, 4254}, {1409, 7124}, {1604, 2199}, {1783, 7003}, {3157, 20818}, {3211, 22144}, {3284, 23073}, {22147, 23071}
X(22124) = isotomic conjugate of polar conjugate of X(20991)
X(22124) = isogonal conjugate of polar conjugate of X(962)
X(22124) = X(92)-isoconjugate of X(963)
X(22125) lies on these lines: {3, 22064}, {6, 142}, {219, 20740}, {222, 3211}, {306, 394}, {20739, 20806}
X(22125) = isogonal conjugate of polar conjugate of X(21285)
X(22125) = isotomic conjugate of polar conjugate of X(1626)
X(22126) lies on these lines: {1, 16699}, {3, 48}, {6, 1125}, {69, 20811}, {72, 20752}, {78, 4574}, {218, 1468}, {220, 993}, {394, 4001}, {2274, 9605}, {2327, 22118}, {2911, 5021}, {3927, 22163}, {4020, 22458}, {4047, 14597}, {17135, 17911}, {20762, 20809}, {20796, 23077}, {22122, 22133}
X(22127) lies on these lines: {3, 48}, {6, 978}, {72, 22163}, {78, 20752}, {101, 15654}, {172, 218}, {222, 348}, {394, 7124}, {610, 10476}, {1613, 16502}, {3496, 20995}, {3940, 22164}, {4020, 20760}, {5776, 15486}, {7078, 20762}, {10453, 17920}, {20739, 22144}, {20741, 22131}, {20745, 20812}, {22158, 23088}
X(22127) = isogonal conjugate of polar conjugate of X(10453)
X(22127) = isotomic conjugate of polar conjugate of X(20992)
X(22127) = X(92)-isoconjugate of X(34445)
X(22128) lies on these lines: {2, 2003}, {3, 22067}, {6, 3306}, {9, 15066}, {57, 1993}, {63, 77}, {72, 23070}, {78, 3157}, {81, 3664}, {84, 11441}, {110, 3220}, {184, 3784}, {221, 11682}, {228, 22161}, {283, 4303}, {320, 17923}, {323, 1443}, {651, 908}, {758, 4351}, {905, 4131}, {960, 8614}, {1203, 5253}, {1259, 23072}, {1331, 1818}, {1332, 3977}, {1437, 11573}, {1473, 3167}, {1790, 4288}, {1795, 22350}, {1797, 22356}, {1812, 4001}, {1943, 14213}, {1944, 14206}, {2979, 5285}, {3193, 4292}, {3292, 3937}, {3305, 17811}, {3916, 22136}, {3917, 3955}, {4511, 11700}, {4855, 7078}, {4867, 6126}, {5310, 7186}, {5422, 5437}, {5440, 22141}, {6507, 7099}, {6515, 20266}, {7171, 11456}, {7289, 20806}, {9037, 20989}, {14597, 22133}, {17976, 22148}, {20746, 22156}, {22060, 22139}
X(22128) = isogonal conjugate of polar conjugate of X(320)
X(22128) = isotomic conjugate of polar conjugate of X(36)
X(22128) = X(19)-isoconjugate of X(80)
X(22129) lies on these lines: {2, 1407}, {3, 1331}, {6, 2243}, {57, 10601}, {63, 77}, {81, 2255}, {220, 15066}, {221, 2975}, {283, 23072}, {329, 17074}, {651, 5744}, {940, 4415}, {958, 1406}, {971, 2000}, {1191, 16948}, {1259, 4303}, {1413, 4296}, {1473, 3796}, {1977, 16781}, {2003, 3928}, {3157, 3916}, {3219, 17811}, {3784, 7085}, {4652, 7078}, {5710, 20076}, {6360, 20477}, {6511, 10607}, {14996, 20059}
X(22129) = isogonal conjugate of polar conjugate of anticomplement of X(45)
X(22129) = isotomic conjugate of polar conjugate of X(999)
X(22129) = X(19)-isoconjugate of X(1000)
X(22130) lies on these lines: {3, 22069}, {6, 226}, {31, 916}, {219, 22119}, {222, 3942}, {306, 394}, {323, 20017}, {1993, 3187}, {2650, 3157}, {14543, 18676}, {17811, 20106}, {17902, 21270}, {20760, 22156}
X(22130) = isogonal conjugate of polar conjugate of X(21270)
X(22130) = isotomic conjugate of polar conjugate of X(23843)
X(22131) lies on these lines: {1, 6}, {3, 906}, {8, 1783}, {41, 1064}, {48, 4303}, {63, 22119}, {101, 10571}, {169, 5452}, {222, 22153}, {277, 1462}, {394, 4001}, {517, 607}, {602, 672}, {692, 19153}, {1409, 3211}, {1802, 22350}, {1814, 17170}, {1951, 11249}, {2172, 3556}, {2178, 21744}, {2207, 3419}, {2286, 20818}, {2289, 22063}, {3157, 20752}, {3434, 17905}, {3827, 18596}, {3927, 22120}, {8608, 11508}, {8735, 10525}, {15905, 22118}, {20741, 22127}
X(22132) lies on these lines: {1, 6}, {3, 2197}, {48, 22350}, {71, 255}, {159, 692}, {181, 6056}, {222, 10319}, {306, 394}, {478, 1766}, {517, 608}, {604, 1066}, {610, 1103}, {651, 4329}, {906, 15905}, {1264, 1332}, {1333, 8069}, {1409, 3157}, {1950, 11248}, {2303, 3085}, {3197, 18598}, {3211, 20752}, {4261, 8071}, {5285, 7074}, {5301, 11508}, {5776, 9370}, {7124, 20818}, {8736, 10526}, {18650, 20744}, {20741, 20745}, {20765, 20770}, {22117, 22139}, {22144, 22147}
X(22133) lies on these lines: {2, 6}, {3, 22073}, {71, 3955}, {219, 3157}, {283, 18591}, {511, 1474}, {572, 5562}, {573, 1092}, {651, 18631}, {2327, 3284}, {7078, 8766}, {14597, 22128}, {20742, 22145}, {22122, 22126}
X(22134) lies on these lines: {1, 6}, {3, 1409}, {47, 1333}, {48, 255}, {63, 16697}, {71, 22083}, {77, 20744}, {394, 22119}, {517, 1880}, {573, 10571}, {577, 828}, {602, 604}, {651, 17134}, {692, 18611}, {906, 2289}, {1064, 2269}, {1332, 3718}, {1397, 2352}, {1682, 7066}, {1766, 4559}, {2268, 21741}, {2280, 21743}, {2286, 3157}, {2288, 4254}, {2327, 3561}, {3167, 20752}, {3211, 7124}, {3692, 4574}, {4047, 17102}, {7352, 15945}, {20745, 22163}
X(22135) lies on these lines: {3, 22075}, {6, 25}, {394, 10316}, {1503, 13854}, {5596, 8879}, {17409, 19149}
X(22135) = isogonal conjugate of polar conjugate of X(5596)
X(22135) = isotomic conjugate of polar conjugate of X(20993)
X(22136) lies on these lines: {1, 15910}, {3, 49}, {6, 4658}, {21, 323}, {63, 23070}, {72, 18447}, {78, 22141}, {81, 6675}, {110, 2915}, {191, 8614}, {219, 3157}, {399, 16117}, {405, 1993}, {442, 3193}, {451, 2895}, {474, 15066}, {500, 2328}, {501, 1030}, {511, 20831}, {942, 2323}, {1330, 4585}, {1332, 3695}, {1994, 5047}, {2979, 20833}, {3560, 16266}, {3564, 21530}, {3916, 22128}, {3940, 7078}, {4205, 15988}, {4423, 16472}, {5422, 16842}, {5706, 17528}, {5752, 9306}, {6883, 12161}, {6985, 15068}, {7193, 11573}, {7580, 11441}, {10601, 16853}, {11004, 16859}, {15018, 17534}, {16408, 17811}, {16855, 17825}, {17814, 19541}, {17971, 22158}, {17976, 23079}, {20740, 22146}, {20762, 20809}, {22161, 22458}
X(22135) = X(92)-isoconjugate of X(34427)
X(22137) lies on these lines: {3, 22077}, {6, 16587}, {48, 3784}, {63, 20808}, {219, 23068}, {20739, 20760}
X(22137) = isogonal conjugate of polar conjugate of X(21289)
X(22137) = isotomic conjugate of polar conjugate of X(20994)
X(22138) lies on these lines: {3, 1176}, {6, 8623}, {48, 3784}, {69, 22143}, {206, 21512}, {255, 3781}, {394, 20794}, {1974, 9821}, {3313, 6660}, {9969, 21513}, {13111, 17500}, {17976, 22458}, {22062, 22151}
X(22139) lies on these lines: {3, 49}, {6, 16058}, {58, 20849}, {63, 17972}, {71, 3955}, {81, 8731}, {110, 199}, {212, 3781}, {219, 7015}, {228, 17976}, {238, 21334}, {323, 4184}, {440, 3564}, {511, 2328}, {573, 9306}, {582, 16422}, {1011, 1993}, {1214, 17975}, {1331, 3690}, {1350, 20841}, {1351, 13615}, {1654, 2905}, {2651, 17778}, {2979, 16064}, {3219, 21318}, {3819, 13329}, {4191, 15066}, {4199, 15988}, {5422, 16373}, {6090, 11350}, {6822, 17349}, {7193, 22097}, {16059, 17811}, {22060, 22128}, {22117, 22132}, {22143, 23081}
X(22139) = isogonal conjugate of polar conjugate of X(1654)
X(22139) = isotomic conjugate of polar conjugate of X(18755)
X(22139) = X(19)-isoconjugate of X(6625)
X(22140) lies on these lines: {3, 15373}, {219, 20785}, {222, 20742}, {394, 7124}, {20741, 20745}, {20807, 20814}
X(22141) lies on these lines: {3, 1331}, {78, 22136}, {219, 1807}, {394, 22142}, {651, 9945}, {1616, 10700}, {1795, 22117}, {3722, 16466}, {3927, 7004}, {4855, 23070}, {5315, 21870}, {5440, 22128}, {7074, 10703}, {16483, 17460}, {23079, 23083}
X(22142) lies on these lines: {3, 22067}, {219, 23071}, {394, 22141}
X(22143) lies on these lines: {3, 895}, {6, 694}, {32, 2936}, {69, 22138}, {71, 20802}, {99, 11596}, {248, 6391}, {648, 2782}, {1576, 2854}, {1942, 15316}, {2055, 21651}, {2393, 6660}, {2407, 9512}, {2452, 13188}, {2510, 22146}, {3095, 8541}, {3284, 8681}, {5467, 7669}, {6321, 8754}, {9214, 12355}, {9976, 15919}, {10765, 21309}, {15143, 15262}, {17976, 20746}, {19597, 22120}, {20740, 20795}, {20766, 22356}, {20785, 20813}, {20796, 22123}, {20806, 22152}, {22122, 23094}, {22139, 23081}, {22144, 22158}, {22145, 22148}
X(22143) = isogonal conjugate of polar conjugate of X(148)
X(22143) = isotomic conjugate of polar conjugate of X(20998)
X(22143) = crosssum of polar conjugates of PU(40)
X(22143) = X(19)-isoconjugate of X(35511)
X(22143) = X(92)-isoconjugate of X(9217)
X(22144) lies on these lines: {3, 906}, {6, 101}, {48, 22122}, {219, 1807}, {239, 21602}, {294, 15251}, {607, 1482}, {952, 1783}, {1421, 5540}, {1565, 1814}, {1951, 22765}, {3157, 22153}, {3211, 22124}, {4361, 21429}, {5299, 16550}, {8735, 10738}, {14578, 15905}, {17976, 20811}, {20739, 22127}, {20752, 23071}, {20762, 20809}, {20769, 20808}, {22086, 22148}, {22123, 22356}, {22132, 22147}, {22143, 22158}, {22146, 22156}
X(22145) lies on these lines: {3, 22084}, {6, 7}, {219, 20740}, {222, 3942}, {345, 394}, {692, 20871}, {1993, 3210}, {2003, 2288}, {2808, 8750}, {20742, 22133}, {20744, 22123}, {22143, 22148}
X(22145) = isogonal conjugate of polar conjugate of X(150)
X(22145) = isotomic conjugate of polar conjugate of X(20999)
X(22145) = X(92)-isoconjugate of X(34179)
X(22146) lies on these lines: {3, 248}, {6, 13}, {30, 13509}, {39, 49}, {112, 5663}, {155, 22120}, {195, 15093}, {232, 10540}, {287, 339}, {394, 4175}, {511, 13115}, {568, 10311}, {577, 23039}, {1154, 10313}, {1562, 17702}, {1968, 18439}, {1970, 14130}, {1971, 2070}, {1993, 22253}, {2079, 2088}, {2420, 10620}, {2510, 22143}, {2871, 11641}, {3289, 22121}, {5938, 14917}, {6102, 10312}, {7735, 18917}, {8779, 10317}, {10316, 18436}, {10766, 14984}, {14961, 22115}, {15905, 18877}, {20740, 22136}, {22144, 22156}
X(22147) lies on these lines: {3, 48}, {6, 7373}, {9, 10246}, {19, 8148}, {281, 12645}, {394, 23089}, {517, 18594}, {610, 12702}, {1375, 20110}, {2256, 6767}, {2323, 10680}, {5049, 16667}, {5120, 17796}, {20752, 22149}, {22124, 23071}, {22132, 22144}
X(22147) = isogonal conjugate of polar conjugate of X(2516)
X(22147) = isotomic conjugate of polar conjugate of X(21000)
X(22147) = X(19)-isoconjugate of X(36606)
X(22148) lies on these lines: {3, 1331}, {6, 6377}, {63, 17972}, {109, 2810}, {222, 295}, {394, 22149}, {1054, 14122}, {1407, 16059}, {3157, 20805}, {3167, 23089}, {3784, 20786}, {3955, 22390}, {4641, 20601}, {7078, 23085}, {10756, 14936}, {17976, 22128}, {20741, 20785}, {20744, 20796}, {22086, 22144}, {22143, 22145}, {22158, 22384}, {22458, 23070}, {23083, 23091}
X(22148) = isogonal conjugate of polar conjugate of X(4440)
X(22148) = isotomic conjugate of polar conjugate of X(9259)
X(22148) = X(19)-isoconjugate of X(6630)
X(22149) lies on these lines: {3, 63}, {57, 16409}, {144, 4192}, {219, 20785}, {222, 17976}, {329, 19540}, {394, 22148}, {846, 3295}, {851, 20078}, {956, 11688}, {968, 6767}, {1282, 6244}, {1376, 4090}, {1403, 1757}, {2223, 16570}, {2318, 3784}, {3218, 16059}, {3219, 16058}, {3504, 23091}, {3684, 16557}, {3955, 23095}, {3980, 9709}, {4067, 15654}, {9965, 16056}, {10025, 19541}, {16574, 19342}, {20745, 20765}, {20752, 22147}, {20797, 22117}, {20818, 22163}
X(22149) = isogonal conjugate of polar conjugate of X(1278)
X(22149) = isotomic conjugate of polar conjugate of X(16969)
X(22149) = X(19)-isoconjugate of X(38247)
X(22149) = X(92)-isoconjugate of X(36614)
X(22150) lies on these lines: {2, 3}, {86, 3001}
X(22151) lies on these lines: {2, 6}, {3, 22087}, {22, 19153}, {23, 6593}, {49, 15074}, {110, 2393}, {182, 5890}, {184, 11511}, {186, 249}, {206, 12220}, {287, 328}, {316, 8744}, {401, 14570}, {525, 3049}, {542, 1568}, {575, 1199}, {576, 1092}, {648, 3260}, {858, 2892}, {895, 3292}, {1147, 8538}, {1176, 11574}, {1332, 20808}, {1350, 10298}, {1351, 6644}, {1352, 7577}, {1503, 3153}, {1531, 10706}, {1570, 15560}, {1576, 3001}, {2071, 2781}, {2072, 3564}, {2930, 15826}, {2987, 14910}, {3060, 19136}, {3167, 10602}, {3266, 17708}, {3284, 4558}, {3313, 19121}, {3926, 22120}, {5038, 22416}, {5050, 7514}, {5622, 13754}, {5651, 9813}, {5866, 10766}, {6090, 11405}, {6390, 22121}, {6636, 19127}, {6660, 9407}, {6776, 18445}, {7464, 9970}, {8541, 9306}, {8549, 11441}, {8705, 19596}, {9512, 21531}, {9723, 15905}, {9967, 18475}, {9968, 12279}, {9971, 13595}, {9977, 14763}, {10564, 10752}, {10989, 19379}, {11179, 15032}, {11180, 15068}, {11470, 13346}, {14649, 18860}, {14853, 18420}, {14927, 19149}, {14984, 18449}, {15038, 18583}, {15053, 19161}, {15516, 19150}, {15818, 19125}, {16163, 19924}, {17206, 22366}, {19118, 21213}, {22062, 22138}
X(22151) = reflection of X(186) in X(15462)
X(22151) = isogonal conjugate of X(8791)
X(22151) = isotomic conjugate of polar conjugate of X(23)
X(22151) = inverse-in-MacBeath-circumconic of X(69)
X(22151) = X(19)-isoconjugate of X(67)
X(22151) = X(92)-isoconjugate of X(3455)
X(22151) = crossdifference of every pair of points on line X(512)X(1843)
X(22152) lies on these lines: {3, 69}, {6, 3229}, {25, 7779}, {160, 3630}, {193, 11328}, {219, 20785}, {237, 20080}, {264, 13108}, {2782, 14615}, {3095, 14913}, {3157, 17976}, {3289, 20233}, {5020, 7774}, {7467, 10513}, {7855, 9917}, {7877, 10790}, {8266, 15533}, {13188, 20477}, {16419, 16990}, {20769, 23086}, {20806, 22143}
X(22152) = isogonal conjugate of polar conjugate of X(20081)
X(22152) = isotomic conjugate of polar conjugate of X(21001)
X(22152) = X(19)-isoconjugate of X(38262)
X(22152) = X(92)-isoconjugate of X(36615)
X(22153) lies on these lines: {3, 48}, {6, 3333}, {9, 12675}, {56, 101}, {169, 354}, {220, 3576}, {222, 22131}, {910, 12704}, {946, 5781}, {2272, 10306}, {2911, 5022}, {3157, 22144}, {3197, 6769}, {3555, 7719}, {3730, 8273}, {7078, 7124}
X(22153) = isogonal conjugate of polar conjugate of anticomplement of X(200)
X(22153) = isogonal conjugate of polar conjugate of X(36845)
X(22153) = isotomic conjugate of polar conjugate of X(21002)
X(22154) lies on these lines: {3, 22090}, {6, 514}, {525, 3049}, {663, 16466}, {810, 22160}, {838, 3733}, {905, 4131}, {1203, 4040}, {1459, 17976}, {5711, 17072}, {6332, 20808}, {7252, 14349}, {17922, 20295}
X(22154) = isogonal conjugate of polar conjugate of anticomplement of X(649)
X(22154) = isotomic conjugate of polar conjugate of X(4057)
X(22154) = X(19)-isoconjugate of X(8050)
X(22155) lies on these lines: {3, 22092}, {6, 665}, {647, 22121}, {905, 4131}, {1459, 22157}, {2196, 22384}, {2530, 7252}, {4435, 16502}, {22086, 22144}
X(22155) = isogonal conjugate of polar conjugate of anticomplement of X(659)
X(22155) = isotomic conjugate of polar conjugate of X(21003)
X(22156) lies on these lines: {3, 4575}, {6, 16592}, {43, 5348}, {78, 22136}, {212, 3781}, {20741, 20813}, {20746, 22128}, {20760, 22130}, {22143, 22145}, {22144, 22146}
X(22156) = isogonal conjugate of polar conjugate of X(21221)
X(22156) = isotomic conjugate of polar conjugate of X(21004)
X(22157) lies on these lines: {3, 22095}, {6, 513}, {521, 2522}, {525, 3049}, {832, 7252}, {1459, 22155}, {5280, 21390}, {20816, 23092}
X(22157) = isogonal conjugate of polar conjugate of X(21301)
X(22157) = isotomic conjugate of polar conjugate of X(21005)
X(22158) lies on these lines: {3, 1332}, {48, 20762}, {219, 2196}, {17971, 22136}, {20760, 23073}, {20794, 20795}, {20796, 22356}, {22127, 23088}, {22143, 22144}, {22148, 22384}
X(22158) = isogonal conjugate of polar conjugate of X(9263)
X(22158) = isotomic conjugate of polar conjugate of X(1979)
X(22158) = X(19)-isoconjugate of X(9295)
X(22158) = X(92)-isoconjugate of X(9265)
X(22159) lies on these lines: {3, 2524}, {6, 512}, {525, 3049}, {647, 22121}, {826, 3050}, {2451, 3800}, {2510, 15451}, {5359, 5996}, {8711, 21006}
X(22159) = isogonal conjugate of polar conjugate of anticomplement of X(669)
X(22159) = isotomic conjugate of polar conjugate of X(21006)
X(22160) lies on these lines: {3, 905}, {21, 17496}, {55, 1734}, {405, 4391}, {514, 21789}, {647, 8673}, {810, 22154}, {1459, 4091}, {2401, 6914}, {3295, 3900}, {3309, 8641}, {3733, 8637}, {3803, 8642}, {5248, 8714}, {6002, 13245}, {16158, 21301}, {20796, 22383}
X(22160) = isogonal conjugate of polar conjugate of anticomplement of X(693)
X(22160) = isotomic conjugate of polar conjugate of X(21007)
X(22160) = isogonal conjugate of polar conjugate of X(17494)
X(22161) lies on these lines: {1, 9959}, {3, 73}, {55, 7186}, {63, 17972}, {219, 20785}, {228, 22128}, {333, 20256}, {394, 17976}, {651, 4192}, {1331, 3917}, {3167, 23095}, {3562, 9840}, {3781, 20804}, {4020, 7116}, {22136, 22458}
X(22161) = isogonal conjugate of polar conjugate of X(6646)
X(22161) = isotomic conjugate of polar conjugate of X(21008)
X(22162) lies on these lines: {3, 22098}, {6, 5883}, {219, 3157}, {905, 4131}, {4574, 20741}, {11573, 22054}
X(22162) = isogonal conjugate of polar conjugate of X(17491)
X(22162) = isotomic conjugate of polar conjugate of X(21009)
X(22163) lies on these lines: {3, 295}, {6, 982}, {48, 3955}, {63, 77}, {71, 3784}, {72, 22127}, {579, 1401}, {846, 2256}, {2200, 20805}, {3684, 20995}, {3927, 22126}, {4334, 17754}, {5120, 5364}, {5227, 14597}, {20739, 23070}, {20745, 22134}, {20818, 22149}
X(22163) = isogonal conjugate of polar conjugate of anticomplement of X(984)
X(22163) = isotomic conjugate of polar conjugate of X(21010)
X(22163) = isogonal conjugate of polar conjugate of X(24349)
X(22164) lies on these lines: {3, 295}, {6, 3874}, {63, 20744}, {71, 11573}, {72, 20752}, {219, 3157}, {2200, 20785}, {2284, 3730}, {3694, 14597}, {3940, 22127}, {4456, 8679}, {17165, 17915}, {20741, 23070}, {20760, 23076}, {22457, 23084}, {23077, 23083}
X(22164) = isogonal conjugate of polar conjugate of X(17165)
X(22164) = isotomic conjugate of polar conjugate of X(20990)
X(22164) = X(92)-isoconjugate of X(34443)
See Kadir Altintas and Ercole Suppa, Hyacinthos 28154.
X(22165) lies on these lines: {2, 6}, {7, 4478}, {8, 7238}, {76, 8352}, {182, 11812}, {315, 11317}, {319, 7263}, {320, 4665}, {376, 15069}, {511, 3845}, {518, 3919}, {519, 4743}, {542, 8703}, {543, 7848}, {545, 17294}, {547, 576}, {549, 8550}, {575, 11539}, {620, 8787}, {625, 16509}, {633, 5349}, {634, 5350}, {1078, 12151}, {1086, 4405}, {1350, 11001}, {1352, 3830}, {1353, 10168}, {1503, 3534}, {2321, 4912}, {2854, 3917}, {2930, 6636}, {2979, 8705}, {3081, 12583}, {3094, 11055}, {3098, 15690}, {3363, 9466}, {3416, 4677}, {3545, 11477}, {3564, 12100}, {3818, 12101}, {3819, 9027}, {3828, 4663}, {3849, 14929}, {3860, 18358}, {3933, 7810}, {3943, 4741}, {4364, 17374}, {4399, 7232}, {4643, 16676}, {4851, 16673}, {4969, 17227}, {4971, 17274}, {5066, 5480}, {5085, 15719}, {5092, 19711}, {5206,7767}, {5254, 7883}, {5476, 10109}, {5569, 7908}, {5585, 11147}, {5648, 6030}, {5921, 15697}, {5965, 15713}, {5969, 14711}, {6101, 12061}, {6776, 15698}, {7277, 17228}, {7485, 8546}, {7750, 9855}, {7751, 8360}, {7759, 8367}, {7768, 8370}, {7794, 8369}, {7811, 8598}, {7813, 15810}, {7820, 19661}, {7821, 12815}, {7854, 8359}, {7869, 8365}, {7896, 8355}, {8353, 11161}, {9830, 15300}, {10519, 19708}, {10541, 15708}, {11179, 11898}, {11645, 19710}, {14645, 19662}, {15685, 18440}, {15687, 18553}, {17132, 17345}, {17133, 17372}, {17243, 17344}, {17246, 17373}, {17272, 17390}, {17273, 17388}, {17287, 17365}, {17288, 17362}, {17295, 17334}, {17296, 17332}
X(22165) = midpoint of X(i) and X(j) for these {i,j}: {2, 15533}, {6, 11160}, {69, 599}, {376, 15069}, {1350, 11180}, {5648, 13169}, {11179, 11898}
X(22165) = reflection of X(i) in X(j) for these {i,j}: {141, 599}, {576, 547}, {597, 141}, {599, 3631}, {1353, 10168}, {1992, 3589}, {3629, 597}, {4663, 3828}, {5480, 11178}, {8550, 549}, {8584, 2}, {8787, 620}, {15687, 18553}
X(22165) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {2, 69, 15533}, {2, 8584, 597}, {69, 141, 3630}, {141, 8584, 2}, {3589, 3620, 141}, {9771, 15598, 11168}
Recalling that triangle centers are functions, at (a,b,c) = (6,9,13), the values of X(22166) and X(22266) are equal.
See Kadir Altintas and Ercole Suppa, Hyacinthos 28177.
X(22166) lies on these lines: {1, 2}, {4902, 7988}
X(22167) lies on these lines: {10, 22172}, {37, 42}, {38, 192}, {75, 244}, {141, 3123}, {145, 984}, {256, 6542}, {536, 4022}, {594, 3122}, {678, 15624}, {688, 21834}, {714, 4043}, {726, 3702}, {740, 4642}, {982, 1278}, {1221, 18059}, {2170, 20864}, {2228, 17229}, {2292, 3993}, {2310, 3056}, {2321, 3778}, {3120, 21927}, {3121, 6378}, {3747, 21061}, {3764, 17299}, {3840, 20892}, {3877, 17460}, {3943, 21035}, {3954, 20686}, {3963, 21100}, {3994, 21080}, {4033, 21238}, {4046, 21936}, {4392, 4788}, {4443, 17233}, {4492, 17311}, {4516, 7237}, {4695, 4709}, {4772, 17063}, {4941, 17236}, {7148, 21024}, {17355, 20456}, {20681, 21809}, {20703, 21804}, {20707, 22168}, {21827, 22206}, {22170, 22175}, {22171, 22173}, {22177, 22193}, {22180, 22185}, {22188, 22211}, {22207, 22210}
X(22168) lies on these lines: {10, 22169}, {1441, 18210}, {2171, 21807}, {3778, 4516}, {20707, 22167}, {20975, 21011}, {22171, 22181}, {22172, 22210}, {22201, 22209}
X(22169) lies on these lines: {10, 22168}, {42, 181}, {71, 20975}, {216, 22389}, {307, 18210}, {6467, 20777}, {20775, 22059}, {20821, 22370}, {22173, 22174}, {22175, 22195}, {22176, 22194}, {22181, 22213}, {22200, 22201}
X(22170) lies on these lines: {10, 22168}, {20975, 21012}, {22167, 22175}, {22186, 22213}
X(22171) lies on these lines: {10, 22200}, {37, 22325}, {321, 3125}, {756, 3954}, {982, 21902}, {3124, 15523}, {3452, 17435}, {3701, 22039}, {3721, 3971}, {3773, 21954}, {3930, 21796}, {7237, 20709}, {20255, 21416}, {21345, 22215}, {21827, 22220}, {22167, 22173}, {22168, 22181}, {22177, 22198}, {22180, 22189}, {22188, 22193}, {22201, 22204}, {22207, 22208}
X(22172) lies on these lines: {9, 20456}, {10, 22167}, {37, 3122}, {42, 4890}, {71, 20984}, {142, 3123}, {192, 17065}, {244, 3663}, {256, 16826}, {291, 17261}, {756, 3986}, {982, 17247}, {1400, 3747}, {1964, 8610}, {2228, 17243}, {2309, 17053}, {3009, 21746}, {3728, 5257}, {3764, 16777}, {3948, 21095}, {3963, 21257}, {4022, 4364}, {4356, 4642}, {4357, 21330}, {4443, 4687}, {4446, 4664}, {4484, 16675}, {4499, 7240}, {4695, 4780}, {4704, 12782}, {4941, 17063}, {20683, 21826}, {20684, 21827}, {20686, 21808}, {20711, 21101}, {21345, 22232}, {22168, 22210}, {22187, 22197}, {22201, 22227}
X(22173) lies on these lines: {2, 2170}, {10, 20684}, {42, 16583}, {43, 17451}, {210, 20706}, {756, 20681}, {2171, 2238}, {2294, 21904}, {3740, 20593}, {3930, 4685}, {4642, 21838}, {4695, 21877}, {16606, 21951}, {20686, 20709}, {21044, 21925}, {21345, 22220}, {21827, 22215}, {22167, 22171}, {22169, 22174}, {22193, 22211}, {22194, 22219}
X(22174) lies on these lines: {2, 256}, {9, 20984}, {10, 22167}, {38, 17065}, {42, 21892}, {238, 19318}, {244, 4357}, {750, 1716}, {756, 3778}, {1213, 3122}, {1962, 2092}, {2228, 4698}, {3123, 3739}, {4022, 4708}, {4772, 4941}, {5224, 21330}, {8040, 20966}, {14815, 17514}, {17063, 17236}, {18904, 21921}, {21827, 22201}, {22169, 22173}, {22176, 22198}, {22182, 22210}, {22203, 22204}
X(22175) lies on these lines: {10, 22194}, {22167, 22170}, {22169, 22195}
X(22176) lies on these lines: {10, 22195}, {22167, 22170}, {22169, 22194}, {22174, 22198}
X(22177) lies on these lines: {228, 1962}, {18671, 20760}, {21827, 22197}, {22167, 22193}, {22169, 22173}, {22171, 22198}, {22184, 22194}
X(22178) lies on these lines: {10, 22168}, {20975, 21016}
X(22179) lies on these lines: {10, 22168}, {20975, 21017}, {22223, 22228}
X(22180) lies on these lines: {42, 3970}, {1930, 4475}, {3125, 7148}, {3728, 3954}, {21827, 22203}, {22167, 22185}, {22171, 22189}, {22181, 22188}, {22190, 22210}
X(22181) lies on these lines: {10, 22204}, {22168, 22171}, {22169, 22213}, {22180, 22188}, {22209, 22218}
X(22182) lies on these lines: {20707, 22167}, {22174, 22210}, {22189, 22196}
X(22183) lies on these lines: {20707, 22167}
X(22184) lies on these lines: {10, 21345}, {37, 4685}, {75, 6379}, {740, 21838}, {756, 20688}, {1015, 4359}, {1107, 4970}, {1500, 3896}, {1962, 6155}, {2229, 17163}, {3121, 21020}, {3210, 16975}, {3696, 16584}, {3741, 6377}, {4093, 4111}, {4457, 21897}, {4651, 21327}, {4709, 21877}, {18904, 21085}, {22167, 22171}, {22177, 22194}, {22206, 22215}
X(22185) lies on these lines: {10, 22232}, {3294, 20681}, {21802, 21803}, {22167, 22180}
X(22186) lies on these lines: {10, 22201}, {1084, 21022}, {3121, 3963}, {21238, 21835}, {22168, 22171}, {22170, 22213}, {22204, 22209}
X(22187) lies on these lines: {1423, 21328}, {20707, 22167}, {22169, 22173}, {22172, 22197}
X(22188) lies on these lines: {22167, 22211}, {22171, 22193}, {22180, 22181}
X(22189) lies on these lines: {10, 22167}, {37, 22293}, {76, 21330}, {244, 20888}, {756, 3970}, {3122, 21024}, {3123, 21240}, {3501, 20984}, {3728, 4890}, {3778, 21071}, {3954, 20711}, {21257, 22028}, {22171, 22180}, {22182, 22196}, {22202, 22210}
X(22190) lies on these lines: {10, 22167}, {76, 244}, {756, 3954}, {3122, 7148}, {3123, 20255}, {3721, 20711}, {6376, 21330}, {22180, 22210}
X(22191) lies on these lines: {10, 22208}, {22167, 22171}, {22215, 22220}, {22222, 22223}
X(22192) lies on these lines: {10, 22207}, {22167, 22171}
X(22193) lies on these lines: {21827, 22225}, {22167, 22177}, {22171, 22188}, {22173, 22211}
X(22194) lies on these lines: {10, 22175}, {3675, 20880}, {3721, 4516}, {3954, 20704}, {4890, 21804}, {20707, 22167}, {22169, 22176}, {22171, 22180}, {22173, 22219}, {22177, 22184}
X(22195) lies on these lines: {10, 22176}, {756, 21804}, {2321, 4516}, {20545, 20633}, {20594, 20864}, {20684, 22206}, {20707, 22167}, {22169, 22175}, {22171, 22188}, {22210, 22214}
X(22196) lies on these lines: {37, 2209}, {181, 756}, {321, 17891}, {2643, 21713}, {22167, 22180}, {22168, 22171}, {22182, 22189}
X(22197) lies on these lines: {1, 41}, {10, 20684}, {28, 19554}, {72, 20706}, {213, 2171}, {960, 20593}, {1953, 2176}, {1959, 16827}, {2218, 9447}, {3294, 21809}, {16524, 18671}, {21044, 21930}, {21827, 22177}, {22167, 22180}, {22172, 22187}, {22210, 22219}, {22218, 22220}
X(22198) lies on these lines: {1962, 4890}, {3061, 20864}, {20684, 21827}, {20707, 22167}, {22171, 22177}, {22174, 22176}
X(22199) lies on these lines: {1, 21838}, {2, 668}, {6, 23374}, {38, 3121}, {39, 42}, {43, 2275}, {75, 6379}, {76, 21223}, {244, 22173}, {292, 3961}, {518, 16584}, {519, 21877}, {672, 20228}, {726, 21345}, {893, 32913}, {982, 6377}, {984, 21827}, {1011, 2241}, {1278, 36645}, {1449, 2276}, {1500, 17018}, {1574, 4651}, {1575, 4541}, {1757, 30646}, {2092, 16778}, {2229, 17135}, {2238, 17053}, {2886, 16592}, {3510, 24575}, {3681, 21830}, {3741, 16606}, {3778, 20462}, {3971, 20363}, {4022, 6375}, {8624, 21750}, {9284, 29655}, {9336, 25502}, {16058, 16781}, {16345, 31490}, {16746, 16887}, {17165, 21327}, {18152, 26815}, {18172, 20255}, {18904, 33064}, {18905, 29673}, {20457, 23638}, {20688, 32925}, {20859, 20870}, {20861, 23636}, {20864, 23362}, {21080, 23488}, {21226, 31008}, {21330, 22171}, {21757, 23579}, {21796, 37657}, {22343, 23415}, {23413, 23418}, {23414, 23416}, {23420, 23436}, {23423, 23428}, {23431, 23452}, {23448, 23451}, {23470, 23538}, {23546, 23548}, {23574, 24534}, {24519, 34063}, {25286, 27035}, {25287, 27091}, {26973, 30955}, {30647, 32912}
X(22200) lies on these lines: {1, 3981}, {2, 20861}, {10, 22171}, {42, 2054}, {51, 21760}, {71, 20461}, {213, 21813}, {740, 21954}, {1196, 1197}, {3051, 20961}, {3122, 16584}, {3125, 3914}, {3271, 21757}, {3720, 20859}, {3721, 4425}, {3774, 21936}, {3778, 21838}, {3948, 22039}, {14599, 20988}, {17889, 20271}, {20684, 21827}, {22169, 22201}
X(22201) lies on these lines: {10, 22186}, {37, 4033}, {142, 1646}, {1084, 21035}, {2092, 21814}, {3121, 3778}, {21798, 21819}, {21827, 22174}, {22168, 22209}, {22169, 22200}, {22171, 22204}, {22172, 22227}
X(22202) lies on these lines: {1, 6}, {10, 22171}, {986, 21883}, {2292, 21820}, {3124, 20653}, {3125, 4647}, {3721, 4037}, {22167, 22180}, {22189, 22210}, {22207, 22225}
X(22203) lies on these lines: {1962, 20703}, {21827, 22180}, {22174, 22204}
X(22204) lies on these lines: {10, 22181}, {2092, 3930}, {22171, 22201}, {22174, 22203}, {22186, 22209}
X(22205) lies on these lines: {37, 16609}, {1334, 21830}, {3709, 7064}, {20684, 21827}, {21795, 21796}
X(22206) lies on these lines: {10, 22171}, {37, 43}, {76, 321}, {141, 21416}, {756, 762}, {984, 21883}, {2321, 3971}, {3097, 21877}, {3124, 8013}, {3125, 21020}, {3208, 21879}, {3681, 21839}, {3728, 21838}, {20684, 22195}, {20690, 21833}, {21827, 22167}, {22184, 22215}
X(22207) lies on these lines: {10, 22192}, {37, 1018}, {2087, 4738}, {22167, 22210}, {22171, 22208}, {22202, 22225}
X(22208) lies on these lines: {10, 22191}, {37, 758}, {22171, 22207}
X(22209) lies on these lines: {10, 22213}, {3121, 4516}, {21043, 21906}, {22168, 22201}, {22181, 22218}, {22186, 22204}, {22210, 22227}, {22211, 22215}
X(22210) lies on these lines: {10, 22175}, {11, 1111}, {2642, 2643}, {17463, 21138}, {18210, 21144}, {22167, 22207}, {22168, 22172}, {22174, 22182}, {22180, 22190}, {22189, 22202}, {22195, 22214}, {22197, 22219}, {22209, 22227}, {22212, 22225}, {22215, 22216}
X(22211) lies on these lines: {22167, 22188}, {22173, 22193}, {22209, 22215}
X(22212) lies on these lines: {4516, 21824}, {22210, 22225}
X(22213) lies on these lines: {10, 22209}, {21047, 21906}, {22169, 22181}, {22170, 22186}
X(22214) lies on these lines: {10, 22167}, {37, 4890}, {210, 21826}, {2321, 3122}, {3123, 21255}, {3663, 21330}, {3728, 3986}, {3778, 3950}, {4029, 21035}, {4431, 17065}, {5257, 21699}, {21100, 21257}, {22195, 22210}
X(22215) lies on these lines: {10, 22192}, {244, 665}, {21345, 22171}, {21827, 22173}, {22184, 22206}, {22191, 22220}, {22209, 22211}, {22210, 22216}
X(22216) lies on these lines: {1962, 14404}, {4132, 7234}, {4453, 14421}, {4730, 21828}, {22210, 22215}
X(22217) lies on these lines: {22168, 22171}, {22221, 22226}
X(22218) lies on these lines: {10, 22186}, {37, 42}, {313, 1084}, {321, 6378}, {561, 2998}, {6375, 20891}, {6377, 20892}, {17451, 20363}, {21257, 21835}, {22181, 22209}, {22197, 22220}
X(22219) lies on these lines: {10, 22167}, {244, 3673}, {2310, 20271}, {3122, 21049}, {3123, 21258}, {22173, 22194}, {22197, 22210}
X(22220) lies on these lines: {10, 22167}, {37, 65}, {244, 726}, {518, 1149}, {740, 4695}, {756, 4090}, {984, 3616}, {986, 4704}, {2170, 20363}, {3122, 3932}, {3123, 3836}, {3125, 20688}, {3728, 3842}, {3778, 4078}, {3790, 17065}, {3930, 21830}, {3993, 4642}, {20366, 20598}, {21345, 22173}, {21827, 22171}, {22191, 22215}, {22197, 22218}
X(22221) lies on these lines: {2491, 21050}, {22217, 22226}
X(22222) lies on these lines: {10, 22229}, {512, 16589}, {665, 4391}, {2524, 21838}, {2533, 3709}, {4147, 21348}, {22191, 22223}
X(22223) lies on these lines: {3766, 14431}, {4455, 22319}, {17990, 21832}, {22179, 22228}, {22191, 22222}, {22210, 22215}
X(22224) lies on these lines: {10, 21056}, {667, 22381}, {798, 21051}, {1577, 21832}, {4079, 22320}, {4705, 9279}, {14407, 21901}, {16589, 21836}, {17072, 20979}, {22191, 22222}
X(22225) lies on these lines: {3125, 21824}, {21827, 22193}, {22202, 22207}, {22209, 22211}, {22210, 22212}
X(22226) lies on these lines: {75, 21351}, {325, 523}, {3221, 3728}, {4516, 22227}, {20711, 21834}, {22217, 22221}
X(22226) = isotomic conjugate of X(35573)
X(22227) lies on these lines: {351, 865}, {1646, 3123}, {4516, 22226}, {22172, 22201}, {22209, 22210}
X(22228) lies on these lines: {9402, 21836}, {22179, 22223}, {22217, 22221}
X(22229) lies on these lines: {10, 22222}, {37, 21051}, {512, 1500}, {523, 21901}, {665, 1734}, {1577, 4140}, {2276, 4367}, {2489, 3709}, {7180, 8611}, {17072, 21348}
X(22230) lies on these lines: {2, 257}, {9, 8238}, {10, 20684}, {37, 42}, {38, 20284}, {1011, 2312}, {1215, 20706}, {1926, 18152}, {2170, 3741}, {2227, 3863}, {2280, 2287}, {2292, 21838}, {3496, 4203}, {3721, 16606}, {3938, 16969}, {4095, 4651}, {4642, 21877}, {15523, 21025}, {16569, 16611}, {21827, 22171}, {22184, 22206}
X(22231) lies on these lines: {21829, 21839}, {22167, 22180}, {22191, 22222}
X(22232) lies on these lines: {10, 22185}, {1962, 21796}, {21345, 22172}, {21827, 22174}, {22167, 22171}
See Kadir Altintas and Peter Moses, Hyacinthos 28156.
X(22233) lies on these lines: {6,1173}, {3567,15750}, {5447,15018}, {9777,11464}, {10545,14627}, {11438,15004}, {13363,15019}
Let ABC be a triangle, G its centroid and A'B'C' its McCay triangle. Let Ka be the symmedian point of GB'C' and Ka' the reflection of Ka in B'C'. Define Kb' and Kc' cyclically. The lines AKa', BKb', CKc' concur in X(22234).
See César Lozada, Hyacinthos 28167.
X(22234) lies on these lines: {2, 10185}, {3, 6}, {23, 15004}, {140, 8584}, {184, 14002}, {524, 632}, {542, 3091}, {546, 5476}, {597, 3628}, {895, 13472}, {1199, 15058}, {1352, 15022}, {1353, 6329}, {1493, 8542}, {1595, 15471}, {1992, 3525}, {1995, 13366}, {2548, 20398}, {2854, 15026}, {3090, 7856}, {3146, 11179}, {3292, 5422}, {3518, 8541}, {3526, 15534}, {3529, 20423}, {3544, 14561}, {3564, 12812}, {3567, 11649}, {3618, 5965}, {3818, 3857}, {4663, 15178}, {5032, 10168}, {5072, 18553}, {5079, 15069}, {5480, 12102}, {5609, 9976}, {5643, 5651}, {9306, 11422}, {10169, 18381}, {10282, 11216}, {11004, 22112}, {11255, 12107}, {11470, 14865}, {12105, 15826}, {12151, 17130}, {12811, 18583}, {14035, 18800}, {14869, 20583}, {14912, 19130}, {15018, 16187}, {17538, 19924}
X(22234) = inverse-in-Brocard-circle of X(22330)
X(22234) = inverse-in-circle-{{X(371),X(372),PU(1),PU(39)}} of X(8589)
X(22234) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 22330), (6, 182, 15520), (6, 575, 576), (6, 5050, 5097), (61, 62, 574), (371, 372, 8589), (575, 576, 182), (575, 5097, 20190), (575, 20190, 5050), (576, 3098, 11477), (3098, 5050, 182), (3592, 3594, 15815), (5050, 5097, 3098), (5050, 11477, 20190), (5097, 20190, 11477), (6419, 6420, 39), (11477, 20190, 3098)
Let ABC be a triangle, G its centroid and A'B'C' its inner Napoleon triangle. Let Ka be the symmedian point of GB'C' and Ka' the reflection of Ka in B'C'. Define Kb' and Kc' cyclically. The lines AKa', BKb', CKc' concur in X(22235).
See César Lozada, Hyacinthos 28167.
X(22235) lies on the Kiepert hyperbola and these lines: {2, 397}, {4, 11408}, {6, 5068}, {13, 20}, {14, 3091}, {15, 5366}, {16, 10188}, {17, 3523}, {18, 5056}, {61, 3839}, {62, 7486}, {396, 3146}, {398, 3854}, {459, 470}, {2041, 9693}, {2043, 14241}, {2044, 14226}, {2045, 3316}, {2046, 3317}, {3424, 5869}, {3522, 5340}, {3543, 12816}, {3832, 5339}, {5059, 5318}, {5237, 15721}, {5343, 16808}, {5352, 15697}, {5485, 11303}, {10303, 10653}, {10304, 16965}, {10611, 22113}, {10654, 12821}, {11289, 18840}, {11290, 18841}, {11304, 18842}, {15640, 16962}, {15717, 16644}
X(22235) = isogonal conjugate of X(22236)
X(22235) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 5068, 22237), (17, 5335, 3523), (5340, 11488, 3522)
See César Lozada, Hyacinthos 28167.
X(22236) lies on these lines: {2, 398}, {3, 6}, {4, 396}, {5, 5339}, {13, 382}, {14, 1656}, {17, 381}, {18, 3526}, {20, 397}, {30, 5340}, {55, 2307}, {140, 16645}, {154, 3129}, {203, 3295}, {302, 22114}, {303, 7773}, {394, 11127}, {395, 631}, {546, 18582}, {550, 10653}, {617, 11289}, {627, 5858}, {628, 11290}, {632, 11543}, {633, 11307}, {634, 5859}, {636, 11297}, {999, 7005}, {1080, 5868}, {1147, 11137}, {1498, 11243}, {1593, 8740}, {1657, 16965}, {1993, 11146}, {2981, 14170}, {3090, 5334}, {3091, 5321}, {3130, 17810}, {3146, 5318}, {3205, 9703}, {3303, 10638}, {3304, 7051}, {3515, 8739}, {3523, 16773}, {3529, 5335}, {3543, 5350}, {3545, 5343}, {3627, 11542}, {3628, 18581}, {3642, 6694}, {3830, 16267}, {3832, 5349}, {3855, 5365}, {5072, 16809}, {5076, 16960}, {5079, 16966}, {5198, 10641}, {5217, 7127}, {5362, 16865}, {5366, 15682}, {5367, 17572}, {5422, 11145}, {5869, 6770}, {6671, 11309}, {6695, 11302}, {9763, 11304}, {10303, 11489}, {10594, 10632}, {10676, 17826}, {11244, 17821}, {11403, 11408}, {11555, 15441}, {13846, 18585}, {13847, 15765}, {14138, 16626}, {15668, 21903}, {15693, 16963}, {15694, 16268}, {15720, 16242}, {17259, 21932}
X(22236) = reflection of X(22238) in X(22331)
X(22236) = isogonal conjugate of X(22235)
X(22236) = inverse-in-Brocard-circle of X(22238)
X(22236) = X(22333)-cross conjugate of X(22238)
X(22236) = X(22334)-Ceva conjugate of X(22238)
X(22236) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 22238), (3, 61, 6), (3, 5611, 5865), (3, 5865, 1350), (3, 11485, 61), (3, 11486, 5237), (6, 11480, 11481), (15, 61, 3), (16, 5352, 3), (39, 10541, 22238), (61, 3389, 6420), (61, 5238, 62), (61, 14539, 7772), (62, 5238, 3), (398, 16772, 2), (576, 21401, 3), (3311, 3365, 6), (3389, 3390, 10646), (5237, 10645, 3)
Let ABC be a triangle, G its centroid and A'B'C' its outer Napoleon triangle. Let Ka be the symmedian point of GB'C' and Ka' the reflection of Ka in B'C'. Define Kb' and Kc' cyclically. Then the lines AKa', BKb', CKc' concur in X(22237).
See César Lozada, Hyacinthos 28167.
X(22237) lies on the Kiepert hyperbola and these lines: {2, 398}, {4, 11409}, {6, 5068}, {13, 3091}, {14, 20}, {15, 10187}, {16, 5365}, {17, 5056}, {18, 3523}, {61, 7486}, {62, 3839}, {395, 3146}, {397, 3854}, {459, 471}, {2042, 9693}, {2043, 14226}, {2044, 14241}, {2045, 3317}, {2046, 3316}, {3424, 5868}, {3522, 5339}, {3543, 12817}, {3832, 5340}, {5059, 5321}, {5238, 15721}, {5344, 16809}, {5351, 15697}, {5485, 11304}, {10303, 10654}, {10304, 16964}, {10653, 12820}, {11289, 18841}, {11290, 18840}, {11303, 18842}, {15640, 16963}, {15717, 16645}
X(22237) = isogonal conjugate of X(22238)
X(22237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 5068, 22235), (18, 5334, 3523), (5339, 11489, 3522)
See César Lozada, Hyacinthos 28167.
X(22238) lies on these lines: {2, 397}, {3, 6}, {4, 395}, {5, 5340}, {13, 1656}, {14, 382}, {17, 3526}, {18, 381}, {20, 398}, {30, 5339}, {56, 7127}, {140, 16644}, {154, 3130}, {202, 3295}, {302, 7773}, {303, 22113}, {383, 5869}, {394, 11126}, {396, 631}, {532, 11302}, {546, 18581}, {550, 10654}, {616, 11290}, {627, 11289}, {628, 5859}, {632, 11542}, {633, 5858}, {634, 11308}, {635, 11298}, {999, 7006}, {1147, 11134}, {1250, 3303}, {1498, 11244}, {1593, 8739}, {1657, 16964}, {1993, 11145}, {2307, 5204}, {3090, 5335}, {3091,f 5318}, {3129, 17810}, {3146, 5321}, {3206, 9703}, {3304, 19373}, {3515, 8740}, {3523, 16772}, {3529, 5334}, {3543, 5349}, {3545, 5344}, {3627, 11543}, {3628, 18582}, {3643, 6695}, {3830, 16268}, {3832, 5350}, {3855, 5366}, {5072, 16808}, {5076, 16961}, {5079, 16967}, {5198, 10642}, {5362, 17572}, {5365, 15682}, {5367, 16865}, {5422, 11146}, {5868, 6773}, {6151, 14169}, {6672, 11310}, {6694, 11301}, {9761, 11303}, {10303, 11488}, {10594, 10633}, {10675, 17827}, {11243, 17821}, {11403, 11409}, {11556, 15442}, {13846, 15765}, {13847, 18585}, {14139, 16627}, {15668, 21932}, {15693, 16962}, {15694, 16267}, {15720, 16241}, {17259, 21903}
X(22238) = reflection of X(22236) in X(22331)
X(22238) = isogonal conjugate of X(22237)
X(22238) = inverse-in-Brocard-circle of X(22236)
X(22238) = X(22333)-cross conjugate of X(22236)
X(22238) = X(22334)-Ceva conjugate of X(22236)
X(22238) = {{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 22236), (3, 62, 6), (3, 5615, 5864), (3, 5864, 1350), (3, 11485, 5238), (3, 11486, 62), (6, 11481, 11480), (15, 5351, 3), (16, 61, 5237), (16, 62, 3), (39, 10541, 22236), (62, 3365, 6419), (62, 14538, 7772), (371, 372, 11486), (397, 16773, 2), (1151, 1152, 11481), (3312, 3389, 6), (3364, 3365, 10645), (5238, 10646, 3)
X(22239) lies on the circumcircle and these lines: {4,2693}, {24,477}, {25,2697}, {28,2694}, {30,5897}, {74,403}, {110,8057}, {111,16318}, {112,6587}, {186,1294}, {468,1297}, {523,1301}, {691,2409}, {841,18533}, {842,6353}, {925,7480}, {1290,7435}, {1295,2074}, {2691,4244}, {3565,7473}, {4240,10420}, {5878,18809}, {5896,10151}, {7471,13398}, {7482,20187}
X(22239) = reflection of X(1301) in the Euler line
X(22239) = polar circle inverse of X(16177)
X(22239) = Collings transform of X(10151)
X(22239) = X(9033)-cross conjugate of X(4)
X(22239) = X(656)-isoconjugate of X(2071)
X(22239) = cevapoint of X(i) and X(j) for these (i,j): {25, 1637}, {523, 10151}
X(22239) = trilinear pole of line {6, 1562}
X(22239) = Λ;(X(1636), X(2433))
X(22239) = barycentric product X(648)*X(11744)
X(22239) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 2071}, {1637, 16177}, {11744, 525}
X(22240) lies on these lines: {2,216}, {3,112}, {6,22}, {20,39}, {23,5158}, {26,10312}, {32,7488}, {53,5133}, {187,10298}, {217,5889}, {376,14961}, {401,3329}, {566,858}, {570,1370}, {574,2071}, {577,6636}, {800,1194}, {1249,7494}, {1500,9538}, {1609,1627}, {1625,11459}, {1968,14118}, {1990,7495}, {1995,11062}, {2070,10986}, {2207,7503}, {2275,4296}, {2276,3100}, {2373,9087}, {2493,18573}, {2697,6795}, {2979,3289}, {3003,7493}, {3087,7500}, {3091,3199}, {3153,5475}, {3269,15072}, {3284,7492}, {3314,11672}, {3331,15305}, {5013,11413}, {5024,21312}, {5359,8573}, {5523,15760}, {6676,16318}, {6997,14576}, {7426,16328}, {7502,10317}, {7512,10316}, {7539,11197}, {7745,12225}, {7761,13219}, {9157,19153}, {9300,13351}, {9605,11414}, {9909,15851}, {10314,13595}, {10979,15246}, {11174,20477}, {15340,18474}, {15574,20806}, {16303,16387}, {19149,19158}
X(22240) = crosssum of X(125) and X(3288)
X(22240) = X(3402)-anticomplementary conjugate of X(8878)
X(22240) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 232, 15355), (6, 22, 10313), (216, 232, 2), (800, 1194, 5304), (11417, 11418, 19121)
X(22241) lies on these lines: {3,69}, {25,8024}, {76,6642}, {99,15574}, {315,12085}, {325,9818}, {394,14961}, {1593,7776}, {1975,7387}, {2071,10513}, {5024,15066}, {7393,7763}, {8369,8573}
X(22242) lies on this line: {3,6}
X(22242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 574, 14630), (6, 1380, 1379), (6, 1384, 3557), (6, 2028, 1380)
X(22243) lies on this line: {3,6}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 574, 14631), (6, 1379, 1380), (6, 1384, 3558), (6, 2029, 1379)
X(22244) lies on the Kiepert hyperbola and these lines: {597,14632}, {599,6177}, {2482,3413}, {3414,5461}
X(22245) lies on the Kiepert hyperbola and these lines: {597,14633}, {599,6178}, {2482,3414}, {3413,5461}
X(22246) lies on these lines: {3,6}, {30,14482}, {538,14535}, {1180,20850}, {1285,15688}, {1383,9909}, {1597,8744}, {2549,15684}, {3054,5319}, {3108,21448}, {3793,5032}, {3815,15703}, {3830,15048}, {3851,5286}, {5054,5304}, {5055,7736}, {5070,5305}, {5354,16419}, {6767,9331}, {7373,9336}, {7735,15694}, {7737,15685}, {7738,17800}, {7739,14269}, {7770,20105}, {8148,9575}, {8362,20080}, {9300,19709}, {13192,20854}, {14996,21526}, {14997,21514}, {15681,18907}, {15722,21843}
X(22246) = midpoint of X(i) and X(j) for these {i,j}: {14482, 14930}
X(22246) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 39, 1384), (6, 3053, 14075), (6, 5013, 5008), (6, 5024, 21309), (6, 5210, 5007), (574, 5041, 6), (5008, 5013, 15655), (5024, 21309, 3), (6199, 6395, 12017), (11485, 11486, 5085), (15603, 21309, 1384)
X(22247) lies on these lines: {2,99}, {30,6721}, {98,15709}, {114,5054}, {140,542}, {141,1153}, {325,5215}, {549,2794}, {597,6680}, {599,3788}, {754,22110}, {1656,9880}, {1992,7764}, {2782,10124}, {2796,19878}, {3055,14762}, {3090,12117}, {3525,14981}, {3526,8724}, {3533,12243}, {3619,8593}, {3624,9881}, {3763,10488}, {5026,19662}, {5070,10992}, {5071,21166}, {5182,7815}, {5477,21356}, {5569,7778}, {5969,6683}, {6033,15701}, {6036,11539}, {6054,15702}, {6055,15561}, {6292,8786}, {7749,7870}, {7801,8860}, {7804,9771}, {7810,7907}, {7813,8859}, {7817,9607}, {7830,7940}, {7833,11149}, {7880,11168}, {8252,13968}, {8253,13908}, {8997,13847}, {9780,9884}, {9875,19872}, {9876,16419}, {10303,10991}, {10722,15698}, {11164,18424}, {11725,19883}, {12042,15713}, {12258,19862}, {13846,13989}, {15810,15814}, {16239,20398}, {18800,21358}
X(22247) = midpoint of X(i) and X(j) for these {i,j}: {2, 620}, {2482, 5461}, {5026, 19662}, {8724, 11623}
X(22247) = reflection of X(i) in X(j) for these {i,j}: {6722, 2}
X(22247) = complement X(5461)
X(22247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 99, 14971), (2, 2482, 5461), (2, 7618, 7844), (2, 7622, 4045), (2, 9167, 620), (115, 2482, 8591), (620, 5461, 2482), (15561, 15694, 6055)
X(22247) = X(2)-daleth conjugate of X(8591)
X(22248) lies on this line: {2,3}
X(22248) = {X(140),X(15690)}-harmonic conjugate of X(10300)
X(22249) lies on these lines: {2,3}, {3292,11694}, {11561,13392}, {11695,13365}, {18400,20396}
X(22249) = midpoint of X(i) and X(j) for these {i,j}: {140,7575}, {468,18571}, {546,10295}, {548,11799}, {7426,12100}, {10096,15646}, {11694,15361}, {12105,15122}
X(22249) = reflection of X(15122) in X(12108)
X(22249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (140, 12100, 7496), (186, 14940, 10295), (468, 18579, 18571), (548, 10096, 11799), (7575, 15646, 7488), (11799, 15646, 548)
X(22250) lies on these lines: {110,12100}, {140,3448}, {546,10733}, {547,5972}, {548,1511}, {5642,12101}, {11812,14683}, {12308,14891}, {12383,12812}
X(22251) lies on these lines: {3,13392}, {5,1511}, {30,15040}, {110,549}, {113,15704}, {125,11539}, {140,3448}, {399,3530}, {541,15714}, {542,15713}, {547,12902}, {550,7728}, {632,15027}, {1353,15462}, {3524,12308}, {3627,14643}, {3628,12383}, {3819,15101}, {3845,12121}, {3857,10733}, {3861,15046}, {5054,14683}, {5642,8703}, {5655,15036}, {5663,15712}, {7471,11749}, {9143,11812}, {10264,14869}, {10283,12778}, {10620,12100}, {10721,19710}, {10819,19116}, {10820,19117}, {11801,15699}, {12041,17504}, {12108,15039}, {12317,15720}, {14677,16534}, {16532,22115}
X(22251) = midpoint of X(3) and X(20125)
X(22251) = {X(10272),X(15035)}-harmonic conjugate of X(550)
X(22252) lies on these lines: {32,8790}, {3186,3511}
X(22252) = antitomic image of X(9230)
X(22252) = X(i)-isoconjugate of X(j) for these (i,j): {695, 18272}, {9236, 19573}, {9288, 19566}, {14946, 18270}
X(22252) = barycentric quotient X(i)/X(j) for these {i,j}: {384, 19566}, {1582, 18272}, {1925, 18276}, {1965, 18271}, {9230, 19573}, {16985, 19585}
X(22253) lies on these lines: {2,14482}, {3,194}, {5,6392}, {6,538}, {25,8267}, {30,193}, {39,15271}, {69,11287}, {76,9605}, {99,1384}, {115,9766}, {141,7739}, {148,3830}, {183,5024}, {187,8716}, {192,6767}, {325,11318}, {330,7373}, {376,3793}, {381,7774}, {382,7762}, {384,20105}, {511,14532}, {524,2549}, {543,10488}, {546,2996}, {574,8667}, {599,4045}, {671,7926}, {754,6144}, {1003,7766}, {1184,19568}, {1351,2782}, {1597,9308}, {1654,11359}, {1655,11108}, {1657,20065}, {1975,3972}, {1992,11159}, {1993,22146}, {1995,9870}, {3053,7781}, {3060,16983}, {3180,11296}, {3181,11295}, {3210,3732}, {3363,5485}, {3629,7737}, {3843,7785}, {3851,13571}, {3926,5305}, {3933,5286}, {5013,7751}, {5041,17130}, {5054,17008}, {5055,7777}, {5073,7823}, {5254,7758}, {5304,8369}, {5309,7778}, {5319,7789}, {5346,7863}, {5355,7801}, {5858,6772}, {5859,6775}, {5969,11173}, {6390,7735}, {7738,7767}, {7748,7890}, {7764,13881}, {7765,7784}, {7770,7839}, {7773,7905}, {7779,7841}, {7780,15815}, {7788,7790}, {7796,7851}, {7797,7881}, {7800,9607}, {7817,7908}, {7827,7868}, {7845,11648}, {7848,15533}, {7861,7916}, {7864,7879}, {7872,7882}, {7887,7906}, {7895,7902}, {8359,15589}, {8556,15482}, {10796,11482}, {11054,11163}, {11185,15484}, {11285,17129}, {11354,17379}, {14712,15681}, {14929,20080}, {15694,17004}, {15703,17005}, {16370,17002}, {16371,17001}, {16417,16997}, {16418,16998}, {16857,17000}, {20794,21177}
X(22253) = reflection of X(i) in X(j) for these {i,j}: {6, 7798}, {69, 15048}, {7737, 3629}, {11159, 1992}, {20080, 14929}
X(22253) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (39, 17131, 15271), (69, 15048, 11287), (99, 14614, 1384), (183, 7757, 5024), (194, 7754, 3), (1003, 7766, 21309), (3933, 5286, 7866), (5254, 7758, 7776), (5309, 7813, 7778), (6390, 7735, 11288), (7765, 7855, 7784), (7781, 7805, 3053), (7839, 20081, 7770)
X(22254) lies on these lines: {2,39}, {30,17941}, {316,5468}, {671,1641}, {868,7809}, {1989,18896}, {5108,7790}
X(22254) = X(798)-isoconjugate of X(20404)
X(22254) = crosssum of X(6041) and X(21906)
X(22254) = barycentric quotient X(99)/X(20404)
X(22254) = {X(2),X(2396)}-harmonic conjugate of X(7799)
X(22255) lies on the cubic K091 and this line: {523,10510}
X(22256) lies on the cubic K091 and these lines: {67,316}, {99,523}
X(22257) lies on the cubic K096 and these lines: {5,8798}, {52,382}, {216,631}, {324,3832}, {548,15912}, {5070,14059}
X(22257) = reflection of X(8798) in X(14363)
X(22257) = X(20)-Ceva conjugate of X(5)
X(22258) lies on the cubic K108 and these lines:{3,15899}, {187,8428}, {858,6390}, {2393,2930}, {5094,14357}
X(22258) = isogonal conjugate of X(11061)
X(22258) = X(i)-cross conjugate of X(j) for these (i,j): {1205, 4}, {3455, 6}
X(22258) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11061}, {896, 10416}, {15900, 16568}
X(22258) = X(23)-vertex conjugate of X(23)
X(22258) = X(25)-vertex conjugate of X(3447)
X(22258) = crosssum of X(2930) and X(15141)
X(22258) = barycentric product X(i)*X(j) for these {i,j}: {6, 14364}, {671, 10417}
X(22258) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11061}, {111, 10416}, {3455, 15900}, {10417, 524}, {14364, 76}
X(22259) lies on the cubic K108 and these lines: {2,13140}, {23,524}, {187,18374}, {1499,5621}, {2393,10355}
X(22259) = isogonal conjugate of X(14360)
X(22259) = anticomplement X(13140)
X(22259) = X(3455)-cross conjugate of X(25)
X(22259) = X(524)-vertex conjugate of X(524)
X(22259) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14360}, {2, 16563}, {75, 2930}, {662, 18310}, {14210, 15899}
X(22259) = barycentric product X(6)X(13574)
X(22259) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 14360}, {31, 16563}, {32, 2930}, {512, 18310}, {13574, 76}
X(22260) lies on the cubic K153 and these lines: on lines {6,512}, {141,523}, {520,6391}, {669,6041}, {850,1502}, {888,3569}, {1499,21850}, {1648,8029}, {1974,2422}, {2492,2872}, {3221,9973}, {3566,15583}, {3589,11183}, {3618,5652}, {4024,21713}, {4108,7806}, {4705,21810}, {5092,9175}, {5996,7777}, {6071,21906}, {6088,9208}, {7927,18311}, {9137,10546}
X(22260) = reflection of X(i) in X(j) for these {i,j}: {5027, 2492}, {9171, 9178}, {9426, 2489}
X(22260) = isogonal conjugate of X(31614)
X(22260) = X(i)-Ceva conjugate of X(j) for these (i,j): {512, 3124}, {850, 115}, {2489, 1084}, {9178, 21906}
X(22260) = X(i)-isoconjugate of X(j) for these (i,j): {249, 799}, {643, 7340}, {662, 4590}, {670, 1101}, {763, 6632}, {1414, 6064}, {4556, 4601}, {4567, 4610}, {4570, 4623}, {4592, 18020}, {4612, 4620}
X(22260) = crosspoint of X(i) and X(j) for these (i,j): {115, 850}, {512, 3124}, {2489, 8754}
X(22260) = crossdifference of every pair of points on line {249, 524}
X(22260) = crosssum of X(i) and X(j) for these (i,j): {99, 4590}, {249, 1576}, {523, 14061}, {524, 14443}
X(22260) = barycentric product X(i)*X(j) for these {i,j}: {6, 8029}, {42, 21131}, {115, 512}, {125, 2489}, {338, 669}, {513, 21833}, {523, 3124}, {525, 2971}, {594, 8034}, {647, 8754}, {649, 21043}, {661, 2643}, {762, 764}, {798, 1109}, {850, 1084}, {868, 2422}, {1365, 3709}, {1648, 9178}, {2088, 15475}, {2207, 5489}, {2333, 21134}, {2501, 20975}, {2799, 15630}, {2970, 3049}, {3120, 4079}, {3121, 4036}, {3122, 4024}, {3125, 4705}, {4092, 7180}, {4117, 20948}, {5466, 21906}, {6328, 8574}, {6535, 21143}, {10278, 19610}, {10630, 14443}, {12079, 14398}
X(22260) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 670}, {338, 4609}, {512, 4590}, {669, 249}, {1084, 110}, {1109, 4602}, {1356, 4565}, {1645, 5118}, {1924, 1101}, {2086, 17941}, {2489, 18020}, {2643, 799}, {2971, 648}, {3122, 4610}, {3124, 99}, {3125, 4623}, {3709, 6064}, {4079, 4600}, {4117, 163}, {4516, 4631}, {4705, 4601}, {7063, 5546}, {7180, 7340}, {8027, 763}, {8029, 76}, {8034, 1509}, {8754, 6331}, {9427, 1576}, {15630, 2966}, {20975, 4563}, {21043, 1978}, {21131, 310}, {21143, 6628}, {21833, 668}, {21906, 5468}
{X(2492),X(5027)}-harmonic conjugate of X(14428)
X(22261) lies on the conic {{A,B,C,X(4),X(5)}}, the cubic K158, and on these lines: {4,8154}, {5,578}, {24,13450}, {53,571}, {311,1975}, {1141,12289}, {1658,5961}, {2165,14533}, {3071,8911}, {3613,11424}, {6293,9512}, {7544,10548}, {8800,12605}, {14674,18436}, {14889,18377}, {15033,16837}
X(22261) = isogonal conjugate of X(5889)
X(22261) = X(i)-cross conjugate of X(j) for these (i,j): {136, 523}, {418, 6}, {21659, 4}
X(22261) = cevapoint of X(i) and X(j) for these (i,j): {3, 12429}
X(22261) = trilinear pole of line {2451, 12077}
X(22261) = barycentric quotient X(6)/X(5889)
X(22262) lies on the cubic K161 and these lines: {159,394}, {206,19615}, {315,5596}
X(22262) = X(19615)-Ceva conjugate of X(32)
X(22262) = X(i)-isoconjugate of X(j) for these (i,j): {2, 20931}, {75, 5596}, {76, 16544}, {274, 21079}, {304, 8879}, {561, 20993}, {668, 21190}, {1969, 22135}
X(22262) = barycentric product X(i)*X(j) for these {i,j}: {66, 19615}, {2156, 19616}, {2353, 19613}
X(22262) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 20931}, {32, 5596}, {560, 16544}, {1501, 20993}, {1918, 21079}, {1919, 21190}, {1974, 8879}, {14575, 22135}, {19615, 315}, {19616, 20641}
X(22263) = lies on the cubic K173 and these lines: {232,1184}, {325,7386}, {511,1181}, {3089,6530}
X(22263) = isogonal conjugate of X(14826)
X(22264) = X[850] - 5 X[15059]
X(22264) lies on the cubic K869 and these lines: {2,879}, {125,647}, {468,512}, {520,11064}, {525,5159}, {690,9209}, {850,15059}, {974,9242}, {1942,14220}, {2433,5094}, {3049,3231}, {3154,15359}, {6698,9030}, {8675,15118}, {11176,14271}
X(22264) = midpoint of X(125) and X(647)
X(22264) = crossdifference of every pair of points on line {4230, 6787}
X(22264) = barycentric product X(525)X(2452)
X(22264) = barycentric quotient X(2452)/X(648)
X(22265) lies on the cubic K873 and these lines: {2,11656}, {4,542}, {74,98}, {99,15035}, {110,1316}, {111,1640}, {113,147}, {115,6794}, {125,14651}, {140,14850}, {146,5984}, {148,17702}, {247,3448}, {541,11177}, {842,3906}, {868,9140}, {1511,13188}, {1648,14834}, {2777,9862}, {2784,12368}, {2794,10721}, {2966,11676}, {5465,6054}, {5622,18338}, {5663,12188}, {6055,11006}, {6321,10733}, {8724,15000}, {10264,14849}, {10766,11646}, {11623,15357}, {12042,15055}, {13169,19905}, {13172,16163}, {15036,21166}, {15928,16261}
X(22265) = midpoint of X(146) and X(5984)
X(22265) = reflection of X(i) in X(j) for these {i,j}: {2, 11656}, {4, 16278}, {74, 98}, {110, 18332}, {147, 113}, {6054, 5465}, {9140, 11632}, {10706, 9144}, {10733, 6321}, {11005, 115}, {11006, 6055}, {13169, 19905}, {13172, 16163}, {13188, 1511}, {14094, 15342}, {15357, 11623}, {15545, 15535}, {18331, 125}
X(22265) = anticomplement of the anticomplement of X(33511)
X(22265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (115, 11005, 14644), (11632, 15545, 15535), (14651, 18331, 125), (15535, 15545, 9140)
Recalling that triangle centers are functions, at (a,b,c) = (6,9,13), the values of X(22166) and X(22266) are equal.
See César Lozada, Hyacinthos 28173.
X(22266) lies on these lines: {1, 2}, {548, 11231}, {1657, 10164}, {3579, 3850}, {3627, 10175}, {3740, 4537}, {3812, 4525}, {3817, 12812}, {3843, 6684}, {3947, 4114}, {4072, 16674}, {4744, 5044}, {5072, 18483}, {5217, 19538}, {9956, 15712}, {10172, 12702}, {12108, 17502}, {14891, 18480}, {15828, 17303}, {17538, 19925}
X(22266) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3617, 4701), (1, 4691, 3625), (1, 19877, 3634), (1, 19883, 15808), (2, 4668, 1125), (1125, 20057, 551), (1698, 19877, 3828), (3244, 19875, 10), (3626, 3634, 19872), (3626, 19872, 19862), (3634, 3828, 1), (3634, 9780, 19862), (4678, 5550, 1), (4691, 20053, 4669), (9780, 19862, 10), (9780, 19872, 3626)
X(22267) lies on these lines:
See Kadir Altintas and Ercole Suppa, Hyacinthos 28175.
X(22268) lies on these lines: {2,14978}, {3,233}, {5,12013}, {97,140}, {195,394}, {216,14938}, {632,14919}
X(22268) = crosssum of X(i) and X(j) for these (i,j): {195,15805}
See Kadir Altintas and Ercole Suppa, Hyacinthos 28176.
X(22268) lies on this line: {4, 12013}
See Antreas Hatzipolakis and Angel Montesdeoca Hyacinthos Hyacinthos 28174 and HG060918.
X(22270) lies on these lines: :{3,6748}, {97,631}, {140,394}, {1073,3526}, {1214,6958}, {1232,3926}, {3525,14919}, {3682,21012}, {13336,17974}
X(22271) lies on these lines: {8, 22272}, {10, 141}, {37, 42}, {44, 1918}, {71, 3059}, {72, 3696}, {75, 3681}, {192, 19998}, {200, 15624}, {313, 22289}, {319, 4553}, {513, 4416}, {517, 4793}, {536, 4685}, {594, 4111}, {668, 6385}, {674, 3686}, {692, 2287}, {740, 3159}, {758, 4732}, {899, 4022}, {984, 3293}, {2874, 4148}, {3294, 4068}, {3555, 16828}, {3664, 9038}, {3688, 17362}, {3690, 4046}, {3740, 4698}, {3779, 17275}, {3789, 4657}, {3842, 4015}, {3873, 4751}, {3941, 21384}, {3943, 7064}, {3952, 4043}, {4053, 21804}, {4061, 8804}, {4097, 15733}, {4134, 4709}, {4399, 14839}, {4517, 17299}, {4557, 21061}, {4661, 4699}, {4686, 22313}, {4690, 17792}, {4735, 21857}, {4738, 22306}, {5044, 15569}, {5739, 11677}, {5814, 22283}, {6007, 17332}, {8053, 16552}, {9054, 17049}, {17135, 18137}, {17330, 21746}, {17751, 20923}, {20694, 21873}, {21035, 21858}, {21083, 21085}, {21881, 21897}, {22274, 22280}, {22282, 22296}, {22291, 22309}
X(22272) lies on these lines: {8, 22271}, {10, 4523}, {42, 1953}, {209, 1824}, {692, 1172}, {1234, 4463}, {4651, 21271}, {21858, 21889}, {22277, 22308}
X(22273) lies on these lines: {10, 4523}, {42, 48}, {46, 3293}, {200, 22276}, {209, 3198}, {916, 11500}, {1486, 2333}, {2801, 22312}, {4651, 21270}, {18747, 20243}, {19998, 20074}, {22278, 22279}, {22280, 22298}, {22281, 22297}, {22286, 22311}
X(22274) lies on these lines: {10, 4523}, {42, 17438}, {228, 21855}, {15624, 21860}, {22271, 22280}, {22289, 22311}
X(22275) lies on these lines: {8, 22300}, {10, 12}, {37, 7109}, {38, 42}, {40, 12548}, {55, 10477}, {69, 22282}, {71, 3693}, {75, 3681}, {306, 4437}, {312, 3869}, {313, 22291}, {321, 14973}, {354, 6682}, {517, 3706}, {537, 4685}, {714, 22316}, {740, 22024}, {986, 3293}, {1233, 22285}, {1234, 4463}, {1918, 3744}, {3210, 4661}, {3690, 3932}, {3876, 19874}, {3909, 20290}, {4001, 8679}, {4030, 9052}, {4061, 17658}, {4113, 4692}, {5044, 16828}, {5718, 9564}, {9020, 22277}, {16574, 16678}, {17137, 18138}, {18057, 22293}, {20693, 21858}, {20716, 22321}, {22306, 22307}
X(22276) lies on these lines: {1, 16455}, {5, 10}, {6, 31}, {8, 15232}, {9, 375}, {37, 181}, {51, 3683}, {63, 8679}, {65, 17056}, {72, 3704}, {100, 1812}, {197, 219}, {200, 22273}, {210, 430}, {220, 2333}, {226, 15282}, {227, 7066}, {306, 4437}, {511, 4640}, {518, 4028}, {528, 4685}, {573, 3185}, {692, 5285}, {756, 21801}, {1155, 3917}, {1376, 3781}, {1402, 2245}, {1631, 2187}, {1869, 7957}, {2258, 4277}, {2318, 4557}, {2321, 14973}, {2323, 20986}, {2389, 2900}, {3190, 15624}, {3293, 5119}, {3428, 3682}, {3434, 4651}, {3579, 13754}, {3681, 20243}, {3792, 17596}, {3827, 8896}, {3869, 4417}, {3870, 9049}, {3931, 10974}, {4061, 8804}, {4259, 17594}, {4271, 20967}, {4531, 4849}, {4646, 10822}, {5752, 12514}, {5943, 15254}, {6690, 6703}, {7998, 9352}, {8013, 21011}, {8568, 22279}, {15733, 22312}, {19998, 20075}
In the plane of a triangle ABC, let
I = incenter;
DEF = intouch triangle;
(O) = circumcircle;
P = perpendicular bisector of segment ID;
Ai = points of intersection of P and (O), and define Bi and Ci cyclically, for i = 1, 2;
Di = reflection of D in IAi, for i = 1, 2;
A' = E1E2∩F1F2, and define B' and C' cyclically;
The lines DA', EB', FC' concur in X(22277). See X(22277). (Angel Montesdeoca, August 6, 2022)
X(22277) lies on these lines: {1, 9049}, {6, 31}, {10, 141}, {37, 4890}, {41, 1631}, {43, 4446}, {44, 21746}, {46, 3293}, {48, 4497}, {65, 21867}, {69, 4651}, {72, 4026}, {181, 4849}, {193, 19998}, {210, 1213}, {218, 1486}, {354, 17245}, {511, 3579}, {524, 4685}, {579, 15624}, {583, 2223}, {742, 22316}, {758, 4085}, {872, 3778}, {1002, 4648}, {1100, 3688}, {1155, 22440}, {1269, 17165}, {1334, 4068}, {1362, 1418}, {1386, 9052}, {1400, 4557}, {1469, 3214}, {1475, 16679}, {1826, 1827}, {1843, 2355}, {1964, 20456}, {2092, 4735}, {2160, 7077}, {2174, 17798}, {2260, 2340}, {2277, 4484}, {2294, 21039}, {2321, 21865}, {2333, 7716}, {2388, 3997}, {2876, 9969}, {3271, 16669}, {3555, 4966}, {3589, 9054}, {3629, 9025}, {3681, 5224}, {3755, 20718}, {3789, 17327}, {3799, 17315}, {3827, 22290}, {3868, 4429}, {3873, 17234}, {3879, 4553}, {3941, 4253}, {4090, 20723}, {4430, 17232}, {4517, 16777}, {4524, 8675}, {4661, 17238}, {4705, 9029}, {4848, 20617}, {4852, 14839}, {4946, 9024}, {5800, 12587}, {5846, 22328}, {6007, 17351}, {9004, 22278}, {9016, 20455}, {9020, 22275}, {9021, 22285}, {9040, 22320}, {9055, 21080}, {13576, 15320}, {15185, 16593}, {17049, 17348}, {17366, 20358}, {19586, 21699}, {21863, 21889}, {22272, 22308}
X(22278) lies on these lines: {1, 16297}, {5, 10}, {42, 244}, {71, 374}, {72, 4714}, {75, 3681}, {165, 7416}, {210, 20718}, {373, 3058}, {375, 516}, {392, 19870}, {518, 4685}, {528, 5943}, {553, 9026}, {1730, 15621}, {3212, 22297}, {3293, 5902}, {3696, 14973}, {3880, 4891}, {4430, 17490}, {9004, 22277}, {14923, 18743}, {18142, 20244}, {21867, 22291}, {21888, 21902}, {22273, 22279}, {22296, 22309}
X(22279) lies on these lines: {10, 141}, {37, 3122}, {42, 1100}, {65, 20713}, {75, 22289}, {86, 4553}, {210, 21014}, {244, 17457}, {291, 16696}, {319, 4651}, {354, 15523}, {513, 894}, {674, 5750}, {1018, 4068}, {1213, 20683}, {1215, 20723}, {1631, 16788}, {3293, 4649}, {3589, 17049}, {3688, 17398}, {3753, 21867}, {3779, 17303}, {3873, 17228}, {3941, 17754}, {3943, 4890}, {4026, 20718}, {4670, 17792}, {4685, 4725}, {5285, 8021}, {6007, 7227}, {8053, 16549}, {8568, 22276}, {9049, 19868}, {14839, 17045}, {16606, 21878}, {16732, 21922}, {17140, 18143}, {17142, 18046}, {17165, 18133}, {17369, 21746}, {17384, 20358}, {21860, 21891}, {22273, 22278}, {22281, 22301}, {22303, 22304}
X(22280) lies on these lines: {10, 116}, {42, 17439}, {100, 3565}, {210, 21711}, {1824, 5139}, {3699, 3799}, {4557, 21859}, {22271, 22274}, {22273, 22298}
X(22281) lies on these lines: {10, 8230}, {42, 17440}, {22271, 22274}, {22273, 22297}, {22279, 22301}
X(22282) lies on these lines: {10, 1368}, {42, 65}, {69, 22275}, {197, 940}, {306, 22299}, {322, 22298}, {517, 4028}, {1824, 17874}, {3827, 8896}, {4651, 22297}, {10441, 11500}, {22271, 22296}, {22273, 22278}
X(22283) lies on these lines: {10, 4523}, {42, 17442}, {55, 5283}, {1228, 4463}, {5814, 22271}
X(22284) lies on these lines: {10, 4523}, {42, 18669}, {514, 22319}
X(22285) lies on these lines: {10, 626}, {42, 2240}, {72, 3696}, {1233, 22275}, {4463, 22296}, {9021, 22277}, {22286, 22291}, {22293, 22308}
X(22286) lies on these lines: {10, 16580}, {42, 4118}, {313, 22288}, {1234, 4463}, {21889, 22316}, {22273, 22311}, {22285, 22291}
X(22287) lies on these lines: {8, 22271}, {10, 21236}, {42, 17443}, {3753, 21867}, {20713, 22292}, {21035, 21889}
X(22288) lies on these lines: {8, 22271}, {10, 21237}, {42, 17444}, {313, 22286}, {3697, 21670}, {4010, 4036}, {21022, 22304}
X(22289) lies on these lines: {10, 37}, {42, 4852}, {75, 22279}, {76, 22292}, {239, 18082}, {308, 17143}, {313, 22271}, {314, 4553}, {321, 21865}, {350, 4651}, {536, 21035}, {1234, 4463}, {3293, 4716}, {3706, 15523}, {4686, 22323}, {5178, 17751}, {13476, 20913}, {17135, 18040}, {20716, 21873}, {21889, 22304}, {22274, 22311}
X(22290) lies on these lines: {8, 22271}, {10, 21239}, {42, 2262}, {517, 22312}, {2357, 21866}, {3827, 22277}, {22273, 22278}
X(22291) lies on these lines: {10, 17047}, {42, 17447}, {313, 22275}, {21867, 22278}, {22271, 22309}, {22285, 22286}
X(22292) lies on these lines: {8, 22328}, {10, 141}, {42, 1107}, {72, 20716}, {76, 22289}, {1233, 22275}, {1909, 4651}, {3678, 20723}, {3681, 6376}, {14973, 20683}, {19998, 21226}, {20691, 21035}, {20713, 22287}, {21868, 22323}
X(22293) lies on these lines: {8, 22327}, {10, 141}, {37, 22189}, {42, 17448}, {72, 20723}, {4735, 20691}, {7148, 21868}, {18057, 22275}, {20683, 21025}, {21024, 21865}, {22285, 22308}
X(22294) lies on these lines: {2, 22325}, {10, 908}, {42, 982}, {51, 4450}, {75, 3681}, {181, 4972}, {517, 4358}, {518, 4706}, {693, 2533}, {752, 20962}, {758, 4674}, {3218, 16506}, {3293, 3868}, {3909, 4645}, {3952, 20718}, {4673, 14923}, {14973, 17163}
X(22295) lies on these lines: {10, 11}, {42, 3742}, {75, 3681}, {210, 4732}, {3753, 21870}
X(22296) lies on these lines: {10, 21243}, {42, 2611}, {313, 22275}, {1824, 1882}, {4463, 22285}, {22271, 22282}, {22278, 22309}
X(22297) lies on these lines: {8, 22271}, {10, 116}, {42, 17451}, {65, 21867}, {210, 21024}, {1233, 22275}, {3212, 22278}, {4059, 9004}, {4651, 22282}, {22273, 22281}
X(22298) lies on these lines: {8, 22271}, {10, 8230}, {42, 17452}, {210, 430}, {313, 22275}, {322, 22282}, {612, 2352}, {872, 21801}, {22273, 22280}, {22308, 22312}
X(22299) lies on these lines: {1, 16287}, {5, 10}, {6, 10480}, {8, 22271}, {9, 12435}, {12, 22076}, {37, 65}, {40, 3185}, {42, 3057}, {72, 1089}, {306, 22282}, {312, 3869}, {375, 18250}, {518, 21080}, {674, 950}, {758, 3159}, {958, 10441}, {1214, 20617}, {1216, 5841}, {1826, 1829}, {1834, 10822}, {1869, 1902}, {2200, 6603}, {2829, 15644}, {3035, 15489}, {3293, 5697}, {3682, 14110}, {3690, 21677}, {3725, 4642}, {3753, 16828}, {3781, 5794}, {3827, 8804}, {3917, 7354}, {3962, 3994}, {4553, 7270}, {4651, 14923}, {5247, 18178}, {5251, 18180}, {5267, 5482}, {5562, 11827}, {8679, 12527}, {17747, 21024}, {20245, 21596}
X(22300) lies on these lines: {1, 5132}, {5, 10}, {8, 22275}, {28, 692}, {35, 18180}, {42, 65}, {51, 6284}, {71, 1212}, {72, 3696}, {171, 18178}, {181, 1834}, {185, 6253}, {197, 5706}, {209, 1829}, {375, 12572}, {389, 5842}, {392, 16828}, {513, 1770}, {518, 22316}, {910, 2200}, {1104, 1918}, {1376, 10441}, {1706, 12435}, {1715, 15622}, {1824, 1882}, {1826, 1902}, {2550, 22301}, {2807, 20420}, {3057, 21321}, {3191, 4557}, {3214, 22313}, {3293, 5903}, {3579, 6097}, {3827, 22277}, {3869, 4651}, {3877, 19874}, {3925, 22076}, {4255, 10473}, {4292, 8679}, {4673, 14923}, {4999, 15489}, {5295, 14973}, {5438, 10439}, {5446, 5840}, {7354, 16980}, {11553, 21319}, {21853, 21874}, {22308, 22317}
X(22301) lies on these lines: {6, 31}, {8, 22271}, {10, 3781}, {69, 22275}, {1155, 22412}, {2550, 22300}, {3588, 4557}, {3728, 21801}, {3869, 17788}, {5853, 22312}, {14624, 21865}, {17792, 22325}, {20694, 21871}, {20697, 21882}, {21011, 21728}, {22279, 22281}
X(22302) lies on these lines: {10, 21247}, {42, 17453}, {209, 21875}
X(22303) lies on these lines: {10, 21248}, {42, 2240}, {4651, 20911}, {22279, 22304}
X(22304) lies on these lines: {10, 16580}, {42, 17457}, {518, 3293}, {3961, 22325}, {20693, 21858}, {21022, 22288}, {21889, 22289}, {22279, 22303}
X(22305) lies on these lines: {10, 21250}, {42, 17459}, {210, 21868}, {536, 4685}, {18057, 22275}, {20713, 20721}
X(22306) lies on these lines: {10, 11}, {37, 1018}, {42, 17460}, {65, 3159}, {72, 3701}, {80, 4553}, {244, 5439}, {517, 4358}, {537, 21080}, {942, 17154}, {2835, 8804}, {3762, 14288}, {3931, 14752}, {4002, 19874}, {4738, 22271}, {20722, 22326}, {22275, 22307}
X(22307) lies on these lines: {10, 908}, {37, 758}, {42, 3899}, {72, 4066}, {517, 4793}, {519, 21080}, {3159, 4067}, {4135, 4525}, {22275, 22306}
X(22308) lies on these lines: {10, 116}, {42, 2170}, {72, 20716}, {891, 20507}, {3753, 21867}, {4651, 21272}, {4730, 21888}, {4738, 22271}, {10914, 22328}, {22272, 22277}, {22285, 22293}, {22298, 22312}, {22300, 22317}, {22310, 22321}
X(22309) lies on these lines: {10, 21252}, {42, 17463}, {4145, 21889}, {22271, 22291}, {22278, 22296}
X(22310) lies on these lines: {10, 21253}, {42, 3708}, {101, 2870}, {4155, 21889}, {21293, 21602}, {22308, 22321}
X(22311) lies on these lines: {10, 8287}, {42, 17467}, {100, 21891}, {2805, 21043}, {4436, 4705}, {4553, 17934}, {22273, 22286}, {22274, 22289}
X(22312) lies on these lines: {7, 4651}, {9, 42}, {10, 141}, {71, 3174}, {72, 3755}, {144, 19998}, {200, 579}, {209, 3059}, {210, 5257}, {516, 5752}, {517, 22290}, {527, 4685}, {758, 21867}, {1738, 5904}, {2092, 4849}, {2321, 20683}, {2801, 22273}, {3056, 4700}, {3293, 5223}, {3662, 4661}, {3681, 4357}, {3686, 3779}, {3707, 21746}, {3778, 21805}, {4029, 7064}, {4058, 21865}, {4067, 20713}, {4878, 21061}, {5853, 22301}, {9054, 17348}, {11038, 19874}, {15733, 22276}, {21039, 22021}, {22298, 22308}
X(22313) lies on these lines: {10, 11}, {37, 14752}, {42, 244}, {65, 3293}, {100, 18191}, {209, 2835}, {210, 321}, {517, 5400}, {518, 4706}, {537, 4685}, {740, 22045}, {891, 20507}, {900, 15914}, {2254, 22323}, {2262, 21858}, {3214, 22300}, {3271, 6154}, {3880, 4742}, {3893, 17751}, {4145, 21889}, {4686, 22271}, {20718, 21805}, {21832, 21888}
X(22314) lies on these lines: {10, 4928}, {42, 1635}, {210, 4155}, {513, 4380}, {812, 4685}, {891, 20507}, {3699, 3799}, {4139, 4524}, {4651, 21297}, {4705, 4825}, {4730, 21894}, {4773, 9032}, {4849, 17989}, {4893, 21727}
X(22315) lies on these lines: {10, 16581}, {42, 17472}, {1234, 4463}, {4083, 4408}
X(22316) lies on these lines: {1, 20150}, {10, 37}, {42, 75}, {192, 4651}, {209, 744}, {239, 1918}, {321, 872}, {518, 22300}, {536, 4685}, {714, 22275}, {730, 17362}, {742, 22277}, {899, 18137}, {1278, 19998}, {2667, 3896}, {4022, 17135}, {4043, 4365}, {4362, 15624}, {4726, 4946}, {21889, 22286}
X(22317) lies on these lines: {10, 141}, {210, 21921}, {1254, 21896}, {3212, 22278}, {4651, 16284}, {20683, 21049}, {22300, 22308}
X(22318) lies on these lines: {10, 3907}, {42, 17478}, {3900, 4036}, {4083, 4408}
X(22319) lies on these lines: {10, 21261}, {512, 3700}, {513, 22322}, {514, 22284}, {693, 2533}, {891, 20507}, {4455, 22223}
X(22320) lies on these lines: {10, 512}, {42, 4367}, {484, 513}, {693, 2533}, {798, 21901}, {814, 4507}, {834, 17072}, {1019, 3293}, {1577, 4132}, {3214, 4784}, {4079, 22224}, {4490, 21727}, {9040, 22277}
X(22321) lies on these lines: {10, 125}, {42, 2611}, {65, 3120}, {72, 3701}, {149, 517}, {150, 20940}, {210, 15523}, {518, 17763}, {526, 18004}, {756, 21319}, {758, 21093}, {1824, 1893}, {2610, 21888}, {2771, 15343}, {2801, 3937}, {2809, 14740}, {2818, 12691}, {3681, 3781}, {3869, 17777}, {4018, 4080}, {4145, 21889}, {4551, 18210}, {12019, 15906}, {16560, 20999}, {20716, 22275}, {22308, 22310}
X(22322) lies on these lines: {10, 21262}, {42, 17458}, {513, 22319}, {4010, 4036}, {4083, 4408}, {5283, 16692}
X(22323) lies on these lines: {10, 537}, {37, 3122}, {42, 678}, {209, 2877}, {291, 4553}, {2254, 22313}, {3293, 4663}, {4651, 4690}, {4686, 22289}, {4730, 21888}, {9016, 20455}, {14404, 21893}, {15523, 21342}, {17154, 18150}, {17351, 18082}, {17448, 22328}, {21868, 22292}
X(22324) lies on these lines: {10, 21263}, {514, 22284}, {4083, 4408}
X(22325) lies on these lines: {1, 16302}, {2, 22294}, {5, 10}, {37, 22171}, {38, 42}, {72, 3293}, {181, 4026}, {210, 321}, {536, 4685}, {740, 14973}, {1215, 20718}, {1376, 1764}, {3057, 17751}, {3681, 17147}, {3877, 18743}, {3961, 22304}, {4891, 9957}, {17792, 22301}
X(22326) lies on these lines: {10, 625}, {72, 3696}, {693, 2533}, {20722, 22306}
X(22327) lies on these lines: {8, 22293}, {10, 3934}, {42, 1100}, {75, 3681}, {321, 20723}, {524, 4685}, {2238, 21865}
X(22328) lies on these lines: {1, 22279}, {8, 22292}, {10, 3934}, {42, 2229}, {72, 3696}, {213, 21865}, {239, 18087}, {274, 4553}, {291, 18172}, {308, 17143}, {732, 17792}, {1089, 20723}, {1107, 21035}, {4651, 17152}, {5846, 22277}, {10914, 22308}, {15523, 20358}, {17448, 22323}, {20694, 21879}
Let P be a point on the circumcircle. Let T be the trilinear pole of the polar of P wrt the Brocard circle. Let T' be the isogonal conjugate of T. The locus of T' as P varies is a hyperbola centered at X(22329). (Randy Hutson, September 8, 2018)
X(22329) lies on these lines: {2, 6}, {4, 11172}, {5, 6179}, {23, 7669}, {30, 98}, {32, 8370}, {76, 8369}, {83, 8367}, {99, 9136}, {111, 6094}, {115, 3849}, {140, 7760}, {187, 543}, {237, 9149}, {297, 6103}, {315, 11318}, {316, 3793}, {351, 523}, {381, 9753}, {468, 648}, {511, 6055}, {530, 6109}, {531, 6108}, {538, 1569}, {542, 1513}, {549, 7757}, {574, 5569}, {598, 3363}, {620, 5215}, {625, 14971}, {736, 6661}, {754, 5461}, {858, 7668}, {892, 16317}, {1078, 5305}
X(22329) = midpoint of X(37785) and X(37786)
X(22329) = isotomic conjugate of X(5503)
X(22329) = complement of X(7840)
X(22329) = anticomplement of X(22110)
X(22330) lies on these lines: {3, 6}, {4, 17503}, {5, 8584}, {23, 13366}, {51, 9544}, {143, 11649}, {323, 5643}, {373, 11004}, {394, 10219}, {397, 16002}, {398, 16001}, {524, 3628}, {542, 546}, {597, 632}, {895, 1173}, {1199, 8718}
X(22330) = midpoint of X(575) and X(576)
X(22330) = isogonal conjugate of X(10185)
X(22330) = inverse-in-Brocard-circle of X(22234)
X(22330) = inverse-in-circle-{{X(371),X(372),PU(1),PU(39)}} of X(8588)
X(22330) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 22234), (61, 62 187), (371, 372, 8588)
X(22331) lies on these lines: {3,6}, {20,5306}, {23,1184}, {112,10594}, {115,5076}, {172,3303}, {230,3091}, {382,7755}, {384,8667}, {439,1992}, {546,7737}, {548,7739}, {550,5319}, {599,14001}, {609,3746}, {632,2548}, {980,21517}, {999,9341}, {1003,6179}, {1285,3090}, {1572,15178}, {1611,1627}, {1657,5309}, {1914,3304}, {1968,5198}, {2207,3518}, {2549,12103}, {3146,7735}, {3517,14581}, {3522,9607}, {3523,9300}, {3524,9606}, {3526,7753}, {3529,5254}, {3534,7765}, {3552,14614}, {3627,3767}, {3628,18907}, {3629,6337}, {3763,3785}, {3793,7795}, {3815,10303}, {3851,14537}, {3926,6144}, {5072,7746}, {5077,7902}, {5079,5475}, {5204,5332}, {5217,7296}, {5266,16672}, {5275,16865}, {5277,16842}, {5286,17538}, {5305,15704}, {5337,21496}, {5346,6781}, {5359,7492}, {5563,7031}, {6103,12173}, {7610,16924}, {7749,15484}, {7759,11288}, {7760,8716}, {7770,8556}, {7778,20065}, {7780,11286}, {7784,8363}, {7793,15271}, {7819,19661}, {7851,14712}, {7907,11184}, {7922,8366}, {8369,14023}, {8778,10311}, {9698,15720}, {9756,12110}, {9766,16925}, {9939,14043}, {11285,12150}, {11291,13847}, {11292,13846}, {11648,17800}, {11672,22333}, {12812,18584}, {14045,19569}, {14869,21843}
X(22331) = midpoint of X(22236) and X(22238)
X(22331) = X(5020)-Ceva conjugate of X(19132)
X(22331) = inverse-in-Brocard-circle of X(22332)
X(22331) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 22332), (3, 7772, 5013), (6, 3053, 5023), (6, 5023, 15815), (6, 9601, 6422), (32, 39, 21309), (32, 1384, 3053), (32, 3053, 6), (32, 5171, 12212), (32, 5206, 5008), (61, 62, 5093), (187, 7772, 3), (1151, 1152, 3098), (3053, 5013, 187), (3592, 3594, 576), (5008, 5206, 9605), (5023, 15815, 5585), (5085, 12212, 6), (5210, 21309, 6)
Let X be a point on the 2nd Brocard circle. The locus of the symmedian point of triangle XPU(1) as X varies is an ellipse with center X(22332). (Randy Hutson, September 8, 2018)
X(22332) lies on these lines: {2, 9607}, {3, 6}, {4, 9606}, {20, 9300}, {45, 988}, {115, 5079}, {140, 7739}, {194, 15271}, {230, 10303}, {232, 11403}, {546, 2549}, {549, 5319}, {599, 16043}, {632, 3767}, {1180, 1611}
X(22332) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 22331), (22236, 22238, 182)
X(22333) lies on these lines: {113, 5076}, {141, 10303}, {1192, 1511}, {11672, 22331}
X(22333) = crosspoint of X(22236) and X(22238)
X(22334) lies on the Jerabek hyperbola and these lines: {3, 13474}, {6, 9968}, {25, 3532}, {54, 1498}, {64, 5198}, {66, 5895}, {67, 12173}, {68, 3627}, {69, 3146}, {72, 1750}, {73, 3303}, {74, 1192}, {265, 5076}, {381, 14861}, {382, 3519}, {389, 3531}, {546, 4846}, {1173, 12290}, {1176, 10541}, {1181, 13472}
X(22334) isogonal conjugate of X(3522)
X(22334) cevapoint of X(22236) and X(22238)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 28188.
X(22335) lies on the conic {{A, B, C, X(4), X(5)}} and these lines: {4, 8254}, {381, 3459}, {546, 1141}, {1263, 3574}, {1487, 3850}, {3845, 15619}
X(22335) = isogonal conjugate of X(25042)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 28188.
X(22336) lies on the Jerabek hyperbola and these lines: {3, 5476}, {51, 67}, {54, 18374}, {69, 7693}, {74, 5480}, {248, 13338}, {895, 8584}, {1173, 8550}, {1176, 6329}, {1177, 10169}, {1503, 14483}, {3431, 14853}, {5486, 9971}, {6776, 14491}, {9969, 13622}, {9973, 17040}, {15360, 20582}, {19136, 19151}
X(22336) = isogonal conjugate of X(7496)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 28188.
X(22337) lies on these lines: {3, 133}, {4, 2972}, {5, 1294}, {30, 107}, {64, 265}, {122, 381}, {1478, 7158}, {1479, 3324}, {1559, 6760}, {1657, 3184}, {2790, 6321}, {2797, 6033}, {2803, 10742}, {2811, 10741}, {2822, 10739}, {2828, 10738}, {2833, 15521}, {2839, 15522}, {2846, 10740}, {2848, 12918}, {3146, 5667}, {3627, 10152}, {3845, 10714}, {7517, 14703}, {7728, 9033}, {9520, 10743}, {9524, 10744}, {9528, 10746}, {9529, 10748}, {10762, 21850}, {11718, 18481}, {11732, 18493}, {14673, 18534}
X(22337) = midpoint of X(3146) and X(5667)
X(22337) = reflection of X(i) in X(j) for these (i,j): (3, 133), (1294,5), (1657, 3184), (10762, 21850)
X(22337) = X(133)-of-X3-ABC reflections-triangle
X(22337) = X(1294)-of-Johnson-triangle
See Antreas Hatzipolakis and César Lozada, Hyacinthos 28188.
X(22338) lies on these lines: {3, 5512}, {4, 10748}, {5, 1296}, {20, 14650}, {30, 111}, {126, 381}, {265, 2780}, {382, 11258}, {543, 3830}, {590, 11835}, {615, 11836}, {1478, 6019}, {1479, 3325}, {2793, 6321}, {2805, 10742}, {2813, 10741}, {2819, 10747}, {2824, 10739}, {2830, 10738}, {2837, 15521}, {2843, 15522}, {2852, 10740}, {2854, 7728}, {3146, 14654}, {3534, 9172}, {3543, 20099}, {3627, 10734}, {3845, 10717}, {7517, 14657}, {7665, 14653}, {9129, 12121}, {9522, 10743}, {9526, 10744}, {9529, 10745}, {9531, 10746}, {10765, 21850}, {11721, 18481}, {14561, 14688}, {14645, 18346}
X(22338) = midpoint of X(i) and X(j) for these {i,j}: {382, 11258}, {3146, 14654}
X(22338) = reflection of X(i) in X(j) for these (i,j): (3, 5512), (20, 14650), (3534, 9172), (10765, 21850), (1296,5)
X(22338) = X(1296)-of-Johnson-triangle
X(22338) = X(5512)-of-X3-ABC-reflections-triangle
X(22339) lies on the cubics K242, K606, K1070 and these lines: {2,2592}, {69,2574}, {99,1113}, {264,1347}, {287,8116}, {306,2582}, {325,523}, {339,1313}, {1114,2373}, {1494,10719}, {2593,2799}, {13219,14807}, {14360,14808}
X(22339) = isotomic conjugate of X(1113)
X(22339) = anticomplement X(8105)
X(22339) = X(i)-Ceva conjugate of X(j) for these (i,j): {6331, 2593}, {15164, 69}
X(22339) = X(i)-cross conjugate of X(j) for these (i,j): {125, 2593}, {1313, 2}, {2574, 2592}
X(22339) = cevapoint of X(2) and X(14807)
X(22339) = crosspoint of X(264) and X(15164)
X(22339) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {63, 14807}, {162, 2593}, {662, 2575}, {1113, 5905}, {1822, 2}, {2575, 21221}, {2576, 193}, {2579, 148}, {2580, 4}, {2583, 3448}, {2586, 6515}, {8115, 8}, {15164, 21270}
X(22339) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2576}, {25, 1822}, {31, 1113}, {32, 2580}, {112, 2579}, {163, 8106}, {184, 2586}, {560, 15164}, {1576, 2589}, {1973, 8115}
X(22339) = barycentric product X(i)*X(j) for these {i,j}: {69, 2592}, {75, 2582}, {76, 2574}, {304, 2588}, {305, 8105}, {525, 15165}, {561, 2578}, {850, 8116}, {1114, 3267}, {1823, 20948}, {1969, 2584}, {2581, 14208}
X(22339) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2576}, {2, 1113}, {63, 1822}, {69, 8115}, {75, 2580}, {76, 15164}, {92, 2586}, {523, 8106}, {525, 2575}, {656, 2579}, {850, 2593}, {1114, 112}, {1313, 8105}, {1577, 2589}, {1823, 163}, {2574, 6}, {2578, 31}, {2581, 162}, {2582, 1}, {2584, 48}, {2588, 19}, {2592, 4}, {8105, 25}, {8115, 15461}, {8116, 110}, {14208, 2583}, {15165, 648}
X(22339) = {X(850),X(3268)}-harmonic conjugate of X(22340)
X(22339) = {P",U"}-harmonic conjugate of X(2), where P" and U" are the isotomic conjugates of the imaginary foci of the orthic inconic
X(22340) lies on the cubics K242, K606, K1070 and these lines: {2,2593}, {69,2575}, {99,1114}, {264,1346}, {287,8115}, {306,2583}, {325,523}, {339,1312}, {1113,2373}, {1494,10720}, {2592,2799}, {13219,14808}, {14360,14807}
X(22340) = isotomic conjugate of X(1114)
X(22340) = anticomplement X(8106)
X(22340) = X(i)-Ceva conjugate of X(j) for these (i,j): {6331, 2592}, {15165, 69}
X(22340) = X(i)-cross conjugate of X(j) for these (i,j): {125, 2592}, {1312, 2}, {2575, 2593}
X(22340) = cevapoint of X(2) and X(14808)
X(22340) = crosspoint of X(264) and X(15165)
X(22340) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {63, 14808}, {162, 2592}, {662, 2574}, {1114, 5905}, {1823, 2}, {2574, 21221}, {2577, 193}, {2578, 148}, {2581, 4}, {2582, 3448}, {2587, 6515}, {8116, 8}, {15165, 21270}
X(22340) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2577}, {25, 1823}, {31, 1114}, {32, 2581}, {112, 2578}, {163, 8105}, {184, 2587}, {560, 15165}, {1576, 2588}, {1973, 8116}
X(22340) = barycentric product X(i)*X(j) for these {i,j}: {69, 2593}, {75, 2583}, {76, 2575}, {304, 2589}, {305, 8106}, {525, 15164}, {561, 2579}, {850, 8115}, {1113, 3267}, {1822, 20948}, {1969, 2585}, {2580, 14208}
X(22340) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2577}, {2, 1114}, {63, 1823}, {69, 8116}, {75, 2581}, {76, 15165}, {92, 2587}, {523, 8105}, {525, 2574}, {656, 2578}, {850, 2592}, {1113, 112}, {1312, 8106}, {1577, 2588}, {1822, 163}, {2575, 6}, {2579, 31}, {2580, 162}, {2583, 1}, {2585, 48}, {2589, 19}, {2593, 4}, {8106, 25}, {8115, 110}, {8116, 15460}, {14208, 2582}, {15164, 648}
X(22340) = {X(850),X(3268)}-harmonic conjugate of X(22339)
X(22340) = {P",U"}-harmonic conjugate of X(2), where P" and U" are the isotomic conjugates of the real foci of the orthic inconic
X(22341) lies on these lines: {1, 3}, {10, 856}, {12, 18641}, {34, 13738}, {48, 577}, {72, 23067}, {73, 228}, {95, 404}, {108, 1294}, {109, 2360}, {184, 3215}, {198, 1035}, {212, 7114}, {216, 2260}, {221, 3185}, {225, 851}, {227, 11214}, {243, 411}, {255, 1092}, {283, 296}, {326, 1259}, {336, 1231}, {417, 8763}, {418, 22344}, {500, 20122}, {580, 19365}, {581, 19366}, {828, 3990}, {912, 22457}, {1042, 3724}, {1071, 20803}, {1075, 8762}, {1248, 1935}, {1284, 18589}, {1399, 2194}, {1400, 18591}, {1408, 2193}, {1435, 4191}, {1465, 16453}, {1474, 1950}, {1708, 19762}, {1745, 13855}, {1788, 6350}, {1816, 1896}, {1825, 21318}, {1875, 7420}, {1877, 13724}, {1882, 3149}, {2169, 19210}, {2720, 2744}, {3485, 6349}, {3682, 7066}, {4055, 7138}, {4225, 4296}, {5433, 7515}, {6198, 7421}, {10090, 14679}, {11375, 17073}, {16451, 17080}, {20727, 22375}, {20967, 22119}, {22053, 22347}, {22072, 22346}, {22363, 22364}
X(22341) = isogonal conjugate of X(1896)
X(22341) = isotomic conjugate of polar conjugate of X(1409)
X(22341) = X(19)-isoconjugate of X(31623)
X(22341) = X(92)-isoconjugate of X(1172)
X(22342) lies on these lines: {3, 201}, {35, 186}, {36, 12005}, {48, 3215}, {50, 1399}, {55, 20838}, {65, 3724}, {73, 228}, {252, 2962}, {477, 2222}, {1155, 15443}, {1393, 16453}, {1451, 2352}, {2171, 2178}, {3465, 7421}, {20277, 20764}, {22061, 22375}
X(22342) = isogonal conjugate of polar conjugate of X(16577)
X(22342) = isotomic conjugate of polar conjugate of X(21741)
X(22342) = {X(22346),X(22347)}-harmonic conjugate of X(3)
X(22343) lies on these lines: {1,4704}, {2,87}, {6,31}, {9,3009}, {37,3248}, {39,20667}, {44,1964}, {86,799}, {190,18170}, {192,18194}, {238,1201}, {256,8843}, {560,4268}, {572,2210}, {869,1743}, {872,16669}, {894,9359}, {899,1740}, {1015,22172}, {1045,17121}, {1149,15485}, {1178,1931}, {1193,5145}, {1334,21760}, {1475,14758}, {1977,21759}, {2053,2275}, {2234,17348}, {2347,20663}, {2667,16666}, {3271,3778}, {3720,17379}, {3736,16477}, {3747,20228}, {3764,5069}, {3840,17178}, {4003,17477}, {4128,21332}, {5053,7122}, {7189,17333}, {16571,16816}, {16604,22174}, {17351,17445}, {17448,22167}, {20456,21746}, {20460,20864}, {21757,21838}
X(22343) = isogonal conjugate of X(32011)
X(22343) = crosssum of X(2) and X(43)
X(22343) = polar conjugate of isotomic conjugate of X(22066)
X(22343) = crosspoint of X(3) and X(87)
X(22344) lies on these lines: {3, 63}, {25, 1466}, {35, 20999}, {46, 15654}, {56, 15854}, {73, 3937}, {100, 9369}, {184, 603}, {418, 22341}, {855, 1210}, {908, 19514}, {942, 7428}, {1106, 2187}, {1437, 4575}, {1470, 3556}, {1818, 22413}, {1828, 3752}, {3185, 5204}, {3689, 15625}, {3911, 13724}, {4188, 17350}, {5122, 16453}, {6705, 13734}, {8192, 10310}, {11509, 22654}, {13738, 15803}, {17102, 18210}, {20775, 20780}, {22364, 22386}, {22378, 22390}
X(22344) = isogonal conjugate of polar conjugate of X(3752)
X(22344) = isotomic conjugate of polar conjugate of X(20228)
X(22344) = X(19)-isoconjugate of X(32017)
X(22345) lies on these lines: {1, 15654}, {3, 63}, {35, 3961}, {36, 1046}, {39, 21744}, {42, 16980}, {48, 577}, {55, 8192}, {56, 3185}, {57, 13738}, {58, 4215}, {100, 4696}, {184, 255}, {197, 10834}, {198, 1466}, {222, 1410}, {283, 7015}, {404, 894}, {851, 4292}, {855, 950}, {859, 942}, {908, 19513}, {1193, 20967}, {1210, 13724}, {1399, 20986}, {1402, 1468}, {1408, 7113}, {1437, 18604}, {1486, 10835}, {1496, 2187}, {1763, 19763}, {1798, 4558}, {1818, 22078}, {1829, 3666}, {1894, 15844}, {2200, 4020}, {2352, 4252}, {2594, 8679}, {3145, 3220}, {3216, 21361}, {3218, 4225}, {3682, 3917}, {3868, 4216}, {3937, 4303}, {4185, 15509}, {4191, 15803}, {4245, 5439}, {5044, 16374}, {5217, 15624}, {6245, 13734}, {6734, 9840}, {7004, 18673}, {7289, 18606}, {9798, 11507}, {10882, 12526}, {10902, 20999}, {12680, 15622}, {13411, 21319}, {17102, 17441}, {17609, 18613}, {18210, 18732}, {20775, 22364}, {20778, 22386}, {20784, 22375}, {20785, 22061}, {22076, 22097}, {22347, 22361}
X(22345) = isogonal conjugate of polar conjugate of X(3666)
X(22345) = isotomic conjugate of polar conjugate of X(2300)
X(22345) = X(19)-isoconjugate of X(30710)
X(22345) = X(92)-isoconjugate of X(2298)
X(22346) lies on these lines: {3, 201}, {36, 5083}, {212, 7125}, {228, 3937}, {1155, 3724}, {1830, 16578}, {7069, 7416}, {8677, 22399}, {15906, 16453}, {22072, 22341}
X(22346) = isogonal conjugate of polar conjugate of X(16578)
X(22346) = isotomic conjugate of polar conjugate of X(21742)
X(22346) = {X(3),X(22342)}-harmonic conjugate of X(22347)
X(22347) lies on these lines: {3, 201}, {35, 7512}, {228, 22072}, {1393, 7420}, {1831, 16579}, {2646, 3724}, {7069, 16287}, {22053, 22341}, {22345, 22361}
X(22347) = isogonal conjugate of polar conjugate of X(16579)
X(22347) = isotomic conjugate of polar conjugate of X(21743)
X(22347) = {X(3),X(22342)}-harmonic conjugate of X(22346)
X(22348) lies on these lines: {3, 23068}, {42, 18210}, {71, 22077}, {73, 228}, {1193, 5320}, {7117, 20229}, {11393, 16580}, {22364, 22422}
X(22348) = isogonal conjugate of polar conjugate of X(16580)
X(22348) = isotomic conjugate of polar conjugate of X(21744)
X(22349) lies on these lines: {3, 23069}, {71, 22438}, {73, 228}, {22384, 22387}
X(22349) = isogonal conjugate of polar conjugate of X(16581)
X(22349) = isotomic conjugate of polar conjugate of X(21745)
X(22350) lies on these lines: {1, 2}, {3, 73}, {5, 2654}, {6, 2289}, {20, 1745}, {21, 3074}, {30, 2635}, {31, 8069}, {33, 5720}, {35, 4300}, {36, 59}, {40, 10571}, {46, 1042}, {48, 22132}, {55, 1064}, {56, 1066}, {58, 1167}, {71, 22083}, {72, 17102}, {109, 2077}, {216, 3990}, {219, 22063}, {221, 10310}, {223, 6282}, {226, 1074}, {227, 14110}, {244, 5570}, {404, 3075}, {515, 4551}, {517, 1457}, {521, 656}, {581, 3601}, {651, 6909}, {672, 3002}, {758, 1735}, {859, 2183}, {908, 1785}, {912, 7004}, {999, 1450}, {1038, 10360}, {1040, 18446}, {1060, 20277}, {1076, 5930}, {1155, 1464}, {1385, 5399}, {1409, 22071}, {1468, 22766}, {1496, 8071}, {1497, 16466}, {1739, 12736}, {1795, 22128}, {1801, 17187}, {1802, 22131}, {1807, 18455}, {1935, 6906}, {1936, 6905}, {2197, 22074}, {2252, 22059}, {2318, 3940}, {2361, 5172}, {2594, 2646}, {2650, 13750}, {2933, 14529}, {3100, 3465}, {3428, 7074}, {3468, 4296}, {3583, 6127}, {3915, 11508}, {4306, 15803}, {4337, 5010}, {5396, 14547}, {6001, 9371}, {6198, 7551}, {7117, 20752}, {9370, 12114}, {10523, 21935}, {20729, 22098}, {20821, 22076}, {22054, 22118}, {22061, 22447}, {22067, 22082}
X(22350) = isogonal conjugate of X(36123)
X(22350) = isogonal conjugate of polar conjugate of X(908)
X(22350) = isotomic conjugate of polar conjugate of X(2183)
X(22350) = crossdifference of every pair of points on line X(19)X(649)
X(22350) = X(19)-isoconjugate of X(34234)
X(22350) = X(92)-isoconjugate of X(909)
X(22351) lies on these lines: {2, 3}, {86, 8588}, {2482, 17271}, {7618, 17346}, {8182, 17378}, {8584, 18755}, {8589, 17277}, {15533, 17206}, {15655, 17379}
X(22351) = {X(2),X(3)}-harmonic conjugate of X(22355)
X(22352) lies on these lines: {2, 1495}, {3, 49}, {6, 21969}, {22, 51}, {23, 5643}, {25, 373}, {26, 13336}, {39, 1501}, {52, 7525}, {54, 15644}, {110, 3819}, {125, 6676}, {154, 5646}, {186, 16836}, {187, 3051}, {199, 13329}, {216, 8779}, {228, 20778}, {376, 11427}, {389, 7512}, {428, 3589}, {511, 1994}, {548, 10610}, {572, 16064}, {575, 3060}, {578, 10323}, {631, 10282}, {1176, 11574}, {1194, 1691}, {1340, 21032}, {1341, 21036}, {1350, 11402}, {1368, 13394}, {1428, 5310}, {1503, 7499}, {1511, 12100}, {1614, 11793}, {1619, 23041}, {1692, 20859}, {1799, 12215}, {1843, 5157}, {1899, 7494}, {1915, 5116}, {1993, 3098}, {2070, 5892}, {2076, 14153}, {2194, 5096}, {2330, 5322}, {2916, 9969}, {2937, 5462}, {2979, 11003}, {3066, 20850}, {3289, 22052}, {3398, 21512}, {3431, 19708}, {3518, 11695}, {3523, 14826}, {3524, 11464}, {3530, 5944}, {3534, 14805}, {3690, 5314}, {3787, 15513}, {3934, 10328}, {3937, 3955}, {4048, 8891}, {4175, 6390}, {5007, 11205}, {5020, 22112}, {5026, 15822}, {5050, 15004}, {5135, 5347}, {5446, 13353}, {5650, 6800}, {5946, 7555}, {6146, 16197}, {6467, 19126}, {6515, 11179}, {6660, 12054}, {6688, 13595}, {6689, 17712}, {6759, 7509}, {6823, 21659}, {7383, 9833}, {7400, 19467}, {7488, 9729}, {7495, 21243}, {7500, 14561}, {7502, 9730}, {7503, 11381}, {7514, 15030}, {7516, 10539}, {7550, 14157}, {7556, 15045}, {7558, 18381}, {7592, 14531}, {7998, 9544}, {8041, 14567}, {8627, 20965}, {8703, 10564}, {8718, 13474}, {9714, 15805}, {9738, 13616}, {9739, 13617}, {9909, 10601}, {10110, 12088}, {10170, 10540}, {10219, 16042}, {10298, 20791}, {10541, 17810}, {10691, 11064}, {11414, 11424}, {11449, 15717}, {11513, 21641}, {11514, 21640}, {11515, 21648}, {11516, 21647}, {11572, 13160}, {13347, 17928}, {13419, 14788}, {13434, 13598}, {13445, 14118}, {13851, 15760}, {14128, 23060}, {14130, 14641}, {14855, 18570}, {15107, 21849}, {17704, 22467}, {20752, 22054}, {20780, 22060}
X(22352) = isogonal conjugate of polar conjugate of X(3589)
X(22352) = isotomic conjugate of polar conjugate of X(5007)
X(22352) = isogonal conjugate of isotomic conjugate of X(7767)
X(22352) = X(92)-isoconjugate of X(3108)
X(22352) = {X(3),X(49)}-harmonic conjugate of X(5447)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 28208.
X(22353) lies on these lines: {5, 568}, {186, 476}, {230, 15355}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 28208.
X(22354) lies on these lines: {41, 2361}, {672, 5036}
X(22355) lies on these lines: {2,3}, {86,8589}, {2482,17297}, {4487,7354}, {7618,17378}, {8182,17346}, {8588,17277}, {15655,17349}, {17206,22165}
X(22355) = {X(2),X(3)}-harmonic conjugate of X(22351)
X(22356) lies on these lines: {1, 1731}, {3, 48}, {6, 1201}, {9, 2317}, {19, 7982}, {37, 21748}, {44, 1319}, {101, 953}, {112, 2755}, {184, 2318}, {220, 2267}, {228, 22372}, {284, 3746}, {374, 16666}, {517, 2173}, {519, 8756}, {520, 647}, {604, 2911}, {610, 7991}, {672, 3446}, {692, 2340}, {899, 5137}, {902, 3285}, {952, 7359}, {1023, 2325}, {1055, 2245}, {1100, 21808}, {1332, 20769}, {1334, 2278}, {1420, 1732}, {1473, 22435}, {1618, 2272}, {1797, 22128}, {1953, 10222}, {2174, 2269}, {2182, 6603}, {2197, 22058}, {2246, 18839}, {2256, 3303}, {2260, 5563}, {2261, 2324}, {2273, 7772}, {2300, 5007}, {2347, 3204}, {2364, 16676}, {3009, 16795}, {3942, 6510}, {3984, 5227}, {4466, 9028}, {5053, 5526}, {5158, 22063}, {7117, 22059}, {8609, 17439}, {15178, 17438}, {20754, 20975}, {20760, 23082}, {20766, 22143}, {20777, 22096}, {20796, 22158}, {22123, 22144}
X(22356) = isogonal conjugate of X(6336)
X(22356) = isotomic conjugate of polar conjugate of X(902)
X(22356) = X(19)-isoconjugate of X(903)
X(22357) lies on these lines: {3, 48}, {228, 22096}, {284, 5563}, {1055, 2278}, {1201, 3285}, {1385, 2173}, {1790, 1797}, {1953, 15178}, {2267, 3207}, {3284, 22063}, {3304, 37519}, {3955, 23081}, {4289, 17474}, {10222, 17438}
X(22357) = isogonal conjugate of polar conjugate of X(551)
X(22357) = isotomic conjugate of polar conjugate of X(21747)
X(22358) lies on these lines: {2, 3}, {86, 10485}, {8586, 17277}
X(22359) lies on these lines: {2, 3}, {86, 10979}, {17277, 22052}
X(22360) lies on these lines: {2, 3}, {86, 12212}, {2271, 16990}, {3329, 17206}, {13331, 17277}
X(22361) lies on these lines: {1, 6875}, {3, 73}, {21, 1936}, {47, 1064}, {55, 1468}, {58, 14547}, {71, 577}, {165, 21147}, {283, 6514}, {411, 1935}, {417, 8763}, {602, 1450}, {896, 1858}, {902, 3057}, {1006, 3075}, {1040, 4652}, {1155, 1254}, {1193, 2361}, {1259, 2318}, {1333, 2269}, {1364, 22076}, {1399, 4300}, {1407, 5204}, {1457, 11012}, {1745, 6876}, {1794, 1795}, {2646, 2650}, {3074, 6905}, {3601, 4257}, {3915, 10966}, {3916, 7004}, {5217, 7074}, {6149, 14794}, {14597, 22054}, {20753, 22390}, {20775, 20780}, {22345, 22347}
X(22361) = isogonal conjugate of polar conjugate of X(5745)
X(22361) = isotomic conjugate of polar conjugate of X(21748)
X(22362) lies on these lines: {3, 23074}, {73, 22422}, {228, 22402}, {14597, 22075}
X(22362) = isogonal conjugate of polar conjugate of X(16582)
X(22362) = isotomic conjugate of polar conjugate of X(21749)
X(22363) lies on these lines: {3, 326}, {25, 18615}, {31, 1974}, {71, 228}, {184, 14597}, {1040, 1473}, {1402, 1918}, {2178, 18611}, {7083, 16583}, {20775, 20780}, {22094, 22402}, {22341, 22364}
X(22363) = isogonal conjugate of polar conjugate of X(16583)
X(22363) = isotomic conjugate of polar conjugate of X(21750)
X(22363) = crosssum of X(4) and X(75)
X(22363) = crosspoint of X(3) and X(31)
X(22364) lies on these lines: {3, 304}, {71, 22367}, {73, 22373}, {228, 22061}, {682, 22368}, {863, 16583}, {20775, 22345}, {22341, 22363}, {22344, 22386}, {22348, 22422}
X(22364) = isogonal conjugate of polar conjugate of X(16584)
X(22364) = isotomic conjugate of polar conjugate of X(21751)
X(22365) lies on these lines: {2, 3}, {86, 10316}, {5224, 14376}, {7767, 18643}, {17206, 20806}
X(22366) lies on these lines: {2, 3}, {86, 10317}, {17206, 22151}
X(22367) lies on these lines: {3, 23077}, {71, 22364}, {228, 20727}, {1818, 22078}, {3690, 20777}, {22061, 22373}
X(22367) = isogonal conjugate of polar conjugate of X(16587)
X(22367) = isotomic conjugate of polar conjugate of X(21752)
X(22368) lies on these lines: {3, 348}, {55, 2295}, {212, 7116}, {408, 22369}, {682, 22364}, {20775, 20780}
X(22368) = isogonal conjugate of polar conjugate of X(16588)
X(22368) = isotomic conjugate of polar conjugate of X(9449)
X(22369) lies on these lines: {3, 69}, {71, 228}, {237, 1030}, {408, 22368}, {851, 5218}, {966, 1011}, {1213, 8053}, {1654, 4184}, {1818, 22076}, {2092, 2223}, {2238, 20992}, {2245, 3779}, {2642, 8638}, {3941, 4272}, {4191, 4648}, {4210, 17300}, {18591, 20728}, {20750, 22054}, {22072, 22079}, {22082, 22373}, {22097, 22412}
X(22369) = isogonal conjugate of polar conjugate of X(16589)
X(22369) = isotomic conjugate of polar conjugate of X(21753)
X(22370) lies on these lines: {1, 3778}, {2, 2269}, {3, 22378}, {9, 1654}, {40, 4645}, {43, 2209}, {46, 3178}, {48, 1332}, {55, 17792}, {57, 17300}, {63, 69}, {75, 21231}, {77, 2197}, {78, 3781}, {87, 2108}, {100, 1253}, {190, 17786}, {192, 1423}, {193, 672}, {219, 20769}, {228, 3504}, {239, 3169}, {304, 4019}, {344, 2183}, {385, 7075}, {573, 3912}, {579, 3879}, {604, 21495}, {894, 3501}, {966, 3305}, {1018, 3729}, {1025, 1419}, {1040, 22418}, {1334, 17257}, {1400, 5933}, {1424, 7783}, {1716, 3747}, {1742, 3888}, {1818, 4855}, {2245, 4851}, {2268, 15988}, {3056, 8299}, {3218, 17375}, {3219, 17343}, {3306, 4648}, {3685, 6210}, {3730, 4416}, {3779, 3870}, {3784, 22413}, {4110, 4595}, {4266, 17353}, {4271, 17279}, {4553, 15624}, {4660, 5119}, {5036, 17311}, {5440, 22083}, {8680, 20930}, {9025, 20992}, {14923, 17868}, {16574, 17296}, {16609, 20171}, {17294, 21061}, {17298, 20367}, {17363, 21384}, {17379, 17754}, {20775, 20787}, {20777, 20794}, {20821, 22169}
X(22370) = isogonal conjugate of polar conjugate of X(6376)
X(22370) = isotomic conjugate of polar conjugate of X(43)
X(22370) = X(3)-Ceva conjugate of X(63)
X(22370) = X(19)-isoconjugate of X(87)
X(22371) lies on these lines: {3, 1331}, {71, 22372}, {184, 23073}, {212, 3270}, {228, 22096}, {1623, 2810}, {20975, 22080}
X(22371) = isogonal conjugate of polar conjugate of X(4370)
X(22371) = isotomic conjugate of polar conjugate of X(1017)
X(22371) = X(92)-isoconjugate of X(2226)
X(22372) lies on these lines: {3, 22067}, {71, 22371}, {228, 22356}, {22080, 22429}
X(22372) = isogonal conjugate of polar conjugate of X(16590)
X(22372) = isotomic conjugate of polar conjugate of X(21754)
X(22373) lies on these lines: {3, 4592}, {73, 22364}, {228, 22375}, {667, 20982}, {3023, 4367}, {3937, 22386}, {7117, 20975}, {20727, 22381}, {20738, 20787}, {20754, 20777}, {22061, 22367}, {22082, 22369}
X(22373) = isogonal conjugate of polar conjugate of X(16592)
X(22373) = isotomic conjugate of polar conjugate of X(21755)
X(22374) lies on these lines: {2, 3}, {4383, 22380}, {25083, 36504}
X(22375) lies on these lines: {3, 3708}, {228, 22373}, {647, 22055}, {20727, 22341}, {20784, 22345}, {22061, 22342}
X(22375) = isogonal conjugate of polar conjugate of X(16598)
X(22375) = isotomic conjugate of polar conjugate of X(21756)
X(22376) lies on these lines: {3, 63}, {36, 20843}, {3893, 8683}, {3937, 22072}, {5122, 7428}, {20780, 22378}
X(22376) = isogonal conjugate of polar conjugate of X(16602)
X(22377) lies on these lines: {2, 3}, {50, 86}, {323, 17206}, {566, 17277}, {3580, 18755}, {17271, 18375}
X(22378) lies on these lines: {3, 22370}, {48, 20777}, {69, 20757}, {71, 20759}, {228, 20775}, {1444, 22449}, {20753, 20781}, {20780, 22376}, {22056, 22079}, {22344, 22390}
X(22378) = isogonal conjugate of polar conjugate of X(16604)
X(22378) = isotomic conjugate of polar conjugate of X(21757)
X(22379) lies on these lines: {3, 23087}, {36, 3738}, {56, 1769}, {526, 3724}, {667, 6085}, {905, 2850}, {1459, 1946}, {3937, 22096}, {4768, 8666}
X(22379) = isogonal conjugate of polar conjugate of X(3960)
X(22379) = isotomic conjugate of polar conjugate of X(21758)
X(22379) = X(19)-isoconjugate of X(36804)
X(22380) lies on these lines: {3, 6}, {980, 18134}, {986, 2276}, {1575, 16583}, {1759, 17596}, {2275, 16787}, {5283, 16062}
X(22381) lies on these lines: {3, 22370}, {25, 2053}, {32, 2209}, {63, 3504}, {87, 19762}, {98, 932}, {184, 15373}, {228, 22061}, {667, 22224}, {1402, 3747}, {1799, 22449}, {2196, 17970}, {2319, 5285}, {14199, 17797}, {20727, 22373}, {20996, 21857}, {22066, 22096}
X(22381) = isogonal conjugate of polar conjugate of X(16606)
X(22381) = isotomic conjugate of polar conjugate of X(21759)
X(22381) = X(19)-isoconjugate of X(31008)
X(22381) = X(92)-isoconjugate of X(27644)
X(22382) lies on these lines: {3, 822}, {48, 8611}, {284, 16612}, {450, 8062}, {662, 18020}, {1813, 9358}, {2249, 2706}, {6332, 8632}, {20731, 20757}
X(22382) = isogonal conjugate of polar conjugate of X(8062)
X(22382) = isotomic conjugate of polar conjugate of X(21761)
X(22383) lies on these lines: {6, 650}, {31, 8641}, {81, 693}, {112, 2719}, {513, 1430}, {514, 21117}, {520, 647}, {521, 2522}, {649, 854}, {654, 6589}, {656, 2523}, {661, 20980}, {667, 838}, {788, 8646}, {810, 822}, {894, 21438}, {905, 4131}, {940, 4885}, {1021, 21173}, {1364, 22432}, {2451, 17418}, {2504, 17094}, {2720, 7115}, {3287, 6590}, {3288, 4449}, {3738, 16612}, {3758, 21611}, {4394, 21786}, {4790, 21007}, {5040, 20983}, {6373, 8633}, {6586, 9404}, {9010, 21005}, {11269, 15280}, {20729, 22059}, {20731, 20757}, {20796, 22160}, {22444, 22445}
X(22383) = isogonal conjugate of X(6335)
X(22383) = isotomic conjugate of polar conjugate of X(667)
X(22383) = X(2)-Ceva conjugate of X(34467)
X(22383) = crossdifference of every pair of points on line X(4)X(8)
X(22383) = polar conjugate of isotomic conjugate of X(23224)
X(22383) = X(19)-isoconjugate of X(668)
X(22384) lies on these lines: {3, 22437}, {31, 2254}, {58, 3960}, {238, 3716}, {514, 21761}, {520, 647}, {580, 2814}, {595, 3887}, {659, 3808}, {810, 22154}, {905, 22093}, {928, 8578}, {1193, 8648}, {1331, 1332}, {1468, 14413}, {1724, 3762}, {1946, 22090}, {2196, 22155}, {3915, 4895}, {3937, 22096}, {22148, 22158}, {22349, 22387}, {23069, 23092}
X(22384) = isogonal conjugate of polar conjugate of X(812)
X(22384) = isotomic conjugate of polar conjugate of X(8632)
X(22384) = X(19)-isoconjugate of X(4562)
X(22384) = X(92)-isoconjugate of X(813)
X(22385) lies on these lines: {3,6}
X(22386) lies on these lines: {3, 4561}, {669, 4128}, {1015, 8637}, {3937, 22373}, {16695, 21138}, {20778, 22345}, {22344, 22364}
X(22386) = isogonal conjugate of polar conjugate of X(6377)
X(22386) = isotomic conjugate of polar conjugate of X(21762)
X(22387) lies on these lines: {3, 23092}, {3736, 4369}, {20731, 20757}, {20828, 22095}, {22349, 22384}
X(22387) = isotomic conjugate of polar conjugate of X(21763)
X(22388) lies on these lines: {3, 4025}, {32, 21122}, {187, 237}, {228, 652}, {1011, 3239}, {2352, 6589}, {4191, 7658}
X(22388) = isogonal conjugate of polar conjugate of X(6586)
X(22389) lies on these lines: {3, 22370}, {48, 184}, {63, 20794}, {69, 22449}, {71, 20775}, {216, 22169}, {237, 2269}, {283, 7015}, {1444, 22060}, {2223, 7122}, {6467, 22070}, {11574, 20821}, {18210, 18606}, {20750, 22054}, {20769, 23079}, {20975, 22058}
X(22389) = isogonal conjugate of polar conjugate of X(1107)
X(22389) = isotomic conjugate of polar conjugate of X(1197)
X(22389) = X(19)-isoconjugate of X(1221)
X(22389) = X(92)-isoconjugate of X(1258)
X(22390) lies on these lines: {3, 48}, {22, 14547}, {42, 5347}, {56, 19133}, {73, 1176}, {182, 2183}, {184, 22097}, {198, 5085}, {212, 3796}, {228, 20778}, {326, 4652}, {511, 2317}, {560, 1193}, {572, 3220}, {603, 1804}, {1400, 5135}, {1790, 4575}, {1890, 17023}, {2174, 5096}, {2260, 5138}, {2293, 20872}, {2318, 5314}, {3955, 22148}, {4259, 21748}, {4265, 7113}, {5132, 9454}, {8766, 17102}, {20753, 22361}, {20775, 22345}, {22344, 22378}
X(22390) = isogonal conjugate of polar conjugate of X(17023)
X(22390) = isotomic conjugate of polar conjugate of X(21764)
Let P be a point on the circumcircle. Let T be the trilinear pole of the polar of P wrt the polar circle (i.e., T is the polar conjugate of P). Let T' be the isogonal conjugate of T. (T' is also the barycentric product X(3)*P.) The locus of T' as P varies is the circumconic {{A,B,C,X(112),X(248)}}, the isogonal conjugate of line X(297)X(525), which is the polar conjugate of the circumcircle. The center of the conic is X(22391). This conic is an ellipse if ABC is acute, and a hyperbola if ABC is obtuse. The conic passes through X(112), X(248), X(1415), X(1576), X(4558), X(14578), X(14908), and X(18877). The perspector of the conic is X(184). (Randy Hutson, September 9, 2018)
The conic {{A,B,C,X(112),X(248)}} is also the locus of barycentric product of circumcircle antipodes. (Randy Hutson, January 15, 2019)
X(22391) lies on these lines: {2, 11610}, {32, 51}, {184, 14600}, {230, 427}, {248, 1899}, {343, 441}, {426, 577}, {578, 14773}, {647, 9306}, {1627, 9753}
X(22391) = isogonal conjugate of polar conjugate of X(157)
X(22391) = isotomic conjugate of polar conjugate of X(2909)
X(22391) = complement of isogonal conjugate of X(157)
X(22391) = X(2)-Ceva conjugate of X(184)
X(22391) = perspector of circumconic centered at X(184)
X(22391) = barycentric product X(i)*X(j) for these {i,j}: {3, 157}, {48, 21374}, {184, 11442}
X(22392) lies on the cubic K1071 these lines: {1,5}, {20,386}, {40,5754}, {42,4301}, {43,9568}, {165,970}, {500,3530}, {581,631}, {991,15717}, {1064,3293}, {2051,5691}, {3017,6960}, {3832,19767}, {4192,7991}, {4658,6915}, {5312,9589}, {5453,16239}, {7982,19648}, {7987,21363}, {9275,13434}, {9706,17104}, {11224,15488}, {16189,19646}
X(22393) lies on these lines: {3,6} et al
X(22394) lies on these lines: {71, 22057}, {255, 6505}, {1214, 4055}, {3747, 3914}, {3915, 4642}, {3917, 22399}, {22409, 22434}
X(22394) = isogonal conjugate of polar conjugate of X(21231)
X(22394) = isotomic conjugate of polar conjugate of X(23621)
X(22395) lies on these lines: {3, 6}
X(22396) lies on these lines: {3, 6}l
X(22397) lies on these lines: {3, 6}
X(22398) lies on these lines: {3, 6}, {982, 2275}, {1107, 4438}
X(22399) lies on these lines: {71, 20728}, {1332, 20778}, {3270, 20749}, {3917, 22394}, {8677, 22346}, {22057, 22418}, {22085, 22093}
X(22399) = isogonal conjugate of polar conjugate of X(21232)
X(22399) = isotomic conjugate of polar conjugate of X(23622)
X(22400) lies on these lines: {63, 212}, {71, 22418}, {1409, 22053}, {3747, 21334}, {3917, 22394}, {22057, 22064}, {22060, 22074}, {22345, 22347}
X(22400) = isogonal conjugate of polar conjugate of X(21233)
X(22400) = isotomic conjugate of polar conjugate of X(23623)
X(22401) lies on these lines: {3, 6}, {20, 232}, {30, 3199}, {115, 11585}, {127, 7821}, {185, 3289}, {230, 16196}, {441, 7789}, {682, 6467}, {980, 18592}, {1015, 1062}, {1038, 2276}, {1040, 2275}, {1060, 1500}, {1194, 7386}, {1196, 1368}, {1506, 15760}, {1589, 8962}, {1625, 10575}, {1843, 11326}, {1968, 11413}, {2207, 21312}, {2549, 6643}, {2883, 11672}, {3146, 15355}, {3269, 5562}, {3291, 16051}, {3522, 22240}, {3546, 3767}, {3548, 7746}, {3815, 6823}, {3917, 22416}, {3926, 6338}, {3933, 15526}, {3964, 6461}, {6337, 6509}, {6748, 9825}, {7603, 10024}, {7736, 10996}, {7748, 15075}, {7749, 10257}, {7756, 12605}, {7801, 14376}, {7816, 15013}, {10311, 17928}, {10313, 22467}, {20727, 22421}, {22057, 22060}, {22064, 22065}
X(22401) = isogonal conjugate of polar conjugate of X(1368)
X(22401) = isotomic conjugate of polar conjugate of X(6467)
X(22402) lies on these lines: {71, 22057}, {228, 22362}, {3778, 4466}, {22094, 22363}
X(22402) = isogonal conjugate of polar conjugate of X(16607)
X(22402) = isotomic conjugate of polar conjugate of X(23624)
X(22403) lies on these lines: {71, 22057}, {22093, 22444}
X(22403) = isogonal conjugate of polar conjugate of X(21234)
X(22403) = isotomic conjugate of polar conjugate of X(23625)
X(22404) lies on these lines: {71, 22077}, {20727, 22069}, {20819, 22411}, {22057, 22434}, {22094, 22439}
X(22404) = isogonal conjugate of polar conjugate of X(21235)
X(22404) = isotomic conjugate of polar conjugate of X(23626)
X(22405) lies on these lines: {3917, 22064}, {22060, 22084}, {22094, 22097}, {22412, 22420}
X(22405) = isogonal conjugate of polar conjugate of X(21236)
X(22405) = isotomic conjugate of polar conjugate of X(23627)
X(22406) lies on these lines: {1818, 22094}, {3917, 22064}, {20821, 22090}, {20823, 22432}, {22067, 22084}
X(22406) = isogonal conjugate of polar conjugate of X(21237)
X(22406) = isotomic conjugate of polar conjugate of X(23628)
X(22407) lies on these lines: {3,6}
X(22408) lies on these lines: {3,6}
X(22409) lies on these lines: {71, 228}, {3917, 20730}, {7116, 17977}, {20727, 22069}, {20736, 22060}, {20757, 22065}, {22077, 22094}, {22394, 22434}
X(22409) = isogonal conjugate of polar conjugate of X(21238)
X(22409) = isotomic conjugate of polar conjugate of X(23629)
X(22410) lies on these lines: {39, 20229}, {216, 22053}, {1473, 7117}, {3917, 22064}, {17102, 18652}, {22057, 22060}, {22059, 22435}
X(22410) = isogonal conjugate of polar conjugate of X(21239)
X(22410) = isotomic conjugate of polar conjugate of X(23630)
X(22411) lies on these lines: {3917, 20820}, {20727, 22416}, {20819, 22404}, {20823, 22069}
X(22411) = isogonal conjugate of polar conjugate of X(17047)
X(22411) = isotomic conjugate of polar conjugate of X(23631)
X(22412) lies on these lines: {69, 3784}, {71, 3917}, {1155, 22301}, {1818, 22078}, {3781, 3916}, {20727, 20819}, {20730, 22073}, {20731, 22062}, {22097, 22369}, {22405, 22420}
X(22412) = isogonal conjugate of polar conjugate of X(21240)
X(22412) = isotomic conjugate of polar conjugate of X(23632)
X(22413) lies on these lines: {39, 21751}, {69, 3937}, {71, 3917}, {1818, 22344}, {3781, 4652}, {3784, 22370}, {20727, 20734}, {20730, 22071}, {20819, 20830}, {20821, 22064}
X(22413) = isogonal conjugate of polar conjugate of X(20255)
X(22413) = isotomic conjugate of polar conjugate of X(22199)
X(22414) lies on these lines: {71, 22083}, {2524, 3049}, {3269, 20825}, {3917, 20727}, {7117, 20729}, {20752, 22098}, {22059, 22428}
X(22414) = isogonal conjugate of polar conjugate of X(21241)
X(22414) = isotomic conjugate of polar conjugate of X(23633)
X(22415) lies on these lines: {71, 7117}, {3917, 20727}
X(22415) = isogonal conjugate of polar conjugate of X(21242)
X(22415) = isotomic conjugate of polar conjugate of X(23634)
X(22416) lies on these lines: {2, 9290}, {3, 248}, {6, 5889}, {39, 3289}, {69, 194}, {185, 216}, {217, 13754}, {232, 5907}, {343, 5254}, {394, 5013}, {574, 1092}, {577, 8565}, {1216, 14961}, {1506, 1568}, {1625, 5876}, {1970, 14118}, {1971, 7488}, {2088, 7749}, {3124, 13881}, {3199, 15030}, {3331, 12162}, {3917, 22401}, {5038, 22151}, {7512, 13509}, {7691, 10313}, {12111, 22240}, {14901, 22109}, {15056, 15355}, {20727, 22411}, {22070, 22432}
X(22416) = isogonal conjugate of polar conjugate of X(21243)
X(22416) = isotomic conjugate of polar conjugate of X(23635)
X(22416) = crosssum of X(4) and X(32)
X(22416) = crosspoint of X(3) and X(76)
X(22417) lies on these lines: {3,6}
X(22418) lies on these lines: {71, 22400}, {212, 5314}, {306, 7004}, {1040, 22370}, {1364, 20732}, {2197, 22053}, {3778, 21334}, {3917, 22064}, {20727, 22411}, {20821, 20824}, {22057, 22399}, {22072, 22076}, {22084, 22435}
X(22418) = isogonal conjugate of polar conjugate of X(21244)
X(22418) = isotomic conjugate of polar conjugate of X(23637)
X(22419) lies on these lines: {3,6}
X(22420) lies on these lines: {216, 3289}, {17052, 21318}, {18591, 22060}, {20727, 22069}, {20738, 22094}, {20821, 22076}, {20822, 22432}
X(22420) = isogonal conjugate of polar conjugate of X(21245)
X(22420) = isotomic conjugate of polar conjugate of X(23639)
X(22421) lies on these lines: {3, 73}, {55, 2274}, {326, 1040}, {426, 22057}, {497, 1740}, {1010, 2654}, {1936, 13588}, {2269, 17187}, {2309, 21321}, {3009, 21333}, {3736, 14547}, {3917, 22064}, {20727, 22401}, {20824, 22449}, {22060, 22074}
X(22421) = isogonal conjugate of polar conjugate of X(21246)
X(22421) = isotomic conjugate of polar conjugate of X(23640)
X(22422) lies on these lines: {73, 22362}, {22061, 22069}, {22348, 22364}
X(22422) = isogonal conjugate of polar conjugate of X(21247)
X(22422) = isotomic conjugate of polar conjugate of X(23641)
X(22423) lies on these lines: {3,6}
X(22424) lies on these lines: {3, 1176}, {39, 3051}, {2525, 5489}, {2979, 9917}, {3095, 10519}, {7767, 20975}, {7795, 14003}, {20821, 22060}
X(22424) = isogonal conjugate of polar conjugate of X(21248)
X(22424) = isotomic conjugate of polar conjugate of X(23642)
X(22425) lies on these lines: {3, 6}, {1500, 3721}, {1759, 2276}, {2223, 20966}, {2240, 21838}, {5051, 16589}, {5283, 17676}
X(22426) lies on these lines: {3, 6}, {37, 4660}, {941, 17300}, {980, 17378}, {1908, 2243}, {2223, 3764}
X(22427) lies on these lines: {3, 20738}, {78, 3781}, {3917, 20755}, {20727, 20734}, {20821, 20824}, {20822, 22070}
X(22427) = isogonal conjugate of polar conjugate of X(21250)
X(22427) = isotomic conjugate of polar conjugate of X(23643)
X(22428) lies on these lines: {55, 4286}, {71, 7117}, {900, 1635}, {1293, 8752}, {2267, 4271}, {3269, 22073}, {3917, 22084}, {20727, 22429}, {20975, 22080}, {22059, 22414}
X(22428) = isogonal conjugate of polar conjugate of X(121)
X(22428) = isotomic conjugate of polar conjugate of X(23644)
X(22429) lies on these lines: {71, 22083}, {3917, 22059}, {20727, 22428}, {22080, 22372}
X(22429) = isogonal conjugate of polar conjugate of X(21251)
X(22429) = isotomic conjugate of polar conjugate of X(23645)
X(22430) lies on these lines: {3, 6}, {1500, 1759}
X(22431) lies on these lines: {3, 6}, {1759, 9331}
X(22432) lies on these lines: {1364, 22383}, {3269, 7117}, {3917, 20820}, {20822, 22420}, {20823, 22406}, {22070, 22416}
X(22432) = isogonal conjugate of polar conjugate of X(21252)
X(22432) = isotomic conjugate of polar conjugate of X(23646)
X(22433) lies on these lines: {3269, 22084}, {20820, 22073}
X(22433) = isogonal conjugate of polar conjugate of X(21253)
X(22433) = isotomic conjugate of polar conjugate of X(23647)
X(22434) lies on these lines: {71, 22094}, {20735, 20756}, {22057, 22404}, {22394, 22409}
X(22434) = isogonal conjugate of polar conjugate of X(21254)
X(22434) = isotomic conjugate of polar conjugate of X(23648)
X(22435) lies on these lines: {71, 3917}, {394, 20780}, {1473, 22356}, {1818, 3784}, {2318, 3937}, {20727, 22088}, {20731, 22066}, {22059, 22410}, {22084, 22418}
X(22435) = isogonal conjugate of polar conjugate of X(21255)
X(22435) = isotomic conjugate of polar conjugate of X(23649)
X(22436) lies on these lines: {3, 6}, {1500, 2243}, {14020, 16589}
X(22437) lies on these lines: {3, 22384}, {3960, 4256}, {7117, 22084}, {20731, 20757}
X(22437) = isogonal conjugate of polar conjugate of X(21255)
X(22437) = isotomic conjugate of polar conjugate of X(23650)
X(22438) lies on these lines: {71, 22349}, {20727, 22069}, {20828, 22095}
X(22438) = isogonal conjugate of polar conjugate of X(21256)
X(22438) = isotomic conjugate of polar conjugate of X(23651)
X(22439) lies on these lines: {63, 20736}, {71, 228}, {216, 20729}, {3917, 20755}, {22094, 22404}
X(22439) = isogonal conjugate of polar conjugate of X(21257)
X(22439) = isotomic conjugate of polar conjugate of X(23652)
X(22440) lies on these lines: {3, 1803}, {71, 3917}, {77, 3270}, {185, 4303}, {216, 22084}, {373, 2635}, {1155, 22277}, {1253, 1362}, {1425, 10884}, {1439, 10167}, {3000, 21746}, {3937, 6467}, {20731, 22071}, {22064, 22070}
X(22440) = isogonal conjugate of polar conjugate of X(21258)
X(22440) = isotomic conjugate of polar conjugate of X(23653)
X(22441) lies on these lines: {4269, 8062}, {20828, 22095}, {22093, 22443}
X(22441) = isogonal conjugate of polar conjugate of X(21259)
X(22441) = isotomic conjugate of polar conjugate of X(23654)
X(22442) lies on these lines: {3, 6}, {1015, 3721}, {1759, 2275}
X(22443) lies on these lines: {44, 513}, {71, 1459}, {522, 579}, {1400, 21960}, {2524, 3049}, {17072, 21388}, {22093, 22441}
X(22443) = isogonal conjugate of polar conjugate of X(21255)
X(22443) = isotomic conjugate of polar conjugate of X(23655)
X(22444) lies on these lines: {812, 4283}, {2524, 3049}, {7117, 22084}, {22093, 22403}, {22383, 22445}
X(22444) = isogonal conjugate of polar conjugate of X(21261)
X(22444) = isotomic conjugate of polar conjugate of X(23656)
X(22445) lies on these lines: {20821, 22090}, {20828, 22095}, {22383, 22444}
X(22445) = isogonal conjugate of polar conjugate of X(21262)
X(22445) = isotomic conjugate of polar conjugate of X(23657)
X(22446) lies on these lines: {20828, 22095}, {22093, 22403}
X(22446) = isogonal conjugate of polar conjugate of X(21263)
X(22446) = isotomic conjugate of polar conjugate of X(23658)
X(22447) lies on these lines: {3, 9247}, {71, 216}, {73, 22099}, {3917, 20755}, {4303, 22098}, {5267, 14963}, {7117, 20750}, {22054, 22073}, {22061, 22350}
X(22447) = isogonal conjugate of polar conjugate of X(3846)
X(22447) = isotomic conjugate of polar conjugate of X(23659)
X(22448) lies on these lines: {3, 6}, {2243, 2275}, {3291, 16048}, {3721, 3976}, {9465, 17522}
X(22449) lies on these lines: {3, 63}, {38, 18758}, {69, 22389}, {71, 20730}, {672, 14096}, {1444, 22378}, {1799, 22381}, {3917, 20727}, {4640, 20878}, {5322, 17798}, {20819, 22058}, {20824, 22421}, {22053, 22066}
X(22449) = isogonal conjugate of polar conjugate of X(21264)
X(22449) = isotomic conjugate of polar conjugate of X(23660)
X(22450) lies on these lines: {3, 6}, {1015, 1759}, {3721, 4694}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 28200.
X(22451) lies on these lines: {4,1511}, {1989,3284}
X(22451) = barycentric quotient X(18487)/X(1539)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 28200.
X(22452) lies on this line: {3,10113}
See César E. Lozada, Hyacinthos 28201.
X(22453) lies on these lines: {35, 976}, {2174, 2273}
X(22453) = isogonal conjugate of X(4680)
See César E. Lozada, Hyacinthos 28201.
X(22454) lies on these lines: {95, 2070}, {252, 3518}
See César E. Lozada, Hyacinthos 28201.
X(22455) lies on these lines: {3, 1494}, {25, 16263}, {32, 8749}, {74, 184}, {186, 5627}, {9139, 14908}, {10151, 16243}, {10152, 13596}
X(22455) = isogonal conjugate of X(1531)
X(22455) = trilinear pole of the line {2433, 3049}
Let A', B', C' be the intersections of line X(4)X(69) and lines BC, CA, AB, resp. The circumcircles of AB'C', BC'A', CA'B' concur in X(22456). (Randy Hutson, October 15, 2018)
Let A"B"C" be the circumsymmedial triangle. Let A* be the pole, wrt the polar circle, of line B"C", and define B* and C* cyclically. The lines AA*, BB*, CC* concur in X(264). The lines A"A*, B"B*, C"C* concur in X(22456). (Randy Hutson, October 15, 2018)
See César E. Lozada, Hyacinthos 28201.
X(22456) lies on the circumcircle and these lines: {4, 2679}, {69, 2706}, {74, 290}, {76, 2710}, {98, 16083}, {99, 22089}, {110, 685}, {111, 16081}, {112, 2966}, {264, 842}, {286, 2699}, {314, 2707}, {340, 9161}, {729, 6531}, {805, 877}, {879, 2713}, {1294, 6394}, {1297, 5999}, {1821, 2249}, {2373, 18024}, {2395, 9091}, {2697, 15915}, {2857, 18022}, {4230, 6037}
X(22456) = isotomic conjugate of X(684)
X(22456) = anticomplement of X(38974)
X(22456) = polar conjugate of X(3569)
X(22456) = polar circle-inverse of X(2679)
X(22456) = trilinear pole of the line {6, 264}
X(22456) = X(63)-isoconjugate of X(2491)
X(22456) = Ψ(X(3), X(76))
X(22456) = Ψ(X(6), X(264))
X(22456) = Ψ(X(32), X(4))
X(22456) = Λ(X(3269), X(9409))
X(22456) = Λ(trilinear polar of X(184))
X(22456) = Λ(trilinear polar of X(237))
X(22456) = Λ(PU(89))
X(22456) = Λ(PU(109))
X(22456) = perspector, wrt circumsymmedial triangle, of polar circle
X(22457) lies on these lines: {3, 201}, {912, 22341}, {3157, 7016}, {9645, 11248}, {22164, 23084}
X(22457) = isogonal conjugate of polar conjugate of X(17479)
X(22457) = isotomic conjugate of polar conjugate of X(21768)
X(22458) lies on these lines: {1, 18174}, {3, 63}, {7, 16415}, {9, 16286}, {57, 16414}, {255, 20803}, {329, 19543}, {496, 15507}, {603, 23067}, {859, 3868}, {942, 4245}, {1437, 15409}, {1634, 17104}, {2200, 20785}, {2801, 15622}, {2810, 5399}, {3218, 16453}, {3219, 16287}, {3305, 16291}, {3647, 8053}, {3682, 11573}, {3876, 16374}, {3881, 18613}, {4020, 22126}, {4696, 5687}, {5044, 19261}, {5273, 16290}, {5439, 19250}, {6763, 16678}, {7483, 21319}, {10436, 16408}, {12635, 15654}, {15905, 20764}, {17976, 22138}, {19513, 20245}, {20794, 23076}, {20797, 23091}, {20802, 23084}, {22136, 22161}, {22148, 23070}
X(22459) lies on these lines: {3, 6}, {1759, 9336}
X(22460) lies on these lines: {3, 6}, {1015, 2243}
See Antreas Hatzipolakis, Paul Yiu, and Peter Moses, Hyacinthos 28215.
X(22461) lies on these lines: {35,37}, {3746,8143}
X(22461) = X(1)-waw conjugate of X(3746)
See Kadir Altintas and Ercole Suppa, Hyacinthos 28218.
X(22462) lies on these lines: {2,3}, {49,373}, {74,11017}, {110,15047}, {156,11465}, {195,15026}, {399,12006}, {1493,12834}, {1511,12046}, {3567,12316}, {5643,9705}, {5898,8254}, {5943,14627}, {6688,13353}, {9704,10601}, {9706,15039}, {10263,10545}{10540,11695}, {12308,13630}, {15024,15087}, {15037,18350}
X(22462) = {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {3,11484,19709}, {7506,11284,5070}, {11414,15701,3}
X(22462) = crossdifference of every pair of points on line X(647)X(13152)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 28213.
X(22463) lies on these lines: {3, 6}, {858, 6036}, {924, 14270}
X(22463) = midpoint of X(3) and X(50)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 28213.
X(22464) lies on the cubic K660 and these lines: {1, 7}, {2, 20223}, {37, 21617}, {44, 5723}, {57, 16548}, {63, 278}, {75, 225}, {85, 4389}, {88, 655}, {109, 2861}, {223, 5905}, {226, 17080}, {239, 17950}, {241, 1086}, {283, 8822}, {320, 664}, {522, 693}, {527, 651}, {553, 17074}, {653, 8755}, {894, 17086}, {903, 17078}, {908, 1465}, {934, 2716}, {948, 4419}, {1020, 20367}, {1068, 1119}, {1072, 3673}, {1214, 5249}, {1254, 13161}, {1358, 13756}, {1427, 3782}, {1440, 4373}, {1441, 4357}, {1445, 4000}, {1447, 1758}, {1456, 17768}, {1457, 17139}, {1737, 18815}, {1804, 11249}, {1936, 7012}, {1937, 2481}, {1943, 4001}, {2302, 18162}, {3262, 6735}, {3666, 6354}, {3755, 7672}, {3868, 5930}, {3912, 4552}, {4572, 18891}, {4656, 5226}, {5219, 16676}, {5222, 12848}, {5228, 17301}, {5236, 8680}, {6180, 17276}, {7053, 10680}, {7279, 14794}, {9312, 17274}, {9965, 18623}, {10404, 15832}, {14564, 16666}
X(22464) = isogonal conjugate of X(2342)
X(22464) = X(50)-of-intouch triangle
X(22464) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7, 347, 77), (7, 1442, 3664), (7, 3672, 7190), (175, 176, 5731), (269, 4862, 7), (279, 4346, 7), (948, 4419, 8545), (3638, 3639, 21578), (3663, 3668, 7)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 28213.
X(22465) lies on these lines: {1, 7}, {522, 3960}, {1068, 1861}, {2323, 5850}, {3333, 16548}, {6745, 16586}, {16272, 18839}
Miscellaneous centers: X(22466)-X(23049)
Centers X(22466)-X(23049) were contributed by César Eliud Lozada, September 11, 2018.
The reciporcal orthologic center of these triangles is X(12241).
X(22466) lies on the Jerabek hyperbola and these lines: {3,2929}, {4,18936}, {5,5504}, {6,17837}, {54,403}, {56,18978}, {64,13399}, {68,5876}, {73,19472}, {74,5894}, {185,11744}, {265,12162}, {381,15317}, {389,3521}, {578,16867}, {895,15044}, {1173,12233}, {1176,19142}, {3426,18381}, {3431,7505}, {4846,13630}, {6145,13851}, {6288,7687}, {6391,15069}, {9927,15316}, {11559,16003}, {11572,15321}, {15002,18388}, {18396,18532}
X(22466) = isogonal conjugate of X(22467)
X(22466) = {X(19083), X(19084)}-harmonic conjugate of X(6)
X(22466) = perspector of 2nd Droz-Farny circle
As a point on the Euler line, X(22467) has Shinagawa coefficients (E-4*F, 4*F).
X(22467) lies on these lines: {2,3}, {49,1511}, {54,5504}, {74,12162}, {107,1105}, {110,185}, {182,11443}, {184,10574}, {323,1092}, {389,1994}, {394,1192}, {567,12006}, {569,15045}, {578,15043}, {974,3047}, {1078,1236}, {1147,5890}, {1181,9544}, {1204,9306}, {1209,20191}, {1587,9682}, {1620,17811}, {1968,15355}, {1975,5866}, {1993,9786}, {2079,5254}, {2888,12359}, {2929,13567}, {2931,12022}, {3043,14708}, {3060,13346}, {3357,15305}, {3431,15317}, {3448,14516}, {3521,14643}, {3567,13352}, {3581,6101}, {3917,7691}, {4297,9590}, {5012,9729}, {5218,9659}, {5265,10832}, {5281,10831}, {5422,11425}, {5446,10564}, {5462,15033}, {5640,11424}, {5643,15023}, {5651,11454}, {5663,18350}, {5877,7891}, {5894,10117}, {5907,11440}, {6241,10539}, {6288,13561}, {6759,15072}, {6800,17821}, {6801,18284}, {7288,9672}, {7689,11459}, {8718,14855}, {8780,12174}, {8907,18910}, {9539,11399}, {9591,12512}, {9637,19366}, {9705,15034}, {9706,15020}, {9932,18916}, {10312,14961}, {10516,15578}, {10540,13491}, {10546,11439}, {10575,14157}, {10605,11441}, {10984,11202}, {11003,19357}, {11064,13568}, {11381,13445}, {11430,13434}, {11468,15058}, {12118,18912}, {12901,14644}, {13289,15030}, {13366,15012}, {13403,16163}, {14249,21396}, {14831,15801}, {14927,20987}, {17854,20771}, {18911,19467}
X(22467) = isogonal conjugate of X(22466)
X(22467) = crosspoint, wrt excentral or tangential triangle, of X(3) and X(2929)
X(22467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 4, 2071), (3, 22, 3522), (3, 2915, 7411), (3, 2937, 548), (3, 14130, 10226), (4, 631, 3548), (22, 3522, 16661), (22, 4232, 23), (24, 12082, 9714), (1593, 1995, 3832), (5004, 5005, 1368), (7387, 7516, 6643), (7387, 14130, 18560), (10226, 14130, 3520), (14002, 17578, 1598), (14709, 14710, 2)
X(22468) lies on these lines: {4,69}, {325,6677}, {801,13567}, {1078,16196}, {3964,7799}
X(22468) = isotomic conjugate of X(22466)
X(22468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (69, 317, 14615), (317, 14615, 316)
X(22469) lies on these lines: {}
X(22470) lies on these lines: {}
X(22471) lies on the line {378,15136}
X(22472) lies on these lines: {}
X(22473) lies on these lines: {}
X(22474) lies on the nine-point circle and these lines: {}
The reciprocal orthologic center of these triangles is X(3).
X(22475) lies on these lines: {1,262}, {2,22697}, {39,13464}, {76,9624}, {511,551}, {515,22682}, {999,22680}, {1125,15819}, {1319,18971}, {1385,12264}, {1386,11710}, {2646,22711}, {2782,12258}, {3295,22556}, {3576,22676}, {3616,6194}, {3656,11171}, {4301,13334}, {5603,7709}, {5901,12263}, {6683,11362}, {7786,7982}, {7976,8227}, {9955,22681}, {10246,22728}, {10595,12782}, {11257,11522}, {11363,22480}, {11364,22521}, {11365,22655}, {11366,22668}, {11367,22672}, {11368,22678}, {11370,22699}, {11371,22700}, {11373,22703}, {11374,22704}, {11375,22705}, {11376,22706}, {11377,22709}, {11378,22710}, {11831,22698}, {12194,21445}, {13883,22720}, {13936,22721}, {14881,15178}, {18991,19063}, {18992,19064}
X(22475) = midpoint of X(i) and X(j) for these {i,j}: {1, 262}, {3656, 11171}
X(22475) = complement of X(22697)
X(22475) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22650, 22713), (262, 22713, 22650)
The reciprocal orthologic center of these triangles is X(12241).
X(22476) lies on these lines: {1,22466}, {2,22941}, {515,22833}, {999,22776}, {1125,22966}, {1319,18978}, {2646,22965}, {3295,22559}, {3576,22951}, {3616,22647}, {5603,22533}, {5886,22955}, {9955,22800}, {10246,22979}, {11363,22483}, {11364,22524}, {11365,22658}, {11368,22747}, {11370,22945}, {11371,22947}, {11373,22956}, {11374,22957}, {11375,22958}, {11376,22959}, {11377,22963}, {11831,22943}, {13883,22976}, {13936,22977}, {18991,19083}, {18992,19084}
X(22476) = midpoint of X(1) and X(22466)
X(22476) = complement of X(22941)
X(22476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22653, 22969), (22466, 22969, 22653)
The reciprocal cyclologic center of these triangles is X(22478).
X(22477) lies on the line {9955,22478}
The reciprocal cyclologic center of these triangles is X(22477).
X(22478) lies on the line {9955,22477}
X(22479) lies on these lines: {3,1829}, {4,2975}, {24,10269}, {25,34}, {28,1851}, {33,10966}, {36,7713}, {39,607}, {55,11396}, {58,1473}, {104,7487}, {184,3556}, {235,22753}, {427,958}, {428,11194}, {604,2354}, {608,5019}, {956,5090}, {988,1039}, {999,11363}, {1112,22586}, {1191,14975}, {1201,2212}, {1452,1470}, {1475,1973}, {1593,1753}, {1597,1900}, {1598,1878}, {1838,4185}, {1843,22769}, {1862,22560}, {1870,14017}, {1902,22770}, {1905,8071}, {3516,5584}, {3575,11390}, {4186,11399}, {5186,22514}, {5253,6353}, {5260,8889}, {5410,19014}, {5411,19013}, {7677,7717}, {11380,22520}, {11381,22778}, {11384,11493}, {11385,11492}, {11386,22744}, {11388,22756}, {11389,22757}, {11392,22759}, {11393,22760}, {11394,22761}, {11395,22762}, {11398,20832}, {11400,22768}, {11576,22781}, {11832,22755}, {12131,22504}, {12132,22565}, {12133,22583}, {12134,22659}, {12135,12513}, {12136,18237}, {12137,12773}, {12138,22775}, {12139,22777}, {12140,19478}, {12141,22774}, {12142,22773}, {12143,22779}, {12144,22780}, {12145,19159}, {12146,22782}, {12147,22595}, {12148,22624}, {13166,19162}, {13668,22783}, {13743,16114}, {13788,22784}, {13884,22763}, {13937,22764}, {22480,22680}, {22481,22771}, {22482,22772}, {22483,22776}
X(22479) = {X(3), X(1829)}-harmonic conjugate of X(11383)
The reciprocal orthologic center of these triangles is X(3).
X(22480) lies on these lines: {4,2896}, {25,262}, {33,22711}, {34,18971}, {235,22682}, {427,15819}, {428,511}, {1593,22676}, {1598,22728}, {1843,12131}, {1907,5188}, {2023,10985}, {2782,7576}, {3518,11272}, {5064,22712}, {5090,22697}, {5410,19064}, {5411,19063}, {6756,12143}, {7487,7709}, {7713,22650}, {10594,14881}, {11363,22475}, {11380,22521}, {11383,22556}, {11385,22672}, {11388,22699}, {11389,22700}, {11390,22703}, {11391,22704}, {11392,22705}, {11393,22706}, {11394,22709}, {11396,22713}, {11398,22729}, {11399,22730}, {11400,22731}, {11401,22732}, {11832,22698}, {13884,22720}, {13937,22721}, {22479,22680}
The reciprocal orthologic center of these triangles is X(3).
X(22481) lies on these lines: {4,617}, {18,25}, {33,22865}, {34,18972}, {235,22831}, {427,630}, {468,6674}, {1593,22843}, {1598,16628}, {1843,5965}, {5090,22851}, {5410,19072}, {5411,19069}, {6756,12142}, {6995,22114}, {7487,22531}, {7713,22651}, {11363,11740}, {11380,22522}, {11383,22557}, {11386,22745}, {11388,22853}, {11389,22854}, {11390,22857}, {11391,22858}, {11392,22859}, {11393,22860}, {11394,22863}, {11396,22867}, {11398,22884}, {11399,22885}, {11400,22886}, {11401,22887}, {11832,22852}, {13884,22876}, {13937,22877}, {22479,22771}
The reciprocal orthologic center of these triangles is X(3).
X(22482) lies on these lines: {4,616}, {17,25}, {33,22910}, {34,18973}, {235,22832}, {427,629}, {428,532}, {468,6673}, {1593,22890}, {1598,16629}, {1843,5965}, {5090,22896}, {5410,19070}, {5411,19071}, {6756,12141}, {6995,22113}, {7487,22532}, {7713,22652}, {11363,11739}, {11380,22523}, {11383,22558}, {11386,22746}, {11388,22898}, {11389,22899}, {11390,22902}, {11391,22903}, {11392,22904}, {11393,22905}, {11394,22908}, {11395,22909}, {11396,22912}, {11398,22929}, {11399,22930}, {11400,22931}, {11401,22932}, {11832,22897}, {13884,22921}, {13937,22922}, {22479,22772}
The reciprocal orthologic center of these triangles is X(12241).
X(22483) lies on these lines: {4,801}, {25,22466}, {33,22965}, {34,18978}, {235,22833}, {427,22966}, {1593,22951}, {1598,22979}, {1843,21652}, {1853,2929}, {5090,22941}, {5410,19084}, {5411,19083}, {6644,22834}, {7487,22533}, {7506,22808}, {7713,22653}, {11363,22476}, {11380,22524}, {11383,22559}, {11386,22747}, {11388,22945}, {11389,22947}, {11390,22956}, {11391,22957}, {11392,22958}, {11393,22959}, {11394,22963}, {11395,22964}, {11396,22969}, {11398,22980}, {11399,22981}, {11400,22982}, {11401,22983}, {11832,22943}, {13884,22976}, {13937,22977}, {19460,22662}, {22467,22581}, {22479,22776}, {22530,22953}
X(22483) = {X(4), X(22750)}-harmonic conjugate of X(22800)
The reciprocal orthologic center of these triangles is X(12158).
X(22484) lies on these lines: {2,371}, {381,6281}, {524,1328}, {542,13810}, {591,6561}, {1327,1992}, {3564,3845}, {3830,6280}, {4677,9906}, {4745,12787}, {5066,6290}, {6319,22562}, {8703,12123}, {11001,12256}, {12296,15640}, {12509,15698}, {13650,13846}, {13711,13932}, {15685,22809}
X(22484) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (591, 6561, 13712), (3845, 15534, 22485)
The reciprocal orthologic center of these triangles is X(12159).
X(22485) lies on these lines: {2,372}, {381,6278}, {524,1327}, {542,13691}, {1328,1992}, {1991,6560}, {3564,3845}, {3830,6279}, {4677,9907}, {4745,12788}, {5066,6289}, {5860,6564}, {6320,22563}, {8703,12124}, {11001,12257}, {12297,15640}, {12510,15698}, {13662,13712}, {13771,13847}, {13834,13850}, {15685,22810}
X(22485) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1991, 6560, 13835), (3845, 15534, 22484)
The reciprocal orthologic center of these triangles is X(6).
X(22486) lies on these lines: {2,51}, {3,11155}, {6,99}, {32,13085}, {39,7618}, {69,5475}, {76,524}, {182,13586}, {183,11173}, {194,5032}, {376,13354}, {384,576}, {538,1992}, {542,11361}, {575,3552}, {597,3094}, {599,7809}, {698,8584}, {732,12156}, {1351,10796}, {1916,11150}, {2782,8593}, {3095,8369}, {3102,11157}, {3103,11158}, {3104,16646}, {3105,16647}, {3106,11153}, {3107,11154}, {3363,7697}, {3407,5039}, {3934,8176}, {4048,12151}, {5038,7782}, {5104,7771}, {5107,7804}, {5976,11163}, {6248,11180}, {7753,14645}, {7770,11477}, {7775,18806}, {7833,19924}, {8359,9821}, {8541,15014}, {8550,19687}, {11059,13410}, {11151,11171}, {11152,18800}, {11160,14994}, {11161,11317}, {11179,11257}, {11288,14848}, {11318,14881}, {13637,22722}, {13757,22723}, {15004,16951}, {22493,22702}, {22494,22701}
X(22486) = reflection of X(i) in X(j) for these (i,j): (69, 9466), (376, 13354), (11152, 18800), (11160, 14994)
X(22486) = {X(6), X(1003)}-harmonic conjugate of X(5182)
The reciprocal orthologic center of these triangles is X(5858).
X(22487) lies on these lines: {2,18}, {5858,7813}, {8584,12155}, {11159,22488}, {12154,15534}, {13637,22878}
The reciprocal orthologic center of these triangles is X(5859).
X(22488) lies on these lines: {2,17}, {5859,7813}, {8584,12154}, {11159,22487}, {12155,15534}, {13637,22923}, {13757,22924}
The reciprocal orthologic center of these triangles is X(12155).
X(22489) lies on these lines: {2,13}, {14,5461}, {17,9763}, {30,21156}, {61,22491}, {99,22577}, {115,5464}, {141,22580}, {376,5478}, {381,6771}, {395,9112}, {396,22572}, {524,16267}, {542,5050}, {543,5470}, {547,5617}, {549,5473}, {551,7975}, {619,671}, {620,9116}, {623,16960}, {633,20394}, {1656,20415}, {3526,16001}, {3582,10062}, {3584,10078}, {3679,11705}, {3828,12781}, {5071,6770}, {5460,6777}, {5472,16645}, {5474,9880}, {6671,19106}, {6722,6778}, {9204,11625}, {11284,13859}, {11295,16808}, {11296,16241}, {11303,13083}, {11542,22495}, {12258,12780}, {13103,15694}, {13908,19076}, {13917,19054}, {13968,19075}, {13982,19053}, {14830,22797}, {19709,22796}, {21358,21360}
X(22489) = inner-Napoleon-circle-inverse of X(35752)
X(22489) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 13, 5463), (2, 5459, 13), (13, 16242, 23006), (619, 671, 9114), (5459, 6669, 2), (6108, 18582, 13)
The reciprocal orthologic center of these triangles is X(12154).
X(22490) lies on these lines: {2,14}, {13,5461}, {18,9761}, {30,21157}, {62,22492}, {99,22578}, {115,5463}, {141,22579}, {376,5479}, {381,6774}, {395,22571}, {396,9113}, {524,16268}, {542,5050}, {543,5469}, {547,5613}, {549,5474}, {551,7974}, {618,671}, {620,9114}, {624,16961}, {634,20395}, {1656,20416}, {3526,16002}, {3582,10061}, {3584,10077}, {3679,11706}, {3828,12780}, {5071,6773}, {5459,6778}, {5471,16644}, {5473,9880}, {6672,19107}, {6722,6777}, {9205,11627}, {11284,13858}, {11295,16242}, {11296,16809}, {11304,13084}, {11543,22496}, {12258,12781}, {13102,15694}, {13908,19074}, {13916,19054}, {13968,19073}, {13981,19053}, {14830,22796}, {19709,22797}, {21358,21359}
X(22490) = outer-Napoleon-circle-inverse of X(36330)
X(22490) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 14, 5464), (2, 5460, 14), (14, 16241, 23013), (618, 671, 9116), (5460, 6670, 2), (6109, 18581, 14)
The reciprocal orthologic center of these triangles is X(12155).
X(22491) lies on these lines: {2,14}, {5,9763}, {13,1992}, {30,9761}, {61,22489}, {69,16809}, {115,22579}, {193,16808}, {298,11185}, {376,13084}, {381,524}, {395,7737}, {398,11305}, {532,3839}, {543,5617}, {3845,5858}, {3849,20428}, {5066,5859}, {5210,16645}, {5321,11295}, {5459,13705}, {5479,7620}, {5613,7617}, {6695,22237}, {6782,12155}, {7618,13102}, {7775,16626}, {9734,9886}, {9762,9770}, {9885,16002}, {11160,22494}, {16630,22572}
X(22491) = reflection of X(376) in X(13084)
X(22491) = reflection of X(22492) in X(381)
X(22491) = anticomplement of X(13083)
X(22491) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (13, 22496, 1992), (381, 20426, 20423), (1352, 7615, 22492), (3642, 5460, 2)
The reciprocal orthologic center of these triangles is X(12154).
X(22492) lies on these lines: {2,13}, {5,9761}, {14,1992}, {30,9763}, {62,22490}, {69,16808}, {115,22580}, {193,16809}, {299,11185}, {376,13083}, {381,524}, {396,7737}, {397,11306}, {532,3545}, {543,5613}, {3845,5859}, {3849,20429}, {5066,5858}, {5210,16644}, {5318,11296}, {5460,13703}, {5478,7620}, {5617,7617}, {6694,22235}, {6783,12154}, {7618,13103}, {7775,16627}, {9734,9885}, {9760,9770}, {9886,16001}, {11160,22493}, {16631,22571}
X(22492) = reflection of X(376) in X(13083)
X(22492) = reflection of X(22491) in X(381)
X(22492) = anticomplement of X(13084)
X(22492) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (14, 22495, 1992), (381, 20425, 20423), (1352, 7615, 22491), (3643, 5459, 2)
The reciprocal orthologic center of these triangles is X(12155).
X(22493) lies on these lines: {2,18}, {13,524}, {14,599}, {69,16809}, {76,12817}, {99,298}, {183,9760}, {302,13083}, {316,22576}, {381,11477}, {617,13084}, {623,16960}, {754,5858}, {2482,6780}, {3180,5459}, {3534,22890}, {3849,6779}, {5464,5569}, {7840,9762}, {9113,9117}, {9763,16966}, {11160,22492}, {11178,20426}, {11295,16964}, {22486,22702}, {22577,23004}
X(22493) = reflection of X(i) in X(j) for these (i,j): (3180, 5459), (22577, 23004)
X(22493) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 15533, 22494), (5464, 9761, 16242)
The reciprocal orthologic center of these triangles is X(12154).
X(22494) lies on these lines: {2,17}, {13,599}, {14,524}, {69,16808}, {76,12816}, {99,299}, {183,9762}, {303,13084}, {316,22575}, {381,11477}, {616,13083}, {624,16961}, {754,5859}, {2482,6779}, {3181,5460}, {3534,22843}, {3849,6780}, {5463,5569}, {7840,9760}, {9112,9115}, {9761,16967}, {11160,22491}, {11178,20425}, {11296,16965}, {22486,22701}, {22578,23005}
X(22494) = reflection of X(i) in X(j) for these (i,j): (3181, 5460), (22578, 23005)
X(22494) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 15533, 22493), (5463, 9763, 16241)
The reciprocal orthologic center of these triangles is X(12155).
X(22495) lies on these lines: {2,17}, {13,524}, {14,1992}, {16,7622}, {61,11295}, {115,22571}, {193,16808}, {298,5459}, {381,576}, {396,5463}, {538,3105}, {542,20425}, {543,22997}, {2996,12816}, {3629,16809}, {5066,16627}, {5464,6783}, {5858,7775}, {6779,9885}, {7774,9760}, {9116,16529}, {9762,22998}, {10646,13083}, {11542,22489}
X(22495) = reflection of X(i) in X(j) for these (i,j): (14, 22573), (298, 5459), (5464, 6783)
X(22495) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 15534, 22496), (1992, 22492, 14)
The reciprocal orthologic center of these triangles is X(12154).
X(22496) lies on these lines: {2,18}, {13,1992}, {14,524}, {15,7622}, {62,11296}, {115,22572}, {193,16809}, {299,5460}, {381,576}, {395,5464}, {532,11054}, {538,3104}, {542,20426}, {543,22998}, {2996,12817}, {3629,16808}, {5066,16626}, {5463,6782}, {5859,7775}, {6780,9886}, {7774,9762}, {9114,16530}, {9760,22997}, {10645,13084}, {11543,22490}
X(22496) = reflection of X(i) in X(j) for these (i,j): (13, 22574), (299, 5460), (5463, 6782)
X(22496) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 15534, 22495), (1992, 22491, 13)
The reciprocal orthologic center of these triangles is X(9729).
X(22497) lies on these lines: {3,22528}, {4,22550}, {6,21652}, {25,2929}, {154,22658}, {184,17837}, {427,22555}, {1974,9968}, {1993,22534}, {3515,22962}, {3516,22549}, {5410,22960}, {5411,22961}, {7395,22834}, {7484,22581}, {7592,22535}, {9777,22530}, {9818,22808}, {11245,18936}, {11284,22973}, {11402,19460}, {11403,22538}, {11405,22830}, {11406,22840}, {11408,22974}, {11409,22975}, {11410,22978}, {16030,19198}, {18386,22816}, {19118,19142}, {19404,19488}
X(22497) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2929, 22970, 25), (19460, 22529, 11402)
Let A'B'C' be the 1st anti-Brocard triangle. X(22498) is the radical center of the circumcircles of triangles AB'C', BC'A', CA'B'. (Randy Hutson, June 7, 2019)
X(22498) lies on these lines: {2,4159}, {3,9772}, {6,1916}, {99,736}, {114,8295}, {147,7897}, {5026,10334}, {5999,6033}, {7840,12215}, {7931,8290}, {12177,22503}, {13586,16508}
X(22498) = X(3407)-of-1st-anti-Brocard-triangle
X(22498) = 1st-anti-Brocard-isogonal conjugate of X(76)
X(22498) = {X(1916), X(8289)}-harmonic conjugate of X(19120)
X(22499) lies on these lines: {511,13029}, {1916,6401}, {4027,11984}, {5989,11986}, {8289,22785}, {8302,11937}, {8303,11938}, {8304,11941}, {8305,11942}, {8306,11959}, {8307,11960}, {8308,11963}, {8309,11964}, {8310,11967}, {8311,11969}, {8312,11971}, {8313,11973}, {8314,11975}, {8315,11977}, {8316,11979}, {8317,11981}, {9772,14167}, {11983,22500}, {19375,19390}
X(22500) lies on these lines: {511,13031}, {1916,6402}, {4027,11985}, {8289,22786}, {8302,11939}, {8304,11943}, {8306,11961}, {8308,11965}, {8310,11970}, {8311,11968}, {8312,11974}, {8313,11972}, {8314,11978}, {8316,11982}, {9772,14168}, {11983,22499}
The reciprocal orthologic center of these triangles is X(9867).
X(22501) lies on these lines: {98,486}, {115,19105}, {542,1328}, {6231,6561}, {6280,22617}, {7840,22562}, {12221,22613}, {22502,22505}
The reciprocal orthologic center of these triangles is X(9868).
X(22502) lies on these lines: {98,485}, {115,19102}, {542,1327}, {6230,6560}, {6279,22646}, {7840,22563}, {12222,22642}, {22501,22505}
The reciprocal orthologic center of these triangles is X(12177).
X(22503) lies on these lines: {2,51}, {3,22679}, {30,8592}, {147,316}, {325,9772}, {850,8704}, {1916,15980}, {2023,8586}, {2080,3329}, {2782,7840}, {3095,7864}, {3314,7697}, {4027,22525}, {5939,5999}, {7709,7774}, {7900,11257}, {8290,11676}, {8291,14538}, {8292,14539}, {8350,18860}, {12177,22498}, {13334,20088}
X(22503) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(34095)
X(22503) = {X(262), X(22677)}-harmonic conjugate of X(2)
The reciprocal orthologic center of these triangles is X(5999).
X(22504) lies on these lines: {3,11711}, {30,22565}, {36,9860}, {55,7970}, {56,98}, {99,3428}, {104,9862}, {114,958}, {115,22753}, {147,2975}, {517,13173}, {542,11194}, {690,22583}, {956,9864}, {993,2792}, {999,11710}, {1001,11724}, {2782,11249}, {2783,22560}, {2784,8666}, {2787,22775}, {2794,12114}, {2799,19159}, {3027,10966}, {3149,13178}, {5584,21166}, {6033,22758}, {6226,22757}, {6227,22756}, {8980,22763}, {9861,22654}, {10053,22766}, {10069,22767}, {10269,12042}, {11492,12180}, {11493,12179}, {12131,22479}, {12176,22520}, {12181,22755}, {12184,22759}, {12185,22760}, {12186,22761}, {12187,22762}, {12188,22765}, {12189,22768}, {13967,22764}, {18761,22505}, {19013,19055}, {19014,19056}, {22680,22769}
The reciprocal orthologic center of these triangles is X(5999).
X(22505) lies on these lines: {3,7899}, {4,147}, {5,2794}, {20,15561}, {30,114}, {98,381}, {99,382}, {115,546}, {146,15545}, {316,5976}, {542,1353}, {543,15687}, {549,6721}, {550,620}, {671,14269}, {690,1539}, {1478,12185}, {1479,12184}, {1657,21166}, {2023,5475}, {2783,22938}, {2784,18483}, {2787,22799}, {2799,19160}, {3023,3585}, {3027,3583}, {3091,9862}, {3543,8724}, {3545,14830}, {3818,22681}, {3830,6054}, {3832,14651}, {3839,5984}, {3843,12188}, {3850,10991}, {3851,14061}, {3853,14981}, {3857,20398}, {3858,11623}, {4027,14041}, {5026,5103}, {5066,6055}, {5149,7825}, {5985,17577}, {6226,18511}, {6227,18509}, {6287,16044}, {7687,15535}, {7728,11005}, {7841,10352}, {7970,18525}, {8980,18538}, {9772,19910}, {9818,9861}, {9860,18492}, {9864,12699}, {9880,14893}, {9955,11710}, {10053,10895}, {10069,10896}, {10086,12953}, {10089,12943}, {10742,10768}, {10753,18440}, {11737,14971}, {12117,15684}, {12176,18502}, {12178,18491}, {12179,18495}, {12180,18497}, {12181,18507}, {12182,18516}, {12183,18517}, {12186,18520}, {12187,18522}, {12189,18542}, {12190,18544}, {13665,19056}, {13785,19055}, {13967,18762}, {14230,22625}, {14233,22596}, {15704,20399}, {17504,22247}, {18761,22504}, {22501,22502}
X(22505) = midpoint of X(i) and X(j) for these {i,j}: {3, 10722}, {4, 6033}, {99, 382}, {146, 15545}, {3543, 8724}, {3830, 6054}, {7728, 11005}, {7970, 18525}, {9864, 12699}, {10742, 10768}, {10753, 18440}, {12117, 15684}, {12181, 18507}
X(22505) = reflection of X(i) in X(j) for these (i,j): (115, 546), (550, 620), (9880, 14893)
X(22505) = complement of X(38741)
X(22505) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 147, 6321), (3830, 13188, 10723), (3843, 12188, 14639), (6033, 6321, 147), (6054, 10723, 13188)
The reciprocal orthologic center of these triangles is X(22507).
X(22506) lies on these lines: {2,18}, {3,22748}, {316,22508}, {325,5983}, {1916,11603}, {4027,22526}, {5965,5982}, {8291,11133}, {16648,22507}
The reciprocal orthologic center of these triangles is X(22506).
X(22507) lies on these lines: {2,98}, {3,22736}, {5,6778}, {14,11603}, {99,633}, {148,16002}, {299,5983}, {616,13172}, {2782,3104}, {5470,20253}, {5479,13103}, {5611,6298}, {5858,13102}, {6033,16626}, {6775,22998}, {6782,11646}, {13349,14905}, {14061,20415}, {14639,16001}, {14651,16627}, {16648,22506}
X(22507) = reflection of X(148) in X(16002)
X(22507) = reflection of X(22509) in X(114)
X(22507) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (114, 22509, 5613), (1352, 5984, 22509), (5617, 22509, 114), (6230, 6231, 5617)
The reciprocal orthologic center of these triangles is X(22509).
X(22508) lies on these lines: {2,17}, {316,22506}, {325,5982}, {1916,11602}, {4027,22527}, {5965,5983}, {8292,11132}, {16649,22509}
The reciprocal orthologic center of these triangles is X(22508).
X(22509) lies on these lines: {2,98}, {3,22737}, {5,6777}, {13,11602}, {99,634}, {148,16001}, {298,5982}, {532,22570}, {617,13172}, {2782,3105}, {5469,20252}, {5478,13102}, {5615,6299}, {5859,13103}, {6033,16627}, {6772,22997}, {6783,11646}, {13350,14904}, {14061,20416}, {14639,16002}, {14651,16626}, {16649,22508}
X(22509) = reflection of X(148) in X(16001)
X(22509) = reflection of X(22507) in X(114)
X(22509) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (114, 22507, 5617), (1352, 5984, 22507), (5613, 22507, 114), (6230, 6231, 5613)
The reciprocal orthologic center of these triangles is X(5979).
X(22510) lies on these lines: {2,3106}, {4,16631}, {5,14}, {13,98}, {15,115}, {16,230}, {18,298}, {30,5470}, {62,6774}, {99,6671}, {187,23005}, {203,10061}, {385,624}, {511,6034}, {524,16268}, {532,16530}, {542,16267}, {618,5983}, {619,11289}, {623,14061}, {635,7901}, {3104,7746}, {3105,3767}, {3107,5309}, {5238,5474}, {5463,22573}, {5479,16964}, {5978,6669}, {5999,6108}, {6036,14538}, {6114,16966}, {6295,11303}, {6321,13350}, {6775,16241}, {6777,6783}, {6778,11542}, {7005,10077}, {9735,11648}, {9753,22694}, {11304,12204}, {11543,22850}, {11602,14138}, {11707,13178}, {13102,22236}, {13103,19780}, {14651,22688}, {16808,22512}
X(22510) = centroid of X(13)X(14)X(15)
X(22510) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (14, 17, 5613), (14, 396, 22997), (15, 115, 23004), (61, 22891, 14), (398, 20253, 14), (6670, 14137, 18), (6777, 16960, 6783)
The reciprocal orthologic center of these triangles is X(5978).
X(22511) lies on these lines: {2,3107}, {4,16630}, {5,13}, {14,98}, {15,230}, {16,115}, {17,299}, {30,5469}, {61,6771}, {99,6672}, {187,23004}, {202,10062}, {385,623}, {511,6034}, {524,16267}, {542,16268}, {618,11290}, {619,5982}, {624,14061}, {636,7901}, {3104,3767}, {3105,7746}, {3106,5309}, {5237,5473}, {5464,22574}, {5478,16965}, {5979,6670}, {5999,6109}, {6036,14539}, {6115,16967}, {6321,13349}, {6582,11304}, {6772,16242}, {6777,11543}, {6778,6782}, {7006,10078}, {9736,11648}, {9753,22693}, {11303,12205}, {11542,22894}, {11603,14139}, {11708,13178}, {13102,19781}, {13103,22238}, {14651,22690}, {16809,22513}
X(22511) = centroid of X(13)X(14)X(16)
X(22511) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (13, 18, 5617), (13, 395, 22998), (16, 115, 23005), (62, 22846, 13), (397, 20252, 13), (6669, 14136, 17), (6778, 16961, 6782)
The reciprocal orthologic center of these triangles is X(5979).
X(22512) lies on these lines: {3,6114}, {4,32}, {14,16}, {15,5613}, {61,6778}, {187,383}, {381,6109}, {398,9113}, {542,6772}, {543,616}, {617,7865}, {619,11297}, {621,3734}, {622,754}, {624,6295}, {1080,5475}, {2549,5334}, {2782,3104}, {3094,22707}, {3098,22861}, {3815,9750}, {5318,18907}, {5343,22531}, {5460,11296}, {5479,16942}, {5978,7880}, {5979,22568}, {5981,7761}, {6033,6115}, {6108,14830}, {6670,11298}, {6774,18581}, {6782,20426}, {6783,11485}, {7051,12951}, {7804,11303}, {9140,21467}, {10638,12941}, {11486,14137}, {16808,22510}, {18582,22797}, {22689,23019}, {22693,22708}, {22906,23013}
X(22512) = reflection of X(22513) in X(115)
X(22512) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 7737, 22513), (14, 19107, 23004)
The reciprocal orthologic center of these triangles is X(5978).
X(22513) lies on these lines: {3,6115}, {4,32}, {13,15}, {16,5617}, {62,6777}, {187,1080}, {381,6108}, {383,5475}, {397,9112}, {542,6775}, {543,617}, {616,7865}, {618,11298}, {621,754}, {622,3734}, {623,6582}, {1250,12942}, {2549,5335}, {2782,3105}, {3094,22708}, {3098,22907}, {3815,9749}, {5321,18907}, {5344,22532}, {5459,11295}, {5478,16943}, {5978,22570}, {5979,7880}, {5980,7761}, {6033,6114}, {6109,14830}, {6669,11297}, {6771,18582}, {6782,11486}, {6783,20425}, {7804,11304}, {9140,21466}, {11485,14136}, {12952,19373}, {16809,22511}, {18581,22796}, {22687,23025}, {22694,22707}, {22862,23006}
X(22513) = reflection of X(22512) in X(115)
X(22513) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 7737, 22512), (13, 19106, 23005), (5335, 6770, 5472)
The reciprocal parallelogic center of these triangles is X(385).
X(22514) lies on these lines: {3,11710}, {36,13174}, {55,7983}, {56,99}, {98,3428}, {104,13172}, {114,22753}, {115,958}, {148,2975}, {517,12178}, {519,12326}, {542,22583}, {543,11194}, {690,22586}, {956,13178}, {993,11599}, {999,11711}, {1001,11725}, {2782,11249}, {2783,22775}, {2785,8301}, {2787,22560}, {2794,19159}, {2799,19162}, {3023,10966}, {3149,9864}, {4027,22520}, {5186,22479}, {5969,22769}, {6319,22756}, {6320,22757}, {6321,22758}, {8782,22744}, {8997,22763}, {9881,16371}, {10086,22766}, {10089,22767}, {11492,13177}, {11493,13176}, {12114,13180}, {12258,16418}, {13175,22654}, {13179,22755}, {13182,22759}, {13183,22760}, {13184,22761}, {13185,22762}, {13188,22765}, {13189,15452}, {13989,22764}, {18761,22515}, {19013,19108}, {19014,19109}
The reciprocal parallelogic center of these triangles is X(385).
X(22515) lies on these lines: {2,15092}, {3,10723}, {4,147}, {5,620}, {30,115}, {76,18547}, {98,382}, {99,381}, {114,546}, {542,1539}, {543,3845}, {549,6722}, {550,6036}, {671,3830}, {690,10113}, {1478,13183}, {1479,13182}, {1656,21166}, {2023,7748}, {2482,5066}, {2777,15535}, {2783,22799}, {2787,22938}, {2794,3627}, {2799,19163}, {3023,3583}, {3027,3585}, {3044,10540}, {3091,13172}, {3146,14651}, {3534,9166}, {3543,9862}, {3818,5969}, {3839,8724}, {3843,13188}, {3850,10992}, {3857,20399}, {3860,15300}, {3861,14981}, {4027,14042}, {5026,19130}, {5055,12117}, {5461,8703}, {5939,9993}, {6054,12355}, {6319,18509}, {6320,18511}, {7747,12829}, {7845,13449}, {7951,15452}, {7983,18525}, {8782,18500}, {8997,18538}, {9167,10109}, {9818,13175}, {9955,11711}, {9996,11185}, {10053,12953}, {10069,12943}, {10086,10895}, {10089,10896}, {10733,18332}, {10742,10769}, {10754,18440}, {11801,15357}, {12041,15359}, {12100,14971}, {12295,16278}, {12699,13178}, {12902,15342}, {13173,18491}, {13174,18492}, {13176,18495}, {13177,18497}, {13179,18507}, {13180,18516}, {13181,18517}, {13184,18520}, {13185,18522}, {13189,18542}, {13190,18544}, {13665,19109}, {13785,19108}, {13989,18762}, {14830,15682}, {15704,20398}, {18761,22514}
X(22515) = midpoint of X(i) and X(j) for these {i,j}: {3, 10723}, {4, 6321}, {98, 382}, {671, 3830}, {3543, 11632}, {6054, 12355}, {7983, 18525}, {10733, 18332}, {10742, 10769}, {10754, 18440}, {12295, 16278}, {12699, 13178}, {12902, 15342}, {13179, 18507}, {14830, 15682}
X(22515) = reflection of X(i) in X(j) for these (i,j): (114, 546), (550, 6036), (2482, 5066), (5026, 19130), (12041, 15359)
X(22515) = complement of X(38730)
X(22515) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 148, 6033), (671, 10722, 12188), (3091, 13172, 15561), (3830, 12188, 10722), (6033, 6321, 148), (10723, 14639, 3), (12355, 14269, 6054)
The reciprocal cyclologic center of these triangles is X(22517).
X(22516) lies on these lines: {}
The reciprocal cyclologic center of these triangles is X(22516).
X(22517) lies on these lines: {}
The reciprocal cyclologic center of these triangles is X(22519).
X(22518) lies on these lines: {}
The reciprocal cyclologic center of these triangles is X(22518).
X(22519) lies on these lines: {}
X(22520) lies on these lines: {3,11490}, {32,56}, {36,10789}, {55,10800}, {83,958}, {98,22753}, {104,10788}, {182,3428}, {384,22779}, {727,4257}, {956,10791}, {995,4279}, {999,11364}, {2080,10269}, {2975,7787}, {3398,11249}, {4027,22514}, {5253,7793}, {6196,16476}, {7976,17034}, {10790,22654}, {10793,22757}, {10794,12110}, {10796,22758}, {10797,22759}, {10798,22760}, {10799,10804}, {10801,22766}, {10802,22767}, {10803,22768}, {11194,12150}, {11380,22479}, {11492,11838}, {11493,11837}, {11839,22755}, {11840,22761}, {11841,22762}, {11842,22765}, {12176,22504}, {12191,22565}, {12192,22583}, {12193,22659}, {12195,12513}, {12196,18237}, {12197,22770}, {12198,12773}, {12199,22775}, {12200,22777}, {12201,19478}, {12202,22778}, {12204,22774}, {12205,22773}, {12206,22780}, {12207,19159}, {12208,22781}, {12209,22782}, {12210,22595}, {12211,22624}, {12212,22769}, {13193,22586}, {13194,22560}, {13195,19162}, {13672,22783}, {13743,16115}, {13792,22784}, {13885,22763}, {13938,22764}, {17023,21010}, {18502,18761}, {18993,19013}, {18994,19014}, {22521,22680}, {22522,22771}, {22523,22772}, {22524,22776}
X(22520) = {X(3), X(12194)}-harmonic conjugate of X(11490)
The reciprocal orthologic center of these triangles is X(3).
X(22521) lies on these lines: {4,3172}, {5,20088}, {6,7709}, {32,262}, {61,22523}, {62,22522}, {83,15819}, {98,5008}, {99,5097}, {182,22676}, {376,5050}, {385,7697}, {511,12150}, {576,3972}, {1003,5093}, {1656,7900}, {2080,3329}, {2548,9754}, {2782,12191}, {3398,7470}, {3524,19661}, {3533,10155}, {5007,12110}, {5171,7878}, {5188,9751}, {5306,14651}, {5480,9862}, {5999,11842}, {6179,10358}, {6194,7787}, {7694,9753}, {7757,15520}, {7785,20576}, {9166,14160}, {10789,22650}, {10790,22655}, {10791,22697}, {10792,22699}, {10793,22700}, {10794,22703}, {10795,22704}, {10797,22705}, {10798,22706}, {10799,22711}, {10800,22713}, {10801,22729}, {10802,22730}, {10803,22731}, {10804,22732}, {11364,22475}, {11380,22480}, {11490,22556}, {11837,22668}, {11838,22672}, {11839,22698}, {11840,22709}, {11841,22710}, {12176,12212}, {12835,18971}, {13860,21309}, {13885,22720}, {13938,22721}, {14537,14639}, {14693,17005}, {14912,15428}, {18502,22681}, {18993,19063}, {18994,19064}, {22520,22680}
X(22521) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 10788, 11676), (32, 262, 21445)
The reciprocal orthologic center of these triangles is X(3).
X(22522) lies on these lines: {18,32}, {62,22521}, {83,630}, {98,22831}, {182,22843}, {628,7787}, {1078,6674}, {3398,12204}, {5965,12212}, {10788,22531}, {10789,22651}, {10790,22656}, {10791,22851}, {10792,22853}, {10793,22854}, {10794,22857}, {10795,22858}, {10796,16627}, {10797,22859}, {10798,22860}, {10799,22865}, {10800,22867}, {10801,22884}, {10802,22885}, {10803,22886}, {10804,22887}, {11364,11740}, {11380,22481}, {11490,22557}, {11837,22669}, {11838,22673}, {11839,22852}, {11840,22863}, {11841,22864}, {11842,16628}, {12110,16965}, {12835,18972}, {13885,22876}, {13938,22877}, {18502,22794}, {18993,19069}, {18994,19072}, {22520,22771}
The reciprocal orthologic center of these triangles is X(3).
X(22523) lies on these lines: {17,32}, {61,22521}, {83,629}, {98,22832}, {182,22890}, {532,12150}, {627,7787}, {1078,6673}, {3398,12205}, {5965,12212}, {10788,22532}, {10789,22652}, {10790,22657}, {10791,22896}, {10792,22898}, {10793,22899}, {10794,22902}, {10795,22903}, {10796,16626}, {10797,22904}, {10798,22905}, {10799,22910}, {10800,22912}, {10801,22929}, {10802,22930}, {10803,22931}, {10804,22932}, {11364,11739}, {11380,22482}, {11490,22558}, {11837,22670}, {11838,22674}, {11839,22897}, {11840,22908}, {11841,22909}, {11842,16629}, {12110,16964}, {12835,18973}, {13885,22921}, {13938,22922}, {18502,22795}, {18993,19071}, {18994,19070}, {22520,22772}
The reciprocal orthologic center of these triangles is X(12241).
X(22524) lies on these lines: {32,22466}, {83,22966}, {98,22833}, {182,22951}, {7787,22647}, {10788,22533}, {10789,22653}, {10790,22658}, {10791,22941}, {10792,22945}, {10793,22947}, {10794,22956}, {10795,22957}, {10796,22955}, {10797,22958}, {10798,22959}, {10799,22965}, {10800,22969}, {10801,22980}, {10802,22981}, {10803,22982}, {10804,22983}, {11364,22476}, {11380,22483}, {11490,22559}, {11839,22943}, {11840,22963}, {11841,22964}, {11842,22979}, {12835,18978}, {13885,22976}, {13938,22977}, {18502,22800}, {18993,19083}, {18994,19084}, {22520,22776}
The reciprocal orthologic center of these triangles is X(12177).
X(22525) lies on these lines: {182,7771}, {325,9755}, {385,575}, {511,5182}, {524,5050}, {576,3972}, {2782,12151}, {4027,22503}, {7894,22234}, {10131,22679}, {11159,20423}
The reciprocal orthologic center of these triangles is X(22507).
X(22526) lies on these lines: {6,22683}, {182,22736}, {4027,22506}, {10131,22748}
The reciprocal orthologic center of these triangles is X(22509).
X(22527) lies on these lines: {6,22685}, {182,22737}, {532,5182}, {4027,22508}, {10131,22749}
The reciprocal orthologic center of these triangles is X(9729).
X(22528) lies on these lines: {2,22581}, {3,22497}, {4,22834}, {20,1204}, {22,1620}, {30,22808}, {64,394}, {69,11440}, {97,19198}, {511,21652}, {1370,22555}, {1619,12279}, {1993,19460}, {2071,5907}, {2979,22534}, {3060,22530}, {3100,22954}, {3101,22840}, {3146,22538}, {3153,22816}, {4296,19472}, {5012,22529}, {6515,18936}, {7488,22962}, {7691,16386}, {11412,21312}, {11414,22550}, {11416,22830}, {11417,22960}, {11418,22961}, {11420,22974}, {11421,22975}, {12086,12294}, {12219,15054}, {13567,22466}, {17811,22966}, {19121,19142}, {19406,19488}, {19407,19489}
X(22528) = midpoint of X(11412) and X(22535)
X(22528) = reflection of X(i) in X(j) for these (i,j): (4, 22834), (3146, 22538)
X(22528) = anticomplement of X(22970)
X(22528) = {X(22581), X(22970)}-harmonic conjugate of X(2)
The reciprocal orthologic center of these triangles is X(9729).
X(22529) lies on these lines: {6,2929}, {54,403}, {182,22581}, {184,22970}, {389,22962}, {567,22808}, {569,22834}, {1147,22955}, {2904,5890}, {5012,22528}, {9306,22973}, {11402,19460}, {11422,22534}, {11423,22535}, {11424,22538}, {11425,22549}, {11426,22550}, {11427,22555}, {11428,22840}, {11429,22954}, {11430,22978}, {11536,22952}, {12233,15472}, {13366,21652}, {14912,18936}, {17809,17837}, {18388,22816}, {19153,22658}, {19365,19472}, {19408,19488}, {19409,19489}
X(22529) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 2929, 22530), (11402, 22497, 19460)
The reciprocal orthologic center of these triangles is X(9729).
X(22530) lies on these lines: {4,18936}, {6,2929}, {25,19460}, {51,21652}, {52,22834}, {185,22538}, {378,19360}, {511,22581}, {568,22808}, {578,22962}, {974,12241}, {3060,22528}, {3567,22750}, {5640,22534}, {5943,22973}, {6217,22947}, {6218,22945}, {6642,22955}, {6746,9969}, {9777,22497}, {9781,22535}, {9786,22549}, {9792,19198}, {10151,22968}, {11432,22550}, {11433,22555}, {11435,22840}, {11436,22954}, {11438,22978}, {17810,17837}, {18390,22816}, {19039,19083}, {19040,19084}, {19366,19472}, {19410,19488}, {19411,19489}, {22483,22953}
X(22530) = midpoint of X(i) and X(j) for these {i,j}: {52, 22834}, {185, 22538}, {22483, 22953}
X(22530) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 2929, 22529), (51, 21652, 22970)
The reciprocal orthologic center of these triangles is X(3).
X(22531) lies on these lines: {2,16627}, {3,299}, {4,16}, {20,6773}, {24,22656}, {30,16628}, {32,16941}, {98,5488}, {104,22771}, {315,11133}, {388,22884}, {397,19780}, {398,16940}, {497,22885}, {515,22651}, {630,631}, {1204,3098}, {3085,22859}, {3086,22860}, {3090,6674}, {3091,22794}, {3104,7709}, {3528,22845}, {4293,18972}, {4294,22865}, {5334,7756}, {5343,22512}, {5344,12815}, {5603,11740}, {5657,22851}, {5869,11481}, {7487,22481}, {7581,19072}, {7582,19069}, {7967,22867}, {8260,22238}, {9862,22745}, {10645,22855}, {10646,22850}, {10783,22853}, {10784,22854}, {10785,22857}, {10786,22858}, {10788,22522}, {10805,22886}, {10806,22887}, {11491,22557}, {11603,14651}, {11843,22669}, {11844,22673}, {11845,22852}, {11846,22863}, {11847,22864}, {12252,14538}, {13886,22876}, {13939,22877}, {16965,22846}
X(22531) = midpoint of X(20) and X(22114)
X(22531) = reflection of X(4) in X(18)
X(22531) = anticomplement of X(16627)
X(22531) = {X(3522), X(6776)}-harmonic conjugate of X(22532)
The reciprocal orthologic center of these triangles is X(3).
X(22532) lies on these lines: {2,16626}, {3,298}, {4,15}, {20,6770}, {24,22657}, {30,16629}, {32,16940}, {98,5487}, {104,22772}, {315,11132}, {376,532}, {388,22929}, {397,16941}, {398,19781}, {497,22930}, {515,22652}, {629,631}, {1204,3098}, {3085,22904}, {3086,22905}, {3090,6673}, {3091,22795}, {3105,7709}, {3528,22844}, {4293,18973}, {4294,22910}, {5335,7756}, {5343,12815}, {5344,22513}, {5603,11739}, {5657,22896}, {5868,11480}, {7487,22482}, {7581,19070}, {7582,19071}, {7967,22912}, {8259,22236}, {9862,22746}, {10645,22894}, {10646,22901}, {10783,22898}, {10784,22899}, {10785,22902}, {10786,22903}, {10788,22523}, {10805,22931}, {10806,22932}, {11491,22558}, {11602,14651}, {11843,22670}, {11844,22674}, {11845,22897}, {11846,22908}, {11847,22909}, {12252,14539}, {13886,22921}, {13939,22922}, {16964,22891}
X(22532) = midpoint of X(20) and X(22113)
X(22532) = reflection of X(4) in X(17)
X(22532) = anticomplement of X(16626)
X(22532) = {X(3522), X(6776)}-harmonic conjugate of X(22531)
The reciprocal orthologic center of these triangles is X(12241).
X(22533) lies on these lines: {2,22953}, {3,22647}, {4,18936}, {5,19361}, {20,1204}, {24,22658}, {26,22550}, {30,22979}, {68,3546}, {104,22776}, {125,2888}, {186,2917}, {206,1614}, {376,22951}, {388,22980}, {497,22981}, {515,22653}, {631,22966}, {1181,22972}, {3085,22958}, {3086,22959}, {3091,22800}, {3448,12111}, {4293,18978}, {4294,22965}, {5603,22476}, {5657,22941}, {5876,18933}, {5925,12244}, {6353,22662}, {6623,22970}, {7487,22483}, {7581,19084}, {7582,19083}, {7967,22969}, {9862,22747}, {10783,22945}, {10784,22947}, {10785,22956}, {10786,22957}, {10788,22524}, {10805,22982}, {10806,22983}, {10938,13491}, {11411,18436}, {11431,22968}, {11457,12250}, {11491,22559}, {11799,18914}, {11845,22943}, {11846,22963}, {11847,22964}, {13886,22976}, {13939,22977}, {14216,22538}, {15532,18946}, {18925,18952}, {19467,22962}
X(22533) = reflection of X(4) in X(22466)
X(22533) = anticomplement of X(22955)
The reciprocal orthologic center of these triangles is X(9729).
X(22534) lies on these lines: {2,21652}, {3,22535}, {22,17837}, {25,5889}, {110,2929}, {1993,22497}, {2979,22528}, {3060,22970}, {5012,19460}, {5640,22530}, {7998,22581}, {11422,22529}, {11439,22538}, {11440,22549}, {11442,22555}, {11443,22830}, {11444,22834}, {11445,22840}, {11446,22954}, {11447,22960}, {11448,22961}, {11449,22962}, {11451,22973}, {11452,22974}, {11453,22975}, {11454,22978}, {11459,22808}, {12270,14683}, {12279,17845}, {12280,13598}, {12825,22979}, {18392,22816}, {18911,18936}, {19122,19142}, {19167,19198}, {19367,19472}, {19412,19488}, {19413,19489}
X(22534) = anticomplement of X(21652)
The reciprocal orthologic center of these triangles is X(9729).
X(22535) lies on these lines: {3,22534}, {4,21652}, {24,17837}, {54,19460}, {74,22549}, {1614,2929}, {3567,22970}, {5890,22750}, {7592,22497}, {7999,22581}, {9781,22530}, {11412,21312}, {11423,22529}, {11455,22538}, {11456,22550}, {11457,12281}, {11458,22830}, {11459,22834}, {11460,22840}, {11461,22954}, {11462,22960}, {11463,22961}, {11464,22962}, {11465,22973}, {11466,22974}, {11467,22975}, {11468,22978}, {12111,22808}, {18394,22816}, {18912,18936}, {19123,19142}, {19168,19198}, {19368,19472}, {19414,19488}, {19415,19489}
X(22535) = reflection of X(i) in X(j) for these (i,j): (4, 21652), (11412, 22528), (12111, 22808)
X(22536) lies on these lines: {372,22553}, {22588,22644}
X(22537) lies on these lines: {371,22554}, {22615,22619}
The reciprocal orthologic center of these triangles is X(9729).
X(22538) lies on these lines: {4,801}, {20,22581}, {24,22978}, {25,22549}, {30,22834}, {33,19472}, {34,22954}, {64,13399}, {125,1885}, {185,22530}, {378,22962}, {382,22808}, {1498,19460}, {1593,2929}, {1595,15432}, {1597,22550}, {3091,22973}, {3146,22528}, {7507,22971}, {9927,11472}, {10151,22966}, {11381,21652}, {11403,22497}, {11424,22529}, {11439,22534}, {11442,11469}, {11455,22535}, {11470,22830}, {11471,22840}, {11473,22960}, {11474,22961}, {11475,22974}, {11476,22975}, {12134,12295}, {12162,21651}, {12293,22979}, {12324,18936}, {13473,16656}, {13488,18488}, {14216,22533}, {15811,17837}, {19124,19142}, {19169,19198}, {19416,19488}, {19417,19489}
X(22538) = midpoint of X(i) and X(j) for these {i,j}: {382, 22808}, {3146, 22528}, {11381, 21652}
X(22538) = reflection of X(i) in X(j) for these (i,j): (20, 22581), (185, 22530)
The reciprocal cyclologic center of these triangles is X(22540).
X(22539) lies on the line {6,22542}
The reciprocal cyclologic center of these triangles is X(22539).
X(22540) lies on the orthocentroidal circle and these lines: {}
The reciprocal orthologic center of these triangles is X(13665).
X(22541) lies on these lines: {2,13662}, {6,1327}, {30,19103}, {371,13666}, {1384,13712}, {1588,13687}, {3068,13701}, {3299,13715}, {3301,13714}, {5410,13668}, {6417,13713}, {7581,13674}, {7583,13692}, {7585,13678}, {7586,13988}, {7969,13702}, {11055,13669}, {11147,12159}, {13651,13846}, {13665,22806}, {13667,18992}, {13672,18994}, {13675,19000}, {13679,19004}, {13680,19006}, {13682,19008}, {13683,19010}, {13685,19012}, {13688,13883}, {13689,19018}, {13693,19024}, {13694,19026}, {13695,19028}, {13696,19030}, {13697,19032}, {13698,19034}, {13699,19038}, {13711,22616}, {13716,19048}, {13717,19050}, {13770,13932}, {18986,18996}, {19014,22783}
X(22541) = {X(6), X(1327)}-harmonic conjugate of X(19099)
The reciprocal cyclologic center of these triangles is X(22543).
X(22542) lies on the line {6,22539}
The reciprocal cyclologic center of these triangles is X(22544).
X(22543) lies on the line {19130,22544}
The reciprocal cyclologic center of these triangles is X(22543).
X(22544) lies on the line {19130,22543}
The reciprocal cyclologic center of these triangles is X(22546).
X(22545) lies on the line {6,22546}
The reciprocal cyclologic center of these triangles is X(22545).
X(22546) lies on the line {6,22545}
The reciprocal cyclologic center of these triangles is X(22548).
X(22547) lies on the line {5092,22548}
The reciprocal cyclologic center of these triangles is X(22547).
X(22548) lies on the line {5092,22547}
The reciprocal orthologic center of these triangles is X(9729).
X(22549) lies on these lines: {3,2929}, {5,22971}, {20,10117}, {25,22538}, {55,19472}, {56,22954}, {64,394}, {68,10264}, {74,22535}, {141,3520}, {185,19460}, {378,22750}, {382,22816}, {1092,2935}, {1151,22960}, {1152,22961}, {1204,21652}, {1350,15073}, {1593,22970}, {2071,2888}, {2917,16163}, {3516,22497}, {3964,15874}, {5085,19142}, {5584,22840}, {5646,7503}, {5925,9914}, {6101,12163}, {9786,22530}, {10620,18436}, {11425,22529}, {11440,22534}, {11472,12084}, {11477,22830}, {11479,22973}, {11480,22974}, {11481,22975}, {12162,18859}, {12307,15644}, {13021,19488}, {13022,19489}, {14130,14926}, {15068,22585}, {15622,22559}, {17928,22833}, {18913,18936}, {19172,19198}
X(22549) = midpoint of X(i) and X(j) for these {i,j}: {20, 22555}, {64, 17837}
X(22549) = reflection of X(i) in X(j) for these (i,j): (3, 22978), (382, 22816), (11477, 22830)
X(22549) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 22550, 22962), (22550, 22962, 2929)
The reciprocal orthologic center of these triangles is X(9729).
X(22550) lies on these lines: {3,2929}, {4,22497}, {5,22555}, {24,12310}, {25,5889}, {26,22533}, {52,12316}, {155,11557}, {999,19472}, {1181,21652}, {1351,7506}, {1593,7703}, {1597,22538}, {1598,22970}, {2070,9920}, {2904,3167}, {3295,22954}, {3311,22960}, {3312,22961}, {3517,12309}, {3527,6642}, {3843,22816}, {5050,19142}, {5446,15136}, {6644,22647}, {6759,17837}, {7387,11820}, {7517,12315}, {8780,9937}, {10306,22840}, {11414,22528}, {11426,22529}, {11432,22530}, {11456,22535}, {11482,22830}, {11484,22973}, {11485,22974}, {11486,22975}, {11801,12084}, {12308,18378}, {13346,13376}, {18914,18936}, {19173,19198}, {19347,19460}, {19418,19488}, {19419,19489}
X(22550) = reflection of X(3) in X(2929)
X(22550) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2929, 22549, 22962), (22549, 22962, 3), (22816, 22971, 3843)
The reciprocal cyclologic center of these triangles is X(22552).
X(22551) lies on these lines: {3,129}, {25,1298}, {130,1598}, {154,14673}, {1181,21661}, {1303,11414}, {6759,22552}, {9920,11641}, {13175,17834}
The reciprocal cyclologic center of these triangles is X(22551).
X(22552) lies on these lines: {6,130}, {25,21661}, {129,17814}, {394,1303}, {1181,1298}, {6759,22551}
X(22553) lies on these lines: {372,22536}, {1328,5491}, {6565,22589}
X(22554) lies on these lines: {371,22537}, {1327,5490}, {6564,22620}
The reciprocal orthologic center of these triangles is X(9729).
X(22555) lies on these lines: {2,2929}, {4,801}, {5,22550}, {20,10117}, {68,18933}, {69,22466}, {376,22978}, {381,15436}, {388,19472}, {427,22497}, {497,22954}, {631,22962}, {1370,22528}, {1503,17837}, {1899,18936}, {1992,22830}, {2550,22840}, {3068,22960}, {3069,22961}, {3153,14516}, {3618,19142}, {3832,22971}, {4549,6643}, {5562,12325}, {6776,19460}, {7386,22581}, {7392,22973}, {11411,18436}, {11427,22529}, {11433,22530}, {11442,22534}, {11457,12281}, {11487,14128}, {11488,22974}, {11489,22975}, {12225,22658}, {12319,12902}, {15435,22968}, {19174,19198}, {19420,19488}, {19421,19489}, {20806,22972}
X(22555) = reflection of X(20) in X(22549)
X(22555) = anticomplement of X(2929)
X(22555) = {X(1899), X(21652)}-harmonic conjugate of X(18936)
The reciprocal orthologic center of these triangles is X(3).
X(22556) lies on these lines: {3,22680}, {35,22650}, {55,262}, {56,22713}, {100,6194}, {197,22655}, {511,4421}, {1376,15819}, {2782,12326}, {3295,22475}, {5687,22697}, {7697,11499}, {7709,11491}, {10310,22676}, {11248,12339}, {11383,22480}, {11490,22521}, {11492,22668}, {11493,22672}, {11494,22678}, {11496,22682}, {11497,22699}, {11498,22700}, {11500,22704}, {11501,22705}, {11502,22706}, {11503,22709}, {11504,22710}, {11507,22729}, {11508,22730}, {11509,18971}, {11510,22732}, {11848,22698}, {11849,22728}, {12178,12329}, {13887,22720}, {13940,22721}, {18491,22681}, {18999,19063}, {19000,19064}
The reciprocal orthologic center of these triangles is X(3).
X(22557) lies on these lines: {3,22771}, {18,55}, {35,22651}, {56,22867}, {100,628}, {197,22656}, {630,1376}, {1001,6674}, {3295,11740}, {5687,22851}, {5965,12329}, {10310,22843}, {11248,12336}, {11383,22481}, {11490,22522}, {11491,22531}, {11492,22669}, {11493,22673}, {11494,22745}, {11496,22831}, {11497,22853}, {11498,22854}, {11499,16627}, {11500,22858}, {11501,22859}, {11502,22860}, {11503,22863}, {11504,22864}, {11507,22884}, {11508,22885}, {11509,18972}, {11510,22887}, {11848,22852}, {11849,16628}, {13887,22876}, {13940,22877}, {18491,22794}, {18999,19069}, {19000,19072}
The reciprocal orthologic center of these triangles is X(3).
X(22558) lies on these lines: {3,22772}, {17,55}, {35,22652}, {56,22912}, {100,627}, {197,22657}, {532,4421}, {629,1376}, {1001,6673}, {3295,11739}, {5687,22896}, {5965,12329}, {10310,22890}, {11248,12337}, {11383,22482}, {11490,22523}, {11491,22532}, {11492,22670}, {11493,22674}, {11494,22746}, {11496,22832}, {11497,22898}, {11498,22899}, {11499,16626}, {11500,22903}, {11501,22904}, {11502,22905}, {11503,22908}, {11504,22909}, {11507,22929}, {11508,22930}, {11509,18973}, {11510,22932}, {11848,22897}, {11849,16629}, {13887,22921}, {13940,22922}, {18491,22795}, {18999,19071}, {19000,19070}
The reciprocal orthologic center of these triangles is X(12241).
X(22559) lies on these lines: {3,22776}, {35,22653}, {55,22466}, {56,22969}, {100,22647}, {197,22658}, {1376,22956}, {3295,22476}, {5687,22941}, {7074,22972}, {10310,22951}, {11383,22483}, {11490,22524}, {11491,22533}, {11494,22747}, {11496,22833}, {11497,22945}, {11498,22947}, {11499,22955}, {11500,22957}, {11501,22958}, {11502,22959}, {11503,22963}, {11504,22964}, {11507,22980}, {11508,22981}, {11509,18978}, {11510,22983}, {11848,22943}, {11849,22979}, {13887,22976}, {13940,22977}, {15622,22549}, {18491,22800}, {18999,19083}, {19000,19084}
The reciprocal cyclologic center of these triangles is X(13025).
X(22560) lies on these lines: {1,6596}, {3,2802}, {11,958}, {35,12653}, {36,2932}, {55,1320}, {56,100}, {63,17638}, {80,956}, {104,376}, {106,3939}, {119,11236}, {149,2975}, {153,529}, {214,999}, {405,16173}, {517,12332}, {518,6326}, {519,12331}, {952,11249}, {993,21630}, {1001,1387}, {1012,14217}, {1145,1376}, {1862,22479}, {2136,13144}, {2771,22583}, {2783,22504}, {2787,22514}, {2800,12330}, {2806,19162}, {2831,19159}, {3035,3085}, {3149,12751}, {3169,21773}, {3680,7280}, {3738,4491}, {3811,22935}, {3928,12767}, {4421,10269}, {5119,17652}, {5204,8668}, {5220,18254}, {5288,9897}, {5289,12740}, {5563,15015}, {5840,12114}, {6174,11239}, {6264,11012}, {6265,10680}, {6366,8301}, {6702,9708}, {6906,13463}, {6913,16174}, {8666,12773}, {8674,22586}, {8730,9945}, {9024,22769}, {10074,10609}, {10087,22766}, {10310,18861}, {10530,18962}, {10738,11235}, {11492,13230}, {11493,13228}, {12641,15180}, {13194,22520}, {13222,22654}, {13235,22744}, {13268,22755}, {13269,22756}, {13270,22757}, {13273,22759}, {13274,22760}, {13275,22761}, {13276,22762}, {13278,22768}, {13922,22763}, {13991,22764}, {18761,22938}, {19013,19112}, {19014,19113}
X(22560) = reflection of X(i) in X(j) for these (i,j): (149, 3813), (3811, 22935), (6264, 11260)
X(22560) = circumperp conjugate of X(14664)
X(22560) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (36, 5541, 2932), (1145, 10090, 1376), (1320, 4996, 55)
X(22561) lies on these lines: {3,8289}, {6,11152}, {99,22564}, {385,16508}, {2482,10810}, {5652,9485}, {8592,11317}
The reciprocal orthologic center of these triangles is X(9891).
X(22562) lies on these lines: {486,490}, {542,6281}, {543,1328}, {642,8786}, {2482,12123}, {6054,9758}, {6290,10488}, {6319,22484}, {6561,9892}, {7840,22501}, {14645,22591}, {22563,22566}
The reciprocal orthologic center of these triangles is X(9893).
X(22563) lies on these lines: {485,489}, {542,6278}, {543,1327}, {641,8786}, {2482,12124}, {6054,9757}, {6289,10488}, {6320,22485}, {6560,9894}, {7840,22502}, {14645,22592}, {22562,22566}
The reciprocal orthologic center of these triangles is X(99).
X(22564) lies on these lines: {2,51}, {76,3849}, {98,10810}, {99,22561}, {187,7757}, {316,7848}, {385,5104}, {524,8592}, {538,8591}, {1003,9301}, {1916,8587}, {2076,14614}, {2080,4027}, {2782,9855}, {3329,8586}, {5162,9888}, {5215,7786}, {5976,7840}, {7793,13085}, {7833,9821}, {7883,18806}, {8290,12151}, {8598,11152}, {8704,9485}, {9772,9773}, {9889,11054}
X(22564) = reflection of X(316) in X(9466)
The reciprocal orthologic center of these triangles is X(9855).
X(22565) lies on these lines: {3,12326}, {30,22504}, {36,9875}, {55,9884}, {56,671}, {104,12243}, {519,13173}, {542,12114}, {543,11194}, {956,9881}, {958,2482}, {993,8301}, {999,12258}, {2782,22680}, {2796,8666}, {2975,8591}, {3428,12117}, {5969,22779}, {8724,22758}, {9830,22769}, {9876,22654}, {9878,22744}, {9880,22753}, {9882,22756}, {9883,22757}, {10054,22766}, {10070,22767}, {10966,12354}, {11492,12346}, {11493,12345}, {11711,16418}, {12132,22479}, {12191,22520}, {12347,22755}, {12350,22759}, {12351,22760}, {12352,22761}, {12353,22762}, {12355,22765}, {12356,22768}, {13178,16371}, {13908,22763}, {13968,22764}, {18761,22566}, {19013,19057}, {19014,19058}
The reciprocal orthologic center of these triangles is X(9855).
X(22566) lies on these lines: {2,5191}, {3,11149}, {4,8591}, {5,542}, {30,114}, {98,5055}, {99,3830}, {115,5066}, {147,3545}, {262,381}, {376,15561}, {382,12117}, {543,3845}, {546,9880}, {547,6055}, {549,2794}, {550,20399}, {620,8703}, {625,5026}, {804,18309}, {1478,12351}, {1479,12350}, {2080,10487}, {2548,6034}, {2796,18483}, {3091,12243}, {3534,10722}, {3583,12354}, {3585,18969}, {3628,10991}, {3656,9864}, {3818,8176}, {3839,6321}, {3843,12355}, {3853,10992}, {5071,11177}, {5182,11318}, {5655,11005}, {5939,10033}, {5969,7775}, {5976,7809}, {6036,15699}, {6721,11539}, {7728,11006}, {7934,9774}, {8355,18800}, {8593,18440}, {8860,10104}, {9166,12188}, {9167,12100}, {9760,22570}, {9762,22568}, {9818,9876}, {9875,18492}, {9878,18500}, {9881,12699}, {9882,18509}, {9883,18511}, {9884,18525}, {9888,11184}, {9955,12258}, {10054,10895}, {10056,12185}, {10070,10896}, {10072,12184}, {10109,14971}, {10488,12177}, {10516,19905}, {12101,15300}, {12191,18502}, {12326,18491}, {12345,18495}, {12346,18497}, {12347,18507}, {12348,18516}, {12349,18517}, {12352,18520}, {12353,18522}, {12356,18542}, {12357,18544}, {13188,14269}, {13665,19058}, {13785,19057}, {13908,18538}, {13968,18762}, {15681,21166}, {18761,22565}, {22562,22563}
X(22566) = midpoint of X(i) and X(j) for these {i,j}: {2, 6033}, {4, 8724}, {99, 3830}, {147, 11632}, {382, 12117}, {3534, 10722}, {3656, 9864}, {5655, 11005}, {7728, 11006}, {8593, 18440}, {9881, 12699}, {9884, 18525}, {12347, 18507}
X(22566) = reflection of X(115) in X(5066)
X(22566) = complement of X(14830)
X(22566) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (147, 3545, 11632), (9166, 19709, 15092), (12188, 19709, 9166)
The reciprocal orthologic center of these triangles is X(22568).
X(22567) lies on these lines: {2,18}, {8594,11054}, {16650,22568}
The reciprocal orthologic center of these triangles is X(22567).
X(22568) lies on these lines: {2,99}, {3,22866}, {2936,3129}, {3104,5463}, {5464,6296}, {5979,22512}, {8724,16626}, {9115,10754}, {9762,22566}, {16650,22567}
X(22568) = anticomplement of X(33460)
X(22568) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (671, 9888, 22570), (2482, 22570, 9886), (7618, 8596, 22570), (8591, 9890, 22570), (9885, 22570, 2482), (9892, 9894, 9885)
The reciprocal orthologic center of these triangles is X(22570).
X(22569) lies on these lines: {2,17}, {8595,11054}, {16651,22570}
The reciprocal orthologic center of these triangles is X(22569).
X(22570) lies on these lines: {2,99}, {3,22911}, {532,22509}, {2936,3130}, {3105,5464}, {5463,6297}, {5978,22513}, {8724,16627}, {9117,10754}, {9760,22566}, {16651,22569}
X(22570) = anticomplement of X(33461)
X(22570) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (671, 9888, 22568), (2482, 22568, 9885), (7618, 8596, 22568), (8591, 9890, 22568), (9886, 22568, 2482), (9892, 9894, 9886)
The reciprocal orthologic center of these triangles is X(8595).
X(22571) lies on these lines: {14,8584}, {17,9886}, {61,22575}, {115,22495}, {395,22490}, {524,5470}, {532,9166}, {543,16267}, {5464,11542}, {10991,16001}, {16631,22492}, {16808,22579}, {16960,22577}
The reciprocal orthologic center of these triangles is X(8594).
X(22572) lies on these lines: {13,8584}, {18,9885}, {62,22576}, {115,22496}, {396,22489}, {524,5469}, {543,16268}, {5463,11543}, {10991,16002}, {16630,22491}, {16809,22580}, {16961,22578}
The reciprocal orthologic center of these triangles is X(8595).
X(22573) lies on these lines: {14,1992}, {115,524}, {148,8594}, {298,9166}, {299,11054}, {381,22579}, {396,543}, {532,5460}, {2482,22892}, {3839,5479}, {5032,9113}, {5459,22691}, {5461,22847}, {5463,22510}, {5464,16267}, {5471,8584}, {5472,9830}, {6114,11163}, {6303,13757}, {6307,13637}, {6775,9763}, {8593,9112}, {8595,8859}, {8860,13084}, {9114,16960}, {9201,9979}, {9760,18582}, {9886,16644}, {10654,22575}, {11632,20425}, {13874,13876}, {13927,13929}, {16529,22578}, {16962,22577}
X(22573) = midpoint of X(i) and X(j) for these {i,j}: {14, 22495}, {148, 8594}, {299, 11054}, {11632, 20425}
X(22573) = X(16)-pedal-to-X(15)-pedal similarity image of X(2)
The reciprocal orthologic center of these triangles is X(8594).
X(22574) lies on these lines: {13,1992}, {115,524}, {148,8595}, {298,11054}, {299,9166}, {381,22580}, {395,543}, {2482,22848}, {3839,5478}, {5032,9112}, {5460,22692}, {5461,22893}, {5463,16268}, {5464,22511}, {5471,9830}, {5472,8584}, {6115,11163}, {6302,13757}, {6306,13637}, {6772,9761}, {8593,9113}, {8594,8859}, {8860,13083}, {9116,16961}, {9200,9979}, {9762,18581}, {9885,16645}, {10653,22576}, {11632,20426}, {13874,13875}, {13927,13928}, {16530,22577}, {16963,22578}
X(22574) = midpoint of X(i) and X(j) for these {i,j}: {13, 22496}, {148, 8595}, {298, 11054}, {11632, 20426}
X(22574) = X(15)-pedal-to-X(16)-pedal similarity image of X(2)
The reciprocal orthologic center of these triangles is X(8595).
X(22575) lies on these lines: {2,11154}, {5,9886}, {13,11317}, {61,22571}, {114,381}, {115,11295}, {303,5464}, {316,22494}, {524,20429}, {598,11603}, {630,11303}, {5321,22579}, {5460,11489}, {5474,13083}, {5479,7620}, {8352,23004}, {9166,11299}, {10654,22573}, {11301,14971}, {11304,13084}, {16809,22577}
X(22575) = reflection of X(5474) in X(13083)
The reciprocal orthologic center of these triangles is X(8594).
X(22576) lies on these lines: {2,11153}, {5,9885}, {14,11317}, {62,22572}, {114,381}, {115,11296}, {302,5463}, {316,22493}, {524,20428}, {598,11602}, {629,11304}, {5318,22580}, {5459,11488}, {5473,13084}, {5478,7620}, {8352,23005}, {9166,11300}, {10653,22574}, {11302,14971}, {11303,13083}, {16808,22578}
X(22576) = reflection of X(5473) in X(13084)
The reciprocal orthologic center of these triangles is X(8595).
X(22577) lies on these lines: {13,543}, {18,671}, {99,22489}, {115,9116}, {382,542}, {2482,5470}, {5459,8591}, {5461,11312}, {5473,11632}, {8596,22113}, {9886,16966}, {16530,22574}, {16809,22575}, {16960,22571}, {16962,22573}, {16964,22579}, {22493,23004}
X(22577) = reflection of X(i) in X(j) for these (i,j): (5473, 11632), (22493, 23004)
X(22577) = {X(671), X(5463)}-harmonic conjugate of X(5469)
The reciprocal orthologic center of these triangles is X(8594).
X(22578) lies on these lines: {14,543}, {17,671}, {99,22490}, {115,9114}, {382,542}, {2482,5469}, {5460,8591}, {5461,11311}, {5474,11632}, {8596,22114}, {9885,16967}, {16529,22573}, {16808,22576}, {16961,22572}, {16963,22574}, {16965,22580}, {22494,23005}
X(22578) = reflection of X(i) in X(j) for these (i,j): (5474, 11632), (22494, 23005)
X(22578) = {X(671), X(5464)}-harmonic conjugate of X(5470)
The reciprocal orthologic center of these triangles is X(8595).
X(22579) lies on these lines: {2,16940}, {4,542}, {14,524}, {15,9886}, {61,597}, {115,22491}, {141,22490}, {381,22573}, {396,9760}, {543,10654}, {599,636}, {3104,5463}, {3181,10754}, {5026,9114}, {5321,22575}, {5459,6034}, {5476,5613}, {6109,9761}, {6114,9763}, {6670,21358}, {8584,23004}, {11160,22114}, {11632,20426}, {15534,16942}, {16808,22571}, {16964,22577}
X(22579) = reflection of X(599) in X(5460)
X(22579) = {X(1992), X(20423)}-harmonic conjugate of X(22580)
The reciprocal orthologic center of these triangles is X(8594).
X(22580) lies on these lines: {2,16941}, {4,542}, {13,524}, {16,9885}, {62,597}, {115,22492}, {141,22489}, {381,22574}, {395,9762}, {543,10653}, {599,635}, {3105,5464}, {3180,10754}, {5026,9116}, {5318,22576}, {5460,6034}, {5476,5617}, {6108,9763}, {6115,9761}, {6669,21358}, {8584,23005}, {11160,22113}, {11632,20425}, {15534,16943}, {16809,22572}, {16965,22578}
X(22580) = reflection of X(599) in X(5459)
X(22580) = {X(1992), X(20423)}-harmonic conjugate of X(22579)
The reciprocal orthologic center of these triangles is X(9729).
X(22581) lies on these lines: {2,22528}, {3,2929}, {20,22538}, {69,18936}, {95,19198}, {141,22966}, {182,22529}, {394,19460}, {511,22530}, {631,22750}, {1038,19472}, {1040,22954}, {1368,5894}, {3357,3546}, {3548,22800}, {3917,21652}, {5907,6696}, {7386,22555}, {7484,22497}, {7998,22534}, {7999,22535}, {10319,22840}, {11487,22955}, {11511,22830}, {11513,22960}, {11514,22961}, {11515,22974}, {11516,22975}, {12358,20417}, {17811,17837}, {18531,22816}, {19126,19142}, {19422,19488}, {19423,19489}, {22467,22483}
X(22581) = midpoint of X(i) and X(j) for these {i,j}: {3, 22834}, {20, 22538}
X(22581) = anticomplement of X(22973)
X(22581) = complement of X(22970)
X(22581) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 22528, 22970), (2, 22970, 22973)
X(22582) lies on these lines: {399,13630}, {974,22585}
The reciprocal orthologic center of these triangles is X(12112).
X(22583) lies on these lines: {1,2778}, {3,11720}, {30,19478}, {36,9904}, {55,7978}, {56,74}, {104,12244}, {110,3428}, {113,958}, {125,22753}, {146,2975}, {399,2779}, {517,13204}, {541,11194}, {542,22514}, {690,22504}, {956,12368}, {999,11709}, {1001,11723}, {1539,18761}, {2771,22560}, {2777,12114}, {2781,19162}, {3028,10966}, {3149,13211}, {5584,15035}, {5663,11249}, {7725,22756}, {7726,22757}, {7728,22758}, {8674,22775}, {8994,22763}, {9517,19159}, {9919,22654}, {9984,22744}, {10065,22766}, {10081,22767}, {10269,12041}, {10620,22765}, {10628,22781}, {11492,12366}, {11493,12365}, {12133,22479}, {12192,22520}, {12369,22755}, {12373,22759}, {12374,22760}, {12377,22761}, {12378,22762}, {12381,22768}, {13969,22764}, {17702,22659}, {19013,19059}, {19014,19060}
The reciprocal orthologic center of these triangles is X(3581).
Let triangle A*B*C* be as described at X(7723). Then X(22584) = X(3)-of A*B*C*. (Randy Hutson, October 15, 2018)
X(22584) lies on these lines: {3,74}, {5,7722}, {30,12219}, {113,10254}, {125,5448}, {146,3410}, {185,15061}, {265,1531}, {381,1986}, {382,12292}, {542,18438}, {567,12227}, {568,7687}, {1112,3843}, {1154,10733}, {1539,7731}, {1656,14708}, {2072,10264}, {2777,18439}, {2781,18440}, {2914,7527}, {3043,18570}, {3448,18404}, {3627,6242}, {3830,12133}, {3851,13148}, {5055,9826}, {5504,11559}, {5562,12121}, {5889,10113}, {5890,20304}, {5907,11562}, {6000,20127}, {6102,14644}, {6243,12295}, {6288,7728}, {7574,18441}, {7724,18453}, {7727,18455}, {9818,12165}, {9976,18449}, {10317,14901}, {10540,13289}, {10657,18468}, {10658,18470}, {11557,15030}, {11561,15060}, {11806,15027}, {11807,16194}, {12273,18561}, {12290,13201}, {12317,18531}, {12375,18457}, {12376,18459}, {12429,12902}, {12901,22115}, {13630,15059}, {14130,15463}, {15043,15088}, {15760,21357}, {17702,18436}, {17835,18451}, {18445,19457}, {18447,19470}, {18462,19484}, {18463,19485}, {18563,22815}, {18917,18933}, {19129,19140}, {19176,19195}
X(22584) = midpoint of X(12290) and X(13201)
X(22584) = reflection of X(i) in X(j) for these (i,j): (3, 7723), (265, 21650), (382, 12292), (5889, 10113), (6243, 12295)
X(22584) = inverse of X(12412) in the Stammler circle
X(22584) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (399, 10620, 12412), (5907, 11562, 14643), (7731, 15305, 1539), (11459, 12270, 1511)
The reciprocal orthologic center of these triangles is X(974).
X(22585) lies on these lines: {6,17837}, {974,22582}, {1514,2914}, {2929,11456}, {15068,22549}
The reciprocal parallelogic center of these triangles is X(323).
X(22586) lies on these lines: {3,11709}, {36,2948}, {55,7984}, {56,110}, {63,10693}, {74,3428}, {104,12383}, {113,22753}, {125,958}, {265,22758}, {399,22765}, {517,12327}, {542,11194}, {690,22514}, {952,12334}, {956,13211}, {993,13605}, {999,11720}, {1001,11735}, {1112,22479}, {1511,10269}, {2163,6126}, {2771,6261}, {2778,5709}, {2781,19159}, {2836,3576}, {2854,22769}, {2975,3448}, {3149,12368}, {3556,15647}, {3560,12261}, {5584,15055}, {5663,11249}, {7732,22756}, {7733,22757}, {8674,22560}, {8998,22763}, {9517,19162}, {10088,22766}, {10091,22767}, {10113,18761}, {11492,13209}, {11493,13208}, {12114,13213}, {12310,22654}, {12903,22759}, {12904,22760}, {13193,22520}, {13210,22744}, {13212,22755}, {13215,22761}, {13216,22762}, {13217,22768}, {13990,22764}, {19013,19110}, {19014,19111}, {19478,22781}
X(22587) lies on these lines: {}
X(22588) lies on these lines: {1328,1989}, {22536,22644}
X(22589) lies on these lines: {381,485}, {486,12240}, {6565,22553}, {16310,22620}
X(22590) lies on the line {371,1328}
The reciprocal orthologic center of these triangles is X(22592).
X(22591) lies on these lines: {5,6}, {487,641}, {488,6561}, {1328,2996}, {5420,12257}, {6337,13701}, {6565,12222}, {7612,10194}, {12601,22615}, {14645,22562}, {22625,22646}
X(22591) = midpoint of X(488) and X(12221)
X(22591) = reflection of X(487) in X(641)
X(22591) = reflection of X(22592) in X(13881)
X(22591) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (486, 22592, 13881), (13881, 22592, 485)
The reciprocal orthologic center of these triangles is X(22591).
X(22592) lies on these lines: {5,6}, {487,6560}, {488,642}, {1327,2996}, {5418,12256}, {6337,13821}, {6564,12221}, {7612,10195}, {12602,22644}, {14645,22563}, {22596,22617}
X(22592) = midpoint of X(487) and X(12222)
X(22592) = reflection of X(488) in X(642)
X(22592) = reflection of X(22591) in X(13881)
X(22592) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (485, 22591, 13881), (13881, 22591, 486)
The reciprocal orthologic center of these triangles is X(22594).
X(22593) lies on these lines: {262,486}, {511,1328}, {6561,22726}, {12221,22614}, {13330,22622}
X(22593) = {X(13330), X(22681)}-harmonic conjugate of X(22622)
The reciprocal orthologic center of these triangles is X(22593).
X(22594) lies on these lines: {2,371}, {3,22726}, {6,12217}, {83,6419}, {99,372}, {182,22716}, {194,6420}, {511,22718}, {575,3734}, {3311,14535}, {3564,6228}, {6033,6230}, {11174,22725}
X(22594) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (486, 487, 6315), (575, 3734, 22623)
The reciprocal orthologic center of these triangles is X(486).
X(22595) lies on these lines: {3,12343}, {30,22784}, {36,9906}, {55,7980}, {56,486}, {104,12256}, {487,2975}, {642,958}, {956,12787}, {993,8225}, {999,12268}, {3428,12123}, {3564,22624}, {6251,22753}, {6280,22757}, {6281,22756}, {6290,22758}, {9921,22654}, {9986,22744}, {10067,22766}, {10083,22767}, {10966,13081}, {11492,12485}, {11493,12484}, {12114,12928}, {12147,22479}, {12210,22520}, {12601,22765}, {12799,22755}, {12948,22759}, {12958,22760}, {13002,22761}, {13003,22762}, {13132,22768}, {13921,22763}, {13933,22764}, {18761,22596}, {19013,19104}, {19014,19105}
The reciprocal orthologic center of these triangles is X(486).
X(22596) lies on these lines: {4,487}, {5,6119}, {30,642}, {381,486}, {382,12123}, {546,576}, {1478,12958}, {1479,12948}, {1597,12984}, {1598,12972}, {3091,12256}, {3583,13081}, {3585,18989}, {3839,12221}, {3843,6281}, {3861,22819}, {5395,14244}, {6280,18511}, {6560,13934}, {6564,7745}, {7980,18525}, {9758,15294}, {9818,9921}, {9906,18492}, {9955,12268}, {9986,18500}, {10067,10895}, {10083,10896}, {12210,18502}, {12343,18491}, {12484,18495}, {12485,18497}, {12699,12787}, {12799,18507}, {12928,18516}, {12938,18517}, {12978,18535}, {13002,18520}, {13003,18522}, {13132,18542}, {13133,18544}, {13665,19105}, {13711,21309}, {13785,19104}, {13921,18538}, {13933,18762}, {14233,22505}, {14269,22809}, {15765,22606}, {18585,22605}, {18761,22595}, {22592,22617}
X(22596) = midpoint of X(i) and X(j) for these {i,j}: {4, 6290}, {382, 12123}, {7980, 18525}, {12699, 12787}, {12799, 18507}
X(22596) = {X(546), X(3818)}-harmonic conjugate of X(22625)
The reciprocal orthologic center of these triangles is X(22598).
X(22597) lies on these lines: {18,486}, {6561,22882}, {12221,22603}, {22626,22794}
The reciprocal orthologic center of these triangles is X(22597).
X(22598) lies on these lines: {2,371}, {3,22882}, {3104,22610}, {3564,22629}, {5339,22627}, {5615,12601}, {6290,16626}, {16645,22881}
X(22598) = anticomplement of X(33449)
X(22598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (486, 487, 6301), (486, 12221, 22600), (642, 22600, 6300), (6301, 22600, 642)
The reciprocal orthologic center of these triangles is X(22600).
X(22599) lies on these lines: {17,486}, {532,1328}, {6561,22927}, {12221,22601}, {22628,22795}
The reciprocal orthologic center of these triangles is X(22599).
X(22600) lies on these lines: {2,371}, {3,22927}, {532,22919}, {3105,22609}, {3564,22627}, {5340,22629}, {5611,12601}, {6290,16627}, {16644,22926}
X(22600) = anticomplement of X(33451)
X(22600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (486, 487, 6300), (486, 12221, 22598), (642, 22598, 6301), (6300, 22598, 642)
The reciprocal orthologic center of these triangles is X(22602).
X(22601) lies on these lines: {13,486}, {148,22603}, {6302,6561}, {12221,22599}, {22605,22998}, {22630,22796}
The reciprocal orthologic center of these triangles is X(22601).
X(22602) lies on these lines: {13,486}, {17,6300}, {61,22605}, {5459,22631}, {11542,22609}, {16808,22611}, {16960,22607}
The reciprocal orthologic center of these triangles is X(22604).
X(22603) lies on these lines: {14,486}, {148,22601}, {6303,6561}, {12221,22597}, {22606,22997}, {22632,22797}
The reciprocal orthologic center of these triangles is X(22603).
X(22604) lies on these lines: {14,486}, {18,6301}, {62,22606}, {5460,22633}, {11543,22610}, {16809,22612}, {16961,22608}
The reciprocal orthologic center of these triangles is X(22601).
X(22605) lies on these lines: {5,6300}, {14,486}, {61,22602}, {381,1991}, {642,18586}, {3564,22635}, {5321,22611}, {6301,15765}, {10654,13929}, {16808,22609}, {16809,22607}, {18585,22596}, {22601,22998}
X(22605) = {X(381), X(6290)}-harmonic conjugate of X(22606)
The reciprocal orthologic center of these triangles is X(22603).
X(22606) lies on these lines: {5,6301}, {13,486}, {62,22604}, {381,1991}, {642,18587}, {3564,22634}, {5318,22612}, {6300,18585}, {10653,13928}, {15765,22596}, {16808,22608}, {16809,22610}, {22603,22997}
X(22606) = {X(381), X(6290)}-harmonic conjugate of X(22605)
The reciprocal orthologic center of these triangles is X(22601).
X(22607) lies on these lines: {13,22609}, {18,486}, {621,6115}, {6300,16966}, {6565,9732}, {13929,16962}, {16809,22605}, {16960,22602}, {16964,22611}
The reciprocal orthologic center of these triangles is X(22603).
X(22608) lies on these lines: {14,22610}, {17,486}, {622,6114}, {6301,16967}, {6565,9732}, {13928,16963}, {16808,22606}, {16961,22604}, {16965,22612}
The reciprocal orthologic center of these triangles is X(22601).
X(22609) lies on these lines: {13,22607}, {16,6300}, {17,486}, {61,22611}, {3105,22600}, {6290,6565}, {11542,22602}, {13929,16267}, {16808,22605}
The reciprocal orthologic center of these triangles is X(22603).
X(22610) lies on these lines: {14,22608}, {15,6301}, {18,486}, {62,22612}, {3104,22598}, {6290,6565}, {11543,22604}, {13928,16268}, {16809,22606}
The reciprocal orthologic center of these triangles is X(22601).
X(22611) lies on these lines: {4,372}, {15,6300}, {61,22609}, {381,13929}, {3104,22598}, {5321,22605}, {16808,22602}, {16964,22607}
The reciprocal orthologic center of these triangles is X(22603).
X(22612) lies on these lines: {4,372}, {16,6301}, {62,22610}, {381,13928}, {3105,22600}, {5318,22606}, {16809,22604}, {16965,22608}
The reciprocal orthologic center of these triangles is X(6316).
X(22613) lies on these lines: {76,486}, {511,6280}, {538,1328}, {639,7864}, {6318,6561}, {12221,22501}, {14881,22642}
The reciprocal orthologic center of these triangles is X(6315).
X(22614) lies on these lines: {83,486}, {754,1328}, {6317,6561}, {12221,22593}, {22643,22803}
The reciprocal orthologic center of these triangles is X(486).
X(22615) lies on these lines: {4,371}, {5,6409}, {6,3627}, {20,5420}, {30,486}, {372,3146}, {376,10577}, {381,5418}, {382,3071}, {546,1151}, {548,8252}, {550,10194}, {590,3843}, {615,1657}, {642,13835}, {1327,6470}, {1503,9975}, {1587,17578}, {1588,3543}, {1598,9682}, {1656,6496}, {2043,16242}, {2044,16241}, {3053,13834}, {3070,3830}, {3091,6200}, {3311,5076}, {3365,19107}, {3390,19106}, {3529,6396}, {3592,12102}, {3628,6411}, {3832,6484}, {3839,9540}, {3845,6429}, {3850,8253}, {3853,6431}, {3858,10195}, {3861,8981}, {5059,6487}, {5064,18289}, {5072,6455}, {5073,13785}, {5079,6451}, {6410,15704}, {6412,12103}, {6425,18538}, {6437,13925}, {6454,11541}, {6460,15682}, {7408,8854}, {7409,8280}, {7500,18290}, {7692,12123}, {8276,18535}, {8976,14269}, {9647,10896}, {9660,10895}, {9677,15033}, {9683,9818}, {12240,14915}, {12601,22591}, {12963,13711}, {12969,13770}, {13836,22809}, {13846,14893}, {13951,17800}, {22537,22619}
X(22615) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 6459, 6564), (4, 6561, 485), (6, 3627, 22644), (20, 6565, 5420), (371, 6564, 13886), (382, 3071, 6560), (3832, 9541, 10576), (6459, 13886, 371), (9541, 10576, 9680), (15704, 18762, 6410)
The reciprocal orthologic center of these triangles is X(13711).
X(22616) lies on these lines: {381,486}, {591,6561}, {3564,13846}, {6337,13701}, {6463,13678}, {13691,13769}, {13711,22541}, {13770,19099}
X(22616) = {X(486), X(1327)}-harmonic conjugate of X(13932)
The reciprocal orthologic center of these triangles is X(13934).
X(22617) lies on these lines: {3,486}, {372,12296}, {485,6251}, {487,6565}, {638,12221}, {642,12322}, {1328,5491}, {6280,22501}, {6463,13678}, {14537,19104}, {22592,22596}
X(22617) = 3rd-anti-tri-squares-isogonal conjugate of X(32498)
X(22617) = {X(3071), X(12601)}-harmonic conjugate of X(486)
X(22618) lies on these lines: {}
X(22619) lies on these lines: {1327,1989}, {22537,22615}
X(22620) lies on these lines: {381,486}, {485,12239}, {5406,13712}, {6560,10133}, {6564,22554}, {16310,22589}
X(22621) lies on the line {372,1327}
The reciprocal orthologic center of these triangles is X(22623).
X(22622) lies on these lines: {262,485}, {511,1327}, {6560,22727}, {12222,22643}, {13330,22593}
X(22622) = {X(13330), X(22681)}-harmonic conjugate of X(22593)
The reciprocal orthologic center of these triangles is X(22622).
X(22623) lies on these lines: {6,12218}, {83,6420}, {99,371}, {182,22718}, {194,6419}, {511,22716}, {575,3734}, {3312,14535}, {3564,6229}, {6033,6231}, {11174,22724}
X(22623) = {X(575), X(3734)}-harmonic conjugate of X(22594)
The reciprocal orthologic center of these triangles is X(485).
X(22624) lies on these lines: {3,12344}, {30,22783}, {36,9907}, {55,7981}, {56,485}, {104,12257}, {488,2975}, {641,958}, {956,12788}, {999,12269}, {3428,12124}, {3564,22595}, {6250,22753}, {6278,22757}, {6279,22756}, {6289,22758}, {9922,22654}, {9987,22744}, {10068,22766}, {10084,22767}, {10966,13082}, {11492,12487}, {11493,12486}, {12114,12929}, {12148,22479}, {12211,22520}, {12602,22765}, {12800,22755}, {12949,22759}, {12959,22760}, {13004,22761}, {13005,22762}, {13134,22768}, {13879,22763}, {13880,22764}, {18761,22625}, {19013,19102}, {19014,19103}
The reciprocal orthologic center of these triangles is X(485).
X(22625) lies on these lines: {4,488}, {5,6118}, {30,641}, {371,18539}, {381,485}, {382,12124}, {546,576}, {1479,12949}, {1597,12985}, {1598,12973}, {3091,12257}, {3583,13082}, {3585,18988}, {3839,12222}, {3843,6278}, {3861,22820}, {5395,14229}, {6279,18509}, {6561,13882}, {6565,7745}, {7981,18525}, {9757,15293}, {9818,9922}, {9907,18492}, {9955,12269}, {9987,18500}, {10068,10895}, {10084,10896}, {12211,18502}, {12344,18491}, {12486,18495}, {12487,18497}, {12699,12788}, {12800,18507}, {12929,18516}, {12939,18517}, {12979,18535}, {13004,18520}, {13005,18522}, {13134,18542}, {13135,18544}, {13665,19103}, {13785,19102}, {13834,21309}, {13879,18538}, {13880,18762}, {14230,22505}, {14269,22810}, {15765,22634}, {18585,22635}, {18761,22624}, {22591,22646}
X(22625) = midpoint of X(i) and X(j) for these {i,j}: {4, 6289}, {382, 12124}, {7981, 18525}, {12699, 12788}, {12800, 18507}
X(22625) = {X(546), X(3818)}-harmonic conjugate of X(22596)
The reciprocal orthologic center of these triangles is X(22627).
X(22626) lies on these lines: {18,485}, {6560,22883}, {12222,22632}, {22597,22794}
The reciprocal orthologic center of these triangles is X(22626).
X(22627) lies on these lines: {2,372}, {3,22883}, {3104,22639}, {3564,22600}, {5339,22598}, {5615,12602}, {6289,16626}, {16645,22880}
X(22627) = anticomplement of X(33448)
X(22627) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (485, 488, 6305), (485, 12222, 22629), (641, 22629, 6304), (6305, 22629, 641)
The reciprocal orthologic center of these triangles is X(22629).
X(22628) lies on these lines: {17,485}, {532,1327}, {6560,22928}, {12222,22630}, {22599,22795}
The reciprocal orthologic center of these triangles is X(22628).
X(22629) lies on these lines: {2,372}, {3,22928}, {532,22917}, {3105,22638}, {3564,22598}, {5340,22600}, {5611,12602}, {6289,16627}, {16644,22925}
X(22629) = anticomplement of X(33450)
X(22629) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (485, 488, 6304), (485, 12222, 22627), (641, 22627, 6305), (6304, 22627, 641)
The reciprocal orthologic center of these triangles is X(22631).
X(22630) lies on these lines: {13,485}, {148,22632}, {6306,6560}, {12222,22628}, {22601,22796}, {22634,22998}
The reciprocal orthologic center of these triangles is X(22630).
X(22631) lies on these lines: {13,485}, {17,6304}, {61,22634}, {5459,22602}, {11542,22638}, {16808,22640}, {16960,22636}
The reciprocal orthologic center of these triangles is X(22633).
X(22632) lies on these lines: {14,485}, {148,22630}, {6307,6560}, {12222,22626}, {22603,22797}, {22635,22997}
The reciprocal orthologic center of these triangles is X(22632).
X(22633) lies on these lines: {14,485}, {18,6305}, {62,22635}, {5460,22604}, {11543,22639}, {16809,22641}, {16961,22637}
The reciprocal orthologic center of these triangles is X(22630).
X(22634) lies on these lines: {5,6304}, {14,485}, {61,22631}, {381,591}, {641,18587}, {3564,22606}, {5321,22640}, {6305,18585}, {10654,13876}, {15765,22625}, {16808,22638}, {16809,22636}, {22630,22998}
X(22634) = {X(381), X(6289)}-harmonic conjugate of X(22635)
The reciprocal orthologic center of these triangles is X(22632).
X(22635) lies on these lines: {5,6305}, {13,485}, {62,22633}, {381,591}, {641,18586}, {3564,22605}, {5318,22641}, {6304,15765}, {10653,13875}, {16808,22637}, {16809,22639}, {18585,22625}, {22632,22997}
X(22635) = {X(381), X(6289)}-harmonic conjugate of X(22634)
The reciprocal orthologic center of these triangles is X(22630).
X(22636) lies on these lines: {13,22638}, {18,485}, {621,6115}, {6304,16966}, {6564,9733}, {13876,16962}, {16809,22634}, {16960,22631}, {16964,22640}
The reciprocal orthologic center of these triangles is X(22632).
X(22637) lies on these lines: {14,22639}, {17,485}, {622,6114}, {6305,16967}, {6564,9733}, {13875,16963}, {16808,22635}, {16961,22633}, {16965,22641}
The reciprocal orthologic center of these triangles is X(22630).
X(22638) lies on these lines: {13,22636}, {16,6304}, {17,485}, {61,22640}, {3105,22629}, {6289,6564}, {11542,22631}, {13876,16267}, {16808,22634}
The reciprocal orthologic center of these triangles is X(22632).
X(22639) lies on these lines: {14,22637}, {15,6305}, {18,485}, {62,22641}, {3104,22627}, {6289,6564}, {11543,22633}, {13875,16268}, {16809,22635}
The reciprocal orthologic center of these triangles is X(22630).
X(22640) lies on these lines: {4,371}, {15,6304}, {61,22638}, {381,13876}, {3104,22627}, {5321,22634}, {16808,22631}, {16964,22636}
The reciprocal orthologic center of these triangles is X(22632).
X(22641) lies on these lines: {4,371}, {16,6305}, {62,22639}, {381,13875}, {3105,22629}, {5318,22635}, {16809,22633}, {16965,22637}
The reciprocal orthologic center of these triangles is X(6312).
X(22642) lies on these lines: {76,485}, {511,6279}, {538,1327}, {640,7864}, {6314,6560}, {12222,22502}, {14881,22613}
The reciprocal orthologic center of these triangles is X(6311).
X(22643) lies on these lines: {83,485}, {754,1327}, {6313,6560}, {12222,22622}, {22614,22803}
The reciprocal orthologic center of these triangles is X(485).
X(22644) lies on these lines: {4,372}, {5,6410}, {6,3627}, {20,5418}, {30,485}, {371,3146}, {376,10576}, {381,5420}, {382,3070}, {546,1152}, {548,8253}, {550,10195}, {590,1657}, {615,3843}, {641,13712}, {1131,8960}, {1328,6471}, {1503,9974}, {1587,3543}, {1588,17578}, {1656,6497}, {2043,16241}, {2044,16242}, {3053,13711}, {3068,9681}, {3071,3830}, {3091,6396}, {3312,5076}, {3364,19107}, {3389,19106}, {3529,6200}, {3594,12102}, {3628,6412}, {3832,6485}, {3839,13935}, {3845,6430}, {3850,8252}, {3853,6432}, {3858,10194}, {3861,13966}, {5059,6486}, {5064,18290}, {5072,6456}, {5073,13665}, {5079,6452}, {6250,21736}, {6409,15704}, {6411,12103}, {6426,18762}, {6438,13993}, {6453,11541}, {6459,15682}, {7408,8855}, {7409,8281}, {7500,18289}, {7690,12124}, {8277,18535}, {8976,9680}, {9682,12085}, {12239,14915}, {12602,22592}, {12962,13651}, {12968,13834}, {13713,22810}, {13847,14893}, {13951,14269}, {22536,22588}
X(22644) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 6460, 6565), (4, 6560, 486), (6, 3627, 22615), (20, 6564, 5418), (372, 6565, 13939), (382, 3070, 6561), (1131, 9541, 8960), (6460, 13939, 372), (15704, 18538, 6409)
The reciprocal orthologic center of these triangles is X(13834).
X(22645) lies on these lines: {381,485}, {1991,6560}, {3564,13847}, {6337,13821}, {6462,13798}, {13651,19100}, {13810,13833}, {13834,19101}
X(22645) = {X(485), X(1328)}-harmonic conjugate of X(13850)
The reciprocal orthologic center of these triangles is X(13882).
X(22646) lies on these lines: {3,485}, {371,12297}, {486,6250}, {488,6564}, {637,12222}, {641,12323}, {1327,5490}, {6279,22502}, {6462,13798}, {14537,19103}, {22591,22625}
X(22646) = 4th-anti-tri-squares-isogonal conjugate of X(32499)
X(22646) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (485, 12124, 5418), (3070, 12602, 485)
The reciprocal orthologic center of these triangles is X(12241).
X(22647) lies on these lines: {2,22466}, {3,22533}, {4,801}, {5,22979}, {8,22941}, {10,22653}, {20,22662}, {22,22658}, {69,11440}, {100,22559}, {145,22969}, {146,5895}, {388,18978}, {394,22972}, {497,22959}, {1270,22947}, {1271,22945}, {2071,2888}, {2896,22747}, {2929,13567}, {2975,22776}, {3085,22980}, {3086,22981}, {3091,22833}, {3434,22956}, {3436,22957}, {3548,22808}, {3616,22476}, {4240,22943}, {5449,22834}, {5562,15103}, {6241,12383}, {6462,22963}, {6463,22964}, {6644,22550}, {7585,19084}, {7586,19083}, {7787,22524}, {8972,22976}, {10116,12118}, {10528,22982}, {10529,22983}, {11064,22971}, {12254,16163}, {13941,22977}, {16013,22978}, {18912,22962}, {18936,22953}
X(22647) = reflection of X(i) in X(j) for these (i,j): (4, 22955), (8, 22941), (20, 22951), (145, 22969), (4240, 22943)
X(22647) = anticomplement of X(22466)
X(22647) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18978, 22958, 388), (22466, 22966, 2), (22959, 22965, 497)
The reciprocal cyclologic center of these triangles is X(616).
X(22648) lies on these lines: {2,3480}, {4,3181}, {14,11601}, {617,2926}, {6106,18581}
X(22648) = anticomplement of X(3480)
The reciprocal cyclologic center of these triangles is X(617).
X(22649) lies on these lines: {2,3479}, {4,3180}, {13,11600}, {532,1337}, {616,2925}, {6107,18582}
X(22649) = anticomplement of X(3479)
The reciprocal orthologic center of these triangles is X(3).
X(22650) lies on these lines: {1,262}, {8,7985}, {10,6194}, {35,22556}, {36,22680}, {40,9903}, {57,18971}, {165,22676}, {355,9902}, {511,3679}, {515,3097}, {517,22728}, {1697,22711}, {1698,15819}, {1699,14839}, {2782,9875}, {3095,5881}, {3099,22678}, {3751,9860}, {5188,9588}, {5587,7697}, {5588,22700}, {5589,22699}, {5691,12782}, {5727,12837}, {7713,22480}, {7982,14881}, {7989,12263}, {8185,22655}, {8186,22668}, {8187,22672}, {8188,22709}, {8189,22710}, {8931,9746}, {9578,22705}, {9581,22706}, {10789,22521}, {10826,22703}, {10827,22704}, {11852,22698}, {13888,22720}, {13942,22721}, {18492,22681}, {19003,19063}, {19004,19064}, {19875,22712}
X(22650) = reflection of X(1) in X(262)
X(22650) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (262, 22713, 22475), (22475, 22713, 1)
The reciprocal orthologic center of these triangles is X(3).
X(22651) lies on these lines: {1,18}, {8,22114}, {10,628}, {35,22557}, {36,22771}, {40,9900}, {57,18972}, {165,22843}, {355,9901}, {515,22531}, {517,16628}, {630,1698}, {1697,22865}, {1699,22831}, {3099,22745}, {3624,6674}, {3751,5965}, {5587,16627}, {5588,22854}, {5589,22853}, {7713,22481}, {8185,22656}, {8186,22669}, {8187,22673}, {8188,22863}, {8189,22864}, {9578,22859}, {9581,22860}, {10789,22522}, {10826,22857}, {10827,22858}, {11852,22852}, {13888,22876}, {13942,22877}, {18492,22794}, {19003,19069}, {19004,19072}
X(22651) = midpoint of X(8) and X(22114)
X(22651) = reflection of X(1) in X(18)
X(22651) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18, 22867, 11740), (11740, 22867, 1)
The reciprocal orthologic center of these triangles is X(3).
X(22652) lies on these lines: {1,17}, {8,22113}, {10,627}, {35,22558}, {36,22772}, {40,9901}, {57,18973}, {165,22890}, {355,9900}, {515,22532}, {517,16629}, {532,3679}, {629,1698}, {1697,22910}, {1699,22832}, {3099,22746}, {3624,6673}, {3751,5965}, {5587,16626}, {5588,22899}, {5589,22898}, {7713,22482}, {8185,22657}, {8186,22670}, {8187,22674}, {8188,22908}, {8189,22909}, {9578,22904}, {9581,22905}, {10789,22523}, {10826,22902}, {10827,22903}, {11852,22897}, {13888,22921}, {13942,22922}, {18492,22795}, {19003,19071}, {19004,19070}
X(22652) = midpoint of X(8) and X(22113)
X(22652) = reflection of X(1) in X(17)
X(22652) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17, 22912, 11739), (11739, 22912, 1)
The reciprocal orthologic center of these triangles is X(12241).
X(22653) lies on these lines: {1,22466}, {10,22647}, {35,22559}, {36,22776}, {40,22840}, {57,18978}, {165,22951}, {515,22533}, {517,22979}, {1697,22965}, {1698,22966}, {1699,22833}, {3099,22747}, {3679,22941}, {5587,22955}, {5588,22947}, {5589,22945}, {7713,22483}, {8185,22658}, {8188,22963}, {8189,22964}, {9578,22958}, {9581,22959}, {10789,22524}, {10826,22956}, {10827,22957}, {11852,22943}, {13888,22976}, {13942,22977}, {18492,22800}, {19003,19083}, {19004,19084}
X(22653) = reflection of X(1) in X(22466)
X(22653) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (22466, 22969, 22476), (22476, 22969, 1)
X(22654) lies on these lines: {1,159}, {3,10}, {4,17111}, {11,4186}, {20,11677}, {22,2975}, {24,104}, {25,34}, {28,3433}, {36,8185}, {55,8192}, {65,1473}, {119,21479}, {198,1212}, {222,14529}, {388,4224}, {405,19836}, {517,12517}, {859,7742}, {956,8193}, {960,20876}, {962,1633}, {963,1436}, {999,11365}, {1043,16876}, {1191,7083}, {1329,16434}, {1406,3937}, {1460,4252}, {1598,22753}, {1602,1610}, {1616,16686}, {1617,1661}, {1995,5253}, {2178,16968}, {2182,12680}, {2551,19649}, {3086,4222}, {3145,8240}, {3189,20871}, {3304,20988}, {3428,11414}, {4185,7354}, {4214,12943}, {4999,19544}, {5204,20989}, {5260,7485}, {5594,22757}, {5595,22756}, {6642,10269}, {7078,8679}, {7293,19860}, {7387,11249}, {7428,8069}, {7517,22765}, {8071,11334}, {8190,11493}, {8191,11492}, {8194,22761}, {8195,22762}, {9630,11396}, {9861,22504}, {9876,22565}, {9908,22659}, {9909,11194}, {9910,18237}, {9911,22770}, {9912,12773}, {9913,22775}, {9914,22778}, {9915,22774}, {9916,22773}, {9917,22779}, {9918,22780}, {9919,22583}, {9920,22781}, {9921,22595}, {9922,22624}, {10037,22766}, {10046,22767}, {10790,22520}, {10831,22759}, {10832,22760}, {10833,10835}, {10834,22768}, {10896,17516}, {11641,19162}, {11853,22755}, {12310,22586}, {12410,12513}, {12411,22777}, {12412,19478}, {12413,19159}, {12414,22782}, {13175,22514}, {13222,22560}, {13680,22783}, {13737,20470}, {13743,16119}, {13800,22784}, {13889,22763}, {13943,22764}, {16828,19286}, {18242,21484}, {19005,19013}, {19006,19014}, {22655,22680}, {22656,22771}, {22657,22772}, {22658,22776}
X(22654) = isogonal conjugate of isotomic conjugate of X(21279)
X(22654) = complement of X(20211)
X(22654) = polar conjugate of isotomic conjugate of X(23122)
X(22654) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3220, 3556), (1, 13730, 1486), (3, 9798, 197), (159, 18610, 1486), (956, 20833, 8193), (999, 20831, 11365), (12513, 20872, 12410)
The reciprocal orthologic center of these triangles is X(3).
X(22655) lies on these lines: {3,3734}, {22,6194}, {24,7709}, {25,262}, {26,9917}, {39,3517}, {76,9715}, {154,511}, {159,9861}, {197,22556}, {237,9752}, {538,10245}, {1598,22682}, {2782,9876}, {3095,9714}, {3515,11257}, {5594,22700}, {5595,22699}, {7387,9918}, {7517,22728}, {8185,22650}, {8190,22668}, {8191,22672}, {8192,22713}, {8193,22697}, {8194,22709}, {8195,22710}, {9754,20885}, {9818,22681}, {10037,22729}, {10046,22730}, {10790,22521}, {10828,22678}, {10829,22703}, {10830,22704}, {10831,22705}, {10832,22706}, {10833,22711}, {10834,22731}, {10835,22732}, {11365,22475}, {11414,22676}, {11853,22698}, {13889,22720}, {13943,22721}, {18954,18971}, {19005,19063}, {19006,19064}, {22654,22680}
The reciprocal orthologic center of these triangles is X(3).
X(22656) lies on these lines: {3,624}, {18,25}, {22,628}, {23,22114}, {24,22531}, {26,9916}, {159,5965}, {197,22557}, {1598,22831}, {5020,6674}, {5594,22854}, {5595,22853}, {7387,9915}, {7517,16628}, {8185,22651}, {8190,22669}, {8191,22673}, {8192,22867}, {8193,22851}, {8194,22863}, {8195,22864}, {9818,22794}, {10037,22884}, {10046,22885}, {10790,22522}, {10828,22745}, {10829,22857}, {10830,22858}, {10831,22859}, {10832,22860}, {10833,22865}, {10834,22886}, {10835,22887}, {11365,11740}, {11414,22843}, {11853,22852}, {13889,22876}, {13943,22877}, {18954,18972}, {19005,19069}, {19006,19072}, {22654,22771}
The reciprocal orthologic center of these triangles is X(3).
X(22657) lies on these lines: {3,623}, {17,25}, {22,627}, {23,22113}, {24,22532}, {26,9915}, {159,5965}, {197,22558}, {532,9909}, {1598,22832}, {5020,6673}, {5594,22899}, {5595,22898}, {7387,9916}, {7517,16629}, {8185,22652}, {8190,22670}, {8191,22674}, {8192,22912}, {8193,22896}, {8194,22908}, {8195,22909}, {9818,22795}, {10037,22929}, {10046,22930}, {10790,22523}, {10828,22746}, {10829,22902}, {10830,22903}, {10831,22904}, {10832,22905}, {10833,22910}, {10834,22931}, {10835,22932}, {11365,11739}, {11414,22890}, {11853,22897}, {13889,22921}, {13943,22922}, {18954,18973}, {19005,19071}, {19006,19070}, {22654,22772}
The reciprocal orthologic center of these triangles is X(12241).
X(22658) lies on these lines: {3,22955}, {22,22647}, {24,22533}, {25,22466}, {154,22497}, {159,2929}, {197,22559}, {1204,1660}, {1598,22833}, {1619,12279}, {1657,9919}, {2070,9920}, {3532,13171}, {3556,15071}, {5594,22947}, {5595,22945}, {5925,9914}, {7517,22979}, {8185,22653}, {8192,22969}, {8193,22941}, {8194,22963}, {8195,22964}, {9818,22800}, {10037,22980}, {10046,22981}, {10790,22524}, {10828,22747}, {10829,22956}, {10830,22957}, {10831,22958}, {10832,22959}, {10833,22965}, {10834,22982}, {10835,22983}, {11365,22476}, {11414,22951}, {11853,22943}, {12163,12412}, {12225,22555}, {13889,22976}, {13943,22977}, {18954,18978}, {19005,19083}, {19006,19084}, {19153,22529}, {22654,22776}
The reciprocal orthologic center of these triangles is X(9833).
X(22659) lies on these lines: {1,90}, {3,914}, {30,22778}, {36,9896}, {55,9933}, {56,68}, {104,11411}, {539,11194}, {956,9928}, {958,1147}, {999,12259}, {2975,6193}, {3428,12118}, {3564,22595}, {9908,22654}, {9923,22744}, {9927,22753}, {9929,22756}, {9930,22757}, {10055,22766}, {10071,22767}, {10269,12359}, {10966,12428}, {11493,12415}, {12114,12422}, {12134,22479}, {12193,22520}, {12418,22755}, {12426,22761}, {12427,22762}, {12429,22765}, {12430,22768}, {13909,22763}, {13970,22764}, {17702,22583}, {18761,22660}, {19013,19061}, {19014,19062}
The reciprocal orthologic center of these triangles is X(9833).
X(22660) lies on these lines: {2,12163}, {3,4549}, {4,155}, {5,389}, {11,7352}, {12,6238}, {20,9707}, {25,9932}, {26,16252}, {30,156}, {49,18563}, {52,113}, {68,381}, {110,6240}, {125,21971}, {140,7689}, {141,11591}, {143,15873}, {146,12086}, {184,12605}, {185,1568}, {343,10024}, {382,3167}, {403,5889}, {427,12162}, {539,3845}, {541,15115}, {542,18383}, {546,576}, {550,5944}, {632,20191}, {858,6241}, {912,946}, {1069,1478}, {1154,15761}, {1181,18531}, {1204,10257}, {1216,6823}, {1479,3157}, {1498,14790}, {1503,18569}, {1531,21659}, {1539,3627}, {1593,9938}, {1594,7703}, {1596,5446}, {1597,12301}, {1598,9937}, {1614,12225}, {1619,5878}, {1658,10192}, {1885,13352}, {1906,11576}, {1907,16194}, {2931,3518}, {3070,10666}, {3071,10665}, {3088,11469}, {3091,11411}, {3548,10605}, {3574,7403}, {3575,10539}, {3580,16868}, {3583,12428}, {3585,18970}, {3843,9936}, {5133,15058}, {5198,12166}, {5318,10662}, {5321,10661}, {5504,7728}, {5562,15760}, {5576,18435}, {5655,7540}, {5663,6247}, {5891,7399}, {5893,16266}, {5894,11250}, {6146,18404}, {6243,11799}, {6561,8909}, {6644,13568}, {6696,18281}, {6804,15805}, {7526,19908}, {7547,11442}, {7706,9825}, {9703,18562}, {9704,18564}, {9818,9908}, {9896,18492}, {9923,18500}, {9928,12699}, {9929,18509}, {9930,18511}, {9933,18525}, {9955,12259}, {10055,10895}, {10071,10896}, {10110,12235}, {10272,12893}, {10295,11449}, {10982,19458}, {11381,15063}, {11438,16238}, {11459,13160}, {11745,13861}, {12061,14984}, {12161,12241}, {12193,18502}, {12309,18535}, {12319,16658}, {12328,18491}, {12415,18495}, {12418,18507}, {12422,18516}, {12423,18517}, {12426,18520}, {12427,18522}, {12430,18542}, {12431,18544}, {13292,18390}, {13665,19062}, {13785,19061}, {13909,18538}, {13970,18762}, {14094,15133}, {14788,15056}, {15305,15559}, {15341,22120}, {15738,20303}, {16534,20772}, {17814,18420}, {18567,19479}, {18761,22659}
X(22660) = midpoint of X(i) and X(j) for these {i,j}: {4, 155}, {68, 12164}, {146, 12302}, {382, 12118}, {1498, 14790}, {5504, 7728}, {9928, 12699}, {9933, 18525}, {12418, 18507}, {14094, 15133}
X(22660) = reflection of X(i) in X(j) for these (i,j): (3, 9820), (5, 5448), (26, 16252), (550, 12038), (5894, 11250)
X(22660) = complement of X(12163)
X(22660) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 5654, 9820), (4, 6193, 12293), (4, 11441, 12134), (5, 6102, 13567), (52, 113, 235), (155, 12293, 6193), (185, 1568, 11585), (381, 12164, 68), (382, 3167, 12118), (3091, 11411, 14852), (3574, 15030, 7403), (5907, 18388, 5), (10024, 18436, 343), (18404, 18445, 6146)
The reciprocal orthologic center of these triangles is X(7387).
X(22661) lies on these lines: {3,20302}, {4,155}, {5,9932}, {20,12302}, {30,9938}, {49,12118}, {64,14790}, {68,265}, {381,9937}, {382,12301}, {539,18568}, {542,9926}, {1147,18388}, {2931,7505}, {3153,11411}, {3564,18377}, {3583,9931}, {3585,19471}, {3832,18427}, {3843,12309}, {5448,11818}, {5654,18350}, {5907,9927}, {6288,15739}, {6564,12424}, {6565,12425}, {6759,17702}, {7689,14791}, {9820,18420}, {10660,16809}, {11457,15133}, {12166,18386}, {12235,18390}, {12271,18392}, {12282,18394}, {12359,18531}, {12417,18406}, {12429,18403}, {13754,18381}, {13851,21651}, {17836,18405}, {18396,19458}, {18414,19486}, {18415,19487}, {18918,18934}, {19130,19141}, {19177,19196}
X(22661) = midpoint of X(382) and X(12301)
X(22661) = reflection of X(3) in X(20302)
X(22661) = {X(155), X(12293)}-harmonic conjugate of X(14516)
The reciprocal orthologic center of these triangles is X(22663).
X(22662) lies on these lines: {20,22647}, {25,22953}, {159,2929}, {235,22466}, {1368,22955}, {1498,17837}, {6146,22750}, {6353,22533}, {10539,22808}, {19460,22483}
The reciprocal orthologic center of these triangles is X(22662).
X(22663) lies on these lines: {5,6}, {974,22953}, {1885,5889}, {11245,17928}, {11264,13630}, {11585,15317}, {12420,13861}, {15316,18952}
X(22663) = midpoint of X(5) and X(12421)
X(22664) lies on these lines: {2,2794}, {3,9743}, {6,98}, {30,9877}, {99,5999}, {114,7710}, {147,3424}, {542,9770}, {1503,6054}, {1513,10722}, {2548,10991}, {2782,9764}, {5652,9775}, {6055,14561}, {8719,21166}, {12042,14535}
X(22664) = midpoint of X(147) and X(3424)
The reciprocal orthologic center of these triangles is X(5858).
X(22665) lies on these lines: {2,18}, {381,7764}, {5858,5965}, {6115,11121}, {7788,22850}, {7837,22855}, {9760,9766}, {13638,22878}, {13758,22879}
The reciprocal orthologic center of these triangles is X(5859).
X(22666) lies on these lines: {2,17}, {381,7764}, {5859,5965}, {6114,11122}, {7788,22894}, {7837,22901}, {9762,9766}, {13638,22923}, {13758,22924}
X(22667) lies on these lines: {142,958}, {942,12513}, {1001,9856}, {1125,18237}, {1467,7091}, {6892,22775}, {9942,12114}, {9945,13205}, {9946,12773}, {12436,22777}
The reciprocal orthologic center of these triangles is X(3).
X(22668) lies on these lines: {262,5597}, {511,11207}, {2782,12345}, {5598,22713}, {5599,15819}, {5601,6194}, {7697,8200}, {7709,11843}, {8186,22650}, {8190,22655}, {8196,22682}, {8197,22697}, {8198,22699}, {11366,22475}, {11384,22480}, {11492,22556}, {11493,22680}, {11822,22676}, {11837,22521}, {11861,22678}, {11865,22703}, {11867,22704}, {11869,22705}, {11871,22706}, {11873,22711}, {11875,22728}, {11877,22729}, {11879,22730}, {11881,22731}, {11883,22732}, {13890,22720}, {13944,22721}, {18495,22681}, {18955,18971}, {19007,19063}, {19008,19064}
The reciprocal orthologic center of these triangles is X(3).
X(22669) lies on these lines: {18,5597}, {628,5601}, {630,5599}, {5598,22867}, {5965,12452}, {8186,22651}, {8190,22656}, {8196,22831}, {8197,22851}, {8198,22853}, {8199,22854}, {8200,16627}, {11366,11740}, {11384,22481}, {11492,22557}, {11493,22771}, {11822,22843}, {11837,22522}, {11843,22531}, {11861,22745}, {11865,22857}, {11867,22858}, {11869,22859}, {11871,22860}, {11873,22865}, {11875,16628}, {11877,22884}, {11879,22885}, {11881,22886}, {11883,22887}, {13890,22876}, {13944,22877}, {18495,22794}, {18955,18972}, {19007,19069}, {19008,19072}
The reciprocal orthologic center of these triangles is X(3).
X(22670) lies on these lines: {17,5597}, {532,11207}, {627,5601}, {629,5599}, {5598,22912}, {5965,12452}, {8186,22652}, {8190,22657}, {8196,22832}, {8197,22896}, {8198,22898}, {8199,22899}, {8200,16626}, {11366,11739}, {11384,22482}, {11492,22558}, {11493,22772}, {11822,22890}, {11837,22523}, {11843,22532}, {11861,22746}, {11865,22902}, {11867,22903}, {11869,22904}, {11871,22905}, {11873,22910}, {11875,16629}, {11877,22929}, {11879,22930}, {11881,22931}, {11883,22932}, {13890,22921}, {13944,22922}, {18495,22795}, {18955,18973}, {19007,19071}, {19008,19070}
The reciprocal orthologic center of these triangles is X(12241).
X(22671) lies on these lines: {55,22675}, {5597,22466}, {5598,22969}, {5599,22966}, {5601,22647}, {8186,22653}, {8190,22658}, {8196,22833}, {8197,22941}, {8198,22945}, {8199,22947}, {8200,22955}, {8201,22963}, {8202,22964}, {11366,22476}, {11384,22483}, {11492,22559}, {11493,22776}, {11822,22951}, {11837,22524}, {11843,22533}, {11861,22747}, {11863,22943}, {11865,22956}, {11867,22957}, {11869,22958}, {11871,22959}, {11873,22965}, {11875,22979}, {11877,22980}, {11879,22981}, {11881,22982}, {11883,22983}, {13890,22976}, {13944,22977}, {18495,22800}, {18955,18978}, {19007,19083}, {19008,19084}
The reciprocal orthologic center of these triangles is X(3).
X(22672) lies on these lines: {262,5598}, {511,11208}, {2782,12346}, {5597,22713}, {5600,15819}, {5602,6194}, {7697,8207}, {7709,11844}, {8187,22650}, {8191,22655}, {8203,22682}, {8204,22697}, {8205,22699}, {8206,22700}, {11253,12477}, {11367,22475}, {11385,22480}, {11492,22680}, {11493,22556}, {11823,22676}, {11838,22521}, {11862,22678}, {11866,22703}, {11868,22704}, {11870,22705}, {11872,22706}, {11874,22711}, {11876,22728}, {11878,22729}, {11880,22730}, {11882,22731}, {11884,22732}, {13891,22720}, {13945,22721}, {18497,22681}, {18956,18971}, {19009,19063}, {19010,19064}
The reciprocal orthologic center of these triangles is X(3).
X(22673) lies on these lines: {18,5598}, {628,5602}, {630,5600}, {5597,22867}, {5965,12453}, {8187,22651}, {8191,22656}, {8203,22831}, {8204,22851}, {8205,22853}, {8206,22854}, {8207,16627}, {11367,11740}, {11385,22481}, {11492,22771}, {11493,22557}, {11823,22843}, {11838,22522}, {11844,22531}, {11862,22745}, {11866,22857}, {11868,22858}, {11870,22859}, {11872,22860}, {11874,22865}, {11876,16628}, {11878,22884}, {11880,22885}, {11882,22886}, {11884,22887}, {13891,22876}, {13945,22877}, {18497,22794}, {18956,18972}, {19009,19069}, {19010,19072}
The reciprocal orthologic center of these triangles is X(3).
X(22674) lies on these lines: {17,5598}, {532,11208}, {627,5602}, {629,5600}, {5597,22912}, {5965,12453}, {8187,22652}, {8191,22657}, {8203,22832}, {8204,22896}, {8205,22898}, {8206,22899}, {8207,16626}, {11367,11739}, {11385,22482}, {11492,22772}, {11493,22558}, {11823,22890}, {11838,22523}, {11844,22532}, {11862,22746}, {11866,22902}, {11868,22903}, {11870,22904}, {11872,22905}, {11874,22910}, {11876,16629}, {11878,22929}, {11880,22930}, {11882,22931}, {11884,22932}, {13891,22921}, {13945,22922}, {18497,22795}, {18956,18973}, {19009,19071}, {19010,19070}
The reciprocal orthologic center of these triangles is X(12241).
X(22675) lies on these lines: {55,22671}, {5597,22969}, {5598,22466}, {5600,22966}, {5602,22647}, {8187,22653}, {8191,22658}, {8203,22833}, {8204,22941}, {8205,22945}, {8206,22947}, {8207,22955}, {8208,22963}, {8209,22964}, {11367,22476}, {11385,22483}, {11492,22776}, {11493,22559}, {11823,22951}, {11838,22524}, {11844,22533}, {11862,22747}, {11864,22943}, {11866,22956}, {11868,22957}, {11870,22958}, {11872,22959}, {11874,22965}, {11876,22979}, {11878,22980}, {11880,22981}, {11882,22982}, {11884,22983}, {13891,22976}, {13945,22977}, {18497,22800}, {18956,18978}, {19009,19083}, {19010,19084}
The reciprocal orthologic center of these triangles is X(3).
X(22676) lies on these lines: {2,22682}, {3,83}, {4,7831}, {20,76}, {30,7697}, {35,22729}, {36,22730}, {39,3522}, {55,18971}, {56,22711}, {69,15428}, {99,1350}, {147,7850}, {165,22650}, {182,22521}, {183,14532}, {315,7710}, {316,7694}, {371,19064}, {372,19063}, {376,511}, {382,22681}, {515,22697}, {517,22713}, {548,3095}, {550,9821}, {1078,9756}, {1503,7811}, {1513,7934}, {1593,22480}, {2023,5210}, {2782,3534}, {2794,9772}, {3098,10000}, {3146,3934}, {3428,22680}, {3528,13334}, {3529,6248}, {3576,22475}, {4297,7976}, {4316,10063}, {4324,10079}, {5085,12150}, {5092,10788}, {5171,7470}, {5999,7771}, {6179,9755}, {6284,22706}, {6661,21167}, {6683,15717}, {7354,22705}, {7768,8721}, {7782,22679}, {7803,9748}, {7828,9752}, {7884,9753}, {7926,9744}, {7937,13862}, {8350,18860}, {8703,11171}, {9466,15683}, {9540,22720}, {9778,14839}, {10304,21163}, {10310,22556}, {11055,15697}, {11248,22731}, {11249,22732}, {11261,14810}, {11299,22694}, {11300,22693}, {11414,22655}, {11822,22668}, {11823,22672}, {11824,22699}, {11825,22700}, {11826,22703}, {11827,22704}, {11828,22709}, {11829,22710}, {12251,17538}, {12512,12782}, {13935,22721}, {14927,14994}
X(22676) = midpoint of X(20) and X(6194)
X(22676) = reflection of X(i) in X(j) for these (i,j): (4, 15819), (382, 22681), (11261, 14810)
X(22676) = anticomplement of X(22682)
X(22676) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (20, 5188, 76), (550, 9821, 11257), (5999, 8722, 7771)
The reciprocal orthologic center of these triangles is X(12177).
X(22677) lies on these lines: {2,51}, {3,5026}, {69,7709}, {114,9743}, {140,13330}, {141,7697}, {182,7771}, {384,22679}, {524,11171}, {575,7793}, {576,7786}, {599,2782}, {1351,10007}, {1352,7761}, {1469,22729}, {2896,11257}, {3056,22730}, {3094,15048}, {3098,10000}, {3314,9772}, {3785,13334}, {8179,8586}, {9751,12216}, {10008,14994}, {10516,22681}, {11179,21163}, {11272,11477}
X(22677) = midpoint of X(69) and X(7709)
X(22677) = reflection of X(11179) in X(21163)
X(22677) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 22503, 262), (22714, 22715, 22712), (22726, 22727, 6194)
The reciprocal orthologic center of these triangles is X(3).
X(22678) lies on these lines: {3,10333}, {4,2896}, {32,262}, {511,7811}, {2782,9878}, {3094,3269}, {3096,15819}, {3098,10000}, {3099,22650}, {5188,7849}, {7793,14881}, {7865,22712}, {9301,13860}, {9857,22697}, {9863,10335}, {9993,22682}, {9994,22699}, {9995,22700}, {9997,22713}, {10038,22729}, {10047,22730}, {10347,11261}, {10828,22655}, {10871,22703}, {10872,22704}, {10873,22705}, {10874,22706}, {10875,22709}, {10876,22710}, {10877,22711}, {10878,22731}, {10879,22732}, {11368,22475}, {11494,22556}, {11861,22668}, {11862,22672}, {11885,22698}, {13892,22720}, {13946,22721}, {18957,18971}, {19011,19063}, {19012,19064}, {22680,22744}
X(22678) = midpoint of X(9863) and X(10335)
The reciprocal orthologic center of these triangles is X(12177).
X(22679) lies on these lines: {3,22503}, {4,2896}, {262,5171}, {315,9772}, {384,22677}, {511,7833}, {2782,9939}, {5188,7752}, {7709,20065}, {7782,22676}, {7802,9863}, {10131,22525}, {11261,12110}, {15819,16921}
The reciprocal orthologic center of these triangles is X(3).
X(22680) lies on these lines: {3,22556}, {36,22650}, {55,22713}, {56,262}, {104,7709}, {511,11194}, {956,22697}, {958,15819}, {999,22475}, {2782,22565}, {2975,6194}, {3428,22676}, {7697,22758}, {10966,22711}, {11249,22780}, {11492,22672}, {11493,22668}, {12114,22703}, {18761,22681}, {19013,19063}, {19014,19064}, {22479,22480}, {22504,22769}, {22520,22521}, {22654,22655}, {22678,22744}, {22682,22753}, {22698,22755}, {22699,22756}, {22700,22757}, {22705,22759}, {22706,22760}, {22709,22761}, {22710,22762}, {22720,22763}, {22721,22764}, {22728,22765}, {22729,22766}, {22730,22767}, {22731,22768}
The reciprocal orthologic center of these triangles is X(3).
X(22681) lies on these lines: {4,2896}, {5,4045}, {30,15810}, {39,3850}, {76,3843}, {262,381}, {382,22676}, {511,3845}, {546,6248}, {547,21163}, {732,18546}, {1478,22706}, {1479,22705}, {2023,18424}, {3091,7709}, {3095,3832}, {3545,11171}, {3583,22711}, {3585,18971}, {3627,3934}, {3818,22505}, {3830,22712}, {3851,11257}, {3853,5188}, {5072,7786}, {6321,9772}, {9466,14893}, {9755,10796}, {9756,12042}, {9818,22655}, {9955,22475}, {10516,22677}, {10895,22729}, {10896,22730}, {12699,22697}, {13330,22593}, {13665,19064}, {13785,19063}, {18491,22556}, {18492,22650}, {18495,22668}, {18497,22672}, {18502,22521}, {18507,22698}, {18509,22699}, {18511,22700}, {18516,22703}, {18517,22704}, {18520,22709}, {18522,22710}, {18525,22713}, {18538,22720}, {18542,22731}, {18544,22732}, {18761,22680}, {18762,22721}
X(22681) = midpoint of X(i) and X(j) for these {i,j}: {4, 7697}, {76, 22728}, {382, 22676}, {3830, 22712}, {6321, 9772}, {12699, 22697}, {18507, 22698}, {18525, 22713}
X(22681) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (546, 6248, 14881), (22593, 22622, 13330)
The reciprocal orthologic center of these triangles is X(3).
X(22682) lies on these lines: {2,22676}, {4,39}, {5,5188}, {11,18971}, {12,22711}, {20,6683}, {30,21163}, {32,9756}, {76,3832}, {98,5008}, {115,5052}, {187,13860}, {235,22480}, {371,22720}, {372,22721}, {381,511}, {382,13334}, {515,22475}, {538,3839}, {546,6248}, {574,8719}, {625,13862}, {1352,7845}, {1478,22730}, {1479,22729}, {1503,7753}, {1513,7603}, {1587,19063}, {1588,19064}, {1598,22655}, {1699,14839}, {2782,3845}, {2794,14537}, {3091,3934}, {3095,3843}, {3146,7786}, {3202,11424}, {3545,22712}, {3627,11272}, {3714,19925}, {3767,9748}, {3830,11171}, {3851,9821}, {5007,9755}, {5097,12188}, {5309,14853}, {5587,22697}, {5603,22713}, {5999,7804}, {6201,22700}, {6202,22699}, {7470,9751}, {7746,9752}, {8196,22668}, {8203,22672}, {8212,22709}, {8213,22710}, {8589,11676}, {9765,9772}, {9993,22678}, {10531,22731}, {10532,22732}, {10893,22703}, {10894,22704}, {10895,22705}, {10896,22706}, {10991,18907}, {11477,17131}, {11496,22556}, {11897,22698}, {12110,21445}, {12263,12571}, {13335,18502}, {13354,15980}, {14492,14639}, {22680,22753}
X(22682) = midpoint of X(i) and X(j) for these {i,j}: {4, 262}, {3830, 11171}
X(22682) = complement of X(22676)
X(22682) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 22728, 7697), (546, 14881, 6248)
The reciprocal orthologic center of these triangles is X(22684).
X(22683) lies on these lines: {2,18}, {3,22684}, {6,22526}, {62,99}, {575,22687}, {576,22689}, {3734,22234}, {5965,22737}, {6033,16627}
X(22683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3734, 22234, 22685), (22882, 22883, 22871)
The reciprocal orthologic center of these triangles is X(22683).
X(22684) lies on these lines: {2,51}, {3,22683}, {398,3104}, {7697,16626}
X(22684) = anticomplement of X(33462)
X(22684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3104, 22702, 22707), (15819, 22686, 22715), (22686, 22714, 15819), (22726, 22727, 22714)
The reciprocal orthologic center of these triangles is X(22686).
X(22685) lies on these lines: {2,17}, {3,22686}, {6,22527}, {61,99}, {575,22689}, {576,22687}, {3734,22234}, {5965,22736}, {6033,16626}
X(22685) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3734, 22234, 22683), (22927, 22928, 22916)
The reciprocal orthologic center of these triangles is X(22685).
X(22686) lies on these lines: {2,51}, {3,22685}, {397,3105}, {7697,16627}
X(22686) = anticomplement of X(33463)
X(22686) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3105, 22701, 22708), (15819, 22684, 22714), (22684, 22715, 15819), (22726, 22727, 22715)
The reciprocal orthologic center of these triangles is X(22688).
X(22687) lies on these lines: {2,13}, {3,22715}, {6,12214}, {15,99}, {61,194}, {62,83}, {182,2782}, {298,22998}, {542,3642}, {575,22683}, {576,22685}, {619,8724}, {620,6771}, {621,6777}, {623,5617}, {627,7785}, {629,16627}, {1916,3106}, {2482,13083}, {5981,8289}, {6034,6772}, {7753,9115}, {9885,16508}, {11174,22691}, {11304,23005}, {11486,14535}, {14061,22846}, {22513,23025}
X(22687) = 1st-Brocard-isogonal conjugate of X(3642)
X(22687) = inverse of X(22689) in the Brocard circle
X(22687) = inverse of X(5979) in the inner-Napoleon circle
X(22687) = X(15)-of-1st-Brocard-triangle
X(22687) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (13, 5463, 5979), (16, 5980, 6582), (182, 3734, 22689), (5463, 6779, 616), (6302, 6306, 6298)
The reciprocal orthologic center of these triangles is X(22687).
X(22688) lies on these lines: {13,262}, {17,3105}, {61,22693}, {511,16267}, {2782,5470}, {3107,7697}, {11272,16627}, {11542,22701}, {13331,22690}, {14651,22510}, {16808,22707}, {16960,22695}
X(22688) = {X(13), X(22691)}-harmonic conjugate of X(3106)
The reciprocal orthologic center of these triangles is X(22690).
X(22689) lies on these lines: {2,14}, {3,22714}, {6,12213}, {16,99}, {61,83}, {62,194}, {182,2782}, {299,22997}, {542,3643}, {575,22685}, {576,22683}, {618,8724}, {620,6774}, {622,6778}, {624,5613}, {628,7785}, {630,16626}, {1916,3107}, {2482,13084}, {5980,8289}, {6034,6775}, {7753,9117}, {9886,16508}, {11174,22692}, {11303,23004}, {11485,14535}, {14061,22891}, {22512,23019}
X(22689) = inverse of X(22687) in the Brocard circle
X(22689) = inverse of X(5978) in the outer-Napoleon circle
X(22689) = X(16)-of-1st-Brocard-triangle
X(22689) = 1st-Brocard-isogonal conjugate of X(3643)
X(22689) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (14, 5464, 5978), (15, 5981, 6295), (182, 3734, 22687), (5464, 6780, 617), (6303, 6307, 6299)
The reciprocal orthologic center of these triangles is X(22689).
X(22690) lies on these lines: {14,262}, {18,3104}, {62,22694}, {511,16268}, {2782,5469}, {3106,7697}, {11272,16626}, {11543,22702}, {13331,22688}, {14651,22511}, {16809,22708}, {16961,22696}
X(22690) = {X(14), X(22692)}-harmonic conjugate of X(3107)
The reciprocal orthologic center of these triangles is X(22687).
X(22691) lies on these lines: {2,3107}, {5,39}, {13,262}, {15,5999}, {17,1916}, {61,98}, {62,3329}, {381,22707}, {396,511}, {630,5976}, {3105,22712}, {5459,22573}, {5470,9760}, {5617,13331}, {6581,11305}, {6694,7792}, {6772,11171}, {7709,16635}, {7786,11290}, {10654,22693}, {11174,22687}, {13876,22724}, {13929,22725}, {15819,22892}, {16267,22701}, {16644,22715}, {16962,22695}
X(22691) = midpoint of X(i) and X(j) for these {i,j}: {13, 3106}, {6772, 22708}
X(22691) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2009, 2010, 6115), (3106, 22688, 13)
The reciprocal orthologic center of these triangles is X(22689).
X(22692) lies on these lines: {2,3106}, {5,39}, {14,262}, {16,5999}, {18,1916}, {61,3329}, {62,98}, {381,22708}, {395,511}, {629,5976}, {3104,22712}, {5460,22574}, {5469,9762}, {5613,13331}, {6294,11306}, {6695,7792}, {6775,11171}, {7709,16634}, {7786,11289}, {10653,22694}, {11174,22689}, {13875,22724}, {13928,22725}, {15819,22848}, {16268,22702}, {16645,22714}, {16963,22696}
X(22692) = midpoint of X(i) and X(j) for these {i,j}: {14, 3107}, {6775, 22707}
X(22692) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2009, 2010, 6114), (3107, 22690, 14)
The reciprocal orthologic center of these triangles is X(22687).
X(22693) lies on these lines: {4,3104}, {5,22715}, {14,262}, {15,13860}, {39,5339}, {61,22688}, {381,511}, {623,13862}, {3095,16628}, {5321,22707}, {5480,22702}, {7685,9993}, {9753,22511}, {10654,22691}, {11300,22676}, {14881,16626}, {16808,22701}, {16809,22695}, {22512,22708}
The reciprocal orthologic center of these triangles is X(22689).
X(22694) lies on these lines: {4,3105}, {5,22714}, {13,262}, {16,13860}, {39,5340}, {62,22690}, {381,511}, {624,13862}, {3095,16629}, {5318,22708}, {5480,22701}, {7684,9993}, {9753,22510}, {10653,22692}, {11299,22676}, {14881,16627}, {16808,22696}, {16809,22702}, {22513,22707}
The reciprocal orthologic center of these triangles is X(22687).
X(22695) lies on these lines: {13,511}, {16,10788}, {18,262}, {3104,22708}, {5475,22696}, {9762,21359}, {16809,22693}, {16960,22688}, {16962,22691}, {16964,22707}, {16966,22715}
The reciprocal orthologic center of these triangles is X(22689).
X(22696) lies on these lines: {14,511}, {15,10788}, {17,262}, {3105,22707}, {5475,22695}, {9760,21360}, {16808,22694}, {16961,22690}, {16963,22692}, {16965,22708}, {16967,22714}
The reciprocal orthologic center of these triangles is X(3).
X(22697) lies on these lines: {1,15819}, {2,22475}, {8,6194}, {10,262}, {65,22705}, {72,22704}, {76,11362}, {355,12783}, {511,3679}, {515,22676}, {517,7697}, {519,22712}, {956,22680}, {1018,6210}, {1737,22730}, {1837,22711}, {2782,3654}, {3057,22706}, {3416,9864}, {3934,7982}, {4424,7235}, {4737,4899}, {5090,22480}, {5188,5881}, {5252,18971}, {5587,22682}, {5687,22556}, {5688,22700}, {5689,22699}, {5690,12782}, {5790,22728}, {6248,7991}, {6684,7976}, {8193,22655}, {8197,22668}, {8204,22672}, {8214,22709}, {8215,22710}, {9588,13334}, {9755,12197}, {9857,22678}, {10039,22729}, {10791,22521}, {10914,22703}, {10915,22731}, {10916,22732}, {12245,12263}, {12699,22681}, {13883,19064}, {13893,22720}, {13936,19063}, {13947,22721}
X(22697) = midpoint of X(8) and X(6194)
X(22697) = reflection of X(i) in X(j) for these (i,j): (1, 15819), (12699, 22681)
X(22697) = anticomplement of X(22475)
The reciprocal orthologic center of these triangles is X(3).
X(22698) lies on these lines: {30,7697}, {76,15774}, {262,402}, {511,1651}, {1650,15819}, {2782,12347}, {4240,6194}, {7709,11845}, {11251,12795}, {11831,22475}, {11832,22480}, {11839,22521}, {11848,22556}, {11852,22650}, {11853,22655}, {11885,22678}, {11897,22682}, {11901,22699}, {11902,22700}, {11903,22703}, {11904,22704}, {11905,22705}, {11906,22706}, {11907,22709}, {11908,22710}, {11909,22711}, {11910,22713}, {11911,22728}, {11912,22729}, {11913,22730}, {11914,22731}, {11915,22732}, {12181,12583}, {13894,22720}, {13948,22721}, {18507,22681}, {18958,18971}, {19017,19063}, {19018,19064}, {22680,22755}
X(22698) = midpoint of X(4240) and X(6194)
X(22698) = reflection of X(i) in X(j) for these (i,j): (262, 402), (1650, 15819), (18507, 22681)
The reciprocal orthologic center of these triangles is X(3).
X(22699) lies on these lines: {6,98}, {76,6281}, {511,5861}, {1161,6275}, {1271,6194}, {1352,22727}, {2782,9882}, {5589,22650}, {5591,15819}, {5595,22655}, {5605,22713}, {5689,22697}, {5875,6273}, {6202,22682}, {6215,7697}, {7709,10783}, {8198,22668}, {8205,22672}, {8216,22709}, {8217,22710}, {8974,22720}, {9994,22678}, {10040,22729}, {10048,22730}, {10792,22521}, {10919,22703}, {10921,22704}, {10923,22705}, {10925,22706}, {10927,22711}, {10929,22731}, {10931,22732}, {11370,22475}, {11388,22480}, {11497,22556}, {11824,22676}, {11901,22698}, {11916,22728}, {13949,22721}, {18509,22681}, {18959,18971}, {22680,22756}
The reciprocal orthologic center of these triangles is X(3).
X(22700) lies on these lines: {6,98}, {76,6278}, {511,5860}, {1160,6274}, {1270,6194}, {1352,22726}, {2782,9883}, {5588,22650}, {5590,15819}, {5594,22655}, {5604,22713}, {5688,22697}, {5874,6272}, {6201,22682}, {6214,7697}, {7709,10784}, {8199,22668}, {8206,22672}, {8218,22709}, {8219,22710}, {8975,22720}, {9995,22678}, {10041,22729}, {10049,22730}, {10793,22521}, {10920,22703}, {10922,22704}, {10924,22705}, {10926,22706}, {10928,22711}, {10930,22731}, {10932,22732}, {11371,22475}, {11389,22480}, {11498,22556}, {11825,22676}, {11902,22698}, {11917,22728}, {13950,22721}, {18511,22681}, {18960,18971}, {22680,22757}
The reciprocal orthologic center of these triangles is X(22687).
X(22701) lies on these lines: {13,511}, {15,11676}, {16,22715}, {17,262}, {61,10796}, {62,385}, {396,3106}, {397,3105}, {2782,22997}, {3107,5464}, {5475,7697}, {5480,22694}, {11542,22688}, {16267,22691}, {16808,22693}, {22486,22494}
X(22701) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7697, 13330, 22702), (22686, 22708, 3105)
The reciprocal orthologic center of these triangles is X(22689).
X(22702) lies on these lines: {14,511}, {15,22714}, {16,11676}, {18,262}, {61,385}, {62,10796}, {395,3107}, {398,3104}, {2782,22998}, {3106,5463}, {5475,7697}, {5480,22693}, {11543,22690}, {16268,22692}, {16809,22694}, {22486,22493}
X(22702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7697, 13330, 22701), (22684, 22707, 3104)
The reciprocal orthologic center of these triangles is X(3).
X(22703) lies on these lines: {11,262}, {12,22731}, {355,7697}, {511,11235}, {1376,15819}, {2782,12348}, {3434,6194}, {7709,10785}, {10523,22729}, {10525,12924}, {10794,22521}, {10826,22650}, {10829,22655}, {10871,22678}, {10893,22682}, {10914,22697}, {10919,22699}, {10920,22700}, {10943,12923}, {10944,22705}, {10945,22709}, {10946,22710}, {10947,22711}, {10948,22730}, {10949,22732}, {11373,22475}, {11390,22480}, {11826,22676}, {11865,22668}, {11866,22672}, {11903,22698}, {11928,22728}, {12114,22680}, {12182,12586}, {13895,22720}, {13952,22721}, {18516,22681}, {18961,18971}, {19023,19063}, {19024,19064}
The reciprocal orthologic center of these triangles is X(3).
X(22704) lies on these lines: {11,22732}, {12,262}, {72,22697}, {355,7697}, {511,11236}, {958,15819}, {2782,12349}, {3436,6194}, {7709,10786}, {10523,22730}, {10526,12934}, {10795,22521}, {10827,22650}, {10830,22655}, {10872,22678}, {10894,22682}, {10921,22699}, {10922,22700}, {10942,12933}, {10950,22706}, {10951,22709}, {10952,22710}, {10953,22711}, {10954,22729}, {10955,22731}, {11374,22475}, {11391,22480}, {11500,22556}, {11827,22676}, {11867,22668}, {11868,22672}, {11904,22698}, {11929,22728}, {12183,12587}, {13896,22720}, {13953,22721}, {18517,22681}, {18962,18971}, {19025,19063}, {19026,19064}
The reciprocal orthologic center of these triangles is X(3).
X(22705) lies on these lines: {1,7697}, {4,22711}, {5,22730}, {12,262}, {56,15819}, {65,22697}, {76,15888}, {388,6194}, {495,10063}, {511,11237}, {1478,12944}, {1479,22681}, {2782,10056}, {3023,9772}, {3085,7709}, {3303,6248}, {3304,3934}, {3584,11171}, {5188,9657}, {5270,9821}, {5434,22712}, {7354,22676}, {9578,22650}, {9654,22728}, {9755,10799}, {10797,22521}, {10831,22655}, {10873,22678}, {10895,22682}, {10944,22703}, {10956,22731}, {10957,22732}, {11375,22475}, {11392,22480}, {11501,22556}, {11869,22668}, {11870,22672}, {11905,22698}, {11930,22709}, {11931,22710}, {12184,12588}, {13897,22720}, {13954,22721}, {19027,19063}, {19028,19064}, {22680,22759}
X(22705) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7697, 22706), (388, 6194, 18971), (495, 10063, 12837)
The reciprocal orthologic center of these triangles is X(3).
X(22706) lies on these lines: {1,7697}, {4,18971}, {5,22729}, {11,262}, {55,15819}, {496,10079}, {497,6194}, {511,11238}, {1478,22681}, {1479,12954}, {2782,10072}, {3027,9772}, {3057,22697}, {3058,22712}, {3086,7709}, {3303,3934}, {3304,6248}, {3582,11171}, {4857,9821}, {5188,9670}, {6284,22676}, {9581,22650}, {9669,22728}, {9755,12835}, {10798,22521}, {10832,22655}, {10874,22678}, {10896,22682}, {10925,22699}, {10926,22700}, {10950,22704}, {10958,22731}, {10959,22732}, {11376,22475}, {11393,22480}, {11502,22556}, {11871,22668}, {11872,22672}, {11906,22698}, {11932,22709}, {11933,22710}, {12185,12589}, {13898,22720}, {13955,22721}, {14986,18982}, {19029,19063}, {19030,19064}, {22680,22760}
X(22706) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7697, 22705), (496, 10079, 12836), (497, 6194, 22711)
The reciprocal orthologic center of these triangles is X(22687).
X(22707) lies on these lines: {4,39}, {14,2782}, {15,22715}, {30,3107}, {61,10796}, {381,22691}, {398,3104}, {511,10654}, {736,6581}, {3094,22512}, {3105,22696}, {5321,22693}, {6775,11171}, {7804,10613}, {16808,22688}, {16964,22695}, {22513,22694}
X(22707) = reflection of X(6775) in X(22692)
X(22707) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2549, 7709, 22708), (3104, 22702, 22684)
The reciprocal orthologic center of these triangles is X(22689).
X(22708) lies on these lines: {4,39}, {13,2782}, {16,22714}, {30,3106}, {62,10796}, {381,22692}, {397,3105}, {511,10653}, {736,6294}, {3094,22513}, {3104,22695}, {5318,22694}, {6772,11171}, {7804,10614}, {16809,22690}, {16965,22696}, {22512,22693}
X(22708) = reflection of X(6772) in X(22691)
X(22708) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2549, 7709, 22707), (3105, 22701, 22686)
The reciprocal orthologic center of these triangles is X(3).
X(22709) lies on these lines: {262,493}, {511,12152}, {2782,12352}, {6194,6462}, {6461,22710}, {7697,8220}, {7709,11846}, {8188,22650}, {8194,22655}, {8210,22713}, {8212,22682}, {8214,22697}, {8216,22699}, {8218,22700}, {8222,15819}, {10669,12994}, {10875,22678}, {10945,22703}, {10951,22704}, {11377,22475}, {11394,22480}, {11503,22556}, {11828,22676}, {11840,22521}, {11907,22698}, {11930,22705}, {11932,22706}, {11947,22711}, {11949,22728}, {11951,22729}, {11953,22730}, {11955,22731}, {11957,22732}, {12186,12590}, {13899,22720}, {13956,22721}, {18520,22681}, {18963,18971}, {19031,19063}, {19032,19064}, {22680,22761}
The reciprocal orthologic center of these triangles is X(3).
X(22710) lies on these lines: {262,494}, {511,12153}, {2782,12353}, {6194,6463}, {6461,22709}, {7697,8221}, {7709,11847}, {8189,22650}, {8195,22655}, {8211,22713}, {8213,22682}, {8215,22697}, {8217,22699}, {8219,22700}, {8223,15819}, {10673,12995}, {10876,22678}, {10946,22703}, {10952,22704}, {11378,22475}, {11395,22480}, {11504,22556}, {11829,22676}, {11841,22521}, {11908,22698}, {11931,22705}, {11933,22706}, {11948,22711}, {11950,22728}, {11952,22729}, {11954,22730}, {11956,22731}, {11958,22732}, {12187,12591}, {13900,22720}, {13957,22721}, {18522,22681}, {18964,18971}, {19033,19063}, {19034,19064}, {22680,22762}
The reciprocal orthologic center of these triangles is X(3).
X(22711) lies on these lines: {1,13078}, {3,22730}, {4,22705}, {11,15819}, {12,22682}, {33,22480}, {55,262}, {56,22676}, {76,9670}, {390,12837}, {497,6194}, {511,3058}, {1479,7697}, {1697,22650}, {1837,22697}, {2023,10987}, {2098,22713}, {2646,22475}, {2782,12354}, {3027,3056}, {3095,4309}, {3295,22728}, {3583,22681}, {3746,14881}, {4294,7709}, {6284,18982}, {9668,10063}, {9772,12185}, {10799,22521}, {10833,22655}, {10877,22678}, {10927,22699}, {10928,22700}, {10947,22703}, {10953,22704}, {10965,22731}, {10966,22680}, {11238,22712}, {11873,22668}, {11874,22672}, {11909,22698}, {11947,22709}, {11948,22710}, {13077,15171}, {13901,22720}, {13958,22721}, {19037,19063}, {19038,19064}
X(22711) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497, 6194, 22706), (3295, 22728, 22729)
The reciprocal orthologic center of these triangles is X(99).
X(22712) lies on these lines: {2,51}, {3,76}, {4,3934}, {5,3096}, {20,6248}, {30,7697}, {35,10079}, {36,10063}, {39,631}, {40,12263}, {69,9744}, {114,3314}, {140,3095}, {141,1513}, {182,385}, {194,3523}, {230,3094}, {264,22062}, {371,19089}, {372,19090}, {376,9466}, {383,3642}, {384,5171}, {519,22697}, {538,3524}, {542,8592}, {543,11167}, {549,7757}, {575,7766}, {576,3329}, {599,6054}, {698,13468}, {726,10164}, {732,5085}, {736,21445}, {842,9832}, {1080,3643}, {1350,13860}, {1351,11174}, {1352,16990}, {1385,7976}, {1587,8992}, {1588,13983}, {1656,7944}, {1799,3425}, {1916,6036}, {2021,21843}, {2080,3972}, {2709,5108}, {2794,7810}, {3058,22706}, {3098,5999}, {3102,5420}, {3103,5418}, {3104,22692}, {3105,22691}, {3106,16242}, {3107,16241}, {3398,6179}, {3399,6680}, {3406,8150}, {3515,12143}, {3525,6683}, {3526,11272}, {3545,22682}, {3582,22730}, {3584,22729}, {3734,8722}, {3815,13330}, {3830,22681}, {4108,8704}, {5007,10359}, {5050,14614}, {5052,7736}, {5055,22728}, {5064,22480}, {5092,8350}, {5204,18982}, {5217,13077}, {5306,13331}, {5432,12837}, {5433,12836}, {5434,22705}, {5657,14839}, {5969,7610}, {5987,12584}, {6309,7751}, {6684,12782}, {6776,14994}, {7422,18304}, {7616,8782}, {7746,10357}, {7770,12110}, {7780,8149}, {7793,13335}, {7804,10788}, {7815,18806}, {7824,9737}, {7841,14639}, {7846,20576}, {7865,22678}, {7870,15561}, {7898,13449}, {7987,9902}, {8556,9756}, {9301,10347}, {9769,15035}, {10267,13110}, {10269,13109}, {11055,15693}, {11151,11152}, {11237,18971}, {11238,22711}, {11672,14252}, {12007,15480}, {13083,21156}, {13084,21157}, {13086,14651}, {13862,16986}, {14711,15698}, {15717,20081}, {19875,22650}
X(22712) = midpoint of X(2) and X(6194)
X(22712) = reflection of X(i) in X(j) for these (i,j): (2, 15819), (3830, 22681)
X(22712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 76, 11257), (3, 183, 98), (140, 3095, 7786), (183, 5976, 76), (194, 3523, 13334), (631, 12251, 39), (1350, 15271, 13860), (3524, 7709, 21163), (3734, 8722, 11676), (3934, 5188, 4), (5085, 8667, 9755), (5980, 5981, 7771), (6194, 15819, 262), (22714, 22715, 22677)
The reciprocal orthologic center of these triangles is X(3).
X(22713) lies on these lines: {1,262}, {8,15819}, {55,22680}, {56,22556}, {145,6194}, {511,3241}, {517,22676}, {519,22697}, {952,7697}, {1482,7977}, {1483,7976}, {2098,22711}, {2099,18971}, {2782,9884}, {3242,7970}, {5597,22672}, {5598,22668}, {5603,22682}, {5604,22700}, {5605,22699}, {5882,11257}, {7709,7967}, {7786,15178}, {7968,19063}, {7969,19064}, {7972,10063}, {8192,22655}, {8210,22709}, {8211,22710}, {9997,22678}, {10247,22728}, {10800,22521}, {10944,22703}, {10950,22704}, {11396,22480}, {11910,22698}, {12782,13607}, {13902,22720}, {13959,22721}, {18525,22681}
X(22713) = midpoint of X(145) and X(6194)
X(22713) = reflection of X(i) in X(j) for these (i,j): (8, 15819), (18525, 22681)
X(22713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22650, 22475), (22475, 22650, 262), (22731, 22732, 262)
The reciprocal orthologic center of these triangles is X(22689).
X(22714) lies on these lines: {2,51}, {3,22689}, {5,22694}, {15,22702}, {16,22708}, {18,3104}, {76,627}, {140,3105}, {182,5980}, {302,23024}, {395,3106}, {2782,5463}, {3107,16242}, {3643,5617}, {5613,9749}, {7709,14145}, {7761,20428}, {7771,13350}, {9885,11171}, {16645,22692}, {16967,22696}
X(22714) = anticomplement of X(33479)
X(22714) = outer-Napoleon-circle-inverse of X(33873)
X(22714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (15819, 22684, 22686), (22677, 22712, 22715), (22726, 22727, 22684)
The reciprocal orthologic center of these triangles is X(22687).
X(22715) lies on these lines: {2,51}, {3,22687}, {5,22693}, {15,22707}, {16,22701}, {17,3105}, {76,628}, {140,3104}, {182,5981}, {303,23018}, {396,3107}, {2782,5464}, {3106,16241}, {3642,5613}, {5617,9750}, {7709,14144}, {7761,20429}, {7771,13349}, {9886,11171}, {16644,22691}, {16966,22695}
X(22715) = anticomplement of X(33478)
X(22715) = inner-Napoleon-circle-inverse of X(33873)
X(22715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (15819, 22686, 22684), (22677, 22712, 22714), (22726, 22727, 22686)
The reciprocal orthologic center of these triangles is X(22717).
X(22716) lies on these lines: {2,1327}, {6,13673}, {83,372}, {99,6200}, {182,22594}, {194,371}, {511,22623}, {639,21737}, {642,14244}, {3734,5092}, {5591,13674}, {6033,13692}, {6312,12968}, {6398,14535}, {6411,13828}, {9892,16508}, {12124,21736}
X(22716) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 13712, 13710), (3734, 5092, 22718)
The reciprocal orthologic center of these triangles is X(22716).
X(22717) lies on these lines: {39,485}, {76,3316}, {511,3068}, {590,3103}, {638,7786}, {1352,7736}, {2023,6230}, {3102,7583}, {3312,6312}, {6314,8976}, {19064,22723}, {22720,22727}, {22724,22726}
The reciprocal orthologic center of these triangles is X(22719).
X(22718) lies on these lines: {2,1328}, {6,13793}, {83,371}, {99,6396}, {182,22623}, {194,372}, {511,22594}, {641,14229}, {3734,5092}, {5590,13794}, {6033,13812}, {6221,14535}, {6316,12963}, {6412,13708}, {9894,16508}
X(22718) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 13835, 13830), (3734, 5092, 22716)
The reciprocal orthologic center of these triangles is X(22718).
X(22719) lies on these lines: {39,486}, {76,3317}, {511,3069}, {615,3102}, {637,7786}, {1352,7736}, {2023,6231}, {3103,7584}, {3311,6316}, {6318,13951}, {19063,22722}, {22721,22726}, {22725,22727}
The reciprocal orthologic center of these triangles is X(3).
X(22720) lies on these lines: {2,19064}, {39,8960}, {262,3068}, {371,22682}, {511,13846}, {590,15819}, {2782,13908}, {3316,19089}, {6194,8972}, {7585,19063}, {7697,8976}, {7709,13886}, {8974,22699}, {8975,22700}, {8980,13910}, {8981,8993}, {8992,13925}, {9540,22676}, {13883,22475}, {13884,22480}, {13885,22521}, {13887,22556}, {13888,22650}, {13889,22655}, {13891,22672}, {13892,22678}, {13893,22697}, {13894,22698}, {13895,22703}, {13896,22704}, {13897,22705}, {13898,22706}, {13899,22709}, {13900,22710}, {13901,22711}, {13902,22713}, {13903,22728}, {13904,22729}, {13905,22730}, {13906,22731}, {13907,22732}, {18538,22681}, {18965,18971}, {22680,22763}, {22717,22727}
The reciprocal orthologic center of these triangles is X(3).
X(22721) lies on these lines: {2,19063}, {6,22720}, {262,3069}, {372,22682}, {511,13847}, {615,15819}, {2782,13968}, {3317,19090}, {6194,13941}, {7586,19064}, {7697,13951}, {7709,13939}, {13935,22676}, {13936,22475}, {13937,22480}, {13938,22521}, {13940,22556}, {13942,22650}, {13943,22655}, {13944,22668}, {13945,22672}, {13946,22678}, {13947,22697}, {13948,22698}, {13949,22699}, {13950,22700}, {13952,22703}, {13953,22704}, {13954,22705}, {13955,22706}, {13956,22709}, {13957,22710}, {13958,22711}, {13959,22713}, {13961,22728}, {13962,22729}, {13963,22730}, {13964,22731}, {13965,22732}, {13966,13984}, {13967,13972}, {13983,13993}, {18762,22681}, {18966,18971}, {22680,22764}, {22719,22726}
The reciprocal orthologic center of these triangles is X(6).
X(22722) lies on these lines: {2,3787}, {39,7585}, {76,13707}, {262,13638}, {371,12110}, {372,13885}, {511,3068}, {538,13639}, {590,13330}, {698,13647}, {732,13648}, {1271,3934}, {2782,13640}, {3103,19090}, {5058,7878}, {5062,6179}, {5861,14994}, {5969,13642}, {6272,13877}, {13637,22486}, {19063,22719}, {19064,22727}
X(22722) = reflection of X(76) in X(13707)
X(22722) = {X(2), X(5052)}-harmonic conjugate of X(22723)
The reciprocal orthologic center of these triangles is X(6).
X(22723) lies on these lines: {2,3787}, {39,7586}, {76,13827}, {262,13758}, {371,13938}, {372,12110}, {511,3069}, {538,13759}, {615,13330}, {698,13766}, {732,13767}, {1270,3934}, {2782,13760}, {3102,19089}, {5058,6179}, {5062,7878}, {5860,14994}, {5969,13761}, {6273,13930}, {13757,22486}, {19063,22726}, {19064,22717}
X(22723) = reflection of X(76) in X(13827)
X(22723) = {X(2), X(5052)}-harmonic conjugate of X(22722)
The reciprocal orthologic center of these triangles is X(22623).
X(22724) lies on these lines: {39,1656}, {262,485}, {371,6222}, {511,13846}, {590,13926}, {641,13878}, {3103,13882}, {6118,13877}, {13875,22692}, {13876,22691}, {22717,22726}
The reciprocal orthologic center of these triangles is X(22594).
X(22725) lies on these lines: {39,1656}, {262,486}, {372,6399}, {511,13847}, {615,13873}, {642,13931}, {3102,13934}, {11174,22594}, {13928,22692}, {13929,22691}, {22719,22727}
The reciprocal orthologic center of these triangles is X(22594).
X(22726) lies on these lines: {2,51}, {3,22594}, {39,19102}, {182,10852}, {615,13873}, {1352,22700}, {3102,7584}, {6228,6289}, {6561,22593}, {11171,13700}, {19063,22723}, {22717,22724}, {22719,22721}
X(22726) = complement of X(33435)
X(22726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6194, 22677, 22727), (22684, 22714, 22727), (22686, 22715, 22727)
The reciprocal orthologic center of these triangles is X(22623).
X(22727) lies on these lines: {2,51}, {39,19105}, {182,10851}, {590,13926}, {1352,22699}, {3103,7583}, {6229,6290}, {6560,22622}, {11171,13820}, {19064,22722}, {22717,22720}, {22719,22725}
X(22727) = complement of X(33434)
X(22727) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6194, 22677, 22726), (22684, 22714, 22726), (22686, 22715, 22726)
The reciprocal orthologic center of these triangles is X(3).
X(22728) lies on these lines: {3,83}, {4,7779}, {5,6194}, {30,7709}, {39,1657}, {76,3843}, {194,3627}, {381,511}, {382,3095}, {517,22650}, {546,12251}, {999,18971}, {1350,11261}, {1351,12188}, {1384,2023}, {1598,22480}, {1656,7914}, {2782,3830}, {3094,15484}, {3104,5340}, {3105,5339}, {3295,22711}, {3526,5188}, {3534,11171}, {3934,5072}, {5055,22712}, {5073,11257}, {5475,22695}, {5790,22697}, {5999,11842}, {6417,19064}, {6418,19063}, {7517,22655}, {7757,15684}, {7785,10335}, {9301,13860}, {9654,22705}, {9655,12836}, {9668,12837}, {9669,22706}, {10007,14535}, {10246,22475}, {10247,22713}, {11849,22556}, {11875,22668}, {11876,22672}, {11911,22698}, {11916,22699}, {11917,22700}, {11928,22703}, {11929,22704}, {11949,22709}, {11950,22710}, {12000,22731}, {12001,22732}, {13334,15696}, {13903,22720}, {13961,22721}, {15688,21163}, {15980,21850}, {22680,22765}
X(22728) = reflection of X(i) in X(j) for these (i,j): (3, 262), (76, 22681), (1350, 11261), (3534, 11171)
X(22728) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 13111, 18501), (7697, 22682, 381), (18971, 22730, 999), (22711, 22729, 3295)
The reciprocal orthologic center of these triangles is X(3).
X(22729) lies on these lines: {1,262}, {3,18971}, {5,22706}, {12,7697}, {35,22676}, {55,10064}, {388,7709}, {495,10063}, {498,15819}, {511,10056}, {611,10053}, {1469,22677}, {1479,22682}, {2782,10054}, {3085,6194}, {3095,15888}, {3295,22711}, {3299,19063}, {3301,19064}, {3303,14881}, {3304,11272}, {3584,22712}, {4317,13334}, {5270,11257}, {5434,11171}, {5563,7786}, {9654,13077}, {10037,22655}, {10038,22678}, {10039,22697}, {10040,22699}, {10041,22700}, {10523,22703}, {10801,22521}, {10802,21445}, {10895,22681}, {10954,22704}, {11398,22480}, {11507,22556}, {11877,22668}, {11878,22672}, {11912,22698}, {11951,22709}, {11952,22710}, {12782,13407}, {13904,22720}, {13962,22721}, {22680,22766}
X(22729) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 262, 22730), (495, 12837, 10063), (3295, 22728, 22711)
The reciprocal orthologic center of these triangles is X(3).
X(22730) lies on these lines: {1,262}, {3,22711}, {5,22705}, {11,7697}, {36,22676}, {56,10080}, {496,10079}, {497,7709}, {499,15819}, {511,10072}, {613,10069}, {999,18971}, {1478,22682}, {1737,22697}, {2782,10070}, {3056,22677}, {3058,11171}, {3086,6194}, {3299,19064}, {3301,19063}, {3303,11272}, {3304,14881}, {3582,22712}, {3746,7786}, {4309,13334}, {4857,11257}, {9669,18982}, {10046,22655}, {10047,22678}, {10048,22699}, {10049,22700}, {10523,22704}, {10801,21445}, {10802,22521}, {10896,22681}, {10948,22703}, {11399,22480}, {11508,22556}, {11879,22668}, {11880,22672}, {11913,22698}, {11953,22709}, {11954,22710}, {13905,22720}, {13963,22721}, {22680,22767}
X(22730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 262, 22729), (496, 12836, 10079), (999, 22728, 18971)
The reciprocal orthologic center of these triangles is X(3).
X(22731) lies on these lines: {1,262}, {12,22703}, {511,11239}, {2782,12356}, {5552,15819}, {6194,10528}, {7697,10942}, {7709,10805}, {10531,22682}, {10679,13112}, {10803,22521}, {10834,22655}, {10878,22678}, {10915,22697}, {10929,22699}, {10930,22700}, {10955,22704}, {10956,22705}, {10958,22706}, {10965,22711}, {11248,22676}, {11400,22480}, {11509,18971}, {11881,22668}, {11882,22672}, {11914,22698}, {11955,22709}, {11956,22710}, {12000,22728}, {12189,12594}, {13906,22720}, {13964,22721}, {18542,22681}, {19047,19063}, {19048,19064}, {22680,22768}
X(22731) = {X(262), X(22713)}-harmonic conjugate of X(22732)
The reciprocal orthologic center of these triangles is X(3).
X(22732) lies on these lines: {1,262}, {11,22704}, {511,11240}, {2782,12357}, {6194,10529}, {7697,10943}, {7709,10806}, {10527,15819}, {10532,22682}, {10680,13113}, {10804,22521}, {10835,22655}, {10879,22678}, {10916,22697}, {10931,22699}, {10932,22700}, {10949,22703}, {10957,22705}, {10959,22706}, {10966,22680}, {11249,22676}, {11401,22480}, {11510,22556}, {11883,22668}, {11884,22672}, {11915,22698}, {11957,22709}, {11958,22710}, {12001,22728}, {12190,12595}, {13907,22720}, {13965,22721}, {18544,22681}, {18967,18971}, {19049,19063}, {19050,19064}
X(22732) = {X(262), X(22713)}-harmonic conjugate of X(22731)
The reciprocal parallelogic center of these triangles is X(3).
X(22733) lies on these lines: {351,13308}, {512,9123}, {804,8592}, {5466,14327}, {9131,13307}, {9135,9147}, {13306,14610}
The reciprocal parallelogic center of these triangles is X(3).
X(22734) lies on these lines: {2,3569}, {23,9420}, {351,13308}, {512,9185}, {804,5466}, {4108,9208}, {9979,13306}
The reciprocal cyclologic center of these triangles is X(3).
X(22735) lies on the cubic K509 and these lines: {2,2782}, {30,11673}, {98,237}, {99,14096}, {115,3117}, {694,804}, {2396,8842}, {2450,8569}, {5149,10328}, {6321,14957}, {11328,12188}
X(22735) = centroid of (degenerate) reflection triangle of ABC wrt 1st Brocard triangle
The reciprocal orthologic center of these triangles is X(22507).
X(22736) lies on these lines: {2,18}, {3,22507}, {76,11603}, {182,22526}, {299,22846}, {384,22748}, {636,16628}, {3314,5983}, {5464,11149}, {5965,22685}, {7697,16627}, {7761,22737}, {10000,22745}, {11306,20378}
X(22736) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18, 628, 22866), (22882, 22883, 22869)
The reciprocal orthologic center of these triangles is X(22509).
X(22737) lies on these lines: {2,17}, {3,22509}, {76,11602}, {182,22527}, {298,22891}, {384,22749}, {635,16629}, {3314,5982}, {5463,11149}, {5965,22683}, {7697,16626}, {7761,22736}, {10000,22746}, {11305,20377}
X(22737) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17, 627, 22911), (22927, 22928, 22914)
The reciprocal cyclologic center of these triangles is X(3).
X(22738) lies on the cubic K509 and these lines: {2,5470}, {4,8450}, {17,930}, {6778,14447}
X(22738) = inverse of X(22846) in the inner-Napoleon circle
The reciprocal cyclologic center of these triangles is X(3).
X(22739) lies on the cubic K509 and these lines: {2,5469}, {4,8451}, {18,930}, {6777,14446}
X(22739) = inverse of X(22891) in the outer-Napoleon circle
X(22739) = inner-Napoleon-circle-inverse of X(36782)
The reciprocal cyclologic center of these triangles is X(22741).
X(22740) lies on the Brocard circle and these lines: {}
The reciprocal cyclologic center of these triangles is X(22740).
X(22741) lies on these lines: {}
The reciprocal cyclologic center of these triangles is X(22743).
X(22742) lies on the Brocard circle and these lines: {}
The reciprocal cyclologic center of these triangles is X(22742).
X(22743) lies on these lines: {}
X(22744) lies on these lines: {3,9941}, {32,56}, {36,3099}, {55,9997}, {104,9862}, {956,9857}, {958,3096}, {999,11368}, {2896,2975}, {3094,22769}, {3098,3428}, {4475,20999}, {5253,10583}, {8782,22514}, {9301,22765}, {9821,11249}, {9873,10871}, {9878,22565}, {9923,22659}, {9981,22774}, {9982,22773}, {9983,22779}, {9984,22583}, {9985,22781}, {9986,22595}, {9987,22624}, {9993,22753}, {9994,22756}, {9995,22757}, {9996,22758}, {10038,22766}, {10047,22767}, {10873,22759}, {10874,22760}, {10875,22761}, {10876,22762}, {10877,10879}, {10878,22768}, {11386,22479}, {11492,11862}, {11493,11861}, {11885,22755}, {12495,12513}, {12496,18237}, {12497,22770}, {12498,12773}, {12499,22775}, {12500,22777}, {12501,19478}, {12502,22778}, {12503,19159}, {12504,22782}, {13210,22586}, {13235,22560}, {13236,19162}, {13685,22783}, {13743,16123}, {13805,22784}, {13892,22763}, {13946,22764}, {18500,18761}, {19011,19013}, {19012,19014}, {22678,22680}, {22745,22771}, {22746,22772}, {22747,22776}
X(22744) = {X(3), X(9941)}-harmonic conjugate of X(11494)
The reciprocal orthologic center of these triangles is X(3).
X(22745) lies on these lines: {15,628}, {16,5872}, {18,32}, {630,3096}, {3094,5965}, {3098,22843}, {3099,22651}, {3105,9982}, {6674,7846}, {9301,16628}, {9821,9981}, {9857,22851}, {9862,22531}, {9878,9989}, {9993,22831}, {9994,22853}, {9995,22854}, {9996,16627}, {9997,22867}, {10000,22736}, {10038,22884}, {10047,22885}, {10828,22656}, {10871,22857}, {10872,22858}, {10873,22859}, {10874,22860}, {10875,22863}, {10876,22864}, {10877,22865}, {10878,22886}, {10879,22887}, {11368,11740}, {11386,22481}, {11494,22557}, {11861,22669}, {11862,22673}, {11885,22852}, {13892,22876}, {13946,22877}, {18500,22794}, {18957,18972}, {19011,19069}, {19012,19072}, {22744,22771}
The reciprocal orthologic center of these triangles is X(3).
X(22746) lies on these lines: {15,5873}, {16,627}, {17,32}, {532,3105}, {629,3096}, {3094,5965}, {3098,22890}, {3099,22652}, {3104,9981}, {6673,7846}, {9301,16629}, {9821,9982}, {9857,22896}, {9862,22532}, {9878,9988}, {9993,22832}, {9994,22898}, {9995,22899}, {9996,16626}, {9997,22912}, {10000,22737}, {10038,22929}, {10047,22930}, {10828,22657}, {10871,22902}, {10872,22903}, {10873,22904}, {10874,22905}, {10875,22908}, {10876,22909}, {10877,22910}, {10878,22931}, {10879,22932}, {11368,11739}, {11386,22482}, {11494,22558}, {11861,22670}, {11862,22674}, {11885,22897}, {13892,22921}, {13946,22922}, {18500,22795}, {18957,18973}, {19011,19071}, {19012,19070}, {22744,22772}
The reciprocal orthologic center of these triangles is X(12241).
X(22747) lies on these lines: {32,22466}, {2896,22647}, {3096,22966}, {3098,22951}, {3099,22653}, {9301,22979}, {9857,22941}, {9862,22533}, {9993,22833}, {9994,22945}, {9995,22947}, {9996,22955}, {9997,22969}, {10038,22980}, {10047,22981}, {10828,22658}, {10871,22956}, {10872,22957}, {10873,22958}, {10874,22959}, {10875,22963}, {10876,22964}, {10877,22965}, {10878,22982}, {10879,22983}, {11368,22476}, {11386,22483}, {11494,22559}, {11885,22943}, {13892,22976}, {13946,22977}, {18500,22800}, {18957,18978}, {19011,19083}, {19012,19084}, {22744,22776}
The reciprocal orthologic center of these triangles is X(22507).
X(22748) lies on these lines: {3,22506}, {15,628}, {315,5983}, {384,22736}, {7802,22749}, {10131,22526}
The reciprocal orthologic center of these triangles is X(22509).
X(22749) lies on these lines: {16,627}, {315,5982}, {384,22737}, {532,7833}, {7802,22748}, {10131,22527}
The reciprocal orthologic center of these triangles is X(9729).
X(22750) lies on these lines: {2,22834}, {3,22497}, {4,801}, {5,22808}, {24,1192}, {25,5889}, {54,403}, {110,235}, {184,6622}, {186,8718}, {206,1614}, {378,22549}, {389,21652}, {631,22581}, {1112,15801}, {1147,6623}, {1181,17837}, {1596,18350}, {1598,11387}, {1660,18945}, {1870,19472}, {3089,6193}, {3090,22973}, {3518,7722}, {3520,22978}, {3567,22530}, {5890,22535}, {6146,22662}, {6197,22840}, {6198,22954}, {6240,10721}, {6353,6759}, {6403,7716}, {7592,19460}, {7699,22833}, {8537,9781}, {10540,21841}, {10632,22974}, {10633,22975}, {10880,22960}, {10881,22961}, {12292,16835}, {14644,20303}, {15033,22968}, {18504,22979}, {18560,22951}, {18916,18936}, {19424,19488}, {19425,19489}
X(22750) = reflection of X(4) in X(22970)
X(22750) = anticomplement of X(22834)
X(22750) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1614, 3542, 19128), (22483, 22800, 4)
The reciprocal cyclologic center of these triangles is X(22752).
X(22751) lies on the circumcircle and these lines: {3,12092}, {4,14103}, {5,22752}, {107,16868}, {110,1658}, {476,18403}
X(22751) = reflection of X(4) in X(14103)
X(22751) = circumperp conjugate of X(12092)
X(22751) = antipode of X(12092) in the circumcircle
The reciprocal cyclologic center of these triangles is X(22751).
X(22752) lies on these lines: {5,22751}, {30,12092}, {186,20957}, {265,5889}, {381,14103}, {10255,10745}
X(22753) lies on these lines: {1,227}, {2,3428}, {3,142}, {4,11}, {5,958}, {8,6915}, {10,6918}, {12,6834}, {20,5253}, {30,7956}, {35,11522}, {36,1012}, {40,392}, {46,12672}, {55,5603}, {57,6001}, {72,12704}, {84,3062}, {98,22520}, {113,22586}, {114,22514}, {115,22504}, {119,11236}, {125,22583}, {127,19159}, {132,19162}, {221,3075}, {235,22479}, {354,18446}, {355,10680}, {371,22763}, {372,22764}, {377,15908}, {381,535}, {388,6848}, {404,962}, {405,5715}, {411,3616}, {496,20420}, {499,6831}, {515,999}, {517,997}, {518,5720}, {546,18761}, {631,5584}, {758,2095}, {859,17188}, {940,1064}, {942,6261}, {944,3304}, {952,18491}, {956,5231}, {960,5709}, {993,3817}, {1006,4423}, {1158,9856}, {1191,3072}, {1193,5706}, {1329,6944}, {1385,5806}, {1389,14497}, {1410,1893}, {1420,16616}, {1466,4295}, {1470,1519}, {1478,1532}, {1479,22766}, {1482,2802}, {1490,3333}, {1512,5252}, {1537,10090}, {1587,19013}, {1588,19014}, {1598,22654}, {2077,16371}, {2098,11501}, {2099,11502}, {2260,5776}, {2346,5703}, {2478,11827}, {2551,6964}, {2717,2728}, {2886,6826}, {2932,14217}, {2975,3091}, {3035,6970}, {3058,10596}, {3073,4252}, {3085,6927}, {3295,4342}, {3303,10595}, {3336,12767}, {3337,15071}, {3339,7971}, {3436,6953}, {3486,5804}, {3555,17857}, {3556,16252}, {3560,9955}, {3574,22781}, {3576,7580}, {3600,12667}, {3614,10599}, {3651,8273}, {3656,4421}, {3678,5780}, {3683,21165}, {3742,18443}, {3816,6827}, {3820,8169}, {3871,5734}, {3925,6854}, {3927,20117}, {4190,11826}, {4298,6260}, {4301,10306}, {4413,5657}, {4999,6824}, {5056,5260}, {5080,6945}, {5085,16792}, {5204,6906}, {5217,6942}, {5251,7988}, {5258,7989}, {5298,7965}, {5427,21669}, {5432,6880}, {5433,6833}, {5434,12115}, {5435,14647}, {5438,6769}, {5443,15175}, {5450,18483}, {5478,22773}, {5479,22774}, {5480,22769}, {5536,5692}, {5550,6986}, {5563,5691}, {5687,7982}, {5708,5884}, {5719,20330}, {5721,11269}, {5732,10177}, {5812,21616}, {5844,8168}, {5882,6744}, {5901,10267}, {5903,13253}, {6201,22757}, {6202,22756}, {6244,16417}, {6245,18237}, {6247,22778}, {6248,22779}, {6249,22780}, {6250,22624}, {6251,22595}, {6253,12116}, {6256,18990}, {6284,6934}, {6361,6940}, {6667,6978}, {6684,16408}, {6690,6954}, {6691,6891}, {6705,21628}, {6832,7958}, {6835,10527}, {6839,11680}, {6844,10589}, {6847,7288}, {6864,19843}, {6883,8167}, {6909,9812}, {6912,9779}, {6922,10200}, {6924,11248}, {6938,15326}, {6941,10895}, {6966,21154}, {6969,10590}, {6979,11681}, {7171,15726}, {7420,10478}, {8071,12047}, {8158,9709}, {8196,11493}, {8203,11492}, {8212,22761}, {8213,22762}, {8666,19925}, {8668,13463}, {8727,15325}, {9624,10902}, {9708,10175}, {9880,22565}, {9927,22659}, {9940,12520}, {9993,22744}, {10113,19478}, {10247,18524}, {10393,16193}, {10597,10786}, {10860,21164}, {10943,18517}, {10950,18967}, {10958,18962}, {11897,22755}, {12001,18518}, {12599,22777}, {12600,22782}, {12705,15803}, {13687,22783}, {13743,16125}, {13807,22784}, {14110,19861}, {14793,18393}, {16203,18481}, {17572,20070}, {22680,22682}, {22771,22831}, {22772,22832}, {22776,22833}
X(22753) = midpoint of X(4) and X(4293)
X(22753) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3149, 11500), (3, 946, 11496), (3, 5886, 1001), (4, 56, 12114), (4, 7681, 10893), (5, 11249, 958), (36, 1699, 1012), (56, 10896, 22760), (355, 10680, 12513), (381, 22765, 22758), (5603, 6905, 55), (5805, 5886, 946), (6834, 10532, 12), (6918, 22770, 10), (22758, 22765, 11194)
X(22754) lies on these lines: {1,11505}, {2,1476}, {9,56}, {10,999}, {100,7320}, {119,1656}, {214,3295}, {442,3086}, {474,1145}, {1125,6260}, {1376,12640}, {3304,3698}, {3616,10427}, {3812,7373}, {5013,6184}, {5253,5435}, {5836,15347}, {6691,9708}, {10269,18237}, {11249,22777}, {11517,17614}, {12709,19861}, {16410,22767}
X(22755) lies on these lines: {3,11848}, {30,3428}, {36,11852}, {55,11910}, {56,402}, {104,11845}, {958,1650}, {999,11831}, {1376,16210}, {1651,11194}, {2975,4240}
X(22756) lies on these lines: {1,8903}, {3,3641}, {6,41}, {36,5589}, {55,5605}, {104,10783}, {956,5689}, {958,5591}, {999,11370}, {1161,11249}, {1271,2975}, {3428,11824}, {5595,22654}, {5861,11194}, {5871,10919}, {6202,22753}, {6215,22758}, {6227,22504}, {6258,18237}, {6263,12773}, {6267,22778}, {6270,22773}, {6271,22774}, {6273,22779}, {6275,22780}, {6277,22781}, {6279,22624}, {6281,22595}, {6319,22514}, {7725,22583}, {7732,22586}, {8198,11493}, {8205,11492}, {8216,22761}, {8217,22762}, {8974,22763}, {9882,22565}, {9929,22659}, {9994,22744}, {10040,22766}, {10048,22767}, {10792,22520}, {10923,22759}, {10925,22760}, {10927,10931}, {10929,22768}, {11388,22479}, {11901,22755}, {11916,22765}, {12513,12627}, {12697,22770}, {12753,22775}, {12801,22777}, {12803,19478}, {12805,19159}, {12807,22782}, {13269,22560}, {13282,19162}, {13690,22783}, {13743,16130}, {13810,22784}, {13949,22764}, {18509,18761}, {22680,22699}, {22771,22853}, {22772,22898}, {22776,22945}
X(22756) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 3641, 11497), (56, 22769, 22757)
X(22757) lies on these lines: {1,8904}, {3,3640}, {6,41}, {36,5588}, {55,5604}, {104,10784}, {956,5688}, {958,5590}, {999,11371}, {1160,11249}, {1270,2975}, {3428,11825}, {5594,22654}, {5860,11194}, {5870,10920}, {6201,22753}, {6214,22758}, {6226,22504}, {6257,18237}, {6262,12773}, {6266,22778}, {6268,22773}, {6269,22774}, {6272,22779}, {6274,22780}, {6276,22781}, {6278,22624}, {6280,22595}, {6320,22514}, {7726,22583}, {7733,22586}, {8199,11493}, {8206,11492}, {8218,22761}, {8219,22762}, {8975,22763}, {9883,22565}, {9930,22659}, {9995,22744}, {10041,22766}, {10049,22767}, {10793,22520}, {10924,22759}, {10926,22760}, {10928,10932}, {10930,22768}, {11389,22479}, {11902,22755}, {11917,22765}, {12513,12628}, {12698,22770}, {12754,22775}, {12802,22777}, {12804,19478}, {12806,19159}, {12808,22782}, {13270,22560}, {13283,19162}, {13691,22783}, {13743,16131}, {13811,22784}, {13950,22764}, {18511,18761}, {22680,22700}, {22771,22854}, {22772,22899}, {22776,22947}
X(22757) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 3640, 11498), (56, 22769, 22756)
X(22758) lies on these lines: {1,90}, {2,104}, {3,10}, {4,2975}, {5,56}, {8,6906}, {11,6929}, {12,6862}, {21,944}, {30,3428}, {35,5881}, {36,5587}, {40,5258}, {48,5778}, {55,952}, {63,517}, {80,11502}, {100,6950}, {110,19478}, {214,15064}, {226,999}, {265,22586}, {381,535}, {388,6824}, {404,5818}, {405,1385}, {474,9956}, {497,6930}, {498,10942}, {519,10679}, {527,3656}, {529,7680}, {550,5584}, {601,10459}, {631,5260}, {758,1482}, {946,8666}, {962,3648}, {1001,2801}, {1006,5731}, {1060,1455}, {1125,16203}, {1329,6958}, {1352,22769}, {1468,5707}, {1470,1737}, {1479,10943}, {1483,3303}, {1484,11238}, {1532,18516}, {1621,7967}, {1656,3822}, {1837,8071}, {2077,3679}, {2099,14988}, {2178,5816}, {2478,10785}, {2550,6948}, {2551,6891}, {2646,14872}, {2829,2886}, {3036,15813}, {3085,6892}, {3086,6893}, {3090,5253}, {3095,22779}, {3149,18480}, {3244,12000}, {3304,5901}, {3359,9623}, {3421,6935}, {3434,5840}, {3436,6833}, {3534,11495}, {3556,9833}, {3576,5251}, {3577,3928}, {3579,21165}, {3600,6846}, {3601,5534}, {3612,17857}, {3616,5811}, {3653,16857}, {3654,6244}, {3655,16418}, {3816,20418}, {3897,12528}, {3913,11849}, {4189,11491}, {4293,6826}, {4421,12331}, {4999,6863}, {5080,6830}, {5126,10157}, {5204,6924}, {5229,6867}, {5248,5882}, {5252,8069}, {5265,6964}, {5288,7982}, {5303,6942}, {5307,7497}, {5433,6959}, {5440,18908}, {5444,5660}, {5552,6977}, {5563,8227}, {5603,5905}, {5613,22774}, {5617,22773}, {5657,6909}, {5690,10310}, {5691,6985}, {5694,5730}, {5770,18391}, {5817,7677}, {5878,22778}, {6033,22504}, {6214,22757}, {6215,22756}, {6256,6842}, {6259,18237}, {6287,22780}, {6288,22781}, {6289,22624}, {6290,22595}, {6321,22514}, {6825,12667}, {6831,10526}, {6837,10532}, {6839,20067}, {6850,19843}, {6859,10590}, {6860,10599}, {6872,12116}, {6888,20060}, {6905,18491}, {6910,10786}, {6917,7354}, {6940,9780}, {6944,7288}, {6951,12248}, {6952,11681}, {6973,10589}, {6980,10742}, {7428,15623}, {7583,19014}, {7584,19013}, {7697,22680}, {7701,11014}, {7728,22583}, {8200,11493}, {8207,11492}, {8220,22761}, {8221,22762}, {8724,22565}, {8757,10571}, {8976,22763}, {9940,19520}, {9947,13624}, {9996,22744}, {10074,11729}, {10085,13369}, {10529,10531}, {10573,11509}, {10596,11240}, {10738,11235}, {10749,19162}, {10796,22520}, {10944,11508}, {10950,11507}, {10993,17784}, {11501,15446}, {12001,13464}, {12332,19914}, {12699,22770}, {12737,15558}, {12856,22777}, {12918,19159}, {12919,22782}, {13188,14663}, {13692,22783}, {13812,22784}, {13951,22764}, {16626,22772}, {16627,22771}, {22776,22955}
X(22758) = midpoint of X(i) and X(j) for these {i,j}: {3, 18519}, {3434, 6938}
X(22758) = reflection of X(i) in X(j) for these (i,j): (3, 993), (55, 6914)
X(22758) = complement of X(12115)
X(22758) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7330, 5887), (2, 104, 10269), (3, 355, 11499), (3, 5790, 1376), (3, 18518, 6796), (3, 18525, 11500), (4, 2975, 11249), (8, 6906, 11248), (10, 5450, 3), (21, 944, 10267), (958, 12114, 3), (5267, 6796, 3), (5790, 18515, 3), (11249, 18761, 4), (22759, 22760, 1)
X(22759) lies on these lines: {1,90}, {2,12}, {3,5252}, {4,10957}, {5,22767}, {8,11509}, {10,1470}, {11,6893}, {21,3476}, {36,9578}, {55,944}, {57,5258}, {65,956}, {104,3085}, {226,8666}, {355,8071}, {405,1319}, {495,22766}, {497,10949}, {498,10269}, {603,10459}, {952,11507}, {993,10106}, {999,11375}, {1001,1388}, {1012,3057}, {1191,7299}, {1317,3303}, {1399,5710}, {1408,19259}, {1420,3646}, {1476,5047}, {1478,6842}, {1479,18761}, {1836,22770}, {2098,11496}, {2099,3868}, {2217,8192}, {2886,18961}, {3086,6898}, {3256,3632}, {3304,3487}, {3340,5288}, {3428,6850}, {3435,10834}, {3485,18967}, {3601,9845}, {3614,6981}, {3624,5193}, {3913,14882}, {4293,6897}, {5204,6940}, {5219,5563}, {5432,6961}, {5584,15326}, {6892,15888}, {6911,10827}, {6913,11376}, {6914,11508}, {6937,9657}, {6941,10895}, {8668,12648}, {9613,11012}, {9654,22765}, {10088,19478}, {10572,18519}, {10680,12047}, {10797,22520}, {10831,22654}, {10873,22744}, {10896,13729}, {10923,22756}, {10924,22757}, {11011,12559}, {11248,12647}, {11392,22479}, {11492,11870}, {11493,11869}, {11499,14793}, {11905,22755}, {11930,22761}, {11931,22762}, {12184,22504}, {12350,22565}, {12373,22583}, {12678,18237}, {12739,12773}, {12763,22775}, {12837,22779}, {12859,22777}, {12903,22586}, {12940,22778}, {12941,22774}, {12942,22773}, {12944,22780}, {12945,19159}, {12946,22781}, {12947,22782}, {12948,22595}, {12949,22624}, {13182,22514}, {13273,22560}, {13296,19162}, {13695,22783}, {13743,16140}, {13815,22784}, {13897,22763}, {13954,22764}, {18838,19860}, {19013,19027}, {19014,19028}, {22680,22705}, {22771,22859}, {22772,22904}, {22776,22958}
X(22759) = anticomplement of X(15843)
X(22759) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22758, 22760), (3, 5252, 11501), (21, 3476, 11510), (104, 3085, 22768), (355, 8071, 11502), (388, 2975, 56)
X(22760) lies on these lines: {1,90}, {2,10958}, {3,1737}, {4,11}, {5,22766}, {8,21}, {12,6824}, {25,2217}, {28,1857}, {35,5727}, {36,6985}, {65,1012}, {80,11499}, {119,10320}, {145,10965}, {355,8069}, {388,6837}, {405,997}, {411,5204}, {474,17606}, {495,16617}, {496,22767}, {497,2975}, {499,6842}, {517,920}, {855,3556}, {944,11510}, {950,993}, {952,11508}, {956,3057}, {960,7082}, {999,10404}, {1001,10394}, {1006,4305}, {1210,1470}, {1319,1898}, {1376,5086}, {1388,21740}, {1420,10864}, {1454,7686}, {1468,2654}, {1478,6841}, {1479,7491}, {1482,12758}, {1603,20989}, {1610,15494}, {1697,5258}, {1776,2098}, {1788,6909}, {2099,11496}, {3058,11111}, {3085,10955}, {3304,3485}, {3428,6284}, {3586,11012}, {3601,5251}, {3612,6883}, {3614,6855}, {3813,10947}, {3924,7004}, {4252,5348}, {4295,21669}, {5172,11500}, {5217,6875}, {5218,5260}, {5229,6870}, {5253,6871}, {5259,13384}, {5288,7962}, {5432,6857}, {5433,6825}, {5584,15338}, {5603,18967}, {5722,8071}, {6796,17010}, {6828,10895}, {6838,7288}, {6867,7173}, {6869,15326}, {6906,11509}, {6911,10826}, {6913,11375}, {6914,11507}, {6924,12019}, {7680,18962}, {7742,18481}, {8581,20323}, {8666,12053}, {8758,21147}, {9657,10883}, {9669,22765}, {10058,10573}, {10091,19478}, {10106,12617}, {10395,17647}, {10448,14547}, {10798,22520}, {10832,22654}, {10874,22744}, {10925,22756}, {10926,22757}, {11114,11194}, {11393,22479}, {11492,11872}, {11493,11871}, {11906,22755}, {11932,22761}, {11933,22762}, {12185,22504}, {12351,22565}, {12374,22583}, {12589,22769}, {12665,12739}, {12679,18237}, {12701,22770}, {12740,12773}, {12836,22779}, {12860,22777}, {12904,22586}, {12950,22778}, {12951,22774}, {12952,22773}, {12954,22780}, {12955,19159}, {12956,22781}, {12957,22782}, {12958,22595}, {12959,22624}, {13183,22514}, {13274,22560}, {13297,19162}, {13696,22783}, {13743,16141}, {13816,22784}, {13898,22763}, {13955,22764}, {14793,15446}, {14800,15079}, {17603,19520}, {18254,22836}, {19013,19029}, {19014,19030}, {22680,22706}, {22771,22860}, {22772,22905}
X(22760) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 90, 5887), (1, 22758, 22759), (3, 1837, 11502), (21, 3486, 55), (56, 10896, 22753), (104, 3086, 56), (355, 8069, 11501), (497, 2975, 10966), (1210, 5450, 1470), (1319, 1898, 6261), (6906, 18391, 11509), (10058, 10573, 11248)
X(22761) lies on these lines: {3,11503}, {36,8188}, {55,8210}, {56,493}, {104,11846}, {956,8214}, {958,8222}, {999,11377}, {2975,6462}, {3428,11828}, {6461,22762}, {8194,22654}, {8201,11493}, {8208,11492}, {8212,22753}, {8216,22756}, {8218,22757}, {8220,22758}, {9838,10945}, {10669,11249}, {10875,22744}, {10966,11947}, {11194,12152}, {11394,22479}, {11840,22520}, {11907,22755}, {11930,22759}, {11932,22760}, {11949,22765}, {11951,22766}, {11953,22767}, {11955,22768}, {12186,22504}, {12352,22565}, {12377,22583}, {12426,22659}, {12513,12636}, {12590,22769}, {12741,12773}, {12765,22775}, {12861,22777}, {12894,19478}, {12986,22778}, {12988,22774}, {12990,22773}, {12992,22779}, {12994,22780}, {12996,19159}, {12998,22781}, {13000,22782}, {13002,22595}, {13004,22624}, {13184,22514}, {13215,22586}, {13275,22560}, {13298,19162}, {13697,22783}, {13743,16161}, {13817,22784}, {13899,22763}, {13956,22764}, {18237,18245}, {18520,18761}, {19013,19031}, {19014,19032}, {22680,22709}, {22770,22841}, {22771,22863}, {22772,22908}, {22776,22963}
X(22761) = {X(3), X(12440)}-harmonic conjugate of X(11503)
X(22762) lies on these lines: {3,11504}, {36,8189}, {55,8211}, {56,494}, {104,11847}, {956,8215}, {958,8223}, {999,11378}, {2975,6463}, {3428,11829}, {6461,22761}, {8195,22654}, {8202,11493}, {8209,11492}, {8213,22753}, {8217,22756}, {8219,22757}, {8221,22758}, {9839,10946}, {10673,11249}, {10876,22744}, {10966,11948}, {11194,12153}, {11395,22479}, {11841,22520}, {11908,22755}, {11931,22759}, {11933,22760}, {11950,22765}, {11952,22766}, {11954,22767}, {11956,22768}, {12187,22504}, {12353,22565}, {12378,22583}, {12427,22659}, {12513,12637}, {12591,22769}, {12742,12773}, {12766,22775}, {12862,22777}, {12895,19478}, {12987,22778}, {12989,22774}, {12991,22773}, {12993,22779}, {12995,22780}, {12997,19159}, {12999,22781}, {13001,22782}, {13003,22595}, {13005,22624}, {13185,22514}, {13216,22586}, {13276,22560}, {13299,19162}, {13698,22783}, {13743,16162}, {13818,22784}, {13900,22763}, {13957,22764}, {18237,18246}, {18522,18761}, {19013,19033}, {19014,19034}, {22680,22710}, {22770,22842}, {22771,22864}, {22772,22909}, {22776,22964}
X(22762) = {X(3), X(12441)}-harmonic conjugate of X(11504)
X(22763) lies on these lines: {2,19014}, {3,8983}, {6,978}, {36,13888}, {55,13902}, {56,3068}, {104,13886}, {371,22753}, {404,19000}, {474,18991}, {485,12114}, {590,958}, {956,13893}, {999,13883}, {1125,13940}, {1376,7969}, {2975,8972}, {3149,9583}, {3304,19066}, {3428,9540}, {3616,18999}, {4413,19065}, {5253,7585}, {6409,11495}, {7580,9615}, {7583,10269}, {8974,22756}, {8975,22757}, {8976,22758}, {8980,22504}, {8981,11249}, {8987,18237}, {8988,12773}, {8991,22778}, {8992,22779}, {8993,22780}, {8995,22781}, {8997,22514}, {8998,22586}, {10966,13901}, {11194,13846}, {11492,13891}, {11493,13890}, {12513,13911}, {13743,16148}, {13848,22784}, {13884,22479}, {13885,22520}, {13889,22654}, {13894,22755}, {13897,22759}, {13898,22760}, {13899,22761}, {13900,22762}, {13903,22765}, {13904,22766}, {13905,22767}, {13906,19030}, {13908,22565}, {13909,22659}, {13910,22769}, {13912,22770}, {13913,22775}, {13914,22777}, {13916,22774}, {13917,22773}, {13918,19159}, {13919,22782}, {13921,22595}, {13922,22560}, {13923,19162}, {13936,16408}, {13947,16862}, {18538,18761}, {22680,22720}, {22771,22876}, {22772,22921}, {22776,22976}
X(22763) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 8983, 13887), (5253, 7585, 19013)
X(22764) lies on these lines: {2,19013}, {3,13940}, {6,978}, {36,13942}, {55,13959}, {56,3069}, {104,13939}, {372,22753}, {404,18999}, {474,18992}, {486,12114}, {615,958}, {956,13947}, {999,13936}, {1125,13887}, {1376,7968}, {2975,13941}, {3304,19065}, {3428,13935}, {3616,19000}, {4413,19066}, {5253,7586}, {6410,11495}, {7584,10269}, {10966,13958}, {11194,13847}, {11249,13966}, {11492,13945}, {11493,13944}, {12513,13973}, {12773,13976}, {13743,16149}, {13849,22784}, {13880,22624}, {13883,16408}, {13893,16862}, {13933,22595}, {13937,22479}, {13938,22520}, {13943,22654}, {13946,22744}, {13948,22755}, {13949,22756}, {13950,22757}, {13951,22758}, {13954,22759}, {13955,22760}, {13956,22761}, {13957,22762}, {13961,22765}, {13962,22766}, {13963,22767}, {13964,19029}, {13967,22504}, {13968,22565}, {13969,22583}, {13970,22659}, {13972,22769}, {13974,18237}, {13975,22770}, {13977,22775}, {13978,22777}, {13979,19478}, {13980,22778}, {13981,22774}, {13982,22773}, {13983,22779}, {13984,22780}, {13985,19159}, {13986,22781}, {13987,22782}, {13988,22783}, {13989,22514}, {13990,22586}, {13991,22560}, {13992,19162}, {18761,18762}, {22680,22721}, {22771,22877}, {22772,22922}, {22776,22977}
X(22764) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 13971, 13940), (5253, 7586, 19014)
X(22765) lies on the cubic K725 and these lines: {1,3}, {4,20067}, {5,2975}, {8,6924}, {21,5901}, {30,104}, {74,6584}, {100,5844}, {110,859}, {119,529}, {140,5253}, {145,6942}, {195,22781}, {355,8666}, {381,535}, {382,11928}, {388,6863}, {399,22586}, {404,5690}, {496,7491}, {499,6971}, {515,12747}, {519,12331}, {573,21773}, {758,6265}, {946,12600}, {952,6905}, {956,5176}, {958,1656}, {993,5886}, {995,5398}, {1012,18515}, {1056,6954}, {1351,9037}, {1478,6980}, {1483,11491}, {1532,10742}, {1598,1878}, {1621,7508}, {1727,17638}, {1951,22144}, {2687,5606}, {2718,6011}, {2800,4973}, {3086,6928}, {3149,18525}, {3218,14988}, {3421,6970}, {3436,6959}, {3526,6681}, {3556,14530}, {3560,5057}, {3600,6825}, {3622,6875}, {3628,5260}, {3843,18761}, {3877,19525}, {4188,12245}, {4189,10595}, {4293,6923}, {4297,16117}, {4299,10525}, {4996,19907}, {5054,10197}, {5123,9708}, {5146,7497}, {5180,5603}, {5251,11230}, {5258,9956}, {5265,6891}, {5267,13464}, {5298,6713}, {5450,12699}, {5694,6763}, {5762,7677}, {5780,17615}, {5840,15326}, {5887,13465}, {6417,19014}, {6418,19013}, {6597,12919}, {6834,20076}, {6842,18990}, {6862,10532}, {6868,14986}, {6882,15325}, {6906,22791}, {6910,10597}, {6915,18357}, {6917,10527}, {6934,10529}, {6936,10586}, {6949,20060}, {6958,7288}, {6962,10805}, {7517,22654}, {9301,22744}, {9654,22759}, {9669,22760}, {10090,19914}, {10620,22583}, {11495,15688}, {11499,12513}, {11500,18526}, {11842,22520}, {11911,22755}, {11916,22756}, {11917,22757}, {11949,22761}, {11950,22762}, {12188,22504}, {12355,22565}, {12429,22659}, {12601,22595}, {12602,22624}, {12684,18237}, {12872,22777}, {12902,19478}, {13093,22778}, {13102,22774}, {13103,22773}, {13108,22779}, {13111,22780}, {13115,19159}, {13126,22782}, {13188,22514}, {13310,19162}, {13713,22783}, {13836,22784}, {13903,22763}, {13961,22764}, {14217,15228}, {15611,17734}, {16628,22771}, {16629,22772}, {17455,19297}, {18519,19541}, {22680,22728}, {22776,22979}
X(22765) = midpoint of X(i) and X(j) for these {i,j}: {1, 5535}, {4, 20067}, {14217, 15228}
X(22765) = reflection of X(6882) in X(15325)
X(22765) = circumperp conjugate of X(3579)
X(22765) = inverse of X(1385) in the circumcircle
X(22765) = inverse of X(13750) in the incircle
X(22765) = inverse of X(1482) in the Stammler circle
X(22765) = isogonal conjugate of antigonal conjugate of X(1389)
X(22765) = X(2070)-of-2nd-circumperp-triangle
X(22765) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,3,37621), (1, 36, 5172), (1, 7280, 14795), (3, 1482, 11849), (3, 8148, 11248), (3, 10247, 55), (3, 10680, 1482), (3, 12001, 3295), (36, 5193, 5126), (40, 5131, 10225), (56, 22767, 999), (1381, 1382, 1385), (1385, 6583, 1), (2095, 10246, 1482), (2446, 2447, 13750), (5204, 11248, 3), (11009, 14792, 14882)
X(22766) lies on these lines: {1,3}, {5,22760}, {11,6917}, {12,6862}, {47,4252}, {104,388}, {149,4190}, {226,5450}, {377,3086}, {404,18391}, {411,4305}, {442,499}, {474,1737}, {495,22759}, {497,6934}, {498,958}, {601,1457}, {611,5135}, {613,4259}, {920,960}, {939,2163}, {952,11501}, {956,10039}, {993,12527}, {1004,11019}, {1012,12047}, {1056,6977}, {1201,1497}, {1210,17647}, {1259,18389}, {1376,10573}, {1436,1781}, {1478,6831}, {1479,22753}, {1537,10044}, {1709,18237}, {1785,4185}, {1788,6940}, {1804,3664}, {1837,6911}, {2164,17443}, {2178,2278}, {2975,3085}, {3149,10572}, {3299,19013}, {3301,19014}, {3485,6906}, {3486,6905}, {3556,7428}, {3560,11375}, {3582,17528}, {3600,6890}, {4293,6836}, {4295,6909}, {4413,18395}, {5248,17010}, {5730,19525}, {5784,15299}, {5880,10094}, {6860,10590}, {6889,7288}, {6918,10826}, {6924,11502}, {6959,10958}, {6984,10589}, {7177,14878}, {8068,10742}, {8581,15518}, {10037,22654}, {10038,22744}, {10040,22756}, {10041,22757}, {10053,22504}, {10054,22565}, {10055,22659}, {10056,11194}, {10057,12773}, {10059,22777}, {10060,22778}, {10061,22774}, {10062,22773}, {10063,22779}, {10064,22780}, {10065,22583}, {10066,22781}, {10067,22595}, {10072,10948}, {10085,12664}, {10086,22514}, {10087,22560}, {10088,22586}, {10090,10609}, {10106,12616}, {10801,22520}, {10950,11499}, {11398,20832}, {11912,22755}, {11951,22761}, {11952,22762}, {12513,12647}, {12903,19478}, {13116,19159}, {13128,22782}, {13311,19162}, {13714,22783}, {13743,16152}, {13837,22784}, {13904,22763}, {13962,22764}, {22680,22729}, {22771,22884}, {22772,22929}, {22776,22980}
X(22766) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 36, 8071), (1, 56, 22767), (1, 3338, 5570), (3, 999, 65), (36, 3612, 3), (36, 5563, 3361), (46, 14803, 3), (55, 56, 11249), (55, 18967, 1482), (56, 10966, 22765), (56, 22768, 3), (999, 1482, 18967), (999, 3295, 12001), (3295, 12001, 5048), (3295, 22765, 10966), (5563, 14803, 46)
X(22767) lies on these lines: {1,3}, {5,22759}, {11,6929}, {12,6959}, {47,1191}, {104,497}, {255,1201}, {378,15500}, {388,6834}, {411,1476}, {474,10039}, {496,22760}, {498,13747}, {499,958}, {613,22769}, {952,11502}, {956,1737}, {997,20588}, {1056,6880}, {1145,1376}, {1210,8666}, {1387,6914}, {1473,1795}, {1478,1532}, {1479,10948}, {1603,15617}, {1745,9363}, {1804,3663}, {2178,4271}, {2478,2975}, {2829,15845}, {3074,21214}, {3085,5253}, {3299,19014}, {3301,19013}, {3434,13279}, {3476,6905}, {3554,15817}, {3560,11376}, {3600,6838}, {3825,15866}, {4186,11399}, {4293,6925}, {4421,10087}, {5252,6911}, {5433,10320}, {5450,12053}, {5533,11238}, {5687,10094}, {5790,10057}, {5840,10947}, {5854,15813}, {6872,14986}, {6917,10957}, {6918,10827}, {6924,11501}, {6967,7288}, {7580,21578}, {8070,10895}, {10046,22654}, {10047,22744}, {10048,22756}, {10049,22757}, {10051,10074}, {10069,22504}, {10070,22565}, {10071,22659}, {10072,11113}, {10073,12773}, {10075,22777}, {10076,22778}, {10077,22774}, {10079,22779}, {10080,22780}, {10081,22583}, {10082,22781}, {10083,22595}, {10084,22624}, {10085,18237}, {10089,22514}, {10091,22586}, {10573,12513}, {10802,22520}, {10896,18761}, {10944,11499}, {11913,22755}, {11953,22761}, {11954,22762}, {12904,19478}, {13117,19159}, {13129,22782}, {13312,19162}, {13715,22783}, {13743,16153}, {13838,22784}, {13905,22763}, {13963,22764}, {16410,22754}, {22680,22730}, {22771,22885}, {22772,22930}, {22776,22981}
X(22767) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3, 11508), (1, 36, 8069), (1, 56, 22766), (1, 3338, 13750), (1, 8071, 11507), (1, 14793, 55), (1, 17437, 65), (3, 999, 1319), (36, 5119, 3), (36, 5563, 13462), (55, 56, 10269), (56, 3428, 36), (56, 10966, 3), (999, 15934, 3304), (999, 22765, 56), (1420, 11012, 7742)
X(22768) lies on these lines: {1,3}, {2,10958}, {11,377}, {12,6833}, {104,3085}, {119,6862}, {198,2278}, {224,10391}, {388,6890}, {404,3486}, {442,10200}, {474,1837}, {497,4190}, {498,10942}, {939,19349}, {944,11501}, {956,10915}, {958,5432}, {993,21075}, {997,1858}, {1012,11375}, {1058,13199}, {1376,5554}, {1468,22072}, {1696,2182}, {2057,3711}, {2178,2268}, {2252,2256}, {2330,12594}, {2361,4252}, {2975,5218}, {3086,6897}, {3434,10959}, {3485,6909}, {3614,6860}, {4293,6899}, {4294,10596}, {4305,6905}, {4413,5794}, {4861,8668}, {4995,11194}, {5252,12616}, {5433,6889}, {5450,13411}, {6256,6831}, {6284,6934}, {6836,7354}, {6911,10572}, {6917,10896}, {6940,18391}, {6955,10947}, {6966,15888}, {6984,7173}, {7951,18542}, {9310,22088}, {10058,11729}, {10785,10957}, {10803,22520}, {10827,18519}, {10834,22654}, {10878,22744}, {10929,22756}, {10930,22757}, {11112,11238}, {11376,12609}, {11400,22479}, {11496,15950}, {11914,22755}, {11955,22761}, {11956,22762}, {12189,22504}, {12356,22565}, {12381,22583}, {12430,22659}, {12513,12648}, {12686,18237}, {12711,17614}, {12739,15528}, {12749,12773}, {12775,22775}, {12874,22777}, {12905,19478}, {13094,22778}, {13104,22774}, {13105,22773}, {13109,22779}, {13112,22780}, {13118,19159}, {13121,22781}, {13130,22782}, {13132,22595}, {13189,15452}, {13217,22586}, {13278,22560}, {13313,19162}, {13716,22783}, {13743,16154}, {13839,22784}, {13906,19030}, {13964,19029}, {16408,17606}, {17611,20849}, {19013,19038}, {19014,19037}, {22680,22731}, {22771,22886}, {22772,22931}, {22776,22982}
X(22768) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3, 11509), (1, 35, 10679), (1, 55, 10965), (1, 10269, 56), (1, 14803, 3), (3, 999, 46), (3, 2646, 55), (3, 22766, 56), (55, 56, 10966), (55, 3304, 2098), (56, 5217, 3428), (104, 3085, 22759), (404, 3486, 11502), (1385, 8069, 11510), (3085, 10805, 10956)
The reciprocal orthologic center of these triangles is X(3).
X(22769) lies on these lines: {1,159}, {3,518}, {6,41}, {19,4327}, {22,3873}, {25,354}, {36,3751}, {38,55}, {57,197}, {65,8192}, {69,2975}, {104,5848}, {141,958}, {182,2810}, {210,7484}, {222,20986}, {375,17825}, {390,1633}, {511,11249}, {524,11194}, {542,19478}, {610,4321}, {611,5135}, {613,22767}, {674,1350}, {732,22779}, {942,9798}, {956,3416}, {984,16560}, {991,2876}, {993,9028}, {999,1386}, {1001,4364}, {1253,20780}, {1279,7083}, {1351,9037}, {1352,22758}, {1466,2933}, {1480,2841}, {1503,12114}, {1593,12680}, {1598,13374}, {1610,3600}, {1617,3185}, {1843,22479}, {2182,8581}, {2330,12594}, {2385,3663}, {2646,19459}, {2781,19162}, {2836,10246}, {2854,22586}, {3056,10966}, {3094,22744}, {3098,9052}, {3296,17562}, {3475,4224}, {3555,8193}, {3564,22595}, {3576,9004}, {3618,5253}, {3619,5260}, {3681,7485}, {3740,16419}, {3742,5020}, {3818,18761}, {3844,9708}, {3870,7293}, {3913,9053}, {3916,15592}, {4185,10404}, {4293,5800}, {4421,9041}, {4430,6636}, {4661,15246}, {4860,20989}, {5045,11365}, {5085,9026}, {5096,5204}, {5138,15654}, {5480,22753}, {5563,16475}, {5584,9049}, {5846,12513}, {5847,8666}, {5965,22771}, {5969,22514}, {6642,13373}, {7395,14872}, {8185,18398}, {9021,12635}, {9024,22560}, {9830,22565}, {10391,16541}, {10829,17625}, {10833,18839}, {11492,12453}, {11493,12452}, {12212,22520}, {12583,22755}, {12588,22759}, {12589,22760}, {12590,22761}, {12591,22762}, {13910,22763}, {13972,22764}, {18613,37519}, {22504,22680}, {22783,22784}
X(22769) = midpoint of X(1) and X(7289)
X(22769) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3220, 1486), (56, 198, 20470), (3242, 4265, 55), (22756, 22757, 56)
The reciprocal orthologic center of these triangles is X(4).
X(22770) lies on these lines: {1,3}, {4,956}, {5,2551}, {8,3149}, {10,6918}, {63,12672}, {104,6361}, {106,15663}, {145,411}, {210,5780}, {219,945}, {347,7053}, {355,4847}, {381,10526}, {387,19543}, {388,6907}, {405,5603}, {442,10532}, {474,5657}, {495,6825}, {496,6827}, {515,12513}, {516,8666}, {518,6261}, {519,11500}, {529,6256}, {573,2256}, {580,1191}, {944,7580}, {946,958}, {952,6985}, {962,1012}, {993,4301}, {1001,13464}, {1006,10595}, {1044,9363}, {1056,6908}, {1058,6987}, {1108,1766}, {1259,11682}, {1260,5730}, {1376,11362}, {1457,7078}, {1478,15908}, {1479,11827}, {1498,2818}, {1532,3436}, {1537,11415}, {1597,1872}, {1621,5734}, {1630,20818}, {1656,19854}, {1657,5840}, {1699,5258}, {1702,19014}, {1703,19013}, {1836,22759}, {1902,22479}, {2800,12330}, {2802,22775}, {2817,9798}, {3086,6922}, {3421,6848}, {3427,5770}, {3555,18446}, {3560,5698}, {3600,6916}, {3617,6915}, {3622,6986}, {3651,7967}, {3654,16417}, {3656,16418}, {3820,6944}, {3889,18444}, {3897,20835}, {3913,6796}, {3927,5887}, {4299,11826}, {4423,9624}, {4679,18493}, {5220,20117}, {5251,11522}, {5288,5691}, {5450,11194}, {5687,6905}, {5690,6911}, {5721,19648}, {5763,5901}, {5795,7682}, {5886,11108}, {6001,22778}, {6600,22836}, {6601,6869}, {6737,11499}, {6831,10527}, {6834,17757}, {6836,10529}, {6842,9654}, {6850,18990}, {6865,14986}, {6868,15171}, {6889,10597}, {6891,15325}, {6893,7956}, {6909,20070}, {6923,9655}, {6925,20076}, {6927,7080}, {6928,9669}, {6932,20060}, {6936,10596}, {6962,10528}, {6980,11929}, {7330,9856}, {7491,9668}, {9911,22654}, {10531,11113}, {10599,17530}, {10609,12776}, {11230,16853}, {11231,16863}, {12197,22520}, {12331,13996}, {12497,22744}, {12520,12675}, {12645,18518}, {12670,12842}, {12671,12687}, {12696,22755}, {12697,22756}, {12698,22757}, {12699,22758}, {12701,22760}, {13329,15287}, {13912,22763}, {13975,22764}, {16293,19860}, {16410,19861}, {18761,22793}, {22761,22841}, {22762,22842}
X(22770) = reflection of X(i) in X(j) for these (i,j): (382, 10525), (3913, 6796), (5763, 5901)
X(22770) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 1482, 3295), (3, 8148, 10679), (3, 10247, 16202), (3, 10680, 999), (3, 12001, 10246), (36, 7991, 10310), (36, 10310, 3), (40, 56, 3), (65, 12704, 2095), (2077, 5204, 3), (3304, 5584, 3576), (7982, 11011, 1482), (7982, 11012, 55), (10902, 16200, 3303), (11012, 16204, 10267), (12702, 22765, 3)
The reciprocal orthologic center of these triangles is X(3).
X(22771) lies on these lines: {3,22557}, {18,56}, {36,22651}, {55,22867}, {104,22531}, {628,2975}, {630,958}, {956,22851}, {999,11740}, {3428,22843}, {5965,22769}, {10966,22865}, {11249,22774}, {11492,22673}, {11493,22669}, {12114,22857}, {16627,22758}, {16628,22765}, {18761,22794}, {19013,19069}, {19014,19072}, {22479,22481}, {22520,22522}, {22654,22656}, {22744,22745}, {22753,22831}, {22755,22852}, {22756,22853}, {22757,22854}, {22759,22859}, {22760,22860}, {22761,22863}, {22762,22864}, {22763,22876}, {22764,22877}, {22766,22884}, {22767,22885}, {22768,22886}
The reciprocal orthologic center of these triangles is X(3).
X(22772) lies on these lines: {3,22558}, {17,56}, {36,22652}, {55,22912}, {104,22532}, {532,11194}, {627,2975}, {629,958}, {956,22896}, {999,11739}, {3428,22890}, {5965,22769}, {10966,22910}, {11249,22773}, {11492,22674}, {11493,22670}, {12114,22902}, {16626,22758}, {16629,22765}, {18761,22795}, {19013,19071}, {19014,19070}, {22479,22482}, {22520,22523}, {22654,22657}, {22744,22746}, {22753,22832}, {22755,22897}, {22756,22898}, {22757,22899}, {22759,22904}, {22760,22905}, {22761,22908}, {22762,22909}, {22763,22921}, {22764,22922}, {22766,22929}, {22767,22930}, {22768,22931}
The reciprocal orthologic center of these triangles is X(13).
X(22773) lies on these lines: {3,12337}, {13,56}, {36,9901}, {55,7975}, {104,6770}, {542,19478}, {616,2975}, {618,958}, {956,12781}, {999,11705}, {3428,5473}, {5478,22753}, {5617,22758}, {6268,22757}, {6270,22756}, {6771,10269}, {9916,22654}, {9982,22744}, {10062,22766}, {10078,22767}, {10966,13076}, {11249,22772}, {11492,12473}, {11493,12472}, {12114,12922}, {12142,22479}, {12205,22520}, {12793,22755}, {12942,22759}, {12952,22760}, {12990,22761}, {12991,22762}, {13103,22765}, {13105,22768}, {13917,22763}, {13982,22764}, {19013,19073}, {19014,19074}
The reciprocal orthologic center of these triangles is X(14).
X(22774) lies on these lines: {3,12336}, {14,56}, {36,9900}, {55,7974}, {542,19478}, {617,2975}, {619,958}, {956,12780}, {999,11706}, {3428,5474}, {5479,22753}, {5613,22758}, {6269,22757}, {6271,22756}, {6774,10269}, {9915,22654}, {9981,22744}, {10061,22766}, {10077,22767}, {10966,13075}, {11249,22771}, {11492,12471}, {11493,12470}, {12114,12921}, {12141,22479}, {12204,22520}, {12792,22755}, {12941,22759}, {12951,22760}, {12988,22761}, {12989,22762}, {13102,22765}, {13104,22768}, {13916,22763}, {13981,22764}, {18761,22797}, {19013,19075}, {19014,19076}
The reciprocal orthologic center of these triangles is X(40).
X(22775) lies on these lines: {3,214}, {4,11}, {35,13253}, {36,1727}, {40,2932}, {46,17654}, {55,10698}, {72,2949}, {80,3149}, {84,3065}, {100,3428}, {119,958}, {153,2975}, {392,2950}, {411,6224}, {515,12747}, {517,13205}, {952,11249}, {956,12751}, {993,21635}, {999,11715}, {1001,6914}, {1012,18393}, {1317,10966}, {1537,10044}, {2771,6261}, {2783,22514}, {2787,22504}, {2802,22770}, {2806,19159}, {2831,19162}, {3035,6954}, {3560,12611}, {5180,6909}, {5204,18861}, {5251,15017}, {5253,6888}, {5450,5886}, {6667,6859}, {6702,6918}, {6713,6862}, {6892,22667}, {6905,12247}, {6906,15950}, {6910,21154}, {6911,12619}, {6980,10742}, {7280,7971}, {7580,12119}, {8068,10894}, {8069,12758}, {8071,11570}, {8674,22583}, {9913,22654}, {10051,10074}, {10267,19907}, {10310,17100}, {10680,12737}, {11492,12463}, {11493,12462}, {11499,19914}, {11571,14793}, {12138,22479}, {12199,22520}, {12499,22744}, {12608,16128}, {12752,22755}, {12753,22756}, {12754,22757}, {12763,22759}, {12765,22761}, {12766,22762}, {12775,22768}, {13370,18238}, {13913,22763}, {13977,22764}, {17660,18446}, {18761,22799}, {19013,19081}, {19014,19082}
X(22775) = reflection of X(153) in X(18242)
X(22775) = circumperp conjugate of X(14690)
X(22775) = inverse of X(11713) in the circumcircle
X(22775) = {X(1537), X(10058)}-harmonic conjugate of X(11496)
The reciprocal orthologic center of these triangles is X(12241).
X(22776) lies on these lines: {3,22559}, {36,22653}, {55,22969}, {56,18978}, {104,22533}, {956,22941}, {958,22957}, {999,22476}, {2929,20838}, {2975,22647}, {3428,22951}, {10966,22965}, {12114,22956}, {18761,22800}, {19013,19083}, {19014,19084}, {22479,22483}, {22520,22524}, {22654,22658}, {22744,22747}, {22753,22833}, {22755,22943}, {22756,22945}, {22757,22947}, {22758,22955}, {22759,22958}, {22760,22959}, {22761,22963}, {22762,22964}, {22763,22976}, {22764,22977}, {22765,22979}, {22766,22980}, {22767,22981}, {22768,22982}
The reciprocal orthologic center of these triangles is X(40).
X(22777) lies on these lines: {3,12333}, {36,9898}, {55,8000}, {56,7160}, {104,12249}, {376,15998}, {956,12777}, {958,12858}, {999,12260}, {1001,13464}, {1490,3428}, {2975,9874}, {5584,12842}, {5920,17624}, {10059,22766}, {10075,22767}, {10966,12863}, {10993,12773}, {11249,22754}, {11492,12465}, {11493,12464}, {12114,12857}, {12139,22479}, {12200,22520}, {12411,22654}, {12436,22667}, {12500,22744}, {12599,22753}, {12789,22755}, {12801,22756}, {12802,22757}, {12856,22758}, {12859,22759}, {12860,22760}, {12861,22761}, {12862,22762}, {12872,22765}, {12874,22768}, {13914,22763}, {13978,22764}, {18761,22801}, {19013,19085}, {19014,19086}
The reciprocal orthologic center of these triangles is X(4).
X(22778) lies on these lines: {1,7169}, {3,12335}, {30,22659}, {36,9899}, {55,7973}, {56,64}, {104,12250}, {154,5584}, {197,9121}, {221,1496}, {956,12779}, {958,2883}, {999,12262}, {1498,3428}, {2777,19478}, {2975,6225}, {3357,10269}, {5878,22758}, {6000,11249}, {6001,22770}, {6247,22753}, {6266,22757}, {6267,22756}, {7355,10966}, {8991,22763}, {9914,22654}, {10060,22766}, {10076,22767}, {11381,22479}, {11492,12469}, {11493,12468}, {12114,12920}, {12202,22520}, {12502,22744}, {12791,22755}, {12940,22759}, {12950,22760}, {12986,22761}, {12987,22762}, {13093,22765}, {13094,22768}, {13980,22764}, {18761,22802}, {19013,19087}, {19014,19088}
X(22778) = {X(1498), X(3428)}-harmonic conjugate of X(3556)
The reciprocal orthologic center of these triangles is X(3).
X(22779) lies on these lines: {36,9902}, {39,958}, {55,7976}, {56,76}, {58,10800}, {104,12251}, {194,2975}, {384,22520}, {511,12114}, {538,11194}, {726,8666}, {732,22769}, {956,12782}, {999,12263}, {1001,5145}, {2782,11249}, {3095,22758}, {3097,5258}, {3428,11257}, {5969,22565}, {6248,22753}, {6272,22757}, {6273,22756}, {8301,15654}, {8992,22763}, {9917,22654}, {9983,22744}, {10063,22766}, {10079,22767}, {10966,13077}, {11492,12475}, {11493,12474}, {12143,22479}, {12513,14839}, {12794,22755}, {12836,22760}, {12837,22759}, {12992,22761}, {12993,22762}, {13108,22765}, {13109,22768}, {13983,22764}, {14881,18761}, {19013,19089}, {19014,19090}
The reciprocal orthologic center of these triangles is X(3).
X(22780) lies on these lines: {3,12339}, {36,9903}, {55,7977}, {56,83}, {104,12252}, {732,22769}, {754,11194}, {956,12783}, {958,6292}, {999,12264}, {2896,2975}, {3428,12122}, {6249,22753}, {6274,22757}, {6275,22756}, {6287,22758}, {8666,17766}, {8993,22763}, {9918,22654}, {10064,22766}, {10080,22767}, {10966,13078}, {11249,22680}, {11492,12477}, {11493,12476}, {12114,12924}, {12144,22479}, {12206,22520}, {12795,22755}, {12944,22759}, {12954,22760}, {12994,22761}, {12995,22762}, {13111,22765}, {13112,22768}, {13984,22764}, {18761,22803}, {19013,19091}, {19014,19092}
The reciprocal orthologic center of these triangles is X(4).
X(22781) lies on these lines: {1,2917}, {3,12341}, {36,9905}, {54,56}, {55,7979}, {104,12254}, {195,22765}, {539,11194}, {956,12785}, {958,1209}, {999,12266}, {1154,11249}, {2888,2975}, {3428,7691}, {3574,22753}, {6276,22757}, {6277,22756}, {6288,22758}, {8995,22763}, {9920,22654}, {9985,22744}, {10066,22766}, {10082,22767}, {10269,10610}, {10628,22583}, {10966,13079}, {11492,12481}, {11493,12480}, {11576,22479}, {12114,12926}, {12208,22520}, {12797,22755}, {12946,22759}, {12956,22760}, {12998,22761}, {12999,22762}, {13121,22768}, {13986,22764}, {18761,22804}, {19013,19095}, {19014,19096}, {19478,22586}
The reciprocal orthologic center of these triangles is X(79).
X(22782) lies on these lines: {3,12342}, {36,12409}, {55,13100}, {56,10266}, {104,12255}, {956,12786}, {958,12937}, {999,12267}, {1621,7354}, {2771,12745}, {2975,12849}, {3428,12556}, {5046,12615}, {6597,15071}, {6949,12623}, {10966,13080}, {11014,12513}, {11491,11826}, {11492,12483}, {11493,12482}, {12114,12927}, {12146,22479}, {12209,22520}, {12414,22654}, {12504,22744}, {12600,22753}, {12798,22755}, {12807,22756}, {12808,22757}, {12919,22758}, {12947,22759}, {12957,22760}, {13000,22761}, {13001,22762}, {13126,22765}, {13128,22766}, {13129,22767}, {13130,22768}, {13465,23016}, {13919,22763}, {13987,22764}, {18761,22805}, {19013,19097}, {19014,19098}
X(22782) = reflection of X(13465) in X(23016)
The reciprocal orthologic center of these triangles is X(13665).
X(22783) lies on these lines: {3,13675}, {30,22624}, {36,13679}, {55,13702}, {56,1327}, {104,13674}, {956,13688}, {958,13694}, {999,13667}, {2975,13678}, {3428,13666}, {10966,13699}, {11492,13683}, {11493,13682}, {12114,13693}, {13668,22479}, {13672,22520}, {13680,22654}, {13685,22744}, {13687,22753}, {13689,22755}, {13690,22756}, {13691,22757}, {13692,22758}, {13695,22759}, {13696,22760}, {13697,22761}, {13698,22762}, {13713,22765}, {13714,22766}, {13715,22767}, {13716,22768}, {13920,22763}, {13988,22764}, {18761,22806}, {19013,19099}, {19014,22541}, {22769,22784}
The reciprocal orthologic center of these triangles is X(13785).
X(22784) lies on these lines: {3,13795}, {30,22595}, {36,13799}, {55,13822}, {56,1328}, {104,13794}, {956,13808}, {958,13814}, {999,13787}, {2975,13798}, {3428,13786}, {10966,13819}, {11492,13803}, {11493,13802}, {12114,13813}, {13788,22479}, {13792,22520}, {13800,22654}, {13805,22744}, {13807,22753}, {13809,22755}, {13810,22756}, {13811,22757}, {13812,22758}, {13815,22759}, {13816,22760}, {13817,22761}, {13818,22762}, {13836,22765}, {13837,22766}, {13838,22767}, {13839,22768}, {13848,22763}, {13849,22764}, {18761,22807}, {19013,19101}, {19014,19100}, {22769,22783}
X(22785) lies on these lines: {3,11967}, {6,6401}, {98,14167}, {6199,11941}, {6200,11973}, {6221,11959}, {6395,11942}, {6396,11971}, {6398,11960}, {6433,11963}, {6434,11964}, {6435,11975}, {6436,11977}, {8289,22499}, {8375,11937}, {8376,11938}, {11983,22786}, {19379,19390}
X(22786) lies on these lines: {3,11968}, {6,6402}, {98,14168}, {6199,11943}, {6200,11972}, {6221,11961}, {6395,11944}, {6396,11974}, {6398,11962}, {6433,11965}, {6434,11966}, {6435,11978}, {6436,11976}, {8289,22500}, {8375,11939}, {8376,11940}, {11983,22785}, {19379,19391}
X(22787) lies on these lines: {10057,12551}, {10442,15298}, {10478,22788}, {11021,18223}, {12435,12647}
X(22788) lies on these lines: {1479,12547}, {10073,12551}, {10442,15299}, {10478,22787}, {10573,12435}, {11021,18224}
X(22789) lies on these lines: {11021,18225}, {12115,12547}, {12435,12648}, {12551,12749}
X(22790) lies on these lines: {11021,18226}, {12116,12547}, {12435,12649}, {12551,12750}
The reciprocal orthologic center of these triangles is X(10).
X(22791) lies on these lines: {1,30}, {2,12702}, {3,962}, {4,145}, {5,10}, {7,7373}, {8,381}, {11,5903}, {12,5697}, {20,10246}, {35,15950}, {38,5492}, {40,140}, {46,11376}, {56,1387}, {57,11373}, {63,19919}, {65,496}, {72,22010}, {80,11280}, {119,13996}, {165,3530}, {226,9957}, {265,7978}, {355,546}, {376,3622}, {382,944}, {390,6869}, {392,8728}, {442,3877}, {484,5433}, {495,3057}, {497,12433}, {515,1483}, {516,550}, {518,21850}, {519,3845}, {528,22836}, {529,22837}, {547,1698}, {548,3576}, {549,1125}, {551,8703}, {632,6684}, {758,3813}, {908,10914}, {912,9856}, {938,1159}, {942,12053}, {956,11415}, {999,4295}, {1000,5261}, {1012,10680}, {1058,6851}, {1145,11681}, {1210,7743}, {1319,1770}, {1388,4299}, {1478,2098}, {1479,2099}, {1480,5711}, {1484,2800}, {1511,11723}, {1519,10942}, {1565,17753}, {1572,5305}, {1595,1902}, {1596,1829}, {1656,5657}, {1657,5731}, {1697,11374}, {1737,10593}, {2095,6847}, {2102,10751}, {2103,10750}, {2140,20328}, {2475,5330}, {2771,3874}, {2802,11698}, {2807,6102}, {2975,3648}, {3091,4678}, {3146,7967}, {3149,10679}, {3241,3830}, {3244,15687}, {3295,3485}, {3333,5586}, {3336,12515}, {3340,5722}, {3416,18358}, {3419,11682}, {3434,5730}, {3476,9655}, {3486,9668}, {3487,6767}, {3488,4323}, {3543,3623}, {3545,3617}, {3560,5698}, {3583,10950}, {3585,10944}, {3600,18541}, {3621,3839}, {3628,7991}, {3633,14893}, {3634,15699}, {3652,6763}, {3671,5045}, {3679,5066}, {3753,17527}, {3754,3816}, {3818,5846}, {3832,20052}, {3834,12610}, {3843,12645}, {3850,4668}, {3851,5818}, {3853,5691}, {3857,4746}, {3858,4701}, {3860,4677}, {3861,5881}, {3869,6841}, {3871,18524}, {3880,16616}, {3884,5499}, {3898,11263}, {3899,21677}, {3913,18491}, {3940,5082}, {3962,5887}, {3988,20117}, {4004,6922}, {4018,8727}, {4029,10445}, {4127,5694}, {4297,15178}, {4318,18447}, {4342,21620}, {4389,10446}, {4861,5057}, {4867,18406}, {5054,5550}, {5055,9780}, {5074,21258}, {5076,10248}, {5119,11375}, {5221,10072}, {5248,5428}, {5250,6675}, {5432,5443}, {5493,10165}, {5554,17556}, {5563,11246}, {5693,7965}, {5708,14986}, {5754,19998}, {5758,6913}, {5761,19541}, {5771,6824}, {5787,7971}, {5805,12700}, {5840,19907}, {5843,11372}, {5853,18482}, {5883,13145}, {5884,6583}, {5905,18519}, {5919,13407}, {6033,7983}, {6097,16678}, {6221,13902}, {6259,12650}, {6264,16128}, {6265,14217}, {6321,7970}, {6398,13959}, {6644,11365}, {6738,18527}, {6762,18540}, {6836,10596}, {6842,10129}, {6905,11849}, {6906,22765}, {6911,10306}, {6914,11249}, {6923,10532}, {6924,11248}, {6925,10597}, {6928,10531}, {6981,8166}, {7173,18395}, {7377,17230}, {7508,11012}, {7514,8193}, {7530,9798}, {7555,9591}, {7561,18453}, {7580,16202}, {7718,18494}, {7728,7984}, {7962,9612}, {7973,14216}, {7989,12811}, {8192,18534}, {8196,11253}, {8203,11252}, {8666,17768}, {9566,19853}, {9625,12107}, {9669,18391}, {9818,12410}, {9905,22051}, {9933,12293}, {9943,13373}, {10021,16139}, {10039,10592}, {10109,19875}, {10164,14869}, {10264,12261}, {10272,12778}, {10284,18242}, {10386,10624}, {10431,10806}, {10572,11011}, {10573,10896}, {10695,10741}, {10696,10747}, {10697,10739}, {10699,15521}, {10700,15522}, {10703,10740}, {10705,12918}, {10733,12898}, {10749,13099}, {10785,13226}, {10800,14880}, {10826,11545}, {10895,12647}, {10912,18516}, {11014,11827}, {11024,16863}, {11539,19862}, {11551,17609}, {11709,14677}, {11725,12042}, {11735,12041}, {11801,13211}, {12102,16189}, {12195,18502}, {12436,16004}, {12454,18495}, {12455,18497}, {12495,18500}, {12512,17502}, {12513,18761}, {12514,16617}, {12619,16174}, {12626,18507}, {12627,18509}, {12628,18511}, {12635,18517}, {12636,18520}, {12637,18522}, {12648,18542}, {12649,18544}, {12735,12943}, {12773,13126}, {13665,19066}, {13785,19065}, {13911,18538}, {13973,18762}, {14269,20050}, {14377,17044}, {14839,14881}, {14923,17757}, {15326,21842}, {15713,19883}, {15808,17504}, {16150,20067}, {16212,18508}, {17563,17614}
X(22791) = midpoint of X(i) and X(j) for these {i,j}: {1, 12699}, {3, 962}, {4, 1482}, {8, 8148}, {265, 7978}, {355, 7982}, {382, 944}, {2102, 10751}, {2103, 10750}, {3241, 3830}, {5758, 8158}, {5787, 7971}, {5905, 18519}, {6033, 7983}, {6259, 12650}, {6264, 16128}, {6265, 14217}, {6321, 7970}, {7728, 7984}, {7973, 14216}, {9933, 12293}, {10695, 10741}, {10696, 10747}, {10697, 10739}, {10699, 15521}, {10700, 15522}, {10703, 10740}, {10705, 12918}, {10733, 12898}, {10749, 13099}, {12626, 18507}
X(22791) = reflection of X(i) in X(j) for these (i,j): (3, 5901), (5, 946), (8, 18357), (40, 140), (355, 546), (1511, 11723), (3416, 18358), (3679, 5066), (4297, 15178), (5884, 6583), (9905, 22051), (9943, 13373), (10264, 12261), (12619, 16174)
X(22791) = complement of X(12702)
X(22791) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 79, 5434), (1, 1836, 18990), (1, 12701, 15171), (3, 5603, 5901), (4, 145, 18525), (4, 20060, 10742), (10, 946, 9955), (946, 7686, 7956), (962, 3616, 6361), (962, 5603, 3), (1482, 18525, 145), (3616, 6361, 3), (3656, 12699, 1), (5603, 6361, 3616), (12702, 18493, 2), (15170, 16137, 1)
The reciprocal orthologic center of these triangles is X(40).
X(22792) lies on these lines: {4,7}, {5,6692}, {30,6260}, {56,1538}, {84,381}, {153,10914}, {377,10157}, {382,1490}, {388,17622}, {515,1483}, {516,12607}, {517,6256}, {546,6245}, {1158,9956}, {1385,2829}, {1466,9579}, {1478,9856}, {1479,12678}, {1699,3304}, {1709,10895}, {1768,17606}, {1836,13601}, {1898,13273}, {2099,5691}, {2475,5927}, {2478,11227}, {2771,12761}, {3057,12763}, {3091,12246}, {3146,5658}, {3579,18242}, {3583,12680}, {3585,12688}, {3824,6913}, {3843,12684}, {3916,6932}, {4298,7956}, {5044,6850}, {5046,10167}, {5049,10531}, {5084,10156}, {5086,9809}, {5122,6834}, {5253,17618}, {5439,13729}, {5450,11230}, {5499,11231}, {5777,6923}, {5887,16128}, {6001,10107}, {6257,18511}, {6258,18509}, {6929,9940}, {7330,15239}, {7971,18525}, {7992,18492}, {8987,18538}, {9654,12705}, {9780,14646}, {9818,9910}, {9955,12114}, {9957,12115}, {10085,10896}, {10728,21740}, {11681,17613}, {12196,18502}, {12330,18491}, {12456,18495}, {12457,18497}, {12496,18500}, {12616,22798}, {12667,12699}, {12668,18507}, {12675,18527}, {12676,18516}, {12677,18517}, {12686,18542}, {12687,18544}, {13665,19068}, {13785,19067}, {13974,18762}, {18237,18761}, {18245,18520}, {18246,18522}
X(22792) = midpoint of X(i) and X(j) for these {i,j}: {4, 6259}, {382, 1490}, {7971, 18525}, {12667, 12699}, {12668, 18507}
X(22792) = reflection of X(i) in X(j) for these (i,j): (1158, 9956), (1385, 12608), (3579, 18242)
X(22792) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 6223, 5787), (1478, 12679, 9856), (5787, 6259, 6223)
The reciprocal orthologic center of these triangles is X(4).
X(22793) lies on these lines: {1,382}, {3,1699}, {4,8}, {5,516}, {7,15008}, {10,546}, {11,1770}, {20,5886}, {30,551}, {35,17605}, {40,381}, {46,10896}, {56,7743}, {57,9669}, {65,3521}, {79,354}, {80,17501}, {140,3817}, {149,3555}, {165,1656}, {226,15171}, {390,5714}, {392,2475}, {484,17606}, {495,10624}, {496,4292}, {497,5045}, {499,5122}, {515,1483}, {519,15687}, {528,21077}, {535,11260}, {548,10165}, {549,12512}, {550,1125}, {631,9779}, {632,10171}, {942,1479}, {944,3543}, {952,3853}, {971,16127}, {999,9579}, {1001,3824}, {1155,7741}, {1156,11662}, {1212,5134}, {1319,10483}, {1387,4311}, {1478,9957}, {1482,3830}, {1538,3149}, {1657,3576}, {1697,9654}, {1698,3851}, {1702,13665}, {1703,13785}, {1709,11928}, {1717,9630}, {2635,5399}, {2646,18393}, {2771,7728}, {2777,12261}, {2778,19506}, {2800,22938}, {2802,22799}, {2807,5446}, {3057,3585}, {3058,13407}, {3090,9778}, {3091,6361}, {3146,5603}, {3295,9580}, {3333,18541}, {3338,11238}, {3474,10591}, {3526,7988}, {3528,5550}, {3529,3616}, {3530,19862}, {3534,7987}, {3544,19877}, {3615,5196}, {3628,10164}, {3652,10032}, {3653,11001}, {3654,3839}, {3655,10595}, {3660,7702}, {3671,12433}, {3679,14269}, {3701,21282}, {3753,5046}, {3832,5657}, {3838,5248}, {3843,5587}, {3845,4745}, {3850,5493}, {3855,9780}, {3861,11362}, {3911,10593}, {3916,11680}, {3944,5266}, {4293,11373}, {4294,11374}, {4295,5225}, {4299,5126}, {4302,11375}, {4309,17718}, {4312,5708}, {4314,5719}, {4324,5443}, {4325,16173}, {4333,5204}, {4338,5221}, {4848,12019}, {5049,10404}, {5054,16192}, {5073,10246}, {5076,7982}, {5119,10895}, {5183,18395}, {5250,17532}, {5270,5919}, {5290,6767}, {5439,9782}, {5536,7701}, {5556,11037}, {5563,16118}, {5697,18513}, {5698,5791}, {5709,5789}, {5715,10267}, {5720,12651}, {5790,7991}, {5804,9800}, {5805,6851}, {5840,9945}, {5844,12102}, {5881,8148}, {5885,6895}, {5899,9626}, {5903,18514}, {6001,22802}, {6240,11363}, {6265,10724}, {6284,12047}, {6797,12764}, {6840,13145}, {6841,7965}, {6915,17618}, {6943,17613}, {6985,11496}, {7686,7706}, {7957,18406}, {7973,18405}, {8976,9616}, {9590,18378}, {9593,15484}, {9624,17800}, {9818,9911}, {10306,18491}, {10308,13243}, {10386,13405}, {10431,10531}, {10446,17361}, {10728,12737}, {10742,14217}, {10916,17768}, {11012,13743}, {11248,19541}, {11365,12085}, {11531,12645}, {11699,17702}, {12053,18990}, {12197,18502}, {12458,18495}, {12459,18497}, {12497,18500}, {12563,15935}, {12696,18507}, {12697,18509}, {12698,18511}, {12703,18542}, {12704,18544}, {12747,13253}, {13369,13374}, {13912,18538}, {13975,18762}, {14869,19878}, {15172,21620}, {15931,16117}, {16160,22936}, {16200,18526}, {17579,17614}, {17748,17764}, {18520,22841}, {18522,22842}, {18761,22770}
X(22793) = midpoint of X(i) and X(j) for these {i,j}: {1, 382}, {4, 12699}, {149, 16128}, {1482, 5691}, {3146, 18481}, {3655, 15682}, {5881, 8148}, {6265, 10724}, {10728, 12737}, {10742, 14217}, {11531, 12645}, {12696, 18507}, {12747, 13253}
X(22793) = reflection of X(i) in X(j) for these (i,j): (3, 9955), (5, 18483), (10, 546), (20, 13624), (40, 9956), (550, 1125), (1071, 6583), (13369, 13374)
X(22793) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 1699, 9955), (3, 9955, 11230), (4, 962, 355), (4, 9812, 12699), (5, 3579, 11231), (20, 5886, 13624), (40, 381, 9956), (79, 4857, 354), (355, 12699, 962), (946, 4297, 5901), (962, 10248, 4), (4297, 5901, 1385), (6684, 12571, 5), (6684, 18483, 12571), (9812, 10248, 962)
The reciprocal orthologic center of these triangles is X(3).
X(22794) lies on these lines: {4,617}, {5,6672}, {18,381}, {30,630}, {62,10612}, {382,22843}, {546,5478}, {1351,3818}, {1478,22860}, {1479,22859}, {3091,22531}, {3583,22865}, {3585,18972}, {3839,22114}, {5318,8260}, {5873,16002}, {6033,11603}, {7747,16808}, {9818,22656}, {9955,11740}, {10895,22884}, {10896,22885}, {12699,22851}, {13665,19072}, {13785,19069}, {14269,22845}, {18491,22557}, {18492,22651}, {18495,22669}, {18497,22673}, {18500,22745}, {18502,22522}, {18507,22852}, {18509,22853}, {18511,22854}, {18516,22857}, {18517,22858}, {18520,22863}, {18522,22864}, {18525,22867}, {18538,22876}, {18542,22886}, {18544,22887}, {18761,22771}, {18762,22877}, {22597,22626}
X(22794) = midpoint of X(i) and X(j) for these {i,j}: {4, 16627}, {382, 22843}, {6033, 11603}, {12699, 22851}, {18507, 22852}, {18525, 22867}
X(22794) = {X(3818), X(3843)}-harmonic conjugate of X(22795)
The reciprocal orthologic center of these triangles is X(3).
X(22795) lies on these lines: {4,616}, {5,6671}, {17,381}, {30,629}, {61,10611}, {382,22890}, {532,3845}, {546,5479}, {1351,3818}, {1478,22905}, {1479,22904}, {3091,22532}, {3583,22910}, {3585,18973}, {3839,22113}, {5321,8259}, {5872,16001}, {6033,11602}, {7747,16809}, {9818,22657}, {9955,11739}, {10895,22929}, {10896,22930}, {12699,22896}, {13665,19070}, {13785,19071}, {14269,22844}, {18491,22558}, {18492,22652}, {18495,22670}, {18497,22674}, {18500,22746}, {18502,22523}, {18507,22897}, {18509,22898}, {18511,22899}, {18516,22902}, {18517,22903}, {18520,22908}, {18522,22909}, {18525,22912}, {18538,22921}, {18542,22931}, {18544,22932}, {18761,22772}, {18762,22922}, {22599,22628}
X(22795) = midpoint of X(i) and X(j) for these {i,j}: {4, 16626}, {382, 22890}, {6033, 11602}, {12699, 22896}, {18507, 22897}, {18525, 22912}
X(22795) = {X(3818), X(3843)}-harmonic conjugate of X(22794)
The reciprocal orthologic center of these triangles is X(13).
X(22796) lies on these lines: {4,616}, {5,6669}, {6,13}, {15,22892}, {30,618}, {114,1080}, {382,5473}, {398,14136}, {543,6298}, {546,5478}, {621,7809}, {626,3642}, {1478,12952}, {1479,12942}, {1656,21156}, {2782,5479}, {2794,6774}, {3091,6770}, {3583,13076}, {3585,18974}, {3830,5463}, {3843,13103}, {3850,20252}, {5066,5459}, {5318,6782}, {5321,6115}, {5474,15561}, {5965,20425}, {6108,22847}, {6670,12042}, {7975,18525}, {9818,9916}, {9901,18492}, {9955,11705}, {9982,18500}, {10061,12185}, {10062,10895}, {10077,12184}, {10078,10896}, {11121,14492}, {12205,18502}, {12337,18491}, {12472,18495}, {12473,18497}, {12699,12781}, {12793,18507}, {12922,18516}, {12932,18517}, {12990,18520}, {12991,18522}, {13105,18542}, {13107,18544}, {13917,18538}, {13982,18762}, {14830,22490}, {16530,16965}, {18581,22513}, {18761,22773}, {18764,22998}, {19709,22489}, {22601,22630}
X(22796) = midpoint of X(i) and X(j) for these {i,j}: {4, 5617}, {382, 5473}, {3830, 5463}, {7975, 18525}, {12699, 12781}, {12793, 18507}
X(22796) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (14, 381, 19130), (381, 3818, 22797), (6777, 16808, 5472)
The reciprocal orthologic center of these triangles is X(14).
X(22797) lies on these lines: {4,617}, {5,6670}, {6,13}, {16,22848}, {30,619}, {114,383}, {382,5474}, {397,14137}, {543,6299}, {546,5479}, {622,7809}, {626,3643}, {1478,12951}, {1479,12941}, {1656,21157}, {2782,5478}, {2794,6771}, {3091,6773}, {3583,13075}, {3585,18975}, {3830,5464}, {3843,13102}, {3850,20253}, {5066,5460}, {5318,6114}, {5321,6783}, {5473,15561}, {5965,20426}, {6109,22893}, {6669,12042}, {7974,18525}, {9818,9915}, {9900,18492}, {9955,11706}, {9981,18500}, {10061,10895}, {10062,12185}, {10077,10896}, {10078,12184}, {11122,14492}, {12204,18502}, {12336,18491}, {12470,18495}, {12471,18497}, {12699,12780}, {12792,18507}, {12921,18516}, {12931,18517}, {12988,18520}, {12989,18522}, {13104,18542}, {13106,18544}, {13916,18538}, {13981,18762}, {14830,22489}, {16529,16964}, {18582,22512}, {18761,22774}, {18765,22997}, {19709,22490}, {22603,22632}
X(22797) = midpoint of X(i) and X(j) for these {i,j}: {4, 5613}, {382, 5474}, {3830, 5464}, {7974, 18525}, {12699, 12780}, {12792, 18507}
X(22797) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (13, 381, 19130), (381, 3818, 22796)
The reciprocal orthologic center of these triangles is X(3).
X(22798) lies on these lines: {4,3648}, {5,3833}, {10,30}, {11,113}, {21,18481}, {46,1749}, {55,5441}, {79,381}, {355,21669}, {382,16113}, {546,16125}, {758,3813}, {1210,11544}, {1385,12617}, {1478,16141}, {1479,16140}, {2475,16138}, {3065,10742}, {3091,16116}, {3583,16142}, {3585,18977}, {3624,16132}, {3650,6734}, {3826,5499}, {3839,20084}, {3843,16150}, {3850,10265}, {4297,12104}, {5694,8727}, {5885,8226}, {6175,10308}, {6245,11230}, {6361,16139}, {7548,16128}, {9818,16119}, {10895,16152}, {10896,16153}, {11684,12699}, {12616,22792}, {12619,19925}, {12620,22801}, {12623,22805}, {13624,15670}, {13665,19080}, {13785,19079}, {16115,18502}, {16117,18491}, {16121,18495}, {16122,18497}, {16123,18500}, {16129,18507}, {16130,18509}, {16131,18511}, {16148,18538}, {16149,18762}, {16154,18542}, {16155,18544}, {16161,18520}, {16162,18522}, {17768,18482}
X(22798) = midpoint of X(i) and X(j) for these {i,j}: {4, 3652}, {355, 21669}, {382, 16113}, {2475, 16138}, {3065, 10742}, {11684, 12699}, {16129, 18507}
X(22798) = reflection of X(i) in X(j) for these (i,j): (1385, 16617), (4297, 12104)
X(22798) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3649, 6841, 9955), (7701, 18492, 16118), (13743, 18525, 5441)
The reciprocal orthologic center of these triangles is X(40).
X(22799) lies on these lines: {3,10728}, {4,145}, {5,2829}, {11,546}, {30,119}, {80,1836}, {100,382}, {104,381}, {214,5087}, {515,12611}, {528,15687}, {550,3035}, {1145,5080}, {1317,3583}, {1387,1478}, {1479,12735}, {1484,3845}, {1539,8674}, {1699,12737}, {1768,18492}, {2783,22515}, {2787,22505}, {2800,18480}, {2801,18482}, {2802,22793}, {2806,19160}, {2831,19163}, {3091,12248}, {3543,13199}, {3627,5840}, {3628,21154}, {3830,10711}, {3843,12773}, {3858,20418}, {5221,12019}, {5434,15180}, {5587,12515}, {5691,6265}, {6256,11729}, {7972,18514}, {9818,9913}, {9955,11715}, {10058,10895}, {10074,10896}, {10087,12953}, {10090,12943}, {10707,14269}, {10759,18440}, {10956,15171}, {11604,14496}, {12199,18502}, {12332,18491}, {12462,18495}, {12463,18497}, {12499,18500}, {12619,19925}, {12699,12751}, {12701,12749}, {12752,18507}, {12753,18509}, {12754,18511}, {12761,16112}, {12762,18517}, {12765,18520}, {12766,18522}, {12775,18542}, {12776,18544}, {13665,19082}, {13785,19081}, {13913,18538}, {13977,18762}, {15704,20400}, {18761,22775}
X(22799) = midpoint of X(i) and X(j) for these {i,j}: {3, 10728}, {4, 10742}, {80, 16128}, {100, 382}, {3627, 11698}, {3830, 10711}, {5691, 6265}, {10759, 18440}, {12699, 12751}, {12752, 18507}
X(22799) = reflection of X(i) in X(j) for these (i,j): (11, 546), (550, 3035), (12619, 19925)
X(22799) = complement of X(38753)
X(22799) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 153, 10738), (1478, 12764, 1387), (1479, 12763, 12735), (3830, 12331, 10724), (10711, 10724, 12331), (10738, 10742, 153)
The reciprocal orthologic center of these triangles is X(12241).
X(22800) lies on these lines: {4,801}, {30,22966}, {113,389}, {143,15873}, {381,15317}, {382,22951}, {546,22833}, {1478,22959}, {1479,22958}, {2072,18488}, {2929,7506}, {3091,22533}, {3548,22581}, {3583,22965}, {3585,18978}, {3843,22979}, {4846,22973}, {5448,18418}, {6644,22802}, {9818,22658}, {9955,22476}, {10895,22980}, {10896,22981}, {12084,22978}, {12699,22941}, {13665,19084}, {13785,19083}, {15043,18504}, {18491,22559}, {18492,22653}, {18500,22747}, {18502,22524}, {18507,22943}, {18509,22945}, {18511,22947}, {18516,22956}, {18517,22957}, {18520,22963}, {18522,22964}, {18525,22969}, {18538,22976}, {18542,22982}, {18544,22983}, {18761,22776}, {18762,22977}, {22808,22972}
X(22800) = midpoint of X(i) and X(j) for these {i,j}: {4, 22955}, {382, 22951}, {12699, 22941}, {18507, 22943}, {18525, 22969}, {22808, 22972}
X(22800) = {X(4), X(22750)}-harmonic conjugate of X(22483)
The reciprocal orthologic center of these triangles is X(40).
X(22801) lies on these lines: {4,9874}, {30,12864}, {381,7160}, {382,12120}, {546,12599}, {1478,12860}, {1479,12859}, {3091,12249}, {3583,12863}, {3585,18979}, {3843,12872}, {8000,18525}, {9818,12411}, {9898,18492}, {9955,12260}, {10059,10895}, {10075,10896}, {12200,18502}, {12333,18491}, {12464,18495}, {12465,18497}, {12500,18500}, {12611,12612}, {12620,22798}, {12699,12777}, {12789,18507}, {12801,18509}, {12802,18511}, {12855,15172}, {12857,18516}, {12858,18482}, {12861,18520}, {12862,18522}, {12874,18542}, {12875,18544}, {13665,19086}, {13785,19085}, {13914,18538}, {13978,18762}, {18761,22777}
X(22801) = midpoint of X(i) and X(j) for these {i,j}: {4, 12856}, {382, 12120}, {8000, 18525}, {12699, 12777}, {12789, 18507}
The reciprocal orthologic center of these triangles is X(4).
X(22802) lies on these lines: {2,18504}, {3,113}, {4,51}, {5,3357}, {20,10282}, {30,156}, {64,381}, {74,16868}, {140,5894}, {146,2888}, {154,1657}, {184,18560}, {195,382}, {221,9668}, {235,1514}, {403,1204}, {541,5449}, {542,12293}, {546,6247}, {548,10192}, {550,11202}, {576,1353}, {578,1885}, {1181,13403}, {1478,12950}, {1479,12940}, {1539,13491}, {1562,8743}, {1568,11413}, {1593,18388}, {1596,13568}, {1614,9934}, {1656,10606}, {1853,3843}, {2192,9655}, {2778,5694}, {2781,5876}, {2818,10525}, {2904,11456}, {3091,7703}, {3146,5656}, {3153,12279}, {3526,8567}, {3534,17821}, {3583,7355}, {3585,6285}, {3830,12315}, {3850,15105}, {4846,9729}, {5073,17845}, {5076,18405}, {5270,11189}, {5448,12084}, {5663,9927}, {6001,22793}, {6145,18550}, {6243,18325}, {6266,18511}, {6267,18509}, {6293,18439}, {6624,15005}, {6644,22800}, {6689,7526}, {6816,16836}, {7401,18489}, {7505,21663}, {7689,15761}, {7973,18525}, {8991,18538}, {9786,22971}, {9818,9914}, {9899,18492}, {9955,12262}, {10060,10895}, {10076,10896}, {10111,12295}, {10274,11805}, {10483,10535}, {10540,18565}, {10575,18404}, {10675,19107}, {10676,19106}, {10990,16219}, {11441,15063}, {11468,12244}, {11695,18537}, {12161,12897}, {12173,13419}, {12174,18396}, {12202,18502}, {12233,13488}, {12335,18491}, {12468,18495}, {12469,18497}, {12502,18500}, {12699,12779}, {12791,18507}, {12920,18516}, {12930,18517}, {12986,18520}, {12987,18522}, {13094,18542}, {13095,18544}, {13665,19088}, {13785,19087}, {13980,18762}, {13997,18809}, {14530,17800}, {14641,14791}, {14915,18569}, {15072,16223}, {15125,18281}, {15811,18494}, {18761,22778}
X(22802) = midpoint of X(i) and X(j) for these {i,j}: {3, 5895}, {4, 5878}, {3146, 9833}, {5073, 17845}, {6293, 18439}, {7973, 18525}, {12699, 12779}, {12791, 18507}
X(22802) = reflection of X(i) in X(j) for these (i,j): (5, 5893), (20, 10282), (64, 20299), (550, 16252), (7689, 15761), (13997, 18809)
X(22802) = complement of X(20427)
X(22802) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 185, 18390), (4, 6225, 14216), (4, 11457, 13851), (4, 12290, 11550), (4, 14216, 18383), (4, 18381, 18376), (64, 381, 20299), (140, 5894, 11204), (550, 16252, 11202), (3146, 5656, 9833), (3526, 8567, 10193), (3843, 13093, 1853), (5878, 14216, 6225), (12244, 14940, 11468), (14216, 18383, 18381)
The reciprocal orthologic center of these triangles is X(3).
X(22803) lies on these lines: {2,8725}, {4,2896}, {5,5092}, {30,6292}, {83,381}, {115,546}, {382,7910}, {732,3818}, {754,3845}, {1478,12954}, {1479,12944}, {1656,9751}, {2548,13331}, {3091,12252}, {3583,13078}, {3585,18983}, {3839,20088}, {3843,13111}, {3851,7919}, {3861,13449}, {6033,11606}, {6274,18511}, {6275,18509}, {7617,8150}, {7842,15687}, {7882,18553}, {7977,18525}, {8993,18538}, {9478,12042}, {9818,9918}, {9903,18492}, {9955,12264}, {10064,10895}, {10080,10896}, {12206,18502}, {12339,18491}, {12476,18495}, {12477,18497}, {12699,12783}, {12795,18507}, {12924,18516}, {12934,18517}, {12994,18520}, {12995,18522}, {13112,18542}, {13113,18544}, {13665,19092}, {13785,19091}, {13984,18762}, {16630,16809}, {16631,16808}, {17766,18483}, {18761,22780}, {22614,22643}
X(22803) = midpoint of X(i) and X(j) for these {i,j}: {4, 6287}, {382, 12122}, {6033, 11606}, {7977, 18525}, {12699, 12783}, {12795, 18507}
X(22803) = complement of X(8725)
The reciprocal orthologic center of these triangles is X(4).
X(22804) lies on these lines: {3,7703}, {4,93}, {5,5944}, {30,1209}, {54,156}, {113,137}, {140,11572}, {195,3843}, {265,10095}, {382,7691}, {539,3845}, {973,6102}, {1478,12956}, {1479,12946}, {1511,1594}, {1539,6153}, {2917,7526}, {3091,12254}, {3153,14128}, {3583,13079}, {3585,18984}, {3627,21230}, {3830,12307}, {3850,8254}, {3851,9707}, {3858,12242}, {3861,13142}, {4846,6145}, {5946,18912}, {5965,21850}, {6000,11802}, {6276,18511}, {6277,18509}, {6286,18514}, {6696,12041}, {7356,18513}, {7579,11449}, {7687,11804}, {7730,12111}, {7979,18525}, {8995,18538}, {9818,9920}, {9905,18492}, {9927,11743}, {9955,12266}, {9985,18500}, {10066,10895}, {10082,10896}, {10110,10115}, {11565,13353}, {11801,13163}, {11808,13754}, {12061,18553}, {12208,18502}, {12316,14269}, {12341,18491}, {12363,18404}, {12480,18495}, {12481,18497}, {12606,18403}, {12699,12785}, {12797,18507}, {12926,18516}, {12936,18517}, {12998,18520}, {12999,18522}, {13121,18542}, {13122,18544}, {13365,13630}, {13367,13413}, {13423,22815}, {13665,19096}, {13785,19095}, {13986,18762}, {15030,18567}, {15052,15091}, {15060,18377}, {15067,18569}, {18761,22781}
X(22804) = midpoint of X(i) and X(j) for these {i,j}: {4, 6288}, {382, 7691}, {3627, 21230}, {7979, 18525}, {12699, 12785}, {12797, 18507}, {13423, 22815}
X(22804) = reflection of X(i) in X(j) for these (i,j): (3, 13565), (140, 20584)
The reciprocal orthologic center of these triangles is X(79).
X(22805) lies on these lines: {4,12146}, {30,13089}, {381,10266}, {382,12556}, {546,12600}, {1478,12957}, {1479,12947}, {3091,12255}, {3583,13080}, {3585,18985}, {3843,13126}, {6595,10742}, {9818,12414}, {9955,12267}, {10895,13128}, {10896,13129}, {12209,18502}, {12342,18491}, {12409,18492}, {12482,18495}, {12483,18497}, {12504,18500}, {12611,12615}, {12623,22798}, {12699,12786}, {12798,18507}, {12807,18509}, {12808,18511}, {12927,18516}, {12937,18517}, {13000,18520}, {13001,18522}, {13100,18525}, {13130,18542}, {13131,18544}, {13665,19098}, {13785,19097}, {13919,18538}, {13987,18762}, {18761,22782}
X(22805) = midpoint of X(i) and X(j) for these {i,j}: {4, 12919}, {382, 12556}, {6595, 10742}, {12699, 12786}, {12798, 18507}, {13100, 18525}
The reciprocal orthologic center of these triangles is X(13665).
X(22806) lies on these lines: {4,13668}, {30,641}, {381,486}, {382,13666}, {546,13687}, {597,3818}, {1478,13696}, {1479,13695}, {3091,13674}, {3583,13699}, {3585,18986}, {3830,13712}, {3843,13713}, {6565,9300}, {9818,13680}, {9955,13667}, {10895,13714}, {10896,13715}, {12699,13688}, {13665,22541}, {13672,18502}, {13675,18491}, {13679,18492}, {13682,18495}, {13683,18497}, {13685,18500}, {13689,18507}, {13690,18509}, {13691,18511}, {13693,18516}, {13694,18517}, {13697,18520}, {13698,18522}, {13702,18525}, {13716,18542}, {13717,18544}, {13785,19099}, {13920,18538}, {13988,18762}, {18761,22783}
X(22806) = midpoint of X(i) and X(j) for these {i,j}: {4, 13692}, {382, 13666}, {3830, 13712}, {12699, 13688}, {13689, 18507}, {13702, 18525}
X(22806) = {X(3818), X(5066)}-harmonic conjugate of X(22807)
The reciprocal orthologic center of these triangles is X(13785).
X(22807) lies on these lines: {4,13788}, {30,642}, {381,485}, {382,13786}, {546,13807}, {597,3818}, {1478,13816}, {1479,13815}, {3091,13794}, {3583,13819}, {3585,18987}, {3830,13835}, {3843,13836}, {6564,9300}, {9818,13800}, {9955,13787}, {10895,13837}, {10896,13838}, {12699,13808}, {13665,19100}, {13785,19101}, {13792,18502}, {13795,18491}, {13799,18492}, {13802,18495}, {13803,18497}, {13805,18500}, {13809,18507}, {13810,18509}, {13811,18511}, {13813,18516}, {13814,18517}, {13817,18520}, {13818,18522}, {13822,18525}, {13839,18542}, {13840,18544}, {13848,18538}, {13849,18762}, {18761,22784}
X(22807) = midpoint of X(i) and X(j) for these {i,j}: {4, 13812}, {382, 13786}, {3830, 13835}, {12699, 13808}, {13809, 18507}, {13822, 18525}
X(22807) = {X(3818), X(5066)}-harmonic conjugate of X(22806)
The reciprocal orthologic center of these triangles is X(9729).
X(22808) lies on these lines: {3,2929}, {5,22750}, {30,22528}, {155,22953}, {265,11585}, {381,22970}, {382,22538}, {394,12429}, {567,22529}, {568,22530}, {2072,6288}, {3519,12358}, {3548,22647}, {3580,7691}, {5055,22973}, {6640,18466}, {6643,10627}, {7506,22483}, {8549,18440}, {9815,22833}, {9818,22497}, {10539,22662}, {11411,18436}, {11459,22534}, {12111,22535}, {12605,18442}, {13474,18403}, {13754,21652}, {14216,18404}, {17837,18451}, {18445,19460}, {18447,19472}, {18449,22830}, {18453,22840}, {18455,22954}, {18457,22960}, {18459,22961}, {18462,19488}, {18463,19489}, {18468,22974}, {18470,22975}, {18563,20127}, {18917,18936}, {19129,19142}, {19176,19198}, {22800,22972}
X(22808) = midpoint of X(12111) and X(22535)
X(22808) = reflection of X(i) in X(j) for these (i,j): (3, 22834), (382, 22538)
The reciprocal orthologic center of these triangles is X(3).
X(22809) lies on these lines: {3,486}, {5,12509}, {30,12221}, {381,487}, {382,3564}, {567,12229}, {568,12237}, {642,5055}, {1657,12256}, {3843,6290}, {3851,6251}, {5899,9921}, {6221,13881}, {6767,13081}, {7373,18989}, {9818,12169}, {9906,12702}, {11459,12274}, {12111,12285}, {12147,18535}, {12320,18531}, {12597,18449}, {12662,18453}, {12910,18455}, {12960,18457}, {12966,18459}, {12980,18468}, {12981,18470}, {13754,21653}, {13836,22615}, {14269,22596}, {15685,22484}, {17839,18451}, {18403,22817}, {18445,19461}, {18447,19473}, {18462,19490}, {18917,18937}, {19129,19143}, {19176,19199}
X(22809) = midpoint of X(12111) and X(12285)
X(22809) = reflection of X(i) in X(j) for these (i,j): (3, 12601), (382, 12296), (1657, 12256)
The reciprocal orthologic center of these triangles is X(3).
X(22810) lies on these lines: {3,485}, {5,12510}, {30,12222}, {381,488}, {382,3564}, {567,12230}, {568,12238}, {641,5055}, {1657,12257}, {3843,6289}, {3851,6250}, {5899,9922}, {6118,15694}, {6398,13881}, {6767,13082}, {7373,18988}, {9818,12170}, {9907,12702}, {11459,12275}, {12111,12286}, {12148,18535}, {12321,18531}, {12598,18449}, {12663,18453}, {12911,18455}, {12961,18457}, {12967,18459}, {12982,18468}, {12983,18470}, {13713,22644}, {13754,21654}, {14269,22625}, {15685,22485}, {17842,18451}, {18403,22818}, {18445,19462}, {18447,19474}, {18463,19491}, {18917,18938}, {19129,19144}, {19176,19200}
X(22810) = midpoint of X(12111) and X(12286)
X(22810) = reflection of X(i) in X(j) for these (i,j): (3, 12602), (382, 12297), (1657, 12257)
The reciprocal orthologic center of these triangles is X(3).
X(22811) lies on these lines: {3,6}, {5,6239}, {30,12223}, {381,6291}, {382,12298}, {488,14984}, {5055,9823}, {6252,18453}, {7362,18447}, {9818,12171}, {11459,12276}, {12111,12287}, {12256,15074}, {12322,18531}, {13754,21655}, {17840,18451}, {18403,22819}, {18445,19463}, {18462,19492}, {18463,19494}, {18917,18941}, {19176,19201}
X(22811) = midpoint of X(12111) and X(12287)
X(22811) = reflection of X(i) in X(j) for these (i,j): (3, 12603), (382, 12298)
X(22811) = {X(3), X(18438)}-harmonic conjugate of X(22812)
The reciprocal orthologic center of these triangles is X(3).
X(22812) lies on these lines: {3,6}, {5,6400}, {30,12224}, {381,6406}, {382,12299}, {487,14984}, {3060,8964}, {5055,9824}, {6404,18453}, {6405,18455}, {7353,18447}, {9818,12172}, {11459,12277}, {12111,12288}, {12257,15074}, {12323,18531}, {13754,21656}, {17843,18451}, {18403,22820}, {18445,19464}, {18462,19495}, {18463,19493}, {18917,18942}, {19176,19202}
X(22812) = midpoint of X(12111) and X(12288)
X(22812) = reflection of X(i) in X(j) for these (i,j): (3, 12604), (382, 12299)
X(22812) = {X(3), X(18438)}-harmonic conjugate of X(22811)
The reciprocal orthologic center of these triangles is X(10670).
X(22813) lies on these lines: {3,485}, {5,13035}, {30,13009}, {381,13051}, {382,13019}, {567,13011}, {568,13013}, {5055,13053}, {9818,13007}, {11459,13015}, {12111,13017}, {13025,18531}, {13037,18449}, {13041,18453}, {13043,18455}, {13045,18457}, {13047,18459}, {13057,18468}, {13059,18470}, {13754,21657}, {17841,18451}, {18403,22821}, {18445,19465}, {18447,19475}, {18463,19497}, {18917,18943}, {19129,19147}, {19176,19203}
X(22813) = midpoint of X(12111) and X(13017)
X(22813) = reflection of X(i) in X(j) for these (i,j): (3, 13039), (382, 13019)
The reciprocal orthologic center of these triangles is X(10674).
X(22814) lies on these lines: {3,486}, {5,13036}, {30,13010}, {381,13052}, {382,13020}, {567,13012}, {568,13014}, {5055,13054}, {9818,13008}, {11459,13016}, {12111,13018}, {13026,18531}, {13038,18449}, {13042,18453}, {13044,18455}, {13046,18457}, {13048,18459}, {13058,18468}, {13060,18470}, {13754,21658}, {17844,18451}, {18403,22822}, {18445,19466}, {18447,19476}, {18462,19496}, {18917,18944}, {19129,19148}, {19176,19204}
X(22814) = midpoint of X(12111) and X(13018)
X(22814) = reflection of X(i) in X(j) for these (i,j): (3, 13040), (382, 13020)
The reciprocal orthologic center of these triangles is X(6243).
X(22815) lies on these lines: {3,54}, {5,6242}, {30,12226}, {265,3519}, {381,6152}, {382,12300}, {539,18436}, {550,7722}, {567,12234}, {568,12242}, {1147,15091}, {1209,10255}, {2072,21230}, {2888,18404}, {2914,7488}, {3574,10254}, {3843,11576}, {5055,9827}, {5907,6288}, {5965,18438}, {6243,18388}, {6255,18453}, {6286,18455}, {7356,18447}, {7542,22051}, {9818,12175}, {9977,18449}, {10024,14449}, {10575,10628}, {10677,18468}, {10678,18470}, {11459,12280}, {11585,11804}, {12022,12899}, {12111,12291}, {12325,18531}, {12965,18457}, {12971,18459}, {13423,22804}, {13754,18442}, {14978,19177}, {17846,18451}, {18400,18439}, {18445,19468}, {18462,19502}, {18463,19503}, {18563,22584}, {18917,18946}, {19129,19150}, {19176,19207}
X(22815) = midpoint of X(12111) and X(12291)
X(22815) = reflection of X(i) in X(j) for these (i,j): (3, 12606), (382, 12300), (13423, 22804)
The reciprocal orthologic center of these triangles is X(9729).
X(22816) lies on these lines: {4,801}, {5,13293}, {30,22978}, {125,15062}, {265,12162}, {381,2929}, {382,22549}, {542,22830}, {3153,22528}, {3583,22954}, {3585,19472}, {3843,22550}, {3845,18428}, {6564,22960}, {6565,22961}, {9927,22833}, {13474,18403}, {13851,21652}, {16808,22974}, {16809,22975}, {17837,18405}, {18386,22497}, {18388,22529}, {18390,22530}, {18392,22534}, {18394,22535}, {18396,19460}, {18404,22834}, {18406,22840}, {18414,19488}, {18415,19489}, {18418,22966}, {18420,22973}, {18531,22581}, {18918,18936}, {19130,19142}, {19177,19198}
X(22816) = midpoint of X(382) and X(22549)
X(22816) = {X(3843), X(22550)}-harmonic conjugate of X(22971)
The reciprocal orthologic center of these triangles is X(3).
X(22817) lies on these lines: {3,18415}, {4,487}, {5,12972}, {30,9921}, {381,12978}, {382,12303}, {486,10898}, {542,12597}, {642,18420}, {3153,12221}, {3564,18569}, {3583,12910}, {3585,19473}, {3843,12311}, {6564,12960}, {6565,12966}, {12169,18386}, {12229,18388}, {12237,18390}, {12274,18392}, {12285,18394}, {12601,18404}, {12662,18406}, {12980,16808}, {12981,16809}, {13851,21653}, {17839,18405}, {18396,19461}, {18403,22809}, {18414,19490}, {18918,18937}, {19130,19143}, {19177,19199}
X(22817) = midpoint of X(382) and X(12303)
The reciprocal orthologic center of these triangles is X(3).
X(22818) lies on these lines: {3,18414}, {4,488}, {5,12973}, {30,9922}, {381,12979}, {382,12304}, {485,10897}, {542,12598}, {641,18420}, {3153,12222}, {3564,18569}, {3583,12911}, {3585,19474}, {3843,12312}, {6564,12961}, {6565,12967}, {12170,18386}, {12230,18388}, {12238,18390}, {12275,18392}, {12286,18394}, {12602,18404}, {12663,18406}, {12982,16808}, {12983,16809}, {13851,21654}, {17842,18405}, {18396,19462}, {18403,22810}, {18415,19491}, {18918,18938}, {19130,19144}, {19177,19200}
X(22818) = midpoint of X(382) and X(12304)
The reciprocal orthologic center of these triangles is X(3).
X(22819) lies on these lines: {4,69}, {5,12974}, {30,641}, {182,14233}, {381,1151}, {382,12305}, {542,9974}, {543,6311}, {3070,18539}, {3071,5476}, {3153,12223}, {3583,6283}, {3585,7362}, {3843,12313}, {3861,22596}, {5076,18511}, {5965,12602}, {6252,18406}, {6564,12962}, {6565,7747}, {9823,18420}, {10667,16808}, {10668,16809}, {12171,18386}, {12231,18388}, {12239,18390}, {12276,18392}, {12287,18394}, {12360,18531}, {12603,18404}, {13851,21655}, {17840,18405}, {18396,19463}, {18403,22811}, {18414,19492}, {18415,19494}, {18918,18941}, {19130,19145}, {19177,19201}
X(22819) = midpoint of X(382) and X(12305)
X(22819) = {X(4), X(3818)}-harmonic conjugate of X(22820)
The reciprocal orthologic center of these triangles is X(3).
X(22820) lies on these lines: {4,69}, {5,12975}, {30,642}, {182,14230}, {381,1152}, {382,12306}, {542,9975}, {543,6315}, {3070,5476}, {3153,12224}, {3583,6405}, {3585,7353}, {3843,12314}, {3861,22625}, {5076,18509}, {5965,12601}, {6404,18406}, {6564,7747}, {6565,12969}, {9824,18420}, {10671,16808}, {10672,16809}, {12172,18386}, {12232,18388}, {12240,18390}, {12277,18392}, {12288,18394}, {12361,18531}, {12604,18404}, {13851,21656}, {17843,18405}, {18396,19464}, {18403,22812}, {18414,19495}, {18415,19493}, {18918,18942}, {19130,19146}, {19177,19202}
X(22820) = midpoint of X(382) and X(12306)
X(22820) = {X(4), X(3818)}-harmonic conjugate of X(22819)
The reciprocal orthologic center of these triangles is X(10670).
X(22821) lies on these lines: {4,488}, {5,13049}, {30,13061}, {381,13055}, {382,13021}, {542,13037}, {3153,13009}, {3583,13043}, {3585,19475}, {3843,13023}, {6564,13045}, {6565,13047}, {13007,18386}, {13011,18388}, {13013,18390}, {13015,18392}, {13017,18394}, {13027,18531}, {13039,18404}, {13041,18406}, {13053,18420}, {13057,16808}, {13059,16809}, {13851,21657}, {17841,18405}, {18396,19465}, {18403,22813}, {18415,19497}, {18918,18943}, {19130,19147}, {19177,19203}
X(22821) = midpoint of X(382) and X(13021)
The reciprocal orthologic center of these triangles is X(10674).
X(22822) lies on these lines: {4,487}, {5,13050}, {30,13062}, {381,13056}, {382,13022}, {542,13038}, {3153,13010}, {3583,13044}, {3585,19476}, {3843,13024}, {6564,13046}, {6565,13048}, {13008,18386}, {13012,18388}, {13014,18390}, {13016,18392}, {13018,18394}, {13028,18531}, {13040,18404}, {13042,18406}, {13054,18420}, {13058,16808}, {13060,16809}, {13851,21658}, {17844,18405}, {18396,19466}, {18403,22814}, {18414,19496}, {18918,18944}, {19130,19148}, {19177,19204}
X(22822) = midpoint of X(382) and X(13022)
The reciprocal cyclologic center of these triangles is X(265).
X(22823) lies on these lines: {4,110}, {5,5961}, {30,13496}, {131,18404}, {381,13558}, {925,3153}, {11801,14854}, {18403,20957}
The reciprocal orthologic center of these triangles is X(14174).
X(22824) lies on these lines: {6,2981}, {511,16247}, {2854,16259}, {14173,16642}, {16638,22826}
The reciprocal orthologic center of these triangles is X(14180).
X(22825) lies on these lines: {6,6151}, {511,16248}, {2854,16260}, {14179,16643}, {16639,22827}
The reciprocal orthologic center of these triangles is X(14174).
X(22826) lies on these lines: {6,8014}, {13,524}, {69,11119}, {2854,16461}, {10217,16459}, {14173,16463}, {16638,22824}
The reciprocal orthologic center of these triangles is X(14180).
X(22827) lies on these lines: {6,8015}, {14,524}, {69,11120}, {2854,16462}, {10218,16460}, {14179,16464}, {16639,22825}
The reciprocal orthologic center of these triangles is X(22829).
X(22828) lies on these lines: {8542,22966}, {9970,22955}, {12584,22962}
The reciprocal orthologic center of these triangles is X(22828).
X(22829) lies on these lines: {6,25}, {54,19142}, {141,9027}, {511,548}, {524,7734}, {597,14913}, {1992,3313}, {2854,6329}, {3564,14128}, {3589,8681}, {3618,15531}, {3629,11574}, {3630,3819}, {3917,6144}, {5097,11255}, {5421,20975}, {5446,15520}, {5462,15516}, {5486,17040}, {6391,8542}, {6776,12290}, {8550,15105}, {8584,17710}, {11649,21852}
X(22829) = midpoint of X(3629) and X(11574)
X(22829) = reflection of X(5462) in X(15516)
X(22829) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 6467, 9969), (6, 19459, 19136)
The reciprocal orthologic center of these triangles is X(9729).
X(22830) lies on these lines: {6,2929}, {511,22978}, {542,22816}, {575,22962}, {895,15044}, {1992,22555}, {3090,8542}, {3520,5622}, {8537,9781}, {8538,22834}, {8539,22840}, {8540,22954}, {8541,22970}, {8548,9818}, {9813,22973}, {10602,19460}, {11405,22497}, {11416,22528}, {11443,22534}, {11458,22535}, {11470,22538}, {11477,22549}, {11482,22550}, {11511,22581}, {17813,17837}, {18449,22808}, {18919,18936}, {19178,19198}, {19369,19472}, {19426,19488}, {19427,19489}, {21639,21652}
X(22830) = midpoint of X(11477) and X(22549)
The reciprocal orthologic center of these triangles is X(3).
X(22831) lies on these lines: {2,22843}, {3,6674}, {4,16}, {5,619}, {11,18972}, {12,22865}, {17,23013}, {98,22522}, {115,398}, {235,22481}, {371,22876}, {372,22877}, {515,11740}, {546,5478}, {628,3091}, {1478,22885}, {1479,22884}, {1587,19069}, {1588,19072}, {1598,22656}, {1699,22651}, {3832,22114}, {3850,7684}, {3855,22845}, {3858,5480}, {5340,16943}, {5349,12815}, {5587,22851}, {5603,22867}, {6201,22854}, {6202,22853}, {6695,20378}, {8196,22669}, {8203,22673}, {8212,22863}, {8213,22864}, {8260,10612}, {9993,22745}, {10531,22886}, {10532,22887}, {10893,22857}, {10894,22858}, {10895,22859}, {10896,22860}, {11496,22557}, {11603,14639}, {11897,22852}, {13687,18585}, {13807,15765}, {16808,22856}, {22753,22771}
X(22831) = midpoint of X(4) and X(18)
X(22831) = reflection of X(3) in X(6674)
X(22831) = complement of X(22843)
X(22831) = {X(3858), X(5480)}-harmonic conjugate of X(22832)
The reciprocal orthologic center of these triangles is X(3).
X(22832) lies on these lines: {2,22890}, {3,6673}, {4,15}, {5,618}, {11,18973}, {12,22910}, {18,23006}, {98,22523}, {115,397}, {235,22482}, {371,22921}, {372,22922}, {381,532}, {515,11739}, {546,5479}, {627,3091}, {1478,22930}, {1479,22929}, {1587,19071}, {1588,19070}, {1598,22657}, {1699,22652}, {3832,22113}, {3850,7685}, {3855,22844}, {3858,5480}, {5339,16942}, {5350,12815}, {5587,22896}, {5603,22912}, {6201,22899}, {6202,22898}, {6694,20377}, {8196,22670}, {8203,22674}, {8212,22908}, {8213,22909}, {8259,10611}, {9993,22746}, {10531,22931}, {10532,22932}, {10893,22902}, {10894,22903}, {10895,22904}, {10896,22905}, {11496,22558}, {11602,14639}, {11897,22897}, {13687,15765}, {13807,18585}, {16809,22900}, {22753,22772}
X(22832) = midpoint of X(4) and X(17)
X(22832) = reflection of X(3) in X(6673)
X(22832) = complement of X(22890)
X(22832) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 16629, 16626), (3858, 5480, 22831)
The reciprocal orthologic center of these triangles is X(12241).
X(22833) lies on these lines: {2,22951}, {4,18936}, {5,12897}, {11,18978}, {12,22965}, {98,22524}, {125,1885}, {235,22483}, {371,22976}, {372,22977}, {378,2929}, {381,22955}, {515,22476}, {546,22800}, {974,22948}, {1478,22981}, {1479,22980}, {1587,19083}, {1588,19084}, {1598,22658}, {1699,22653}, {3091,22647}, {3574,10151}, {5587,22941}, {5603,22969}, {6201,22947}, {6202,22945}, {7699,22750}, {7706,10095}, {8212,22963}, {8213,22964}, {9815,22808}, {9927,22816}, {9993,22747}, {10531,22982}, {10532,22983}, {10893,22956}, {10894,22957}, {10895,22958}, {10896,22959}, {11250,22962}, {11496,22559}, {11897,22943}, {17928,22549}, {22753,22776}
X(22833) = midpoint of X(4) and X(22466)
X(22833) = complement of X(22951)
X(22833) = {X(381), X(22979)}-harmonic conjugate of X(22955)
The reciprocal orthologic center of these triangles is X(9729).
X(22834) lies on these lines: {2,22750}, {3,2929}, {4,22528}, {5,22970}, {30,22538}, {52,22530}, {68,3546}, {125,16196}, {155,19460}, {569,22529}, {1060,19472}, {1062,22954}, {1092,22953}, {1209,10257}, {1352,3548}, {1368,5562}, {1656,22973}, {2072,18488}, {4549,6643}, {5449,22647}, {6247,11585}, {6644,22483}, {7395,22497}, {7723,16003}, {8251,22840}, {8538,22830}, {10634,22974}, {10635,22975}, {10897,22960}, {10898,22961}, {11411,18936}, {11444,22534}, {11459,22535}, {12362,21663}, {12605,16111}, {17814,17822}, {18404,22816}, {18531,20427}, {19131,19142}, {19179,19198}, {19428,19488}, {19429,19489}
X(22834) = midpoint of X(i) and X(j) for these {i,j}: {3, 22808}, {4, 22528}
X(22834) = reflection of X(i) in X(j) for these (i,j): (3, 22581), (52, 22530)
X(22834) = complement of X(22750)
The reciprocal cyclologic center of these triangles is X(946).
X(22835) lies on these lines: {1,10893}, {2,13528}, {4,1319}, {5,10}, {11,1519}, {30,18857}, {36,1012}, {119,3880}, {474,2077}, {496,12608}, {515,1387}, {516,6681}, {912,12611}, {962,6931}, {1155,6833}, {1537,1737}, {1837,10598}, {1878,3259}, {2096,3086}, {3057,6941}, {3091,5176}, {3660,18238}, {3698,6975}, {3838,5886}, {4881,10724}, {5048,5252}, {5057,6837}, {5080,6957}, {5126,18483}, {5180,6860}, {5183,6879}, {5193,12114}, {5570,12047}, {5587,17618}, {5720,11235}, {6256,11373}, {6261,9669}, {6834,12701}, {6841,20288}, {6958,12699}, {6966,9812}, {7741,12672}, {9614,11500}, {9943,18856}, {10531,11375}, {10593,12616}, {10596,17718}, {10785,12679}, {10827,11522}, {10957,18839}, {11238,18446}, {12053,18242}
X(22835) = midpoint of X(i) and X(j) for these {i,j}: {4, 1319}, {11, 1519}, {1537, 1737}
X(22835) = reflection of X(i) in X(j) for these (i,j): (5570, 13374), (9943, 18856)
X(22835) = complement of X(13528)
X(22835) = inverse of X(7681) in the nine-point circle
X(22835) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (496, 12608, 12675), (946, 3817, 7680), (946, 7681, 7686), (5603, 6968, 5252)
The reciprocal orthologic center of these triangles is X(442).
X(22836) lies on these lines: {1,2}, {3,758}, {4,6326}, {20,5538}, {21,5692}, {30,18243}, {35,3869}, {36,3868}, {40,6876}, {46,4084}, {48,22021}, {55,3878}, {56,214}, {57,12559}, {63,3612}, {65,5440}, {72,993}, {79,17579}, {80,11681}, {100,5903}, {182,518}, {191,4189}, {224,4292}, {226,17647}, {326,3664}, {329,4305}, {354,17614}, {376,16132}, {377,11263}, {381,18549}, {404,5902}, {405,10176}, {474,5883}, {500,540}, {515,10526}, {516,6261}, {517,6796}, {524,5453}, {528,22791}, {535,18481}, {550,17768}, {908,10572}, {912,5450}, {920,17010}, {944,6903}, {946,12437}, {950,21616}, {952,12607}, {958,3678}, {960,5248}, {986,4256}, {991,17770}, {999,3881}, {1046,4257}, {1055,17736}, {1155,4018}, {1259,18389}, {1319,3555}, {1320,21398}, {1376,3754}, {1392,13143}, {1479,11813}, {1482,2802}, {1807,10570}, {1837,3814}, {2099,5687}, {2136,16200}, {2268,21078}, {2278,4053}, {2320,7161}, {2800,11248}, {2801,12114}, {2900,3817}, {2975,5904}, {3061,4251}, {3157,11700}, {3158,7982}, {3159,3191}, {3189,5603}, {3218,3901}, {3295,3884}, {3303,3898}, {3304,3892}, {3336,4188}, {3338,11520}, {3419,11375}, {3496,4262}, {3553,17355}, {3554,4856}, {3560,20117}, {3576,11523}, {3601,12514}, {3647,16370}, {3649,11112}, {3680,14497}, {3681,3897}, {3689,10914}, {3735,18755}, {3743,19765}, {3746,3877}, {3813,5901}, {3816,12433}, {3822,5794}, {3825,5722}, {3833,16408}, {3871,5697}, {3873,5563}, {3876,5251}, {3880,13374}, {3894,4881}, {3916,3962}, {3918,9709}, {3927,4127}, {3951,4525}, {3970,9310}, {3984,4134}, {3988,5220}, {3991,6603}, {4006,4390}, {4015,9708}, {4297,18446}, {4299,5905}, {4302,11415}, {4347,10571}, {4421,4930}, {4658,18465}, {4851,17073}, {4852,18261}, {4973,5204}, {5057,11015}, {5086,7951}, {5119,11682}, {5180,20066}, {5221,16371}, {5239,7006}, {5240,7005}, {5253,18398}, {5426,16865}, {5438,11529}, {5441,11114}, {5443,11680}, {5497,19582}, {5506,16859}, {5535,6942}, {5541,11280}, {5587,6873}, {5693,6906}, {5694,6914}, {5696,8543}, {5720,6866}, {5736,18698}, {5853,13464}, {5854,19907}, {6224,20060}, {6282,12512}, {6598,6829}, {6600,22770}, {6692,17706}, {6701,17528}, {6909,15071}, {6924,22935}, {6940,15016}, {6958,10265}, {6972,9803}, {7269,17151}, {7354,10609}, {7373,20116}, {7483,21677}, {7987,18444}, {8227,12625}, {8728,11281}, {9619,16973}, {10246,12513}, {10247,10912}, {10269,12005}, {10393,12572}, {10543,11113}, {10950,17757}, {10965,15558}, {11009,14923}, {11014,12245}, {11235,18493}, {11236,12738}, {11260,15178}, {11571,17100}, {11684,17549}, {12436,12563}, {13746,17188}, {15654,20760}, {15792,17512}, {18254,22760}
X(22836) = midpoint of X(i) and X(j) for these {i,j}: {1, 3811}, {3, 12635}, {946, 12437}, {1482, 3913}, {4421, 4930}
X(22836) = reflection of X(i) in X(j) for these (i,j): (3813, 5901), (11260, 15178)
X(22836) = inverse of X(5529) in the hexyl circle
X(22836) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 2, 30143), (1, 78, 10), (1, 997, 1125), (1, 3216, 3924), (1, 3632, 4861), (1, 3870, 3244), (1, 5312, 17016), (1, 5313, 5262), (1, 19861, 551), (8, 498, 10), (35, 4867, 3869), (55, 5730, 3878), (145, 5552, 10573), (3935, 4861, 3632), (5552, 10573, 10), (6737, 13411, 10)
The reciprocal orthologic center of these triangles is X(1145).
X(22837) lies on these lines: {1,2}, {3,2802}, {30,13463}, {35,3885}, {36,14923}, {72,5048}, {100,21842}, {101,4051}, {141,18261}, {214,1388}, {405,3898}, {515,10525}, {517,5450}, {518,576}, {529,22791}, {535,12699}, {758,1482}, {944,6264}, {952,3813}, {956,2098}, {958,3884}, {962,12543}, {993,3057}, {999,3754}, {1145,5433}, {1319,10914}, {1320,2975}, {1329,1387}, {1385,3880}, {1392,3467}, {1442,17151}, {1479,21630}, {1483,5499}, {2099,3874}, {3304,5883}, {3338,3919}, {3436,11813}, {3445,6095}, {3553,4856}, {3554,17355}, {3555,11011}, {3576,3680}, {3612,3895}, {3678,5289}, {3730,4919}, {3746,3897}, {3753,20323}, {3814,11376}, {3817,10599}, {3825,11373}, {3829,18357}, {3868,11009}, {3869,5288}, {3877,5258}, {3889,5425}, {3890,5251}, {3893,5440}, {3913,10246}, {3968,16408}, {4067,11682}, {4193,16173}, {4430,16126}, {5119,5267}, {5176,7741}, {5248,9957}, {5330,5692}, {5438,11525}, {5690,5854}, {5693,10698}, {5696,14151}, {5853,13607}, {5882,21627}, {5901,12607}, {6265,11256}, {6597,14497}, {6647,14377}, {6762,16200}, {6914,10284}, {6941,12751}, {7962,12514}, {8256,15325}, {8668,10269}, {9802,20066}, {10165,12640}, {10247,12635}, {10953,12053}, {11010,12653}, {11194,12702}, {11235,18525}, {11236,18493}, {11524,15015}, {12740,15863}, {13464,21077}, {18393,20060}, {19907,20400}
X(22837) = midpoint of X(i) and X(j) for these {i,j}: {3, 10912}, {5882, 21627}, {6265, 11256}
X(22837) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3632, 4511), (1, 4853, 997), (1, 12629, 3811), (1, 19860, 551), (8, 499, 10), (145, 10527, 12647), (956, 2098, 3878), (997, 4853, 3626), (1320, 2975, 5697), (1388, 5687, 214), (6264, 11014, 944), (10527, 12647, 10)
X(22838) lies on these lines: {6,22839}, {64,485}, {371,6525}, {3068,3183}, {18288,18289}
X(22839) lies on these lines: {6,22838}, {64,486}, {372,6525}, {3069,3183}, {8281,17830}, {18288,18290}
The reciprocal orthologic center of these triangles is X(9729).
X(22840) lies on these lines: {19,22970}, {40,22653}, {55,2929}, {65,775}, {71,22466}, {2550,22555}, {3101,22528}, {3197,17837}, {3611,21652}, {5415,22960}, {5416,22961}, {5584,22549}, {6197,22750}, {7688,22978}, {8251,22834}, {8539,22830}, {9816,22973}, {10306,22550}, {10319,22581}, {10636,22974}, {10637,22975}, {10902,22962}, {11406,22497}, {11428,22529}, {11435,22530}, {11445,22534}, {11460,22535}, {11471,22538}, {18406,22816}, {18453,22808}, {18921,18936}, {19133,19142}, {19181,19198}, {19350,19460}, {19432,19488}, {19433,19489}
The reciprocal orthologic center of these triangles is X(4).
X(22841) lies on these lines: {1,11828}, {3,11377}, {4,8214}, {10,8212}, {40,493}, {46,11953}, {65,11947}, {515,12636}, {516,9838}, {517,10669}, {946,8222}, {962,6462}, {1702,19032}, {1703,19031}, {1836,11930}, {1902,11394}, {2800,13275}, {2802,12765}, {3057,18963}, {5119,11951}, {5812,10951}, {5840,12741}, {6001,12986}, {6361,11846}, {6461,22842}, {7982,8210}, {7991,8188}, {8194,9911}, {8201,12458}, {8208,12459}, {8216,12697}, {8218,12698}, {8220,12699}, {10306,11503}, {10875,12497}, {10945,12700}, {10981,12441}, {11840,12197}, {11907,12696}, {11932,12701}, {11949,12702}, {11955,12703}, {11957,12704}, {13899,13912}, {13956,13975}, {18520,22793}, {22761,22770}
The reciprocal orthologic center of these triangles is X(4).
X(22842) lies on these lines: {1,11829}, {3,11378}, {4,8215}, {10,8213}, {40,494}, {46,11954}, {65,11948}, {515,12637}, {516,9839}, {517,10673}, {946,8223}, {962,6463}, {1702,19034}, {1703,19033}, {1836,11931}, {1902,11395}, {2800,13276}, {2802,12766}, {3057,18964}, {5119,11952}, {5812,10952}, {5840,12742}, {6001,12987}, {6361,11847}, {6461,22841}, {7982,8211}, {7991,8189}, {8195,9911}, {8202,12458}, {8209,12459}, {8217,12697}, {8219,12698}, {8221,12699}, {10306,11504}, {10876,12497}, {10946,12700}, {10981,12440}, {11841,12197}, {11908,12696}, {11933,12701}, {11950,12702}, {11956,12703}, {11958,12704}, {13900,13912}, {13957,13975}, {18522,22793}, {22762,22770}
The reciprocal orthologic center of these triangles is X(3).
X(22843) lies on these lines: {2,22831}, {3,14}, {4,630}, {15,22862}, {20,622}, {30,16627}, {35,22884}, {36,22885}, {55,18972}, {56,22865}, {165,22651}, {182,22522}, {371,19072}, {372,19069}, {382,22794}, {515,22851}, {517,22867}, {548,14538}, {550,5473}, {631,6674}, {1350,5965}, {1593,22481}, {2043,13666}, {2044,13786}, {3098,22745}, {3411,13349}, {3428,22771}, {3522,22114}, {3534,22494}, {3576,11740}, {5352,21156}, {5983,9749}, {6284,22860}, {6772,16772}, {7354,22859}, {7748,11480}, {7782,11133}, {9540,22876}, {10310,22557}, {10646,22856}, {11248,22886}, {11249,22887}, {11414,22656}, {11822,22669}, {11823,22673}, {11824,22853}, {11825,22854}, {11826,22857}, {11827,22858}, {11828,22863}, {11829,22864}, {13935,22877}, {14139,21159}
X(22843) = midpoint of X(20) and X(628)
X(22843) = reflection of X(i) in X(j) for these (i,j): (4, 630), (382, 22794)
X(22843) = anticomplement of X(22831)
X(22843) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 5339, 21157), (550, 14541, 5473), (1350, 15696, 22890)
The reciprocal orthologic center of these triangles is X(22845).
X(22844) lies on these lines: {2,17}, {3,5965}, {15,11008}, {16,3631}, {61,3629}, {69,5237}, {298,7860}, {382,5864}, {524,5238}, {546,16626}, {550,5474}, {618,3412}, {3104,22901}, {3244,22912}, {3528,22532}, {3626,22896}, {3851,16629}, {3855,22832}, {5340,21359}, {5351,5464}, {5463,22236}, {5487,12821}, {5858,16964}, {5982,6778}, {11309,16960}, {12815,16645}, {14269,22795}
X(22844) = anticomplement of X(33465)
X(22844) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (627, 22113, 629), (629, 22113, 17), (22927, 22928, 627)
The reciprocal orthologic center of these triangles is X(22844).
X(22845) lies on these lines: {2,18}, {3,5965}, {15,3631}, {16,11008}, {62,3629}, {69,5238}, {299,7860}, {382,5865}, {524,5237}, {546,16627}, {550,5473}, {619,3411}, {3105,22855}, {3244,22867}, {3528,22531}, {3626,22851}, {3851,16628}, {3855,22831}, {5339,21360}, {5352,5463}, {5464,22238}, {5488,12820}, {5859,16965}, {11310,16961}, {12815,16644}, {14269,22794}
X(22845) = anticomplement of X(33464)
X(22845) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (628, 22114, 630), (630, 22114, 18), (22882, 22883, 628)
The reciprocal orthologic center of these triangles is X(616).
X(22846) lies on these lines: {2,5470}, {3,16631}, {5,13}, {14,6770}, {15,115}, {16,13103}, {17,628}, {61,16628}, {182,18362}, {299,22736}, {542,10612}, {618,6674}, {621,16529}, {630,6669}, {1080,5478}, {3054,5473}, {3107,7697}, {5237,12815}, {5352,21156}, {5965,10611}, {6772,22893}, {6778,18581}, {8859,12205}, {9982,16808}, {10062,22885}, {10078,22884}, {11303,22866}, {11542,22855}, {14061,22687}, {16941,18582}, {16960,22849}, {16965,22531}, {19069,19074}, {19072,19073}
X(22846) = reflection of X(i) in X(j) for these (i,j): (618, 6674), (630, 6669)
X(22846) = complement of X(14145)
X(22846) = inverse of X(22738) in the inner-Napoleon circle
X(22846) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (13, 22511, 62), (182, 18362, 22891)
The reciprocal orthologic center of these triangles is X(616).
X(22847) lies on these lines: {2,11121}, {5,13}, {30,10617}, {115,618}, {141,6034}, {381,22861}, {383,9756}, {398,6771}, {549,5469}, {616,16645}, {628,16644}, {630,6673}, {3642,7746}, {3643,18362}, {5461,22573}, {6036,6109}, {6108,22796}, {6118,13876}, {6775,22891}, {9166,14904}, {10654,16628}, {11290,14145}, {16267,22855}, {16962,22849}
X(22847) = midpoint of X(115) and X(22848)
X(22847) = {X(6034), X(14061)}-harmonic conjugate of X(22893)
The reciprocal orthologic center of these triangles is X(14).
X(22848) lies on these lines: {2,6151}, {3,14}, {16,22797}, {99,11121}, {114,6108}, {115,618}, {140,14137}, {381,22862}, {396,630}, {617,5471}, {629,6674}, {641,13875}, {642,13928}, {1649,9200}, {2482,22574}, {3411,16529}, {3589,22892}, {6303,13701}, {6307,13821}, {6772,14145}, {6780,22849}, {7749,22866}, {9886,11147}, {10653,16627}, {15819,22692}, {16268,22856}, {16963,22850}
X(22848) = midpoint of X(i) and X(j) for these {i,j}: {99, 11121}, {6780, 22849}
X(22848) = reflection of X(115) in X(22847)
The reciprocal orthologic center of these triangles is X(616).
X(22849) lies on these lines: {15,18}, {16,22114}, {628,16966}, {3411,19780}, {6780,22848}, {16628,16809}, {16960,22846}, {16962,22847}, {16964,22861}
X(22849) = reflection of X(6780) in X(22848)
X(22849) = {X(16628), X(22850)}-harmonic conjugate of X(16809)
The reciprocal orthologic center of these triangles is X(14).
X(22850) lies on these lines: {2,3170}, {6,17}, {14,299}, {15,628}, {16,5613}, {303,22866}, {2381,11601}, {3104,22871}, {3105,16627}, {3643,11132}, {6114,7779}, {6672,22998}, {7788,22665}, {10646,22531}, {11301,16241}, {11543,22510}, {16628,16809}, {16941,18582}, {16963,22848}, {16965,22862}, {18581,22114}
X(22850) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18, 22855, 6), (628, 22861, 15), (16809, 22849, 16628), (16967, 22901, 16961)
The reciprocal orthologic center of these triangles is X(3).
X(22851) lies on these lines: {1,630}, {2,11740}, {8,628}, {10,18}, {65,22859}, {72,22858}, {355,12780}, {515,22843}, {517,16627}, {519,22867}, {956,22771}, {1018,6191}, {1698,6674}, {1737,22885}, {1837,22865}, {3057,22860}, {3416,5965}, {3617,22114}, {3626,22845}, {5090,22481}, {5252,18972}, {5587,22831}, {5657,22531}, {5687,22557}, {5688,22854}, {5689,22853}, {5690,12781}, {5790,16628}, {8193,22656}, {8197,22669}, {8204,22673}, {8214,22863}, {8215,22864}, {9857,22745}, {10039,22884}, {10791,22522}, {10914,22857}, {10915,22886}, {10916,22887}, {12699,22794}, {13883,19072}, {13893,22876}, {13936,19069}, {13947,22877}
X(22851) = midpoint of X(8) and X(628)
X(22851) = reflection of X(i) in X(j) for these (i,j): (1, 630), (12699, 22794)
X(22851) = anticomplement of X(11740)
The reciprocal orthologic center of these triangles is X(3).
X(22852) lies on these lines: {18,402}, {30,16627}, {628,4240}, {630,1650}, {5965,12583}, {6674,15183}, {11251,12792}, {11740,11831}, {11832,22481}, {11839,22522}, {11845,22531}, {11848,22557}, {11852,22651}, {11853,22656}, {11885,22745}, {11897,22831}, {11901,22853}, {11902,22854}, {11903,22857}, {11904,22858}, {11905,22859}, {11906,22860}, {11907,22863}, {11908,22864}, {11909,22865}, {11910,22867}, {11911,16628}, {11912,22884}, {11913,22885}, {11914,22886}, {11915,22887}, {13894,22876}, {13948,22877}, {18507,22794}, {18958,18972}, {19017,19069}, {19018,19072}, {22755,22771}
X(22852) = midpoint of X(628) and X(4240)
X(22852) = reflection of X(i) in X(j) for these (i,j): (18, 402), (18507, 22794)
The reciprocal orthologic center of these triangles is X(3).
X(22853) lies on these lines: {6,17}, {628,1271}, {630,5591}, {1161,6271}, {5589,22651}, {5595,22656}, {5605,22867}, {5689,22851}, {5875,6270}, {6202,22831}, {6215,16627}, {8198,22669}, {8205,22673}, {8216,22863}, {8217,22864}, {8974,22876}, {9994,22745}, {10040,22884}, {10048,22885}, {10783,22531}, {10792,22522}, {10919,22857}, {10921,22858}, {10923,22859}, {10925,22860}, {10927,22865}, {10929,22886}, {10931,22887}, {11370,11740}, {11388,22481}, {11497,22557}, {11824,22843}, {11901,22852}, {11916,16628}, {13949,22877}, {18509,22794}, {18959,18972}, {22756,22771}
The reciprocal orthologic center of these triangles is X(3).
X(22854) lies on these lines: {6,17}, {628,1270}, {630,5590}, {1160,6269}, {5588,22651}, {5594,22656}, {5604,22867}, {5688,22851}, {5874,6268}, {6201,22831}, {6214,16627}, {8199,22669}, {8206,22673}, {8218,22863}, {8219,22864}, {8975,22876}, {9995,22745}, {10041,22884}, {10049,22885}, {10784,22531}, {10793,22522}, {10920,22857}, {10922,22858}, {10924,22859}, {10926,22860}, {10928,22865}, {10930,22886}, {10932,22887}, {11371,11740}, {11389,22481}, {11498,22557}, {11825,22843}, {11902,22852}, {11917,16628}, {13950,22877}, {18511,22794}, {18960,18972}, {22757,22771}
The reciprocal orthologic center of these triangles is X(616).
X(22855) lies on these lines: {6,17}, {16,628}, {61,22861}, {299,11133}, {3105,22845}, {5464,5859}, {5873,16964}, {6778,13103}, {7837,22665}, {10645,22531}, {11542,22846}, {16267,22847}, {16529,19780}, {16627,16809}, {16628,16808}, {18582,22114}
X(22855) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 22850, 18), (16627, 22856, 16809), (16960, 22894, 16966)
The reciprocal orthologic center of these triangles is X(14).
X(22856) lies on these lines: {6,16628}, {14,299}, {15,18}, {16,5471}, {62,22862}, {628,18581}, {630,16967}, {3104,5334}, {5321,6777}, {6672,6780}, {10646,22843}, {16268,22848}, {16627,16809}, {16808,22831}, {16961,23013}
X(22856) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5334, 22114, 22861), (16809, 22855, 16627)
The reciprocal orthologic center of these triangles is X(3).
X(22857) lies on these lines: {11,18}, {12,22886}, {355,16627}, {628,3434}, {630,1376}, {5965,12586}, {10523,22884}, {10525,12921}, {10785,22531}, {10794,22522}, {10826,22651}, {10829,22656}, {10871,22745}, {10893,22831}, {10914,22851}, {10919,22853}, {10920,22854}, {10943,12922}, {10944,22859}, {10945,22863}, {10946,22864}, {10947,22865}, {10948,22885}, {10949,22887}, {11373,11740}, {11390,22481}, {11826,22843}, {11865,22669}, {11866,22673}, {11903,22852}, {11928,16628}, {12114,22771}, {13895,22876}, {13952,22877}, {18516,22794}, {18961,18972}, {19023,19069}, {19024,19072}
The reciprocal orthologic center of these triangles is X(3).
X(22858) lies on these lines: {11,22887}, {12,18}, {72,22851}, {355,16627}, {628,3436}, {630,958}, {5965,12587}, {10523,22885}, {10526,12931}, {10786,22531}, {10795,22522}, {10827,22651}, {10830,22656}, {10872,22745}, {10894,22831}, {10921,22853}, {10922,22854}, {10942,12932}, {10950,22860}, {10951,22863}, {10952,22864}, {10953,22865}, {10954,22884}, {10955,22886}, {11374,11740}, {11391,22481}, {11500,22557}, {11827,22843}, {11867,22669}, {11868,22673}, {11904,22852}, {11929,16628}, {13896,22876}, {13953,22877}, {18517,22794}, {18962,18972}, {19025,19069}, {19026,19072}
The reciprocal orthologic center of these triangles is X(3).
X(22859) lies on these lines: {1,16627}, {4,22865}, {5,22885}, {12,18}, {56,630}, {65,22851}, {388,628}, {495,10062}, {1478,12941}, {1479,22794}, {3027,11603}, {3085,22531}, {5261,22114}, {5965,12588}, {7354,22843}, {9578,22651}, {9654,16628}, {10797,22522}, {10831,22656}, {10873,22745}, {10895,22831}, {10923,22853}, {10924,22854}, {10944,22857}, {10956,22886}, {10957,22887}, {11375,11740}, {11392,22481}, {11501,22557}, {11869,22669}, {11870,22673}, {11905,22852}, {11930,22863}, {11931,22864}, {13897,22876}, {13954,22877}, {14145,18974}, {19027,19069}, {19028,19072}, {22759,22771}
X(22859) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 16627, 22860), (388, 628, 18972)
The reciprocal orthologic center of these triangles is X(3).
X(22860) lies on these lines: {1,16627}, {4,18972}, {5,22884}, {11,18}, {55,630}, {496,10078}, {497,628}, {1478,22794}, {1479,12951}, {3023,11603}, {3057,22851}, {3086,22531}, {5274,22114}, {5965,12589}, {6284,22843}, {9581,22651}, {9669,16628}, {10798,22522}, {10832,22656}, {10874,22745}, {10896,22831}, {10925,22853}, {10926,22854}, {10950,22858}, {10958,22886}, {10959,22887}, {11376,11740}, {11393,22481}, {11502,22557}, {11871,22669}, {11872,22673}, {11906,22852}, {11932,22863}, {11933,22864}, {13076,14145}, {13898,22876}, {13955,22877}, {19029,19069}, {19030,19072}, {22760,22771}
X(22860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 16627, 22859), (497, 628, 22865)
The reciprocal orthologic center of these triangles is X(616).
X(22861) lies on these lines: {4,16}, {5,19780}, {14,148}, {15,628}, {32,16627}, {61,22855}, {381,22847}, {624,22866}, {3098,22512}, {3104,5334}, {5321,16628}, {6114,10646}, {6782,16940}, {7693,21466}, {7737,9996}, {8260,11486}, {9982,16808}, {10653,19130}, {16964,22849}
X(22861) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (15, 22850, 628), (5334, 22114, 22856)
The reciprocal orthologic center of these triangles is X(14).
X(22862) lies on these lines: {4,16}, {6,23013}, {13,99}, {15,22843}, {62,22856}, {381,22848}, {628,5335}, {630,18582}, {1250,22884}, {3054,5473}, {3105,22845}, {5318,16627}, {5321,8260}, {6115,14145}, {7747,11486}, {11133,11303}, {11308,16966}, {12017,22906}, {14137,23004}, {16808,16943}, {16965,22850}, {19373,22885}, {22513,23006}
The reciprocal orthologic center of these triangles is X(3).
X(22863) lies on these lines: {18,493}, {628,6462}, {630,8222}, {5965,12590}, {6461,22864}, {8188,22651}, {8194,22656}, {8210,22867}, {8212,22831}, {8214,22851}, {8216,22853}, {8218,22854}, {8220,16627}, {10669,12988}, {10875,22745}, {10945,22857}, {10951,22858}, {11377,11740}, {11394,22481}, {11503,22557}, {11828,22843}, {11840,22522}, {11846,22531}, {11907,22852}, {11930,22859}, {11932,22860}, {11947,22865}, {11949,16628}, {11951,22884}, {11953,22885}, {11955,22886}, {11957,22887}, {13899,22876}, {13956,22877}, {18520,22794}, {18963,18972}, {19031,19069}, {19032,19072}, {22761,22771}
The reciprocal orthologic center of these triangles is X(3).
X(22864) lies on these lines: {18,494}, {628,6463}, {630,8223}, {5965,12591}, {6461,22863}, {8189,22651}, {8195,22656}, {8211,22867}, {8213,22831}, {8215,22851}, {8217,22853}, {8219,22854}, {8221,16627}, {10673,12989}, {10876,22745}, {10946,22857}, {10952,22858}, {11378,11740}, {11395,22481}, {11504,22557}, {11829,22843}, {11841,22522}, {11847,22531}, {11908,22852}, {11931,22859}, {11933,22860}, {11948,22865}, {11950,16628}, {11952,22884}, {11954,22885}, {11956,22886}, {11958,22887}, {13900,22876}, {13957,22877}, {18522,22794}, {18964,18972}, {19033,19069}, {19034,19072}, {22762,22771}
The reciprocal orthologic center of these triangles is X(3).
X(22865) lies on these lines: {1,13075}, {3,22885}, {4,22859}, {11,630}, {12,22831}, {18,55}, {33,22481}, {56,22843}, {390,22114}, {497,628}, {1479,16627}, {1697,22651}, {1837,22851}, {2098,22867}, {2646,11740}, {3056,5965}, {3295,16628}, {3583,22794}, {4294,22531}, {5432,6674}, {10799,22522}, {10833,22656}, {10877,22745}, {10927,22853}, {10928,22854}, {10947,22857}, {10953,22858}, {10965,22886}, {10966,22771}, {11603,13183}, {11873,22669}, {11874,22673}, {11909,22852}, {11947,22863}, {11948,22864}, {12952,14145}, {13076,15171}, {13901,22876}, {13958,22877}, {19037,19069}, {19038,19072}
X(22865) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497, 628, 22860), (3295, 16628, 22884)
The reciprocal orthologic center of these triangles is X(22568).
X(22866) lies on these lines: {2,18}, {3,22568}, {76,16241}, {303,22850}, {624,22861}, {1078,3643}, {3642,7746}, {6294,11171}, {6298,10104}, {7749,22848}, {11303,22846}
X(22866) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18, 628, 22736), (630, 22869, 22871)
The reciprocal orthologic center of these triangles is X(3).
X(22867) lies on these lines: {1,18}, {8,630}, {55,22771}, {56,22557}, {145,628}, {517,22843}, {519,22851}, {952,16627}, {1482,7974}, {1483,7975}, {2098,22865}, {2099,18972}, {3242,5965}, {3244,22845}, {3616,6674}, {3623,22114}, {5597,22673}, {5598,22669}, {5603,22831}, {5604,22854}, {5605,22853}, {7967,22531}, {7968,19069}, {7969,19072}, {8192,22656}, {8210,22863}, {8211,22864}, {9997,22745}, {10247,16628}, {10800,22522}, {10944,22857}, {10950,22858}, {11396,22481}, {11910,22852}, {13902,22876}, {13959,22877}, {18525,22794}
X(22867) = midpoint of X(145) and X(628)
X(22867) = reflection of X(i) in X(j) for these (i,j): (8, 630), (18525, 22794)
X(22867) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22651, 11740), (11740, 22651, 18), (22886, 22887, 18)
The reciprocal orthologic center of these triangles is X(22869).
X(22868) lies on these lines: {2,39}, {3,22869}, {621,7758}, {698,3104}, {732,3105}, {3095,16626}, {5981,7751}
X(22868) = anticomplement of X(33466)
X(22868) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (39, 22913, 6581), (6294, 22913, 39), (6314, 6318, 6294)
The reciprocal orthologic center of these triangles is X(22868).
X(22869) lies on these lines: {2,18}, {3,22868}, {98,14541}, {3098,22914}, {3642,7755}, {5865,9756}, {5965,22916}, {6287,7684}, {6295,7751}, {6582,7780}, {10645,20081}
X(22869) = circumtangential isogonal conjugate of X(62)
X(22869) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (22866, 22871, 630), (22882, 22883, 22736)
The reciprocal orthologic center of these triangles is X(22871).
X(22870) lies on these lines: {2,32}, {3,22871}, {732,3104}, {6287,7685}
X(22870) = anticomplement of X(33468)
X(22870) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6292, 22915, 6296), (6297, 22915, 6292), (6313, 6317, 6297)
The reciprocal orthologic center of these triangles is X(22870).
X(22871) lies on these lines: {2,18}, {3,22870}, {13,13571}, {14,7814}, {3095,16627}, {3104,22850}, {3643,7796}, {3818,22916}, {5965,22914}, {6298,7764}, {6299,7759}, {16626,16628}
X(22871) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (628, 22114, 61), (630, 22869, 22866), (22882, 22883, 22683)
The reciprocal orthologic center of these triangles is X(22873).
X(22872) lies on these lines: {2,1327}, {30,6305}, {2044,13687}, {3104,23011}, {5460,13928}, {13692,16626}, {16645,22874}
X(22872) = anticomplement of X(33470)
X(22872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1327, 22917), (2, 13712, 13704), (13678, 13712, 22917), (13701, 22917, 13706), (13704, 22917, 13701)
The reciprocal orthologic center of these triangles is X(22872).
X(22873) lies on these lines: {11489,22875}, {19072,22879}, {22876,22883}, {22880,22882}
The reciprocal orthologic center of these triangles is X(22875).
X(22874) lies on these lines: {2,1328}, {30,6301}, {2043,13807}, {3104,23012}, {5460,13850}, {13812,16626}, {16645,22872}
X(22874) = anticomplement of X(33472)
X(22874) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1328, 22919), (2, 13835, 13824), (13798, 13835, 22919), (13821, 22919, 13826), (13824, 22919, 13821)
The reciprocal orthologic center of these triangles is X(22874).
X(22875) lies on these lines: {11489,22873}, {19069,22878}, {22877,22882}, {22881,22883}
The reciprocal orthologic center of these triangles is X(3).
X(22876) lies on these lines: {2,19072}, {6,6674}, {18,3068}, {371,22831}, {590,630}, {628,8972}, {5965,13910}, {7585,19069}, {8974,22853}, {8975,22854}, {8976,16627}, {8981,13916}, {9540,22843}, {11740,13883}, {13884,22481}, {13885,22522}, {13886,22531}, {13887,22557}, {13888,22651}, {13889,22656}, {13890,22669}, {13891,22673}, {13892,22745}, {13893,22851}, {13894,22852}, {13895,22857}, {13896,22858}, {13897,22859}, {13898,22860}, {13899,22863}, {13900,22864}, {13901,22865}, {13902,22867}, {13903,16628}, {13904,22884}, {13905,22885}, {13906,22886}, {13907,22887}, {13917,13925}, {18538,22794}, {18965,18972}, {22763,22771}, {22873,22883}
X(22876) = {X(6), X(6674)}-harmonic conjugate of X(22877)
The reciprocal orthologic center of these triangles is X(3).
X(22877) lies on these lines: {2,19069}, {6,6674}, {18,3069}, {372,22831}, {615,630}, {628,13941}, {5965,13972}, {7586,19072}, {11740,13936}, {13935,22843}, {13937,22481}, {13938,22522}, {13939,22531}, {13940,22557}, {13942,22651}, {13943,22656}, {13944,22669}, {13945,22673}, {13946,22745}, {13947,22851}, {13948,22852}, {13949,22853}, {13950,22854}, {13951,16627}, {13952,22857}, {13953,22858}, {13954,22859}, {13955,22860}, {13956,22863}, {13957,22864}, {13958,22865}, {13959,22867}, {13961,16628}, {13962,22884}, {13963,22885}, {13964,22886}, {13965,22887}, {13966,13981}, {13982,13993}, {18762,22794}, {18966,18972}, {22764,22771}, {22875,22882}
X(22877) = {X(6), X(6674)}-harmonic conjugate of X(22876)
The reciprocal orthologic center of these triangles is X(5858).
X(22878) lies on these lines: {2,22879}, {13637,22487}, {13638,22665}, {13644,22923}, {19069,22875}, {19072,22883}
The reciprocal orthologic center of these triangles is X(5858).
X(22879) lies on these lines: {2,22878}, {13757,22487}, {13758,22665}, {13763,22924}, {19069,22882}, {19072,22873}
The reciprocal orthologic center of these triangles is X(22627).
X(22880) lies on these lines: {18,485}, {590,22883}, {630,13882}, {641,13875}, {6118,13876}, {6305,13850}, {6674,11312}, {12815,22925}, {16645,22627}, {22873,22882}
The reciprocal orthologic center of these triangles is X(22598).
X(22881) lies on these lines: {18,486}, {615,22882}, {630,13934}, {642,13928}, {6301,13932}, {6674,11312}, {12815,22926}, {16645,22598}, {22875,22883}
The reciprocal orthologic center of these triangles is X(22598).
X(22882) lies on these lines: {2,18}, {3,22598}, {615,22881}, {5965,22928}, {6289,16627}, {6561,22597}, {19069,22879}, {22873,22880}, {22875,22877}
X(22882) = complement of X(33437)
X(22882) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18, 22114, 22883), (628, 22845, 22883), (22683, 22871, 22883), (22736, 22869, 22883)
The reciprocal orthologic center of these triangles is X(22627).
X(22883) lies on these lines: {2,18}, {3,22627}, {590,22880}, {3642,8960}, {5965,22927}, {6290,16627}, {6560,22626}, {19072,22878}, {22873,22876}, {22875,22881}
X(22883) = complement of X(33436)
X(22883) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18, 22114, 22882), (628, 22845, 22882), (22683, 22871, 22882), (22736, 22869, 22882)
The reciprocal orthologic center of these triangles is X(3).
X(22884) lies on these lines: {1,18}, {3,18972}, {5,22860}, {12,16627}, {35,22843}, {55,10061}, {388,22531}, {495,10062}, {498,630}, {499,6674}, {611,5965}, {628,3085}, {1250,22862}, {1479,22831}, {3295,16628}, {3299,19069}, {3301,19072}, {10037,22656}, {10038,22745}, {10039,22851}, {10040,22853}, {10041,22854}, {10077,10612}, {10078,22846}, {10523,22857}, {10801,22522}, {10895,22794}, {10954,22858}, {11398,22481}, {11507,22557}, {11877,22669}, {11878,22673}, {11912,22852}, {11951,22863}, {11952,22864}, {12815,22930}, {13904,22876}, {13962,22877}, {22766,22771}
X(22884) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18, 22885), (3295, 16628, 22865)
The reciprocal orthologic center of these triangles is X(3).
X(22885) lies on these lines: {1,18}, {3,22865}, {5,22859}, {11,16627}, {36,22843}, {56,10077}, {496,10078}, {497,22531}, {498,6674}, {499,630}, {613,5965}, {628,3086}, {999,16628}, {1478,22831}, {1737,22851}, {3299,19072}, {3301,19069}, {10046,22656}, {10047,22745}, {10048,22853}, {10049,22854}, {10061,10612}, {10062,22846}, {10523,22858}, {10802,22522}, {10896,22794}, {10948,22857}, {11399,22481}, {11508,22557}, {11879,22669}, {11880,22673}, {11913,22852}, {11953,22863}, {11954,22864}, {12815,22929}, {13905,22876}, {13963,22877}, {14986,22114}, {19373,22862}, {22767,22771}
X(22885) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18, 22884), (999, 16628, 18972)
The reciprocal orthologic center of these triangles is X(3).
X(22886) lies on these lines: {1,18}, {12,22857}, {628,10528}, {630,5552}, {5965,12594}, {10531,22831}, {10679,13104}, {10803,22522}, {10805,22531}, {10834,22656}, {10878,22745}, {10915,22851}, {10929,22853}, {10930,22854}, {10942,16627}, {10955,22858}, {10956,22859}, {10958,22860}, {10965,22865}, {11248,22843}, {11400,22481}, {11509,18972}, {11881,22669}, {11882,22673}, {11914,22852}, {11955,22863}, {11956,22864}, {12000,16628}, {13906,22876}, {13964,22877}, {18542,22794}, {19047,19069}, {19048,19072}, {22768,22771}
X(22886) = {X(18), X(22867)}-harmonic conjugate of X(22887)
The reciprocal orthologic center of these triangles is X(3).
X(22887) lies on these lines: {1,18}, {11,22858}, {628,10529}, {630,10527}, {5965,12595}, {10532,22831}, {10680,13106}, {10804,22522}, {10806,22531}, {10835,22656}, {10879,22745}, {10916,22851}, {10931,22853}, {10932,22854}, {10943,16627}, {10949,22857}, {10957,22859}, {10959,22860}, {10966,22771}, {11249,22843}, {11401,22481}, {11510,22557}, {11883,22669}, {11884,22673}, {11915,22852}, {11957,22863}, {11958,22864}, {12001,16628}, {13907,22876}, {13965,22877}, {18544,22794}, {18967,18972}, {19049,19069}, {19050,19072}
X(22887) = {X(18), X(22867)}-harmonic conjugate of X(22886)
The reciprocal parallelogic center of these triangles is X(3).
X(22888) lies on these lines: {351,9201}, {9135,22933}, {13305,14610}
The reciprocal parallelogic center of these triangles is X(3).
X(22889) lies on these lines: {2,14447}, {351,9201}, {3569,22934}, {6137,9979}
The reciprocal orthologic center of these triangles is X(3).
X(22890) lies on these lines: {2,22832}, {3,13}, {4,629}, {16,22906}, {20,621}, {30,16626}, {35,22929}, {36,22930}, {55,18973}, {56,22910}, {165,22652}, {182,22523}, {371,19070}, {372,19071}, {376,532}, {382,22795}, {515,22896}, {517,22912}, {548,14539}, {550,5474}, {631,6673}, {1350,5965}, {1593,22482}, {2043,13786}, {2044,13666}, {3098,22746}, {3412,13350}, {3522,22113}, {3534,22493}, {5351,21157}, {5982,9750}, {6284,22905}, {6775,16773}, {7354,22904}, {7748,11481}, {7782,11132}, {9540,22921}, {10310,22558}, {10645,22900}, {11248,22931}, {11249,22932}, {11414,22657}, {11822,22670}, {11823,22674}, {11824,22898}, {11825,22899}, {11826,22902}, {11827,22903}, {11828,22908}, {11829,22909}, {13935,22922}, {14138,21158}
X(22890) = midpoint of X(20) and X(627)
X(22890) = reflection of X(i) in X(j) for these (i,j): (4, 629), (382, 22795)
X(22890) = anticomplement of X(22832)
X(22890) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 5340, 21156), (550, 14540, 5474), (1350, 15696, 22843)
The reciprocal orthologic center of these triangles is X(617).
X(22891) lies on these lines: {2,5469}, {3,16630}, {5,14}, {13,6773}, {15,13102}, {16,115}, {18,627}, {62,16629}, {182,18362}, {298,22737}, {383,5479}, {532,5460}, {542,10611}, {619,6673}, {622,16530}, {629,6670}, {3054,5474}, {3106,7697}, {5238,12815}, {5351,21157}, {5965,10612}, {6775,22847}, {6777,18582}, {8859,12204}, {9981,16809}, {10061,22930}, {10077,22929}, {11304,22911}, {11543,22901}, {14061,22689}, {16940,18581}, {16961,22895}, {16964,22532}, {19070,19075}, {19071,19076}
X(22891) = reflection of X(i) in X(j) for these (i,j): (619, 6673), (629, 6670)
X(22891) = complement of X(14144)
X(22891) = inverse of X(22739) in the outer-Napoleon circle
X(22891) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (14, 22510, 61), (182, 18362, 22846)
The reciprocal orthologic center of these triangles is X(13).
X(22892) lies on these lines: {2,2981}, {3,13}, {15,22796}, {99,11122}, {114,6109}, {115,619}, {140,14136}, {381,22906}, {395,629}, {396,532}, {616,5472}, {630,6673}, {641,13876}, {642,13929}, {1649,9201}, {2482,22573}, {3412,16530}, {3589,22848}, {6302,13701}, {6306,13821}, {6775,14144}, {6779,22895}, {7749,22911}, {9885,11147}, {10654,16626}, {15819,22691}, {16267,22900}, {16962,22894}
X(22892) = midpoint of X(i) and X(j) for these {i,j}: {99, 11122}, {6779, 22895}
X(22892) = reflection of X(115) in X(22893)
The reciprocal orthologic center of these triangles is X(617).
X(22893) lies on these lines: {2,11122}, {5,14}, {30,10616}, {115,619}, {141,6034}, {381,22907}, {395,532}, {397,6774}, {549,5470}, {617,16644}, {627,16645}, {629,6674}, {1080,9756}, {3642,18362}, {3643,7746}, {5461,22574}, {6036,6108}, {6109,22797}, {6118,13875}, {6772,22846}, {9166,14905}, {10653,16629}, {11289,14144}, {16268,22901}, {16963,22895}
X(22893) = midpoint of X(115) and X(22892)
X(22893) = {X(6034), X(14061)}-harmonic conjugate of X(22847)
The reciprocal orthologic center of these triangles is X(13).
X(22894) lies on these lines: {2,3171}, {6,17}, {13,298}, {15,5617}, {16,627}, {302,22911}, {2380,11600}, {3104,16626}, {3105,22916}, {3642,11133}, {6115,7779}, {6671,22997}, {7788,22666}, {10645,22532}, {11302,16242}, {11542,22511}, {16629,16808}, {16940,18581}, {16962,22892}, {16964,22906}, {18582,22113}
X(22894) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17, 22901, 6), (627, 22907, 16), (16808, 22895, 16629), (16966, 22855, 16960)
The reciprocal orthologic center of these triangles is X(617).
X(22895) lies on these lines: {14,532}, {15,22113}, {16,17}, {627,16967}, {3412,19781}, {5474,6778}, {6779,22892}, {16629,16808}, {16961,22891}, {16963,22893}, {16965,22907}
X(22895) = reflection of X(6779) in X(22892)
X(22895) = {X(16629), X(22894)}-harmonic conjugate of X(16808)
The reciprocal orthologic center of these triangles is X(3).
X(22896) lies on these lines: {1,629}, {2,11739}, {8,627}, {10,17}, {65,22904}, {72,22903}, {355,12781}, {515,22890}, {517,16626}, {519,22912}, {532,3679}, {956,22772}, {1018,6192}, {1698,6673}, {1737,22930}, {1837,22910}, {3057,22905}, {3416,5965}, {3617,22113}, {3626,22844}, {5090,22482}, {5252,18973}, {5587,22832}, {5657,22532}, {5687,22558}, {5688,22899}, {5689,22898}, {5690,12780}, {5790,16629}, {8193,22657}, {8197,22670}, {8204,22674}, {8214,22908}, {8215,22909}, {9857,22746}, {10039,22929}, {10791,22523}, {10914,22902}, {10915,22931}, {10916,22932}, {12699,22795}, {13883,19070}, {13893,22921}, {13936,19071}, {13947,22922}
X(22896) = midpoint of X(8) and X(627)
X(22896) = reflection of X(i) in X(j) for these (i,j): (1, 629), (12699, 22795)
X(22896) = anticomplement of X(11739)
The reciprocal orthologic center of these triangles is X(3).
X(22897) lies on these lines: {17,402}, {30,16626}, {532,1651}, {627,4240}, {629,1650}, {5965,12583}, {6673,15183}, {11251,12793}, {11739,11831}, {11832,22482}, {11839,22523}, {11845,22532}, {11848,22558}, {11852,22652}, {11853,22657}, {11885,22746}, {11897,22832}, {11901,22898}, {11902,22899}, {11903,22902}, {11904,22903}, {11905,22904}, {11906,22905}, {11907,22908}, {11908,22909}, {11909,22910}, {11910,22912}, {11911,16629}, {11912,22929}, {11913,22930}, {11914,22931}, {11915,22932}, {13894,22921}, {13948,22922}, {18507,22795}, {18958,18973}, {19017,19071}, {19018,19070}, {22755,22772}
X(22897) = midpoint of X(627) and X(4240)
X(22897) = reflection of X(i) in X(j) for these (i,j): (17, 402), (18507, 22795)
The reciprocal orthologic center of these triangles is X(3).
X(22898) lies on these lines: {6,17}, {532,5861}, {627,1271}, {629,5591}, {1161,6270}, {5589,22652}, {5595,22657}, {5689,22896}, {5875,6271}, {6202,22832}, {6215,16626}, {8198,22670}, {8205,22674}, {8216,22908}, {8217,22909}, {8974,22921}, {9994,22746}, {10040,22929}, {10048,22930}, {10783,22532}, {10792,22523}, {10919,22902}, {10921,22903}, {10923,22904}, {10925,22905}, {10927,22910}, {10929,22931}, {10931,22932}, {11370,11739}, {11388,22482}, {11497,22558}, {11824,22890}, {11901,22897}, {11916,16629}, {13949,22922}, {18509,22795}, {18959,18973}, {22756,22772}
The reciprocal orthologic center of these triangles is X(3).
X(22899) lies on these lines: {6,17}, {532,5860}, {627,1270}, {629,5590}, {1160,6268}, {5588,22652}, {5594,22657}, {5604,22912}, {5688,22896}, {5874,6269}, {6201,22832}, {6214,16626}, {8199,22670}, {8206,22674}, {8218,22908}, {8219,22909}, {8975,22921}, {9995,22746}, {10041,22929}, {10049,22930}, {10784,22532}, {10793,22523}, {10920,22902}, {10922,22903}, {10924,22904}, {10926,22905}, {10928,22910}, {10930,22931}, {10932,22932}, {11371,11739}, {11389,22482}, {11498,22558}, {11825,22890}, {11902,22897}, {11917,16629}, {13950,22922}, {18511,22795}, {18960,18973}, {22757,22772}
The reciprocal orthologic center of these triangles is X(13).
X(22900) lies on these lines: {6,16629}, {13,298}, {15,5472}, {16,17}, {61,22906}, {627,18582}, {629,16966}, {3105,5335}, {5318,6778}, {6671,6779}, {10645,22890}, {16267,22892}, {16626,16808}, {16809,22832}, {16960,23006}
X(22900) = isogonal conjugate of X(37747)
X(22900) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5335, 22113, 22907), (16808, 22901, 16626)
The reciprocal orthologic center of these triangles is X(617).
X(22901) lies on these lines: {6,17}, {14,532}, {15,627}, {62,22907}, {298,11132}, {3104,22844}, {5463,5858}, {5872,16965}, {6777,13102}, {7837,22666}, {10646,22532}, {11543,22891}, {16268,22893}, {16530,19781}, {16626,16808}, {16629,16809}, {18581,22113}
X(22901) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 22894, 17), (16626, 22900, 16808), (16961, 22850, 16967)
The reciprocal orthologic center of these triangles is X(3).
X(22902) lies on these lines: {11,17}, {12,22931}, {355,16626}, {532,11235}, {627,3434}, {629,1376}, {5965,12586}, {10523,22929}, {10525,12922}, {10785,22532}, {10794,22523}, {10826,22652}, {10829,22657}, {10871,22746}, {10893,22832}, {10914,22896}, {10919,22898}, {10920,22899}, {10943,12921}, {10944,22904}, {10945,22908}, {10946,22909}, {10947,22910}, {10948,22930}, {10949,22932}, {11373,11739}, {11390,22482}, {11826,22890}, {11865,22670}, {11866,22674}, {11903,22897}, {11928,16629}, {12114,22772}, {13895,22921}, {13952,22922}, {18516,22795}, {18961,18973}, {19023,19071}, {19024,19070}
The reciprocal orthologic center of these triangles is X(3).
X(22903) lies on these lines: {11,22932}, {12,17}, {72,22896}, {355,16626}, {532,11236}, {627,3436}, {629,958}, {5965,12587}, {10523,22930}, {10526,12932}, {10786,22532}, {10795,22523}, {10827,22652}, {10830,22657}, {10872,22746}, {10894,22832}, {10921,22898}, {10922,22899}, {10942,12931}, {10950,22905}, {10951,22908}, {10952,22909}, {10953,22910}, {10954,22929}, {10955,22931}, {11374,11739}, {11391,22482}, {11500,22558}, {11827,22890}, {11867,22670}, {11868,22674}, {11904,22897}, {11929,16629}, {13896,22921}, {13953,22922}, {18517,22795}, {18962,18973}, {19025,19071}, {19026,19070}
The reciprocal orthologic center of these triangles is X(3).
X(22904) lies on these lines: {1,16626}, {4,22910}, {5,22930}, {12,17}, {56,629}, {65,22896}, {388,627}, {495,10061}, {532,11237}, {1478,12942}, {1479,22795}, {3027,11602}, {3085,22532}, {5261,22113}, {5965,12588}, {7354,22890}, {9654,16629}, {10797,22523}, {10831,22657}, {10873,22746}, {10895,22832}, {10923,22898}, {10924,22899}, {10944,22902}, {10956,22931}, {10957,22932}, {11375,11739}, {11392,22482}, {11501,22558}, {11869,22670}, {11905,22897}, {11930,22908}, {11931,22909}, {13897,22921}, {13954,22922}, {14144,18975}, {19027,19071}, {19028,19070}, {22759,22772}
X(22904) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 16626, 22905), (388, 627, 18973)
The reciprocal orthologic center of these triangles is X(3).
X(22905) lies on these lines: {1,16626}, {4,18973}, {5,22929}, {11,17}, {55,629}, {496,10077}, {497,627}, {532,11238}, {1478,22795}, {1479,12952}, {3023,11602}, {3057,22896}, {3086,22532}, {5274,22113}, {5965,12589}, {6284,22890}, {9581,22652}, {9669,16629}, {10798,22523}, {10832,22657}, {10874,22746}, {10896,22832}, {10925,22898}, {10926,22899}, {10950,22903}, {10958,22931}, {10959,22932}, {11376,11739}, {11393,22482}, {11502,22558}, {11871,22670}, {11872,22674}, {11906,22897}, {11932,22908}, {11933,22909}, {13075,14144}, {13898,22921}, {13955,22922}, {19029,19071}, {19030,19070}, {22760,22772}
X(22905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 16626, 22904), (497, 627, 22910)
The reciprocal orthologic center of these triangles is X(13).
X(22906) lies on these lines: {4,15}, {6,23006}, {14,99}, {16,22890}, {61,22900}, {193,532}, {381,22892}, {627,5334}, {629,18581}, {3054,5474}, {3104,22844}, {5318,8259}, {5321,16626}, {6114,14144}, {7051,22930}, {7747,11485}, {10638,22929}, {11132,11304}, {11307,16967}, {12017,22862}, {14136,23005}, {16809,16942}, {16964,22894}, {22512,23013}
The reciprocal orthologic center of these triangles is X(617).
X(22907) lies on these lines: {4,15}, {5,19781}, {13,148}, {16,627}, {32,16626}, {62,22901}, {69,532}, {381,22893}, {623,22911}, {3098,22513}, {3105,5335}, {5318,16629}, {6115,10645}, {6783,16941}, {7693,21467}, {7737,9996}, {8259,11485}, {9981,16809}, {10654,19130}, {16965,22895}
X(22907) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (16, 22894, 627), (5335, 22113, 22900)
The reciprocal orthologic center of these triangles is X(3).
X(22908) lies on these lines: {17,493}, {532,12152}, {627,6462}, {629,8222}, {5965,12590}, {6461,22909}, {8188,22652}, {8194,22657}, {8210,22912}, {8212,22832}, {8214,22896}, {8216,22898}, {8218,22899}, {8220,16626}, {10669,12990}, {10875,22746}, {10945,22902}, {10951,22903}, {11377,11739}, {11394,22482}, {11503,22558}, {11828,22890}, {11840,22523}, {11846,22532}, {11907,22897}, {11930,22904}, {11932,22905}, {11947,22910}, {11949,16629}, {11951,22929}, {11953,22930}, {11955,22931}, {11957,22932}, {13899,22921}, {13956,22922}, {18520,22795}, {18963,18973}, {19031,19071}, {19032,19070}, {22761,22772}
The reciprocal orthologic center of these triangles is X(3).
X(22909) lies on these lines: {17,494}, {532,12153}, {627,6463}, {629,8223}, {5965,12591}, {6461,22908}, {8189,22652}, {8195,22657}, {8211,22912}, {8213,22832}, {8215,22896}, {8217,22898}, {8219,22899}, {8221,16626}, {10673,12991}, {10876,22746}, {10946,22902}, {10952,22903}, {11378,11739}, {11395,22482}, {11504,22558}, {11829,22890}, {11841,22523}, {11847,22532}, {11908,22897}, {11931,22904}, {11933,22905}, {11948,22910}, {11950,16629}, {11952,22929}, {11954,22930}, {11956,22931}, {11958,22932}, {13900,22921}, {13957,22922}, {18522,22795}, {18964,18973}, {19033,19071}, {19034,19070}, {22762,22772}
The reciprocal orthologic center of these triangles is X(3).
X(22910) lies on these lines: {1,13076}, {3,22930}, {4,22904}, {11,629}, {12,22832}, {17,55}, {33,22482}, {56,22890}, {390,22113}, {497,627}, {532,3058}, {1479,16626}, {1697,22652}, {1837,22896}, {2098,22912}, {2646,11739}, {3056,5965}, {3295,16629}, {3583,22795}, {4294,22532}, {5432,6673}, {10799,22523}, {10833,22657}, {10927,22898}, {10928,22899}, {10947,22902}, {10953,22903}, {10965,22931}, {10966,22772}, {11602,13183}, {11873,22670}, {11874,22674}, {11909,22897}, {11947,22908}, {11948,22909}, {12951,14144}, {13075,15171}, {13901,22921}, {13958,22922}, {19037,19071}, {19038,19070}
X(22910) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497, 627, 22905), (3295, 16629, 22929)
The reciprocal orthologic center of these triangles is X(22570).
X(22911) lies on these lines: {2,17}, {3,22570}, {76,16242}, {302,22894}, {623,22907}, {1078,3642}, {3643,7746}, {6299,10104}, {6581,11171}, {7749,22892}, {11304,22891}
X(22911) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17, 627, 22737), (629, 22914, 22916)
The reciprocal orthologic center of these triangles is X(3).
X(22912) lies on these lines: {1,17}, {8,629}, {55,22772}, {56,22558}, {145,627}, {517,22890}, {519,22896}, {532,3241}, {952,16626}, {1482,7975}, {1483,7974}, {2098,22910}, {2099,18973}, {3242,5965}, {3244,22844}, {3616,6673}, {3623,22113}, {5597,22674}, {5598,22670}, {5603,22832}, {5604,22899}, {7967,22532}, {7968,19071}, {7969,19070}, {8192,22657}, {8210,22908}, {8211,22909}, {9997,22746}, {10247,16629}, {10800,22523}, {10944,22902}, {10950,22903}, {11396,22482}, {11910,22897}, {13902,22921}, {13959,22922}, {18525,22795}
X(22912) = midpoint of X(145) and X(627)
X(22912) = reflection of X(i) in X(j) for these (i,j): (8, 629), (18525, 22795)
X(22912) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22652, 11739), (11739, 22652, 17), (22931, 22932, 17)
The reciprocal orthologic center of these triangles is X(22914).
X(22913) lies on these lines: {2,39}, {3,22914}, {622,7758}, {698,3105}, {732,3104}, {3095,16627}, {5980,7751}
X(22913) = anticomplement of X(33467)
X(22913) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (39, 22868, 6294), (6314, 6318, 6581), (6581, 22868, 39)
The reciprocal orthologic center of these triangles is X(22913).
X(22914) lies on these lines: {2,17}, {3,22913}, {98,14540}, {3098,22869}, {3643,7755}, {5864,9756}, {5965,22871}, {6287,7685}, {6295,7780}, {6582,7751}, {10646,20081}
X(22914) = circumtangential isogonal conjugate of X(61)
X(22914) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (22911, 22916, 629), (22927, 22928, 22737)
The reciprocal orthologic center of these triangles is X(22916).
X(22915) lies on these lines: {2,32}, {3,22916}, {732,3105}, {6287,7684}
X(22915) = anticomplement of X(33469)
X(22915) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6292, 22870, 6297), (6296, 22870, 6292), (6313, 6317, 6296)
The reciprocal orthologic center of these triangles is X(22915).
X(22916) lies on these lines: {2,17}, {3,22915}, {13,7814}, {14,13571}, {3095,16626}, {3105,22894}, {3642,7796}, {3818,22871}, {5965,22869}, {6298,7759}, {6299,7764}, {16627,16629}
X(22916) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (627, 22113, 62), (629, 22914, 22911), (22927, 22928, 22685)
The reciprocal orthologic center of these triangles is X(22918).
X(22917) lies on these lines: {2,1327}, {30,6304}, {532,22629}, {2043,13687}, {3105,23002}, {5459,13929}, {13692,16627}, {16644,22919}
X(22917) = anticomplement of X(33471)
X(22917) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1327, 22872), (2, 13712, 13706), (13678, 13712, 22872), (13701, 22872, 13704), (13706, 22872, 13701)
The reciprocal orthologic center of these triangles is X(22917).
X(22918) lies on these lines: {532,3068}, {11488,22920}, {19070,22924}, {22921,22928}, {22925,22927}
The reciprocal orthologic center of these triangles is X(22920).
X(22919) lies on these lines: {2,1328}, {30,6300}, {532,22600}, {2044,13807}, {3105,23003}, {5459,13850}, {13812,16627}, {16644,22917}
X(22919) = anticomplement of X(33473)
X(22919) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1328, 22874), (2, 13835, 13826), (13798, 13835, 22874), (13821, 22874, 13824), (13826, 22874, 13821)
The reciprocal orthologic center of these triangles is X(22919).
X(22920) lies on these lines: {532,3069}, {11488,22918}, {19071,22923}, {22922,22927}, {22926,22928}
The reciprocal orthologic center of these triangles is X(3).
X(22921) lies on these lines: {2,19070}, {6,6673}, {17,3068}, {371,22832}, {532,6305}, {590,629}, {627,8972}, {5965,13910}, {7585,19071}, {8974,22898}, {8975,22899}, {8976,16626}, {8981,13917}, {9540,22890}, {11739,13883}, {13884,22482}, {13885,22523}, {13886,22532}, {13887,22558}, {13889,22657}, {13891,22674}, {13893,22896}, {13894,22897}, {13895,22902}, {13896,22903}, {13897,22904}, {13898,22905}, {13899,22908}, {13900,22909}, {13901,22910}, {13902,22912}, {13903,16629}, {13904,22929}, {13905,22930}, {13906,22931}, {13907,22932}, {18538,22795}, {18965,18973}, {22763,22772}, {22918,22928}
X(22921) = {X(6), X(6673)}-harmonic conjugate of X(22922)
The reciprocal orthologic center of these triangles is X(3).
X(22922) lies on these lines: {2,19071}, {6,6673}, {17,3069}, {372,22832}, {532,6301}, {615,629}, {627,13941}, {5965,13972}, {7586,19070}, {11739,13936}, {13935,22890}, {13937,22482}, {13938,22523}, {13939,22532}, {13940,22558}, {13942,22652}, {13943,22657}, {13944,22670}, {13945,22674}, {13946,22746}, {13947,22896}, {13948,22897}, {13949,22898}, {13950,22899}, {13951,16626}, {13952,22902}, {13953,22903}, {13954,22904}, {13955,22905}, {13956,22908}, {13957,22909}, {13958,22910}, {13959,22912}, {13961,16629}, {13962,22929}, {13963,22930}, {13964,22931}, {13965,22932}, {13966,13982}, {13981,13993}, {18762,22795}, {18966,18973}, {22764,22772}, {22920,22927}
X(22922) = {X(6), X(6673)}-harmonic conjugate of X(22921)
The reciprocal orthologic center of these triangles is X(5859).
X(22923) lies on these lines: {2,22924}, {532,3068}, {13637,22488}, {13638,22666}, {13644,22878}, {19070,22928}, {19071,22920}
The reciprocal orthologic center of these triangles is X(5859).
X(22924) lies on these lines: {2,22923}, {532,3069}, {13757,22488}, {13758,22666}, {13763,22879}, {19070,22918}, {19071,22927}
The reciprocal orthologic center of these triangles is X(22629).
X(22925) lies on these lines: {17,485}, {532,6305}, {590,22928}, {629,13882}, {641,13876}, {6118,13875}, {6304,13850}, {6673,11311}, {12815,22880}, {16644,22629}, {22918,22927}
The reciprocal orthologic center of these triangles is X(22600).
X(22926) lies on these lines: {17,486}, {532,6301}, {615,22927}, {629,13934}, {642,13929}, {6300,13932}, {6673,11311}, {12815,22881}, {16644,22600}, {22920,22928}
The reciprocal orthologic center of these triangles is X(22600).
X(22927) lies on these lines: {2,17}, {3,22600}, {615,22926}, {5965,22883}, {6289,16626}, {6561,22599}, {19071,22924}, {22918,22925}, {22920,22922}
X(22927) = complement of X(33439)
X(22927) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17, 22113, 22928), (627, 22844, 22928), (22685, 22916, 22928), (22737, 22914, 22928)
The reciprocal orthologic center of these triangles is X(22629).
X(22928) lies on these lines: {2,17}, {3,22629}, {590,22925}, {3643,8960}, {5965,22882}, {6290,16626}, {6560,22628}, {19070,22923}, {22918,22921}, {22920,22926}
X(22928) = complement of X(33438)
X(22928) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17, 22113, 22927), (627, 22844, 22927), (22685, 22916, 22927), (22737, 22914, 22927)
The reciprocal orthologic center of these triangles is X(3).
X(22929) lies on these lines: {1,17}, {3,18973}, {5,22905}, {12,16626}, {35,22890}, {388,22532}, {495,10061}, {498,629}, {499,6673}, {532,10056}, {611,5965}, {627,3085}, {1479,22832}, {3295,16629}, {3299,19071}, {3301,19070}, {10037,22657}, {10038,22746}, {10039,22896}, {10040,22898}, {10077,22891}, {10078,10611}, {10523,22902}, {10801,22523}, {10895,22795}, {10954,22903}, {11398,22482}, {11507,22558}, {11877,22670}, {11878,22674}, {11912,22897}, {11951,22908}, {11952,22909}, {12815,22885}, {13904,22921}, {13962,22922}, {22766,22772}
X(22929) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 17, 22930), (3295, 16629, 22910)
The reciprocal orthologic center of these triangles is X(3).
X(22930) lies on these lines: {1,17}, {3,22910}, {5,22904}, {11,16626}, {36,22890}, {56,10078}, {496,10077}, {497,22532}, {498,6673}, {499,629}, {532,10072}, {613,5965}, {627,3086}, {1478,22832}, {1737,22896}, {3299,19070}, {3301,19071}, {7051,22906}, {10046,22657}, {10048,22898}, {10049,22899}, {10061,22891}, {10062,10611}, {10523,22903}, {10802,22523}, {10896,22795}, {10948,22902}, {11399,22482}, {11508,22558}, {11880,22674}, {11913,22897}, {11953,22908}, {11954,22909}, {12815,22884}, {13905,22921}, {13963,22922}, {14986,22113}
X(22930) = {X(1), X(17)}-harmonic conjugate of X(22929)
The reciprocal orthologic center of these triangles is X(3).
X(22931) lies on these lines: {1,17}, {12,22902}, {532,11239}, {627,10528}, {629,5552}, {5965,12594}, {10531,22832}, {10679,13105}, {10803,22523}, {10805,22532}, {10834,22657}, {10878,22746}, {10915,22896}, {10929,22898}, {10930,22899}, {10942,16626}, {10955,22903}, {10956,22904}, {10958,22905}, {10965,22910}, {11248,22890}, {11400,22482}, {11509,18973}, {11881,22670}, {11882,22674}, {11914,22897}, {11955,22908}, {11956,22909}, {12000,16629}, {13906,22921}, {13964,22922}, {18542,22795}, {19047,19071}, {19048,19070}, {22768,22772}
X(22931) = {X(17), X(22912)}-harmonic conjugate of X(22932)
The reciprocal orthologic center of these triangles is X(3).
X(22932) lies on these lines: {1,17}, {11,22903}, {532,11240}, {627,10529}, {629,10527}, {5965,12595}, {10532,22832}, {10680,13107}, {10804,22523}, {10806,22532}, {10835,22657}, {10879,22746}, {10916,22896}, {10931,22898}, {10932,22899}, {10943,16626}, {10949,22902}, {10957,22904}, {10959,22905}, {10966,22772}, {11249,22890}, {11401,22482}, {11510,22558}, {11883,22670}, {11884,22674}, {11915,22897}, {11957,22908}, {11958,22909}, {12001,16629}, {13907,22921}, {13965,22922}, {18544,22795}, {18967,18973}, {19049,19071}, {19050,19070}
X(22932) = {X(17), X(22912)}-harmonic conjugate of X(22931)
The reciprocal parallelogic center of these triangles is X(3).
X(22933) lies on these lines: {351,9200}, {9135,22888}, {13304,14610}
The reciprocal parallelogic center of these triangles is X(3).
X(22934) lies on these lines: {2,14446}, {351,9200}, {3569,22889}, {6138,9979}
The reciprocal orthologic center of these triangles is X(191).
X(22935) lies on the cubic K798 and these lines: {1,6797}, {3,191}, {10,140}, {11,6881}, {20,16128}, {30,21635}, {35,17638}, {72,4996}, {80,2646}, {100,517}, {104,6986}, {119,6831}, {149,5886}, {153,18481}, {355,6224}, {376,9809}, {381,15017}, {404,5885}, {515,11698}, {528,11729}, {550,18243}, {631,9803}, {942,10090}, {1125,1484}, {1155,11571}, {1319,7972}, {1482,5541}, {1537,10993}, {2800,3579}, {2801,15481}, {2802,19907}, {2932,4855}, {3576,5531}, {3811,22560}, {3871,17652}, {3916,12532}, {4413,6264}, {5126,10074}, {5587,12747}, {5603,20095}, {5660,10742}, {5790,9897}, {5818,20085}, {5840,9945}, {5887,17100}, {5901,21630}, {6261,12332}, {6702,20104}, {6901,11604}, {6924,22836}, {7508,10176}, {7743,13274}, {8674,11699}, {8715,10284}, {9802,10595}, {9856,12775}, {9955,10738}, {9957,10087}, {10225,14988}, {10247,12653}, {11219,13151}, {12645,21842}, {12699,13199}, {12702,13253}, {12737,15178}, {13145,17654}, {13146,13743}, {20117,22936}
X(22935) = midpoint of X(i) and X(j) for these {i,j}: {1, 12331}, {3, 6326}, {20, 16128}, {100, 6265}, {104, 12738}, {119, 10609}, {153, 18481}, {355, 6224}, {1482, 5541}, {1537, 10993}, {3811, 22560}, {6261, 12332}, {12699, 13199}, {12702, 13253}, {13146, 13743}
X(22935) = reflection of X(i) in X(j) for these (i,j): (80, 9956), (104, 13624), (12737, 15178)
X(22935) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3035, 12619, 11231), (3576, 5531, 12773), (5660, 12119, 10742), (6326, 15015, 3), (10087, 12740, 9957), (10090, 12739, 942)
The reciprocal orthologic center of these triangles is X(7701).
X(22936) lies on the cubic K798 and these lines: {1,13465}, {3,7701}, {5,12615}, {10,30}, {21,104}, {35,3065}, {58,8143}, {65,1749}, {79,17605}, {140,21635}, {191,517}, {355,15680}, {549,18243}, {758,11260}, {1155,16118}, {1770,13852}, {2475,9956}, {3648,3916}, {3651,5927}, {3683,13624}, {4861,11278}, {4999,12611}, {5251,13145}, {5260,12515}, {5426,15178}, {5428,17502}, {5499,11231}, {5694,6914}, {5885,7489}, {5886,14450}, {6701,20107}, {6853,16128}, {6888,12600}, {6906,18259}, {10021,11230}, {10058,14883}, {12769,13126}, {15674,16116}, {16139,21669}, {16160,22793}, {16617,17768}, {20117,22935}
X(22936) = midpoint of X(i) and X(j) for these {i,j}: {1, 13465}, {3, 7701}, {21, 3652}, {191, 13743}, {355, 15680}, {3648, 16159}, {3651, 16138}, {12769, 13126}, {16139, 21669}
X(22936) = reflection of X(2475) in X(9956)
X(22936) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4640, 18480, 3579), (10021, 11263, 11230)
The reciprocal orthologic center of these triangles is X(6326).
X(22937) lies on the cubic K798 and these lines: {2,16159}, {3,191}, {10,30}, {21,517}, {35,1749}, {40,13743}, {71,2290}, {79,1155}, {140,11263}, {165,7701}, {442,11231}, {500,896}, {516,16160}, {582,4414}, {631,14450}, {758,1385}, {846,8143}, {946,10021}, {1006,5885}, {1482,5426}, {3651,3652}, {3654,15677}, {3656,15672}, {3683,9955}, {3916,4511}, {3925,13852}, {4995,13995}, {5122,16140}, {5273,18517}, {5432,14526}, {5499,6684}, {5603,15676}, {5657,15680}, {5886,15674}, {6675,11230}, {6701,20104}, {6841,7965}, {6902,11604}, {7743,16155}, {9956,16113}, {10164,11277}, {10246,16126}, {10895,16118}, {11010,17636}, {11259,21376}, {11699,16164}, {16138,17613}, {19861,21165}
X(22937) = midpoint of X(i) and X(j) for these {i,j}: {3, 191}, {21, 16139}, {40, 13743}, {3651, 3652}, {3654, 15677}
X(22937) = reflection of X(i) in X(j) for these (i,j): (946, 10021), (5499, 6684), (11699, 16164)
X(22937) = complement of X(16159)
X(22937) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 13465, 16132), (35, 1749, 17637), (165, 7701, 16117), (191, 16132, 13465)
The reciprocal parallelogic center of these triangles is X(1).
X(22938) lies on these lines: {3,10724}, {4,145}, {5,3035}, {11,30}, {80,5560}, {100,381}, {104,382}, {119,546}, {214,9955}, {355,14217}, {516,12619}, {528,3845}, {548,21154}, {549,6667}, {550,6713}, {946,11567}, {962,19914}, {1145,18357}, {1317,3585}, {1385,16174}, {1387,1388}, {1478,12735}, {1484,2829}, {1539,2771}, {1699,6265}, {1770,20118}, {1836,10073}, {2550,6929}, {2783,22505}, {2787,22515}, {2800,22793}, {2802,18480}, {2806,19163}, {2831,19160}, {3045,10540}, {3091,13199}, {3543,12248}, {3579,6702}, {3656,7972}, {3818,9024}, {3830,10707}, {3839,20095}, {3843,12331}, {3850,10993}, {3857,20400}, {4996,13743}, {5066,6174}, {5533,7354}, {5541,18492}, {5690,10525}, {5691,12737}, {5848,21850}, {5886,12119}, {6033,10769}, {6284,8068}, {6321,10768}, {6734,19919}, {6924,10893}, {7728,10778}, {8148,12531}, {8674,10113}, {9803,10248}, {9812,12247}, {9818,13222}, {10057,12701}, {10058,12953}, {10074,12943}, {10087,10895}, {10090,10896}, {10308,11604}, {10711,14269}, {10739,10772}, {10740,10777}, {10741,10770}, {10747,10771}, {10750,10782}, {10751,10781}, {10755,18440}, {10773,15521}, {10774,15522}, {10780,12918}, {12019,12764}, {12047,12743}, {12611,18483}, {13194,18502}, {13205,18491}, {13228,18495}, {13230,18497}, {13235,18500}, {13268,18507}, {13269,18509}, {13270,18511}, {13271,18516}, {13272,18517}, {13275,18520}, {13276,18522}, {13278,18542}, {13279,18544}, {13665,19113}, {13785,19112}, {13922,18538}, {13991,18762}, {16173,18481}, {18240,18527}, {18761,22560}
X(22938) = midpoint of X(i) and X(j) for these {i,j}: {3, 10724}, {4, 10738}, {80, 12699}, {104, 382}, {355, 14217}, {962, 19914}, {1484, 3627}, {3830, 10707}, {5691, 12737}, {6033, 10769}, {6321, 10768}, {7728, 10778}, {8148, 12531}, {10739, 10772}, {10740, 10777}, {10741, 10770}, {10747, 10771}, {10750, 10782}, {10751, 10781}, {10755, 18440}, {10773, 15521}, {10774, 15522}, {10780, 12918}, {13268, 18507}
X(22938) = reflection of X(i) in X(j) for these (i,j): (119, 546), (214, 9955), (550, 6713), (1145, 18357), (1385, 16174), (3579, 6702), (12611, 18483)
X(22938) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 149, 10742), (1478, 13274, 12735), (1479, 13273, 1387), (3830, 12773, 10728), (10707, 10728, 12773), (10738, 10742, 149)
The reciprocal cyclologic center of these triangles is X(22940).
X(22939) lies on these lines: {}
The reciprocal cyclologic center of these triangles is X(22939).
X(22940) lies on these lines: {}
The reciprocal orthologic center of these triangles is X(12241).
X(22941) lies on these lines: {1,22966}, {2,22476}, {8,22647}, {10,22466}, {65,775}, {72,22957}, {515,22951}, {517,22955}, {519,22969}, {956,22776}, {1737,22981}, {1837,22965}, {3057,22959}, {3679,22653}, {5090,22483}, {5252,18978}, {5587,22833}, {5657,22533}, {5687,22559}, {5688,22947}, {5689,22945}, {5790,22979}, {8193,22658}, {8214,22963}, {8215,22964}, {9857,22747}, {10039,22980}, {10791,22524}, {10914,22956}, {10915,22982}, {10916,22983}, {12699,22800}, {13883,19084}, {13893,22976}, {13936,19083}, {13947,22977}
X(22941) = midpoint of X(8) and X(22647)
X(22941) = reflection of X(i) in X(j) for these (i,j): (1, 22966), (12699, 22800)
X(22941) = anticomplement of X(22476)
The reciprocal cyclologic center of these triangles is X(1320).
X(22942) lies on these lines: {1,1145}, {57,3021}, {1280,11019}, {5563,6011}
X(22942) = inverse of X(3035) in the incircle
The reciprocal orthologic center of these triangles is X(12241).
X(22943) lies on these lines: {30,22951}, {402,22466}, {1650,22966}, {4240,22647}, {11831,22476}, {11832,22483}, {11839,22524}, {11845,22533}, {11848,22559}, {11852,22653}, {11853,22658}, {11885,22747}, {11897,22833}, {11901,22945}, {11902,22947}, {11903,22956}, {11904,22957}, {11905,22958}, {11906,22959}, {11907,22963}, {11908,22964}, {11909,22965}, {11910,22969}, {11911,22979}, {11912,22980}, {11913,22981}, {11914,22982}, {11915,22983}, {13894,22976}, {13948,22977}, {18507,22800}, {18958,18978}, {19017,19083}, {19018,19084}, {22755,22776}
X(22943) = midpoint of X(4240) and X(22647)
X(22943) = reflection of X(i) in X(j) for these (i,j): (1650, 22966), (18507, 22800)
X(22944) lies on these lines: {1161,13630}, {12241,22945}
The reciprocal orthologic center of these triangles is X(12241).
X(22945) lies on these lines: {6,17837}, {1271,22647}, {2929,8903}, {5589,22653}, {5591,22966}, {5595,22658}, {5605,22969}, {5689,22941}, {6202,22833}, {6215,22955}, {6218,22530}, {8216,22963}, {8217,22964}, {8974,22976}, {9994,22747}, {10040,22980}, {10048,22981}, {10783,22533}, {10792,22524}, {10919,22956}, {10921,22957}, {10923,22958}, {10925,22959}, {10927,22965}, {10929,22982}, {10931,22983}, {11370,22476}, {11388,22483}, {11497,22559}, {11824,22951}, {11901,22943}, {11916,22979}, {12241,22944}, {13949,22977}, {18509,22800}, {18959,18978}, {22756,22776}
X(22946) lies on these lines: {1160,13630}, {12241,22947}
The reciprocal orthologic center of these triangles is X(12241).
X(22947) lies on these lines: {6,17837}, {1270,22647}, {2929,8904}, {5588,22653}, {5590,22966}, {5594,22658}, {5604,22969}, {5688,22941}, {6201,22833}, {6214,22955}, {6217,22530}, {8218,22963}, {8219,22964}, {8975,22976}, {9995,22747}, {10041,22980}, {10049,22981}, {10784,22533}, {10793,22524}, {10920,22956}, {10922,22957}, {10924,22958}, {10926,22959}, {10928,22965}, {10930,22982}, {10932,22983}, {11371,22476}, {11389,22483}, {11498,22559}, {11825,22951}, {11902,22943}, {11917,22979}, {12241,22946}, {13950,22977}, {18511,22800}, {18960,18978}, {22757,22776}
X(22948) lies on these lines: {4,3521}, {6,6241}, {24,8718}, {30,6152}, {52,12897}, {113,1594}, {155,378}, {389,13202}, {403,9729}, {974,22833}, {1154,13420}, {1493,2914}, {1593,2904}, {1843,6240}, {1885,1986}, {3520,11591}, {3574,6000}, {3575,11817}, {5890,5895}, {6030,15086}, {6102,16880}, {7576,10575}, {7729,18912}, {7999,15103}, {10594,15072}, {13431,13754}
X(22949) lies on these lines: {74,195}, {381,6241}, {974,22971}, {1205,1992}, {2452,13489}, {5654,12281}, {7699,20299}, {11468,12163}, {17505,18394}
X(22950) lies on these lines: {6,11455}, {54,22972}, {382,3567}, {399,11702}, {1173,15084}, {5888,7514}, {5890,11807}, {12281,16176}, {13403,13423}
The reciprocal orthologic center of these triangles is X(12241).
X(22951) lies on these lines: {2,22833}, {3,2929}, {4,22966}, {20,22647}, {30,22943}, {35,22980}, {36,22981}, {55,18978}, {56,22965}, {110,2883}, {165,22653}, {182,22524}, {371,19084}, {372,19083}, {376,22533}, {382,22800}, {515,22941}, {517,22969}, {1593,22483}, {3098,22747}, {3428,22776}, {3576,22476}, {4549,10627}, {6284,22959}, {7354,22958}, {7691,16386}, {9540,22976}, {9627,19472}, {10310,22559}, {10575,12121}, {11248,22982}, {11249,22983}, {11414,22658}, {11824,22945}, {11825,22947}, {11826,22956}, {11827,22957}, {11828,22963}, {11829,22964}, {12118,13491}, {13935,22977}, {15644,18442}, {17818,22953}, {18560,22750}
X(22951) = midpoint of X(20) and X(22647)
X(22951) = reflection of X(i) in X(j) for these (i,j): (4, 22966), (382, 22800)
X(22951) = anticomplement of X(22833)
The reciprocal orthologic center of these triangles is X(19481).
X(22952) lies on these lines: {389,6677}, {1147,2929}, {1181,21652}, {1493,11802}, {6102,11557}, {11536,22529}, {11806,12897}, {15120,19511}, {15134,19480}
The reciprocal orthologic center of these triangles is X(22663).
X(22953) lies on these lines: {2,22533}, {6,17837}, {25,22662}, {155,22808}, {185,10112}, {974,22663}, {1092,22834}, {10116,10938}, {17818,22951}, {18936,22647}, {22483,22530}
X(22953) = reflection of X(22483) in X(22530)
The reciprocal orthologic center of these triangles is X(9729).
X(22954) lies on these lines: {1,18978}, {33,22970}, {34,22538}, {35,22962}, {36,22978}, {55,2929}, {56,22549}, {497,22555}, {1040,22581}, {1062,22834}, {1250,22975}, {2066,22960}, {2192,17837}, {2330,19142}, {3100,22528}, {3270,21652}, {3583,22816}, {5414,22961}, {6198,22750}, {6284,19505}, {7071,22497}, {8540,22830}, {9627,22466}, {9817,22973}, {10638,22974}, {10895,22971}, {11429,22529}, {11436,22530}, {11446,22534}, {11461,22535}, {12888,18970}, {18455,22808}, {18922,18936}, {19182,19198}, {19354,19460}, {19434,19488}, {19435,19489}
The reciprocal orthologic center of these triangles is X(12241).
X(22955) lies on these lines: {1,22958}, {2,22533}, {3,22658}, {4,801}, {5,5504}, {11,22981}, {12,22980}, {30,22943}, {49,8550}, {54,5972}, {110,185}, {155,2929}, {355,22956}, {381,22833}, {517,22941}, {578,22973}, {952,22969}, {1147,22529}, {1351,7506}, {1352,3548}, {1368,22662}, {1478,18978}, {1479,22965}, {2071,5907}, {2072,6288}, {3292,15801}, {5587,22653}, {5878,10539}, {5886,22476}, {6214,22947}, {6215,22945}, {6642,22530}, {7583,19084}, {7584,19083}, {7728,18350}, {8220,22963}, {8221,22964}, {8976,22976}, {9970,22828}, {9996,22747}, {10796,22524}, {10942,22982}, {10943,22983}, {11472,12084}, {11487,22581}, {11499,22559}, {12421,16238}, {13352,22968}, {13951,22977}, {22758,22776}
X(22955) = midpoint of X(4) and X(22647)
X(22955) = reflection of X(i) in X(j) for these (i,j): (3, 22966), (4, 22800)
X(22955) = complement of X(22533)
X(22955) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 22979, 22833), (22958, 22959, 1)
The reciprocal orthologic center of these triangles is X(12241).
X(22956) lies on these lines: {11,22466}, {12,22982}, {355,22955}, {1376,22559}, {3434,22647}, {10523,22980}, {10785,22533}, {10794,22524}, {10826,22653}, {10829,22658}, {10871,22747}, {10893,22833}, {10914,22941}, {10919,22945}, {10920,22947}, {10944,22958}, {10945,22963}, {10946,22964}, {10947,22965}, {10948,22981}, {10949,22983}, {11373,22476}, {11390,22483}, {11826,22951}, {11903,22943}, {11928,22979}, {12114,22776}, {13895,22976}, {13952,22977}, {18516,22800}, {18961,18978}, {19023,19083}, {19024,19084}
The reciprocal orthologic center of these triangles is X(12241).
X(22957) lies on these lines: {11,22983}, {12,22466}, {72,22941}, {355,22955}, {958,22776}, {3436,22647}, {10523,22981}, {10786,22533}, {10795,22524}, {10827,22653}, {10830,22658}, {10872,22747}, {10894,22833}, {10921,22945}, {10922,22947}, {10950,22959}, {10951,22963}, {10952,22964}, {10953,22965}, {10954,22980}, {10955,22982}, {11374,22476}, {11391,22483}, {11500,22559}, {11827,22951}, {11904,22943}, {11929,22979}, {13896,22976}, {13953,22977}, {18517,22800}, {18962,18978}, {19025,19083}, {19026,19084}
The reciprocal orthologic center of these triangles is X(12241).
X(22958) lies on these lines: {1,22955}, {4,22965}, {12,22466}, {56,22966}, {65,775}, {388,18978}, {495,22980}, {1479,22800}, {3085,22533}, {6198,22750}, {7354,22951}, {9578,22653}, {9654,22979}, {10797,22524}, {10831,22658}, {10873,22747}, {10895,22833}, {10923,22945}, {10924,22947}, {10944,22956}, {10956,22982}, {10957,22983}, {11375,22476}, {11392,22483}, {11501,22559}, {11905,22943}, {11930,22963}, {11931,22964}, {13897,22976}, {13954,22977}, {19027,19083}, {19028,19084}, {22759,22776}
X(22958) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22955, 22959), (388, 22647, 18978)
The reciprocal orthologic center of these triangles is X(12241).
X(22959) lies on these lines: {1,22955}, {4,18978}, {5,22980}, {11,22466}, {55,22966}, {496,22981}, {497,22647}, {1478,22800}, {1870,19472}, {3057,22941}, {6284,22951}, {9581,22653}, {9669,22979}, {10798,22524}, {10832,22658}, {10874,22747}, {10896,22833}, {10925,22945}, {10926,22947}, {10950,22957}, {10958,22982}, {10959,22983}, {11376,22476}, {11393,22483}, {11502,22559}, {11906,22943}, {11932,22963}, {11933,22964}, {13898,22976}, {13955,22977}, {19029,19083}, {19030,19084}
X(22959) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22955, 22958), (497, 22647, 22965)
The reciprocal orthologic center of these triangles is X(9729).
X(22960) lies on these lines: {6,2929}, {372,22962}, {1151,22549}, {2066,22954}, {2067,19472}, {3068,22555}, {3311,22550}, {5410,22497}, {5412,22970}, {5415,22840}, {6200,22978}, {6413,22466}, {6564,22816}, {10880,22750}, {10897,22834}, {10961,22973}, {11417,22528}, {11447,22534}, {11462,22535}, {11473,22538}, {11513,22581}, {17819,17837}, {18457,22808}, {18923,18936}, {19183,19198}, {19355,19460}, {19436,19488}, {19438,19489}, {21640,21652}
X(22960) = {X(6), X(2929)}-harmonic conjugate of X(22961)
The reciprocal orthologic center of these triangles is X(9729).
X(22961) lies on these lines: {6,2929}, {371,22962}, {1152,22549}, {3069,22555}, {3312,22550}, {5411,22497}, {5413,22970}, {5414,22954}, {5416,22840}, {6396,22978}, {6414,22466}, {6502,19472}, {6565,22816}, {10881,22750}, {10898,22834}, {10963,22973}, {11418,22528}, {11448,22534}, {11463,22535}, {11474,22538}, {11514,22581}, {17820,17837}, {18459,22808}, {18924,18936}, {19184,19198}, {19356,19460}, {19437,19489}, {19439,19488}, {21641,21652}
X(22961) = {X(6), X(2929)}-harmonic conjugate of X(22960)
The reciprocal orthologic center of these triangles is X(9729).
X(22962) lies on these lines: {3,2929}, {5,13293}, {15,22975}, {16,22974}, {24,1533}, {35,22954}, {36,19472}, {54,9729}, {110,185}, {113,3521}, {186,8718}, {371,22961}, {372,22960}, {378,22538}, {382,22971}, {389,22529}, {511,19142}, {575,22830}, {578,22530}, {631,22555}, {1147,13630}, {1658,8717}, {3515,22497}, {6642,18418}, {6644,22800}, {6723,14130}, {6759,13491}, {7488,22528}, {8907,15078}, {10902,22840}, {11250,22833}, {11449,22534}, {11464,22535}, {11702,14708}, {12084,22968}, {12584,22828}, {13367,21652}, {17821,17837}, {18912,22647}, {18925,18936}, {19185,19198}, {19357,19460}, {19440,19488}, {19441,19489}, {19467,22533}
X(22962) = midpoint of X(3) and X(2929)
X(22962) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 22550, 22549), (2929, 22549, 22550)
The reciprocal orthologic center of these triangles is X(12241).
X(22963) lies on these lines: {493,22466}, {6461,22964}, {6462,22647}, {8188,22653}, {8194,22658}, {8210,22969}, {8212,22833}, {8214,22941}, {8216,22945}, {8218,22947}, {8220,22955}, {8222,22966}, {10875,22747}, {10945,22956}, {10951,22957}, {11377,22476}, {11394,22483}, {11503,22559}, {11828,22951}, {11840,22524}, {11846,22533}, {11907,22943}, {11930,22958}, {11932,22959}, {11947,22965}, {11949,22979}, {11951,22980}, {11953,22981}, {11955,22982}, {11957,22983}, {13899,22976}, {13956,22977}, {18520,22800}, {18963,18978}, {19031,19083}, {19032,19084}, {22761,22776}
The reciprocal orthologic center of these triangles is X(12241).
X(22964) lies on these lines: {494,22466}, {6461,22963}, {6463,22647}, {8189,22653}, {8195,22658}, {8211,22969}, {8213,22833}, {8215,22941}, {8217,22945}, {8219,22947}, {8221,22955}, {8223,22966}, {10876,22747}, {10946,22956}, {10952,22957}, {11378,22476}, {11395,22483}, {11504,22559}, {11829,22951}, {11841,22524}, {11847,22533}, {11908,22943}, {11931,22958}, {11933,22959}, {11948,22965}, {11950,22979}, {11952,22980}, {11954,22981}, {11956,22982}, {11958,22983}, {13900,22976}, {13957,22977}, {18522,22800}, {18964,18978}, {19033,19083}, {19034,19084}, {22762,22776}
The reciprocal orthologic center of these triangles is X(12241).
X(22965) lies on these lines: {1,18978}, {3,22981}, {4,22958}, {11,22966}, {12,22833}, {33,22483}, {56,22951}, {497,22647}, {1697,22653}, {1837,22941}, {2098,22969}, {2646,22476}, {3295,22979}, {3583,22800}, {4294,22533}, {10799,22524}, {10833,22658}, {10877,22747}, {10927,22945}, {10928,22947}, {10947,22956}, {10953,22957}, {10965,22982}, {10966,22776}, {11909,22943}, {11947,22963}, {11948,22964}, {13901,22976}, {13958,22977}, {19037,19083}, {19038,19084}
X(22965) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (497, 22647, 22959), (3295, 22979, 22980)
The reciprocal orthologic center of these triangles is X(12241).
X(22966) lies on these lines: {1,22941}, {2,22466}, {3,22658}, {4,22951}, {5,12897}, {6,2929}, {8,22969}, {11,22965}, {12,18978}, {30,22800}, {55,22959}, {56,22958}, {83,22524}, {113,5893}, {141,22581}, {378,22549}, {427,22483}, {498,22980}, {499,22981}, {590,22976}, {615,22977}, {631,22533}, {958,22776}, {1125,22476}, {1147,13630}, {1181,9705}, {1209,10257}, {1376,22559}, {1493,11802}, {1650,22943}, {1656,22979}, {1698,22653}, {1885,22970}, {3068,19084}, {3069,19083}, {3096,22747}, {4550,11250}, {5181,13367}, {5552,22982}, {5590,22947}, {5591,22945}, {5907,11598}, {6640,18466}, {8222,22963}, {8223,22964}, {8542,22828}, {10151,22538}, {10527,22983}, {11449,15748}, {17811,22528}, {18418,22816}
X(22966) = midpoint of X(i) and X(j) for these {i,j}: {1, 22941}, {3, 22955}, {4, 22951}, {8, 22969}, {1650, 22943}
X(22966) = complement of X(22466)
X(22966) = {X(2), X(22647)}-harmonic conjugate of X(22466)
The reciprocal orthologic center of these triangles is X(22968).
X(22967) lies on these lines: {4,15887}, {6,64}, {546,5462}, {974,22968}, {3357,12161}, {3629,5894}, {5925,14831}, {6241,15011}, {6247,18388}, {6644,6759}, {7529,12315}, {9729,22973}, {11250,13754}, {11381,15010}
The reciprocal orthologic center of these triangles is X(22967).
X(22968) lies on these lines: {5,12897}, {6,17837}, {389,5893}, {546,12235}, {974,22967}, {1514,15887}, {1593,2929}, {5448,18418}, {7687,13488}, {10110,12236}, {10151,22530}, {11431,22533}, {12084,22962}, {13352,22955}, {15033,22750}, {15435,22555}
X(22968) = {X(22466), X(22971)}-harmonic conjugate of X(22970)
The reciprocal orthologic center of these triangles is X(12241).
X(22969) lies on these lines: {1,22466}, {8,22966}, {55,22776}, {56,22559}, {145,22647}, {517,22951}, {519,22941}, {952,22955}, {2098,22965}, {2099,18978}, {5603,22833}, {5604,22947}, {5605,22945}, {7967,22533}, {7968,19083}, {7969,19084}, {8192,22658}, {8210,22963}, {8211,22964}, {9997,22747}, {10247,22979}, {10800,22524}, {10944,22956}, {10950,22957}, {11396,22483}, {11910,22943}, {13902,22976}, {13959,22977}, {18525,22800}
X(22969) = midpoint of X(145) and X(22647)
X(22969) = reflection of X(i) in X(j) for these (i,j): (8, 22966), (18525, 22800)
X(22969) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22653, 22476), (22476, 22653, 22466), (22982, 22983, 22466)
The reciprocal orthologic center of these triangles is X(9729).
X(22970) lies on these lines: {2,22528}, {4,801}, {5,22834}, {6,17837}, {19,22840}, {24,1533}, {25,2929}, {33,22954}, {34,19472}, {51,21652}, {52,1596}, {184,22529}, {185,235}, {193,11470}, {275,19198}, {378,22978}, {381,22808}, {403,9729}, {1425,1858}, {1593,22549}, {1598,22550}, {1660,21659}, {1843,1906}, {1885,22966}, {1974,19142}, {1986,15063}, {3060,22534}, {3089,5878}, {3567,22535}, {3574,10151}, {3575,13202}, {5412,22960}, {5413,22961}, {5448,22979}, {6622,15740}, {6623,22533}, {8541,22830}, {10019,16622}, {10564,13488}, {10641,22974}, {10642,22975}, {11433,18936}, {19446,19488}, {19447,19489}
X(22970) = midpoint of X(4) and X(22750)
X(22970) = anticomplement of X(22581)
X(22970) = complement of X(22528)
X(22970) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 22528, 22581), (6, 17837, 19460), (6, 22972, 17837), (25, 22497, 2929), (51, 21652, 22530), (22466, 22971, 22968), (22581, 22973, 2), (22971, 22972, 22466)
The reciprocal orthologic center of these triangles is X(974).
X(22971) lies on these lines: {4,2929}, {6,17837}, {113,195}, {974,22949}, {7699,22750}, {9786,22802}, {10895,22954}, {10896,19472}, {11064,22647}, {13352,22979}
X(22971) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (22466, 22970, 22972), (22968, 22970, 22466)
The reciprocal orthologic center of these triangles is X(54).
X(22972) lies on these lines: {6,17837}, {24,1192}, {54,22950}, {64,21650}, {154,22497}, {382,13419}, {394,22647}, {1181,22533}, {6759,10938}, {7074,22559}, {9512,17703}, {11472,12084}, {11807,12316}, {12308,18378}, {17810,21652}, {17811,22528}, {20806,22555}, {22800,22808}
X(22972) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17837, 22970, 6), (22466, 22970, 22971)
The reciprocal orthologic center of these triangles is X(9729).
X(22973) lies on these lines: {2,22528}, {5,12897}, {373,21652}, {542,15119}, {578,22955}, {1656,22834}, {2929,5020}, {4846,22800}, {5943,22530}, {9306,22529}, {9729,22967}, {9813,22830}, {9815,18388}, {9817,22954}, {9826,15012}, {10601,19460}, {10643,22974}, {10644,22975}, {10961,22960}, {10963,22961}, {11451,22534}, {11465,22535}, {17825,17837}, {18928,18936}, {19137,19142}, {19188,19198}, {19372,19472}, {19448,19488}, {19449,19489}
X(22973) = complement of X(22581)
X(22973) = {X(2), X(22970)}-harmonic conjugate of X(22581)
The reciprocal orthologic center of these triangles is X(9729).
X(22974) lies on these lines: {6,2929}, {16,22962}, {7051,19472}, {10632,22750}, {10634,22834}, {10636,22840}, {10638,22954}, {10641,22970}, {10643,22973}, {10645,22978}, {11408,22497}, {11420,22528}, {11452,22534}, {11466,22535}, {11475,22538}, {11480,22549}, {11485,22550}, {11488,22555}, {11515,22581}, {16808,22816}, {17826,17837}, {18468,22808}, {18929,18936}, {19190,19198}, {19363,19460}, {19450,19488}, {19451,19489}, {21647,21652}
X(22974) = {X(6), X(2929)}-harmonic conjugate of X(22975)
The reciprocal orthologic center of these triangles is X(9729).
X(22975) lies on these lines: {6,2929}, {15,22962}, {1250,22954}, {10633,22750}, {10635,22834}, {10637,22840}, {10642,22970}, {10644,22973}, {10646,22978}, {11409,22497}, {11421,22528}, {11453,22534}, {11467,22535}, {11476,22538}, {11481,22549}, {11486,22550}, {11489,22555}, {11516,22581}, {16809,22816}, {17827,17837}, {18470,22808}, {18930,18936}, {19191,19198}, {19364,19460}, {19373,19472}, {19452,19488}, {19453,19489}, {21648,21652}
X(22975) = {X(6), X(2929)}-harmonic conjugate of X(22974)
The reciprocal orthologic center of these triangles is X(12241).
X(22976) lies on these lines: {2,19084}, {6,22977}, {371,22833}, {590,22966}, {7585,19083}, {8972,22647}, {8974,22945}, {8975,22947}, {8976,22955}, {9540,22951}, {13883,22476}, {13884,22483}, {13885,22524}, {13886,22533}, {13887,22559}, {13888,22653}, {13889,22658}, {13892,22747}, {13893,22941}, {13894,22943}, {13895,22956}, {13896,22957}, {13898,22959}, {13899,22963}, {13900,22964}, {13901,22965}, {13902,22969}, {13903,22979}, {13904,22980}, {13905,22981}, {13906,22982}, {13907,22983}, {18538,22800}, {18965,18978}, {22763,22776}
The reciprocal orthologic center of these triangles is X(12241).
X(22977) lies on these lines: {2,19083}, {6,22976}, {372,22833}, {615,22966}, {3069,22466}, {7586,19084}, {13935,22951}, {13936,22476}, {13937,22483}, {13938,22524}, {13939,22533}, {13940,22559}, {13941,22647}, {13942,22653}, {13943,22658}, {13946,22747}, {13947,22941}, {13948,22943}, {13949,22945}, {13950,22947}, {13951,22955}, {13952,22956}, {13953,22957}, {13954,22958}, {13955,22959}, {13956,22963}, {13957,22964}, {13958,22965}, {13959,22969}, {13961,22979}, {13962,22980}, {13963,22981}, {13964,22982}, {13965,22983}, {18762,22800}, {18966,18978}, {22764,22776}
The reciprocal orthologic center of these triangles is X(9729).
X(22978) lies on these lines: {3,2929}, {24,22538}, {30,22816}, {35,19472}, {36,22954}, {74,5562}, {376,22555}, {378,22970}, {511,22830}, {550,13289}, {1656,22971}, {2071,5907}, {3098,15074}, {3357,5876}, {3519,20417}, {3520,22750}, {4550,11250}, {5092,19142}, {5448,19511}, {6200,22960}, {6396,22961}, {7688,22840}, {7689,10627}, {7691,13348}, {9818,22973}, {10605,19460}, {10606,17837}, {10645,22974}, {10646,22975}, {11410,22497}, {11430,22529}, {11438,22530}, {11454,22534}, {11468,22535}, {12084,22800}, {12359,12901}, {16013,22647}, {16111,18442}, {18931,18936}, {19192,19198}, {19454,19488}, {19455,19489}
X(22978) = midpoint of X(3) and X(22549)
X(22978) = circumtangential isogonal conjugate of X(22467)
The reciprocal orthologic center of these triangles is X(12241).
X(22979) lies on these lines: {3,2929}, {5,22647}, {30,22533}, {195,5893}, {381,22833}, {517,22653}, {999,18978}, {1598,22483}, {1656,22966}, {3295,22965}, {3843,22800}, {5448,22970}, {5790,22941}, {6417,19084}, {6418,19083}, {7517,22658}, {9301,22747}, {9654,22958}, {9669,22959}, {10112,11744}, {10246,22476}, {10247,22969}, {10620,20427}, {11842,22524}, {11849,22559}, {11911,22943}, {11916,22945}, {11917,22947}, {11928,22956}, {11929,22957}, {11949,22963}, {11950,22964}, {12000,22982}, {12001,22983}, {12111,12282}, {12293,22538}, {12825,22534}, {12902,18439}, {13352,22971}, {13903,22976}, {13961,22977}, {18504,22750}, {19362,19460}, {22765,22776}
X(22979) = reflection of X(3) in X(22466)
X(22979) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18978, 22981, 999), (22833, 22955, 381), (22965, 22980, 3295)
The reciprocal orthologic center of these triangles is X(12241).
X(22980) lies on these lines: {1,22466}, {3,18978}, {5,22959}, {12,22955}, {35,22951}, {388,22533}, {495,22958}, {498,22966}, {1479,22833}, {3085,22647}, {3295,22965}, {3299,19083}, {3301,19084}, {10037,22658}, {10038,22747}, {10039,22941}, {10040,22945}, {10041,22947}, {10523,22956}, {10801,22524}, {10895,22800}, {10954,22957}, {11398,22483}, {11507,22559}, {11912,22943}, {11951,22963}, {11952,22964}, {13904,22976}, {13962,22977}, {18447,19472}, {22766,22776}
X(22980) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22466, 22981), (3295, 22979, 22965)
The reciprocal orthologic center of these triangles is X(12241).
X(22981) lies on these lines: {1,22466}, {3,22965}, {11,22955}, {36,22951}, {496,22959}, {497,22533}, {499,22966}, {999,18978}, {1478,22833}, {1737,22941}, {3086,22647}, {3299,19084}, {3301,19083}, {10046,22658}, {10047,22747}, {10048,22945}, {10049,22947}, {10523,22957}, {10802,22524}, {10896,22800}, {10948,22956}, {11399,22483}, {11508,22559}, {11913,22943}, {11953,22963}, {11954,22964}, {13905,22976}, {13963,22977}, {18455,22808}, {22767,22776}
X(22981) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 22466, 22980), (999, 22979, 18978)
The reciprocal orthologic center of these triangles is X(12241).
X(22982) lies on these lines: {1,22466}, {12,22956}, {5552,22966}, {10528,22647}, {10531,22833}, {10803,22524}, {10805,22533}, {10834,22658}, {10878,22747}, {10915,22941}, {10929,22945}, {10930,22947}, {10942,22955}, {10955,22957}, {10956,22958}, {10958,22959}, {10965,22965}, {11248,22951}, {11400,22483}, {11509,18978}, {11914,22943}, {11955,22963}, {11956,22964}, {12000,22979}, {13906,22976}, {13964,22977}, {18542,22800}, {19047,19083}, {19048,19084}, {22768,22776}
X(22982) = {X(22466), X(22969)}-harmonic conjugate of X(22983)
The reciprocal orthologic center of these triangles is X(12241).
X(22983) lies on these lines: {1,22466}, {11,22957}, {10527,22966}, {10529,22647}, {10532,22833}, {10804,22524}, {10806,22533}, {10835,22658}, {10879,22747}, {10916,22941}, {10931,22945}, {10932,22947}, {10943,22955}, {10949,22956}, {10957,22958}, {10959,22959}, {10966,22776}, {11249,22951}, {11401,22483}, {11510,22559}, {11915,22943}, {11957,22963}, {11958,22964}, {12001,22979}, {13907,22976}, {13965,22977}, {18544,22800}, {18967,18978}, {19049,19083}, {19050,19084}
X(22983) = {X(22466), X(22969)}-harmonic conjugate of X(22982)
The reciprocal parallelogic center of these triangles is X(12241).
X(22984) lies on the line {351,22985}
The reciprocal parallelogic center of these triangles is X(12241).
X(22985) lies on the line {351,22984}
The reciprocal cyclologic center of these triangles is X(974).
X(22986) lies on the line {113,5893}
The reciprocal orthologic center of these triangles is X(22988).
X(22987) lies on these lines: {}
The reciprocal orthologic center of these triangles is X(22987).
X(22988) lies on these lines: {}
The reciprocal cyclologic center of these triangles is X(22990).
X(22989) lies on the line {5572,22990}
The reciprocal cyclologic center of these triangles is X(22989).
X(22990) lies on the line {5572,22989}
The reciprocal orthologic center of these triangles is X(442).
X(22991) lies on these lines: {3,11281}, {10,12864}, {1020,3333}, {1125,5763}, {2346,5703}, {6265,12521}, {9957,12855}, {10582,12120}, {11019,12599}, {12777,20007}
X(22991) = midpoint of X(3) and X(16134)
The reciprocal orthologic center of these triangles is X(12732).
X(22992) lies on these lines: {3,12731}, {10,12864}, {3428,12777}, {3652,12516}, {5049,12855}, {6943,9874}, {8273,15998}, {12260,14986}
X(22992) = midpoint of X(3) and X(12731)
X(22993) lies on these lines: {2,178}, {8,8390}, {9,363}, {10,9836}, {210,17607}, {236,11923}, {518,11026}, {936,8111}, {958,8109}, {960,9805}, {1125,11039}, {1329,8380}, {1376,8107}, {2886,8377}, {3035,13260}, {3036,12733}, {3740,11222}, {5044,12488}, {5745,11854}, {5777,12673}, {6732,7028}, {8140,8580}, {8385,18230}, {9783,18228}, {9847,18247}, {11527,15829}, {11530,12879}, {11856,18227}, {11892,18229}, {11922,18234}, {12561,18249}, {12574,18250}, {12707,18251}, {12719,18252}, {12759,18254}, {12851,18255}, {12878,18257}, {12882,18259}, {12886,18248}, {16135,18253}, {17621,18236}
X(22993) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11685, 8113), (8, 8390, 12633)
X(22994) lies on these lines: {2,8114}, {8,178}, {9,164}, {10,9837}, {188,8135}, {210,17608}, {518,11027}, {958,8110}, {960,9806}, {1125,11040}, {1329,8381}, {1376,8108}, {2886,8378}, {3035,13261}, {3036,12734}, {3452,12885}, {3740,11223}, {5044,12489}, {5273,11887}, {5745,11855}, {5777,12674}, {7028,8138}, {8140,8580}, {8242,10494}, {8386,18230}, {9787,18228}, {9849,18247}, {10233,16016}, {11528,15829}, {11857,18227}, {11893,18229}, {11925,18234}, {11926,18235}, {12562,18249}, {12576,18250}, {12708,18251}, {12720,18252}, {12760,18254}, {12852,18255}, {12881,18248}, {12883,18257}, {12887,18259}, {16136,18253}, {17623,18236}
X(22994) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11686, 8114), (8, 8392, 12634)
The reciprocal cyclologic center of these triangles is X(22996).
X(22995) lies on the line {1125,22996}
The reciprocal cyclologic center of these triangles is X(22995).
X(22996) lies on the Spieker circle and these lines: {1125,22995}, {3755,4906}
The reciprocal orthologic center of these triangles is X(22998).
X(22997) lies on these lines: {5,14}, {15,542}, {16,524}, {30,6778}, {99,532}, {115,16267}, {187,8724}, {194,617}, {230,9113}, {298,619}, {299,22689}, {511,23007}, {512,22999}, {523,15743}, {543,22495}, {2782,22701}, {5460,16966}, {5463,8593}, {5469,16960}, {5470,11542}, {5965,9115}, {5969,23000}, {6054,6109}, {6671,22894}, {6772,22509}, {9114,23006}, {9760,22496}, {16001,20425}, {18765,22797}, {22603,22606}, {22632,22635}
X(22997) = reflection of X(i) in X(j) for these (i,j): (13, 6783), (15, 9117), (298, 619), (22998, 187)
X(22997) = isogonal conjugate of X(32908)
X(22997) = X(13)-antipedal-to-X(14)-antipedal similarity image of X(14)
X(22997) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (14, 396, 22510), (14, 16529, 396), (6777, 16962, 6109)
The reciprocal orthologic center of these triangles is X(22997).
X(22998) lies on these lines: {5,13}, {15,524}, {16,542}, {30,6777}, {115,16268}, {187,8724}, {194,616}, {230,9112}, {298,22687}, {299,618}, {385,532}, {511,23014}, {512,23008}, {523,11586}, {543,22496}, {2782,22702}, {5459,16967}, {5464,8593}, {5469,11543}, {5470,16961}, {5965,9117}, {5969,23009}, {6054,6108}, {6672,22850}, {6775,22507}, {9116,23013}, {9762,22495}, {16002,20426}, {18764,22796}, {22601,22605}, {22630,22634}
X(22998) = isogonal conjugate of X(32906)
X(22998) = reflection of X(i) in X(j) for these (i,j): (14, 6782), (16, 9115), (299, 618), (22997, 187)
X(22998) = X(14)-antipedal-to-X(13)-antipedal similarity image of X(13)
X(22998) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (13, 395, 22511), (13, 16530, 395), (6778, 16963, 6108)
The reciprocal orthologic center of these triangles is X(14181).
X(22999) lies on these lines: {13,23007}, {16,3231}, {61,23017}, {511,6321}, {512,22997}, {622,11582}
The reciprocal orthologic center of these triangles is X(6582).
X(23000) lies on these lines: {13,538}, {15,385}, {16,6581}, {17,76}, {61,23018}, {62,12215}, {194,622}, {698,3105}, {3095,3818}, {3643,7757}, {5969,22997}, {14539,14880}
The reciprocal orthologic center of these triangles is X(6298).
X(23001) lies on these lines: {13,754}, {16,6296}, {17,83}, {61,23019}, {623,9866}, {732,3105}, {6287,19130}
The reciprocal orthologic center of these triangles is X(13705).
X(23002) lies on these lines: {16,13706}, {17,1327}, {61,23020}, {3105,22917}, {13692,23011}
The reciprocal orthologic center of these triangles is X(13825).
X(23003) lies on these lines: {16,13826}, {17,1328}, {61,23021}, {3105,22919}, {13812,23012}
The reciprocal parallelogic center of these triangles is X(23005).
X(23004) lies on these lines: {4,3105}, {6,13102}, {14,16}, {15,115}, {61,5254}, {62,5471}, {98,11602}, {99,623}, {148,621}, {187,22511}, {396,5470}, {511,6321}, {512,23007}, {617,18582}, {619,16966}, {624,14041}, {635,17128}, {636,7911}, {1080,5479}, {2549,3106}, {2782,20428}, {3054,5474}, {3104,7748}, {3107,5475}, {5237,20416}, {5318,6778}, {5460,16242}, {5464,20112}, {5469,6109}, {5613,16808}, {5978,6115}, {5983,7925}, {6036,21158}, {6108,8859}, {6671,14061}, {6672,13586}, {6694,7923}, {6774,10646}, {6777,10722}, {7684,14639}, {7685,11676}, {7746,16630}, {8352,22575}, {8584,22579}, {9117,16267}, {11303,22689}, {11542,16529}, {14137,22862}, {14539,15980}, {22493,22577}
X(23004) = midpoint of X(i) and X(j) for these {i,j}: {148, 621}, {6777, 19106}, {22493, 22577}
X(23004) = reflection of X(i) in X(j) for these (i,j): (15, 115), (99, 623), (1080, 5479), (14539, 15980)
X(23004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (14, 19107, 22512), (15, 115, 22510), (5470, 6780, 396), (5479, 6114, 16809), (6321, 11646, 23005)
The reciprocal parallelogic center of these triangles is X(23004).
X(23005) lies on these lines: {4,3104}, {6,13103}, {13,15}, {16,115}, {61,5472}, {62,5254}, {98,11603}, {99,624}, {148,622}, {187,22510}, {383,5478}, {395,5469}, {511,6321}, {512,23014}, {616,18581}, {618,16967}, {623,14041}, {635,7911}, {636,17128}, {2549,3107}, {2782,20429}, {3054,5473}, {3105,7748}, {3106,5475}, {5238,20415}, {5321,6777}, {5459,16241}, {5460,8595}, {5463,20112}, {5470,6108}, {5617,16809}, {5979,6114}, {5982,7925}, {6036,21159}, {6109,8859}, {6671,13586}, {6672,14061}, {6695,7923}, {6771,10645}, {6778,10722}, {7684,11676}, {7685,14639}, {7746,16631}, {8352,22576}, {8584,22580}, {9115,16268}, {11304,22687}, {11543,16530}, {14136,22906}, {14538,15980}, {22494,22578}
X(23005) = midpoint of X(i) and X(j) for these {i,j}: {148, 622}, {6778, 19107}, {22494, 22578}
X(23005) = reflection of X(i) in X(j) for these (i,j): (16, 115), (99, 624), (383, 5478), (14538, 15980)
X(23005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (13, 19106, 22513), (16, 115, 22511), (5469, 6779, 395), (5478, 6115, 16808), (6321, 11646, 23004)
The reciprocal parallelogic center of these triangles is X(23004).
X(23006) lies on these lines: {2,13}, {3,5472}, {4,6782}, {6,22906}, {14,9880}, {15,5473}, {18,22832}, {62,5254}, {99,6783}, {115,11486}, {187,20425}, {381,9115}, {511,23023}, {512,23028}, {1250,10062}, {1351,5477}, {3105,11257}, {5318,5617}, {5471,6321}, {5475,5615}, {5478,18581}, {5611,6781}, {6771,11481}, {6777,10722}, {7746,16629}, {9114,22997}, {10078,19373}, {10646,21156}, {16001,22238}, {16530,16809}, {16960,22900}, {22513,22862}
X(23006) = homothetic center of antipedal triangle of X(13) and 1st isodynamic-Dao triangle
X(23006) = antipedal-circle-of-X(13)-inverse of X(16)
X(23006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (13, 6779, 5463), (13, 16242, 22489), (616, 5335, 6115), (5335, 6115, 13), (5473, 9112, 15), (8595, 9762, 5463), (11486, 13103, 115)
The reciprocal parallelogic center of these triangles is X(14187).
X(23007) lies on these lines: {13,22999}, {16,237}, {61,23022}, {511,22997}, {512,23004}, {10653,11002}
The reciprocal orthologic center of these triangles is X(14177).
X(23008) lies on these lines: {14,23014}, {15,3231}, {62,23023}, {511,6321}, {512,22998}, {621,11581}
The reciprocal orthologic center of these triangles is X(6295).
X(23009) lies on these lines: {14,538}, {15,6294}, {16,385}, {18,76}, {61,12215}, {62,23024}, {194,621}, {698,3104}, {3095,3818}, {3642,7757}, {5969,22998}, {14538,14880}
The reciprocal orthologic center of these triangles is X(6299).
X(23010) lies on these lines: {14,754}, {15,6297}, {18,83}, {62,23025}, {624,9866}, {732,3104}, {6287,19130}
The reciprocal orthologic center of these triangles is X(13703).
X(23011) lies on these lines: {15,13704}, {18,1327}, {62,23026}, {3104,22872}, {13692,23002}
The reciprocal orthologic center of these triangles is X(13823).
X(23012) lies on these lines: {15,13824}, {18,1328}, {62,23027}, {3104,22874}, {13812,23003}
The reciprocal parallelogic center of these triangles is X(23005).
X(23013) lies on these lines: {2,14}, {3,5471}, {4,6783}, {6,22862}, {13,9880}, {16,5474}, {17,22831}, {61,5254}, {99,6782}, {115,11485}, {187,20426}, {381,9117}, {511,23017}, {512,23022}, {1351,5477}, {3104,11257}, {5321,5613}, {5472,6321}, {5475,5611}, {5479,18582}, {5615,6781}, {6774,11480}, {6778,10722}, {7051,10077}, {7746,16628}, {9116,22998}, {10061,10638}, {10645,21157}, {16002,22236}, {16529,16808}, {16961,22856}, {22512,22906}
X(23013) = antipedal-circle-of-X(14)-inverse of X(15)
X(23013) = homothetic center of antipedal triangle of X(14) and 2nd isodynamic-Dao triangle
X(23013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (14, 6780, 5464), (14, 16241, 22490), (617, 5334, 6114), (5334, 6114, 14), (5474, 9113, 16), (8594, 9760, 5464), (11485, 13102, 115)
The reciprocal parallelogic center of these triangles is X(14185).
X(23014) lies on these lines: {14,23008}, {15,237}, {62,23028}, {511,22998}, {512,23005}, {10654,11002}
The reciprocal orthologic center of these triangles is X(10266).
X(23015) lies on these lines: {3,16145}, {10,191}, {758,12745}, {6265,12524}, {6952,7701}
X(23015) = midpoint of X(3) and X(16145)
The reciprocal orthologic center of these triangles is X(11604).
X(23016) lies on these lines: {3,12745}, {10,191}, {758,12524}, {1749,10266}, {3652,12519}, {6853,12660}, {13465,22782}
X(23016) = midpoint of X(i) and X(j) for these {i,j}: {3, 12745}, {13465, 22782}
The reciprocal orthologic center of these triangles is X(14181).
X(23017) lies on these lines: {14,512}, {15,14182}, {61,22999}, {511,23013}, {5475,23023}, {10654,23022}
X(23217) = isogonal conjugate of polar conjugate of X(34990)
The reciprocal orthologic center of these triangles is X(6582).
X(23018) lies on these lines: {4,69}, {6,12214}, {14,5969}, {15,6581}, {61,23000}, {303,22715}, {538,10654}, {698,3104}, {3098,5981}, {3107,3589}
The reciprocal orthologic center of these triangles is X(6298).
X(23019) lies on these lines: {4,83}, {15,6296}, {61,23001}, {732,3104}, {754,10654}, {22512,22689}
The reciprocal orthologic center of these triangles is X(13705).
X(23020) lies on these lines: {4,1327}, {15,13706}, {61,23002}, {3104,22872}
The reciprocal orthologic center of these triangles is X(13825).
X(23021) lies on these lines: {4,1328}, {15,13826}, {61,23003}, {3104,22874}
The reciprocal parallelogic center of these triangles is X(14187).
X(23022) lies on these lines: {14,511}, {15,14188}, {61,23007}, {512,23013}, {10654,23017}
The reciprocal orthologic center of these triangles is X(14177).
X(23023) lies on these lines: {13,512}, {16,14178}, {62,23008}, {511,23006}, {5475,23017}, {10653,23028}
The reciprocal orthologic center of these triangles is X(6295).
X(23024) lies on these lines: {4,69}, {6,12213}, {13,5969}, {16,6294}, {62,23009}, {302,22714}, {538,10653}, {698,3105}, {3098,5980}, {3106,3589}
The reciprocal orthologic center of these triangles is X(6299).
X(23025) lies on these lines: {4,83}, {16,6297}, {62,23010}, {732,3105}, {754,10653}, {22513,22687}
The reciprocal orthologic center of these triangles is X(13703).
X(23026) lies on these lines: {4,1327}, {16,13704}, {62,23011}, {3105,22917}
The reciprocal orthologic center of these triangles is X(13823).
X(23027) lies on these lines: {4,1328}, {16,13824}, {62,23012}, {3105,22919}
The reciprocal parallelogic center of these triangles is X(14185).
X(23028) lies on these lines: {13,511}, {16,14186}, {62,23014}, {512,23006}, {10653,23023}
X(23029) lies on the line {2,3603}
X(23029) = complement of X(3603)
X(23030) lies on the line {2,3604}
X(23030) = complement of X(3604)
X(23031) lies on the line {2,3602}
X(23031) = complement of X(3602)
X(23032) lies on the line {2,16840}
X(23033) lies on these lines: {}
X(23034) lies on these lines: {}
The reciprocal parallelogic center of these triangles is X(79).
X(23035) lies on these lines: {351,23036}, {8702,9131}
The reciprocal parallelogic center of these triangles is X(79).
X(23036) lies on these lines: {351,23035}, {8702,9979}
The reciprocal cyclologic center of these triangles is X(23038).
X(23037) lies on the reflection circle and these lines: {}
The reciprocal cyclologic center of these triangles is X(23037).
X(23038) lies on the Yiu circle and these lines: {}
The reciprocal eulerologic center of these triangles is X(11459).
X(23039) lies on these lines: {2,568}, {3,49}, {4,2889}, {5,3060}, {20,5876}, {22,10540}, {26,18350}, {30,2979}, {51,5055}, {52,1656}, {68,3519}, {69,265}, {110,7502}, {140,5889}, {143,3090}, {156,7512}, {182,15087}, {183,18322}, {195,569}, {323,14805}, {343,2072}, {373,15703}, {376,5663}, {381,511}, {382,5907}, {389,3526}, {399,2916}, {546,15056}, {547,5640}, {548,6241}, {549,5890}, {550,12111}, {567,1993}, {577,22146}, {631,6102}, {632,15043}, {1350,12083}, {1351,12039}, {1352,9019}, {1511,10298}, {1568,10254}, {1614,6030}, {1657,12162}, {1658,7691}, {1994,7550}, {2070,9306}, {2781,5655}, {2937,10539}, {3091,10263}, {3153,15108}, {3313,18440}, {3419,18330}, {3522,13491}, {3523,13630}, {3525,12006}, {3530,10574}, {3534,6000}, {3544,16982}, {3567,3628}, {3581,6644}, {3627,15058}, {3819,5054}, {3830,15030}, {3851,5446}, {4549,7723}, {5056,10095}, {5067,15026}, {5068,13421}, {5070,5462}, {5071,11002}, {5072,10110}, {5449,22815}, {5609,7492}, {5650,5892}, {6090,14070}, {6193,11821}, {6288,18569}, {6293,10282}, {6592,13505}, {6759,13564}, {7386,18917}, {7393,12160}, {7485,13339}, {7503,16266}, {7506,17834}, {7509,12161}, {7516,7592}, {7517,17814}, {7528,11487}, {7574,11649}, {7577,15110}, {7729,11204}, {7731,10272}, {8681,9967}, {8703,15072}, {8717,12308}, {9729,15720}, {10201,12824}, {10219,16625}, {10224,21230}, {10264,12273}, {10299,11592}, {10575,13348}, {10628,11202}, {11381,17800}, {11442,14791}, {11451,15699}, {11562,15040}, {11660,13160}, {12100,20791}, {12103,12279}, {12290,15704}, {12294,18535}, {12825,20127}, {13346,14130}, {13504,14072}, {14683,15101}, {14845,21849}, {14855,15688}, {14915,15681}, {15022,18874}, {15024,16881}, {15028,16239}, {15032,15246}, {15082,15723}, {15687,16261}, {15693,16836}, {16163,22584}, {17702,18564}, {18392,18572}, {19129,20806}, {19709,21969}
X(23039) = reflection of X(i) in X(j) for these (i,j): (2, 15067), (3, 3917), (4, 15060), (51, 10170), (52, 5943), (381, 5891), (382, 16194), (3830, 15030), (7729, 11204)
X(23039) = anticomplement of X(5946)
X(23039) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 394, 22115), (3, 5562, 18436), (3, 9703, 18475), (5, 11412, 6243), (5, 14449, 9781), (20, 5876, 18439), (22, 15068, 10540), (51, 10170, 5055), (52, 5943, 13321), (52, 11793, 1656), (185, 5447, 3), (1216, 5562, 3), (3292, 18475, 9703), (5876, 10627, 20), (6101, 11591, 4), (11412, 11444, 5)
The reciprocal eulerologic center of these triangles does not exist
As a point on the Euler line, X(23040) has Shinagawa coefficients (16*F, E-16*F).
X(23040) lies on these lines: {2,3}, {54,20421}, {112,15515}, {185,3431}, {1249,15109}, {1614,11204}, {3043,15055}, {3098,8537}, {8567,9707}, {8588,10312}, {11454,12038}, {11468,13367}, {11470,17508}, {12112,17821}
X(23040) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 378, 17506), (3, 3520, 21844), (3, 10226, 20), (3, 11250, 10298), (20, 6143, 4), (186, 3520, 1593), (1593, 15750, 3517), (3431, 11270, 185), (3520, 21844, 4), (3524, 3528, 10996), (10298, 11250, 3529), (15750, 17506, 21844)
The reciprocal eulerologic center of these triangles is X(23042).
X(23041) lies on these lines: {2,154}, {3,206}, {6,24}, {64,15578}, {66,140}, {159,182}, {161,10601}, {511,11202}, {631,5596}, {1176,17928}, {1177,1511}, {1350,7488}, {1352,7542}, {1495,19124}, {1498,7509}, {1658,19139}, {1974,13367}, {2393,5050}, {2781,15035}, {3147,6776}, {3313,9715}, {3515,19125}, {3517,9969}, {3526,6697}, {3589,7401}, {3827,10202}, {5092,6759}, {5480,7487}, {6000,17508}, {6643,16252}, {7405,9833}, {7544,17845}, {8550,15585}, {9924,15582}, {10303,20079}, {10541,15581}, {11449,19121}, {13289,15141}, {14561,23049}, {14788,20300}
X(23041) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 206, 19149), (6, 17821, 15577), (159, 182, 8549), (182, 10282, 159), (3515, 19125, 19161), (7488, 20806, 1350)
The reciprocal eulerologic center of these triangles is X(23041).
X(23042) lies on these lines: {3,19132}, {5,182}, {6,3517}, {154,5050}, {159,575}, {184,11433}, {389,19125}, {511,11202}, {576,15577}, {578,1974}, {1092,19121}, {1147,19154}, {1351,17821}, {1353,15585}, {1498,12017}, {1971,5034}, {3357,5092}, {3564,10192}, {3618,9833}, {5085,6000}, {5171,15257}, {5596,20299}, {5656,10984}, {5965,10274}, {6467,9707}, {6593,13289}, {9306,19131}, {9968,15578}, {10182,19126}, {10539,19129}, {11204,17508}, {14561,18400}, {15139,16187}, {15582,22234}, {19118,19357}, {19127,21167}
X(23042) = midpoint of X(154) and X(5050)
X(23042) = reflection of X(11204) in X(17508)
X(23042) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (182, 206, 6759), (5092, 19149, 3357)
The reciprocal eulerologic center of these triangles is X(4).
X(23043) lies on these lines: {2,2777}, {4,11564}, {5,16219}, {113,11202}, {154,18561}, {1539,2781}, {5663,18376}, {6000,7728}, {10628,16194}, {10706,18400}, {10721,13619}, {11744,13623}, {13293,15646}
There is not eulerologic center (Ara, Ehrmann-side).
X(23044) lies on these lines: {2,3}, {6759,9908}, {9645,10831}, {13754,19141}
X(23044) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 10243, 26), (22, 7503, 376), (22, 15078, 7512), (376, 6353, 6803), (7387, 14070, 22), (9909, 18534, 7387)
There is not eulerologic center (Atik, outer-Garcia).
X(23045) lies on these lines: {4,8}, {496,10863}, {971,8582}, {3091,10569}, {3304,17604}, {6245,10855}, {8581,9581}, {8583,10157}, {9709,10860}, {9711,15587}, {9842,11019}, {12019,13227}
X(23045) = {X(9947), X(10241)}-harmonic conjugate of X(8)
There is not eulerologic center (Ehrmann-mid, submedial)
As a point on the Euler line, X(23046) has Shinagawa coefficients (5, 21).
X(23046) lies on these lines: {2,3}, {538,22681}, {590,6476}, {615,6477}, {671,14692}, {754,20112}, {1327,7584}, {1328,7583}, {3625,22791}, {3630,21850}, {3633,3656}, {4668,18357}, {4691,18483}, {4995,18514}, {5298,18513}, {5318,16268}, {5321,16267}, {5476,12007}, {5876,21849}, {6144,20423}, {6417,14241}, {6418,14226}, {10706,11801}, {10733,11694}, {10895,15170}, {11381,18874}, {12295,22251}, {12571,13607}, {13364,16194}, {13451,18435}, {13482,18350}, {18424,18907}
X(23046) = reflection of X(2) in X(14892)
X(23046) = complement of X(15689)
X(23046) = inverse of X(15684) in the orthocentroidal circle
X(23046) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 3543, 17538), (2, 15684, 548), (140, 3543, 19710), (382, 3854, 12811), (382, 5071, 12100), (549, 15684, 15686), (3146, 15694, 15690), (3543, 3855, 19709), (3543, 15022, 15698), (3543, 15698, 17800), (3543, 19709, 140), (3544, 5073, 16239), (5055, 15684, 15706), (5072, 15684, 2), (14093, 15684, 15683), (18586, 18587, 3522)
There is not eulerologic center (Euler, Ehrmann-vertex)
As a point on the Euler line, X(23047) has Shinagawa coefficients (F, E+5*F).
X(23047) lies on these lines: {2,3}, {125,13568}, {265,13292}, {578,18376}, {946,12135}, {973,1112}, {1398,5229}, {1503,11572}, {1514,13474}, {1699,5090}, {1829,19925}, {1879,6748}, {1902,18483}, {1986,11801}, {2883,11550}, {3564,8537}, {3574,12241}, {3817,11363}, {5448,12134}, {5480,11470}, {5893,11381}, {6146,18383}, {6403,15056}, {6746,13754}, {7699,12289}, {7718,9779}, {7745,16318}, {10880,18538}, {10881,18762}, {10895,11393}, {10896,11392}, {11245,12233}, {11402,18945}, {12022,18394}, {12162,15432}, {12370,18379}, {18405,19467}, {18474,22660}
X(23047) = inverse of X(12173) in the orthocentroidal circle
X(23047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 235, 428), (4, 381, 235), (4, 403, 6756), (4, 546, 10151), (4, 1885, 13473), (4, 3855, 3089), (4, 6623, 5198), (4, 7378, 11403), (4, 7541, 407), (4, 7563, 430), (4, 15559, 13488), (4, 18560, 3853), (5, 3627, 1658), (1595, 3845, 4), (3146, 8889, 3516), (3861, 13488, 4)
The reciprocal eulerologic center of these triangles is X(23049).
X(23048) lies on these lines: {4,11458}, {6,18400}, {30,10250}, {154,14848}, {182,10169}, {381,17813}, {542,11216}, {576,13292}, {597,11202}, {1350,10193}, {1351,1853}, {1503,15520}, {2393,5476}, {3153,11443}, {6000,20423}, {8541,18390}, {8549,22802}, {9927,11255}, {10192,18583}, {10249,19924}, {10602,18388}, {11206,13366}, {11405,18396}, {11477,20299}, {18449,18474}
X(23048) = midpoint of X(i) and X(j) for these {i,j}: {381, 17813}, {1351, 1853}
X(23048) = reflection of X(i) in X(j) for these (i,j): (182, 10169), (1350, 10193), (10192, 18583)
The reciprocal eulerologic center of these triangles is X(23048).
X(23049) lies on these lines: {4,6}, {30,10249}, {66,21850}, {159,19130}, {206,567}, {265,1351}, {381,2393}, {511,14852}, {542,11216}, {576,18383}, {858,1350}, {895,18434}, {1352,10297}, {1853,2781}, {1995,15577}, {3546,21167}, {5476,18400}, {5925,15579}, {6403,14644}, {6642,10182}, {7464,15578}, {7529,9920}, {7547,15073}, {8537,18394}, {8548,18377}, {10113,13248}, {10169,11179}, {10516,11188}, {10602,18386}, {11255,18379}, {11416,18392}, {11470,11572}, {13434,17845}, {14561,23041}, {18430,18440}, {18494,19136}
X(23049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (12022, 14853, 6), (18430, 18449, 18440)
See Angel Montesdeoca, HG300818.
X(23050) lies on these lines: {1,475}, {9,8750}, {19,25}, {34,1883}, {75,1897}, {200,3192}, {210,3195}, {318,5263}, {474,17102}, {594,2331}, {975,6198}, {1041,5236}, {1249,2345}, {1876,3242}, {2207,7079}, {2550,7952}, {8270,11677}, {12329,20613} {98,6530}, {107,685}, {112,2966}, {648,17932}, {2422,2442}, {14273,15459}
See Angel Montesdeoca, HG300818.
X(23051) lies on these lines: {10,4000}, {19,38}, {37,614}, {63,82}, {65,3242}, {75,16750}, {158,20883}, {225,8801}, {759,907}, {969,3873}, {1910,17467}, {2186,17445}, {2345,3677}, {3668,11677}, {8769,17446}, {16517,18785}
See Angel Montesdeoca, HG300818.
X(23052) lies on these lines: {1,19}, {4,3663}, {33,3666}, {34,6180}, {38,1096}, {63,162}, {75,1895}, {158,20883}, {278,3677}, {281,7174}, {474,17102}, {518,2331}, {811,3403}, {982,1435}, {984,7079}, {986,11471}, {1040,19649}, {1210,1861}, {1767,8270}, {1783,5223}, {1859,17599}, {3242,14571}, {4310,5236}, {4847,17903}, {5573,17917}
See Angel Montesdeoca, HG300818.
X(23053) lies on these lines: {2,6}, {671,3524}, {1153,2549}, {3545,13449}, {5067,7812}, {5210,20112}, {7607,11172}, {7612,11179}, {11147,16509}, {14568,15709}
See Angel Montesdeoca, HG300818.
X(23054) lies on these lines: {1992,16509}, {4232,8860}
See Angel Montesdeoca, HG300818.
X(23055) lies on these lines: {2,6}, {98,11172}, {99,5485}, {115,8182}, {187,7615}, {376,671}, {381,9752}, {598,1285}, {1384,3363}, {2549,5569}, {3090,7812}, {3524,14568}, {3533,7760}, {3543,9756}, {3545,10788}, {3785,11318}, {5067,6179}, {5461,16041}, {6054,9754}, {7617,7737}, {7619,7798}, {7620,8598}, {7710,11177}, {7757,15702}, {7810,14064}, {7817,16043}, {9166,14907}, {9167,17131}, {9209,14977}, {9741,11054}, {9759,11061}, {11159,16509}, {12150,18842} : :
X(23055) = reflection of X(1007) in X(2)
See Emmanuel José García and Angel Montesdeoca, AdGeom 4943 and HG100918.
X(23056) lies on these lines: {926,2170}, {2246,4845}, {3119,3900}, {4162,7004} : :
See Emmanuel José García and Angel Montesdeoca, AdGeom 4943 and HG200918.
X(23056) lies on these lines: {1,2254}, {145,3716}, {513,4162}, {519,14430}, {663,14077}, {891,3251}, {905,4959}, {1635,3722}, {2814,16200}, {2832,10699}, {3244,3762}, {3295,8648}, {3900,14414}, {8572,20315}
X(23057) = reflection of X(i) in X(j) for thiese (i,j): (2254,14413), (14413,1)
See Kadir Altintas and Angel Montesdeoca, HG110918.
X(23058) lies on these lines: {1,1146}, {2,3160}, {4,9}, {5,5514}, {41,5727}, {101,5881}, {142,10004}, {219,4034}, {220,3679}, {282,7100}, {610,5787}, {728,6735}, {910,5691}, {938,1449}, {1212,1698}, {1375,16832}, {1419,5942}, {1446,18634}, {1737,16572}, {2082,9581}, {2262,5806}, {2324,4007}, {2886,5574}, {3061,17284}, {3119,5219}, {3632,6603}, {3673,4858}, {3684,12625}, {4136,4901}, {4515,4873}, {4534,11376}, {4875,5231}, {5437,20205}, {5540,10826}, {5880,15725}, {6506,7741}, {6706,20195}, {6913,7367}, {7988,13609}, {7991,17747}, {8558,9579}, {9367,16975}, {17435,20271}
X(23058) = midpoint of X(i) and X(j) for these {i,j}: {3160, 10405}, {7090, 14121}
X(23058) = reflection of X10004) in X(142)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 28223.
X(23059) lies on these lines: {3,74}, {21,6001}, {46,17104}, {60,65}, {229,13750}, {517,1437}, {1768,1789}, {1790,10902}, {3615,6831}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 28223.
X(23060) lies on these lines: {3,74}, {30,12242}, {143,17714}, {546,13470}, {1173,5899}, {1493,13391}, {1503,13565}, {3518,12006}, {3857,15432}, {7525,15083}, {10263,11423}, {10594,13364}, {10610,14865}, {11017,14157}, {11264,16618}, {12010,20304}, {12088,16982}, {12105,15012}, {12107,13630}, {12812,20190}, {15806,17712}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 28226.
X(23061) lies on these lines: {2,576}, {3,54}, {6,5888}, {23,110}, {30,14094}, {49,7555}, {51,16042}, {67,524}, {69,8542}, {111,8586}, {155,12082}, {182,11004}, {184,6030}, {186,15020}, {193,11511}, {352,3291}, {394,1995}, {403,15029}, {468,15360}, {542,5189}, {575,1994}, {852,14919}, {1147,7556}, {1173,3628}, {1199,5447}, {1216,7550}, {1350,15080}, {1351,5640}, {1568,3091}, {2071,15021}, {2072,15025}, {2076,20976}, {2452,9159}, {2889,12242}, {2930,9019}, {2937,9705}, {2987,14510}, {3098,11003}, {3124,15514}, {3146,12278}, {3231,5111}, {3266,9146}, {3448,5965}, {3525,14156}, {3529,12118}, {3580,5159}, {3581,15035}, {4232,11470}, {5028,9463}, {5050,21766}, {5094,8537}, {5097,5650}, {5104,14567}, {5297,19369}, {5422,11482}, {5562,7527}, {5609,13391}, {5611,11131}, {5615,11130}, {5651,10545}, {6090,10546}, {6243,12106}, {6515,8538}, {7292,8540}, {7464,13445}, {7512,9706}, {7545,10263}, {7575,15034}, {7772,8623}, {8541,11160}, {9143,19924}, {9155,9301}, {9306,14002}, {9968,11206}, {9972,21243}, {10116,11271}, {10297,15044}, {10300,11245}, {10552,14712}, {10564,15055}, {10706,18325}, {10733,18323}, {11440,13346}, {11449,17834}, {11451,17811}, {12164,12279}, {13248,15126}, {13366,15246}, {13421,13621}, {13431,18128}, {13595,21969}, {15057,15122}, {15062,18436}, {15520,22112}, {16982,18369}, {19128,19504}
X(23061) = reflection of X(i) in X(j) for these {i,j}: {23, 3292}, {54, 15137}, {110, 323}, {895, 10510}, {15054, 7464}, {15107, 110}
X(23061) = isotomic conjugate of isogonal conjugate of X(39231)
X(23061) = crossdifference of every pair of points on line {1640, 12073}
X(23061) = crosspoint of X(i) and X(j) for these (i,j): {249, 892}
X(23061) = crosssum of X(i) and X(j) for these (i,j): {115, 351}, {187, 13366}
X(23061) = barycentric product X(i)*X(j) for these {i,j}: {3266, 10558}, {5468, 10562}
X(23061) = trilinear product of X(10558) and X(14210)
X(23061) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {897, 2888}, {923, 17035}, {2148, 8591}, {2167, 14360}
X(23061) = barycentric quotient X(i)/X(j) for these {i,j}: {10558, 111}, {10562, 5466}
X(23061) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 576, 15019), (2, 15019, 5643), (3, 1993, 11422), (3, 11422, 5012), (23, 323, 3292), (23, 3292, 110), (394, 11477, 1995), (575, 3917, 7496), (895, 10510, 11416), (1351, 15066, 5640), (1993, 2979, 5012), (1994, 7496, 575), (1995, 11477, 3060), (2979, 11422, 3), (5097, 5650, 15018), (5643, 15019, 12834), (5651, 11002, 10545), (7464, 15054, 13445), (7492, 9716, 184), (7575, 22115, 15034), (8586, 9225, 20977), (9225, 20977, 111)
See Randy Hutson, Hyacinthos 28227.
Let A38B38C38 be Gemini triangle 38. Let A' be the center of conic {{A,B,C,B38,C38}}, and define B' and C' cyclically. The lines AA', BB', CC' concur in X(23062). (Randy Hutson, January 15, 2019)
X(23062) lies on these lines: {7,354}, {57,10509}, {85,142}, {269,4626}, {279,1418}, {658,1445}, {664,3174}, {738,1434}, {934,2369}, {1446,10004}, {1996,8232}, {2191,4350}, {6046,7233}, {8732,17093}, {10481,15841}, {11495,14189}
X(23062) = isogonal conjugate of X(6602)
X(23062) = isotomic conjugate of X(728)
X(23062) = barycentric square of X(555)
X(23062) = X(i)-beth conjugate of X(j) for these (i,j): {85, 10004}, {4616, 269}
X(23062) = X(i)-cross conjugate of X(j) for these (i,j): {279, 1088}, {2170, 3676}
XX(23062) = cevapoint of X(i) and X(j) for these (i,j): {7, 8732}, {57, 4350}, {279, 479}, {2170, 3676}
X(23062) = crosssum of X(3022) and X(6607)
(23062) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6602}, {6, 480}, {8, 14827}, {9, 1253}, {31, 728}, {32, 5423}, {33, 1802}, {41, 200}, {55, 220}, {101, 4105}, {212, 7079}, {219, 7071}, {341, 9447}, {346, 2175}, {607, 1260}, {644, 8641}, {657, 3939}, {692, 4130}, {1110, 3119}, {1146, 6066}, {1252, 3022}, {1334, 2328}, {1500, 6061}, {2192, 7368}, {2194, 4515}, {2212, 3692}, {2318, 2332}, {2346, 8551}, {3063, 4578}, {4524, 5546}, {6065, 14936}, {7054, 7064}, {7074, 7367}, {8012, 10482}
X(23062) = barycentric product X(i)*X(j) for these {i,j}: {7, 1088}, {75, 479}, {76, 738}, {85, 279}, {269, 6063}, {273, 7056}, {331, 7177}, {348, 1847}, {555, 555}, {561, 7023}, {693, 4626}, {873, 6046}, {1119, 7182}, {1407, 20567}, {1434, 1446}, {1502, 7366}, {3261, 4617}, {3676, 4569}, {4077, 4616}, {4635, 7178}, {18810, 21314}
X(23062) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 480}, {2, 728}, {6, 6602}, {7, 200}, {34, 7071}, {56, 1253}, {57, 220}, {75, 5423}, {77, 1260}, {85, 346}, {222, 1802}, {223, 7368}, {226, 4515}, {244, 3022}, {269, 55}, {273, 7046}, {278, 7079}, {279, 9}, {331, 7101}, {348, 3692}, {479, 1}, {513, 4105}, {514, 4130}, {552, 1098}, {555, 6731}, {604, 14827}, {658, 644}, {664, 4578}, {693, 4163}, {738, 6}, {757, 6061}, {934, 3939}, {1014, 2328}, {1086, 3119}, {1088, 8}, {1106, 2175}, {1111, 4081}, {1119, 33}, {1254, 7064}, {1358, 2310}, {1396, 2332}, {1398, 2212}, {1407, 41}, {1418, 8012}, {1422, 7367}, {1427, 1334}, {1434, 2287}, {1435, 607}, {1439, 2318}, {1441, 4082}, {1446, 2321}, {1475, 8551}, {1847, 281}, {3668, 210}, {3669, 657}, {3673, 4012}, {3674, 3965}, {3676, 3900}, {4017, 4524}, {4350, 6600}, {4554, 6558}, {4566, 4069}, {4569, 3699}, {4573, 7259}, {4616, 643}, {4617, 101}, {4625, 7256}, {4626, 100}, {4635, 645}, {4637, 5546}, {5435, 4936}, {6046, 756}, {6063, 341}, {6612, 7118}, {6614, 692}, {7023, 31}, {7045, 6065}, {7053, 212}, {7056, 78}, {7143, 872}, {7147, 1500}, {7177, 219}, {7178, 4171}, {7182, 1265}, {7185, 4073}, {7195, 4319}, {7197, 612}, {7203, 21789}, {7204, 4517}, {7216, 3709}, {7339, 1110}, {7366, 32}, {7371, 6726}, {10481, 3059}, {10509, 6605}, {14256, 2324}, {17096, 1021}, {20618, 3949}
See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28238.
X(23063) is the 4th intersection, other than the vertices of the incentral triangle, of the incentral inellipse and the incentral circle. (Randy Hutson, October 15, 2018)
X(23063) lies on the incentral inellipse, the incentral circle, and on these lines: {115,244}, {678,1283}, {756,8701}, {2310,3024}, {7004,14101}
See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28238.
X(23064) lies on these lines: {30, 511}, {6578, 8701}
See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28238.
X(23065) lies on these lines: {517, 3723}
See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28238.
X(23066) lies on these lines: {30, 511}
X(23067) lies on these lines: {3, 201}, {46, 15443}, {55, 11028}, {56, 214}, {72, 22341}, {100, 108}, {101, 109}, {110, 15439}, {219, 296}, {222, 295}, {228, 1214}, {603, 22458}, {643, 4564}, {1020, 4551}, {1260, 7011}, {1331, 1813}, {1376, 6358}, {1393, 16414}, {1708, 2352}, {1825, 11248}, {2222, 6011}, {2599, 11849}, {3185, 8270}, {3428, 11713}, {4561, 4571}, {4574, 23084}, {7078, 20764}, {17975, 17976}
X(23067) = isogonal conjugate of polar conjugate of X(4552)
X(23067) = isotomic conjugate of polar conjugate of X(4559)
X(23067) = X(19)-isoconjugate of X(4560)
X(23067) = X(92)-isoconjugate of X(7252)
X(23068) lies on these lines: {3, 22348}, {219, 22137}, {1260, 23071}, {3157, 7016}
X(23068) = isogonal conjugate of polar conjugate of X(17481)
X(23068) = isotomic conjugate of polar conjugate of X(21771)
X(23069) lies on these lines: {3, 22349}, {3157, 7016}, {22384, 23092}
X(23069) = isogonal conjugate of polar conjugate of X(17482)
X(23069) = isotomic conjugate of polar conjugate of X(21772)
X(23070) lies on these lines: {1, 399}, {3, 73}, {5, 651}, {6, 5708}, {30, 3562}, {63, 22136}, {72, 22128}, {81, 6147}, {109, 5399}, {140, 17074}, {195, 3461}, {221, 1482}, {381, 8757}, {394, 3927}, {912, 18447}, {942, 2003}, {1071, 18455}, {1079, 1454}, {1393, 14627}, {1419, 5709}, {1498, 12684}, {1771, 18524}, {1935, 7489}, {4306, 5398}, {4855, 22141}, {4860, 16472}, {5221, 16473}, {5706, 18541}, {5707, 6180}, {5779, 17814}, {5790, 9370}, {10571, 22765}, {15066, 15650}, {20739, 22163}, {20741, 22164}, {22148, 22458}
X(23070) = isogonal conjugate of polar conjugate of X(17483)
X(23070) = isotomic conjugate of polar conjugate of X(21773)
X(23071) lies on these lines: {1, 195}, {3, 73}, {5, 3562}, {6, 15934}, {30, 651}, {35, 8614}, {72, 18447}, {81, 5719}, {201, 7100}, {219, 22142}, {221, 12702}, {382, 8757}, {394, 3940}, {399, 3465}, {484, 6126}, {517, 1456}, {549, 17074}, {582, 4306}, {912, 18455}, {943, 5453}, {1149, 7373}, {1203, 5045}, {1260, 23068}, {1419, 3587}, {1459, 17976}, {1935, 13743}, {2392, 20872}, {3173, 18445}, {4551, 18524}, {4574, 20741}, {4585, 16086}, {5172, 6149}, {5440, 22128}, {5758, 18624}, {6180, 18541}, {8144, 12528}, {9370, 18525}, {20752, 22144}, {22124, 22147}
X(23071) = isogonal conjugate of polar conjugate of X(17484)
X(23071) = isotomic conjugate of polar conjugate of X(19297)
X(23071) = X(19)-isoconjugate of X(21739)
X(23071) = X(92)-isoconjugate of X(19302)
X(23072) lies on these lines: {3, 73}, {34, 2095}, {47, 1617}, {58, 999}, {109, 1413}, {221, 22770}, {283, 22129}, {495, 4340}, {517, 1394}, {580, 1407}, {651, 3149}, {942, 1453}, {991, 5399}, {1012, 3562}, {1060, 3927}, {1092, 7053}, {1259, 22128}, {1456, 12704}, {1771, 9370}, {1935, 6913}, {3075, 6918}, {3167, 20805}, {3664, 11374}, {6149, 7742}, {7011, 7335}, {8757, 19541}, {9538, 13243}, {11700, 12635}, {15905, 20764}
X(23072) = isogonal conjugate of polar conjugate of X(9965)
X(23072) = isotomic conjugate of polar conjugate of X(37519)
X(23073) lies on these lines: {3, 48}, {6, 5563}, {19, 10222}, {45, 16554}, {184, 22371}, {218, 7113}, {222, 1797}, {284, 3303}, {610, 7982}, {944, 7359}, {1388, 1731}, {1482, 2173}, {1732, 5126}, {2256, 3746}, {2286, 22122}, {2323, 3207}, {3284, 22124}, {7124, 22123}, {13462, 16670}, {16189, 18594}, {16547, 16884}, {17455, 22767}, {20760, 22158}
X(23073) = isogonal conjugate of polar conjugate of X(3241)
X(23073) = X(19)-isoconjugate of X(36588)
X(23074) lies on these lines: {1, 159}, {3, 22362}
X(23074) = isogonal conjugate of polar conjugate of X(21215)
X(23074) = isotomic conjugate of polar conjugate of X(21774)
X(23075) lies on these lines: {1, 7083}, {3, 326}, {31, 15370}, {219, 7015}, {255, 7193}, {2300, 3167}, {3186, 3732}, {3564, 15976}, {20764, 23076}
X(23075) = isogonal conjugate of polar conjugate of X(21216)
X(23075) = isotomic conjugate of polar conjugate of X(21775)
X(23076) lies on these lines: {3, 304}, {219, 23077}, {863, 21216}, {3157, 23083}, {19597, 23078}, {20760, 22164}, {20764, 23075}, {20794, 22458}, {20805, 23091}
X(23076) = isogonal conjugate of polar conjugate of X(17486)
X(23076) = isotomic conjugate of polar conjugate of X(21776)
X(23077) lies on these lines: {3, 22367}, {219, 23076}, {17976, 22138}, {20739, 20760}, {20796, 22126}, {22164, 23083}
X(23077) = isogonal conjugate of polar conjugate of X(21217)
X(23077) = isotomic conjugate of polar conjugate of X(21777)
X(23078) lies on these lines: {3, 348}, {255, 7193}, {19597, 23076}
X(23078) = isogonal conjugate of polar conjugate of X(21218)
X(23078) = isotomic conjugate of polar conjugate of X(21778)
X(23079) lies on these lines: {3, 69}, {48, 20762}, {71, 20796}, {219, 7015}, {1030, 1634}, {1654, 16372}, {2895, 20848}, {3511, 3882}, {4254, 11328}, {4648, 16420}, {7078, 20793}, {8681, 18591}, {11343, 20139}, {17778, 20845}, {17976, 22136}, {20740, 20795}, {20769, 22389}, {22141, 23083}
X(23079) = isogonal conjugate of polar conjugate of X(1655)
X(23079) = isotomic conjugate of polar conjugate of X(21779)
X(23080) lies on these lines: {3, 22370}, {219, 20785}, {1332, 20794}, {7078, 17976}, {20762, 20818}
X(23080) = isogonal conjugate of polar conjugate of X(21219)
X(23080) = isotomic conjugate of polar conjugate of X(21780)
X(23081) lies on these lines: {3, 1331}, {219, 23082}, {3955, 22357}, {20760, 22158}, {22139, 22143}
X(23081) = isogonal conjugate of polar conjugate of X(17487)
X(23081) = isotomic conjugate of polar conjugate of X(21781)
X(23082) lies on these lines: {3, 22067}, {219, 23081}, {20760, 22356}
X(23082) = isogonal conjugate of polar conjugate of X(17488)
X(23082) = isotomic conjugate of polar conjugate of X(21782)
X(23083) lies on these lines: {3, 4592}, {3157, 23076}, {20739, 23088}, {20760, 23084}, {20766, 20796}, {22141, 23079}, {22143, 22144}, {22148, 23091}, {22164, 23077}
X(23083) = isogonal conjugate of polar conjugate of X(21220)
X(23083) = isotomic conjugate of polar conjugate of X(21783)
X(23084) lies on these lines: {3, 3708}, {525, 6516}, {647, 906}, {4574, 23067}, {20739, 20764}, {20760, 23083}, {20802, 22458}, {22164, 22457}
X(23084) = isogonal conjugate of polar conjugate of X(6758)
X(23084) = isotomic conjugate of polar conjugate of X(21784)
X(23084) = X(19)-isoconjugate of X(7372)
X(23085) lies on these lines: {3, 63}, {56, 4650}, {329, 19514}, {404, 17350}, {603, 7193}, {5687, 9369}, {5744, 9840}, {7078, 22148}, {7288, 15507}, {15803, 16059}
X(23085) = isogonal conjugate of polar conjugate of X(17490)
X(23085) = isotomic conjugate of polar conjugate of X(21785)
X(23086) lies on these lines: {3, 22370}, {28, 330}, {48, 3955}, {56, 87}, {69, 22096}, {104, 932}, {219, 2196}, {295, 20753}, {603, 7193}, {604, 11328}, {982, 18194}, {1332, 20787}, {1333, 2162}, {1436, 2319}, {1437, 20805}, {1472, 7121}, {3733, 4361}, {6384, 18749}, {8843, 20992}, {20765, 20799}, {20769, 22152}, {20793, 22118}, {20796, 20818}
X(23086) = isogonal conjugate of polar conjugate of X(330)
X(23086) = isotomic conjugate of polar conjugate of X(2162)
X(23086) = X(63)-cross conjugate of X(3)
X(23086) = X(19)-isoconjugate of X(192)
X(23086) = X(92)-isoconjugate of X(2176)
X(23087) lies on these lines: {3, 22379}, {56, 3738}, {521, 22091}, {667, 9048}, {900, 10074}, {905, 9051}, {999, 1769}, {1331, 1813}, {1459, 4091}, {1795, 8677}, {3733, 4063}, {4491, 14812}, {4768, 12513}, {22148, 22158}
X(23087) = isogonal conjugate of polar conjugate of X(21222)
X(23087) = isotomic conjugate of polar conjugate of X(21786)
X(23088) lies on these lines: {3, 22370}, {2200, 20794}, {3167, 20796}, {20739, 23083}, {20760, 22164}, {22127, 22158}
X(23088) = isogonal conjugate of polar conjugate of X(21223)
X(23088) = isotomic conjugate of polar conjugate of X(21787)
X(23089) lies on these lines: {3, 63}, {81, 7373}, {101, 1407}, {144, 16435}, {189, 952}, {198, 3928}, {222, 20818}, {329, 19517}, {394, 22147}, {527, 15509}, {3167, 22148}, {3210, 3732}, {4383, 21362}, {5294, 21542}, {7193, 22117}, {9965, 11347}
X(23089) = isogonal conjugate of polar conjugate of X(4452)
X(23089) = isotomic conjugate of polar conjugate of X(1616)
X(23089) = X(19)-isoconjugate of X(6553)
X(23090) lies on these lines: {3, 822}, {6, 16612}, {110, 677}, {112, 6081}, {219, 8611}, {284, 2432}, {425, 2501}, {448, 525}, {520, 3733}, {521, 650}, {662, 7045}, {905, 4131}, {1172, 2431}, {3676, 18199}, {4765, 21007}, {7253, 15146}, {10015, 17925}
X(23090) = isogonal conjugate of polar conjugate of X(7253)
X(23090) = isotomic conjugate of polar conjugate of X(21789)
X(23090) = X(19)-isoconjugate of X(4566)
X(23091) lies on these lines: {3, 4561}, {3504, 22149}, {4574, 20760}, {20797, 22458}, {20805, 23076}, {22148, 23083}
X(23091) = isogonal conjugate of polar conjugate of X(21224)
X(23091) = isotomic conjugate of polar conjugate of X(21790)
X(23092) lies on these lines: {3, 22387}, {6, 4369}, {905, 4131}, {3049, 15419}, {4481, 7252}, {17217, 17921}, {20816, 22157}, {22384, 23069}
X(23092) = isogonal conjugate of polar conjugate of X(17217)
X(23092) = isotomic conjugate of polar conjugate of X(16695)
X(23093) lies on these lines: {3, 4025}, {647, 8673}, {652, 20760}, {3239, 16058}, {7658, 16059}
X(23093) = isogonal conjugate of polar conjugate of X(21225)
X(23093) = isotomic conjugate of polar conjugate of X(21791)
X(23094) lies on these lines: {3, 22370}, {48, 20762}, {219, 20794}, {1332, 20775}, {3167, 20752}, {4020, 7015}, {22122, 22143}
X(23094) = isogonal conjugate of polar conjugate of X(21226)
X(23094) = isotomic conjugate of polar conjugate of X(21792)
X(23095) lies on these lines: {3, 48}, {101, 182}, {184, 1331}, {218, 19554}, {222, 17972}, {255, 20765}, {284, 16516}, {613, 19561}, {1437, 20805}, {2182, 20430}, {3167, 22161}, {3955, 22149}, {5009, 21769}, {20794, 22458}
X(23095) = isogonal conjugate of polar conjugate of X(4393)
X(23095) = isotomic conjugate of polar conjugate of X(21793)
X(23095) = X(19)-isoconjugate of X(27494)
If you have GeoGebra, you can view X(23096).
See Telv Cohl and Peter Moses, Hyacinthos 28244.
X(23096) lies on the circumcircle and these lines: {23,20185}, {25,1291}, {468,930}, {691,3518}, {2070,3565}, {2696,7576}, {10420,13595}, {11635,13621}
K244 Moses images: X(23097)-X(23110)
If a point P on the circumcircle of a triangle ABC has barycentrics p : q : r, then then point a^2 q r (c^2 q + b^2 r) : : lies on the cubic K244. The following fourteen examples of K244 Moses images were contributed by Peter Moses, September 13, 2018. See also the preamble just before X(23342).
The Moses K244 image of P is the trilinear cube of the isogonal conjugate of P. (Randy Hutson, November 30, 2018)
X(23907) lies on the cubic K244 and these lines: {4, 69}, {30, 14254}, {94, 10733}, {858, 18279}, {1495, 15454}, {1568, 11251}, {9003, 15063}, {16163, 16240}
X(23097) = trilinear cube of X(30)
X(23097) = isotomic conjugate of isogonal conjugate of X(3081)
X(23097) = barycentric product X(i)*X(j) for these {i,j}: {76, 3081}, {1099, 14206}, {3163, 3260}
X(23097) = barycentric quotient X(i)/X(j) for these {i,j}: {1099, 2349}, {3081, 6}, {3163, 74}, {14401, 14380}, {16163, 14919}, {16240, 8749}
X(23908) lies on the cubic K244 and these lines: {3, 2421}, {5, 76}, {32, 1092}, {446, 511}, {684, 690}, {2080, 10411}, {6394, 14941}, {9419, 11672}
X(23098) = trilinear cube of X(511)
X(23098) = barycentric product X(i)*X(j) for these {i,j}: {325, 11672}, {3569, 15631}
X(23098) = barycentric quotient X(i)/X(j) for these {i,j}: {2967, 16081}, {9419, 1976}, {11672, 98}
X(23909) lies on the cubic K244 and these lines: {32, 669}, {39, 512}, {76, 523}, {887, 2491}, {1499, 3095}, {1649, 3005}, {2793, 14272}, {4079, 21700}, {6071, 21906}, {9009, 13330}, {9178, 14263}, {14443, 20975}
X(23099) = reflection of X(i) in X(j) for these {i,j}: {887, 2491}, {14824, 39}
X(23099) = reflection of X(14824) in the Brocard axis
X(23099) = isogonal conjugate of the isotomic conjugate of X(22260)
X(23099) = X(i)-Ceva conjugate of X(j) for these (i,j): {523, 3124}, {669, 1084}
X(23099) = crosspoint of X(i) and X(j) for these (i,j): {523, 3124}, {669, 1084}
X(23099) = crossdifference of every pair of points on line {385, 3266}
X(23099) = crosssum of X(110) and X(4590)
X(23099) = trilinear cube of X(512)
X(23099) = X(i)-isoconjugate of X(j) for these (i,j): {249, 4602}, {799, 4590}, {1101, 4609}, {4600, 4623}, {4601, 4610}, {4620, 4631}, {4625, 6064}, {7257, 7340}
X(23099) = barycentric product X(i)*X(j) for these {i,j}: {6, 22260}, {32, 8029}, {115, 669}, {338, 9426}, {512, 3124}, {523, 1084}, {647, 2971}, {667, 21833}, {762, 8027}, {798, 2643}, {850, 9427}, {882, 2086}, {1109, 1924}, {1356, 3700}, {1500, 8034}, {1577, 4117}, {1918, 21131}, {1919, 21043}, {2489, 20975}, {3049, 8754}, {3121, 4705}, {3122, 4079}, {3249, 6535}, {3569, 15630}, {7063, 7178}, {9178, 21906}
X(23099) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 4609}, {669, 4590}, {1084, 99}, {1356, 4573}, {2086, 880}, {2643, 4602}, {2971, 6331}, {3121, 4623}, {3124, 670}, {3249, 6628}, {4117, 662}, {7063, 645}, {8029, 1502}, {9426, 249}, {9427, 110}, {21833, 6386}, {22260, 76}
X(239100) lies on the cubic K244 and these lines: {76, 3261}, {85, 514}, {649, 14377}, {693, 20880}, {1111, 21132}, {3673, 21201}, {19594, 21118}
X(23100) = reflection of X(14825) in X(2140)
X(23100) = isotomic conjugate of the isogonal conjugate of X(6545)
X(23100) = trilinear cube of X(514)
X(23100) = X(i)-isoconjugate of X(j) for these (i,j): {101, 1110}, {560, 6632}, {651, 6066}, {692, 1252}, {1253, 4619}, {1415, 6065}, {2149, 3939}, {2251, 6551}
X(23100) = crossdifference of every pair of points on line {6066, 9459}
X(23100) = barycentric product X(i)*X(j) for these {i,j}: {76, 6545}, {561, 764}, {693, 1111}, {850, 17205}, {1086, 3261}, {1090, 4569}, {1502, 21143}, {1577, 16727}, {1928, 8027}, {2973, 4025}, {4572, 7336}, {6063, 21132}, {7192, 21207}, {7199, 16732}, {16726, 20948}
X(23100) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 3939}, {76, 6632}, {244, 692}, {279, 4619}, {338, 4103}, {513, 1110}, {514, 1252}, {522, 6065}, {663, 6066}, {693, 765}, {764, 31}, {903, 6551}, {1086, 101}, {1090, 3900}, {1111, 100}, {1358, 109}, {1565, 1331}, {2969, 8750}, {2973, 1897}, {3120, 4557}, {3249, 1501}, {3261, 1016}, {3669, 2149}, {3676, 59}, {3942, 906}, {4466, 4574}, {4858, 644}, {4957, 4752}, {5532, 4105}, {6545, 6}, {6548, 9268}, {6549, 901}, {6550, 902}, {7192, 4570}, {7199, 4567}, {7336, 663}, {8027, 560}, {8034, 1918}, {8042, 1333}, {8661, 9459}, {14442, 1017}, {15634, 677}, {16726, 163}, {16727, 662}, {16732, 1018}, {17197, 5546}, {17205, 110}, {17880, 4571}, {21131, 1500}, {21132, 55}, {21133, 3730}, {21134, 3690}, {21143, 32}, {21202, 14887}, {21207, 3952}
X(23101) lies on the cubic K244 and these lines: {76, 3262}, {78, 1482}, {517, 14260}
X(23101) = trilinear cube of X(517)
X(23101) = barycentric product X(10015)X(15632)
X(23101) = barycentric quotient X(i)/X(j) for these {i,j}: {15632, 13136}, {21664, 16082}
X(23102) lies on the cubic K244 and these lines: {1, 728}, {8, 14947}, {76, 3263}, {1259, 3423}, {2481, 4518}, {2826, 3762}, {3126, 14506}, {3675, 3912}, {4712, 6184}
X(23102) = X(3263)-Ceva conjugate of X(4437)
X(23102) = X(1438)-isoconjugate of X(6185)
X(23102) = crosspoint of X(i) and X(j) for these (i,j): {3263, 4437}
X(23102) = trilinear cube of X(518)
X(23102) = barycentric product X(i)*X(j) for these {i,j}: {518, 4437}, {3263, 6184}, {3912, 4712}, {3932, 16728}
X(23102) = barycentric quotient X(i)/X(j) for these {i,j}: {518, 6185}, {1362, 1462}, {4437, 2481}, {4712, 673}, {6184, 105}
X(23103) lies on the cubic K244 and these lines: {76, 3265}, {523, 15318}, {525, 14059}, {684, 2848}, {3357, 22089}
X(23103) = trilinear cube of X(520)
X(23103) = barycentric quotient X(2972)/X(15352)
X(23104) lies on the cubic K244 and these lines: {318, 522}, {341, 4163}, {663, 10570}, {3701, 4397}
X(23104) = trilinear cube of X(522)
X(23104) = X(i)-isoconjugate of X(j) for these (i,j): {604, 4619}, {692, 7339}, {1110, 6614}, {1262, 1415}, {1461, 2149}
X(23104) = barycentric product X(i)*X(j) for these {i,j}: {646, 1090}, {1978, 5532}, {3261, 4081}, {4397, 4858}, {6332, 21666}
X(23104) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 4619}, {11, 1461}, {514, 7339}, {522, 1262}, {764, 7366}, {1086, 6614}, {1090, 3669}, {1111, 4617}, {1146, 109}, {2310, 1415}, {2968, 1813}, {3119, 692}, {3239, 59}, {4081, 101}, {4130, 1110}, {4163, 1252}, {4391, 7045}, {4397, 4564}, {4858, 934}, {5532, 649}, {6545, 7023}, {21131, 7143}, {21132, 1407}, {21666, 653}
X(23105) lies on the cubics K244 and K589 and on these lines: {4, 512}, {5, 523}, {68, 520}, {76, 850}, {99, 14734}, {110, 14781}, {338, 15359}, {525, 10279}, {647, 7746}, {670, 14728}, {690, 16003}, {826, 1209}, {868, 5489}, {924, 18381}, {1093, 18808}, {1116, 5664}, {2395, 3767}, {3548, 15421}, {4108, 14002}, {6041, 7755}, {6130, 14270}, {6249, 12073}, {7253, 14777}, {10278, 11007}
X(23105) = reflection of X(i) in X(j) for these {i,j}: {5664, 1116}, {14270, 6130}
X(23105) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2395, 3767, 8574)
X(23105) = isotomic conjugate of the isogonal conjugate of X(8029)
X(23105) = X(i)-Ceva conjugate of X(j) for these (i,j): {850, 338}, {14618, 115}
X(23105) = X(i)-isoconjugate of X(j) for these (i,j): {110, 1101}, {163, 249}, {250, 4575}, {1983, 9273}, {2617, 14587}
X(23105) = crosspoint of X(i) and X(j) for these (i,j): {338, 850}, {523, 8901}
X(23105) = crossdifference of every pair of points on line {50, 3289}
X(23105) = trilinear cube of X(523)
X(23105) = pole wrt polar circle of line X(249)X(250)
X(23105) = Kirikami-Euler image of X(115)
X(23105) = trilinear product of vertices of Schroeter triangle
X(23105) = barycentric product X(i)*X(j) for these {i,j}: {76, 8029}, {115, 850}, {125, 14618}, {313, 21131}, {338, 523}, {339, 2501}, {525, 2970}, {1109, 1577}, {1502, 22260}, {2052, 5489}, {2643, 20948}, {3261, 21043}, {3267, 8754}, {4024, 21207}, {4036, 16732}, {8901, 18314}
X(23105) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 110}, {125, 4558}, {338, 99}, {339, 4563}, {523, 249}, {661, 1101}, {850, 4590}, {868, 2421}, {1084, 14574}, {1109, 662}, {1365, 4565}, {1648, 5467}, {2501, 250}, {2623, 14587}, {2643, 163}, {2970, 648}, {3120, 4556}, {3124, 1576}, {3708, 4575}, {4024, 4570}, {4036, 4567}, {4092, 5546}, {5489, 394}, {8029, 6}, {8288, 9145}, {8754, 112}, {8901, 18315}, {14618, 18020}, {15328, 18879}, {20902, 4592}, {21043, 101}, {21044, 4636}, {21046, 1331}, {21131, 58}, {21134, 1790}, {21207, 4610}, {21833, 692}, {22260, 32}
X(23106) lies on the cubic K244 and these lines: {2, 39}, {1649, 6077}, {2482, 16733}, {2793, 14278}, {6390, 9177}, {7813, 21906}
X(23106) = isotomic conjugate of the isogonal conjugate of X(8030)
X(23106) = X(923)-isoconjugate of X(10630)
X(23106) = trilinear cube of X(524)
X(23106) = barycentric product X(i)*X(j) for these {i,j}: {76, 8030}, {2482, 3266}
X(23106) = barycentric quotient X(i)/X(j) for these {i,j}: {524, 10630}, {1366, 7316}, {1649, 9178}, {2482, 111}, {5095, 8753}, {6390, 15398}, {7067, 5547}, {8030, 6}, {14444, 3124}
X(23107) lies on the cubic K244 and these lines: {76, 2394}, {647, 14376}, {3265, 3933}
X(23107) = trilinear cube of X(525)
X(23107) = barycentric product X(i)*X(j) for these {i,j}: {305, 5489}, {338, 4143}, {339, 3265}, {3267, 15526}, {14208, 17879}
X(23107) = barycentric quotient X(i)/X(j) for these {i,j}: {338, 6529}, {339, 107}, {2972, 1576}, {3265, 250}, {4143, 249}, {5489, 25}, {15526, 112}, {17879, 162}
X(23108) lies on the cubic K244 and these lines: {76, 3268}, {690, 14670}, {14270, 14385}
X(23108) = trilinear cube of X(526)
X(23108) = barycentric product X(3268)*X(18334)
X(23108) = barycentric quotient X(18334)/X(476)
X(23109) lies on the cubics K244 and K1065 and on these lines: {3, 2574}, {4, 16071}, {523, 20408}, {684, 690}, {5489, 14499}, {9173, 11638}
X(23109) = crosspoint of X(1313) and X(2574)
X(23109) = crosssum of X(1113) and X(15461)
X(23109) = trilinear cube of X(2574)
X(23109) = X(2586)-isoconjugate of X(15461)
X(23109) = barycentric quotient X(15166)/X(1113)
X(23110) lies on the cubics K244 and K1065 and on these lines: {3, 2575}, {4, 16070}, {523, 20409}, {684, 690}, {5489, 14500}, {9174, 11638}
X(23110) = crosspoint of X(1312) and X(2575)
X(23110) = crosssum of X(1114) and X(15460)
X(23110) = trilinear cube of X(2575)
X(23110) = X(2587)-isoconjugate of X(15460)
X(23110) = barycentric quotient X(15167)/X(1114)
See Antreas Hatzipolakis, César Lozada, and Ercole Suppa, , Hyacinthos 28213 and Hyacinthos 28248.
X(23111) lies on this line: {49,50}
X(23112) lies on these lines: {3, 22394}, {6, 16577}, {219, 22119}, {329, 2427}, {394, 23113}, {916, 22057}, {4055, 23171}, {6505, 20744}, {18676, 21271}, {23121, 23139}
X(23112) = isogonal conjugate of polar conjugate of X(21271)
X(23113) lies on these lines: {3, 22399}, {6, 16578}, {219, 20740}, {394, 23112}, {651, 2427}, {662, 1625}, {906, 1813}, {1332, 4561}, {4558, 7254}, {6510, 20744}, {17906, 21272}, {22119, 23129}
X(23113) = isogonal conjugate of polar conjugate of X(21272)
X(23113) = isotomic conjugate of polar conjugate of X(23845)
X(23114) lies on these lines: {3, 22400}, {6, 16579}, {63, 16697}, {219, 23129}, {255, 20803}, {345, 4574}, {394, 23112}, {1214, 20744}, {1764, 4559}, {3927, 7078}, {18163, 21770}, {18677, 21273}, {20797, 22117}, {20799, 23175}, {22119, 22125}
X(23114) = isogonal conjugate of polar conjugate of X(21273)
X(23114) = isotomic conjugate of polar conjugate of X(23846)
X(23115) lies on these lines: {3, 6}, {20, 8743}, {24, 10313}, {30, 2207}, {63, 22119}, {112, 2138}, {127, 7776}, {155, 3289}, {230, 3548}, {232, 7387}, {248, 15316}, {394, 441}, {1038, 5280}, {1040, 5299}, {1062, 16502}, {1092, 8779}, {1184, 1368}, {1370, 3162}, {1498, 1625}, {1576, 20993}, {1634, 23172}, {1968, 12085}, {1975, 15013}, {2072, 13881}, {2548, 15760}, {2549, 12605}, {3087, 7401}, {3148, 23606}, {3172, 21312}, {3199, 18534}, {3269, 12163}, {3529, 8744}, {3546, 7735}, {3547, 7736}, {3549, 3815}, {3692, 22132}, {3767, 11585}, {3926, 20806}, {5254, 18531}, {5286, 6643}, {5359, 7386}, {6337, 22151}, {6389, 7758}, {6390, 6461}, {6638, 23174}, {6642, 10311}, {6748, 7528}, {7855, 15526}, {8721, 19149}, {10312, 17928}, {10323, 22240}, {10594, 15355}, {11441, 13509}, {12362, 15048}, {16781, 18455}, {20739, 23131}, {22125, 22126}
X(23115) = isogonal conjugate of polar conjugate of X(1370)
X(23115) = isogonal conjugate of isotomic conjugate of X(28419)
X(23115) = isotomic conjugate of polar conjugate of X(159)
\
X(23115) = X(19)-isoconjugate of X(13575)
X(23115) = X(92)-isoconjugate of X(34207)
X(23115) = crossdifference of every pair of points on the radical axis of any pair of {1st, 2nd and 3rd pedal circles of X(4)}
X(23116) lies on these lines: {3, 22402}, {6, 16580}, {219, 22119}, {2273, 18734}, {3211, 22145}, {5280, 18730}, {17492, 18680}, {20336, 20806}, {20760, 23074}, {22156, 23075}
X(23116) = isogonal conjugate of polar conjugate of X(17492)
X(23116) = isotomic conjugate of polar conjugate of X(23847)
X(23117) lies on these lines: {3, 22403}, {6, 16581}, {219, 22119}, {7254, 23147}, {18681, 21274}, {22156, 23193}
X(23117) = isogonal conjugate of polar conjugate of X(21274)
X(23117) = isotomic conjugate of polar conjugate of X(23848)
X(23118) lies on these lines: {3, 22404}, {6, 2887}, {219, 22137}, {17910, 21275}, {20739, 22130}, {20806, 23123}, {22119, 23139}, {22156, 23143}
X(23118) = isogonal conjugate of polar conjugate of X(21275)
X(23118) = isotomic conjugate of polar conjugate of X(23849)
X(23119) lies on these lines: {3, 22405}, {6, 5249}, {63, 22145}, {239, 1993}, {306, 394}, {7193, 22348}, {22156, 22161}, {23124, 23130}
X(23119) = isogonal conjugate of polar conjugate of X(21276)
X(23119) = isotomic conjugate of polar conjugate of X(23850)
X(23120) lies on these lines: {3, 22406}, {6, 908}, {306, 394}, {323, 6542}, {1790, 2197}, {1993, 1999}, {6332, 20808}, {17976, 22156}, {20811, 23137}, {22128, 22145}
X(23120) = isogonal conjugate of polar conjugate of X(21277)
X(23120) = isotomic conjugate of polar conjugate of X(1324)
X(23121) lies on these lines: {3, 22409}, {6, 1215}, {63, 20747}, {219, 7015}, {394, 20742}, {17912, 21278}, {20739, 22130}, {20769, 22126}, {22137, 22156}, {23112, 23139}
X(23121) = isogonal conjugate of polar conjugate of X(21280)
X(23121) = isotomic conjugate of polar conjugate of X(23852)
X(23122) lies on these lines: {3, 22410}, {6, 57}, {63, 22119}, {81, 13577}, {189, 1783}, {306, 394}, {971, 3195}, {1071, 16466}, {1433, 6765}, {1473, 22348}, {1771, 3293}, {3173, 22145}, {17284, 17811}, {22123, 23140}, {22144, 23089}
X(23122) = isogonal conjugate of polar conjugate of X(21279)
X(23122) = isotomic conjugate of polar conjugate of X(22654)
X(23123) lies on these lines: {3, 22411}, {6, 2886}, {394, 20807}, {3173, 22131}, {20739, 23128}, {20806, 23118}, {20811, 22130}
X(23123) = isogonal conjugate of polar conjugate of X(21278)
X(23123) = isotomic conjugate of polar conjugate of X(23851)
X(23124) lies on these lines: {3, 22412}, {6, 3739}, {63, 77}, {69, 20744}, {326, 22134}, {332, 23131}, {651, 20245}, {2323, 7175}, {17137, 17913}, {17206, 22126}, {17976, 22138}, {20739, 20806}, {20742, 22133}, {22161, 23079}, {23119, 23130}, {23193, 23526}
X(23125) lies on these lines: {3, 22413}, {6, 75}, {63, 77}, {651, 20348}, {1760, 21767}, {17976, 20805}, {20739, 20747}, {20742, 22132}, {20806, 22145}, {20808, 22125}, {22148, 22152}, {23075, 23526}
X(23125) = isogonal conjugate of polar conjugate of X(21281)
X(23125) = isotomic conjugate of polar conjugate of X(23853)
X(23126) lies on these lines: {3, 22414}, {6, 519}, {219, 22142}, {394, 4001}, {525, 3049}, {20741, 22144}, {20752, 22162}, {20813, 22146}, {22123, 23135}
X(23126) = isogonal conjugate of polar conjugate of X(21282)
X(23126) = isotomic conjugate of polar conjugate of X(23854)
X(23127) lies on these lines: {3, 22415}, {6, 551}, {219, 1807}, {394, 4001}
X(23127) = isogonal conjugate of polar conjugate of X(21283)
X(23127) = isotomic conjugate of polar conjugate of X(23855)
X(23128) lies on these lines: {3, 248}, {5, 6}, {20, 13509}, {26, 1971}, {32, 13754}, {39, 1147}, {52, 10311}, {112, 12111}, {115, 9927}, {157, 2909}, {172, 7352}, {187, 7689}, {217, 18445}, {230, 12359}, {232, 10539}, {394, 441}, {458, 1235}, {520, 8574}, {525, 1975}, {539, 5309}, {574, 12038}, {577, 1216}, {1069, 16502}, {1092, 14961}, {1614, 22240}, {1625, 8743}, {1914, 6238}, {1968, 12162}, {1970, 7526}, {2207, 18451}, {2549, 12118}, {3053, 12163}, {3167, 9605}, {3289, 22120}, {3815, 9820}, {5007, 15083}, {5286, 6193}, {5448, 5475}, {5449, 7746}, {5462, 10314}, {5523, 14516}, {5562, 8779}, {5889, 10312}, {6237, 10315}, {6422, 8909}, {7592, 9755}, {7735, 11411}, {7745, 22660}, {7748, 14901}, {7881, 15066}, {8882, 19194}, {9620, 9928}, {10313, 11412}, {10317, 18436}, {14965, 20806}, {20739, 23123}, {22131, 23137}
X(23129) lies on these lines: {3, 22418}, {6, 3452}, {219, 23114}, {306, 394}, {3173, 20744}, {3940, 7078}, {20739, 23123}, {20745, 20748}, {20808, 20812}, {22119, 23113}, {22145, 23140}
X(23129) = isogonal conjugate of polar conjugate of X(21286)
X(23129) = isotomic conjugate of polar conjugate of X(2933)
X(23130) lies on these lines: {2, 6}, {3, 22420}, {72, 18447}, {306, 22123}, {511, 2203}, {651, 18632}, {1092, 5752}, {7085, 22139}, {20739, 22130}, {20809, 23137}, {23119, 23124}
X(23130) = isogonal conjugate of polar conjugate of X(21287)
X(23130) = isotomic conjugate of polar conjugate of X(2915)
X(23131) lies on these lines: {1, 19259}, {3, 73}, {6, 5745}, {63, 16697}, {306, 394}, {332, 23124}, {651, 23512}, {1010, 3562}, {1790, 22118}, {1812, 22126}, {3719, 4574}, {4559, 21375}, {5783, 17811}, {6617, 22119}, {20739, 23115}, {20812, 23151}
X(23131) = isogonal conjugate of polar conjugate of X(20245)
X(23131) = isotomic conjugate of polar conjugate of X(23361)
X(23132) lies on these lines: {3, 22422}, {6, 16582}, {159, 14529}, {3157, 23074}, {22130, 22164}, {23068, 23076}
X(23132) = isogonal conjugate of polar conjugate of X(21288)
X(23132) = isotomic conjugate of polar conjugate of X(23856)
X(23133) lies on these lines: {3, 1176}, {6, 6292}, {63, 20808}, {394, 22120}, {1369, 8792}, {3933, 22121}, {7767, 22151}, {15141, 15270}
X(23133) = isogonal conjugate of polar conjugate of X(1369)
X(23133) = isotomic conjugate of polar conjugate of X(2916)
X(23134) lies on these lines: {3, 20738}, {6, 6376}, {394, 7124}, {20739, 20747}, {20808, 20812}, {20809, 22131}, {22136, 23080}, {22370, 23519}
X(23134) = isogonal conjugate of polar conjugate of anticomplement of X(2162)
X(23134) = isotomic conjugate of polar conjugate of X(23857)
X(23135) lies on these lines: {3, 22428}, {6, 644}, {219, 1807}, {345, 394}, {20739, 23136}, {22123, 23126}, {22133, 22146}, {22139, 22143}
X(23135) = isogonal conjugate of polar conjugate of X(21290)
X(23135) = isotomic conjugate of polar conjugate of X(23858)
X(23135) = X(92)-isoconjugate of X(34184)
X(23136) lies on these lines: {3, 22429}, {6, 16590}, {219, 22142}, {394, 22123}, {20739, 23135}, {22139, 23082}
X(23136) = isogonal conjugate of polar conjugate of X(21291)
X(23136) = isotomic conjugate of polar conjugate of X(23859)
X(23137) lies on these lines: {3, 22432}, {6, 11}, {394, 20807}, {2504, 22145}, {20809, 23130}, {20811, 23120}, {22131, 23128}, {22144, 22146}
X(23137) = isogonal conjugate of polar conjugate of X(21293)
X(23137) = isotomic conjugate of polar conjugate of X(23402)
X(23138) lies on these lines: {3, 22433}, {6, 8287}, {20807, 22133}, {22145, 22146}
X(23138) = isogonal conjugate of polar conjugate of X(21294)
X(23138) = isotomic conjugate of polar conjugate of X(23860)
X(23139) lies on these lines: {3, 22434}, {6, 16598}, {63, 20768}, {219, 22156}, {647, 1331}, {17914, 21295}, {22119, 23118}, {23112, 23121}
X(23139) = isogonal conjugate of polar conjugate of X(21295)
X(23139) = isotomic conjugate of polar conjugate of X(23861)
X(23140) lies on these lines: {3, 22435}, {6, 5437}, {63, 77}, {189, 7359}, {524, 20266}, {1407, 2323}, {1473, 3292}, {1818, 22117}, {2003, 7308}, {2289, 7099}, {3157, 3940}, {3167, 3784}, {3682, 23072}, {4001, 17073}, {5440, 7078}, {7232, 20268}, {17814, 18540}, {17917, 21296}, {20739, 22153}, {20744, 22127}, {22123, 23122}, {22145, 23129}, {22356, 23089}
X(23140) = isogonal conjugate of polar conjugate of X(21296)
X(23140) = isotomic conjugate of polar conjugate of X(5204)
X(23140) = X(19)-isoconjugate of X(7319)
X(23141) lies on these lines: {3, 22384}, {6, 3960}, {905, 4131}, {1191, 3887}, {1332, 4561}, {1797, 22086}, {2254, 16466}, {3762, 4383}, {4895, 16483}, {22090, 22160}, {22144, 22145}
X(23141) = isogonal conjugate of polar conjugate of X(21297)
X(23141) = isotomic conjugate of polar conjugate of X(4491)
X(23142) lies on these lines: {3, 22438}, {6, 4892}, {219, 23069}, {20739, 22130}, {20816, 22157}
X(23142) = isogonal conjugate of polar conjugate of X(21298)
X(23142) = isotomic conjugate of polar conjugate of X(23862)
X(23143) lies on these lines: {3, 22439}, {6, 43}, {219, 7015}, {222, 7182}, {394, 7124}, {20747, 22149}, {22156, 23118}
X(23143) = isogonal conjugate of polar conjugate of X(21299)
X(23143) = isotomic conjugate of polar conjugate of X(23863)
X(23144) lies on these lines: {3, 1803}, {6, 7}, {48, 1804}, {57, 16438}, {63, 77}, {155, 23070}, {218, 1445}, {221, 3868}, {241, 2911}, {268, 1815}, {307, 23151}, {377, 9370}, {603, 1259}, {1004, 4551}, {1037, 1362}, {1062, 1071}, {1407, 17092}, {1419, 2323}, {1439, 3211}, {1442, 2256}, {1449, 2003}, {1498, 3562}, {1813, 7053}, {1993, 9965}, {2808, 7071}, {3100, 12669}, {3197, 7291}, {3561, 23072}, {4306, 16471}, {5249, 10601}, {5273, 17074}, {5776, 21279}, {7074, 7411}, {7078, 10884}, {7177, 22153}, {7289, 19350}, {8271, 16465}, {8757, 10982}, {18650, 20744}, {22125, 22131}
X(23144) = isogonal conjugate of polar conjugate of X(6604)
X(23144) = isotomic conjugate of polar conjugate of X(1617)
X(23144) = X(19)-isoconjugate of X(6601)
X(23145) lies on these lines: {3, 22441}, {6, 8062}, {219, 23189}, {521, 650}, {3049, 15411}, {7254, 23146}, {20816, 22157}, {21348, 21388}
X(23145) = isogonal conjugate of polar conjugate of X(21300)
X(23145) = isotomic conjugate of polar conjugate of X(23864)
X(23146) lies on these lines: {3, 22443}, {6, 522}, {218, 657}, {219, 1459}, {525, 3049}, {652, 17975}, {2522, 23090}, {2911, 6586}, {3063, 3309}, {7254, 23145}
X(23146) = isogonal conjugate of polar conjugate of X(21302)
X(23146) = isotomic conjugate of polar conjugate of X(23865)
X(23147) lies on these lines: {3, 22444}, {6, 812}, {525, 3049}, {7254, 23117}, {22144, 22145}, {22383, 23148}
X(23147) = isogonal conjugate of polar conjugate of X(21303)
X(23147) = isotomic conjugate of polar conjugate of X(23866)
X(23148) lies on these lines: {3, 22445}, {6, 3835}, {6332, 20808}, {20816, 22157}, {22383, 23147}
X(23148) = isogonal conjugate of polar conjugate of X(21304)
X(23148) = isotomic conjugate of polar conjugate of X(23867)
X(23149) lies on these lines: {3, 22446}, {7254, 23117}, {20816, 22157}
X(23149) = isogonal conjugate of polar conjugate of X(21305)
X(23149) = isotomic conjugate of polar conjugate of X(23403)
X(23150) lies on these lines: {1, 6}, {3, 9247}, {48, 22133}, {78, 20770}, {222, 7183}, {283, 22070}, {304, 20742}, {394, 7124}, {517, 7119}, {2083, 20254}, {3157, 22163}, {4020, 7116}, {6056, 12836}, {7066, 12835}, {7193, 23620}, {20762, 20809}, {20766, 23165}, {22162, 23070}, {22164, 23071}
X(23150) = isogonal conjugate of polar conjugate of X(4388)
X(23150) = isotomic conjugate of polar conjugate of X(23868)
X(23150) = X(19)-isoconjugate of X(7224)
X(23150) = X(92)-isoconjugate of X(34250)
X(23151) lies on these lines: {2, 218}, {3, 63}, {6, 4357}, {7, 2287}, {8, 13727}, {41, 11343}, {56, 18206}, {57, 16412}, {69, 219}, {81, 3616}, {141, 2911}, {198, 16574}, {200, 9441}, {213, 940}, {220, 3912}, {222, 348}, {239, 3673}, {307, 23144}, {329, 6996}, {379, 20347}, {394, 4001}, {599, 17796}, {672, 21477}, {857, 21285}, {894, 5783}, {942, 19309}, {965, 10436}, {1376, 20683}, {1429, 21384}, {1804, 16731}, {1959, 5730}, {2256, 3879}, {2271, 3666}, {2318, 20731}, {3218, 11329}, {3219, 16367}, {3713, 3729}, {3868, 19310}, {3869, 7291}, {3876, 19314}, {4361, 16732}, {4384, 5228}, {4513, 17294}, {4641, 5021}, {5044, 19313}, {5282, 21981}, {5439, 19321}, {5526, 17284}, {5711, 16830}, {5776, 10444}, {16551, 21078}, {16844, 19716}, {18747, 21276}, {20806, 22122}, {20812, 23131}, {22097, 23620}, {22152, 23094}
X(23151) = isogonal conjugate of polar conjugate of X(4441)
X(23151) = isotomic conjugate of polar conjugate of X(1001)
X(23151) = X(19)-isoconjugate of X(1002)
See Antreas Hatzipolakis, César Lozada, and Ercole Suppa, Hyacinthos 28253 and Hyacinthos 28256.
X(23152) lies on these lines: {80, 517}, {88, 105}, {354, 3025}, {513, 17660}, {953, 2646}, {1319, 4351}, {3057, 3326}, {3259, 17605}, {5048, 10702}
X(23152) = reflection of X(3057) in X(13756)
X(23152) = X(476)-of-Ursa-minor triangle
X(23152) = X(14731)-of-intouch triangle
See Antreas Hatzipolakis, César Lozada, Hyacinthos 28254.
X(23153) lies on these lines: {1, 3025}, {35, 953}, {36, 106}, {80, 517}, {513, 7972}, {3259, 7951}, {5119, 15737}, {5697, 18340}, {5903, 6788}
X(23153) = reflection of X(1) in X(13756)
X(23153) = X(13756)-of-Aquila triangle
X(23153) = X(18319)-of-Ursa-minor triangle
See Antreas Hatzipolakis, César Lozada, Hyacinthos 28255.
X(23154) lies on these lines: {1, 855}, {3, 1331}, {8, 2810}, {48, 3284}, {51, 942}, {63, 22076}, {65, 8679}, {72, 3917}, {73, 22345}, {78, 3784}, {184, 3157}, {197, 1406}, {201, 3942}, {221, 8192}, {222, 1425}, {228, 4303}, {283, 22161}, {373, 5439}, {511, 3868}, {513, 6284}, {912, 5562}, {944, 2818}, {970, 3218}, {971, 11381}, {1193, 1401}, {1437, 23070}, {1473, 7078}, {2390, 3057}, {2392, 3874}, {2807, 15071}, {2808, 12111}, {2841, 5697}, {2842, 3878}, {3060, 12109}, {3313, 9021}, {3690, 3927}, {3781, 3951}, {3782, 18178}, {3819, 3876}, {4020, 22070}, {4185, 6180}, {4306, 13738}, {5044, 5650}, {5905, 10441}, {5907, 12528}, {6147, 18180}, {8614, 20986}, {10364, 21279}, {11246, 22300}, {20727, 20785}, {22344, 22350}
X(23154) = reflection of X(i) in X(j) for these (i,j): (72, 11573), (185, 1071)
X(23154) = isogonal conjugate of polar conjugate of X(3782)
X(23154) = isotomic conjugate of isogonal conjugate of X(23196)
X(23154) = isotomic conjugate of polar conjugate of X(17053)
X(23154) = X(19)-isoconjugate of X(2985)
X(23154) = {X(72), X(11573)}-harmonic conjugate of X(3917)
See Antreas Hatzipolakis, César Lozada, Hyacinthos 28255.
X(23155) lies on these lines: {1, 2392}, {2, 375}, {8, 11573}, {81, 1469}, {100, 3784}, {210, 7998}, {354, 3060}, {511, 3873}, {518, 2979}, {674, 4430}, {1401, 4850}, {1993, 22769}, {2807, 11220}, {2810, 3681}, {2842, 3899}, {3567, 13373}, {3705, 3909}, {3742, 5640}, {3888, 5014}, {3938, 7186}, {4661, 9026}, {5889, 12675}, {7391, 12586}, {11444, 14872}, {12111, 12680}, {17063, 20962}
See Antreas Hatzipolakis, César Lozada, Hyacinthos 28255.
X(23156) lies on these lines: {1, 2392}, {10, 8679}, {52, 12005}, {511, 3874}, {942, 9037}, {970, 4973}, {1125, 15049}, {2779, 18481}, {2801, 5562}, {2842, 3869}, {2979, 5904}, {3060, 18398}, {3678, 3917}, {3754, 16980}, {4020, 14963}, {6583, 10263}, {11793, 15064}
See Antreas Hatzipolakis, César Lozada, Hyacinthos 28255.
X(23157) lies on these lines: {1, 2392}, {375, 19878}, {511, 3881}, {519, 11573}, {1125, 8679}, {2810, 3678}, {2842, 3878}, {3616, 15049}, {3784, 8715}, {3819, 4015}, {5045, 9037}, {5883, 16980}
X(23158) lies on these lines: {2, 8