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(40001) lies on these lines: {2, 37}, {76, 18744}, {82, 17763}, {304, 17241}, {313, 18151}, {1089, 13741}, {1230, 20916}, {1930, 17283}, {3702, 32850}, {3718, 17335}, {3912, 18714}, {4044, 20445}, {4673, 5100}, {10159, 33944}, {17285, 18697}, {17788, 17791}, {17789, 18143}, {20444, 20917}, {20915, 20927}, {32930, 33760}
X(40002) lies on these lines: {2, 3108}, {69, 7394}, {75, 33091}, {76, 1369}, {1272, 6636}, {7768, 37349}, {8024, 14360}, {9464, 19583}, {14023, 16952}, {20934, 39728}, {33090, 33944}
X(40002) = anticomplement of X(3108)
X(40003) lies on these lines: {2, 32}, {69, 14247}, {76, 38946}, {827, 7767}, {7826, 14885}, {10159, 40000}
X(40004) lies on these lines: {2, 39735}, {37, 16727}, {75, 3873}, {76, 17234}, {85, 4751}, {86, 2481}, {274, 20448}, {310, 4043}, {870, 16709}, {1218, 2350}
X(40005) lies on these lines: {2, 40008}, {76, 4043}, {310, 2388}, {561, 33932}, {1500, 23989}, {6063, 33298}, {17911, 17913}, {18031, 18140}, {29433, 39797}
X(40005) = isotomic conjugate of X(8053)
X(40006) lies on these lines: {1, 2}, {69, 3730}, {75, 17758}, {76, 4043}, {100, 29473}, {101, 34065}, {141, 1500}, {304, 4568}, {334, 29757}, {1018, 17137}, {1043, 29775}, {1330, 20533}, {1930, 3930}, {1978, 33778}, {2140, 17143}, {2141, 17295}, {2276, 16887}, {2321, 20888}, {3263, 4006}, {3454, 26590}, {3501, 17296}, {3695, 4437}, {3726, 24166}, {3797, 24068}, {3881, 24631}, {3933, 6184}, {3969, 20913}, {3970, 20911}, {3987, 26562}, {3996, 17682}, {4103, 33932}, {4153, 24057}, {4551, 28777}, {4851, 17750}, {6376, 17240}, {6381, 21071}, {7270, 29743}, {8715, 24586}, {12782, 33087}, {14210, 33299}, {16060, 33771}, {16549, 30941}, {16589, 17243}, {17144, 17761}, {17206, 24047}, {17231, 20691}, {17232, 24190}, {17280, 17499}, {18047, 29792}, {18152, 40008}, {18720, 20914}, {20932, 20933}, {21067, 33931}, {22011, 33935}, {24170, 30945}, {29789, 35978}, {30949, 32104}
X(40006) = anticomplement of X(2350)
X(40007) lies on these lines: {2, 2350}, {75, 3681}, {76, 17135}, {1330, 1369}, {3952, 18138}, {16684, 37632}, {17018, 30946}, {17149, 29824}, {18133, 30941}, {20012, 32105}, {24215, 27635}, {29814, 36854}
X(40008) lies on these lines: {2, 40005}, {76, 17135}, {310, 29767}, {561, 18137}, {6063, 17077}, {18031, 18064}, {18152, 40006}
Points on cubics: X(40009)-X(40046)
This preamble is contributed by Clark Kimberling, October 13, 2020; modified January 31, 2021.
In column 1 of the following table, the appearance of u(a,b,c) in a row means that the points indicated in column 2 lie on the cubic
u(a,b,c)(by-cz)(ax+by)(ax+cz) + u(b,c,a)(cz-ax)(by+cz)(by+cz) + u(c,a,b)(ax-by)(cz+ax)(cz+by) = 0.
The appearance of {i,j} in column 2 means that {X(i),X(j)} are a pair of X(560)-isoconjugates that lie on the cubic.
b+c | {2998,6374} |
(b+c)^2 | {18133,40010}, {18140,40013} |
a^2 (b+c)^2 | {17758,18152}, {18137,39735} |
(b+c)(b+c-a) | {18135,40012} |
(b+c)^2 cos^2 A | {18134,40011} |
(b+c)(2a-b-c) | {4358,20568}, {18145,39994}, {39995,40039}, {39996,40040}, {39997,40041} |
(b+c)(3a+b+c) | {18135,40012} |
(b+c)(-3a+b+c) | {18134,40013}, {20934,40026} |
(b+c)(4a+b+c) | {4671,205690} |
(b+c)(2a+3b+3c) | {4359,32018} |
(b+c)(-a+2b+2c) | {18146,40021}, {30829,40029} |
(b+c)(a^2+b^2+c^2+a(a+b+c)) | {870,33931} |
(b+c)(a+2b+2c)) | {19804,40023} |
(b+c)(bc+ca+ab+a(a+b+c)) | {20913,40024} |
(b+c)(bc+ca+ab-a(a+b+c)) | {3948,40017}, {18032,20947} |
(b+c)(bc+ca+ab-2a(a+b+c)) | {31060,40031} |
(b+c)(2(bc+ca+ab)-a(a+b+c)) | {30758,40028}, {30830,40030} |
(b+c)(abc+a(a^2+b^2+c^2)) | {10159,40020}, {33944,40033} |
(b+c)(2abc+a(a^2+b^2+c^2)) | {32000,40032} |
(b+c)(abc+a(bc+ca+ab)) | {10,310}, {4043,40004} |
(b+c)(abc-a(bc+ca+ab)) | {17758,18152} |
(b+c)(2abc-a(bc+ca+ab)) | {20923,40025} |
(b+c)(b^2c^2+c^2a^2+a^2b^2+a^2bc) | {3934,31630} |
(b+c)(b^2c^2+c^2a^2+a^2b^2-a^2bc) | {39,40016} |
(b+c)(2a+b+c) | {274,321}, {35058,40034} |
(b+c)(abc-a(a^2+b^2+c^2)) | {83,8024}, {1031,40035}, {1369,40036}, {20933,40037}, {33938,40038} |
X(40009) lies on these lines: {76, 17907}, {83, 26209}, {305, 315}, {2207, 36793}, {4150, 20914}, {28695, 31636}
X(40009) = isotomic conjugate of X(159)
X(40009) = polar conjugate of X(3162)
X(40009) = X(4)-cross conjugate of X(76)
X(40009) = trilinear pole of line X(3267)X(33294)
X(40010) lies on these lines: {2, 18040}, {7, 18147}, {27, 18742}, {75, 24046}, {86, 13741}, {272, 18738}, {312, 39700}, {335, 18137}, {350, 8049}, {673, 29437}, {2296, 30963}, {4286, 29712}, {4360, 29454}, {6376, 30598}, {6384, 30596}, {14621, 18046}, {18143, 27145}, {18149, 20932}, {18739, 37633}, {20028, 30939}, {29486, 29772}
X(40010) = isotomic conjugate of X(3216)
X(40011) lies on these lines: {2, 349}, {8, 313}, {29, 264}, {76, 333}, {85, 18726}, {92, 20926}, {272, 1234}, {312, 27801}, {1235, 19768}, {1259, 34387}, {1305, 1311}, {1502, 28660}, {19607, 28917}
X(40011) = isotomic conjugate of X(579)
X(40011) = polar conjugate of isogonal conjugate of isotomic conjugate of X(5125)
X(40012) lies on these lines: {2, 34283}, {4, 18141}, {10, 982}, {83, 940}, {98, 8690}, {141, 34258}, {226, 17234}, {312, 4052}, {321, 3662}, {345, 30866}, {801, 25934}, {1751, 14829}, {2051, 18134}, {3963, 6539}, {4035, 37865}, {4417, 14554}, {6557, 36805}, {8033, 32014}, {10453, 13576}, {14534, 37674}, {17678, 19792}, {17758, 18136}, {17786, 24177}
X(40012) = isogonal conjugate of X(16946)
X(40012) = isotomic conjugate of X(4383)
X(40012) = polar conjugate of X(4186)
X(40012) = cevapoint of X(1086) and X(4391)
X(40012) = trilinear pole of line X(523)X(3777)
X(40013) lies on the Kiepert hyperbola and these lines: {2, 3770}, {4, 37482}, {10, 38}, {75, 6539}, {76, 16703}, {81, 83}, {98, 19649}, {141, 321}, {226, 4358}, {239, 29757}, {312, 4080}, {873, 18140}, {1086, 28654}, {1150, 1751}, {1577, 8042}, {2051, 3936}, {3416, 4863}, {3720, 30982}, {3765, 26978}, {3912, 22010}, {3948, 17758}, {4049, 4391}, {5192, 18169}, {5741, 14554}, {7248, 10404}, {8024, 16727}, {8025, 18046}, {14534, 37633}, {14829, 24624}, {17147, 18040}, {17307, 30599}, {17790, 26842}, {18059, 24731}, {19742, 29484}, {20917, 28606}, {26540, 37874}, {27797, 28605}, {30807, 36907}, {32782, 34258}
X(40013) = isogonal conjugate of X(2220)
X(40013) = isotomic conjugate of X(32911)
X(40013) = polar conjugate of X(4222)
X(40013) = trilinear pole of line X(523)X(2530)
X(40013) = cevapoint of X(1086) and X(1577)
X(40014) lies on these lines: {75, 3617}, {76, 4052}, {85, 5226}, {274, 8056}, {279, 37758}, {286, 30939}, {304, 20568}, {334, 20943}, {341, 1111}, {767, 1293}, {870, 3445}, {1088, 27829}, {2481, 3680}, {6383, 21615}, {7319, 21296}, {10563, 32104}, {19604, 31643}, {20569, 27820}, {20942, 21605}, {24796, 36926}, {27834, 37130}, {32018, 33934}
X(40014) = isotomic conjugate of X(1743)
X(40015) lies on these lines: {75, 17903}, {305, 20914}, {312, 18629}, {341, 1370}, {2064, 14615}
X(40015) = isotomic conjugate of X(1763)
X(40015) = polar conjugate of X(36103)
X(40015) = X(4)-cross conjugate of X(75)
X(40016) lies on the Kiepert hyperbola and these lines: {2, 308}, {4, 18022}, {10, 18833}, {76, 19562}, {83, 1207}, {98, 689}, {99, 34452}, {141, 31630}, {251, 3407}, {262, 305}, {561, 18066}, {690, 18008}, {804, 17995}, {1916, 4609}, {3051, 9230}, {11606, 23962}, {16890, 18901}, {16893, 18896}, {24624, 37204}, {34087, 34294}
X(40016) = isogonal conjugate of X(41331)
X(40016) = isotomic conjugate of X(3051)
X(40016) = polar conjugate of X(27369)
X(40016) = cevapoint of X(i) and X(j) for these {i,j}: {75, 18050}, {76, 1502}
X(40016) = trilinear pole of line X(523)X(14603)
X(40016) = trilinear product X(i)*X(j) for these {i,j}: {2, 18833}, {75, 308}, {76, 3112}, {82, 1502}, {83, 561}, {251, 1928}, {523, 37204}, {670, 18070}, {689, 1577}, {850, 4593}, {1799, 1969}, {1926, 14970}, {3115, 20627}, {3405, 18024}, {4577, 20948}, {6385, 18082}, {6386, 10566}, {18022, 34055}, {18090, 38812}, {18097, 40072}, {20889, 31622}, {30505, 33778}, {32085, 40364}, {37221, 40074}
X(40017) lies on these lines: {2, 799}, {4, 811}, {10, 274}, {76, 4602}, {83, 1509}, {86, 741}, {98, 36036}, {99, 8299}, {142, 34021}, {226, 4554}, {292, 31996}, {310, 321}, {350, 9505}, {670, 1086}, {1581, 18298}, {2051, 34020}, {2311, 17206}, {2394, 33805}, {2669, 3783}, {3834, 30938}, {4049, 20568}, {4080, 4639}, {4440, 36860}, {4444, 31001}, {4583, 18157}, {4589, 4645}, {4623, 25536}, {6384, 30953}, {6539, 16748}, {7245, 16712}, {7304, 37676}, {11611, 20924}, {16705, 30669}, {17234, 34022}, {17758, 18140}, {30588, 30990}, {30964, 31006}, {30992, 30993}, {30997, 32020}, {39786, 39925}
X(40017) = isogonal conjugate of X(41333)
X(40017) = isotomic conjugate of X(2238)
X(40017) = polar conjugate of X(862)
X(40017) = cevapoint of X(i) and X(j) for these {i,j}: {2, 30941}, {6, 16876}, {75, 3948}, {334, 335}, {514, 23822}, {1086, 3766}, {18827, 36800}
X(40017) = trilinear pole of line X(75)X(523)
X(40017) = trilinear product X(i)*X(j) for these {i,j}: {2, 18827}, {7, 36800}, {27, 337}, {58, 18895}, {75, 37128}, {76, 741}, {81, 334}, {86, 335}, {99, 4444}, {274, 291}, {292, 310}, {331, 1808}, {333, 7233}, {513, 4639}, {514, 4589}, {561, 18268}, {660, 7199}, {670, 3572}, {693, 4584}, {799, 876}, {875, 4602}, {982, 40834}, {1019, 4583}, {1434, 4518}, {1577, 36066}, {1581, 8033}, {1911, 6385}, {1916, 17103}, {1930, 39276}, {2311, 6063}, {4017, 36806}, {4369, 18829}, {4374, 37134}, {4481, 41072}, {4562, 7192}, {4610, 35352}, {5378, 16727}, {17096, 36801}, {30663, 30940}, {30669, 32010}, {33295, 40098}, {39747, 40093}, {39950, 40094}
X(40018) lies on these lines: {7, 3264}, {76, 39710}, {313, 4373}, {673, 29541}, {903, 3596}, {1269, 36588}, {6548, 35519}
X(40019) lies on these lines: {}
X(40020) lies on these lines: on lines {18137, 40006}, {18152, 40007}
X(40021) lies on these lines: {2, 39960}, {10, 4392}, {83, 14996}, {321, 17227}, {1029, 18141}, {1751, 5372}, {4080, 17232}, {30588, 30829}
X(40021) = isotomic conjugate of X(14997)
X(40022) lies on these lines: {2, 39}, {3, 16276}, {4, 16275}, {22, 1078}, {25, 183}, {32, 16950}, {51, 69}, {83, 5359}, {99, 7485}, {111, 1239}, {115, 8890}, {141, 3981}, {251, 6179}, {262, 31630}, {311, 7494}, {315, 6997}, {316, 7394}, {325, 37439}, {338, 8556}, {350, 612}, {428, 7750}, {614, 1909}, {1007, 1232}, {1184, 7770}, {1235, 6353}, {1241, 8770}, {1269, 30758}, {1369, 7533}, {1370, 11185}, {1611, 11324}, {1613, 24256}, {1627, 3972}, {1915, 8177}, {1975, 7484}, {1995, 33651}, {2052, 37187}, {2979, 33798}, {3596, 26234}, {3734, 16951}, {3760, 5268}, {3761, 5272}, {3785, 6995}, {3846, 18067}, {3917, 18906}, {3963, 26274}, {4074, 21001}, {4417, 18052}, {4563, 17811}, {5025, 21248}, {5249, 21590}, {5475, 8878}, {5651, 37894}, {5943, 14994}, {6374, 16986}, {6394, 6641}, {6636, 7771}, {7398, 14615}, {7467, 22712}, {7499, 37688}, {7500, 14907}, {7667, 32819}, {7752, 37990}, {7782, 15246}, {7802, 34603}, {7878, 34482}, {9230, 16990}, {10327, 17143}, {10565, 30737}, {11174, 33769}, {13595, 26233}, {13881, 30785}, {15004, 39099}, {15437, 32983}, {15466, 18022}, {17234, 18138}, {18142, 18143}, {18835, 29634}, {19188, 34384}, {20965, 32451}, {21415, 25961}, {21609, 21617}, {26257, 34481}, {30786, 31255}, {33854, 34283}, {34816, 37876}
X(40022) = isotomic conjugate of X(39951)
X(40022) = polar conjugate of isogonal conjugate of X(3785)
X(40023) lies on these lines: on lines {75, 3701}, {76, 30713}, {85, 321}, {274, 312}, {286, 318}, {304, 20569}, {767, 8694}, {870, 2334}, {2481, 4385}, {4606, 37130}, {5556, 32099}, {6385, 28659}, {20568, 33935}, {31643, 39126}
X(40023) = isotomic conjugate of X(1449)
X(40023) = polar conjugate of X(5338)
X(40024) lies on these lines: {2, 30940}, {10, 350}, {83, 2238}, {226, 10030}, {274, 17758}, {308, 594}, {321, 1921}, {3112, 4651}, {3783, 5263}, {4444, 7199}, {4665, 31625}, {11599, 39028}, {14534, 37676}, {21443, 34475}, {21897, 25368}, {29792, 34016}
X(40024) = isotomic conjugate of X(24512)
X(40025) lies on these lines: {9, 274}, {33, 286}, {37, 85}, {75, 210}, {76, 2321}, {312, 6385}, {331, 1826}, {870, 34445}, {2481, 3875}, {4664, 39735}, {6383, 20335}, {18032, 20930}, {18159, 39467}
X(40025) = isotomic conjugate of X(21384)
X(40026) lies on these lines: {75, 4678}, {85, 36621}, {274, 36603}, {767, 8699}, {20568, 33780}, {20925, 32018}, {20942, 21605}
X(40026) = isotomic conjugate of X(3973)
X(40027) lies on these lines: {1, 32011}, {2, 17448}, {7, 24495}, {75, 3840}, {86, 18192}, {244, 8026}, {310, 30957}, {312, 27494}, {335, 18743}, {350, 4373}, {673, 36630}, {675, 29227}, {903, 34020}, {2296, 30950}, {4106, 38238}, {4479, 36588}, {4871, 6384}, {14621, 36614}, {17149, 31002}, {17234, 20528}, {20335, 27498}, {30947, 39741}
X(40027) = isotomic conjugate of X(16569)
X(40028) lies on these lines: {75, 966}, {76, 4087}, {85, 350}, {274, 988}, {312, 334}, {767, 28847}, {4385, 32018}, {4479, 18032}, {20930, 39735}, {30758, 30830}
X(40028) = isotomic conjugate of X(3751)
X(40029) lies on these lines: {75, 4723}, {85, 4358}, {274, 39963}, {312, 20568}, {767, 6014}, {2481, 4900}, {18146, 20569}
X(40029) = isotomic conjugate of X(16670)
X(40030) lies on the Kiepert hyperbola and these lines: {4, 30941}, {10, 3761}, {69, 13576}, {310, 34258}, {17758, 18135}
X(40030) = isotomic conjugate of X(37657)
X(40030) = trilinear pole of the line X(523)X(4411)
X(40031) lies on these lines: {2, 39952}, {10, 24524}, {321, 31028}, {4080, 30964}
X(40031) = isotomic conjugate of X(37673)
X(40032) lies on these lines: {2, 800}, {69, 185}, {76, 253}, {95, 16035}, {235, 264}, {311, 36889}, {3260, 8797}
X(40032) = isotomic conjugate of X(1593)
X(40033) lies on these lines: {2, 21021}, {7, 7211}, {12, 7249}, {27, 1840}, {75, 24169}, {86, 1215}, {310, 1237}, {312, 14621}, {321, 6650}, {4385, 6384}, {17725, 30598}, {17762, 20715}, {17763, 18099}, {20934, 39728}
X(40033) = isotomic conjugate of X(29821)
X(40034) lies on these lines: {10, 35538}, {75, 596}, {76, 321}, {141, 21412}, {274, 27163}, {670, 1509}, {1921, 18050}, {1930, 35544}, {1978, 18140}, {3159, 18133}, {3262, 14615}, {3739, 6374}, {4075, 6376}, {4087, 33940}, {4485, 33945}, {17495, 29765}, {18040, 22011}, {18135, 26774}, {18146, 35652}, {18152, 33775}, {20924, 21596}, {21240, 21435}, {21595, 21598}, {33764, 34016}
X(40034) = isotomic conjugate of isogonal conjugate of X(17147)
X(40035) lies on these lines: {2, 39999}, {6, 76}, {75, 29673}, {304, 17786}, {305, 3314}, {570, 7799}, {626, 24733}, {1031, 7779}, {1502, 17949}, {2896, 28677}, {3313, 7768}, {7788, 14615}, {18835, 24732}, {20934, 21083}, {32452, 39468}
X(40035) = isotomic conjugate of X(14370)
X(40036) lies on these lines: {76, 38946}, {1369, 5189}, {7878, 18018}, {20933, 21064}
X(40036) = isogonal conjugate of X(39)-Ceva conjugate of X(32)
X(40036) = isotomic conjugate of X(2916)
X(40036) = polar conjugate of X(8792)
X(40037) lies on these lines: {1369, 20934}, {8024, 20933}, {17087, 28780}
X(40037) = isotomic conjugate of X(16555)
X(40038) lies on these lines: {2, 16720}, {75, 29673}, {86, 7194}, {335, 3782}, {673, 24631}, {1369, 39723}, {3665, 7249}, {3673, 6384}, {3961, 20955}, {8024, 33938}, {20924, 29656}, {24326, 39745}, {27918, 39746}, {29655, 33940}
X(40038) = isotomic conjugate of X(3961)
Let P and U be the circumcircle intercepts of the Nagel line. Then X(40039) = isotomic conjugate of {P,U}-harmonic conjugate of X(1). (Randy Hutson, October 29, 2020)
X(40039) lies on these lines: {2, 4033}, {7, 18133}, {27, 6335}, {75, 21208}, {86, 668}, {310, 6386}, {313, 17205}, {903, 18145}, {6376, 39704}, {6548, 21606}, {6650, 17790}, {18149, 20937}
X(40040) lies on these lines: {4358, 39699}, {18145, 30939}
X(40041) lies on these lines: {519, 39995}, {18145, 39997}, {20568, 39699}
X(40042) lies on these lines: {3589, 7839}, {39998, 39999}, {40000, 40002}
X(40043) lies on these lines: {2, 39999}, {76, 1031}, {141, 28677}, {15523, 28676}, {39998, 40000}
X(40044) lies on these lines: {75, 33091}, {85, 17371}, {21598, 39999}, {33944, 40003}, {39998, 40001}
X(40045) lies on these lines: {39998, 40002}, {39999, 40003}
X(40046) lies on these lines: {76, 1369}, {39998, 40003}
X(40047) lies on the cubic K039 and these lines: {74, 15478}, {131, 15329}, {186, 925}, {13496, 13754}
X(40047) = circumcircle inverse of X(40048)
X(40048) lies on the Jerabek circumhyperbola and these lines: {68, 526}, {265, 924}, {523, 5504}, {690, 34801}, {2970, 15328}, {3566, 34802}, {6391, 9003}, {9033, 15316}, {11559, 20184}
X(40048) = isogonal conjugate of X(40049)
X(40048) = circumcircle-inverse of X(40047)
X(40049) lies on these lines: {2, 3}, {99, 16167}, {110, 924}, {476, 925}, {523, 23181}, {1147, 39371}, {1304, 13398}, {1624, 3233}, {3258, 23217}, {3565, 9060}, {14480, 36829}, {16166, 20185}, {17702, 39986}
X(40049) = isogonal conjugate of X(40048)
X(40049) = circumcircle-inverse of X(30512)
X(40049) = X(523)-vertex conjugate of X(30512)
X(40049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1113, 1114, 30512}, {3658, 7477, 37964}, {4226, 7468, 7482}, {4230, 7472, 7468}, {7468, 7480, 7471}, {7471, 15329, 7480}
X(40050) lies on these lines: {2, 1241}, {4, 683}, {69, 4173}, {75, 23664}, {76, 141}, {83, 9516}, {99, 15270}, {194, 35540}, {304, 20727}, {305, 1368}, {315, 670}, {706, 33786}, {1235, 5117}, {1613, 3978}, {1975, 16084}, {3266, 7906}, {3673, 18891}, {3926, 28438}, {4176, 20023}, {5025, 35524}, {7760, 16285}, {7770, 9230}, {11059, 31406}, {14376, 34254}, {18840, 40016}, {39129, 40009}
X(40050) = isotomic conjugate of X(1974)
X(40050) = isogonal conjugate of isotomic conjugate of X(40360)
X(40050) = polar conjugate of X(36417)
Dao-perspeconics: X(40051)-X(40070)
This preamble and centers X(40051)-X(40070) were contributed by César Eliud Lozada, October 14, 2020.
Let ABC, A'B'C' be two perspective triangles, neither inscribed in the other. Let T1 be the triangle bounded by the lines BC', CA', AB' and let T2 be the triangle bounded by the lines BA', CB', AC'. Then the vertices of T1 and T2 lie all on a conic (Dao Thanh Oai, October 13, 2020). This conic will be named here the Dao-perspeconic of ABC and A'B'C'.
The appearance of (T, n) in the following partial list means that the center of the Dao-perspeconic of triangles ABC and T is X(n):
(ABC-X3 reflections, 3), (anti-Aquila, 40051), (anti-Ara, 40052), (anti-Conway, 15648), (2nd anti-Conway, 15649), (anti-excenters-reflections, 40053), (anti-Honsberger, 40054), (anti-inverse-in-incircle, 7800), (anti-tangential-midarc, 40055), (Apus, 40056), (Aquila, 15650), (Ara, 15651), (4th Brocard, 40057), (9th Brocard, 2996), (circummedial, 15652), (circumorthic, 15653), (2nd circumperp, 15654), (circumsymmedial, 15655), (Conway, 15656), (2nd Conway, 966), (5th Euler, 40058), (excenters-reflections, 40059), (extangents, 40060), (outer-Garcia, 10), (Gossard, 402), (Honsberger, 15657), (infinite-altitude, 3), (inverse-in-Conway, 40061), (inverse-in-incircle, 15658), (Johnson, 5), (2nd Johnson-Yff, 40062), (1st Kenmotu diagonals, 15659), (2nd Kenmotu diagonals, 15660), (Mandart-incircle, 40062), (midheight, 15661), (2nd mixtilinear, 15662), (3rd mixtilinear, 15663), (4th mixtilinear, 40063), (5th mixtilinear, 1), (6th mixtilinear, 40064), (orthic axes, 40065), (reflection, 15664), (1st Sharygin, 40066), (inner-squares, 40067), (outer-squares, 40068), (2nd inner-Vecten, 1132), (2nd outer-Vecten, 1131), (1st Zaniah, 40069), (2nd Zaniah, 40070)
Definitions of all triangles above mentioned can be found in the index of triangles.
X(40051) lies on these lines: {1,15650}, {3647,11281}
X(40051) = midpoint of X(1) and X(15650)
X(40052) lies on these lines: {25,15651}, {1843,19595}, {3867,9969}
X(40053) lies on these lines: {3,13474}, {4,33580}, {11414,18840}
X(40054) lies on these lines: {141,206}, {1974,17409}
X(40055) lies on these lines: {2,10571}, {1042,1402}
X(40056) lies on these lines: {2271,9406}, {15817,32664}
X(40057) lies on these lines: {111,251}, {15820,15899}
X(40058) lies on these lines: {39,15880}, {141,3787}
X(40059) lies on these lines: {10,3090}, {3340,10563}
X(40060) lies on these lines: {228,1334}, {15830,38015}
X(40061) lies on these lines: {10,3781}, {10471,10473}
X(40062) lies on the line {15280,15845}
X(40063) lies on these lines: {3,15855}, {41,37541}, {55,32625}, {101,1615}, {165,198}, {284,11051}, {2267,15288}
X(40063) = center of the cross-perspeconic of these triangles: ABC and 4th mixtilinear
X(40064) lies on these lines: {55,1419}, {223,15856}, {14522,14547}
X(40065) lies on these lines: {2,15905}, {4,6}, {5,38292}, {9,34231}, {25,37665}, {30,15851}, {51,6618}, {69,36794}, {193,458}, {216,376}, {232,7714}, {264,1992}, {275,459}, {281,1743}, {284,37417}, {317,3618}, {340,3619}, {378,1285}, {386,37379}, {389,3183}, {391,11109}, {427,5304}, {469,37666}, {562,2963}, {566,35503}, {572,37410}, {577,631}, {579,37028}, {1033,1597}, {1073,14362}, {1119,4644}, {1449,7952}, {1585,7586}, {1586,7585}, {1609,3520}, {1656,33636}, {1724,7498}, {1745,22063}, {1785,16667}, {1870,3553}, {1885,33893}, {1968,13342}, {1993,6819}, {2193,6988}, {2548,6622}, {3068,3536}, {3069,3535}, {3079,17810}, {3088,30435}, {3090,3284}, {3091,36413}, {3147,5063}, {3329,37187}, {3524,36748}, {3528,36751}, {3529,5158}, {3554,6198}, {3815,38282}, {3945,26003}, {4254,37305}, {4383,37276}, {5024,37460}, {5065,6353}, {5081,5749}, {5094,37689}, {5120,7412}, {5200,5410}, {5222,7282}, {5413,19219}, {5422,6820}, {5839,7046}, {6524,15004}, {6620,12167}, {6621,15873}, {6623,15484}, {6803,23115}, {6995,14930}, {7378,16318}, {7401,22120}, {7487,9605}, {7494,10313}, {7577,9722}, {7718,9575}, {7735,8889}, {8553,35473}, {8779,11427}, {9748,37074}, {10299,22052}, {10979,21735}, {11348,20208}, {11513,36701}, {11514,36703}, {13567,19039}, {14860,15077}, {16328,35489}, {22124,34048}, {22240,34608}, {34545,37192}, {36743,37441}, {37448,37681}
X(40065) = polar conjugate of the isogonal conjugate of X(17809)
X(40065) = polar conjugate of the isotomic conjugate of X(3523)
X(40065) = barycentric product X(i)*X(j) for these {i, j}: {4, 3523}, {264, 17809}, {631, 11282}
X(40065) = trilinear product X(i)*X(j) for these {i, j}: {19, 3523}, {92, 17809}
X(40065) = intersection, other than A,B,C, of conics {{A, B, C, X(4), X(3523)}} and {{A, B, C, X(6), X(17809)}}
X(40065) = crosssum of X(3) and X(15851)
X(40065) = orthosymmedial-circle-inverse of X(1249)
X(40065) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 27377, 32001), (4, 6, 1249), (4, 33630, 53), (6, 1249, 5702), (6, 3087, 4), (6, 6748, 393), (6, 6749, 3087), (193, 458, 32000), (393, 3087, 6748), (393, 6748, 4), (1587, 1588, 12233), (7736, 10311, 6353), (19039, 19040, 13567), (19041, 19042, 427)
X(40066) lies on these lines: {6651,15864}, {8424,16372}, {8845,8932}
X(40067) lies on these lines: {6,641}, {25,371}, {32,8939}, {6680,40068}
X(40068) lies on these lines: {6,642}, {25,372}, {32,8943}, {6680,40067}
X(40068) = {X(372), X(8855)}-harmonic conjugate of X(8996)
X(40069) lies on these lines: {1,11051}, {281,1886}
X(40070) lies on these lines: {277,5745}, {3680,15853}
X(40071) lies on these lines: {10, 75}, {42, 1241}, {69, 11573}, {99, 19842}, {183, 19844}, {190, 4456}, {274, 19808}, {304, 305}, {321, 1228}, {325, 19839}, {336, 3682}, {346, 27250}, {349, 6358}, {350, 37042}, {668, 7270}, {683, 2333}, {714, 23664}, {1010, 1909}, {1078, 19841}, {1231, 26942}, {1969, 18022}, {1975, 19845}, {1978, 33805}, {2064, 21595}, {3695, 20235}, {3719, 19807}, {3765, 19281}, {3948, 16583}, {3975, 37086}, {4087, 18835}, {4150, 20914}, {4384, 19792}, {4386, 33731}, {7283, 16085}, {7763, 19795}, {8024, 19835}, {18135, 19785}, {18140, 19786}, {18145, 19796}, {18152, 19787}, {18153, 19790}, {19794, 32832}, {19798, 40025}, {19806, 30022}, {19810, 28660}, {19811, 34384}, {19822, 34284}, {20917, 37097}, {21063, 21094}
X(40071) = isotomic conjugate of X(1474)
X(40071) = polar conjugate of isogonal conjugate of isotomic conjugate of X(8747)
X(40072) lies on these lines: {38, 75}, {76, 1211}, {86, 4485}, {264, 305}, {274, 1920}, {312, 28659}, {314, 3706}, {321, 4469}, {333, 20665}, {668, 22275}, {670, 18816}, {869, 7033}, {1812, 4631}, {1921, 3666}, {3596, 3703}, {3665, 6063}, {6386, 20566}, {7018, 18891}, {8024, 31089}, {13588, 14195}, {16703, 35543}, {18138, 21596}
X(40072) = isotomic conjugate of X(1402)
X(40072) = polar conjugate of isogonal conjugate of isotomic conjugate of X(1880)
X(40073) lies on these lines: {6, 76}, {264, 305}, {311, 20023}, {315, 3313}, {393, 3926}, {570, 7763}, {670, 14615}, {1975, 12143}, {3596, 35551}, {4150, 20641}, {6374, 35542}, {6382, 35547}, {7774, 8024}, {7792, 40025}, {8264, 9865}, {16276, 32085}, {16989, 39998}, {17907, 34254}, {18024, 20563}, {19562, 35530}, {20806, 31636}, {20968, 38842}, {23642, 33734}, {39129, 40009}
X(40073) = isogonal conjugate of X(40146)
X(40073) = isotomic conjugate of X(2353)
X(40073) = polar conjugate of isogonal conjugate of X(34254)
X(40074) lies on these lines: {6, 33301}, {76, 524}, {251, 308}, {264, 305}, {311, 33769}, {316, 9019}, {328, 18024}, {338, 3978}, {523, 14603}, {670, 3260}, {702, 9865}, {892, 1236}, {1235, 38294}, {2393, 39266}, {3266, 18023}, {4590, 15014}, {7840, 8024}, {8859, 26235}, {14295, 33919}, {18896, 35542}, {20944, 21094}, {22329, 40025}, {37765, 37804}
X(40074) = isotomic conjugate of X(3455)
X(40074) = polar conjugate of isogonal conjugate of X(37804)
X(40075) lies on these lines: {75, 33120}, {76, 4358}, {86, 310}, {274, 33129}, {305, 561}, {693, 784}, {1233, 18152}, {1909, 32927}, {1920, 8024}, {1921, 3266}, {3836, 18066}, {3936, 20924}, {4766, 17789}, {7018, 21415}, {7112, 20944}, {17234, 18054}, {18037, 24602}, {18835, 20880}, {18895, 35545}, {20893, 21241}, {20947, 29854}, {25760, 33930}, {33108, 33933}, {34284, 37759}
X(40075) = isotomic conjugate of X(6187)
X(40076) lies on the cubic K039 and these lines: {3, 2772}, {27, 116}, {58, 22084}, {63, 35342}, {101, 1796}, {103, 186}, {222, 36075}, {2392, 17972}, {4466, 14377}, {5196, 39993}
X(40076) = isogonal conjugate of X(5134)
X(40076) = isogonal conjugate of the anticomplement of X(17729)
X(40076) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5134}, {37, 5196}
X(40076) = trilinear pole of line {1459, 2308}
X(40076) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5134}, {58, 5196}
X(40077) lies on the cubic K039 and these lines: {3, 2421}, {186, 2698}, {419, 2679}, {511, 2966}, {805, 15391}
X(40077) = reflection of X(2966) in the Lemoine axis
X(40077) = circumcircle-inverse of X(9513)
X(40077) = isogonal conjugate of X(38947)
X(40077) = X(i)-isoconjugate of X(j) for these (i,j): {1, 38947}, {1316, 1581}
X(40077) = barycentric product X(385)*X(9513)
X(40077) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 38947}, {1691, 1316}, {9513, 1916}
X(40078) lies on the cubic K039 and these lines: {3, 351}, {126, 4235}, {186, 1296}, {187, 4558}, {3455, 6091}, {7472, 34171}, {10717, 13586}, {14417, 34161}
X(40078) = isogonal conjugate of X(34169)
X(40078) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34169}, {897, 10418}, {7472, 23894}
X(40078) = cevapoint of X(187) and X(9177)
X(40078) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34169}, {187, 10418}, {5467, 7472}, {9177, 31655}
X(40079) lies on the cubic K039 and these lines: {3, 525}, {74, 187}, {98, 186}, {237, 1503}, {378, 35906}, {2071, 2966}, {3520, 32545}, {5621, 34369}, {5866, 6394}, {6091, 11589}, {7418, 34366}, {13754, 17974}, {14355, 15032}, {15407, 36212}
p> X(40079) = circumcircle-inverse of X(879)X(40080) lies on the cubic K039 and these lines: {3, 684}, {74, 3455}, {112, 186}, {132, 2409}, {248, 10766}, {2781, 5191}, {2794, 7422}, {2881, 23350}, {5649, 38699}, {5866, 11589}, {5961, 18876}, {8429, 14998}, {9475, 28343}, {19165, 21525}
X(40080) = circumcircle-inverse of X(35909)
X(40080) = X(i)-isoconjugate of X(j) for these (i,j): {542, 8767}, {2247, 6330}, {18312, 36046}
X(40080) = barycentric product X(i)*X(j) for these {i,j}: {441, 842}, {2409, 35911}, {5641, 8779}, {34211, 35909}
X(40080) = barycentric quotient X(i)/X(j) for these {i,j}: {842, 6330}, {2445, 35907}, {8779, 542}, {35911, 2419}
X(40081) lies on the conic {{A,B,C,X(1), X(3)}}, the cubic K039, and these lines: {3, 2779}, {29, 124}, {102, 186}, {283, 4996}, {758, 1807}, {7100, 11700}, {7424, 39992}
X(40081) =isogonal conjugate of X(38945)
X(40081) =X(i)-isoconjugate of X(j) for these (i,j): {1, 38945}, {65, 7424}
X(40081) =trilinear pole of line {652, 21748}
X(40081) =barycentric quotient X(i)/X(j) for these {i,j}: {6, 38945}, {284, 7424}
X(40082) lies on the cubic K039 and these lines: {3, 113}, {24, 5879}, {25, 38956}, {107, 1105}, {133, 6644}, {186, 1294}, {1204, 2972}, {1609, 28783}, {1658, 38621}, {2071, 10152}, {3515, 34426}, {5866, 6394}, {6716, 17928}, {6760, 13997}, {7488, 38714}, {7526, 36520}, {9530, 15078}, {10714, 37941}, {12096, 13754}, {15469, 15478}
X(40082) = isogonal conjugate of X(34170)
X(40082) = isogonal conjugate of the anticomplement of X(12096)
X(40082) = circumcircle-inverse of X(11744)
X(40082) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34170}, {92, 15262}, {158, 2071}, {1784, 38937}
X(40082) = crosspoint of X(5504) and X(5897)
X(40082) = crosssum of X(403) and X(15311)
X(40082) = barycentric product X(394)*X(11744)
X(40082) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34170}, {184, 15262}, {577, 2071}, {11744, 2052}, {18877, 38937}, {22239, 15352}
X(40082) = {X(3),X(14703)}-harmonic conjugate of X(3184)
X(40083) lies on the cubic K039 and these lines: {3, 690}, {74, 6091}, {99, 186}, {114, 4230}, {187, 13754}, {684, 34157}, {2931, 2936}, {3455, 5961}, {7468, 34174}, {12177, 32599}, {15478, 18876}
X(40083) = isogonal conjugate of X(34175)
X(40083) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34175}, {1821, 2493}, {14984, 36120}
X(40083) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34175}, {237, 2493}, {2421, 14221}, {3289, 14984}, {14966, 7468}
X(40084) lies on the cubic K039 and these lines: {3, 2775}, {120, 4238}, {186, 1292}, {187, 906}, {5172, 5866}, {6091, 34442}
X(40084) = isogonal conjugate of X(34173)
The cubic pK(X(594), X(3995)) is given by
(b+c) (b+c) (y/(c+a)-z/(a+b)) (x/(b+c)+y/(c+a)) (x/(b+c)+z/(a+b))+(c+a) (c+a) (z/(a+b)-x/(b+c)) (y/(c+a)+z/(a+b)) (y/(c+a)+x/(b+c))+(a+b) (a+b) (x/(b+c)-y/(c+a)) (z/(a+b)+x/(b+c)) (z/(a+b)+y/(c+a)) = 0.
Let La be the line tangent to this cubic at A, and define Lb and Lc cyclically. The lines La, Lb, Lc concur in X(40085). (Peter Moses, October 16, 2020)
The cubic passes through the following 14 points: A, B, C, the vertices of the cevian tiangle of X(3995), the vertices of the anticevian triangle of X(10), and X(i) for i = 10, 37 ,321 ,3159, 3995}. (Peter Moses, October 16, 2020)
X(40085) lies on these lines: {6, 3891}, {37, 39}, {79, 32846}, {86, 1255}, {141, 321}, {335, 4043}, {536, 22012}, {594, 3954}, {674, 1824}, {756, 1213}, {1575, 22013}, {2161, 21061}, {2171, 3649}, {2321, 22035}, {3175, 17392}, {3982, 22034}, {4024, 21143}, {4365, 15320}, {17307, 31025}, {21067, 21858}, {21257, 34475}
X(40085) = X(39747)-Ceva conjugate of X(10)
X(40085) = X(i)-cross conjugate of X(j) for these (i,j): {3122, 523}, {6535, 10}
X(40085) = X(i)-isoconjugate of X(j) for these (i,j): {58, 32911}, {81, 595}, {86, 2220}, {110, 4063}, {162, 22154}, {163, 20295}, {593, 3293}, {662, 4057}, {849, 3995}, {1333, 4360}, {1412, 3871}, {1576, 20949}, {1790, 4222}, {2206, 18140}, {4132, 4556}, {4567, 8054}, {4575, 17922}
X(40085) = cevapoint of X(i) and X(j) for these (i,j): {826, 3120}, {3124, 6367}, {3125, 4024}
X(40085) = crosspoint of X(596) and X(40013)
X(40085) = crosssum of X(595) and X(2220)
X(40085) = trilinear pole of line {3005, 4705}
X(40085) = crossdifference of every pair of points on line {4057, 22154}
X(40085) = barycentric product X(i)*X(j) for these {i,j}: {10, 596}, {37, 40013}, {321, 39798}, {523, 8050}, {594, 39747}, {1089, 39949}, {3701, 20615}, {4024, 37205}, {4036, 34594}
X(40085) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 4360}, {37, 32911}, {42, 595}, {210, 3871}, {213, 2220}, {321, 18140}, {512, 4057}, {523, 20295}, {594, 3995}, {596, 86}, {647, 22154}, {661, 4063}, {756, 3293}, {1577, 20949}, {1824, 4222}, {2501, 17922}, {3120, 21208}, {3122, 8054}, {4024, 4129}, {4705, 4132}, {6535, 4075}, {8013, 4065}, {8050, 99}, {20615, 1014}, {37205, 4610}, {39747, 1509}, {39798, 81}, {39949, 757}, {40013, 274}
The cubic pK(X(1086), X(20295)) is given by
(b+c) (b+c) (y/(c-a)-z/(a-b)) (x/(b-c)+y/(c-a)) (x/(b-c)+z/(a-b))+(c+a) (c+a) (z/(a-b)-x/(b-c)) (y/(c-a)+z/(a-b)) (y/(c-a)+x/(b-c))+(a+b) (a+b) (x/(b-c)-y/(c-a)) (z/(a-b)+x/(b-c)) (z/(a-b)+y/(c-a)) = 0.
Let La be the line tangent to this cubic at A, and define Lb and Lc cyclically. The lines La, Lb, Lc concur in X(40086). (Peter Moses, October 16, 2020)
The cubic passes through the following 14 points: A, B, C, the vertices of the cevian tiangle of X(20295), the vertices of the anticevian triangle of X(514), and X(i) for i = 513, 514, 693, 14078, 20295. (Peter Moses, October 16, 2020)
X(40086) lies on these lines: {513, 11813}, {522, 596}, {523, 2530}, {659, 27167}, {661, 1639}, {764, 4036}, {834, 24720}, {900, 4017}, {1290, 34594}, {3261, 35367}, {3699, 8050}, {3733, 18108}, {19947, 31947}, {21051, 28213}, {21173, 24161}, {21260, 28195}, {29362, 39798}, {35353, 40013}, {37135, 37205}
X(40086) = midpoint of X(764) and X(4036)
X(40086) = reflection of X(i) in X(j) for these {i,j}: {31946, 3837}, {31947, 19947}
X(40086) = X(8050)-Ceva conjugate of X(596)
X(40086) = X(i)-cross conjugate of X(j) for these (i,j): {4024, 514}, {21143, 1086}, {30591, 523}
X(40086) = X(i)-isoconjugate of X(j) for these (i,j): {100, 595}, {101, 32911}, {109, 3871}, {110, 3293}, {163, 3995}, {190, 2220}, {692, 4360}, {765, 4057}, {1110, 20295}, {1252, 4063}, {1331, 4222}, {4132, 4570}, {18140, 32739}, {20949, 23990}
X(40086) = cevapoint of X(764) and X(3120)
X(40086) = crosspoint of X(596) and X(8050)
X(40086) = crosssum of X(595) and X(4057)
X(40086) = trilinear pole of line {3125, 4530}
X(40086) = crossdifference of every pair of points on line {595, 2220}
X(40086) = barycentric product X(i)*X(j) for these {i,j}: {513, 40013}, {514, 596}, {523, 39747}, {693, 39798}, {1086, 8050}, {1577, 39949}, {3120, 37205}, {4391, 20615}, {16732, 34594}
X(40086) = barycentric quotient X(i)/X(j) for these {i,j}: {244, 4063}, {513, 32911}, {514, 4360}, {523, 3995}, {596, 190}, {649, 595}, {650, 3871}, {661, 3293}, {667, 2220}, {693, 18140}, {1015, 4057}, {1086, 20295}, {1111, 20949}, {2969, 17922}, {3120, 4129}, {3125, 4132}, {3837, 27044}, {3937, 22154}, {4024, 4075}, {4988, 4065}, {6545, 21208}, {6591, 4222}, {8050, 1016}, {20615, 651}, {21143, 8054}, {34594, 4567}, {37205, 4600}, {39747, 99}, {39798, 100}, {39949, 662}, {40013, 668}
X(40087) lies on these lines: {2, 1978}, {10, 18833}, {37, 27035}, {38, 75}, {76, 6539}, {274, 27163}, {305, 31130}, {321, 1921}, {333, 33764}, {350, 4365}, {668, 17165}, {670, 873}, {799, 32939}, {874, 1621}, {1920, 4359}, {1965, 4418}, {1966, 32914}, {2170, 30074}, {3112, 5263}, {3210, 30964}, {3403, 5271}, {3617, 20023}, {3995, 18140}, {4033, 18052}, {4087, 26234}, {4110, 18054}, {4572, 6063}, {4699, 6374}, {4772, 6383}, {6376, 32925}, {9230, 28604}, {15523, 30631}, {17063, 31002}, {17141, 25294}, {17143, 17163}, {17147, 31008}, {17151, 18078}, {17495, 34020}, {18059, 24325}, {18064, 32922}, {20440, 31004}, {23538, 24343}, {27798, 35532}, {28660, 33935}, {30632, 32778}, {32025, 33769}, {32930, 39044}
X(40087) = anticomplement of X(21827)
X(40087) = isotomic conjugate of X(40148)
X(40087) = isotomic conjugate of the isogonal conjugate of X(4360)
X(40087) = X(i)-cross conjugate of X(j) for these (i,j): {20295, 1978}, {21208, 20949}
X(40087) = X(i)-isoconjugate of X(j) for these (i,j): {32, 39798}, {560, 596}, {669, 34594}, {1501, 40013}, {1918, 39949}, {1924, 37205}, {1980, 8050}, {2175, 20615}, {2205, 39747}
X(40087) = cevapoint of X(i) and X(j) for these (i,j): {75, 40034}, {20949, 21208}
X(40087) = trilinear pole of line {4129, 20949}
X(40087) = barycentric product X(i)*X(j) for these {i,j}: {75, 18140}, {76, 4360}, {310, 3995}, {561, 32911}, {595, 1502}, {668, 20949}, {670, 4129}, {1928, 2220}, {1978, 20295}, {3293, 6385}, {3871, 20567}, {4063, 6386}, {4132, 4602}, {21208, 31625}
X(40087) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 39798}, {76, 596}, {85, 20615}, {274, 39949}, {310, 39747}, {561, 40013}, {595, 32}, {670, 37205}, {799, 34594}, {1978, 8050}, {2220, 560}, {3293, 213}, {3871, 41}, {3995, 42}, {4057, 1919}, {4063, 667}, {4065, 20970}, {4075, 1500}, {4129, 512}, {4132, 798}, {4222, 1973}, {4360, 6}, {8054, 1977}, {18140, 1}, {20295, 649}, {20949, 513}, {21208, 1015}, {27044, 3009}, {32911, 31}
X(40087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6382, 1978}, {75, 561, 310}, {75, 17149, 17155}, {321, 1921, 18152}, {4359, 35543, 1920}, {6382, 10009, 2}, {20889, 21020, 75}
X(40088) lies on these lines: {37, 308}, {38, 75}, {76, 594}, {313, 18891}, {668, 33769}, {871, 1268}, {1218, 14624}, {1278, 30638}, {1502, 3596}, {1920, 3739}, {1978, 18137}, {4043, 18152}, {4772, 30637}, {6376, 28593}, {9230, 17790}, {20891, 35543}, {21238, 24732}, {21615, 28659}
X(40088) = isotomic conjugate of the isogonal conjugate of X(17143)
X(40088) = X(31625)-Ceva conjugate of X(6386)
X(40088) = X(i)-isoconjugate of X(j) for these (i,j): {32, 2350}, {560, 13476}, {1501, 17758}, {2205, 39950}
X(40088) = barycentric product X(i)*X(j) for these {i,j}: {75, 18152}, {76, 17143}, {310, 4043}, {561, 17277}, {1502, 1621}, {1928, 4251}, {1978, 20954}, {3996, 20567}, {4151, 4602}, {4651, 6385}, {6386, 17494}
X(40088) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 2350}, {76, 13476}, {310, 39950}, {561, 17758}, {1621, 32}, {2486, 3121}, {3294, 1918}, {3996, 41}, {4040, 1919}, {4043, 42}, {4151, 798}, {4251, 560}, {4651, 213}, {6385, 39734}, {14004, 1973}, {17143, 6}, {17277, 31}, {17494, 667}, {17761, 3248}, {18152, 1}, {20954, 649}, {21007, 1980}, {29447, 16679}, {33765, 1106}
X(40088) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 561, 6385}, {1502, 3596, 6386}, {3728, 20889, 75}
X(40088) lies on these lines: {2, 36645}, {38, 75}, {76, 27797}, {850, 4608}, {1920, 24589}, {1921, 1978}, {3264, 40075}, {4671, 6382}, {6381, 18891}, {17786, 18054}, {18075, 32922}, {28660, 40034}
X(40089) = isotomic conjugate of the isogonal conjugate of X(17160)
X(40089) = X(i)-isoconjugate of X(j) for these (i,j): {32, 39981}, {560, 39697}, {1501, 39994}
X(40089) = barycentric product X(i)*X(j) for these {i,j}: {75, 18145}, {76, 17160}, {561, 37680}, {668, 21606}, {1928, 33882}, {1978, 21297}, {4145, 4602}, {6385, 31855}, {6386, 21385}
X(40089) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 39981}, {76, 39697}, {561, 39994}, {4145, 798}, {4491, 1919}, {17160, 6}, {18145, 1}, {21297, 649}, {21385, 667}, {21606, 513}, {21714, 4079}, {31855, 213}, {33882, 560}, {37680, 31}
X(40089) = {X(1921),X(35543)}-harmonic conjugate of X(1978)
X(40090) lies on these lines: {10,75}, {850,4608}, {14210,35544}
X(40091) lies on these lines: {1, 21}, {2, 37610}, {3, 1616}, {6, 6767}, {10, 4514}, {11, 17734}, {32, 16969}, {35, 1201}, {36, 106}, {40, 5573}, {42, 5315}, {43, 25439}, {46, 28011}, {55, 995}, {71, 16488}, {101, 1914}, {109, 1319}, {145, 1724}, {171, 551}, {172, 9327}, {187, 9259}, {212, 7962}, {238, 519}, {244, 484}, {284, 16685}, {386, 1191}, {392, 3744}, {405, 37542}, {512, 1326}, {517, 1279}, {572, 21769}, {580, 1482}, {581, 16202}, {582, 8148}, {602, 7982}, {614, 5119}, {672, 16784}, {674, 16796}, {727, 898}, {748, 3679}, {750, 25055}, {859, 23404}, {946, 24160}, {962, 24159}, {978, 8715}, {986, 30148}, {997, 3749}, {999, 3052}, {1001, 4279}, {1015, 5030}, {1018, 33854}, {1058, 5292}, {1064, 34486}, {1086, 28174}, {1104, 9957}, {1125, 5255}, {1126, 1203}, {1193, 3746}, {1253, 9819}, {1293, 12029}, {1331, 10700}, {1334, 5299}, {1450, 3256}, {1453, 37556}, {1457, 2078}, {1471, 18421}, {1739, 7292}, {1770, 23675}, {1834, 15172}, {1870, 8750}, {1918, 16484}, {2176, 2241}, {2177, 5313}, {2209, 15485}, {2242, 21793}, {2275, 24047}, {2308, 16474}, {2361, 5048}, {3011, 30384}, {3017, 15170}, {3072, 13464}, {3073, 5882}, {3216, 3871}, {3218, 4694}, {3241, 17127}, {3244, 5247}, {3246, 3880}, {3290, 5011}, {3303, 16466}, {3616, 5264}, {3622, 37522}, {3636, 37607}, {3730, 16502}, {3822, 33106}, {3924, 5697}, {3938, 5692}, {3961, 10176}, {3997, 16503}, {4252, 7373}, {4253, 14974}, {4259, 16794}, {4264, 16777}, {4290, 16672}, {4301, 37570}, {4306, 34040}, {4322, 34043}, {4364, 25432}, {4424, 7191}, {4482, 10027}, {4642, 37563}, {4692, 32930}, {4695, 5541}, {4803, 16690}, {4857, 21935}, {4868, 29821}, {4880, 17449}, {4881, 35281}, {4975, 17763}, {5053, 9456}, {5080, 24222}, {5180, 33148}, {5259, 10459}, {5301, 33628}, {5398, 10247}, {5445, 28096}, {5493, 24171}, {5687, 17749}, {5710, 16302}, {5883, 29820}, {5903, 28082}, {6051, 20715}, {6905, 32486}, {7031, 9310}, {7280, 32577}, {7290, 31393}, {7299, 37738}, {7322, 31435}, {7798, 17262}, {8624, 38865}, {9316, 13462}, {9441, 28228}, {10197, 17717}, {10246, 37469}, {10571, 11510}, {10595, 37530}, {10624, 23537}, {11010, 24443}, {11529, 21059}, {11813, 17719}, {12000, 36754}, {12047, 28027}, {12702, 17054}, {16490, 21747}, {16497, 18900}, {16501, 23344}, {16785, 21764}, {17053, 37508}, {17125, 19875}, {17126, 38314}, {17152, 33953}, {17541, 29381}, {17686, 29383}, {18393, 33127}, {20040, 27660}, {20703, 27785}, {21214, 25440}, {24231, 28026}, {24390, 24880}, {24864, 38455}, {26687, 29697}, {26725, 29689}, {30108, 35274}, {31855, 37680}
X(40091) = reflection of X(30117) in X(1279)
X(40091) = isogonal conjugate of X(39697)
X(40091) = isogonal conjugate of the isotomic conjugate of X(17160)
X(40091) = X(i)-Ceva conjugate of X(j) for these (i,j): {5376, 101}, {30576, 5053}
X(40091) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39697}, {2, 39981}, {6, 39994}
X(40091) = crosspoint of X(i) and X(j) for these (i,j): {106, 1126}, {110, 9268}, {765, 901}
X(40091) = crosssum of X(i) and X(j) for these (i,j): {244, 900}, {519, 1125}, {523, 1647}, {1086, 21115}
X(40091) = crossdifference of every pair of points on line {661, 1213}
X(40091) = barycentric product X(i)*X(j) for these {i,j}: {1, 37680}, {6, 17160}, {31, 18145}, {75, 33882}, {81, 31855}, {100, 21385}, {101, 21297}, {190, 4491}, {662, 4145}, {692, 21606}, {1897, 23141}, {4556, 21714}, {5376, 38979}
X(40091) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 39994}, {6, 39697}, {31, 39981}, {4145, 1577}, {4491, 514}, {17160, 76}, {18145, 561}, {21297, 3261}, {21385, 693}, {23141, 4025}, {31855, 321}, {33882, 1}, {37680, 75}
X(40091) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 595, 58}, {1, 1046, 3881}, {1, 1621, 4653}, {1, 3915, 595}, {1, 8616, 993}, {1, 32913, 3892}, {36, 1149, 106}, {36, 16489, 1149}, {55, 995, 4256}, {55, 16483, 995}, {392, 3744, 30115}, {902, 1149, 36}, {902, 16489, 106}, {999, 3052, 4257}, {1015, 17735, 5030}, {1104, 9957, 15955}, {1191, 3295, 386}, {1193, 3746, 33771}, {1914, 3230, 101}, {2176, 2241, 4251}, {3052, 16486, 999}, {4653, 4658, 10458}, {4653, 38832, 58}, {14974, 16781, 4253}
X(40092) lies on this line: {2,38}, {1268,35352}
X(40093) lies on these lines: {2,39717}, {10,274}, {75,308}, {83,16549}, {86,4553}, {239,292}, {335,1268}, {3864,29633}, {4075,18140}, {4444,21385}, {4876,17023}, {19973,20345}, {29767,37128}, {32010,32780}
X(40093) = barycentric product X(i)*X(j) for these {i, j}: {291, 18140}, {292, 40087}, {334, 32911}, {335, 4360}, {595, 18895}, {660, 20949}
X(40093) = barycentric quotient X(i)/X(j) for these (i, j): (291, 39798), (334, 40013), (335, 596), (595, 1914), (2220, 2210)
X(40093) = trilinear product X(i)*X(j) for these {i, j}: {291, 4360}, {292, 18140}, {334, 595}, {335, 32911}, {337, 4222}, {660, 20295}
X(40093) = trilinear quotient X(i)/X(j) for these (i, j): (334, 596), (335, 39798), (595, 2210), (2220, 14599)
X(40093) = trilinear pole of the line {3995, 20295}
X(40093) = intersection, other than A,B,C, of conics {{A, B, C, X(10), X(3293)}} and {{A, B, C, X(75), X(16887)}}
X(40093) = cevapoint of X(1575) and X(22279)
X(40093) = X(i)-isoconjugate-of-X(j) for these {i,j}: {596, 2210}, {1914, 39798}
X(40093) = X(i)-reciprocal conjugate of-X(j) for these (i,j): (291, 39798), (334, 40013), (335, 596), (595, 1914)
X(40093) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (291, 334, 18827), (18827, 40095, 334)
X(40094) lies on these lines: {2,3112}, {10,274}, {75,40024}, {292,16819}, {335,4359}, {350,6541}, {874,13576}, {1921,3263}, {3783,32922}, {3978,20486}, {4562,30109}, {4876,29960}, {17143,17761}, {26752,26978}, {30997,32035}
X(40094) = barycentric product X(i)*X(j) for these {i, j}: {291, 18152}, {292, 40088}, {334, 17277}, {335, 17143}, {1621, 18895}
X(40094) = barycentric quotient X(i)/X(j) for these (i, j): (291, 2350), (334, 17758), (335, 13476), (1621, 1914), (2486, 39786)
X(40094) = trilinear product X(i)*X(j) for these {i, j}: {291, 17143}, {292, 18152}, {334, 1621}, {335, 17277}, {337, 14004}, {660, 20954}
X(40094) = trilinear quotient X(i)/X(j) for these (i, j): (334, 13476), (335, 2350), (1621, 2210)
X(40094) = trilinear pole of the line {4043, 20954}
X(40094) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(16887)}} and {{A, B, C, X(10), X(4651)}}
X(40094) = X(1914)-isoconjugate-of-X(2350)
X(40094) = X(i)-reciprocal conjugate of-X(j) for these (i,j): (291, 2350), (334, 17758), (335, 13476), (1621, 1914)
X(40094) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (291, 334, 40017), (4518, 18895, 4583)
X(40095) lies on these lines: {2,4562}, {10,274}, {75,31625}, {292,16815}, {335,4688}, {1268,35352}, {3252,4751}, {3263,19955}, {4389,36801}, {4876,29596}, {9780,22116}, {17292,21264}, {19950,33931}, {19951,30758}
X(40095) = barycentric product X(i)*X(j) for these {i, j}: {291, 18145}, {292, 40089}, {334, 37680}, {335, 17160}, {660, 21606}
X(40095) = barycentric quotient X(i)/X(j) for these (i, j): (291, 39982), (334, 39994), (335, 39697)
X(40095) = trilinear product X(i)*X(j) for these {i, j}: {291, 17160}, {292, 18145}, {334, 40091}, {335, 37680}, {660, 21297}, {813, 21606}
X(40095) = trilinear quotient X(i)/X(j) for these (i, j): (334, 39697), (335, 39982)
X(40095) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(21297)}} and {{A, B, C, X(10), X(31855)}}
X(40095) = X(1914)-isoconjugate-of-X(39982)
X(40095) = X(i)-reciprocal conjugate of-X(j) for these (i,j): (291, 39982), (334, 39994), (335, 39697)
X(40095) = {X(334), X(40093)}-harmonic conjugate of X(18827)
X(40096) lies on these lines: {1,16702}, {3,34814}, {6,31}, {187,21009}, {512,1326}, {922,3285}, {1333,4068}, {16777,21829}, {20675,33704}, {20999,23366}
X(40097) lies on the circumcircle and these lines: {4, 123}, {24, 104}, {25, 2968}, {28, 39435}, {74, 31384}, {99, 4244}, {105, 6353}, {110, 7435}, {186, 2694}, {242, 2723}, {403, 2687}, {650, 32688}, {691, 37965}, {759, 30733}, {915, 3542}, {925, 4246}, {1294, 7414}, {1297, 4231}, {1300, 31385}, {1305, 4250}, {1783, 8687}, {1897, 9058}, {2370, 4222}, {2373, 7438}, {2693, 37979}, {2720, 15385}, {2752, 37777}, {3565, 4238}, {3651, 5897}, {3658, 13398}, {4220, 34168}, {4242, 13397}, {10420, 37966}, {26253, 39436}, {30267, 39434}
X(40097) = Stevanovic-circle-inverse of X(32688)
X(40097) = polar-circle-inverse of X(123)
X(40097) = Collings transform of X(i) for these i: {431, 39167}
X(40097) = X(i)-cross conjugate of X(j) for these (i,j): {521, 4}, {650, 34277}, {3435, 15385}, {14312, 104}
X(40097) = cevapoint of X(i) and X(j) for these (i,j): {25, 650}, {431, 523}, {521, 39167}
X(40097) = trilinear pole of line {6, 1854}
X(40097) = Ψ(X(6), X(1854))
X(40097) = X(i)-isoconjugate of X(j) for these (i,j): {3, 21186}, {63, 6588}, {109, 123}, {197, 4025}, {205, 15413}, {478, 6332}, {514, 22132}, {521, 21147}, {656, 16049}, {905, 1766}, {1459, 3436}, {7254, 21074}, {20928, 22383}
X(40097) = barycentric product X(i)*X(j) for these {i,j}: {108, 34277}, {1783, 8048}, {3435, 6335}, {4391, 15385}
X(40097) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 21186}, {25, 6588}, {112, 16049}, {650, 123}, {692, 22132}, {1783, 3436}, {1897, 20928}, {3435, 905}, {8048, 15413}, {8750, 1766}, {15385, 651}, {32674, 21147}, {34277, 35518}
X(40098) lies on the cubic K768 and these lines: {2, 19897}, {239, 291}, {334, 3263}, {335, 726}, {660, 20683}, {894, 24479}, {1015, 35172}, {1916, 17789}, {3507, 18787}, {3948, 4583}, {4562, 6542}, {7233, 9436}, {15149, 17927}, {17798, 30664}, {18891, 18895}, {19308, 34067}
X(40098) = isotomic conjugate of X(4366)
X(40098) = isotomic conjugate of the anticomplement of X(26582)
X(40098) = isotomic conjugate of the complement of X(6653)
X(40098) = X(i)-cross conjugate of X(j) for these (i,j): {75, 1916}, {141, 40017}, {523, 4583}, {1086, 4444}, {26582, 2}
X(40098) = X(i)-isoconjugate of X(j) for these (i,j): {6, 8300}, {9, 12835}, {31, 4366}, {32, 39044}, {238, 1914}, {239, 2210}, {350, 14599}, {593, 4094}, {692, 4375}, {849, 35068}, {1110, 35119}, {1333, 4368}, {1428, 3684}, {1691, 18786}, {1911, 6652}, {1921, 18892}, {1933, 17493}, {2150, 3027}, {2201, 7193}, {2238, 5009}, {3573, 8632}, {18264, 27916}, {18891, 18894}, {27855, 32739}
X(40098) = cevapoint of X(i) and X(j) for these (i,j): {2, 6653}, {1086, 4444}
X(40098) = trilinear pole of line {918, 3837}
X(40098) = barycentric product X(i)*X(j) for these {i,j}: {75, 30663}, {256, 30642}, {291, 334}, {292, 18895}, {335, 335}, {876, 4583}, {1916, 30669}, {1928, 18267}, {1934, 18787}, {4444, 4562}, {4518, 7233}, {4589, 35352}, {23596, 37207}
X(40098) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8300}, {2, 4366}, {10, 4368}, {12, 3027}, {56, 12835}, {75, 39044}, {239, 6652}, {291, 238}, {292, 1914}, {295, 7193}, {334, 350}, {335, 239}, {514, 4375}, {594, 35068}, {660, 3573}, {693, 27855}, {741, 5009}, {756, 4094}, {876, 659}, {984, 3802}, {1086, 35119}, {1215, 4154}, {1581, 18786}, {1911, 2210}, {1916, 17493}, {1922, 14599}, {3572, 8632}, {3862, 16514}, {3864, 3783}, {3912, 27919}, {4444, 812}, {4518, 3685}, {4562, 3570}, {4583, 874}, {4876, 3684}, {6542, 27926}, {6645, 4027}, {7233, 1447}, {7245, 4396}, {14598, 18892}, {18267, 560}, {18787, 1580}, {18827, 33295}, {18895, 1921}, {18897, 18894}, {22116, 8299}, {23596, 4486}, {30642, 1909}, {30657, 172}, {30663, 1}, {30669, 385}, {35352, 4010}, {40017, 30940}
X(40099) lies on these lines: {75, 1916}, {239, 256}, {257, 4357}, {1967, 24575}, {3687, 3797}, {3688, 3903}, {3865, 27447}, {4027, 8424}, {7018, 20891}, {17280, 27805}, {17302, 32010}, {18891, 21442}, {23868, 30670}
X(40099) = isotomic conjugate of X(6645)
X(40099) = isotomic conjugate of the anticomplement of X(26558)
X(40099) = X(26558)-cross conjugate of X(2)
X(40099) = X(i)-isoconjugate of X(j) for these (i,j): {31, 6645}, {57, 10799}, {171, 172}, {894, 7122}, {904, 7369}, {1252, 7207}, {1691, 18787}, {1911, 27982}, {1933, 30669}, {2149, 3023}, {2330, 7175}, {3955, 7119}, {4579, 20981}
X(40099) = trilinear pole of line {3910, 4486}
X(40099) = barycentric product X(i)*X(j) for these {i,j}: {256, 7018}, {257, 257}, {291, 30643}, {1916, 17493}, {1934, 18786}, {4451, 7249}, {18895, 30658}
X(40099) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6645}, {11, 3023}, {55, 10799}, {239, 27982}, {244, 7207}, {256, 171}, {257, 894}, {893, 172}, {894, 7369}, {904, 7122}, {982, 7188}, {1432, 7175}, {1581, 18787}, {1916, 30669}, {3865, 7184}, {3903, 4579}, {4366, 4027}, {4451, 7081}, {4496, 4400}, {7015, 3955}, {7018, 1909}, {7249, 7176}, {17493, 385}, {18786, 1580}, {27805, 18047}, {30643, 350}, {30658, 1914}, {32010, 17103}
X(40100) lies on the Johnson circle and these lines: {2, 38614}, {3, 3259}, {4, 38954}, {5, 901}, {20, 38617}, {30, 953}, {140, 38705}, {381, 31841}, {382, 38586}, {513, 10738}, {517, 10742}, {550, 38707}, {952, 31512}, {1478, 13756}, {1479, 3025}, {1656, 22102}, {2070, 39479}, {3585, 23153}, {3627, 38682}, {5722, 33645}, {6073, 38755}, {7517, 10016}, {12645, 18326}, {18342, 38385}
X(40100) = midpoint of X(382) and X(38586)
X(40100) = reflection of X(i) in X(j) for these {i,j}: {3, 3259}, {20, 38617}, {901, 5}, {18342, 38385}, {38584, 31841}, {38954, 4}
X(40100) = anticomplement of X(38614)
X(40100) = X(901)-of-Johnson-triangle
X(40100) = {X(381),X(38584)}-harmonic conjugate of X(31841)
X(40100) lies on the circumcircle and these lines: {4, 121}, {9, 29014}, {19, 29149}, {24, 32704}, {25, 9059}, {28, 34594}, {99, 4247}, {100, 4222}, {101, 17314}, {109, 1724}, {110, 4248}, {186, 2692}, {242, 1308}, {404, 13397}, {925, 7419}, {1294, 7444}, {1295, 7447}, {1297, 7434}, {1305, 4245}, {2373, 7448}, {3518, 26713}, {3565, 4234}, {6353, 9088}, {7459, 26703}, {7478, 10420}, {8074, 35182}, {8756, 32686}, {15383, 35186}
X(40101) = polar-circle-inverse of X(121)
X(40101) = X(519)-cross conjugate of X(4)
X(40101) = X(i)-isoconjugate of X(j) for these (i,j): {3, 1739}, {63, 8610}, {71, 16753}, {88, 22428}, {121, 36058}, {1797, 17465}, {5440, 39264}, {21427, 32659}
X(40101) = cevapoint of X(25) and X(8756)
X(40101) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 1739}, {25, 8610}, {28, 16753}, {902, 22428}, {8752, 39264}, {8756, 121}, {15383, 1797}, {38462, 21427}
Let ABC be a triangle, P a point and A'B'C' the circumcevian triangle of P. Let Ab, Ac be the orthogonal projections of P in A'C and A'B, respectively, and build Bc, Ba and Ca, Cb cyclically. Let A"B"C" be the triangle bounded by the lines AbAc, BcBa and CaCb. Then A"B"C" and ABC are perspective. (Abdilkadir Altintas, problem 1540).
If P=x:y:z (barycentrics) then the given perspector Q(P) is the isogonal conjugate of (2*(b^2*z+c^2*y)*a^2*y*z*cos(A)-(a^2*y*z+b^2*x*z+c^2*x*y)*b*c*x-2*(b^3*z^2*cos(B)+c^3*y^2*cos(C))*a*x)*a : :.
The appearance of (i, j) in the following partial list means that Q(X(i))=X(j): (1, 15446), (2, 40102), (3, 4), (4, 22261), (6, 40103), (13, 40104), (14, 40105), (15, 15), (16, 16), (23, 468), (36, 1), (54, 3459), (59, 650), (186, 523), (187, 10630), (249, 523), (250, 647), (501, 1), (1157, 4), (2065, 230), (2070, 3459) (César Lozada, October 20, 2020).
X(40102) lies on these lines: {2,14908}, {3,3266}, {25,37778}, {32,468}, {184,524}, {2200,4062}, {5181,9516}, {5967,14600}, {7493,10547}\
X(40102) = isogonal conjugate of X(11188)
X(40102) = trilinear pole of the line {690, 3049}
X(40102) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(468)}} and {{A, B, C, X(3), X(25)}}
See X(40102).
X(40103) lies on these lines: {2,32457}, {6,9716}, {25,11580}, {69,34898}, {111,7492}, {694,8617}, {1383,3291}, {6094,17008}, {8585,39389}, {8589,39576}, {8770,15246}, {34288,37689}
X(40103) = isogonal conjugate of X(15534)
X(40103) = isotomic conjugate of the anticomplement of X(39576)
X(40103) = anticomplement of the complementary conjugate of X(22165)
X(40103) = barycentric product X(523)*X(33638)
X(40103) = trilinear product X(661)*X(33638)
X(40103) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(16042)}}
X(40103) = cevapoint of X(6) and X(15655)
X(40103) = X(25)-vertex conjugate of-X(1383)
See X(40102).
X(40104) lies on the Kiepert hyperbola and these lines: {2,3200}, {13,11136}, {94,6105}, {11140,37848}
X(40104) = isogonal conjugate of X(36979)
X(40104) = intersection, other than A,B,C, of Kiepert hyperbola and conic {{A, B, C, X(15), X(1141)}}
See X(40102).
X(40105) lies on the Kiepert hyperbola and these lines: {2,3201}, {14,11135}, {94,6104}, {11140,37850}
X(40105) = isogonal conjugate of X(36981)
X(40105) = intersection, other than A,B,C, of Kiepert hyperbola and conic {{A, B, C, X(16), X(1141)}}
X(40106) lies on this line:: {8,192}
X(40107) is the radical trace of the Ehrmann cirles of the 1st and 2nd Ehrmann inscribed triangles. (Randy Hutson, December 18, 2020)
X(40107) lies on these lines: {2, 576}, {3, 67}, {4, 7883}, {5, 141}, {6, 3411}, {20, 1352}, {30, 18553}, {39, 15993}, {54, 69}, {76, 22677}, {114, 3314}, {125, 7998}, {126, 16938}, {140, 524}, {183, 6036}, {193, 39561}, {262, 16986}, {298, 6774}, {299, 6771}, {325, 15819}, {340, 37124}, {343, 3819}, {382, 1350}, {394, 15135}, {487, 12974}, {488, 12975}, {518, 5885}, {546, 25561}, {548, 1503}, {549, 8550}, {550, 11645}, {597, 632}, {620, 32135}, {858, 3917}, {1176, 9705}, {1351, 3763}, {1353, 3630}, {1469, 37719}, {1506, 13330}, {1656, 5476}, {1843, 15559}, {1972, 15595}, {1992, 3525}, {2080, 7820}, {2393, 5447}, {2781, 11591}, {2854, 20379}, {2979, 5169}, {3056, 37720}, {3090, 20423}, {3094, 7765}, {3095, 6292}, {3096, 12251}, {3292, 7495}, {3398, 7826}, {3399, 10292}, {3416, 37727}, {3522, 11180}, {3523, 11179}, {3528, 33751}, {3530, 3564}, {3548, 11511}, {3580, 5650}, {3589, 5097}, {3618, 15520}, {3619, 5067}, {3628, 20582}, {3629, 15516}, {3642, 22737}, {3643, 22736}, {3832, 31670}, {3843, 10516}, {3853, 18358}, {3933, 13334}, {4045, 32515}, {4309, 12589}, {4317, 12588}, {4663, 11231}, {5012, 15108}, {5054, 15533}, {5079, 38072}, {5085, 11898}, {5104, 7747}, {5171, 7795}, {5182, 33259}, {5449, 6698}, {5477, 39560}, {5651, 32223}, {5891, 11799}, {5921, 21734}, {5972, 15066}, {5980, 25559}, {5981, 25560}, {6143, 8537}, {6228, 6229}, {6393, 14994}, {6515, 32068}, {6640, 8538}, {6697, 14076}, {6721, 7778}, {6723, 37638}, {6776, 15717}, {6791, 39576}, {6937, 10477}, {6998, 17297}, {7486, 14853}, {7493, 9306}, {7499, 34986}, {7505, 11470}, {7509, 10112}, {7525, 15582}, {7552, 9970}, {7752, 31958}, {7756, 11646}, {7758, 13086}, {7767, 13335}, {7769, 39099}, {7771, 38748}, {7782, 14928}, {7800, 9737}, {7811, 35925}, {7813, 11171}, {7818, 37348}, {7833, 10992}, {7836, 12177}, {7841, 19662}, {7865, 37242}, {7869, 37466}, {7870, 38751}, {7877, 10359}, {7880, 37459}, {7909, 10753}, {7915, 20576}, {7922, 37446}, {7931, 38227}, {7934, 23514}, {7999, 11704}, {8252, 9975}, {8253, 9974}, {8263, 13348}, {8541, 37119}, {8542, 18281}, {8548, 15115}, {8549, 23329}, {8584, 11539}, {8681, 12359}, {9003, 23108}, {9019, 10627}, {9466, 15980}, {9714, 37485}, {9967, 24572}, {9968, 14862}, {9971, 37484}, {9972, 11416}, {9976, 15061}, {9977, 15137}, {10303, 11160}, {10304, 13399}, {10350, 16898}, {10357, 12203}, {10541, 15720}, {10625, 29959}, {11303, 16001}, {11304, 16002}, {11411, 13347}, {11412, 14789}, {11444, 18504}, {11459, 15063}, {11579, 15057}, {13083, 33385}, {13084, 33384}, {13169, 15034}, {13564, 19596}, {13862, 33706}, {14485, 18840}, {14499, 25407}, {14500, 25408}, {15074, 15532}, {15080, 24981}, {15082, 37648}, {15178, 28538}, {15360, 16042}, {15462, 32244}, {15534, 15694}, {15605, 25738}, {15644, 16789}, {15696, 18440}, {16241, 16530}, {16242, 16529}, {16921, 22486}, {17004, 36859}, {17271, 21554}, {17529, 26543}, {17702, 33533}, {17800, 36990}, {18114, 23098}, {18381, 34787}, {18388, 23039}, {18400, 34118}, {18583, 34573}, {18800, 33274}, {19905, 23235}, {20191, 32283}, {20415, 34509}, {20416, 34508}, {21849, 37439}, {21969, 37990}, {22112, 37644}, {22493, 32909}, {22494, 32907}, {22866, 33418}, {22911, 33419}, {23327, 34788}, {24309, 29255}, {29323, 39884}, {31394, 33087}, {31848, 36165}, {31857, 33884}, {32317, 34114}, {32782, 37521}, {32863, 37527}, {33081, 37619}, {33217, 35431}, {33245, 35377}, {33362, 33363}, {34885, 35375}, {37450, 37671}
X(40107) = midpoint of X(i) and X(j) for these {i,j}: {3, 34507}, {67, 12584}, {69, 182}, {549, 22165}, {1350, 3818}, {1352, 3098}, {1353, 3630}, {18381, 34787}
X(40107) = reflection of X(i) in X(j) for these {i,j}: {575, 140}, {576, 25555}, {3629, 15516}, {5097, 3589}, {8550, 20190}, {9968, 14862}, {18583, 34573}, {19130, 24206}, {20301, 6698}, {20423, 25565}, {24206, 141}, {25556, 5972}, {32135, 620}
X(40107) = anticomplement of X(25555)
X(40107) = complement of X(576)
X(40107) = complement of the isogonal conjugate of X(7607)
X(40107) = medial-isogonal conjugate of X(15850)
X(40107) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 15850}, {661, 35132}, {7607, 10}, {35178, 4369}
X(40107) = crossdifference of every pair of points on line {2492, 3050}
X(40107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 576, 25555}, {3, 599, 34507}, {140, 575, 10168}, {549, 8550, 20190}, {627, 628, 1078}, {635, 636, 626}, {639, 640, 625}, {1351, 3763, 38317}, {1352, 10519, 3098}, {1656, 11477, 5476}, {3314, 22712, 114}, {3620, 10519, 1352}, {3629, 38110, 15516}, {3917, 37636, 21243}, {6228, 6229, 7761}, {11477, 21358, 1656}
Let BA, CA be the intersections of lines CA, AB, resp., and the antiparallel to BC through X(2). Define CB, AB, AC, BC cyclically. Triangles ABACA, ABBCB, ACBCC are similar to each other and inversely similar to ABC. Let SA be the similitude center of triangles ABBCB and ACBCC. Define SB and SC cyclically. X(40108) is the circumcenter of triangle SASBSC. (Randy Hutson, October 29, 2020)
X(40108) lies on these lines: {2, 2782}, {3, 83}, {5, 4045}, {6, 22677}, {24, 22480}, {30, 21163}, {35, 22711}, {36, 18971}, {39, 140}, {55, 22730}, {56, 22729}, {76, 3526}, {182, 10007}, {194, 3525}, {498, 22705}, {499, 22706}, {511, 549}, {517, 22475}, {538, 7619}, {574, 2023}, {620, 24256}, {631, 3095}, {632, 3934}, {730, 11231}, {1078, 39093}, {1656, 7919}, {1916, 38750}, {2021, 3815}, {2080, 3329}, {3090, 32522}, {3094, 31958}, {3102, 22727}, {3103, 22726}, {3104, 22686}, {3105, 22684}, {3106, 16241}, {3107, 16242}, {3311, 19063}, {3312, 19064}, {3398, 7824}, {3523, 9821}, {3530, 5188}, {3533, 31276}, {3576, 22650}, {3589, 37459}, {3628, 6248}, {5026, 39498}, {5038, 22525}, {5054, 22712}, {5969, 7606}, {6200, 35839}, {6396, 35838}, {6642, 22655}, {6655, 10242}, {6771, 33479}, {6774, 33478}, {7583, 22720}, {7584, 22721}, {7612, 32978}, {7694, 22505}, {7757, 8860}, {7771, 11842}, {7787, 22679}, {7792, 14693}, {7803, 9754}, {8359, 34510}, {8719, 35930}, {9466, 10124}, {9743, 37071}, {9744, 9996}, {9755, 10104}, {9756, 14880}, {10160, 11176}, {10246, 22713}, {10267, 22556}, {10269, 22680}, {10303, 12251}, {10359, 33004}, {12054, 37334}, {12143, 37119}, {13330, 21843}, {13357, 31406}, {14839, 38028}, {14869, 32521}, {15026, 27375}, {15122, 16324}, {15701, 33706}, {16202, 22732}, {16203, 22731}, {16239, 31239}, {22515, 37348}, {22678, 26316}, {22697, 26446}, {22698, 26451}, {22699, 26341}, {22700, 26348}, {22703, 26492}, {22704, 26487}, {22724, 32497}, {22725, 32494}, {32454, 38762}, {32465, 33416}, {32466, 33417}, {33273, 38225}, {35002, 37455}, {36177, 38613}, {37647, 39266}
X(40108) = midpoint of X(i) and X(j) for these {i,j}: {2, 11171}, {3, 262}, {6, 22677}, {39, 15819}, {76, 32519}, {182, 11261}, {2080, 22503}, {3094, 31958}, {3095, 6194}, {3102, 22727}, {3103, 22726}, {3104, 22686}, {3105, 22684}, {3106, 22715}, {3107, 22714}, {7697, 7709}, {22676, 22728}, {22712, 32447}
X(40108) = reflection of X(i) in X(j) for these {i,j}: {262, 11272}, {11261, 10007}, {14881, 262}, {15819, 140}, {22681, 5}, {24256, 32149}
X(40108) = complement of X(7697)
X(40108) = X(22681)-of-Johnson-triangle
X(40108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7709, 7697}, {3, 7786, 11272}, {3, 11174, 10796}, {3, 11272, 14881}, {3, 22728, 22676}, {262, 22676, 22728}, {632, 32448, 3934}, {3628, 32516, 6248}, {5054, 32447, 22712}, {6683, 13334, 5}, {7697, 11171, 7709}
X(40109) lies on the curve Q158 and these lines: {2, 36}, {42, 517}, {43, 484}, {44, 513}, {100, 752}, {730, 17763}, {750, 2267}, {908, 3724}, {1011, 5172}, {1319, 3720}, {1403, 33098}, {1468, 19543}, {2077, 37400}, {3035, 15447}, {3240, 3245}, {3783, 14513}, {4203, 29846}, {5057, 5143}, {5078, 16405}, {5122, 16056}, {5126, 30950}, {5131, 16569}, {5176, 31330}, {9037, 37676}, {11269, 19647}, {16058, 29661}, {16778, 30852}, {19540, 22765}, {24405, 32856}, {28845, 36002}, {29632, 35992}
X(40109) = isogonal conjugate of X(40110)
X(40109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5080, 30981}, {36, 5080, 28377}
X(40110) lies on the circumconic having center X(9), and on the curve Q157, and on these lines: {190, 5692}, {662, 4276}, {1492, 2278}
X(40110) = isogonal conjugate of X(40109)
X(40111) lies on these lines: {2, 9703}, {3, 9544}, {5, 578}, {23, 15039}, {30, 110}, {49, 140}, {54, 3628}, {155, 1192}, {156, 550}, {182, 11539}, {184, 549}, {186, 32608}, {195, 16881}, {215, 15325}, {230, 9696}, {323, 2070}, {394, 7502}, {395, 3201}, {396, 3200}, {399, 2071}, {403, 3043}, {511, 37936}, {539, 5972}, {542, 14156}, {546, 18350}, {547, 567}, {548, 1614}, {631, 9704}, {632, 32046}, {1154, 3292}, {1216, 5944}, {1353, 8263}, {1437, 5428}, {1493, 5462}, {1495, 13391}, {1511, 13754}, {1568, 18572}, {1656, 9545}, {1993, 12106}, {2072, 32423}, {2979, 7555}, {3167, 6644}, {3202, 32521}, {3205, 16772}, {3206, 16773}, {3289, 35324}, {3518, 14449}, {3530, 9705}, {3564, 15462}, {3580, 11597}, {3627, 10539}, {3845, 13352}, {3850, 37472}, {3853, 37495}, {3857, 11424}, {3860, 13482}, {5054, 11003}, {5055, 11935}, {5066, 15033}, {5305, 9603}, {5453, 17104}, {5504, 23323}, {5562, 32171}, {5609, 6000}, {5651, 15699}, {5663, 34152}, {5876, 12038}, {5886, 9586}, {5899, 35265}, {5946, 34986}, {6090, 7514}, {6101, 10282}, {6150, 33526}, {6640, 18356}, {6759, 15704}, {7525, 9707}, {7530, 8780}, {7542, 21230}, {8254, 14788}, {9621, 26446}, {9653, 10592}, {9666, 10593}, {9706, 13353}, {10151, 15463}, {10224, 14516}, {10226, 12111}, {10257, 10264}, {10610, 11793}, {10620, 37948}, {11004, 13321}, {11064, 37938}, {11250, 11441}, {11412, 12107}, {11430, 15060}, {11449, 15331}, {11464, 23039}, {11591, 13367}, {11695, 36153}, {11812, 13339}, {11818, 37645}, {12105, 23061}, {12112, 35452}, {12278, 18567}, {12383, 18403}, {13160, 15806}, {13292, 22955}, {13340, 26881}, {13363, 13366}, {13434, 35018}, {13451, 13595}, {14791, 37669}, {15034, 18571}, {15035, 37968}, {15040, 37941}, {15067, 18475}, {15068, 18570}, {15122, 15132}, {15686, 37480}, {16238, 32358}, {16266, 33586}, {19504, 37951}, {20424, 31830}, {23236, 25739}, {23293, 34331}, {26882, 37484}, {32139, 35602}, {34397, 37935}, {35259, 39522}, {37496, 37925}
X(40111) = midpoint of X(i) and X(j) for these {i,j}: {110, 22115}, {323, 2070}, {399, 2071}, {1568, 30714}, {12112, 35452}, {12383, 18403}, {14157, 37477}, {23236, 25739}, {37496, 37925}
X(40111) = reflection of X(i) in X(j) for these {i,j}: {403, 10272}, {10264, 10257}, {15646, 1511}, {18572, 1568}, {37938, 11064}, {37947, 1495}
X(40111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {156, 1092, 550}, {11449, 18436, 15331}, {18350, 34148, 546}
X(40112) lies on these lines: {2, 6}, {23, 35266}, {30, 110}, {287, 37858}, {297, 9141}, {376, 6800}, {381, 6090}, {401, 8591}, {441, 14919}, {468, 15360}, {511, 5642}, {525, 1636}, {541, 10564}, {542, 858}, {549, 5890}, {671, 2986}, {1092, 38323}, {1154, 15361}, {1495, 19924}, {1499, 9137}, {1503, 9143}, {1995, 20423}, {2434, 38951}, {2450, 22566}, {2482, 18334}, {3167, 31152}, {3431, 35254}, {3524, 21766}, {3534, 26864}, {3564, 9140}, {3581, 18579}, {4563, 7799}, {5107, 10418}, {5133, 25561}, {5476, 5651}, {5477, 39602}, {5648, 10510}, {5650, 10168}, {5972, 32225}, {6034, 9225}, {6390, 9146}, {7552, 9820}, {7575, 11694}, {8550, 9716}, {8703, 15080}, {9155, 37461}, {10294, 10295}, {10539, 34613}, {10546, 21850}, {11002, 20192}, {11130, 35303}, {11131, 35304}, {11284, 14848}, {11412, 34351}, {11422, 30739}, {13394, 33884}, {13623, 15759}, {15020, 37934}, {15107, 37904}, {15122, 20126}, {15303, 32220}, {15448, 37909}, {16092, 32583}, {18911, 32216}, {25565, 37990}, {29181, 35265}, {30685, 31173}, {32269, 37907}, {32515, 34094}, {32599, 38064}, {33879, 38110}, {34148, 34664}
X(40112) = midpoint of X(i) and X(j) for these {i,j}: {2, 323}, {3292, 13857}, {5648, 10510}, {5655, 37477}, {9143, 10989}, {15360, 23061}
X(40112) = reflection of X(i) in X(j) for these {i,j}: {2, 11064}, {23, 35266}, {858, 13857}, {3580, 2}, {3581, 18579}, {7426, 5642}, {7575, 11694}, {15107, 37904}, {15360, 468}, {20126, 15122}, {32111, 5655}, {32220, 15303}, {32225, 5972}
X(40112) = reflection of X(9158) in the Orthic axis
X(40112) = isotomic conjugate of the polar conjugate of X(10295)
X(40112) = X(i)-isoconjugate of X(j) for these (i,j): {19, 34802}, {661, 9060}
X(40112) = crossdifference of every pair of points on line {512, 34417}
X(40112) = anticomplement of polar conjugate of X(37984)
X(40112) = barycentric product X(i)*X(j) for these {i,j}: {69, 10295}, {99, 9003}
X(40112) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 34802}, {110, 9060}, {9003, 523}, {10295, 4}
X(40112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {323, 11064, 3580}, {323, 22151, 1993}, {8115, 8116, 15066}, {15066, 37645, 14389}, {22151, 37669, 11064}
X(40113) lies on these lines: {3, 13623}, {6, 17}, {30, 110}, {265, 3292}, {323, 14643}, {631, 13630}, {1092, 3521}, {1511, 10294}, {1568, 12902}, {3564, 15027}, {6053, 35001}, {10272, 23061}, {11064, 15061}, {12293, 17505}, {13392, 22248}, {13754, 38728}, {16534, 37496}
X(40113) = reflection of X(22248) in X(13392)
X(40114) lies on these lines: {6, 25}, {23, 14984}, {30, 110}, {49, 7530}, {156, 31815}, {237, 14908}, {468, 5622}, {1596, 15033}, {1614, 37458}, {5651, 32216}, {6000, 15106}, {6090, 14915}, {6644, 6800}, {6759, 37196}, {9306, 11645}, {9703, 18534}, {10293, 10295}, {11003, 26255}, {12099, 37962}, {12106, 15043}, {12824, 18449}, {13171, 21663}, {13198, 15448}, {14791, 18350}, {15066, 18435}, {15139, 36201}, {15462, 35266}, {20772, 35265}
X(40114) = reflection of X(i) in X(j) for these {i,j}: {25, 1495}, {37980, 20772}
X(40114) = isogonal conjugate of the isotomic conjugate of X(7464)
X(40114) = X(75)-isoconjugate of X(10293)
X(40114) = crossdifference of every pair of points on line {525, 37648}
X(40114) = barycentric product X(6)*X(7464)
X(40114) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 10293}, {7464, 76}
X(40114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {154, 19596, 1495}, {184, 1495, 18374}, {184, 18374, 34397}, {10540, 37477, 5655}, {35265, 37980, 20772}
X(40115) lies on these lines: {3, 6}, {30, 111}, {352, 5663}, {381, 8585}, {542, 9872}, {647, 30230}, {2393, 34106}, {3291, 35001}, {5655, 14653}, {7464, 11580}, {11799, 24855}, {15685, 34481}, {15759, 38862}, {15993, 20126}, {20481, 31861}, {22115, 39689}
X(40115) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 37811, 182}
Let A', B', C' be the intersections of line X(4)X(9) and lines BC, CA, AB, resp. The circumcircles of AB'C', BC'A', CA'B' concur in X(40116). (Randy Hutson, October 29, 2020)
X(40116) lies on the circumcircle and these lines: {4, 1566}, {9, 2739}, {10, 2741}, {19, 2717}, {71, 2738}, {98, 17927}, {99, 15411}, {102, 2338}, {103, 2272}, {104, 911}, {105, 5089}, {107, 17926}, {108, 650}, {109, 652}, {110, 677}, {112, 21789}, {281, 2723}, {905, 934}, {910, 972}, {1826, 2688}, {1897, 9057}, {2333, 2700}, {2432, 36067}, {2725, 7719}, {8750, 26716}, {10535, 32726}, {14776, 22108}
X(40116) = isogonal conjugate of X(39470)
X(40116) = Stevanovic-circle-inverse of X(108)
X(40116) = polar-circle-inverse of X(1566)
X(40116) = polar conjugate of the isotomic conjugate of X(677)
X(40116) = polar conjugate of the isogonal conjugate of X(32642)
X(40116) = X(i)-cross conjugate of X(j) for these (i,j): {926, 4}, {8608, 1252}, {32642, 677}
X(40116) = cevapoint of X(i) and X(j) for these (i,j): {647, 39690}, {650, 5089}
X(40116) = trilinear pole of line {6, 3270}
X(40116) = Ψ(X(3), X(101))
X(40116) = Ψ(X(6), X(3270))
X(40116) = Λ(X(651), X(653))
X(40116) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39470}, {63, 676}, {513, 26006}, {516, 905}, {656, 14953}, {910, 4025}, {1456, 6332}, {1459, 30807}, {1886, 4131}, {2398, 3942}, {3270, 24015}, {22383, 35517}, {23696, 39063}, {23973, 34591}
X(40116) = barycentric product X(i)*X(j) for these {i,j}: {4, 677}, {92, 36039}, {100, 36122}, {103, 1897}, {264, 32642}, {653, 2338}, {911, 6335}, {1783, 36101}, {2424, 15742}, {3681, 36109}, {7046, 24016}, {7101, 32668}, {8750, 18025}, {17233, 32701}
X(40116) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39470}, {25, 676}, {101, 26006}, {103, 4025}, {112, 14953}, {677, 69}, {911, 905}, {1783, 30807}, {1815, 30805}, {1897, 35517}, {2338, 6332}, {2424, 1565}, {7128, 24015}, {8750, 516}, {24016, 7056}, {32642, 3}, {32657, 4091}, {32668, 7177}, {32701, 14377}, {36039, 63}, {36056, 4131}, {36101, 15413}, {36122, 693}
X(40117) lies on the circumcircle and these lines: {4, 972}, {19, 102}, {28, 26702}, {55, 31893}, {74, 1903}, {84, 103}, {104, 1436}, {105, 7154}, {106, 7129}, {109, 1783}, {110, 13138}, {112, 32652}, {189, 37378}, {242, 2724}, {268, 281}, {271, 2365}, {280, 26703}, {607, 1433}, {650, 36067}, {653, 934}, {739, 7151}, {1172, 26701}, {1301, 24019}, {1311, 7020}, {2173, 2732}, {2192, 32726}, {2249, 2357}, {2291, 7008}, {2333, 29056}, {2716, 8756}, {2739, 8074}, {3176, 8886}, {3341, 7156}, {7046, 38902}, {8059, 32674}, {13395, 14543}, {32714, 36079}
X(40117) = X(37141)-Ceva conjugate of X(108)
X(40117) = X(i)-cross conjugate of X(j) for these (i,j): {650, 282}, {652, 1172}, {1946, 1433}, {3900, 4}, {32652, 13138}, {32674, 1783}
X(40117) = Stevanovic-circle-inverse of X(36067)
X(40117) = polar-circle-inverse of X(5514)
X(40117) = polar conjugate of X(17896)
X(40117) = polar conjugate of the isotomic conjugate of X(13138)
X(40117) = polar conjugate of the isogonal conjugate of X(32652)
X(40117) = Collings transform of X(7367)
X(40117) = X(i)-isoconjugate of X(j) for these (i,j): {3, 14837}, {7, 10397}, {40, 905}, {48, 17896}, {63, 6129}, {77, 14298}, {109, 16596}, {198, 4025}, {221, 6332}, {222, 8058}, {223, 521}, {322, 22383}, {329, 1459}, {342, 36054}, {347, 652}, {514, 7078}, {522, 7011}, {525, 2360}, {647, 8822}, {650, 7013}, {656, 1817}, {1461, 7358}, {1813, 38357}, {1819, 7178}, {2187, 15413}, {2199, 35518}, {2331, 4131}, {3194, 24018}, {3195, 30805}, {4091, 7952}, {4391, 7114}, {4587, 38374}, {7254, 21075}
X(40117) = cevapoint of X(i) and X(j) for these (i,j): {19, 650}, {607, 1946}, {3900, 7367}
X(40117) = trilinear pole of line {6, 33}
X(40117) = Ψ(X(3), X(9))
X(40117) = Ψ(X(6), X(33))
X(40117) = barycentric product X(i)*X(j) for these {i,j}: {4, 13138}, {84, 1897}, {92, 36049}, {108, 280}, {109, 7020}, {162, 39130}, {189, 1783}, {190, 7129}, {264, 32652}, {271, 36127}, {281, 37141}, {282, 653}, {309, 8750}, {318, 8059}, {645, 2358}, {648, 1903}, {651, 7003}, {664, 7008}, {668, 7151}, {811, 2357}, {1436, 6335}, {2192, 18026}, {4554, 7154}, {7367, 13149}, {32674, 34404}
X(40117) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 17896}, {19, 14837}, {25, 6129}, {33, 8058}, {41, 10397}, {84, 4025}, {108, 347}, {109, 7013}, {112, 1817}, {162, 8822}, {189, 15413}, {280, 35518}, {282, 6332}, {607, 14298}, {650, 16596}, {692, 7078}, {1415, 7011}, {1433, 4131}, {1436, 905}, {1783, 329}, {1897, 322}, {1903, 525}, {2192, 521}, {2208, 1459}, {2357, 656}, {2358, 7178}, {3900, 7358}, {7003, 4391}, {7008, 522}, {7020, 35519}, {7118, 652}, {7129, 514}, {7151, 513}, {7154, 650}, {8059, 77}, {8750, 40}, {13138, 69}, {14776, 15501}, {18344, 38357}, {32652, 3}, {32674, 223}, {32676, 2360}, {32713, 3194}, {32714, 14256}, {36049, 63}, {36127, 342}, {37141, 348}, {39130, 14208}
X(40118) lies on the circumcircle and these lines: {2, 10420}, {4, 691}, {5, 11635}, {23, 925}, {24, 935}, {25, 476}, {30, 3565}, {69, 10425}, {74, 3566}, {99, 186}, {107, 37777}, {110, 468}, {111, 2501}, {112, 230}, {183, 2855}, {378, 2696}, {427, 1291}, {523, 3563}, {542, 35191}, {827, 37943}, {858, 13398}, {930, 21284}, {1287, 3518}, {1289, 37951}, {1290, 4231}, {1292, 37979}, {1296, 10295}, {1297, 36166}, {1300, 14618}, {1302, 37962}, {1304, 6353}, {1995, 16167}, {2691, 7414}, {2693, 7422}, {2694, 7425}, {2697, 7418}, {2715, 36472}, {3542, 10423}, {4232, 9060}, {5189, 20185}, {6103, 23969}, {6792, 35188}, {7464, 20187}, {10098, 18533}, {10101, 31384}, {12131, 14734}, {13397, 37959}, {20189, 37920}, {39193, 39828}
X(40118) = reflection of X(3563) in the Euler line
X(40118) = isogonal conjugate of X(14984)
X(40118) = polar-circle-inverse of X(16188)
X(40118) = orthoptic-circle-of-Steiner-inellipe-inverse of X(16221)
X(40118) = Collings transform of X(39021)
X(40118) = X(542)-cross conjugate of X(4)
X(40118) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14984}, {63, 2493}, {656, 7468}, {810, 14221}
X(40118) = cevapoint of X(25) and X(6103)
X(40118) = trilinear pole of line {6, 14273}
X(40118) = barycentric product X(16081)*X(40083)
X(40118) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 14984}, {25, 2493}, {112, 7468}, {648, 14221}, {6103, 16188}, {6531, 34175}, {40083, 36212}
X(40119) lies on the circumcircle and these lines: {4, 2696}, {23, 3565}, {24, 10098}, {25, 691}, {30, 20187}, {74, 20186}, {99, 468}, {107, 16315}, {110, 8681}, {111, 2489}, {112, 3291}, {186, 1296}, {403, 30247}, {476, 4232}, {523, 2374}, {925, 7426}, {935, 6353}, {1290, 7438}, {1294, 36166}, {1995, 10420}, {2373, 36168}, {2691, 4231}, {2693, 7418}, {2694, 7423}, {2697, 7417}, {2971, 15398}, {6090, 10425}, {9084, 36898}, {10295, 30256}, {11635, 13595}, {13398, 37980}, {16167, 26255}, {33638, 37969}, {37951, 39382}
X(40119) = reflection of X(2374) in the Euler line
X(40119) = polar-circle-inverse of X(31655)
X(40119) = X(2854)-cross conjugate of X(4)
X(40119) = Ψ(X(3), X(351))
X(40119) = X(i)-isoconjugate of X(j) for these (i,j): {63, 10418}, {656, 7472}
X(40119) = barycentric product X(17983)*X(40078)
X(40119) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 10418}, {112, 7472}, {8753, 34169}, {40078, 6390}
X(40120) lies on the circumcircle and the lines: {2, 135}, {4, 3565}, {24, 99}, {25, 925}, {110, 6353}, {112, 3542}, {378, 20187}, {403, 691}, {427, 20185}, {468, 10420}, {476, 37777}, {487, 1306}, {488, 1307}, {847, 39416}, {935, 37951}, {1292, 31384}, {1296, 18533}, {4231, 13397}, {5897, 7422}, {5966, 36898}, {7418, 34168}, {11635, 37943}, {16167, 37962}, {26706, 31385}, {33638, 35480}
X(40120) = polar-circle-inverse of X(31842)
X(40120) = orthoptic-circle-of-Steiner-inellipe-inverse of X(135)
X(40120) = isogonal conjugate of X(34382)
X(40120) = X(3564)-cross conjugate of X(4)
X(40120) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34382}, {31842, 36051}
X(40120) = cevapoint of X(i) and X(j) for these (i,j): {25, 230}, {193, 35296}
X(40120) = trilinear pole of line {6, 38359}
X(40120) = Λ(X(3), X(6467))
X(40120) = Λ(X(68), X(69))
X(40120) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34382}, {230, 31842}
X(40121) lies on these lines: {3, 19164}, {5, 2794}, {25, 111}, {26, 19165}, {127, 6676}, {132, 6756}, {206, 1511}, {1297, 9715}, {1576, 39857}, {2799, 22105}, {2871, 14574}, {2881, 14270}, {2909, 6102}, {3202, 5944}, {3542, 13200}, {3549, 10749}, {5027, 9517}, {5938, 10313}, {5946, 19156}, {6031, 7493}, {7395, 38699}, {7507, 10735}, {7514, 14649}, {9714, 13310}, {9969, 28343}, {10547, 14885}, {10766, 19125}, {11819, 19160}, {12362, 14689}, {13236, 14691}, {14676, 15562}, {14900, 21841}, {15818, 18876}
X(40121) = midpoint of X(i) and X(j) for these {i,j}: {3, 19164}, {112, 11641}, {5938, 10313}, {14676, 15562}
X(40121) = reflection of X(38624) in X(34217)
X(40121) = barycentric product X(25)*X(28726)
X(40121) = barycentric quotient X(28726)/X(305)
X(40121) = {X(112),X(9157)}-harmonic conjugate of X(11641)
X(40122) lies on the cubic K1161 and these lines: {6, 538}, {729, 8667}, {3053, 3231}, {3288, 33979}
X(40122) = isotomic conjugate of anticomplement of X(40125)
X(40123) lies on these lines: {2, 6}, {4, 8024}, {22, 3926}, {25, 3933}, {76, 6997}, {251, 14001}, {304, 10327}, {305, 315}, {427, 7776}, {1194, 7758}, {1196, 7855}, {1369, 16063}, {1799, 7763}, {1975, 7500}, {2548, 8891}, {2549, 19568}, {2979, 4176}, {3266, 7386}, {3785, 7485}, {4872, 19799}, {5133, 32816}, {6337, 6636}, {6340, 31101}, {6995, 32830}, {7391, 9464}, {7392, 39998}, {7484, 7767}, {7493, 7796}, {7494, 26233}, {7495, 32825}, {7762, 11324}, {8362, 39951}, {10691, 14929}, {16276, 32833}, {16951, 20065}, {18018, 28706}, {18916, 37450}, {25053, 32458}, {32064, 33796}, {32815, 34603}, {32817, 34608}, {32824, 37900}, {32828, 37990}, {39978, 40022}
X(40123) = anticomplement of X(1184)
X(40123) = isotomic conjugate of the isogonal conjugate of X(37485)
X(40123) = barycentric product X(76)*X(37485)
X(40123) = barycentric quotient X(37485)/X(6)
X(40123) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 193, 5359}, {305, 315, 1370}, {7796, 33651, 34254}, {10327, 39732, 304}, {33651, 34254, 7493}
X(40124) lies on these lines: {2, 64}, {25, 17808}, {612, 10375}, {3162, 39951}, {7484, 33581}
X(40124) = X(1496)-complementary conjugate of X(15259)
X(40125) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 159}, {22, 6337}, {25, 39}, {160, 6503}, {1125, 15497}, {1184, 19459}, {1486, 3666}, {2482, 39857}, {5359, 32621}, {6292, 7484}, {9909, 11165}
X(40125) = complement of the isogonal conjugate of X(37485)
X(40125) = complement of isotomic conjugate of X(40122)
X(40125) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 1184}, {37485, 10}
X(40125) = X(2)-Ceva conjugate of X(1184)
X(40125) = barycentric product X(5286)*X(37485)
X(40126) lies on these lines: {2, 3933}, {3, 9465}, {6, 373}, {23, 1384}, {25, 32}, {111, 21309}, {115, 15433}, {468, 2452}, {612, 4515}, {1180, 16419}, {1194, 1611}, {1351, 9463}, {1627, 9909}, {1995, 5354}, {3051, 9777}, {3066, 5039}, {3266, 22253}, {3767, 5094}, {5007, 30734}, {5020, 5359}, {5024, 11580}, {5093, 39024}, {5254, 31152}, {5286, 30739}, {5304, 16317}, {5309, 32216}, {11173, 20977}, {11324, 17128}, {14567, 26864}, {15302, 20481}, {31404, 37439}, {31885, 34417}
X(40127) lies on these lines: {1, 8074}, {2, 7}, {6, 3756}, {8, 9310}, {11, 5819}, {25, 1604}, {37, 5218}, {41, 938}, {56, 6554}, {101, 18391}, {108, 281}, {169, 3086}, {198, 33849}, {220, 1788}, {346, 5205}, {497, 910}, {612, 4336}, {614, 5304}, {631, 16601}, {919, 2726}, {956, 19309}, {1055, 5731}, {1108, 3290}, {1146, 3476}, {1212, 7288}, {1436, 4224}, {1696, 2345}, {1743, 5121}, {2082, 14986}, {2246, 5838}, {2256, 5275}, {2280, 10580}, {2291, 9057}, {2348, 17728}, {3011, 37689}, {3161, 14439}, {3177, 17081}, {3207, 3486}, {3212, 26658}, {3241, 17439}, {3474, 17747}, {3501, 26062}, {3600, 27541}, {3616, 17451}, {3684, 36845}, {3689, 17314}, {4000, 26007}, {4223, 38902}, {4293, 5179}, {4315, 5199}, {4339, 37055}, {5011, 30305}, {5089, 6353}, {5222, 9502}, {5540, 10072}, {5657, 6998}, {5703, 21808}, {6921, 25082}, {7176, 30694}, {7228, 30754}, {10106, 23058}, {16502, 28016}, {16780, 28080}, {16845, 25086}, {16997, 17316}, {17567, 25066}, {20752, 37657}, {24477, 37658}, {32625, 37254}
X(40128) lies on these lines: {1, 26258}, {2, 1743}, {6, 17728}, {609, 5179}, {612, 2324}, {614, 5304}, {910, 3914}, {2323, 5276}, {2348, 37646}, {2911, 5275}, {3008, 26229}, {3011, 7735}, {3290, 5306}, {3912, 17001}, {4644, 30742}, {4896, 31071}, {5299, 28018}, {5305, 23536}, {5750, 17124}, {17023, 26279}, {20072, 30798}, {26265, 39595}
X(40129) lies on these lines: {2, 6}, {9, 11031}, {32, 411}, {39, 6986}, {57, 2312}, {100, 10315}, {232, 4233}, {284, 4220}, {579, 19649}, {614, 2257}, {938, 16502}, {949, 5222}, {961, 7119}, {1108, 7191}, {1172, 16318}, {1210, 5299}, {1249, 37394}, {1333, 10313}, {1901, 37456}, {2548, 6991}, {3149, 30435}, {3767, 6828}, {5007, 6915}, {5254, 6895}, {5280, 13411}, {5286, 6836}, {5305, 6831}, {5319, 6943}, {5324, 39690}, {5746, 26118}, {6894, 7745}, {7466, 10311}, {8557, 26242}, {15048, 37428}, {22240, 36018}
X(40130) lies on these lines: {2, 11175}, {6, 373}, {32, 1495}, {39, 3231}, {51, 1196}, {110, 5354}, {184, 1184}, {194, 35275}, {230, 30516}, {353, 38010}, {511, 9463}, {732, 30749}, {1180, 3819}, {1194, 1613}, {1843, 14580}, {1995, 5039}, {2021, 3117}, {2030, 11003}, {2225, 17053}, {2502, 5008}, {3053, 35268}, {3787, 20859}, {3981, 21969}, {5097, 39024}, {5305, 11064}, {5306, 5642}, {5309, 13857}, {5359, 9306}, {6656, 14467}, {7882, 14463}, {8617, 15082}, {8627, 35007}, {12212, 20998}, {12294, 35325}, {13366, 39764}, {15820, 39691}, {30435, 35259}
X(40131) lies on these lines: {1, 41}, {2, 7}, {3, 16601}, {6, 354}, {10, 17742}, {12, 208}, {19, 25}, {31, 16970}, {38, 16517}, {40, 1334}, {44, 4860}, {45, 1155}, {46, 3730}, {56, 1212}, {65, 220}, {72, 19309}, {78, 19310}, {85, 6559}, {120, 5880}, {165, 846}, {172, 16968}, {190, 30758}, {200, 3930}, {218, 942}, {219, 5173}, {239, 26274}, {284, 4228}, {346, 32932}, {388, 6554}, {404, 25082}, {474, 25066}, {497, 5819}, {518, 37658}, {609, 37817}, {610, 2268}, {728, 1706}, {936, 33299}, {965, 16352}, {966, 5227}, {975, 18596}, {1002, 3751}, {1055, 3576}, {1146, 5252}, {1174, 39943}, {1190, 2264}, {1194, 2277}, {1196, 21796}, {1201, 9575}, {1202, 2257}, {1281, 3501}, {1319, 34522}, {1376, 3693}, {1434, 32024}, {1449, 7191}, {1475, 3333}, {1478, 5179}, {1541, 11372}, {1572, 3230}, {1617, 15288}, {1642, 5091}, {1697, 39587}, {1698, 17744}, {1731, 26228}, {1743, 5272}, {1759, 2198}, {1760, 4687}, {1770, 17732}, {1836, 17747}, {1837, 21049}, {1929, 3097}, {2099, 6603}, {2171, 2324}, {2178, 5322}, {2182, 17603}, {2183, 29639}, {2256, 2262}, {2266, 2294}, {2267, 22099}, {2269, 2270}, {2287, 5208}, {2291, 9058}, {2303, 5324}, {2316, 39393}, {2321, 10327}, {2329, 19860}, {2345, 26040}, {2646, 3207}, {3008, 10520}, {3011, 7735}, {3061, 19861}, {3085, 7719}, {3099, 15485}, {3125, 9620}, {3145, 5277}, {3177, 7176}, {3247, 3920}, {3263, 3729}, {3329, 36406}, {3338, 4253}, {3423, 24320}, {3496, 5250}, {3601, 37254}, {3616, 33950}, {3660, 22163}, {3673, 17682}, {3679, 5525}, {3684, 3870}, {3691, 39581}, {3692, 29641}, {3726, 16973}, {3748, 16777}, {3811, 3970}, {3812, 30618}, {3838, 30755}, {3916, 19313}, {3927, 19321}, {3951, 19316}, {3980, 17355}, {3984, 19318}, {3991, 5687}, {4007, 33091}, {4034, 33090}, {4051, 36846}, {4258, 37080}, {4363, 30748}, {4384, 26234}, {4390, 9623}, {4513, 5836}, {4648, 7289}, {4652, 19314}, {4659, 31130}, {4666, 16503}, {4875, 12513}, {4911, 17671}, {5011, 5119}, {5020, 20760}, {5022, 32636}, {5044, 16852}, {5253, 26690}, {5261, 27541}, {5283, 13738}, {5286, 23536}, {5297, 16548}, {5308, 7291}, {5320, 16972}, {5341, 16675}, {5359, 16470}, {5440, 19322}, {5526, 5902}, {5587, 21044}, {5781, 10391}, {5838, 10580}, {6167, 9312}, {6180, 34855}, {6714, 25557}, {6734, 26036}, {7081, 21387}, {7084, 8751}, {7146, 25930}, {7290, 21764}, {7292, 16670}, {7297, 16672}, {7410, 26878}, {7412, 17916}, {7484, 22060}, {7736, 20785}, {7964, 37499}, {7994, 21809}, {8074, 31397}, {8583, 39244}, {8609, 33925}, {8804, 26052}, {9578, 23058}, {9593, 24443}, {10129, 30787}, {10388, 17452}, {10857, 19649}, {11018, 25514}, {11108, 25086}, {11227, 16434}, {11688, 38869}, {14828, 27475}, {16059, 25074}, {16193, 22153}, {16408, 25068}, {16409, 25075}, {16412, 25083}, {16502, 28011}, {16552, 17736}, {16567, 21382}, {16580, 31261}, {16589, 37225}, {16667, 30350}, {16779, 29820}, {16780, 28082}, {16823, 21384}, {16831, 20602}, {16849, 31445}, {16998, 39252}, {17001, 26247}, {17007, 17270}, {17022, 21370}, {17056, 39690}, {17064, 17737}, {17107, 24796}, {17683, 20880}, {17745, 18398}, {18615, 23203}, {19297, 34879}, {21258, 30617}, {21872, 37567}, {22108, 26275}, {24005, 26063}, {24471, 25878}, {24512, 36404}, {24590, 37555}, {26244, 29828}, {27129, 33867}, {28043, 37580}, {30385, 30556}, {30386, 30557}, {30400, 32556}, {30401, 32555}, {32561, 37579}, {37272, 37597}
X(40131) = {X(6203),X(6204)}-harmonic conjugate of X(7)
X(40132) lies on these lines: {2, 3}, {51, 37669}, {69, 5651}, {110, 14912}, {125, 35904}, {182, 35260}, {184, 18928}, {193, 6090}, {264, 10603}, {373, 3618}, {895, 5642}, {1007, 37804}, {1196, 5319}, {1249, 14580}, {1285, 5913}, {1352, 37643}, {1495, 25406}, {1992, 3292}, {2892, 6698}, {2986, 14494}, {3066, 11064}, {3068, 10963}, {3069, 10961}, {3260, 34229}, {3266, 32817}, {3291, 7735}, {3589, 8547}, {3819, 33522}, {4319, 5218}, {4320, 7288}, {5085, 15448}, {5268, 31452}, {5297, 37696}, {5304, 16317}, {5544, 38110}, {5640, 37645}, {5646, 21167}, {5656, 37475}, {5921, 26869}, {5943, 11427}, {5972, 14561}, {6337, 11059}, {6688, 34750}, {6699, 18489}, {6719, 35282}, {6776, 35259}, {7292, 37697}, {7612, 34289}, {7665, 9155}, {7736, 10314}, {7765, 34481}, {8549, 10192}, {9172, 23583}, {9214, 15398}, {9306, 11225}, {9826, 20125}, {9936, 18934}, {10519, 32269}, {10546, 18911}, {10643, 11489}, {10644, 11488}, {11061, 32241}, {11185, 37803}, {11469, 34469}, {12828, 32244}, {13567, 14826}, {15030, 18931}, {16187, 32223}, {16276, 19583}, {18289, 35812}, {18290, 35813}, {18852, 34334}, {21356, 32225}, {21448, 37689}, {29181, 31860}, {35283, 37638}
X(40133) lies on these lines: {1, 6}, {2, 4875}, {19, 1398}, {39, 4646}, {40, 5022}, {41, 1319}, {42, 22317}, {56, 910}, {57, 7955}, {58, 34862}, {65, 1475}, {69, 25887}, {75, 27340}, {81, 16699}, {101, 24928}, {145, 3693}, {169, 999}, {172, 294}, {210, 39244}, {241, 2275}, {269, 2124}, {279, 1418}, {322, 25971}, {354, 1202}, {387, 15852}, {496, 5179}, {517, 4253}, {519, 4515}, {536, 17158}, {579, 31793}, {583, 7957}, {604, 2264}, {650, 21105}, {672, 3057}, {673, 7176}, {948, 3772}, {1015, 16583}, {1030, 35202}, {1086, 10481}, {1146, 1210}, {1170, 18889}, {1200, 22088}, {1201, 9502}, {1249, 1841}, {1323, 17366}, {1334, 5919}, {1385, 4251}, {1420, 3207}, {1427, 23653}, {1434, 27000}, {1451, 7118}, {1572, 5021}, {1575, 21896}, {1766, 8158}, {2260, 2262}, {2266, 37080}, {2271, 9619}, {2280, 2646}, {2310, 10939}, {2340, 3780}, {2348, 9310}, {2391, 10521}, {3008, 6692}, {3241, 25082}, {3244, 3991}, {3290, 5304}, {3501, 3880}, {3576, 4258}, {3579, 5030}, {3600, 5819}, {3666, 17014}, {3679, 25068}, {3686, 12447}, {3691, 25917}, {3721, 21342}, {3730, 9957}, {3739, 27304}, {3815, 25614}, {3890, 4520}, {4051, 5836}, {4255, 9592}, {4262, 13624}, {4308, 5838}, {4350, 6610}, {4383, 25930}, {4513, 36846}, {4642, 23649}, {4856, 25078}, {5011, 37582}, {5065, 5301}, {5305, 15251}, {5540, 5563}, {5584, 36743}, {5839, 20007}, {6184, 12640}, {6554, 14986}, {6736, 8568}, {6743, 17362}, {6764, 17299}, {7208, 24790}, {7735, 16020}, {7743, 24045}, {8273, 36744}, {9312, 24600}, {9441, 33863}, {9797, 17314}, {10460, 37593}, {10914, 16549}, {11019, 21049}, {11997, 36635}, {11998, 21764}, {12053, 17747}, {13370, 32625}, {14100, 20978}, {16679, 21867}, {16716, 16726}, {16728, 33296}, {16834, 25083}, {17609, 21808}, {17721, 28052}, {18663, 19790}, {19861, 37658}, {20905, 26818}, {24352, 30625}, {24597, 25939}, {25055, 25086}, {25067, 37681}, {26563, 26964}, {27253, 31269}, {29571, 37662}, {30271, 37507}, {34497, 34855}, {35092, 35116}, {37500, 37551}, {37665, 39587}
X(40133) = complement of X(16284)
X(40133) = crossdifference of every pair of points on line X(513)X(5537) (the de Longchamps line of the excentral triangle, and the radical axis of any pair of {1st, 2nd and 3rd antipedal circles of X(1)})
X(40134) lies on these lines: {2, 905}, {25, 1946}, {111, 2687}, {230, 231}, {513, 21786}, {612, 3900}, {649, 6615}, {1639, 2509}, {1734, 5268}, {2522, 3239}, {3803, 26249}, {4468, 27400}, {4521, 16612}, {4893, 14413}, {5020, 22160}, {7484, 22091}, {9058, 32685}, {14298, 22383}, {16757, 31209}, {21894, 31946}, {24562, 25084}, {25009, 26146}
X(40134) = complement of isotomic conjugate of X(9058)
X(40134) = crosspoint of X(2) and X(9058)
X(40134) = crosssum of X(6) and X(9001)
X(40135) lies on these lines: {3, 6}, {115, 1990}, {230, 37911}, {232, 15262}, {237, 21639}, {419, 11596}, {647, 657}, {1843, 34416}, {3163, 16310}, {5702, 7735}, {6128, 18487}, {6749, 7747}, {8721, 18919}, {8749, 14581}, {8779, 14567}, {9407, 20975}, {10991, 15471}, {11060, 11079}, {11443, 37465}, {12167, 33578}, {14537, 34288}, {14836, 39593}, {15525, 23967}, {23976, 23992}, {34570, 37941}, {36212, 37784}, {37665, 39602}
X(40136) lies on these lines: on lines {6, 17}, {32, 393}, {115, 6748}, {216, 14836}, {570, 36422}, {571, 6781}, {577, 7765}, {800, 11062}, {3051, 31883}, {3163, 39018}, {3767, 40065}, {5065, 5355}, {5309, 15905}, {6709, 10220}, {7735, 38282}, {8573, 9699}
X(40136) = barycentric product X(397)*X(398)
X(40137) lies on these lines: {44, 513}, {521, 4521}, {2490, 9001}, {3239, 3900}, {3887, 14350}, {3910, 20318}, {4131, 31209}, {5375, 15632}, {14303, 15313}
X(40138) lies on these lines: {2, 648}, {4, 6}, {19, 1475}, {20, 3284}, {32, 37460}, {44, 7952}, {69, 11331}, {112, 5063}, {184, 6525}, {193, 340}, {216, 3523}, {232, 4232}, {281, 1100}, {297, 1992}, {376, 36427}, {378, 14836}, {468, 2452}, {470, 37640}, {471, 37641}, {550, 15905}, {577, 3522}, {685, 35906}, {1033, 3516}, {1119, 17366}, {1217, 36752}, {1384, 37934}, {1585, 19054}, {1586, 19053}, {1609, 32534}, {1640, 18808}, {1656, 15851}, {1657, 38292}, {1785, 16670}, {1968, 33871}, {2331, 3554}, {3003, 35486}, {3088, 7772}, {3089, 5319}, {3091, 15860}, {3172, 7738}, {3515, 8573}, {3535, 32787}, {3536, 32788}, {3543, 18487}, {3553, 7129}, {3589, 32000}, {3618, 9308}, {3629, 32001}, {3854, 36412}, {4846, 18850}, {5007, 7487}, {5032, 37174}, {5094, 7736}, {5306, 6353}, {5309, 6623}, {5667, 9408}, {5967, 6531}, {6032, 37665}, {6110, 10653}, {6111, 10654}, {6524, 11402}, {6618, 17809}, {7046, 17369}, {7412, 37503}, {7739, 14581}, {7748, 34569}, {7757, 35940}, {8014, 8737}, {8015, 8738}, {8553, 17506}, {8557, 23710}, {8882, 38808}, {8889, 9300}, {9722, 35487}, {10295, 16303}, {10299, 36751}, {10312, 33872}, {11063, 21844}, {12174, 35711}, {14361, 23292}, {14614, 37187}, {16666, 34231}, {17555, 37654}, {18533, 34288}, {21735, 36748}, {30435, 37458}, {31400, 37118}, {35481, 39176}, {35484, 39662}, {36744, 37289}
Hodpieces: X(40139)-X(40173)
This preamble is based on notes received from Radosław Żak (October 29, 2020) and Peter Moses (October 29-30, 2020).
In the plane of a triangle ABC, let P be a point, not on a sideline of ABC, and let DEF be the cevian triangle of P. The isogonal conjugate of line EF is a conic. Let A' be the center of of the conic, and define B' and C' cyclically. Then the lines AA', BB', CC' concur in a point here named the hodpiece of P, denoted by H(P). The name hodpiece is taken from James Joyce's book, Finnegans Wake. The unique point P such that H(P) = P, indexed below as X(40139), is named the Bloom point after Leopold Bloom, the main character in Joyce's Ulysses. The point H(X(5)) = X(40140) is the Dedalus point, and the H(X(7)) = X(40141), the Zana point.
An article (in Polish) about hodpieces by Żak won a gold medal in a competition for high school students organized by the Polish Mathematical Society. For an English translation, see Isogonal conjugate and a few properties of the point X(25).
If P = p : q : r (barycentrics), then H(P) = a2/(p*(-a2/p + b2/q + c2/r) : : .
Let P* = P-Ceva conjugate of X(6). Then H(P) = isogonal conjugate of P*-cross conjugate of P.
The appearance of (i,j) in the following list means that H(X(i)) = X(j):
(1,57), (2,25), (3,459), (4,394), (5,40140), (6,2), (7,40141), (9,1422), (10,40142), (13,40156), (14,40157), (15, 40158), (16,40159), (19,6513), (21,40160), (25,6384), (28,40161), (31,6384), (32,40162), (37,40143), (39,40163), (41,40164), (48,40165), (54,324), (55,36620), (56,6557), (57,200), (58,321), (59, 40166), (61,40167), (62,40168), (63,40169), (64,40170), (69,40144), (75,40145), (76,40146), (81,42), (83,3051), (86,40147), (87,40171), (88,40172), (162,37755), (163,6358), (190,40148), (249,8029), (251,8024), (259,16664), (266,7028), (275,418), (284,40149), (288,3078), (493,8038), (512,37880), (514,40150), (588,8035), (589,8036), (644,40151), (648,184), (651,55), (662,756), (765,8042), (1016,8027), (1073,3079), (1126,8025), (1170,8012), (1171,8013), (1172,401523), (1252,6545), (1262,23615), (1461,7046), (1783,222), (2226,8028), (2298,40153), (2981,8014), (2982,8021), (3939,40154), (4558,14593), (4577,8041), (4629,8040), (4638,8028), (5381,8027), (6151,8015), (6185,23612), (7121,8026), (8115,25), (8116, 25), (9268,6545), (10630,8030), (13138,6611), (18018,36414), (20332,40155), (23964,23616), (23984,23614), (345071,6382), (34536,23611), (34537,23610), (34538,23613), (34568,3081), (34574,8030), (36049,196), (38810,8022), (38826,8039), (38828,6555), (38830,8023)
Note that H(X(2)) = H(X(8115)) = H(X(8116)) = X(25).
For Vu Thanh Tung's generalization to U-hodpieces, see the preamble just before X(40212).
X(40139) is the fixed point of the hodpiece transform.
X(40139) lies on the cubic K102 and these lines: (pending)
X(40140) lies on these lines: {24,3432}, {18883,45832}
X(40140) = hodpiece of X(5)
X(40140) = X(54)-reciprocal conjugate of-X(2888)
X(40140) = intersection, other than A, B, C, of circumconics {A, B, C, X(2), X(24)} and {A, B, C, X(97), X(25044)}
X(40140) = barycentric product X(95)*X(3432)
X(40140) = barycentric quotient X(54)/X(2888)
X(40140) = trilinear quotient X(i)/X(j) for these (i, j): (2167, 2888), (2169, 45800)
X(40141) lies on these lines: {2, 1814}, {6, 5089}, {48, 672}, {212, 2340}, {218, 222}, {219, 3693}, {650, 11502}, {2194, 37908}, {5063, 14578}, {19350, 32677}, {26706, 32726}
X(40141) = isogonal conjugate of X(37800)
X(40141) = hodpiece of X(7)
X(40141) = crossdifference of every pair of points on line X(11934)X(21185)
X(40142) lies on these lines: {2, 8044}, {48, 28606}, {184, 386}, {2359, 38822}
X(40142) = isogonal conjugate of X(21076
X(40140) = hodpiece of X(10)
X(40143) lies on these lines: {1, 229}, {2, 1029}, {502, 1224}, {1255, 21353}, {3733, 8029}, {19623, 35058}
X(40143) = isogonal conjugate of X(21873)
X(40143) = hodpiece of X(37)
X(40144) lies on these lines: {2, 2138}, {6, 17409}, {37, 21148}, {111, 39417}, {378, 3108}, {428, 34288}, {455, 2386}, {1241, 40009}, {2165, 16318}, {2207, 13854}, {3172, 39951}, {6339, 37784}, {6753, 34212}, {8770, 14580}, {14910, 21213}, {15262, 34608}, {23115, 36414}
X(40144) = isogonal conjugate of X(28419)
X(40144) = polar conjugate of isotomic conjugate of X(34207)
X(40145) lies on these lines: lines {2, 7357}, {748, 19559}, {2174, 2276}, {7296, 26892}
X(40145) = isogonal conjugate of X(20444)
X(40145) = hodpiece of X(75)
X(40146) lies on these lines: {2, 66}, {32, 39466}, {39, 184}, {1501, 27369}, {1976, 13854}, {2001, 18018}, {3051, 14575}, {3852, 36414}, {9306, 34138}, {15389, 19558}, {19156, 37649}
X(40146) = isogonal conjugate of X(40073)
X(40146) = hodpiece of X(76)
X(40147) lies on these lines: {2, 2140}, {6, 34444}, {111, 6577}, {213, 2350}, {672, 39798}, {941, 3588}, {995, 39965}, {1218, 39735}, {2183, 39974}, {2205, 38346}
X(40147) = isogonal conjugate of X(29767)
X(40148) = hodpiece of X(86)
X(40148) lies on these lines: {1, 596}, {2, 8050}, {31, 16679}, {39, 14751}, {42, 1100}, {86, 3112}, {87, 32925}, {213, 2308}, {593, 595}, {741, 1621}, {756, 3248}, {899, 3791}, {902, 1402}, {1015, 8041}, {1042, 1319}, {1201, 1245}, {1459, 40086}, {1977, 21827}, {2296, 17394}, {2309, 40085}, {3223, 24661}, {3231, 23533}, {3720, 30982}, {3730, 30651}, {3920, 31111}, {4075, 39748}, {5311, 7032}, {17150, 18792}, {17193, 39712}, {18194, 26037}, {37132, 37205}
X(40148) = isogonal conjugate of X(4360)
X(40148) = isotomic conjugate of X(40087)
X(40148) = hodpiece of X(190)
X(40149) lies on the Kiepert hyperbola and these lines: {2, 92}, {4, 65}, {7, 37181}, {8, 37189}, {10, 201}, {19, 1708}, {27, 653}, {28, 1940}, {34, 5136}, {57, 5307}, {76, 331}, {98, 108}, {226, 1826}, {243, 4219}, {264, 34258}, {275, 1409}, {286, 1396}, {321, 8736}, {393, 17903}, {485, 1659}, {486, 13390}, {651, 2986}, {664, 31631}, {671, 18026}, {801, 1944}, {857, 18588}, {1029, 7282}, {1068, 3085}, {1172, 2982}, {1426, 1867}, {1427, 16732}, {1446, 20618}, {1737, 1838}, {1785, 4424}, {1788, 14018}, {1812, 1943}, {1824, 1893}, {1825, 1873}, {1848, 2051}, {1860, 2181}, {1865, 6354}, {1868, 12709}, {1869, 4848}, {1870, 5397}, {1891, 3429}, {1897, 3896}, {1947, 17950}, {2052, 6521}, {2333, 16609}, {3668, 8808}, {3696, 7046}, {3772, 17902}, {3931, 7952}, {4213, 17985}, {4296, 11103}, {4331, 17871}, {4554, 8781}, {4605, 22000}, {4654, 38461}, {5174, 13583}, {5236, 17758}, {5905, 6504}, {6198, 7073}, {6830, 13599}, {6844, 31363}, {6905, 22341}, {7098, 14016}, {7178, 14618}, {7554, 8762}, {13405, 23710}, {14213, 22464}, {14571, 18676}, {16603, 21016}, {16608, 17862}, {17863, 37543}, {17869, 21924}, {17918, 19786}, {20928, 23600}, {28950, 30807}, {33133, 37770}, {37263, 38860}, {37788, 40012}
X(40149) = isogonal conjugate of X(2193)
X(40149) = isotomic conjugate of X(1812)
X(40149) = hodpiece of X(284)
X(40149) = polar conjugate of X(21)
X(40149) = antigonal conjugate of polar conjugate of X(425)
X(40149) = cevapoint of X(i) and X(j) for these {i,j}: {1, 1744}, {65, 1880}, {225, 1826}
X(40149) = crosspoint of X(92) and X(2052)
X(40149) = crosssum of X(48) and X(577)
X(40149) = crossdifference of every pair of points on line X(1946)X(36054)
X(40149) = Danneels point of X(92)
X(40149) = trilinear pole of line X(523)X(24006)
X(40149) = perspector of ABC and orthoanticevian triangle of X(1441)
X(40149) = pole wrt polar circle of trilinear polar of X(21) (line X(521)X(650))
X(40149) = trilinear product X(i)*X(j) for these {i,j}: {62, 95}, {108, 1577}
X(40149) = barycentric product X(108)*X(850)
X(40150) lies on these lines: {2, 39026}, {31624, 31634}
X(40150) = isogonal conjugate of X(21202)
X(40150) = hodpiece of X(514)
X(40151) lies on these lines: {1, 2137}, {2, 27825}, {6, 9050}, {7, 1997}, {55, 1293}, {56, 1149}, {57, 1122}, {63, 27819}, {65, 3680}, {222, 38828}, {388, 6556}, {553, 4052}, {951, 1466}, {1376, 31343}, {1407, 38266}, {1412, 33628}, {1434, 16711}, {1458, 38289}, {2415, 32933}, {3161, 8051}, {3218, 27827}, {3304, 14261}, {3339, 10563}, {4373, 21454}, {5228, 7153}, {5437, 24151}, {17743, 27830}, {26627, 27823}
X(40151) = isogonal conjugate of X(3161)
X(40151) = hodpiece of X(644)
X(40151) = cevapoint of X(649) and X(1357)
X(40152) lies on these lines: {1, 1779}, {2, 7}, {3, 73}, {28, 1935}, {40, 3182}, {42, 22069}, {48, 3173}, {65, 10901}, {71, 1214}, {72, 856}, {97, 22128}, {109, 1297}, {219, 1073}, {223, 573}, {225, 1217}, {276, 349}, {278, 24310}, {283, 951}, {284, 2003}, {394, 1804}, {651, 1817}, {916, 23171}, {1020, 36908}, {1102, 3719}, {1334, 16577}, {1396, 4269}, {1407, 37500}, {1410, 22076}, {1422, 6282}, {1427, 2245}, {1465, 5755}, {1764, 34050}, {1812, 1949}, {1813, 14919}, {1936, 4219}, {2183, 11347}, {2252, 26934}, {2260, 37543}, {2318, 23067}, {3074, 37275}, {3075, 7549}, {3682, 7066}, {4055, 22057}, {4466, 18588}, {5751, 14547}, {6360, 34287}, {7175, 23602}, {7177, 8813}, {8021, 20122}, {8804, 8808}, {13726, 37523}, {15934, 18477}, {16609, 20235}, {18876, 32660}, {22270, 37612}, {23207, 39796}, {26931, 37872}, {37264, 37694}
X(40152) = isogonal conjugate of X(8748)
X(40152) = isotomic conjugate of polar conjugate of X(73)
X(40152) = hodpiece of X(11172)
X(40152) = crossdifference of every pair of points on line X(663)X(3064)
X(40152) = X(i)-isoconjugate of X(j) for these {i,j}: {19, 29}, {92, 2299}
X(40152) = trilinear product X(i)*X(j) for these {i,j}: {48, 307}, {63, 73}
X(40152) = barycentric product X(63)*X(1214)
X(40153) lies on these lines:s {1, 19259}, {2, 6}, {21, 1191}, {31, 2274}, {42, 18185}, {55, 3736}, {56, 58}, {57, 16700}, {63, 16696}, {110, 28479}, {171, 18792}, {213, 4641}, {221, 5323}, {238, 18169}, {292, 28643}, {386, 16374}, {553, 17205}, {595, 17524}, {614, 18165}, {958, 27660}, {1001, 10458}, {1010, 5710}, {1014, 1407}, {1043, 20037}, {1171, 4629}, {1193, 4267}, {1201, 10457}, {1203, 20744}, {1333, 1790}, {1453, 37523}, {1724, 19243}, {1964, 16687}, {1999, 30939}, {2185, 7303}, {2193, 22119}, {2300, 3666}, {2999, 18163}, {3052, 4184}, {3218, 18601}, {3306, 16736}, {3733, 8027}, {3772, 17167}, {3782, 17139}, {4216, 4252}, {4257, 19254}, {4363, 30599}, {4393, 16722}, {4481, 7252}, {4653, 16483}, {4658, 30116}, {5208, 17597}, {5315, 19247}, {5711, 25526}, {7290, 17194}, {7304, 18021}, {9022, 19835}, {9575, 16699}, {10455, 31993}, {13588, 37540}, {16468, 18192}, {16470, 18724}, {16685, 28606}, {16717, 30647}, {16753, 27003}, {17173, 33129}, {17174, 33133}, {17182, 17720}, {17189, 37543}, {17202, 19786}, {17599, 35623}, {19262, 36746}, {19550, 36754}, {20182, 21769}, {32939, 34063}
X(40153) = isogonal conjugate of X(14624)
X(40153) = hodpiece of X(2298)
X(40153) = cevapoint of X(1193) and X(2300)
X(40153) = crosspoint of X(i) and X(j) for these {i,j}: {58, 1178}, {81, 593}, {1014, 1509}
X(40153) = crosssum of X(i) and X(j) for these {i,j}: {10, 1215}, {37, 594}, {210, 1500}
X(40153) = crossdifference of every pair of points on line X(512)X(3700)
X(40153) = trilinear product X(i)*X(j) for these {i,j}: {57, 4267}, {58, 3666}, {81, 1193}, {86, 2300}, {163, 3004}, {593, 2292}, {662, 6371}, {757, 2092}, {849, 1211}, {960, 1412}, {1014, 2269}, {1333, 4357}, {1408, 3687}, {1437, 1848}, {1444, 2354}, {1509, 3725}, {1576, 4509}, {1790, 1829}, {2194, 3674}, {3733, 3882}
X(40154) lies on these lines: {2, 37206}, {7, 3434}, {55, 1292}, {57, 169}, {85, 8817}, {222, 1462}, {226, 15490}, {269, 2191}, {279, 1617}, {354, 14268}, {479, 3660}, {1014, 3598}, {1119, 34855}, {3664, 19604}, {8814, 24471}
X(40154) = isogonal conjugate of X(6600)
X(40154) = hodpiece of X(3939)
X(40155) lies on these lines: {2, 38}, {6, 2109}, {31, 813}, {42, 649}, {43, 660}, {55, 1911}, {192, 39918}, {292, 16515}, {2276, 3252}, {3097, 30663}, {4562, 36817}, {4583, 32925}, {6376, 24421}, {12782, 40098}, {17596, 18787}, {17756, 36906}, {19567, 27853}, {20358, 20456}, {22116, 37596}, {24420, 30963}, {24426, 37678}
X(40155) = isogonal conjugate of X(3253)
X(40155) = hodpiece of X(20332)
X(40156) lies on these lines: {2, 2992}, {16, 184}, {62, 8919}, {186, 34394}, {3480, 5616}, {5063, 40157}, {8739, 14165}, {15412, 35443}
X(40156) = hodpiece of X(13)
X(40157) lies on these lines: {2, 2993}, {15, 184}, {61, 8918}, {186, 34395}, {3479, 5612}, {5063, 40156}, {8740, 14165}, {15412, 35444}
X(40157) = hodpiece of X(14)
X(40158) lies on these lines: {2, 19776}, {4, 8014}, {13, 34296}, {14, 3440}, {17, 8919}, {18, 32461}, {2394, 20578}, {8737, 16080}, {11078, 11121}, {11550, 12816}
X(40158) = hodpiece of X(15)
X(40159) lies on these lines: {2, 19777}, {4, 8015}, {13, 3441}, {14, 34295}, {17, 32460}, {18, 8918}, {2394, 20579}, {8738, 16080}, {11092, 11122}, {11550, 12817}
X(40159) = hodpiece of X(16)
X(40160) lies on these lines: {2, 2995}, {12, 73}, {56, 225}, {65, 15267}, {86, 19607}, {222, 226}, {348, 349}, {1214, 6358}, {1400, 37646}, {5930, 10570}, {19701, 37695}, {25525, 37523}
X(40160) = hodpiece of X(21)
X(40161) lies on these lines: {2, 2335}, {10, 55}, {37, 6358}, {71, 440}, {219, 306}, {272, 32779}, {281, 17776}, {345, 40071}, {2318, 3695}, {3682, 7515}, {25515, 33116}
X(40161) = hodpiece of X(28)
X(40161) = isotomic conjugate of polar conjugate of X(41506)
X(40162) lies on these lines: {2, 2998}, {4, 3978}, {10, 6382}, {76, 3981}, {83, 3224}, {98, 3222}, {226, 18275}, {264, 37892}, {305, 1916}, {670, 21001}, {850, 23610}, {2996, 20023}, {3407, 24733}, {19606, 20965}
X(40162) = hodpiece of X(32)
X(40163) lies on these lines: {2, 1031}, {76, 14370}, {251, 11606}, {262, 8928}, {1916, 8856}, {10159, 33665}, {32085, 37892}
X(40163) = hodpiece of X(39)
X(40164) lies on these lines: {2, 1931}, {75, 8033}, {81, 6650}, {86, 4425}, {333, 27483}, {335, 20362}, {1089, 40033}, {1268, 32780}, {1434, 7249}, {2296, 18757}, {3120, 6628}, {5196, 8049}, {7192, 8029}, {24041, 31632}, {25496, 30598}
X(40164) = hodpiece of X(41)
X(40165) lies on these lines: {2, 1947}, {8, 7049}, {29, 3362}, {333, 18751}, {1948, 2994}, {6521, 34591}, {34234, 37279}
X(40165) = hodpiece of X(48)
X(40166) lies on these lines: {2, 650}, {11, 15914}, {226, 514}, {278, 2401}, {312, 4391}, {497, 885}, {498, 35100}, {513, 1836}, {522, 4847}, {523, 17874}, {652, 4382}, {654, 812}, {666, 31633}, {850, 20896}, {905, 24789}, {918, 36038}, {1088, 24002}, {1211, 1577}, {1479, 11247}, {1734, 32865}, {3126, 3925}, {3900, 4863}, {3914, 23811}, {4036, 15523}, {4077, 21104}, {4106, 5928}, {4554, 31619}, {4791, 29594}, {4823, 21198}, {5432, 11124}, {6545, 23760}, {6923, 8760}, {10947, 11927}, {11393, 18344}, {12647, 14077}, {14298, 23813}, {16732, 21141}, {17420, 30591}, {21132, 23615}, {30613, 33110}, {30713, 35519}
X(40166) = isotomic conjugate of X(31615)
X(40166) = Danneels point of X(693)
X(40166) = hodpiece of X(59)
X(40167) lies on these lines: {2, 19712}, {4, 36304}, {13, 8174}, {14, 39134}, {18, 3489}, {275, 8741}, {3131, 32627}, {5487, 19779}, {11122, 11144}
X(40167) = hodpiece of X(61)
X(40168) lies on these lines: {2, 19713}, {4, 36305}, {13, 39135}, {14, 8175}, {17, 3490}, {275, 8742}, {3132, 32628}, {5488, 19778}, {11121, 11143}
X(40168) = hodpiece of X(62)
X(40169) lies on these lines: {2, 7219}, {4, 1448}, {19, 15259}, {33, 2285}, {204, 612}, {1249, 2345}, {2000, 40015}, {2303, 4183}
X(40169) = hodpiece of X(63)
X(40170) lies on these lines: {2, 15851}, {20, 33893}, {69, 37878}, {122, 23608}, {1032, 11064}, {1105, 3091}, {3523, 3532}, {5273, 9533}, {7396, 34168}, {32831, 34403}
X(40170) = hodpiece of X(64)
X(40171) lies on these lines: {2, 1334}, {87, 8616}, {256, 13097}, {1221, 40025}, {3208, 31008}, {23415, 37677}
X(40171) = hodpiece of X(87)
X(40172) lies on these lines: {1, 1168}, {2, 80}, {42, 663}, {45, 55}, {57, 840}, {200, 6065}, {484, 13589}, {759, 28210}, {1319, 1647}, {1644, 5440}, {1807, 3478}, {2099, 34431}, {3689, 4908}, {3992, 17780}, {5727, 14629}, {15343, 24402}, {21805, 23344}
X(40172) = hodpiece of X(88)
X(40173) lies on these lines: {2, 9514}, {22, 3447}, {32, 14164}, {1993, 35910}, {5012, 9513}, {6328, 36163}
X(40173) = hodpiece of X(523)
X(40174) lies on the cubic K1162 and these lines: {2, 64}, {25, 1249}, {154, 36413}, {614, 1042}, {1297, 10565}, {3079, 3172}, {3424, 7398}, {7386, 17808}, {7392, 20207}, {15246, 15874}, {15589, 40032}
X(40175) lies on the cubic K1162 and these lines: {2, 269}, {25, 7079}, {614, 6554}, {7083, 28070}, {15487, 40124}
X(40176) lies on the cubic K1162 and these lines: {2, 6359}, {204, 612}, {6554, 7386}
X(40177) lies on the cubic K1162 and these lines: {2, 2139}, {25, 800}, {1184, 40124}
X(40178) lies on the cubic K1162 and these lines: {2, 159}, {4, 3162}, {10, 15487}, {76, 1370}, {83, 6997}, {321, 11677}, {459, 33584}, {614, 36907}, {671, 39842}, {2996, 7391}, {5395, 7394}, {7386, 18840}, {7392, 18841}, {7735, 16277}, {18845, 37349}
X(40179) lies on the cubic K1162 and these lines: {2, 3933}, {4, 3162}, {6, 7392}, {25, 1249}, {32, 34608}, {115, 15437}, {216, 1194}, {233, 7736}, {251, 7714}, {376, 1627}, {612, 2345}, {614, 6554}, {631, 1180}, {1184, 5286}, {1196, 5319}, {1285, 7500}, {1370, 5354}, {1560, 8889}, {3618, 40022}, {4000, 15487}, {5368, 34481}, {6353, 9465}, {6392, 11324}, {6995, 30435}, {6997, 34482}, {7408, 18907}, {7499, 37689}, {7766, 37895}, {8267, 32817}, {8877, 36877}, {8878, 16041}, {8879, 14091}, {10299, 38862}, {11433, 15595}, {16045, 39998}, {16949, 32822}, {16989, 37891}, {37439, 37665}, {37669, 40130}
X(40180) lies on the cubic K1162 and these lines: {2, 269}, {388, 612}, {478, 1122}, {614, 1042}, {1427, 15487}, {1435, 3162}
X(40181) lies on the cubic K1162 and these lines: {2, 17742}, {9, 33163}, {10, 15487}, {25, 7079}, {37, 614}, {169, 29667}, {612, 1184}, {1213, 40131}, {1766, 37456}, {2345, 7386}, {3162, 23050}, {3305, 17755}, {4204, 21838}, {16593, 32777}
X(40182) lies on the cubic K1162 and these lines: {2, 14259}, {612, 23051}, {907, 7485}, {1184, 7772}, {3763, 17810}, {7386, 18840}
X(40183) lies on the cubic K1162 and these lines: {2, 6359}, {25, 34}, {612, 10375}, {15487, 36908}
X(40184) lies on the cubic K1162 and these lines: {2, 169}, {19, 614}, {612, 40125}, {2298, 4224}, {2345, 7386}, {4359, 24605}, {5272, 16545}
X(40185) lies on the cubic K1162 and these lines: {2, 2138}, {7386, 40125}, {7494, 34207}, {15487, 18589}, {28419, 34254}
X(40186) lies on the cubic K1162 and these lines: {2, 2139}, {1249, 3162}, {3344, 5304}, {13854, 35968}, {15487, 36908}, {36417, 39020}
X(40187) lies on the cubics K169 and K657, and also on these lines: {2, 3933}, {3, 907}, {64, 159}, {269, 17742}, {1907, 8801}
X(40187) = barycentric product X(i)*X(j) for these {i,j}: {17811, 18840}, {32000, 34817}, {32830, 39951}
X(40187) = barycentric quotient X(i)/X(j) for these {i,j}: {1593, 6995}, {5065, 30435}, {17811, 3618}, {18840, 37874}, {32830, 40022}, {34817, 15740}
X(40187) = {X(907),X(14259)}-harmonic conjugate of X(3)
X(40188) lies on the conic {{A,B,C,X(1),X(2)}}, the cubics K169 and K1062, and on these lines: {1, 159}, {2, 169}, {20, 1219}, {40, 39959}, {46, 291}, {57, 5299}, {69, 17742}, {77, 2172}, {269, 2138}, {278, 7195}, {330, 5088}, {961, 1448}, {985, 3338}, {1280, 3868}, {1973, 3942}, {2224, 16780}, {3333, 39958}, {4222, 36122}, {14953, 39747}
X(40188) = isogonal conjugate of X(17742)
X(40188) = X(i)-cross conjugate of X(j) for these (i,j): {25, 269}, {1565, 1019}, {16502, 1}
X(40188) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17742}, {2, 12329}, {6, 10327}, {9, 8270}, {55, 28739}, {63, 23050}, {78, 20613}, {100, 2509}, {1801, 1826}, {4557, 17498}, {7123, 11677}
X(40188) = cevapoint of X(649) and X(3942)
X(40188) = barycentric product X(i)*X(j) for these {i,j}: {1, 39732}, {81, 36907}
X(40188) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 10327}, {6, 17742}, {25, 23050}, {31, 12329}, {56, 8270}, {57, 28739}, {608, 20613}, {614, 11677}, {649, 2509}, {1019, 17498}, {1437, 1801}, {7289, 28409}, {16502, 15487}, {36907, 321}, {39732, 75}
X(40188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 18725, 18727}, {7291, 17170, 18596}
X(40189) lies on the cubic K169 and these lines: {2, 14259}, {6, 3917}, {20, 13575}, {22, 907}, {1350, 4175}, {7392, 18840}
X(40189) = isogonal conjugate of X(40222)
X(40189) = barycentric product X(i)*X(j) for these {i,j}: {18840, 37485}, {39951, 40123}
X(40189) = barycentric quotient X(i)/X(j) for these {i,j}: {37485, 3618}, {40123, 40022}
X(40190) lies on the cubics K041, K055, and K169, and on lines {6, 20}, {1285, 27082}, {18841, 37874}
X(40190) = X(33580)-cross conjugate of X(6995)
X(40190) = X(i)-isoconjugate of X(j) for these (i,j): {1496, 18840}, {17811, 23051}
X(40190) = barycentric product X(i)*X(j) for these {i,j}: {6995, 15740}, {30435, 37874}
X(40190) = barycentric quotient X(i)/X(j) for these {i,j}: {3618, 32830}, {6995, 32000}, {30435, 17811}, {33580, 33537}
X(40191) lies on the cubic K1162 and these lines: {2, 14259}, {40125, 40179}
X(40191) = X(1184)-cross conjugate of X(40179)
X(40191) = barycentric product X(39978)*X(40179)
X(40191) = barycentric quotient X(1184)/X(40182)
X(40192) lies on the cubic K1162 and these lines: {2, 40190}, {612, 40175}, {1184, 40174}, {7386, 37665}, {40177, 40178}
X(40192) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 40174}, {2155, 18840}
X(40192) = X(2)-Ceva conjugate of X(40174)
X(40193) lies on the cubic K1162 and these lines: {2, 17742}, {612, 23051}, {614, 40125}, {1435, 3162}, {2191, 37538}, {4000, 15487}
X(40193) = X(1184)-cross conjugate of X(614)
X(40193) = barycentric quotient X(1184)/X(40181)
X(40194) lies on the cubic K1162 and these lines: {612, 39951}, {1184, 40175}, {40174, 40184}, {40178, 40183}
X(40194) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 40175}, {1106, 23051}
X(40194) = X(2)-Ceva conjugate of X(40175)
X(40195) lies on the cubic K1162 and these lines: {2, 40190}, {25, 40182}, {40124, 40125}, {40180, 40181}
X(40195) = X(1184)-cross conjugate of X(40124)
X(40196) lies on these lines: {20, 154}, {30, 1351}, {69, 15311}, {1885, 15740}, {1993, 5059}, {2777, 35513}, {3146, 11433}, {3543, 17810}, {3619, 4550}, {5890, 13598}, {7691, 33522}, {10304, 20725}, {10574, 15887}, {12233, 31371}, {16251, 20477}, {16386, 35260}
Points associated with Vu parallels conics: X(40197)-X(40211)
This preamble is based on notes received from Vu Thanh Tung, October 31, 2020.
In the plane of a triangle ABC, let P = p:q:r and U = u:v:w (barycentrics) be points. Let A1 be the point on BC such that PA1 is parallel to AU, and define B1 and C1 cyclically. Let A2 be the point on BC such that PA2 is parallel to AP, and define B2 and C2 cyclically. The six points A1, A2, B1, B2, C1, C2 lies on a conic, here named the Vu parallels conic of P and U. See Vu Parallels Conic.
Peter Moses (October 31, 2020) found that V(P,U) = (p*u + r*u + p*v)*(p*u + q*u + p*w)*(p^3*r^2*u^3*v^2 - p^2*q*r^2*u^3*v^2 - 4*p*q^2*r^2*u^3*v^2 - 2*q^3*r^2*u^3*v^2 - 2*p*q*r^3*u^3*v^2 - 2*q^2*r^3*u^3*v^2 - 6*p^2*q*r^2*u^2*v^3 - 10*p*q^2*r^2*u^2*v^3 - 4*q^3*r^2*u^2*v^3 - 5*p^2*r^3*u^2*v^3 - 11*p*q*r^3*u^2*v^3 - 6*q^2*r^3*u^2*v^3 - 2*p*r^4*u^2*v^3 - 2*q*r^4*u^2*v^3 - 2*p^2*q*r^2*u*v^4 - 3*p*q^2*r^2*u*v^4 - q^3*r^2*u*v^4 - 2*p^2*r^3*u*v^4 - 3*p*q*r^3*u*v^4 - q^2*r^3*u*v^4 - 2*p^3*q*r*u^3*v*w - 3*p^2*q^2*r*u^3*v*w - 2*p*q^3*r*u^3*v*w - 3*p^2*q*r^2*u^3*v*w - 8*p*q^2*r^2*u^3*v*w - 4*q^3*r^2*u^3*v*w - 2*p*q*r^3*u^3*v*w - 4*q^2*r^3*u^3*v*w - 3*p^3*q*r*u^2*v^2*w - 8*p^2*q^2*r*u^2*v^2*w - 10*p*q^3*r*u^2*v^2*w - 2*q^4*r*u^2*v^2*w - p^3*r^2*u^2*v^2*w - 15*p^2*q*r^2*u^2*v^2*w - 32*p*q^2*r^2*u^2*v^2*w - 14*q^3*r^2*u^2*v^2*w - 6*p^2*r^3*u^2*v^2*w - 21*p*q*r^3*u^2*v^2*w - 16*q^2*r^3*u^2*v^2*w - 2*p*r^4*u^2*v^2*w - 4*q*r^4*u^2*v^2*w - 2*p^3*q*r*u*v^3*w - 10*p^2*q^2*r*u*v^3*w - 14*p*q^3*r*u*v^3*w - 3*q^4*r*u*v^3*w - 2*p^3*r^2*u*v^3*w - 21*p^2*q*r^2*u*v^3*w - 37*p*q^2*r^2*u*v^3*w - 13*q^3*r^2*u*v^3*w - 11*p^2*r^3*u*v^3*w - 26*p*q*r^3*u*v^3*w - 13*q^2*r^3*u*v^3*w - 3*p*r^4*u*v^3*w - 3*q*r^4*u*v^3*w - 2*p^2*q^2*r*v^4*w - 3*p*q^3*r*v^4*w - 4*p^2*q*r^2*v^4*w - 6*p*q^2*r^2*v^4*w - 2*p^2*r^3*v^4*w - 3*p*q*r^3*v^4*w + p^3*q^2*u^3*w^2 - p^2*q^2*r*u^3*w^2 - 2*p*q^3*r*u^3*w^2 - 4*p*q^2*r^2*u^3*w^2 - 2*q^3*r^2*u^3*w^2 - 2*q^2*r^3*u^3*w^2 - p^3*q^2*u^2*v*w^2 - 6*p^2*q^3*u^2*v*w^2 - 2*p*q^4*u^2*v*w^2 - 3*p^3*q*r*u^2*v*w^2 - 15*p^2*q^2*r*u^2*v*w^2 - 21*p*q^3*r*u^2*v*w^2 - 4*q^4*r*u^2*v*w^2 - 8*p^2*q*r^2*u^2*v*w^2 - 32*p*q^2*r^2*u^2*v*w^2 - 16*q^3*r^2*u^2*v*w^2 - 10*p*q*r^3*u^2*v*w^2 - 14*q^2*r^3*u^2*v*w^2 - 2*q*r^4*u^2*v*w^2 - 4*p^3*q^2*u*v^2*w^2 - 10*p^2*q^3*u*v^2*w^2 - 3*p*q^4*u*v^2*w^2 - 8*p^3*q*r*u*v^2*w^2 - 32*p^2*q^2*r*u*v^2*w^2 - 37*p*q^3*r*u*v^2*w^2 - 6*q^4*r*u*v^2*w^2 - 4*p^3*r^2*u*v^2*w^2 - 32*p^2*q*r^2*u*v^2*w^2 - 68*p*q^2*r^2*u*v^2*w^2 - 24*q^3*r^2*u*v^2*w^2 - 10*p^2*r^3*u*v^2*w^2 - 37*p*q*r^3*u*v^2*w^2 - 24*q^2*r^3*u*v^2*w^2 - 3*p*r^4*u*v^2*w^2 - 6*q*r^4*u*v^2*w^2 - 2*p^3*q^2*v^3*w^2 - 4*p^2*q^3*v^3*w^2 - p*q^4*v^3*w^2 - 4*p^3*q*r*v^3*w^2 - 14*p^2*q^2*r*v^3*w^2 - 13*p*q^3*r*v^3*w^2 - 2*p^3*r^2*v^3*w^2 - 16*p^2*q*r^2*v^3*w^2 - 24*p*q^2*r^2*v^3*w^2 - 6*p^2*r^3*v^3*w^2 - 13*p*q*r^3*v^3*w^2 - p*r^4*v^3*w^2 - 5*p^2*q^3*u^2*w^3 - 2*p*q^4*u^2*w^3 - 6*p^2*q^2*r*u^2*w^3 - 11*p*q^3*r*u^2*w^3 - 2*q^4*r*u^2*w^3 - 10*p*q^2*r^2*u^2*w^3 - 6*q^3*r^2*u^2*w^3 - 4*q^2*r^3*u^2*w^3 - 2*p^3*q^2*u*v*w^3 - 11*p^2*q^3*u*v*w^3 - 3*p*q^4*u*v*w^3 - 2*p^3*q*r*u*v*w^3 - 21*p^2*q^2*r*u*v*w^3 - 26*p*q^3*r*u*v*w^3 - 3*q^4*r*u*v*w^3 - 10*p^2*q*r^2*u*v*w^3 - 37*p*q^2*r^2*u*v*w^3 - 13*q^3*r^2*u*v*w^3 - 14*p*q*r^3*u*v*w^3 - 13*q^2*r^3*u*v*w^3 - 3*q*r^4*u*v*w^3 - 2*p^3*q^2*v^2*w^3 - 6*p^2*q^3*v^2*w^3 - p*q^4*v^2*w^3 - 4*p^3*q*r*v^2*w^3 - 16*p^2*q^2*r*v^2*w^3 - 13*p*q^3*r*v^2*w^3 - 2*p^3*r^2*v^2*w^3 - 14*p^2*q*r^2*v^2*w^3 - 24*p*q^2*r^2*v^2*w^3 - 4*p^2*r^3*v^2*w^3 - 13*p*q*r^3*v^2*w^3 - p*r^4*v^2*w^3 - 2*p^2*q^3*u*w^4 - 2*p^2*q^2*r*u*w^4 - 3*p*q^3*r*u*w^4 - 3*p*q^2*r^2*u*w^4 - q^3*r^2*u*w^4 - q^2*r^3*u*w^4 - 2*p^2*q^3*v*w^4 - 4*p^2*q^2*r*v*w^4 - 3*p*q^3*r*v*w^4 - 2*p^2*q*r^2*v*w^4 - 6*p*q^2*r^2*v*w^4 - 3*p*q*r^3*v*w^4) : :
and T(P,U) = (p*u + r*u + p*v)*(p*u + q*u + p*w)*(3*p^2*q*r*u^3*v + 5*p*q^2*r*u^3*v + 2*q^3*r*u^3*v + 2*p*q*r^2*u^3*v + 2*q^2*r^2*u^3*v + p^3*r*u^2*v^2 + 10*p^2*q*r*u^2*v^2 + 14*p*q^2*r*u^2*v^2 + 5*q^3*r*u^2*v^2 + 4*p^2*r^2*u^2*v^2 + 11*p*q*r^2*u^2*v^2 + 7*q^2*r^2*u^2*v^2 + 2*p*r^3*u^2*v^2 + 2*q*r^3*u^2*v^2 + p^3*r*u*v^3 + 8*p^2*q*r*u*v^3 + 10*p*q^2*r*u*v^3 + 3*q^3*r*u*v^3 + 5*p^2*r^2*u*v^3 + 10*p*q*r^2*u*v^3 + 5*q^2*r^2*u*v^3 + 2*p*r^3*u*v^3 + 2*q*r^3*u*v^3 + p^2*q*r*v^4 + p*q^2*r*v^4 + p^2*r^2*v^4 + p*q*r^2*v^4 + p^2*q^2*u^3*w + p*q^3*u^3*w + 4*p*q^2*r*u^3*w + 2*q^3*r*u^3*w + 2*q^2*r^2*u^3*w + 3*p^3*q*u^2*v*w + 10*p^2*q^2*u^2*v*w + 8*p*q^3*u^2*v*w + q^4*u^2*v*w + 12*p^2*q*r*u^2*v*w + 28*p*q^2*r*u^2*v*w + 10*q^3*r*u^2*v*w + 10*p*q*r^2*u^2*v*w + 11*q^2*r^2*u^2*v*w + 2*q*r^3*u^2*v*w + 5*p^3*q*u*v^2*w + 14*p^2*q^2*u*v^2*w + 10*p*q^3*u*v^2*w + q^4*u*v^2*w + 4*p^3*r*u*v^2*w + 28*p^2*q*r*u*v^2*w + 40*p*q^2*r*u*v^2*w + 10*q^3*r*u*v^2*w + 10*p^2*r^2*u*v^2*w + 28*p*q*r^2*u*v^2*w + 14*q^2*r^2*u*v^2*w + 4*p*r^3*u*v^2*w + 5*q*r^3*u*v^2*w + 2*p^3*q*v^3*w + 5*p^2*q^2*v^3*w + 3*p*q^3*v^3*w + 2*p^3*r*v^3*w + 10*p^2*q*r*v^3*w + 10*p*q^2*r*v^3*w + 5*p^2*r^2*v^3*w + 8*p*q*r^2*v^3*w + p*r^3*v^3*w + 4*p^2*q^2*u^2*w^2 + 5*p*q^3*u^2*w^2 + q^4*u^2*w^2 + 10*p*q^2*r*u^2*w^2 + 5*q^3*r*u^2*w^2 + 4*q^2*r^2*u^2*w^2 + 2*p^3*q*u*v*w^2 + 11*p^2*q^2*u*v*w^2 + 10*p*q^3*u*v*w^2 + q^4*u*v*w^2 + 10*p^2*q*r*u*v*w^2 + 28*p*q^2*r*u*v*w^2 + 8*q^3*r*u*v*w^2 + 12*p*q*r^2*u*v*w^2 + 10*q^2*r^2*u*v*w^2 + 3*q*r^3*u*v*w^2 + 2*p^3*q*v^2*w^2 + 7*p^2*q^2*v^2*w^2 + 5*p*q^3*v^2*w^2 + 2*p^3*r*v^2*w^2 + 11*p^2*q*r*v^2*w^2 + 14*p*q^2*r*v^2*w^2 + 4*p^2*r^2*v^2*w^2 + 10*p*q*r^2*v^2*w^2 + p*r^3*v^2*w^2 + 2*p^2*q^2*u*w^3 + 2*p*q^3*u*w^3 + 4*p*q^2*r*u*w^3 + q^3*r*u*w^3 + q^2*r^2*u*w^3 + 2*p^2*q^2*v*w^3 + 2*p*q^3*v*w^3 + 2*p^2*q*r*v*w^3 + 5*p*q^2*r*v*w^3 + 3*p*q*r^2*v*w^3)*(p^2*r^2*u^3*v + 4*p*q*r^2*u^3*v + 2*q^2*r^2*u^3*v + p*r^3*u^3*v + 2*q*r^3*u^3*v + 4*p^2*r^2*u^2*v^2 + 10*p*q*r^2*u^2*v^2 + 4*q^2*r^2*u^2*v^2 + 5*p*r^3*u^2*v^2 + 5*q*r^3*u^2*v^2 + r^4*u^2*v^2 + 2*p^2*r^2*u*v^3 + 4*p*q*r^2*u*v^3 + q^2*r^2*u*v^3 + 2*p*r^3*u*v^3 + q*r^3*u*v^3 + 3*p^2*q*r*u^3*w + 2*p*q^2*r*u^3*w + 5*p*q*r^2*u^3*w + 2*q^2*r^2*u^3*w + 2*q*r^3*u^3*w + 3*p^3*r*u^2*v*w + 12*p^2*q*r*u^2*v*w + 10*p*q^2*r*u^2*v*w + 2*q^3*r*u^2*v*w + 10*p^2*r^2*u^2*v*w + 28*p*q*r^2*u^2*v*w + 11*q^2*r^2*u^2*v*w + 8*p*r^3*u^2*v*w + 10*q*r^3*u^2*v*w + r^4*u^2*v*w + 2*p^3*r*u*v^2*w + 10*p^2*q*r*u*v^2*w + 12*p*q^2*r*u*v^2*w + 3*q^3*r*u*v^2*w + 11*p^2*r^2*u*v^2*w + 28*p*q*r^2*u*v^2*w + 10*q^2*r^2*u*v^2*w + 10*p*r^3*u*v^2*w + 8*q*r^3*u*v^2*w + r^4*u*v^2*w + 2*p^2*q*r*v^3*w + 3*p*q^2*r*v^3*w + 2*p^2*r^2*v^3*w + 5*p*q*r^2*v^3*w + 2*p*r^3*v^3*w + p^3*q*u^2*w^2 + 4*p^2*q^2*u^2*w^2 + 2*p*q^3*u^2*w^2 + 10*p^2*q*r*u^2*w^2 + 11*p*q^2*r*u^2*w^2 + 2*q^3*r*u^2*w^2 + 14*p*q*r^2*u^2*w^2 + 7*q^2*r^2*u^2*w^2 + 5*q*r^3*u^2*w^2 + 4*p^3*q*u*v*w^2 + 10*p^2*q^2*u*v*w^2 + 4*p*q^3*u*v*w^2 + 5*p^3*r*u*v*w^2 + 28*p^2*q*r*u*v*w^2 + 28*p*q^2*r*u*v*w^2 + 5*q^3*r*u*v*w^2 + 14*p^2*r^2*u*v*w^2 + 40*p*q*r^2*u*v*w^2 + 14*q^2*r^2*u*v*w^2 + 10*p*r^3*u*v*w^2 + 10*q*r^3*u*v*w^2 + r^4*u*v*w^2 + 2*p^3*q*v^2*w^2 + 4*p^2*q^2*v^2*w^2 + p*q^3*v^2*w^2 + 2*p^3*r*v^2*w^2 + 11*p^2*q*r*v^2*w^2 + 10*p*q^2*r*v^2*w^2 + 7*p^2*r^2*v^2*w^2 + 14*p*q*r^2*v^2*w^2 + 5*p*r^3*v^2*w^2 + p^3*q*u*w^3 + 5*p^2*q^2*u*w^3 + 2*p*q^3*u*w^3 + 8*p^2*q*r*u*w^3 + 10*p*q^2*r*u*w^3 + 2*q^3*r*u*w^3 + 10*p*q*r^2*u*w^3 + 5*q^2*r^2*u*w^3 + 3*q*r^3*u*w^3 + 2*p^3*q*v*w^3 + 5*p^2*q^2*v*w^3 + p*q^3*v*w^3 + 2*p^3*r*v*w^3 + 10*p^2*q*r*v*w^3 + 8*p*q^2*r*v*w^3 + 5*p^2*r^2*v*w^3 + 10*p*q*r^2*v*w^3 + 3*p*r^3*v*w^3 + p^2*q^2*w^4 + p^2*q*r*w^4 + p*q^2*r*w^4 + p*q*r^2*w^4) : :
Let V(P,U) denote the center, and T(P,U) the perspector, of the Vu parallels conic of P and U. The appearance of (i,j,k) in the following list means that V(X(i),X(j)) = X(k): (1,2,40197), (1,6,40199), (2,3,40201), (2,4,40203), (2,6,40305), (2,6,40205), (3,4,14767), (3,5,6709), (3,6,40209)
The appearance of (i,j,k) in the following list means that T(X(i),X(j)) = X(k): (1,2,40198), (1,6,40200), (2,3,40202), (2,4,40204), (2,6,40206), (3,4,40207), (3,5,40208), (3,6,40210)
Barycentrics (2*a + b)*(2*a + c)*(5*a^3*b^2 + 23*a^2*b^3 + 6*a*b^4 + 14*a^3*b*c + 67*a^2*b^2*c + 79*a*b^3*c + 10*b^4*c + 5*a^3*c^2 + 67*a^2*b*c^2 + 154*a*b^2*c^2 + 50*b^3*c^2 + 23*a^2*c^3 + 79*a*b*c^3 + 50*b^2*c^3 + 6*a*c^4 + 10*b*c^4) : :
Barycentrics (2*a + b)*(2*a + c)*(14*a^3*b + 56*a^2*b^2 + 46*a*b^3 + 4*b^4 + 10*a^3*c + 95*a^2*b*c + 173*a*b^2*c + 46*b^3*c + 29*a^2*c^2 + 95*a*b*c^2 + 56*b^2*c^2 + 10*a*c^3 + 14*b*c^3)*(10*a^3*b + 29*a^2*b^2 + 10*a*b^3 + 14*a^3*c + 95*a^2*b*c + 95*a*b^2*c + 14*b^3*c + 56*a^2*c^2 + 173*a*b*c^2 + 56*b^2*c^2 + 46*a*c^3 + 46*b*c^3 + 4*c^4) : :
Barycentrics a*(a^2 + b^2 + a*c)*(a^2 + a*b + c^2)*(a^8*b^2 - a^7*b^3 - 4*a^6*b^4 - 8*a^5*b^5 - 10*a^4*b^6 - 6*a^3*b^7 - 3*a^2*b^8 - a*b^9 - 2*a^8*b*c - 3*a^7*b^2*c - 7*a^6*b^3*c - 15*a^5*b^4*c - 23*a^4*b^5*c - 20*a^3*b^6*c - 17*a^2*b^7*c - 6*a*b^8*c - 3*b^9*c + a^8*c^2 - 3*a^7*b*c^2 - 10*a^6*b^2*c^2 - 25*a^5*b^3*c^2 - 42*a^4*b^4*c^2 - 47*a^3*b^5*c^2 - 42*a^2*b^6*c^2 - 21*a*b^7*c^2 - 7*b^8*c^2 - a^7*c^3 - 7*a^6*b*c^3 - 25*a^5*b^2*c^3 - 50*a^4*b^3*c^3 - 63*a^3*b^4*c^3 - 67*a^2*b^5*c^3 - 35*a*b^6*c^3 - 16*b^7*c^3 - 4*a^6*c^4 - 15*a^5*b*c^4 - 42*a^4*b^2*c^4 - 63*a^3*b^3*c^4 - 78*a^2*b^4*c^4 - 49*a*b^5*c^4 - 25*b^6*c^4 - 8*a^5*c^5 - 23*a^4*b*c^5 - 47*a^3*b^2*c^5 - 67*a^2*b^3*c^5 - 49*a*b^4*c^5 - 26*b^5*c^5 - 10*a^4*c^6 - 20*a^3*b*c^6 - 42*a^2*b^2*c^6 - 35*a*b^3*c^6 - 25*b^4*c^6 - 6*a^3*c^7 - 17*a^2*b*c^7 - 21*a*b^2*c^7 - 16*b^3*c^7 - 3*a^2*c^8 - 6*a*b*c^8 - 7*b^2*c^8 - a*c^9 - 3*b*c^9) : :
Barycentrics a*(a^2 + b^2 + a*c)*(a^2 + a*b + c^2)*(3*a^7*b + 6*a^6*b^2 + 12*a^5*b^3 + 15*a^4*b^4 + 13*a^3*b^5 + 10*a^2*b^6 + 4*a*b^7 + b^8 + a^7*c + 6*a^6*b*c + 16*a^5*b^2*c + 24*a^4*b^3*c + 27*a^3*b^4*c + 22*a^2*b^5*c + 12*a*b^6*c + 4*b^7*c + 4*a^6*c^2 + 14*a^5*b*c^2 + 34*a^4*b^2*c^2 + 40*a^3*b^3*c^2 + 44*a^2*b^4*c^2 + 22*a*b^5*c^2 + 10*b^6*c^2 + 6*a^5*c^3 + 17*a^4*b*c^3 + 33*a^3*b^2*c^3 + 40*a^2*b^3*c^3 + 27*a*b^4*c^3 + 13*b^5*c^3 + 10*a^4*c^4 + 17*a^3*b*c^4 + 34*a^2*b^2*c^4 + 24*a*b^3*c^4 + 15*b^4*c^4 + 6*a^3*c^5 + 14*a^2*b*c^5 + 16*a*b^2*c^5 + 12*b^3*c^5 + 4*a^2*c^6 + 6*a*b*c^6 + 6*b^2*c^6 + a*c^7 + 3*b*c^7)*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 10*a^4*b^4 + 6*a^3*b^5 + 4*a^2*b^6 + a*b^7 + 3*a^7*c + 6*a^6*b*c + 14*a^5*b^2*c + 17*a^4*b^3*c + 17*a^3*b^4*c + 14*a^2*b^5*c + 6*a*b^6*c + 3*b^7*c + 6*a^6*c^2 + 16*a^5*b*c^2 + 34*a^4*b^2*c^2 + 33*a^3*b^3*c^2 + 34*a^2*b^4*c^2 + 16*a*b^5*c^2 + 6*b^6*c^2 + 12*a^5*c^3 + 24*a^4*b*c^3 + 40*a^3*b^2*c^3 + 40*a^2*b^3*c^3 + 24*a*b^4*c^3 + 12*b^5*c^3 + 15*a^4*c^4 + 27*a^3*b*c^4 + 44*a^2*b^2*c^4 + 27*a*b^3*c^4 + 15*b^4*c^4 + 13*a^3*c^5 + 22*a^2*b*c^5 + 22*a*b^2*c^5 + 13*b^3*c^5 + 10*a^2*c^6 + 12*a*b*c^6 + 10*b^2*c^6 + 4*a*c^7 + 4*b*c^7 + c^8) : :
Barycentrics (2*a^4 - 3*a^2*b^2 + b^4 - 2*a^2*c^2 - b^2*c^2)*(-2*a^4 + 2*a^2*b^2 + 3*a^2*c^2 + b^2*c^2 - c^4)*(-5*a^16*b^4 + 48*a^14*b^6 - 171*a^12*b^8 + 310*a^10*b^10 - 315*a^8*b^12 + 180*a^6*b^14 - 53*a^4*b^16 + 6*a^2*b^18 - 14*a^16*b^2*c^2 + 114*a^14*b^4*c^2 - 305*a^12*b^6*c^2 + 273*a^10*b^8*c^2 + 178*a^8*b^10*c^2 - 548*a^6*b^12*c^2 + 419*a^4*b^14*c^2 - 127*a^2*b^16*c^2 + 10*b^18*c^2 - 5*a^16*c^4 + 114*a^14*b^2*c^4 - 380*a^12*b^4*c^4 + 257*a^10*b^6*c^4 + 171*a^8*b^8*c^4 + 240*a^6*b^10*c^4 - 870*a^4*b^12*c^4 + 573*a^2*b^14*c^4 - 100*b^16*c^4 + 48*a^14*c^6 - 305*a^12*b^2*c^6 + 257*a^10*b^4*c^6 - 68*a^8*b^6*c^6 + 128*a^6*b^8*c^6 + 557*a^4*b^10*c^6 - 1017*a^2*b^12*c^6 + 400*b^14*c^6 - 171*a^12*c^8 + 273*a^10*b^2*c^8 + 171*a^8*b^4*c^8 + 128*a^6*b^6*c^8 - 106*a^4*b^8*c^8 + 565*a^2*b^10*c^8 - 860*b^12*c^8 + 310*a^10*c^10 + 178*a^8*b^2*c^10 + 240*a^6*b^4*c^10 + 557*a^4*b^6*c^10 + 565*a^2*b^8*c^10 + 1100*b^10*c^10 - 315*a^8*c^12 - 548*a^6*b^2*c^12 - 870*a^4*b^4*c^12 - 1017*a^2*b^6*c^12 - 860*b^8*c^12 + 180*a^6*c^14 + 419*a^4*b^2*c^14 + 573*a^2*b^4*c^14 + 400*b^6*c^14 - 53*a^4*c^16 - 127*a^2*b^2*c^16 - 100*b^4*c^16 + 6*a^2*c^18 + 10*b^2*c^18) : :
Barycentrics (2*a^4-(3*b^2+2*c^2)*a^2+(b^2-c^2)*b^2)*(2*a^4-(2*b^2+3*c^2)*a^2-(b^2-c^2)*c^2)*(2*(7*b^2+5*c^2)*a^14-(112*b^4+143*b^2*c^2+69*c^4)*a^12+3*(118*b^6+62*c^6+(149*b^2+115*c^2)*b^2*c^2)*a^10-2*(290*b^8+127*c^8+(182*b^4+133*b^2*c^2+108*c^4)*b^2*c^2)*a^8+2*(b^2-c^2)*(265*b^8-93*c^8+(79*b^4+84*b^2*c^2+15*c^4)*b^2*c^2)*a^6-(b^2-c^2)^2*(264*b^8+69*c^8-(237*b^4+217*b^2*c^2+207*c^4)*b^2*c^2)*a^4+(62*b^8-10*c^8-(219*b^4+78*b^2*c^2-113*c^4)*b^2*c^2)*(b^2-c^2)^3*a^2-2*(b^2-c^2)^5*(2*b^4-21*b^2*c^2+7*c^4)*b^2)*(2*(5*b^2+7*c^2)*a^14-(69*b^4+143*b^2*c^2+112*c^4)*a^12+3*(62*b^6+118*c^6+(115*b^2+149*c^2)*b^2*c^2)*a^10-2*(127*b^8+290*c^8+(108*b^4+133*b^2*c^2+182*c^4)*b^2*c^2)*a^8+2*(b^2-c^2)*(93*b^8-265*c^8-(15*b^4+84*b^2*c^2+79*c^4)*b^2*c^2)*a^6-(b^2-c^2)^2*(69*b^8+264*c^8-(207*b^4+217*b^2*c^2+237*c^4)*b^2*c^2)*a^4+(10*b^8-62*c^8-(113*b^4-78*b^2*c^2-219*c^4)*b^2*c^2)*(b^2-c^2)^3*a^2+2*(b^2-c^2)^5*(7*b^4-21*b^2*c^2+2*c^4)*c^2) : :
Barycentrics (a^2 + 3*b^2 - c^2)*(a^2 - b^2 + 3*c^2)* (12*a^12 - 27*a^10*b^2 - 27*a^8*b^4 + 74*a^6*b^6 - 18*a^4*b^8 - 15*a^2*b^10 + b^12 - 27*a^10*c^2 + 18*a^8*b^2*c^2 + 46*a^6*b^4*c^2 - 44*a^4*b^6*c^2 + 5*a^2*b^8*c^2 + 2*b^10*c^2 - 27*a^8*c^4 + 46*a^6*b^2*c^4 + 124*a^4*b^4*c^4 + 10*a^2*b^6*c^4 - 17*b^8*c^4 + 74*a^6*c^6 - 44*a^4*b^2*c^6 + 10*a^2*b^4*c^6 + 28*b^6*c^6 - 18*a^4*c^8 + 5*a^2*b^2*c^8 - 17*b^4*c^8 - 15*a^2*c^10 + 2*b^2*c^10 + c^12) : :
Barycentrics (a^2 + 3*b^2 - c^2)*(a^2 - b^2 + 3*c^2)*(12*a^12 - 29*a^10*b^2 - 28*a^8*b^4 + 90*a^6*b^6 - 28*a^4*b^8 - 29*a^2*b^10 + 12*b^12 - 25*a^10*c^2 + 5*a^8*b^2*c^2 + 20*a^6*b^4*c^2 + 20*a^4*b^6*c^2 + 5*a^2*b^8*c^2 - 25*b^10*c^2 - 13*a^8*c^4 + 68*a^6*b^2*c^4 + 86*a^4*b^4*c^4 + 68*a^2*b^6*c^4 - 13*b^8*c^4 + 62*a^6*c^6 - 40*a^4*b^2*c^6 - 40*a^2*b^4*c^6 + 62*b^6*c^6 - 38*a^4*c^8 + a^2*b^2*c^8 - 38*b^4*c^8 - 5*a^2*c^10 - 5*b^2*c^10 + 7*c^12)*(12*a^12 - 25*a^10*b^2 - 13*a^8*b^4 + 62*a^6*b^6 - 38*a^4*b^8 - 5*a^2*b^10 + 7*b^12 - 29*a^10*c^2 + 5*a^8*b^2*c^2 + 68*a^6*b^4*c^2 - 40*a^4*b^6*c^2 + a^2*b^8*c^2 - 5*b^10*c^2 - 28*a^8*c^4 + 20*a^6*b^2*c^4 + 86*a^4*b^4*c^4 - 40*a^2*b^6*c^4 - 38*b^8*c^4 + 90*a^6*c^6 + 20*a^4*b^2*c^6 + 68*a^2*b^4*c^6 + 62*b^6*c^6 - 28*a^4*c^8 + 5*a^2*b^2*c^8 - 13*b^4*c^8 - 29*a^2*c^10 - 25*b^2*c^10 + 12*c^12) : :
Barycentrics (2*a^2 + b^2)*(2*a^2 + c^2)*(5*a^6*b^4 + 23*a^4*b^6 + 6*a^2*b^8 + 14*a^6*b^2*c^2 + 67*a^4*b^4*c^2 + 79*a^2*b^6*c^2 + 10*b^8*c^2 + 5*a^6*c^4 + 67*a^4*b^2*c^4 + 154*a^2*b^4*c^4 + 50*b^6*c^4 + 23*a^4*c^6 + 79*a^2*b^2*c^6 + 50*b^4*c^6 + 6*a^2*c^8 + 10*b^2*c^8) : :
Barycentrics (2*a^2 + b^2)*(2*a^2 + c^2)*(14*a^6*b^2 + 56*a^4*b^4 + 46*a^2*b^6 + 4*b^8 + 10*a^6*c^2 + 95*a^4*b^2*c^2 + 173*a^2*b^4*c^2 + 46*b^6*c^2 + 29*a^4*c^4 + 95*a^2*b^2*c^4 + 56*b^4*c^4 + 10*a^2*c^6 + 14*b^2*c^6)*(10*a^6*b^2 + 29*a^4*b^4 + 10*a^2*b^6 + 14*a^6*c^2 + 95*a^4*b^2*c^2 + 95*a^2*b^4*c^2 + 14*b^6*c^2 + 56*a^4*c^4 + 173*a^2*b^2*c^4 + 56*b^4*c^4 + 46*a^2*c^6 + 46*b^2*c^6 + 4*c^8) : :
Barycentrics (-3*a^6*b^2 + 7*a^4*b^4 - 5*a^2*b^6 + b^8 - a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 5*b^6*c^2 + 2*a^4*c^4 + 3*a^2*b^2*c^4 + 7*b^4*c^4 - a^2*c^6 - 3*b^2*c^6)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + 3*a^6*c^2 - 3*a^4*b^2*c^2 - 3*a^2*b^4*c^2 + 3*b^6*c^2 - 7*a^4*c^4 - 3*a^2*b^2*c^4 - 7*b^4*c^4 + 5*a^2*c^6 + 5*b^2*c^6 - c^8) : :
The center of the Vu parallels conic of X(3) and X(5) is X(14767).
The center of the Vu parallels conic of X(3) and X(5) is X(6709).
U-Hodpieces: X(40212)-X(40218)
This preamble is based on notes received from Vu Thanh Tung, November 1, 2020.
The definition of hodpiece in the preamble just before X(40137) generalizes as follows. Let P be a point, not on a sideline of ABC, and let DEF be the cevian triangle of P. Let U = u:v:w be a point. The P-reciprocal conjugate of U (defined as u/p : v/q : w/r in the Glossary of ETC), of the line EF is a conic. Let A' be the center of the conic, and define B' and C' cyclically. Then the lines AA', BB', CC' concur in the point
u / (p*(-u/p + v/q + w/r)) : v / (q*(u/p - v/q + w/r)) : w / (r*(u/p + v/q - w/r)),
here named the U-hodpiece of P, so that the hodpiece of P is the X(6)-hodpiece of P.
X(40212) lies on these lines: {1, 9786}, {2, 7}, {40, 196}, {84, 5928}, {108, 7070}, {198, 223}, {278, 2270}, {610, 34032}, {934, 34499}, {1020, 1763}, {1419, 7125}, {1422, 34371}, {1435, 2183}, {1490, 3182}, {1706, 6358}, {1766, 1767}, {3074, 3361}, {3342, 7078}, {5909, 38290}, {7183, 33066}, {9121, 15498}, {19366, 37993}, {22464, 39592}
X(40212) = X(i)-Ceva conjugate of X(j) for these (i,j): {329, 223}, {7013, 40}
X(40212) = X(i)-isoconjugate of X(j) for these (i,j): {9, 1256}, {84, 282}, {189, 2192}, {271, 7129}, {280, 1436}, {285, 1903}, {309, 7118}, {1433, 7003}, {1440, 7367}, {2208, 34404}, {7054, 7157}
X(40212) = barycentric product X(i)*X(j) for these {i,j}: {7, 1103}, {40, 347}, {221, 322}, {223, 329}, {227, 8822}, {342, 7078}, {2324, 14256}, {3318, 7045}, {7013, 7952}
X(40212) = barycentric quotient X(i)/X(j) for these {i,j}: {40, 280}, {56, 1256}, {198, 282}, {221, 84}, {223, 189}, {227, 39130}, {329, 34404}, {347, 309}, {1103, 8}, {1254, 7157}, {2187, 2192}, {2199, 1436}, {2331, 7003}, {2360, 285}, {3195, 7008}, {3209, 7129}, {3318, 24026}, {6611, 1422}, {7078, 271}, {7114, 1433}, {7952, 7020}
X(40213) lies on these lines: {2, 1577}, {27, 1019}, {333, 1021}, {661, 2051}, {693, 5249}, {3687, 4391}, {3703, 4086}, {3737, 17188}, {4467, 20879}, {6545, 23100}
X(40213) = X(4560)-Ceva conjugate of X(4858)
X(40213) = crosspoint of X(4560) and X(26856)
X(40213) = X(i)-isoconjugate of X(j) for these (i,j): {42, 4619}, {59, 4559}, {1018, 24027}, {1020, 1110}, {1262, 4557}, {1402, 31615}, {2149, 4551}, {3952, 23979}, {4566, 23990}, {7115, 23067}
X(40213) = barycentric product X(i)*X(j) for these {i,j}: {11, 18155}, {99, 1090}, {314, 21132}, {333, 40166}, {1014, 23104}, {1019, 23978}, {1021, 23989}, {1111, 7253}, {1146, 7199}, {1577, 26856}, {2287, 23100}, {3239, 16727}, {3737, 34387}, {4391, 17197}, {4397, 17205}, {4560, 4858}, {4625, 5532}, {7192, 24026}, {7257, 7336}, {18191, 35519}
X(40213) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 4551}, {81, 4619}, {333, 31615}, {764, 1042}, {1019, 1262}, {1021, 1252}, {1086, 1020}, {1090, 523}, {1111, 4566}, {1146, 1018}, {2170, 4559}, {2310, 4557}, {3733, 24027}, {3737, 59}, {4081, 4069}, {4560, 4564}, {4858, 4552}, {5532, 4041}, {6545, 1427}, {7004, 23067}, {7192, 7045}, {7199, 1275}, {7203, 7339}, {7252, 2149}, {7253, 765}, {7336, 4017}, {8042, 1407}, {16726, 1461}, {16727, 658}, {16732, 4605}, {17197, 651}, {17205, 934}, {17219, 6516}, {17925, 7128}, {18155, 4998}, {18191, 109}, {21044, 21859}, {21132, 65}, {21789, 1110}, {23100, 1446}, {23104, 3701}, {23105, 1091}, {23615, 210}, {23978, 4033}, {24026, 3952}, {26856, 662}, {34591, 4574}, {40166, 226}
X(40214) lies on the cubic K577 and these lines: {1, 229}, {2, 662}, {3, 60}, {6, 593}, {21, 90}, {31, 1326}, {35, 17104}, {36, 9275}, {41, 1931}, {46, 37294}, {48, 28606}, {55, 110}, {57, 77}, {58, 5313}, {63, 37783}, {65, 37405}, {86, 17173}, {99, 32933}, {100, 7095}, {101, 33761}, {162, 37441}, {163, 4262}, {186, 500}, {222, 4565}, {226, 18653}, {249, 9273}, {261, 5278}, {270, 7501}, {321, 27958}, {323, 17454}, {386, 849}, {394, 7054}, {445, 14165}, {572, 21363}, {584, 757}, {759, 37525}, {842, 36069}, {960, 37032}, {991, 4575}, {1029, 8818}, {1098, 4189}, {1150, 7058}, {1214, 18609}, {1444, 4280}, {1474, 14014}, {1479, 3615}, {1812, 27174}, {1836, 5196}, {1837, 37158}, {1993, 36744}, {1994, 4271}, {2003, 35192}, {2167, 4560}, {2174, 3219}, {2193, 18605}, {2194, 4184}, {2206, 3736}, {2287, 6514}, {2326, 24553}, {2605, 9213}, {2646, 11101}, {3187, 19623}, {3240, 6043}, {3285, 40153}, {3295, 33669}, {3450, 4267}, {3578, 7799}, {4210, 5135}, {4251, 30581}, {4258, 38811}, {4287, 4383}, {4511, 17512}, {4558, 6511}, {4591, 40215}, {4610, 8033}, {4637, 9533}, {4641, 16702}, {5009, 17187}, {5010, 5127}, {5012, 5132}, {5794, 37152}, {6061, 20835}, {6507, 24635}, {7096, 40145}, {7113, 17011}, {10572, 13746}, {11375, 37369}, {11507, 23059}, {11680, 19642}, {14355, 22094}, {14570, 17479}, {14829, 30606}, {16579, 34544}, {17139, 26830}, {17147, 18042}, {17168, 17197}, {18048, 40013}, {18165, 33325}, {22130, 32661}, {24041, 24504}, {27644, 27661}, {31393, 33903}, {32950, 35916}, {37571, 37816}
X(40214) = isogonal conjugate of X(8818)
X(40214) = isogonal conjugate of the isotomic conjugate of X(34016)
X(40214) = X(662)-Ceva conjugate of X(14838)
X(40214) = X(i)-cross conjugate of X(j) for these (i,j): {500, 1442}, {2174, 17104}, {9404, 110}, {17454, 35}, {20982, 2605}, {22094, 4467}, {35192, 35193}
X(40214) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8818}, {6, 6757}, {10, 2160}, {37, 79}, {42, 30690}, {65, 7110}, {94, 3724}, {213, 20565}, {226, 7073}, {321, 6186}, {476, 2610}, {512, 15455}, {661, 6742}, {758, 1989}, {1789, 8736}, {1826, 7100}, {1983, 10412}, {2166, 2245}, {2171, 3615}, {3700, 26700}, {4024, 13486}, {4041, 38340}, {4092, 35049}, {4242, 14582}, {4585, 15475}, {6370, 32678}, {8606, 40149}, {11060, 35550}, {21873, 30602}
X(40214) = cevapoint of X(i) and X(j) for these (i,j): {35, 2174}, {284, 501}, {2605, 20982}, {3024, 9404}, {17104, 35192}
X(40214) = crosspoint of X(249) and X(662)
X(40214) = crosssum of X(i) and X(j) for these (i,j): {37, 21863}, {79, 14844}, {115, 661}, {4988, 21044}
X(40214) = trilinear pole of line {526, 2605}
X(40214) = crossdifference of every pair of points on line {4041, 4838}
X(40214) = barycentric product X(i)*X(j) for these {i,j}: {6, 34016}, {7, 35193}, {21, 1442}, {35, 86}, {58, 319}, {75, 17104}, {77, 11107}, {81, 3219}, {85, 35192}, {99, 2605}, {101, 16755}, {110, 4467}, {163, 18160}, {249, 8287}, {261, 2594}, {274, 2174}, {283, 7282}, {284, 17095}, {314, 1399}, {323, 24624}, {333, 2003}, {593, 3969}, {662, 14838}, {757, 3678}, {811, 23226}, {1014, 4420}, {1101, 17886}, {1154, 39277}, {1171, 3578}, {1255, 17190}, {1333, 33939}, {1414, 35057}, {1444, 6198}, {2185, 16577}, {2611, 24041}, {3268, 36069}, {3615, 7279}, {4556, 7265}, {4567, 7202}, {4573, 9404}, {4590, 20982}, {6149, 14616}, {7799, 34079}, {17454, 32014}, {18020, 22094}, {32679, 37140}
X(40214) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 6757}, {6, 8818}, {35, 10}, {50, 2245}, {58, 79}, {60, 3615}, {81, 30690}, {86, 20565}, {110, 6742}, {186, 860}, {284, 7110}, {319, 313}, {323, 3936}, {500, 442}, {526, 6370}, {662, 15455}, {759, 2166}, {1333, 2160}, {1399, 65}, {1437, 7100}, {1442, 1441}, {1511, 6739}, {2003, 226}, {2174, 37}, {2194, 7073}, {2206, 6186}, {2477, 2594}, {2594, 12}, {2605, 523}, {2611, 1109}, {2624, 2610}, {3024, 6741}, {3219, 321}, {3578, 1230}, {3647, 4647}, {3678, 1089}, {3969, 28654}, {4420, 3701}, {4467, 850}, {4565, 38340}, {6149, 758}, {7186, 2887}, {7202, 16732}, {7266, 17886}, {8287, 338}, {9273, 39295}, {9404, 3700}, {11107, 318}, {14838, 1577}, {14975, 1824}, {16577, 6358}, {16718, 20886}, {16755, 3261}, {17095, 349}, {17104, 1}, {17190, 4359}, {17454, 1213}, {17886, 23994}, {18160, 20948}, {20982, 115}, {21741, 2171}, {22094, 125}, {22342, 201}, {23226, 656}, {24624, 94}, {32671, 32678}, {33939, 27801}, {34016, 76}, {34079, 1989}, {35057, 4086}, {35192, 9}, {35193, 8}, {35195, 27529}, {36069, 476}, {37140, 32680}
X(40214) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35, 17104, 35193}, {284, 1790, 81}, {501, 15792, 1}, {662, 2185, 2}
X(40215) lies on the cubic K577 and these lines: {1, 39148}, {2, 3257}, {6, 2226}, {31, 106}, {36, 16944}, {55, 840}, {57, 88}, {81, 1019}, {89, 679}, {354, 14190}, {593, 4556}, {999, 1318}, {1168, 5902}, {1262, 1407}, {1320, 3873}, {1417, 7248}, {1478, 36590}, {2094, 36887}, {3218, 4585}, {3418, 36058}, {4080, 17483}, {4582, 32933}, {4591, 40214}, {4615, 8033}, {4674, 32913}, {4945, 31164}, {4997, 31053}, {5332, 9456}, {8034, 23345}, {9352, 14193}, {11246, 19636}, {34583, 39154}, {36814, 37604}
X(40215) = X(i)-Ceva conjugate of X(j) for these (i,j): {679, 106}, {3257, 3960}
X(40215) = X(i)-cross conjugate of X(j) for these (i,j): {654, 901}, {7113, 106}, {17455, 36}, {34586, 1443}
X(40215) = X(i)-isoconjugate of X(j) for these (i,j): {2, 40172}, {9, 14584}, {44, 80}, {55, 14628}, {519, 2161}, {655, 4895}, {759, 3943}, {902, 18359}, {1168, 4370}, {1319, 36910}, {1411, 2325}, {1639, 2222}, {1807, 8756}, {1960, 36804}, {2006, 3689}, {2251, 20566}, {3285, 15065}, {3992, 34079}, {4358, 6187}, {4768, 32675}, {16704, 34857}, {21805, 24624}
X(40215) = cevapoint of X(i) and X(j) for these (i,j): {6, 14260}, {36, 17455}, {654, 3025}, {2316, 39148}
X(40215) = crosssum of X(i) and X(j) for these (i,j): {1635, 35092}, {3943, 4370}, {4530, 6544}
X(40215) = trilinear pole of line {36, 39478}
X(40215) = crossdifference of every pair of points on line {4895, 21805}
X(40215) = barycentric product X(i)*X(j) for these {i,j}: {36, 903}, {75, 16944}, {88, 3218}, {106, 320}, {214, 679}, {901, 4453}, {1022, 4585}, {1320, 1443}, {1797, 17923}, {2316, 17078}, {3257, 3960}, {4089, 9268}, {4591, 4707}, {4615, 21828}, {6336, 22128}, {7113, 20568}, {9456, 20924}, {17191, 30575}
X(40215) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 40172}, {36, 519}, {56, 14584}, {57, 14628}, {88, 18359}, {106, 80}, {214, 4738}, {320, 3264}, {654, 1639}, {758, 3992}, {903, 20566}, {1318, 36590}, {1417, 1411}, {1870, 38462}, {1983, 1023}, {2245, 3943}, {2316, 36910}, {2323, 2325}, {2361, 3689}, {3218, 4358}, {3257, 36804}, {3724, 21805}, {3738, 4768}, {3792, 4439}, {3960, 3762}, {4511, 4723}, {4585, 24004}, {4674, 15065}, {4881, 4487}, {4973, 4975}, {7113, 44}, {8648, 4895}, {9456, 2161}, {16944, 1}, {17191, 16729}, {17455, 4370}, {21758, 1635}, {21828, 4120}, {22128, 3977}, {34586, 1145}, {36058, 1807}, {39148, 36909}
X(40215) = {X(999),X(14260)}-harmonic conjugate of X(1318)
X(40216) lies on these lines: {38, 16727}, {75, 3873}, {85, 3681}, {92, 15149}, {274, 3112}, {313, 1233}, {321, 1930}, {561, 33933}, {693, 2886}, {756, 1111}, {1086, 8041}, {1441, 4967}, {2350, 4359}, {2481, 5284}, {2550, 13577}, {2995, 25590}, {2997, 10436}, {3925, 23989}, {4651, 20448}, {4972, 39712}, {6063, 33108}, {6358, 20901}, {8049, 20718}, {11680, 32023}, {14549, 17863}, {20632, 24199}, {20892, 30047}, {30473, 30636}, {32092, 39950}
X(40216) = isotomic conjugate of X(1621)
X(40216) = isotomic conjugate of the anticomplement of X(3925)
X(40216) = isotomic conjugate of the complement of X(33110)
X(40216) = isotomic conjugate of the isogonal conjugate of X(13476)
X(40216) = X(39734)-anticomplementary conjugate of X(2890)
X(40216) = X(40004)-Ceva conjugate of X(17758)
X(40216) = X(i)-cross conjugate of X(j) for these (i,j): {594, 76}, {2294, 1446}, {3925, 2}, {15523, 40013}, {21020, 321}, {21026, 39994}, {21924, 2052}, {23989, 693}
X(40216) = X(i)-isoconjugate of X(j) for these (i,j): {6, 4251}, {31, 1621}, {32, 17277}, {59, 38365}, {101, 21007}, {184, 14004}, {560, 17143}, {692, 4040}, {1252, 38346}, {1253, 38859}, {1333, 3294}, {1397, 3996}, {1501, 18152}, {1576, 4151}, {1917, 40088}, {2149, 38347}, {2150, 20616}, {2206, 4651}, {8750, 22160}, {14827, 33765}, {17494, 32739}, {17761, 23990}, {18892, 40094}
X(40216) = cevapoint of X(i) and X(j) for these (i,j): {2, 33110}, {75, 33943}, {523, 1111}, {1086, 2530}, {4858, 6362}
X(40216) = crosspoint of X(75) and X(40005)
X(40216) = trilinear pole of line {918, 1577}
X(40216) = barycentric product X(i)*X(j) for these {i,j}: {10, 40004}, {75, 17758}, {76, 13476}, {313, 39950}, {321, 39734}, {561, 2350}
X(40216) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4251}, {2, 1621}, {10, 3294}, {11, 38347}, {12, 20616}, {75, 17277}, {76, 17143}, {92, 14004}, {244, 38346}, {279, 38859}, {312, 3996}, {313, 4043}, {321, 4651}, {513, 21007}, {514, 4040}, {561, 18152}, {693, 17494}, {905, 22160}, {1088, 33765}, {1111, 17761}, {1502, 40088}, {1577, 4151}, {2170, 38365}, {2350, 31}, {3261, 20954}, {4024, 21727}, {13476, 6}, {16732, 2486}, {17758, 1}, {18895, 40094}, {20888, 29773}, {23807, 27168}, {39734, 81}, {39950, 58}, {40004, 86}
X(40216) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 16708, 17140}, {75, 40004, 13476}
X(40217) lies on these lines: {2, 38}, {57, 4998}, {63, 813}, {312, 4583}, {321, 693}, {337, 4876}, {518, 27919}, {660, 3681}, {1911, 3938}, {3252, 3930}, {3509, 3570}, {3661, 40098}, {3675, 3912}, {3961, 18787}, {4441, 18034}, {4562, 17294}, {6063, 6358}, {6654, 9451}, {8047, 32863}, {16708, 40017}, {17780, 24628}, {21101, 24318}, {24326, 39712}, {33676, 39959}, {36483, 36800}
X(40217) = anticomplement of X(27942)
X(40217) = isotomic conjugate of X(6654)
X(40217) = isotomic conjugate of the isogonal conjugate of X(3252)
X(40217) = X(335)-Ceva conjugate of X(3912)
X(40217) = X(4437)-cross conjugate of X(3912)
X(40217) = X(i)-isoconjugate of X(j) for these (i,j): {31, 6654}, {105, 1914}, {238, 1438}, {242, 32658}, {294, 1428}, {659, 919}, {673, 2210}, {812, 32666}, {1416, 3684}, {1429, 2195}, {2201, 36057}, {2481, 14599}, {4435, 32735}, {5009, 18785}, {7193, 8751}, {8632, 36086}, {18031, 18892}
X(40217) = cevapoint of X(3930) and X(4712)
X(40217) = crosspoint of X(335) and X(40098)
X(40217) = trilinear pole of line {918, 3932}
X(40217) = crossdifference of every pair of points on line {2210, 8632}
X(40217) = barycentric product X(i)*X(j) for these {i,j}: {75, 22116}, {76, 3252}, {291, 3263}, {334, 518}, {335, 3912}, {337, 1861}, {672, 18895}, {918, 4562}, {1934, 4447}, {2254, 4583}, {3717, 7233}, {3930, 40017}, {3932, 18827}, {4088, 4589}, {4518, 9436}, {4639, 24290}, {17755, 40098}
X(40217) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6654}, {241, 1429}, {291, 105}, {292, 1438}, {295, 36057}, {334, 2481}, {335, 673}, {337, 31637}, {518, 238}, {660, 36086}, {665, 8632}, {672, 1914}, {813, 919}, {876, 1027}, {918, 812}, {1026, 3573}, {1458, 1428}, {1818, 7193}, {1861, 242}, {2196, 32658}, {2223, 2210}, {2254, 659}, {3252, 6}, {3263, 350}, {3286, 5009}, {3675, 27846}, {3693, 3684}, {3717, 3685}, {3912, 239}, {3930, 2238}, {3932, 740}, {4088, 4010}, {4437, 17755}, {4447, 1580}, {4518, 14942}, {4562, 666}, {4712, 8299}, {4876, 294}, {4966, 4974}, {5089, 2201}, {5378, 5377}, {7077, 2195}, {8299, 8300}, {9436, 1447}, {9454, 14599}, {9455, 18892}, {15149, 31905}, {17755, 4366}, {18157, 30940}, {18895, 18031}, {20683, 3747}, {22116, 1}, {24290, 21832}, {25083, 20769}, {27919, 6652}, {30671, 29956}, {30941, 33295}, {34067, 32666}, {36801, 36802}
X(40218) lies on the cubic K577 and these lines: {2, 222}, {55, 104}, {57, 514}, {196, 40151}, {200, 36819}, {202, 14359}, {203, 14358}, {345, 1016}, {519, 23703}, {603, 37043}, {996, 38955}, {1397, 2720}, {1997, 13136}, {3086, 28347}, {3476, 10428}, {5435, 37136}, {6630, 37683}, {14266, 14584}, {15635, 17625}, {23615, 39771}, {34523, 36795}, {36037, 36845}
X(40218) = X(34234)-Ceva conjugate of X(3911)
X(40218) = X(i)-cross conjugate of X(j) for these (i,j): {44, 104}, {14425, 1309}, {14584, 7}
X(40218) = X(i)-isoconjugate of X(j) for these (i,j): {9, 14260}, {517, 2316}, {1320, 2183}, {1769, 5548}, {2427, 23838}, {2804, 32665}, {6735, 9456}
X(40218) = cevapoint of X(i) and X(j) for these (i,j): {44, 1317}, {4530, 39771}
X(40218) = crosssum of X(2183) and X(23980)
X(40218) = trilinear pole of line {900, 1319}
X(40218) = barycentric product X(i)*X(j) for these {i,j}: {7, 36944}, {1319, 18816}, {3762, 37136}, {3911, 34234}, {4358, 34051}, {13136, 30725}
X(40218) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 14260}, {104, 1320}, {519, 6735}, {900, 2804}, {909, 2316}, {1317, 1145}, {1319, 517}, {1404, 2183}, {1647, 35015}, {1846, 21664}, {1877, 1785}, {2720, 901}, {3259, 3326}, {3911, 908}, {10428, 1318}, {12832, 119}, {13136, 4582}, {14027, 3259}, {30725, 10015}, {32641, 5548}, {32669, 32665}, {34051, 88}, {34234, 4997}, {36944, 8}, {37136, 3257}, {39771, 23757}
X(40219) lies on the cubic K169 and these lines: {2, 64}, {25, 40190}, {2139, 40189}
X(40219) = X(69)-Ceva conjugate of X(40190)
X(40220) lies on the cubic K169 and these lines: {1, 40190}, {2, 269}, {64, 17742}, {3692, 6574}, {7097, 40189}
X(40220) = barycentric product X(1219)*X(12565)X(40221) lies on the cubic K169 and these lines: {2, 2139}, {25, 64}, {269, 2184}, {1073, 13567}, {1301, 1619}, {3343, 14390}, {13575, 40190}, {14457, 37072}
X(40221) = X(69)-Ceva conjugate of X(64)
X(40221) = barycentric product X(17807)*X(34403)
X(40221) = barycentric quotient X(17807)/X(1249)
X(40221) = perspector of pedal triangle of X(20) and anticevian triangle of X(64)
X(40221) = {X(3343),X(17811)}-harmonic conjugate of X(14390)
X(40222) lies on the cubic K169 and these lines: {2, 159}, {6, 39978}, {69, 40189}, {2138, 40190}
X(40222) = isogonal conjugate of X(40189)
X(40222) = X(25)-cross conjugate of X(40190)
X(40222) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40189}, {23051, 37485}
X(40222) = barycentric product X(3618)*X(40178)
X(40222) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40189}, {3618, 40123}, {30435, 37485}, {40178, 18840}
X(40223) lies on the cubic K169 and these lines: {1, 64}, {2, 6359}, {25, 269}, {1422, 14524}, {2139, 17742}, {5738, 7177}, {40188, 40190}
X(40223) = X(69)-Ceva conjugate of X(269)
X(40223) = barycentric product X(i)*X(j) for these {i,j}: {279, 16389}, {348, 8899}
X(40223) = barycentric quotient X(i)/X(j) for these {i,j}: {8899, 281}, {16389, 346}
X(40224) lies on the cubic K169 and these lines: {2, 14259}, {159, 40190}
X(40225) lies on the cubic K169 and these lines: {1, 40189}, {2, 17742}, {159, 269}, {1763, 40190}
X(40226) lies on the cubic K169 and these lines: {1, 40187}, {2, 40194}, {6, 200}, {20, 1219}
X(40227) lies on the cubic K169 and these lines: {2, 40190}, {64, 40189}
X(40228) lies on the cubic K1163 and these lines: {6, 110}, {542, 17854}, {7728, 14984}, {8681, 24981}
X(40229) lies on the cubic K1163 and this line: {25, 69}
X(40230) lies on the cubic K1163 and these lines: {25, 111}, {69, 146}, {2794, 38323}, {9517, 39904}
X(40231) lies on the cubic K1163 and this line: {69, 111}
X(40232) lies on the cubic K1163 and these lines: {23, 2353}, {66, 69}, {111, 1289}, {5485, 16277}, {14376, 16051}
X(40233) lies on the cubic K1163 and this line: {111, 2393}
X(40234) lies on the Moses-Parry circle, the cubic K1163, and these lines: {6, 1562}, {20, 112}, {111, 1289}, {115, 235}, {187, 16318}, {1368, 1560}, {2079, 3515}, {3569, 14391}, {5913, 14580}, {8428, 9909}, {15078, 21397}
X(40235) is the singular focus of the cubic K1163.
X(40235) lies these lines: {3, 126}, {235, 1560}, {2373, 37201}, {3542, 30247}, {5656, 9968}
Tetrahedral projections: X(40236)-X(40296)
This preamble and centers X(40236)-X(40296) were contributed by César Eliud Lozada, November 4, 2020.
Let ABC be a triangle on a plane XY. Consider three segments AA', BB', CC' with lengths U, V, W, respectively, and each having one fixed extreme in A, B and C, respectively, and the other extremes free to move outside the plane XY. Suppose that these segments are rotated around their fixed extremes in such a way that their free extremes coincide at a point D, forming, together with the sides of ABC, the edges of a tetrahedron ABCD. Let D* be the orthogonal projection of D on the plane of ABC. The point D* is here named the tetrahedral projection of ABC by (U, V, W) or the tetrahedral projection of ABC to A'B'C'.
The point D* has barycentric coordinates:
D* = a2 (SA - U2) + SB W2 + SC V2 : b2 (SB - V2) + SC U2 + SA W2 : c2 (SC - W2) + SA V2 + SB U2 (1)
Z(D), the Z-coordinate of D , i.e., the height of the point D measured from D* and orthogonally to the plane of ABC, is given by:
Z(D) = ±sqrt(∑ [2 (a2 U2 + V2 W2) SA - a2 U4] - (a b c)2)/(2 S)
(2)
Equation (2) shows that D is real or imaginary according to the sign of the quantity under the square root. If this quantity is zero then D and D* coincide on the plane of ABC. Moreover, the ± sign indicates that there are two possible points D and D', each in different sides with respect to the plane of ABC.
Equation (1) shows that if U, V, W are real numbers then D* is always real and also that, if U, V, W are cyclic values, i.e., if there exists a degree-1 function ƒ(a,b,c) such that U=ƒ(a,b,c), V=ƒ(b,c,a) and W=ƒ(c,a,b), then D* is a triangle center.
Some calculated values:
Definitions of all triangles above mentioned can be found in the index of triangles.
Preamble edited on June 28, 2022.
X(40236) lies on these lines: {2, 3}, {98, 8784}, {114, 29317}, {147, 511}, {182, 9993}, {183, 36990}, {194, 8721}, {325, 29181}, {385, 1503}, {516, 1281}, {1350, 3314}, {1352, 6194}, {2080, 9862}, {2456, 10353}, {2794, 14712}, {2896, 5188}, {3095, 40278}, {3329, 5480}, {3398, 12252}, {3424, 37667}, {3818, 22712}, {5085, 7875}, {5171, 9873}, {5207, 5976}, {5476, 9774}, {5986, 18400}, {5987, 17702}, {5992, 29057}, {6033, 9772}, {6054, 19924}, {6310, 11381}, {6776, 7766}, {7710, 7774}, {7735, 14927}, {7759, 9764}, {7761, 22676}, {7797, 12203}, {7802, 36997}, {7809, 38745}, {7836, 30270}, {7837, 11477}, {7868, 31884}, {8844, 20539}, {9474, 36899}, {9744, 31670}, {9753, 39750}, {9756, 17004}, {9821, 40253}, {10334, 13355}, {10516, 16986}, {11177, 11645}, {12830, 15514}, {14931, 23698}, {15072, 40254}, {16989, 25406}, {17984, 30737}, {19570, 38664}, {29323, 38227}, {33706, 34507}, {35389, 39882}
X(40236) = reflection of X(i) in X(j) for these (i,j): (20, 11676), (5189, 36173), (5984, 385), (5999, 1513), (7779, 147), (9862, 2080), (15683, 9855), (40246, 3543)
X(40236) = anticomplement of X(5999)
X(40236) = intersection, other than A,B,C, of conics {{A, B, C, X(25), X(34214)}} and {{A, B, C, X(98), X(420)}}
X(40236) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 13862, 2), (4, 37182, 2), (5, 37455, 2), (382, 40279, 4), (1513, 5999, 2), (5059, 33244, 20), (6039, 6040, 5), (17578, 33018, 4), (20854, 21536, 420)
X(40237) lies on these lines: {30, 111}, {574, 3830}, {3534, 8585}, {9872, 19924}
X(40238) lies on these lines: {3, 6}, {98, 7944}, {4027, 6656}, {10345, 40250}, {12203, 37243}, {12252, 40239}
X(40238) = {X(1342), X(1343)}-harmonic conjugate of X(35422)
X(40239) lies on these lines: {3, 10333}, {30, 2456}, {83, 546}, {182, 40250}, {550, 10350}, {575, 10796}, {2782, 35377}, {5171, 7908}, {12110, 32448}, {12177, 32515}, {12252, 40238}, {32139, 33786}
X(40240) lies on these lines: {4, 1173}, {30, 12002}, {51, 6240}, {113, 14627}, {125, 35482}, {235, 37505}, {381, 10112}, {389, 974}, {397, 35715}, {398, 35714}, {403, 12242}, {524, 40247}, {539, 3850}, {542, 546}, {578, 3542}, {1493, 16534}, {1596, 14862}, {2914, 3574}, {3088, 20299}, {3357, 11433}, {3845, 10116}, {3853, 18128}, {5097, 22660}, {5480, 18383}, {5946, 12897}, {5972, 37472}, {6756, 10110}, {7507, 10982}, {9781, 21659}, {9927, 19130}, {10095, 17702}, {10182, 11425}, {10282, 15873}, {10619, 34484}, {11225, 12162}, {11245, 13474}, {11424, 37119}, {11432, 22802}, {11793, 13142}, {12022, 13419}, {12605, 21849}, {13382, 13488}, {13567, 25563}, {13851, 32377}, {14865, 20417}, {14940, 15033}, {15807, 16881}, {17810, 34785}, {18369, 30714}, {18388, 35488}, {18555, 37347}, {29317, 32191}, {33332, 36253}
X(40240) = midpoint of X(i) and X(j) for these {i,j}: {3853, 18128}, {10110, 12241}, {11793, 13142}, {13382, 13488}, {15807, 16881}
X(40240) = crosssum of X(3) and X(12006)
X(40241) lies on these lines: {1503, 12111}, {3060, 7553}, {3146, 11645}, {5012, 7566}, {5640, 13419}, {6241, 34798}, {7558, 15080}, {7998, 12134}, {9705, 31181}, {9833, 11449}, {10298, 14864}, {11439, 16659}, {11440, 34780}, {11454, 14216}, {11750, 15305}, {12279, 12280}, {12283, 15084}, {13163, 15024}, {13445, 17845}, {18381, 26881}, {29012, 34799}, {38397, 38435}
X(40242) lies on these lines: {3, 18379}, {4, 1495}, {20, 9927}, {26, 10733}, {30, 5889}, {54, 35480}, {74, 1657}, {195, 5073}, {382, 1614}, {550, 23294}, {1147, 10296}, {1498, 10721}, {1593, 9920}, {2931, 11413}, {3043, 40276}, {3520, 34786}, {3529, 11457}, {3567, 6240}, {3830, 9707}, {5876, 18561}, {5890, 21659}, {6143, 18376}, {7488, 16013}, {7999, 12605}, {9781, 13403}, {10116, 34796}, {10295, 26917}, {10483, 19368}, {11412, 12219}, {11444, 18564}, {11449, 18403}, {11455, 16655}, {11459, 12278}, {11462, 35820}, {11463, 35821}, {11465, 31833}, {11466, 19106}, {11467, 19107}, {11572, 35475}, {11704, 13851}, {11750, 22949}, {12111, 18562}, {12173, 15033}, {12283, 29012}, {12290, 12291}, {14157, 17845}, {14644, 32534}, {15072, 18565}, {15685, 34469}, {17800, 32608}, {18383, 35473}, {18405, 35477}, {23040, 32767}, {29323, 39874}
X(40242) = reflection of X(i) in X(j) for these (i,j): (6241, 12289), (12111, 18562), (12278, 18563), (34797, 21659)
X(40242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 34785, 26882), (20, 25739, 11468), (12278, 18563, 11459), (13403, 18559, 9781), (13851, 21844, 11704), (17845, 35490, 14157), (21659, 34797, 5890)
X(40243) lies on these lines: {3, 6}, {3069, 36711}, {3843, 39661}, {6460, 36712}, {14242, 36714}, {14269, 35830}, {14930, 36702}
X(40243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 39658, 3), (372, 8416, 6395), (1152, 9605, 3), (6395, 11917, 3312), (6410, 7772, 39649), (6410, 39649, 3), (21309, 40268, 40244)
X(40244) lies on these lines: {3, 6}, {3068, 36712}, {3843, 39660}, {6459, 36711}, {11292, 32814}, {14227, 36709}, {14269, 35831}, {14930, 36717}
X(40244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 39649, 3), (371, 8396, 6199), (1151, 9605, 3), (6199, 11916, 3311), (6409, 7772, 39658), (6409, 39658, 3), (21309, 40268, 40243)
X(40245) lies on these lines: {1, 3}, {100, 6934}, {149, 6890}, {1259, 10526}, {1376, 6917}, {1399, 36747}, {3560, 26066}, {4421, 34696}, {5763, 33814}, {5812, 11517}, {5840, 12332}, {5841, 11500}, {5844, 8668}, {6796, 21077}, {6831, 10525}, {6833, 11680}, {6862, 11496}, {6911, 25681}, {6928, 11502}, {11231, 37224}, {13346, 38607}, {26446, 37228}
X(40245) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 1482, 22766), (3, 10679, 2646), (3, 35448, 14110), (3, 37541, 34339), (46, 2077, 3), (10306, 35000, 11248), (10310, 11509, 3), (11248, 11249, 55), (11248, 35238, 26285)
X(40246) lies on these lines: {2, 3}, {148, 3849}, {316, 8591}, {524, 8596}, {530, 25166}, {531, 25156}, {543, 7779}, {671, 14712}, {1992, 33683}, {6781, 9166}, {7748, 34604}, {7809, 15300}, {7823, 15534}, {7840, 20094}, {8584, 20088}, {8593, 29012}, {9889, 11606}, {11161, 19924}, {22165, 32819}
X(40246) = reflection of X(i) in X(j) for these (i,j): (2, 8597), (8591, 316), (9855, 8352), (14712, 671), (15683, 5999), (20094, 7840), (37901, 36174), (40236, 3543)
X(40246) = anticomplement of X(9855)
X(40246) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5077, 11361, 2), (7833, 11317, 2), (8352, 9855, 2), (8598, 14041, 2), (13586, 37350, 2)
X(40247) lies on these lines: {2, 13382}, {3, 64}, {4, 15606}, {5, 16254}, {51, 3544}, {52, 5072}, {185, 3525}, {373, 389}, {511, 546}, {524, 40240}, {575, 15083}, {632, 5876}, {1154, 12811}, {1216, 3627}, {1352, 18383}, {3060, 3091}, {3146, 11444}, {3292, 35500}, {3529, 3917}, {3545, 14531}, {3628, 10219}, {3850, 16982}, {3851, 21849}, {3855, 21969}, {3856, 12002}, {3857, 5446}, {3859, 13421}, {5056, 14831}, {5076, 10625}, {5079, 5943}, {5092, 32139}, {5447, 12103}, {5462, 12812}, {5650, 6241}, {5663, 12108}, {5889, 15022}, {6102, 6688}, {6643, 14864}, {7486, 16226}, {7568, 16534}, {7723, 38795}, {7999, 11381}, {9730, 40284}, {10263, 13570}, {10303, 12111}, {11439, 36987}, {11541, 32062}, {12109, 31836}, {12219, 15029}, {12358, 38791}, {12825, 38729}, {13348, 15067}, {13598, 23039}, {13857, 35482}, {14826, 34785}, {14862, 16197}, {14915, 32142}, {15025, 21649}, {15034, 21650}, {18553, 18569}, {22660, 24206}
X(40247) = midpoint of X(i) and X(j) for these {i,j}: {4, 15606}, {5462, 31834}, {5562, 10110}, {5876, 9729}, {5907, 11793}, {12109, 31836}
X(40247) = reflection of X(i) in X(j) for these (i,j): (12002, 3856), (15012, 3628)
X(40247) = complement of X(13382)
X(40247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3628, 15012, 11695), (3819, 5907, 12162), (3917, 15058, 13474), (5876, 10170, 9729), (5891, 5907, 11793), (11444, 15030, 15644)
X(40248) lies on these lines: {2, 3}, {98, 8860}, {114, 599}, {183, 6054}, {230, 11179}, {511, 11184}, {542, 7610}, {598, 39656}, {1351, 11163}, {1352, 11168}, {1503, 15597}, {2782, 9743}, {2794, 5569}, {3055, 31670}, {3815, 20423}, {4846, 24855}, {5050, 38227}, {5663, 9759}, {6055, 11646}, {6776, 23055}, {7694, 8182}, {8722, 31173}, {8859, 9755}, {9744, 22329}, {9753, 14848}, {9756, 11645}, {11177, 17004}, {11178, 15271}, {11180, 34229}, {15819, 21358}, {17008, 39899}, {18440, 37688}, {22712, 23234}
X(40248) = midpoint of X(7694) and X(8182)
X(40248) = anti-Artzt-to-Artzt similarity image of X(3)
X(40248) = X(7610)-of-Artzt-triangle
X(40248) = X(3)-of-Artzt-of-Artzt-triangle
X(40248) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1513, 381), (3, 381, 5077), (549, 10011, 2)
X(40249) lies on these lines: {3, 214}, {4, 30274}, {57, 5884}, {84, 6912}, {142, 12616}, {499, 11219}, {515, 942}, {546, 971}, {758, 37623}, {944, 5083}, {946, 12711}, {1071, 1210}, {1125, 6001}, {1158, 4512}, {2095, 3874}, {2801, 18242}, {3149, 18389}, {3244, 24474}, {3678, 5771}, {3754, 37281}, {3811, 5709}, {3817, 6245}, {5439, 12664}, {5450, 18443}, {5693, 5744}, {5745, 20117}, {5768, 6246}, {6905, 15556}, {6927, 18397}, {6949, 12691}, {6960, 9964}, {7971, 19861}, {9776, 15016}, {10122, 12671}, {10571, 12016}, {11018, 13464}, {12114, 30143}, {12436, 34339}, {12564, 13374}, {12672, 17603}, {12687, 19860}, {13369, 37290}, {31649, 34862}, {31671, 40265}
X(40249) = midpoint of X(i) and X(j) for these {i,j}: {942, 9942}, {1071, 6260}, {3874, 11500}, {5884, 6261}
X(40249) = reflection of X(6705) in X(9940)
X(40249) = trilinear product X(1210)*X(11012)
X(40250) lies on these lines: {2, 3}, {76, 6287}, {147, 32447}, {148, 10335}, {182, 40239}, {262, 6033}, {511, 7848}, {538, 18553}, {1352, 32515}, {2023, 5475}, {2080, 9993}, {2782, 3818}, {2794, 10796}, {3095, 7905}, {3398, 9873}, {3734, 5031}, {3972, 38741}, {4045, 29012}, {5480, 35431}, {5663, 40254}, {6249, 7747}, {7748, 22803}, {7761, 24256}, {7777, 32528}, {7823, 13111}, {8721, 32516}, {9862, 11842}, {9863, 18503}, {10033, 11632}, {10345, 40238}, {10356, 30270}, {10358, 36997}, {13334, 40278}, {13449, 22682}, {15048, 39884}, {18907, 38136}, {20428, 22693}, {20429, 22694}, {22512, 36759}, {22513, 36760}, {22515, 22681}, {32134, 36998}, {34615, 34734}
X(40250) = midpoint of X(i) and X(j) for these {i,j}: {4, 37242}, {15048, 39884}
X(40250) = reflection of X(10796) in X(19130)
X(40250) = tetrahedral projection of ABC to 1st Brocard triangle
X(40250) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 6655, 382), (4, 37336, 3), (381, 13860, 5), (3851, 7887, 5)
X(40251) lies on these lines: {2, 1495}, {353, 511}, {575, 1383}, {2782, 11655}
X(40252) lies on these lines: {3, 6}, {4, 8782}, {76, 9996}, {194, 9862}, {262, 7940}, {2782, 9873}, {2896, 12251}, {3399, 10345}, {5976, 7752}, {6033, 8149}, {6194, 7932}, {6248, 18500}, {6656, 32521}, {7697, 10356}, {7811, 34510}, {7846, 11272}, {7884, 33706}, {7942, 22712}, {9983, 22678}, {10038, 12837}, {10047, 12836}, {10063, 10873}, {10079, 10874}, {10263, 39684}, {10346, 35925}, {13108, 18503}, {15821, 40107}, {31670, 31982}, {35700, 38733}
X(40252) = reflection of X(9983) in X(32151)
X(40252) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3094, 9821, 3), (3095, 9821, 32), (9821, 35248, 5188), (9983, 22678, 32151), (34870, 35002, 3)
X(40253) lies on these lines: {3, 10333}, {76, 36997}, {384, 35387}, {511, 7893}, {3095, 9862}, {3146, 12251}, {3314, 5188}, {6776, 32476}, {7876, 13354}, {9821, 40236}, {13862, 35430}
X(40253) = reflection of X(9983) in X(9863)
X(40254) lies on these lines: {3, 695}, {4, 51}, {511, 2549}, {1181, 11325}, {1204, 35476}, {5167, 9744}, {5309, 31850}, {5562, 7791}, {5663, 40250}, {5889, 6655}, {6310, 9729}, {6759, 27369}, {7709, 11674}, {9730, 37348}, {11444, 33021}, {11695, 32968}, {11793, 16043}, {12111, 37336}, {13630, 40279}, {13754, 37242}, {14831, 33017}, {15028, 33020}, {15043, 16044}, {15072, 40236}, {16226, 33016}, {34783, 37243}
X(40254) = crosssum of X(3) and X(35930)
X(40255) lies on these lines: {1, 3}, {945, 39173}, {958, 6929}, {1145, 11499}, {1532, 10526}, {1872, 22479}, {2975, 6938}, {3913, 22775}, {5840, 12114}, {5886, 25875}, {6265, 11517}, {6834, 11681}, {6838, 20060}, {6911, 37828}, {6923, 22759}, {6959, 22753}, {10043, 10090}, {10525, 22758}, {10785, 13279}, {11194, 34708}
X(40255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 1482, 11508), (3, 10680, 1319), (3, 35460, 10310), (3428, 10966, 3), (5119, 11012, 3), (11248, 11249, 56), (11249, 35239, 26286), (13528, 34880, 3)
X(40256) lies on these lines: {1, 6950}, {3, 214}, {4, 484}, {8, 20}, {10, 6923}, {46, 499}, {55, 5884}, {57, 13464}, {72, 13528}, {100, 5693}, {104, 5697}, {165, 6261}, {191, 2950}, {355, 40264}, {516, 10525}, {517, 5450}, {519, 24467}, {551, 37612}, {601, 4424}, {758, 11248}, {912, 8715}, {920, 4848}, {944, 1768}, {950, 10051}, {962, 5535}, {993, 37562}, {1012, 37567}, {1071, 37568}, {1376, 5780}, {1388, 25485}, {1389, 5903}, {1479, 10265}, {1490, 16558}, {1537, 5433}, {1621, 15016}, {1697, 13607}, {1709, 31673}, {1727, 6938}, {1788, 26333}, {2077, 3869}, {2093, 7098}, {2098, 11715}, {2771, 32141}, {2829, 5690}, {3218, 7982}, {3295, 12005}, {3336, 5603}, {3337, 10595}, {3357, 3579}, {3359, 3452}, {3474, 26332}, {3560, 3754}, {3576, 17548}, {3652, 5790}, {3655, 32905}, {3874, 10679}, {3877, 37561}, {3881, 37622}, {3884, 10269}, {3892, 12000}, {3898, 16203}, {4084, 37533}, {4301, 37532}, {4640, 31788}, {4868, 36742}, {4973, 10680}, {5010, 21740}, {5119, 5882}, {5128, 6844}, {5180, 6972}, {5248, 34339}, {5250, 10165}, {5330, 38693}, {5445, 6941}, {5493, 6245}, {5553, 7162}, {5687, 14740}, {5709, 6705}, {5734, 23958}, {5842, 33899}, {5887, 25440}, {6211, 29497}, {6223, 12849}, {6361, 14647}, {6763, 12245}, {6871, 10175}, {6905, 37572}, {6914, 30147}, {6924, 10225}, {6952, 18393}, {6958, 11813}, {7967, 37563}, {7971, 35242}, {8227, 31224}, {9588, 26878}, {9624, 27003}, {9803, 20066}, {10310, 31806}, {10698, 21842}, {10826, 24042}, {11491, 15071}, {11496, 31870}, {11499, 31803}, {11500, 13465}, {12114, 12702}, {12647, 37002}, {12667, 14646}, {14110, 17613}, {14988, 22836}, {15528, 26358}, {17102, 20324}, {18389, 37287}, {18491, 31871}, {19919, 38112}, {20070, 24468}, {31663, 37837}, {36866, 38755}, {37469, 37598}, {37822, 37828}
X(40256) = midpoint of X(i) and X(j) for these {i,j}: {40, 1158}, {5493, 6245}, {12114, 12702}
X(40256) = reflection of X(i) in X(j) for these (i,j): (6796, 3579), (12608, 6684), (22836, 26285), (22837, 32153), (37837, 31663), (40257, 3), (40264, 355)
X(40256) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (40, 63, 11362), (1768, 11010, 944), (3359, 12514, 6684), (5445, 34789, 6941), (6914, 35004, 30147), (11496, 36279, 31870)
In the plane of a triangle ABC, let
O = circumcenter;
A' = reflection of A in O, and define B'; and C' cyclically;
H = orthocenter;
A''B''C'' = circumcevian triangle of H wrt A''B''C'';
Ab = AC∩B'A'', and define Bc and Ca cyclically;
Ac = AB∩C'A'', and define Ba and Cb cyclically;
Ao = circumcenter of AAbAc, and define Bo and Cocyclically;
σ = the affine transformation that maps ABC onto AoBoCocyclically;
I = incenter;
Then σ(I) = X(40257). Moreover, if X = x : y : z, then
σ(X) = (-a+b+c)^2 (a^4-2 a^2 (b-c)^2+(b-c)^2 (b^2-b c+c^2)) x-a^2 (a-c) c (a-b+c)^2 y-a^2 (a-b) b (a+b-c)^2 z : : .
See X(40257). (Angel Montesdeoca, June 28, 2022)
X(40257) lies on these lines: {1, 4}, {3, 214}, {5, 30147}, {8, 6326}, {10, 6863}, {20, 5180}, {40, 4511}, {56, 5884}, {78, 6962}, {80, 6941}, {84, 2320}, {104, 15071}, {221, 11700}, {355, 6980}, {484, 6942}, {499, 10265}, {517, 6796}, {519, 37700}, {551, 6245}, {758, 11249}, {912, 8666}, {952, 3813}, {958, 20117}, {962, 20066}, {971, 15178}, {993, 5887}, {997, 5837}, {999, 12005}, {1012, 34471}, {1071, 1319}, {1125, 6862}, {1158, 3576}, {1385, 5248}, {1388, 11715}, {1482, 11500}, {1532, 10950}, {1537, 6284}, {1727, 37618}, {2098, 12739}, {2099, 3149}, {2360, 17515}, {2646, 12672}, {2771, 32153}, {2829, 19907}, {2975, 5693}, {3057, 33597}, {3304, 10122}, {3428, 5730}, {3616, 6888}, {3655, 6259}, {3656, 34745}, {3754, 6911}, {3811, 12640}, {3869, 11012}, {3872, 17857}, {3874, 10680}, {3877, 10902}, {3884, 10267}, {3890, 34486}, {3892, 12001}, {3895, 7982}, {3898, 16202}, {4084, 37532}, {4301, 37533}, {4861, 5881}, {5141, 5587}, {5253, 15016}, {5443, 6830}, {5538, 6361}, {5697, 10087}, {5731, 15680}, {5790, 40260}, {5812, 34647}, {5842, 22791}, {5886, 30143}, {5903, 6905}, {6003, 35050}, {6224, 37437}, {6264, 20085}, {6705, 6892}, {6831, 15950}, {6834, 10573}, {6906, 37525}, {6910, 10165}, {6924, 35004}, {6928, 11813}, {6933, 10175}, {6949, 12247}, {6950, 37616}, {6974, 9948}, {7680, 37737}, {7681, 37730}, {7992, 30392}, {9669, 16174}, {9799, 38314}, {9942, 24929}, {10246, 12114}, {10283, 16160}, {10609, 11826}, {10786, 12647}, {11010, 13253}, {11260, 32159}, {11372, 30284}, {11567, 28160}, {11928, 12737}, {12246, 12255}, {12520, 37611}, {12635, 22770}, {12645, 12738}, {12675, 24928}, {12699, 40265}, {12705, 13384}, {14986, 18467}, {14988, 26286}, {15955, 37699}, {18389, 26437}, {18480, 33281}, {18493, 40259}, {18761, 31871}, {21635, 37821}, {22753, 31870}, {22758, 31803}, {23340, 25439}, {25440, 37562}, {26087, 28204}, {28082, 32486}, {28194, 37531}, {32905, 37727}, {33899, 38028}
X(40257) = midpoint of X(i) and X(j) for these {i,j}: {1, 6261}, {944, 6256}, {1158, 7971}, {1482, 11500}, {5882, 6260}, {12635, 22770}
X(40257) = reflection of X(i) in X(j) for these (i,j): (5450, 1385), (6796, 37837), (12616, 1125), (37727, 32905), (40256, 3), (40265, 12699)
X(40257) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18446, 5882), (3, 6265, 30144), (946, 5882, 950), (3428, 5730, 31806), (3576, 7971, 1158), (6326, 11014, 8), (6949, 12247, 18395), (10698, 11491, 5697), (13464, 13607, 40270), (15071, 21842, 104)
X(40258) lies on these lines: {6, 12308}, {382, 576}, {511, 8547}, {575, 5907}, {3818, 15019}, {5092, 21766}, {5476, 14094}, {5890, 12584}, {7516, 20190}, {9970, 37077}, {11422, 32305}, {11935, 17508}, {15032, 32599}, {15087, 16010}
X(40259) lies on these lines: {3, 40265}, {4, 21842}, {5, 3884}, {11, 65}, {515, 546}, {1389, 37718}, {1484, 3881}, {1621, 6796}, {1699, 5450}, {3585, 11715}, {3843, 40264}, {5126, 18483}, {5330, 5587}, {5603, 37702}, {5790, 15862}, {5882, 17605}, {5884, 18393}, {5886, 35016}, {6256, 9779}, {6261, 38021}, {6701, 38028}, {7504, 38134}, {7743, 13464}, {8070, 30384}, {11680, 31806}, {11813, 20117}, {12005, 12047}, {12611, 31871}, {12650, 30308}, {16160, 33592}, {18480, 19907}, {18493, 40257}, {37621, 38062}, {37722, 38039}
X(40259) = reflection of X(40260) in X(5)
X(40259) = X(40260)-of-Johnson-triangle
X(40259) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 34352, 38183), (11, 946, 31870), (11813, 26470, 20117)
X(40260) lies on these lines: {3, 40264}, {4, 11661}, {5, 3884}, {10, 119}, {12, 31870}, {21, 5587}, {35, 6246}, {140, 515}, {631, 38411}, {946, 3614}, {1158, 19875}, {1210, 10955}, {1385, 6702}, {1698, 5450}, {1737, 12005}, {3057, 16174}, {3576, 7705}, {3647, 26446}, {3652, 38755}, {3843, 40265}, {4187, 10175}, {5123, 6684}, {5499, 18242}, {5559, 5603}, {5790, 40257}, {5818, 6853}, {5882, 17606}, {5884, 18395}, {5953, 31759}, {6256, 9780}, {6949, 37710}, {7967, 15079}, {10165, 17619}, {10609, 32910}, {11681, 31806}, {12616, 12671}, {12650, 30315}, {19843, 34918}, {19925, 37290}, {24042, 37568}, {37230, 38162}, {37561, 38133}
X(40260) = midpoint of X(10609) and X(32910)
X(40260) = reflection of X(40259) in X(5)
X(40260) = X(40259)-of-Johnson-triangle
X(40260) = {X(10), X(119)}-harmonic conjugate of X(20117)
X(40261) lies on these lines: {2, 1495}, {30, 10173}, {3055, 11574}
X(40262) lies on these lines: {3, 9}, {20, 22792}, {21, 10157}, {35, 9856}, {100, 31798}, {140, 515}, {355, 6954}, {376, 6259}, {404, 11227}, {411, 5440}, {474, 10156}, {517, 6796}, {549, 6245}, {550, 6260}, {631, 5787}, {916, 15489}, {942, 6905}, {944, 5126}, {946, 10386}, {993, 9947}, {1071, 5122}, {1329, 4297}, {1385, 6911}, {1538, 6284}, {3149, 5806}, {3158, 8158}, {3419, 6962}, {3520, 12136}, {3522, 5658}, {3524, 9799}, {3528, 6223}, {3530, 6705}, {3576, 16408}, {3579, 6261}, {3601, 19541}, {3824, 37281}, {4188, 10167}, {4189, 5927}, {4255, 9620}, {4314, 7956}, {4640, 31821}, {4855, 7580}, {5010, 12688}, {5691, 37600}, {5703, 5805}, {5722, 6927}, {5731, 17567}, {5842, 9955}, {6001, 31663}, {6449, 19068}, {6450, 19067}, {6668, 19925}, {6745, 31799}, {6862, 18480}, {6891, 18481}, {6924, 9940}, {7161, 14794}, {7280, 12680}, {7681, 31795}, {8726, 16417}, {9942, 31837}, {9957, 11491}, {10164, 33899}, {10304, 12246}, {10884, 16371}, {11012, 34790}, {11220, 37307}, {12114, 17502}, {12608, 28146}, {13411, 20420}, {16845, 38318}, {17558, 38108}, {17573, 37526}, {17580, 38122}, {17616, 37293}, {18242, 28160}, {18446, 37582}, {24299, 37251}, {25440, 31787}, {31231, 37605}, {31937, 33862}, {36999, 37692}, {37623, 37700}
X(40262) = midpoint of X(i) and X(j) for these {i,j}: {20, 22792}, {550, 6260}, {1385, 11500}, {1490, 34862}, {3579, 6261}, {6796, 37837}, {9942, 31837}, {37623, 37700}
X(40262) = reflection of X(6705) in X(3530)
X(40262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 936, 31658), (3, 1490, 34862), (3, 5720, 31445), (411, 5440, 31793), (1071, 6942, 5122), (3149, 24929, 5806), (6905, 33597, 942)
X(40263) lies on the cubic K680 and these lines: {1, 1898}, {2, 13369}, {3, 9}, {4, 912}, {5, 1071}, {7, 6849}, {10, 37401}, {19, 37489}, {20, 31837}, {30, 72}, {33, 3157}, {35, 7701}, {37, 500}, {40, 18518}, {46, 18491}, {52, 916}, {58, 2341}, {63, 6985}, {65, 79}, {90, 37579}, {119, 12616}, {140, 10167}, {191, 210}, {200, 35448}, {222, 37696}, {226, 6841}, {329, 6851}, {354, 9955}, {355, 5836}, {376, 3876}, {381, 942}, {382, 517}, {389, 2808}, {392, 34773}, {405, 13151}, {474, 17616}, {495, 12711}, {496, 17625}, {511, 22036}, {515, 3878}, {518, 12699}, {546, 24475}, {550, 31835}, {568, 2262}, {631, 11220}, {651, 6198}, {758, 31673}, {908, 37356}, {943, 29007}, {944, 3890}, {946, 2801}, {952, 12672}, {960, 18481}, {990, 36754}, {1012, 33596}, {1062, 34048}, {1066, 2310}, {1158, 11499}, {1214, 35194}, {1385, 5259}, {1467, 38271}, {1478, 1858}, {1482, 9856}, {1519, 10943}, {1656, 9940}, {1657, 31793}, {1698, 40296}, {1699, 18544}, {1709, 11248}, {1745, 24430}, {1750, 5709}, {1824, 13754}, {1836, 18517}, {1837, 18516}, {1872, 12162}, {1902, 12293}, {1935, 3465}, {2096, 6885}, {2261, 37506}, {2772, 31728}, {2886, 18243}, {3057, 28204}, {3062, 6769}, {3073, 9355}, {3149, 24467}, {3219, 3651}, {3339, 18529}, {3359, 7992}, {3421, 12529}, {3487, 10394}, {3526, 11227}, {3555, 22791}, {3560, 18446}, {3601, 28444}, {3652, 4640}, {3654, 4662}, {3656, 34791}, {3678, 31730}, {3680, 8148}, {3681, 6361}, {3698, 13145}, {3753, 17653}, {3817, 12005}, {3818, 24476}, {3827, 34775}, {3843, 5806}, {3845, 24473}, {3874, 18483}, {3927, 37411}, {3931, 5492}, {4005, 16113}, {4084, 34648}, {4292, 28452}, {4297, 20117}, {4303, 7069}, {4420, 10308}, {4523, 29040}, {5045, 8581}, {5076, 31822}, {5251, 16132}, {5533, 12611}, {5534, 10679}, {5570, 10896}, {5587, 15071}, {5657, 9961}, {5658, 6825}, {5687, 17615}, {5690, 18908}, {5694, 14110}, {5696, 36973}, {5714, 6866}, {5728, 6147}, {5731, 31838}, {5758, 36991}, {5761, 37434}, {5768, 6893}, {5770, 6848}, {5787, 6928}, {5790, 9947}, {5811, 6827}, {5817, 6887}, {5840, 12665}, {5884, 19925}, {5885, 38140}, {5886, 12675}, {5891, 11573}, {5902, 18492}, {5918, 31663}, {5928, 18531}, {6000, 29958}, {6223, 6850}, {6245, 6882}, {6260, 6842}, {6261, 22758}, {6264, 10222}, {6684, 15064}, {6734, 37406}, {6831, 13257}, {6833, 37713}, {6845, 31053}, {6863, 9942}, {6864, 36996}, {6883, 10884}, {6899, 31018}, {6913, 37615}, {6914, 33597}, {6915, 13243}, {6918, 37612}, {6920, 18444}, {6948, 12246}, {6958, 18238}, {6990, 31019}, {7082, 7742}, {7411, 26878}, {7580, 26921}, {7688, 16143}, {7957, 28146}, {7989, 15016}, {8143, 37593}, {8227, 13373}, {8726, 30326}, {9578, 18545}, {9579, 18397}, {9614, 18543}, {9708, 18251}, {9844, 12433}, {9848, 31792}, {9928, 37194}, {9943, 26446}, {9957, 18526}, {10085, 10269}, {10391, 11374}, {10525, 12679}, {10728, 12532}, {10826, 18838}, {10855, 16863}, {10861, 17582}, {10864, 37611}, {10895, 13750}, {10914, 37705}, {10950, 34697}, {11230, 26201}, {11412, 31836}, {11496, 16112}, {11500, 32159}, {11529, 30290}, {12047, 26475}, {12259, 37368}, {12526, 12702}, {12572, 28459}, {12608, 26470}, {12709, 37730}, {12738, 16138}, {12773, 24928}, {13624, 18515}, {13743, 24929}, {14923, 34627}, {15030, 23154}, {15528, 23513}, {15800, 22793}, {16116, 20292}, {16465, 37447}, {17484, 37433}, {17637, 22798}, {17649, 33899}, {17745, 37509}, {18254, 38761}, {18440, 34381}, {18534, 37547}, {18541, 37544}, {19541, 37532}, {21669, 34772}, {23156, 31751}, {28164, 31806}, {28208, 31165}, {30304, 37534}, {31786, 31821}, {35631, 38485}, {36865, 37837}, {37251, 37582}
X(40263) = midpoint of X(i) and X(j) for these {i,j}: {4, 12528}, {5691, 5693}, {10728, 12532}, {12664, 18239}, {12688, 14872}, {18525, 40266}
X(40263) = reflection of X(i) in X(j) for these (i,j): (1, 31937), (3, 5777), (20, 31837), (65, 18480), (550, 31835), (946, 31871), (1071, 5), (1482, 9856), (1657, 31793), (3555, 22791), (3874, 18483), (4297, 20117), (5884, 19925), (5887, 31803), (10202, 5927), (10914, 37705), (11412, 31836), (11500, 32159), (12680, 1385), (12688, 31828), (12702, 34790), (14110, 5694), (15071, 34339), (17637, 22798), (17649, 33899), (17660, 12611), (18481, 960), (18526, 9957), (23156, 31751), (23340, 12672), (24473, 3845), (24474, 4), (24475, 546), (24476, 3818), (31730, 3678), (31786, 31821), (31788, 9947), (37562, 355), (37585, 72), (38761, 18254)
X(40263) = anticomplement of X(13369)
X(40263) = circumcenter of triangle A*B*C* as described at X(5905)
X(40263) = X(1071)-of-Johnson-triangle
X(40263) = intersection, other than A,B,C, of conics {{A, B, C, X(265), X(268)}} and {{A, B, C, X(282), X(2166)}}
X(40263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18540, 37234), (5, 1071, 10202), (40, 18528, 18518), (84, 5720, 3), (355, 6259, 6923), (936, 7171, 3), (1012, 37700, 33596), (1071, 5927, 5), (1490, 7330, 3), (1709, 17857, 11248), (1745, 24430, 37565), (3560, 18446, 24299), (3927, 37411, 37584), (4654, 10399, 942), (5534, 12705, 10679), (5587, 15071, 34339), (5787, 37822, 6928), (9940, 10157, 1656), (9947, 31788, 5790), (17781, 31938, 72)
X(40264) lies on these lines: {1, 4}, {3, 40260}, {56, 6246}, {355, 40256}, {382, 40265}, {2800, 18525}, {2829, 33899}, {3576, 5154}, {3843, 40259}, {4188, 5587}, {4297, 6958}, {5450, 6924}, {6796, 26086}, {6921, 10175}, {6931, 10165}, {6941, 36975}, {6959, 19925}, {6971, 18481}, {7354, 12832}, {9655, 31870}, {10265, 37002}, {10896, 11715}, {11681, 12119}, {12114, 37251}, {18242, 28186}, {19535, 38134}, {22793, 23960}, {28208, 37837}
X(40264) = reflection of X(i) in X(j) for these (i,j): (5450, 18480), (40256, 355), (40265, 382)
X(40265) lies on these lines: {3, 40259}, {4, 7161}, {145, 515}, {382, 40264}, {516, 10525}, {946, 3612}, {3843, 40260}, {4305, 9580}, {5450, 28146}, {6796, 22793}, {6848, 18483}, {6890, 31730}, {7967, 16118}, {9579, 13607}, {9668, 31870}, {12699, 40257}, {18499, 31803}, {31671, 40249}
X(40265) = reflection of X(i) in X(j) for these (i,j): (6796, 22793), (40257, 12699), (40264, 382)
X(40266) lies on these lines: {1, 399}, {3, 960}, {4, 14988}, {5, 10129}, {30, 3869}, {40, 5694}, {46, 37251}, {63, 13465}, {65, 381}, {72, 3426}, {78, 35000}, {221, 18447}, {355, 2800}, {382, 517}, {392, 13369}, {518, 8148}, {550, 9961}, {758, 12699}, {912, 1482}, {942, 18493}, {952, 3885}, {993, 3652}, {1071, 10246}, {1385, 15071}, {1537, 10943}, {1656, 34339}, {1657, 14110}, {1698, 13145}, {1768, 32612}, {1836, 37230}, {1854, 18455}, {1858, 37234}, {2099, 18761}, {2390, 18435}, {2778, 38790}, {2801, 37727}, {2818, 12162}, {3057, 18526}, {3340, 18540}, {3534, 31165}, {3579, 5692}, {3654, 3678}, {3655, 3884}, {3656, 3874}, {3697, 38066}, {3812, 5055}, {3827, 18440}, {3843, 7686}, {3868, 22791}, {3877, 34773}, {3878, 18481}, {3901, 31162}, {3940, 35448}, {4067, 28194}, {4084, 18483}, {5054, 25917}, {5248, 33858}, {5250, 37292}, {5450, 6265}, {5587, 35004}, {5603, 24475}, {5657, 31835}, {5687, 35460}, {5697, 28204}, {5730, 35459}, {5777, 5790}, {5884, 5886}, {5885, 8227}, {5902, 9955}, {5903, 18480}, {6326, 26285}, {6583, 11522}, {6825, 18231}, {6841, 39542}, {6882, 33899}, {6914, 21740}, {6958, 14647}, {6971, 12616}, {6980, 12608}, {7171, 15829}, {7330, 7971}, {7741, 11571}, {7986, 16466}, {7991, 18528}, {7992, 37611}, {7995, 37531}, {8715, 12738}, {9856, 18544}, {10106, 34698}, {10167, 31838}, {10540, 14529}, {10573, 18516}, {10620, 10693}, {10624, 34745}, {10680, 37252}, {10942, 13257}, {11230, 15016}, {11376, 11570}, {11682, 35457}, {11849, 37700}, {12331, 17857}, {12515, 25440}, {12526, 37584}, {12532, 14923}, {12675, 37624}, {12705, 37533}, {12709, 15934}, {12758, 37738}, {14269, 16616}, {15726, 17800}, {16200, 26200}, {18254, 37828}, {18446, 37621}, {18491, 37567}, {20117, 26446}, {22765, 24467}, {22793, 37625}, {24806, 35194}, {25414, 37708}, {31019, 33668}, {31788, 31821}, {34718, 34790}, {34880, 35451}
X(40266) = reflection of X(i) in X(j) for these (i,j): (3, 5887), (40, 5694), (65, 31937), (355, 31803), (382, 12688), (1482, 12672), (1657, 14110), (3534, 31165), (3868, 22791), (4084, 18483), (5691, 31828), (5903, 18480), (9961, 550), (10620, 10693), (11571, 12611), (12645, 14872), (12702, 72), (12773, 17638), (14923, 37705), (15071, 1385), (18481, 3878), (18525, 40263), (18526, 3057), (24474, 9856), (25413, 355), (31788, 31821), (37562, 5777), (37625, 22793)
X(40266) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (65, 31937, 381), (5777, 37562, 5790), (25917, 40296, 5054)
X(40267) lies on these lines: {1, 22792}, {3, 119}, {4, 496}, {20, 17757}, {30, 10306}, {65, 971}, {84, 18480}, {153, 5687}, {221, 18340}, {381, 10199}, {382, 515}, {452, 38031}, {516, 12640}, {517, 18239}, {529, 8158}, {944, 1537}, {956, 37437}, {1012, 9654}, {1158, 5790}, {1317, 40272}, {1420, 1538}, {1479, 30283}, {1490, 28160}, {1532, 37002}, {1656, 5450}, {1657, 11500}, {1699, 9657}, {2098, 34789}, {2800, 12645}, {3295, 12115}, {3338, 10864}, {3421, 31777}, {3436, 6244}, {3534, 6796}, {3585, 22766}, {3617, 14646}, {3830, 12001}, {4297, 25681}, {5048, 12953}, {5073, 5842}, {5080, 37022}, {5229, 8727}, {5570, 12680}, {5587, 34862}, {5708, 5787}, {5779, 5794}, {5841, 37411}, {6001, 18525}, {6260, 18481}, {6850, 9708}, {6906, 31479}, {6918, 18516}, {6935, 10592}, {6941, 12248}, {7354, 19541}, {7373, 26333}, {7686, 18541}, {7952, 10731}, {7971, 28204}, {9613, 9856}, {9709, 31775}, {10246, 12608}, {10525, 40290}, {10572, 12678}, {10724, 25416}, {11249, 34740}, {11849, 18545}, {11928, 12761}, {12246, 33899}, {12330, 18518}, {12650, 22793}, {12666, 14988}, {12763, 26358}, {14647, 18357}, {16127, 18499}, {18237, 18519}, {21077, 28164}, {22758, 31493}, {25415, 36999}, {31822, 33697}
X(40267) = reflection of X(i) in X(j) for these (i,j): (1, 22792), (3, 6256), (84, 18480), (1657, 11500), (5787, 31673), (12246, 33899), (12650, 22793), (12773, 12761), (18481, 6260)
X(40267) = {X(4), X(3600)}-harmonic conjugate of X(7956)
X(40268) lies on these lines: {3, 6}, {4, 10513}, {5, 14484}, {194, 14532}, {1270, 36709}, {1271, 36714}, {3640, 12697}, {3641, 12698}, {5590, 6202}, {5591, 6201}, {6214, 36711}, {6215, 36712}, {6226, 6319}, {6227, 6320}, {7725, 7733}, {7726, 7732}, {7758, 29181}, {7855, 36990}, {9748, 33185}, {10927, 18960}, {10928, 18959}, {12753, 13270}, {12754, 13269}, {12805, 13283}, {12806, 13282}, {15312, 34938}, {21542, 37521}
X(40268) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1160, 1161, 6), (1350, 9605, 3), (3095, 33878, 3), (5024, 5188, 3), (5864, 5865, 575), (9821, 10983, 3), (12305, 39649, 3), (12306, 39658, 3), (23115, 34815, 3), (30270, 30435, 3)
X(40269) lies on these lines: {1, 29007}, {7, 80}, {8, 3255}, {9, 2320}, {55, 4661}, {144, 145}, {497, 4430}, {971, 7672}, {1156, 10698}, {1445, 18450}, {1864, 3873}, {2099, 16112}, {2646, 15481}, {2771, 11041}, {3059, 4711}, {3100, 3751}, {3240, 7004}, {3241, 12532}, {3487, 5045}, {3616, 5825}, {3681, 5281}, {3811, 5223}, {3889, 18220}, {3957, 30223}, {4313, 5904}, {4323, 31803}, {4860, 27778}, {5086, 5832}, {5261, 14872}, {5265, 12675}, {5686, 7080}, {5704, 12005}, {5729, 7677}, {5731, 18397}, {5759, 35250}, {5779, 8543}, {7069, 29814}, {7226, 14547}, {7678, 20330}, {8581, 30340}, {10399, 11037}, {10950, 17768}, {11372, 11526}, {11502, 23958}, {12669, 12671}, {13243, 37541}, {14151, 19907}, {15587, 38092}, {17018, 24430}, {17620, 39779}, {17636, 20085}, {30312, 31657}
X(40269) = reflection of X(i) in X(j) for these (i,j): (7, 18412), (390, 10394)
X(40269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1864, 3873, 5274), (3681, 10391, 5281)
X(40270) lies on these lines: {1, 4}, {3, 21625}, {8, 3646}, {10, 6767}, {30, 12577}, {40, 10580}, {354, 10624}, {355, 18530}, {390, 3333}, {496, 13405}, {514, 32195}, {516, 5045}, {517, 6744}, {519, 4015}, {527, 3881}, {528, 12436}, {596, 28557}, {938, 11362}, {942, 12575}, {999, 4314}, {1125, 3813}, {1210, 3303}, {1837, 8162}, {2177, 28018}, {3058, 4292}, {3085, 10172}, {3086, 10389}, {3244, 5289}, {3295, 6684}, {3296, 4312}, {3304, 4304}, {3698, 34699}, {3746, 3911}, {3748, 13411}, {3913, 9843}, {3946, 30148}, {3947, 9669}, {4114, 4338}, {4297, 7373}, {4298, 5049}, {4301, 15934}, {4460, 28644}, {4882, 17559}, {5082, 10582}, {5129, 9797}, {5436, 34625}, {5493, 5708}, {5542, 12699}, {5572, 18241}, {5703, 37704}, {5763, 10222}, {5850, 15008}, {6361, 10980}, {6601, 12864}, {6692, 8715}, {6738, 9957}, {6765, 26105}, {6766, 37423}, {7982, 14563}, {8227, 10578}, {8236, 10165}, {9589, 30350}, {9785, 11529}, {10122, 18839}, {10198, 24386}, {10385, 15803}, {10386, 12512}, {11036, 31162}, {11518, 30305}, {12005, 12710}, {12245, 30337}, {12563, 22791}, {12572, 34791}, {13374, 16201}, {15174, 25405}, {18391, 37556}, {18527, 19925}, {18990, 28172}, {19843, 38316}, {20008, 36922}, {28158, 31776}, {28164, 31795}, {28228, 31794}, {29655, 39559}, {31435, 36845}
X(40270) = midpoint of X(i) and X(j) for these {i,j}: {942, 12575}, {3244, 5795}, {4298, 15171}, {5045, 15172}, {5542, 15006}, {6738, 9957}, {12433, 31792}, {12572, 34791}
X(40270) = reflection of X(17706) in X(6744)
X(40270) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 497, 21620), (1, 1058, 946), (1, 3488, 5882), (1, 9614, 3475), (390, 3333, 31730), (497, 21620, 18483), (938, 31393, 11362), (942, 15170, 12575), (946, 5882, 1490), (3058, 17609, 4292), (3295, 11019, 6684), (5049, 15171, 4298), (12710, 12915, 12005), (13464, 13607, 40257), (21625, 30331, 3)
X(40271) lies on these lines: {3, 12}, {4, 26437}, {226, 9657}, {515, 1836}, {535, 17532}, {912, 4338}, {993, 10895}, {2476, 5229}, {3585, 22758}, {3626, 37567}, {3822, 5204}, {4293, 6830}, {6224, 12831}, {18962, 37468}, {22791, 40272}, {31266, 37605}
X(40272) lies on these lines: {3, 11}, {4, 26358}, {515, 2098}, {1317, 40267}, {1388, 9670}, {3419, 3626}, {3583, 11499}, {3825, 5217}, {4193, 5225}, {4294, 6941}, {5046, 8165}, {5687, 12764}, {5697, 5881}, {10087, 18542}, {10896, 25440}, {22791, 40271}
X(40272) = {X(1479), X(10090)}-harmonic conjugate of X(9669)
X(40273) lies on these lines: {1, 3627}, {3, 5284}, {4, 145}, {5, 40}, {8, 3843}, {10, 3850}, {11, 3336}, {12, 37563}, {20, 18493}, {30, 551}, {46, 10593}, {79, 37722}, {140, 516}, {143, 2807}, {165, 632}, {226, 15172}, {354, 11544}, {355, 3845}, {381, 962}, {382, 5603}, {484, 7173}, {495, 12701}, {496, 1836}, {497, 6147}, {515, 3853}, {517, 546}, {519, 14893}, {547, 6684}, {548, 1125}, {549, 8227}, {550, 5886}, {944, 3830}, {1387, 7354}, {1479, 12433}, {1483, 3656}, {1484, 16159}, {1519, 20420}, {1656, 6361}, {1657, 3616}, {1770, 15325}, {2951, 38111}, {3091, 12702}, {3146, 10246}, {3241, 38335}, {3485, 9668}, {3526, 9778}, {3530, 11230}, {3534, 38022}, {3543, 10595}, {3545, 20070}, {3576, 15704}, {3579, 3628}, {3583, 37730}, {3614, 11010}, {3622, 33703}, {3624, 15712}, {3634, 12812}, {3636, 28172}, {3649, 4857}, {3652, 5536}, {3653, 19710}, {3654, 7989}, {3655, 33699}, {3671, 18527}, {3679, 23046}, {3828, 14892}, {3832, 5790}, {3839, 12245}, {3851, 5657}, {3856, 11362}, {3857, 7991}, {3858, 5587}, {3859, 28228}, {3861, 4301}, {3874, 31828}, {4292, 7743}, {4295, 9669}, {4338, 17728}, {5057, 24390}, {5066, 9956}, {5072, 9780}, {5073, 5731}, {5076, 10247}, {5119, 10592}, {5274, 5708}, {5443, 15338}, {5482, 29349}, {5493, 11231}, {5698, 31493}, {5714, 6767}, {5719, 12047}, {5734, 18526}, {5771, 6841}, {5805, 37534}, {5882, 33697}, {5903, 12019}, {6265, 13146}, {6284, 18393}, {6824, 31671}, {6915, 35000}, {6960, 38114}, {6972, 34126}, {7514, 9911}, {7956, 37356}, {7967, 17578}, {7982, 37705}, {8144, 34036}, {8226, 26878}, {8703, 38021}, {8727, 37532}, {9579, 11373}, {9580, 10386}, {9612, 37556}, {9626, 37947}, {9654, 30305}, {9856, 14988}, {10164, 16239}, {10165, 33923}, {10175, 12811}, {10222, 12102}, {10283, 11522}, {10591, 36279}, {10707, 14450}, {10944, 18513}, {10950, 18514}, {11012, 31649}, {11036, 18530}, {11246, 37720}, {11365, 12084}, {11372, 24467}, {11698, 14217}, {11735, 34584}, {12100, 12512}, {12101, 28204}, {12103, 13624}, {12108, 19862}, {12645, 14269}, {12679, 32214}, {12688, 24475}, {13373, 15726}, {13407, 15170}, {13451, 31760}, {13464, 28160}, {13607, 28208}, {13925, 31439}, {14869, 35242}, {14891, 19883}, {14986, 18541}, {15178, 28164}, {15326, 37735}, {15684, 38314}, {15686, 25055}, {15699, 30308}, {15759, 34638}, {15808, 31666}, {16118, 16173}, {16417, 26129}, {16881, 31728}, {17768, 24387}, {18492, 38138}, {18990, 20323}, {19541, 32141}, {19709, 34632}, {21669, 22765}, {21677, 31159}, {24703, 31419}, {26725, 31651}, {29309, 34466}, {33668, 37433}, {33814, 37251}, {34123, 37256}, {35272, 37435}, {36002, 37621}, {38038, 38602}, {38044, 38761}
X(40273) = midpoint of X(i) and X(j) for these {i,j}: {1, 3627}, {4, 22791}, {5, 12699}, {382, 34773}, {946, 22793}, {962, 5690}, {1483, 5691}, {1484, 34789}, {1537, 22938}, {3655, 33699}, {3656, 15687}, {3845, 31162}, {3874, 31828}, {4301, 18480}, {5882, 33697}, {7982, 37705}, {9812, 38034}, {10222, 31673}, {11698, 14217}, {12679, 32214}, {12688, 24475}, {33668, 37433}
X(40273) = reflection of X(i) in X(j) for these (i,j): (10, 3850), (140, 9955), (546, 18483), (548, 1125), (3579, 3628), (5901, 946), (9956, 12571), (12103, 13624), (18357, 546), (18480, 3861), (31673, 12102), (31728, 16881), (31730, 3530), (34638, 15759)
X(40273) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (20, 18493, 38028), (381, 962, 5690), (382, 5603, 34773), (496, 1836, 24470), (944, 10248, 3830), (1479, 39542, 12433), (1483, 15687, 5691), (1699, 12699, 5), (3091, 12702, 38042), (3579, 3817, 3628), (3656, 5691, 1483), (6284, 18393, 37737), (6361, 9779, 1656), (7965, 26470, 16160), (9580, 11374, 10386), (9956, 12571, 5066), (11230, 31730, 3530), (11522, 18481, 10283), (12047, 15171, 5719), (12699, 26446, 9589)
X(40274) lies on these lines: {3, 6}, {385, 6312}, {488, 9541}, {637, 6561}, {639, 6565}, {1078, 6316}, {6813, 10576}, {8956, 33586}, {13828, 33273}, {32419, 32808}
X(40274) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 3102, 372), (39, 3098, 40275), (371, 6396, 32), (371, 11825, 372), (371, 35840, 6419), (1160, 39649, 19145), (6221, 12962, 371), (12305, 39648, 2459)
X(40275) lies on these lines: {3, 6}, {385, 6316}, {638, 6560}, {640, 6564}, {1078, 6312}, {6811, 10577}, {7484, 8956}, {13708, 33273}, {32421, 32809}
X(40275) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 3103, 371), (39, 3098, 40274), (372, 6200, 32), (372, 11824, 371), (372, 35841, 6420), (1161, 39658, 19146), (6398, 12969, 372), (12306, 39679, 2460)
X(40276) lies on these lines: {3, 64}, {26, 10628}, {49, 34786}, {54, 18376}, {110, 34785}, {156, 5448}, {184, 7547}, {206, 18553}, {381, 10274}, {567, 18434}, {578, 18386}, {1503, 10224}, {1614, 7577}, {3043, 40242}, {3153, 9833}, {5878, 13619}, {6143, 14216}, {9704, 18405}, {10594, 11808}, {11459, 23358}, {12279, 13293}, {12281, 13289}, {14157, 22802}, {15060, 32391}, {15311, 15332}, {16000, 16868}, {17824, 18378}, {26883, 35480}
X(40276) = {X(6759), X(10539)}-harmonic conjugate of X(10282)
X(40277) lies on these lines: {2, 3}, {5476, 8787}, {7777, 12355}
X(40277) = {X(381), X(35930)}-harmonic conjugate of X(5066)
X(40278) lies on these lines: {3, 3096}, {4, 11171}, {5, 7913}, {20, 6033}, {30, 7775}, {140, 3818}, {147, 9821}, {315, 35705}, {316, 1657}, {548, 7761}, {631, 6287}, {1153, 11645}, {1503, 10104}, {1513, 14880}, {2782, 8721}, {3095, 40236}, {3627, 5475}, {5167, 10575}, {7764, 29317}, {7802, 38744}, {7858, 22728}, {7898, 17538}, {8722, 32151}, {9744, 14881}, {12054, 13862}, {12252, 26316}, {13334, 40250}, {14692, 20081}, {16924, 22681}, {29012, 32190}, {33014, 38742}
X(40279) lies on these lines: {2, 3}, {76, 6033}, {114, 7863}, {115, 14880}, {147, 13108}, {182, 7902}, {183, 32151}, {265, 38520}, {315, 32521}, {316, 9821}, {511, 7843}, {1078, 10722}, {2023, 7748}, {2549, 32516}, {2794, 10104}, {3095, 7858}, {3098, 5031}, {3398, 7856}, {3818, 24256}, {3934, 9996}, {4846, 30496}, {5092, 7861}, {5188, 13449}, {5475, 14881}, {6310, 13754}, {6321, 11257}, {7694, 7758}, {7728, 38523}, {7746, 12042}, {7749, 38749}, {7752, 35002}, {7756, 39809}, {7782, 38730}, {7790, 12054}, {7801, 22566}, {7823, 9301}, {7828, 26316}, {7854, 22505}, {7860, 33706}, {7936, 22712}, {7946, 12251}, {9744, 32448}, {9753, 32134}, {9863, 38744}, {9993, 18502}, {10242, 22676}, {10741, 38522}, {10742, 38521}, {10749, 38529}, {12188, 32528}, {12203, 14639}, {12918, 38525}, {13630, 40254}, {19127, 34981}, {22338, 38524}, {25157, 37824}, {25167, 37825}, {32152, 39838}, {38526, 38953}
X(40279) = orthocentroidal circle-inverse of-X(37243)
X(40279) = tetrahedral projection of ABC to 2nd Neuberg triangle
X(40279) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4, 37243), (3, 381, 5025), (3, 33233, 549), (4, 16044, 381), (4, 37348, 5), (4, 40236, 382), (5, 33185, 547), (376, 33259, 3), (381, 7770, 5)
X(40280) lies on these lines: {2, 5655}, {3, 6}, {4, 7693}, {5, 7703}, {20, 12006}, {30, 5640}, {51, 3534}, {125, 10938}, {140, 10574}, {143, 3522}, {184, 17701}, {185, 3526}, {186, 34513}, {265, 18911}, {373, 381}, {376, 5946}, {399, 5651}, {546, 15028}, {547, 15305}, {548, 3567}, {549, 5890}, {550, 15043}, {631, 13630}, {632, 12111}, {974, 38794}, {1112, 35485}, {1154, 3524}, {1204, 34864}, {1511, 11003}, {1656, 15030}, {1657, 5462}, {2070, 35268}, {2781, 38064}, {2854, 11179}, {2979, 12100}, {3060, 8703}, {3066, 35237}, {3090, 13491}, {3146, 15026}, {3426, 5544}, {3523, 6102}, {3525, 5876}, {3528, 10263}, {3529, 10095}, {3530, 5889}, {3533, 14128}, {3543, 13364}, {3627, 15024}, {3628, 6241}, {3819, 15701}, {3830, 5943}, {3832, 32205}, {3845, 11451}, {3850, 11465}, {3851, 10575}, {3917, 15693}, {4550, 10620}, {4846, 7728}, {5012, 15035}, {5054, 5650}, {5055, 6000}, {5066, 11455}, {5068, 32137}, {5070, 12162}, {5072, 11381}, {5076, 14641}, {5446, 15696}, {5562, 15720}, {5891, 15082}, {5904, 15229}, {5913, 30515}, {6090, 18445}, {6101, 15717}, {6288, 6815}, {6293, 25563}, {6403, 37934}, {6644, 6800}, {6688, 16194}, {6776, 16270}, {7464, 15018}, {7496, 33533}, {7502, 15053}, {7574, 7706}, {7575, 15080}, {7722, 10294}, {7999, 12108}, {8717, 34417}, {9744, 12093}, {9781, 15704}, {9826, 20127}, {9833, 32184}, {10110, 17800}, {10254, 23515}, {10299, 10627}, {10303, 11591}, {10304, 13391}, {10540, 35259}, {10605, 32620}, {10653, 11624}, {10654, 11626}, {11204, 38633}, {11412, 15712}, {11424, 15047}, {11444, 14869}, {11799, 37648}, {11806, 15040}, {12045, 15703}, {12112, 16042}, {12308, 16187}, {13321, 15688}, {13451, 15686}, {13570, 35403}, {14093, 36987}, {14269, 14845}, {14389, 15122}, {14708, 18580}, {14831, 15700}, {15041, 16223}, {15055, 18570}, {15056, 16239}, {15695, 21849}, {16003, 24206}, {16222, 38788}, {16658, 23410}
X(40280) = midpoint of X(i) and X(j) for these {i,j}: {376, 11002}, {5890, 7998}, {13321, 15688}, {15045, 20791}, {15072, 16261}
X(40280) = reflection of X(i) in X(j) for these (i,j): (373, 5892), (381, 373), (5891, 15082), (7998, 549), (11002, 5946), (13321, 16226), (14269, 14845), (16261, 5), (23039, 7998)
X(40280) = Brocard circle-inverse of-X(37477)
X(40280) = X(16261)-of-Johnson-triangle
X(40280) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 37477), (3, 182, 14805), (3, 389, 37484), (3, 568, 13340), (3, 9730, 568), (3, 15037, 13352), (3, 36752, 37472), (3, 36753, 37495), (3, 37481, 6243), (3, 37514, 13353), (52, 17704, 3), (140, 10574, 34783), (182, 37470, 3), (568, 9730, 37481), (568, 13340, 6243), (5092, 32110, 3), (5943, 14855, 3830), (9729, 16836, 9730), (9730, 16836, 3), (10575, 11695, 3851), (11465, 12279, 3850), (13340, 37481, 568), (30260, 30261, 566)
X(40281) lies on these lines: {3, 1180}, {30, 143}, {3060, 14532}, {5663, 40250}, {5889, 11287}, {5946, 35930}, {6102, 37242}, {7739, 37473}, {11286, 15043}, {15048, 19161}
X(40281) = midpoint of X(i) and X(j) for these {i,j}: {6102, 37242}, {15048, 19161}
X(40282) lies on these lines: {3, 74}, {351, 2854}, {511, 8644}, {542, 9125}, {2782, 9123}, {9129, 9142}, {9130, 9145}, {9156, 33962}, {35357, 39689}
X(40282) = reflection of X(40283) in X(351)
X(40282) = crosspoint of X(843) and X(14948)
X(40282) = crosssum of X(543) and X(5108)
X(40282) = X(351)-of-1st-Parry-triangle
X(40282) = {X(110), X(9215)}-harmonic conjugate of X(3)
X(40283) lies on these lines: {3, 111}, {351, 2854}, {511, 647}, {543, 9189}, {1649, 5969}, {2502, 5467}, {2782, 9185}, {5106, 9177}, {5663, 9138}, {7664, 15000}, {9129, 9145}, {9130, 9142}
X(40283) = reflection of X(40282) in X(351)
X(40283) = crossdifference of every pair of points on line {X(1316), X(9125)}
X(40283) = X(351)-of-2nd-Parry-triangle
X(40283) = {X(111), X(9216)}-harmonic conjugate of X(3)
X(40284) lies on these lines: {5, 2883}, {52, 5054}, {376, 10110}, {389, 3525}, {511, 11592}, {1657, 5943}, {3060, 3523}, {3146, 15028}, {5462, 12100}, {5876, 12045}, {5907, 15703}, {9730, 40247}, {10095, 12002}, {10124, 12006}, {10219, 13630}, {11465, 13474}, {11591, 15012}, {11793, 37481}, {12103, 13363}, {13382, 15045}, {15043, 15606}, {15718, 21849}
X(40285) lies on these lines: {3, 64}, {6, 18383}, {155, 18400}, {161, 18436}, {381, 6145}, {394, 34785}, {546, 34117}, {1181, 7507}, {1503, 18569}, {1594, 11456}, {2393, 15083}, {3818, 19149}, {5878, 6240}, {6225, 12112}, {6293, 7517}, {7503, 32379}, {9833, 11441}, {10274, 37506}, {10628, 12310}, {10982, 18376}, {11591, 15577}, {12173, 13419}, {12324, 37119}, {15068, 34782}, {17824, 18405}, {18358, 34118}, {18445, 31724}, {23325, 36752}, {32767, 37514}, {34781, 37444}, {34786, 36747}
X(40285) = reflection of X(32321) in X(6759)
X(40285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1498, 18451, 6759), (17824, 18405, 36749)
X(40286) lies on these lines: {30, 3068}, {187, 13846}, {385, 13657}, {597, 40287}, {1160, 7583}, {3070, 38425}, {7374, 13886}, {8960, 8980}, {8975, 18511}, {8976, 13638}, {8981, 35945}, {12602, 13879}, {13910, 18440}
X(40287) lies on these lines: {30, 3069}, {187, 13847}, {385, 13777}, {597, 40286}, {1161, 7584}, {3071, 38426}, {7000, 13939}, {10991, 13967}, {12601, 13933}, {13758, 13951}, {13949, 18509}, {13966, 35944}, {13972, 18440}
X(40288) lies on these lines: {371, 3629}, {1151, 1503}, {3529, 9540}, {12974, 13910}, {15815, 40289}
X(40289) lies on these lines: {372, 3629}, {1152, 1503}, {3529, 13935}, {12975, 13972}, {15815, 40288}
X(40290) lies on these lines: {2, 12114}, {8, 2829}, {11, 6256}, {84, 355}, {515, 3057}, {1476, 7681}, {1490, 34773}, {1532, 15866}, {7995, 37708}, {10525, 40267}, {10893, 14986}, {10947, 37001}, {11827, 17615}, {12629, 12700}, {12761, 38669}, {26492, 38319}
X(40291) lies on these lines: {5, 1511}, {23, 32235}, {25, 19140}, {74, 7556}, {110, 576}, {125, 15080}, {399, 37489}, {542, 1495}, {3629, 20772}, {3818, 32227}, {5092, 16165}, {5642, 10546}, {5663, 12105}, {7712, 9140}, {9976, 26864}, {10117, 12315}, {11060, 20998}, {11800, 32284}, {12584, 35259}, {13394, 20301}, {15035, 16187}, {15448, 32423}
X(40291) = midpoint of X(23) and X(32235)
X(40291) = {X(110), X(34417)}-harmonic conjugate of X(25556)
X(40292) lies on these lines: {1, 3}, {8, 20846}, {10, 11344}, {11, 6883}, {12, 6985}, {21, 3434}, {80, 9708}, {90, 31445}, {197, 11334}, {212, 1064}, {219, 2174}, {222, 4337}, {255, 4300}, {278, 378}, {347, 2071}, {387, 16452}, {388, 3651}, {390, 37106}, {405, 1479}, {411, 3085}, {474, 6690}, {497, 1006}, {498, 3149}, {528, 10058}, {601, 22361}, {674, 36740}, {859, 1486}, {920, 12711}, {943, 3485}, {954, 38454}, {956, 37286}, {958, 3419}, {960, 11517}, {984, 3465}, {993, 4304}, {1001, 30384}, {1011, 33137}, {1012, 4302}, {1030, 2256}, {1036, 1794}, {1125, 37282}, {1212, 1752}, {1253, 22350}, {1259, 12514}, {1260, 5692}, {1478, 7580}, {1496, 4303}, {1593, 1838}, {1621, 30305}, {1698, 16293}, {1714, 16287}, {1780, 4267}, {1858, 26921}, {2328, 4276}, {2550, 37306}, {2975, 4305}, {3058, 28466}, {3086, 6986}, {3145, 9798}, {3173, 13754}, {3560, 6284}, {3583, 6913}, {3585, 37411}, {3586, 5251}, {3600, 37105}, {3616, 37301}, {3624, 16410}, {4189, 20075}, {4292, 12511}, {4293, 7411}, {4299, 37426}, {4423, 23708}, {4996, 9802}, {5047, 10591}, {5218, 6905}, {5225, 6920}, {5248, 10624}, {5259, 9614}, {5428, 10386}, {5432, 6911}, {5441, 37292}, {5540, 15288}, {5687, 32157}, {6737, 8715}, {6825, 10523}, {6842, 10953}, {6906, 37000}, {6908, 10629}, {6909, 7676}, {6988, 10321}, {7489, 9668}, {7514, 15253}, {7741, 11108}, {7951, 19541}, {8192, 23850}, {9655, 16117}, {9818, 37695}, {10039, 11500}, {10198, 37229}, {10385, 21161}, {10590, 36002}, {11365, 13738}, {11496, 37302}, {11502, 26446}, {12114, 37287}, {12953, 18407}, {13730, 23361}, {13743, 18499}, {15175, 15909}, {16058, 33138}, {16173, 38031}, {16346, 19858}, {16418, 31140}, {17549, 34625}, {18481, 22759}, {18961, 37401}, {20834, 30366}, {22097, 30269}, {34868, 37246}, {35193, 38850}
X(40292) = intersection, other than A,B,C, of conics {{A, B, C, X(21), X(7742)}} and {{A, B, C, X(57), X(3422)}}
X(40292) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3, 7742), (1, 5010, 15931), (3, 999, 37578), (3, 3295, 37579), (3, 26357, 8071), (35, 36, 30282), (35, 5119, 55), (55, 56, 24929), (55, 2099, 3295), (55, 3428, 1), (55, 5217, 32613), (1697, 10902, 11508), (3601, 11012, 22766), (5010, 14793, 3), (5010, 31508, 35), (5173, 24929, 1), (5217, 37564, 3), (11492, 11493, 34879), (14801, 14802, 35202), (26357, 37601, 3)
X(40293) lies on these lines: {1, 3}, {25, 5121}, {47, 2122}, {90, 34862}, {100, 36977}, {104, 1788}, {279, 14878}, {378, 7744}, {382, 12764}, {388, 6940}, {404, 3436}, {405, 6691}, {474, 1329}, {497, 37403}, {499, 1012}, {529, 16371}, {601, 1450}, {920, 17649}, {956, 8256}, {993, 8582}, {1106, 22350}, {1398, 1845}, {1406, 34586}, {1413, 36052}, {1436, 1723}, {1479, 37022}, {1604, 1743}, {1737, 12114}, {1768, 18237}, {1770, 22753}, {1838, 37245}, {2829, 3149}, {2932, 5854}, {3086, 6909}, {3435, 36058}, {3560, 5433}, {3585, 6918}, {3824, 37692}, {3911, 5450}, {4188, 7080}, {4292, 21616}, {4295, 5253}, {4311, 6736}, {4316, 37411}, {4413, 10827}, {4996, 27383}, {5229, 6946}, {5267, 9843}, {5445, 9708}, {5687, 38455}, {6700, 37282}, {6745, 37309}, {6882, 18961}, {6891, 10523}, {6905, 12667}, {6906, 7288}, {6911, 7354}, {6926, 10629}, {6985, 15326}, {7951, 16408}, {8668, 17648}, {8679, 36741}, {9612, 37244}, {9709, 37710}, {10483, 19541}, {10526, 32554}, {10589, 21669}, {10590, 17531}, {11415, 34758}, {11500, 21578}, {11502, 18481}, {11570, 12635}, {12047, 25524}, {13587, 34619}, {13738, 27657}, {15654, 37257}, {15817, 36743}, {16417, 31141}, {16572, 32625}, {17606, 18761}, {17768, 37308}, {19537, 35023}, {20842, 22654}, {20849, 30362}, {22758, 24914}, {22759, 26446}, {28348, 28393}, {30283, 37706}, {36972, 37707}
X(40293) = X(1)-Gimel conjugate of-X(56)
X(40293) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 36, 7742), (3, 56, 8069), (3, 1470, 8071), (36, 46, 56), (46, 30323, 2093), (55, 56, 24928), (56, 2098, 999), (56, 5204, 32612), (56, 10310, 1), (56, 37567, 10680), (57, 37561, 22766), (999, 35448, 2098), (1155, 34880, 11249), (1385, 13601, 1), (1420, 2077, 11508), (5126, 26285, 11510), (7280, 14793, 3), (10680, 35448, 8148), (32612, 37582, 56), (36279, 37535, 26437)
X(40294) lies on these lines: {1, 3}, {1597, 2969}, {3434, 37234}, {6883, 10596}, {6985, 10528}, {7580, 32213}, {10530, 37356}, {10915, 18518}, {18545, 37411}
X(40294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7688, 10269), (55, 3428, 13624), (10679, 35251, 55), (11248, 12703, 10679), (37533, 37584, 37544)
X(40295) lies on these lines: {1, 3}, {6985, 20076}, {10527, 37234}, {10530, 37406}, {10916, 18519}, {32214, 37022}
X(40295) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (56, 10310, 13624), (10680, 35252, 56), (10680, 35448, 1), (11249, 12704, 10680)
X(40296) lies on these lines: {1, 3}, {2, 31937}, {5, 9943}, {10, 13369}, {30, 3812}, {140, 6001}, {355, 4002}, {377, 18480}, {382, 5918}, {442, 22798}, {515, 3918}, {546, 15726}, {549, 960}, {550, 7686}, {631, 5887}, {912, 3678}, {971, 3826}, {975, 7986}, {1071, 3697}, {1158, 6883}, {1538, 6831}, {1656, 12688}, {1698, 40263}, {1737, 37401}, {1770, 28459}, {1827, 37414}, {2355, 37117}, {2478, 10940}, {2771, 3035}, {2800, 31838}, {2801, 4540}, {2818, 17704}, {3090, 9961}, {3524, 3869}, {3530, 14988}, {3555, 3654}, {3655, 10914}, {3698, 18525}, {3742, 22791}, {3753, 4190}, {3816, 9955}, {3827, 5092}, {3833, 18483}, {4067, 5884}, {5054, 25917}, {5439, 6899}, {5440, 33858}, {5690, 12675}, {5777, 6889}, {5790, 12680}, {5806, 28146}, {5818, 11220}, {5836, 34773}, {5880, 18482}, {5883, 31730}, {5886, 6890}, {6833, 9856}, {6836, 22793}, {6876, 9352}, {6903, 20292}, {6907, 10395}, {6911, 12520}, {6977, 12672}, {6989, 14647}, {7171, 18761}, {9942, 33899}, {10157, 31828}, {10172, 31871}, {10572, 28458}, {10693, 38728}, {10884, 11499}, {11112, 28208}, {12512, 31870}, {13374, 28174}, {15071, 31423}, {15693, 31165}, {17647, 28204}, {28154, 31822}, {28160, 31805}, {28168, 37468}, {28202, 37428}
X(40296) = midpoint of X(i) and X(j) for these {i,j}: {3, 34339}, {5, 9943}, {10, 13369}, {550, 7686}, {942, 3579}, {1385, 31788}, {5690, 12675}, {5836, 34773}, {5884, 31837}, {5885, 31663}, {9940, 31787}, {9942, 33899}, {10222, 31798}, {12512, 31870}, {13145, 13624}, {31786, 35004}
X(40296) = reflection of X(13373) in X(9940)
X(40296) = complement of X(31937)
X(40296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 46, 3579), (65, 3612, 9957), (165, 15016, 24474), (1385, 3579, 55), (1385, 18856, 9940), (3359, 8726, 10267), (3576, 16209, 3), (3579, 9940, 16216), (3660, 9957, 5045), (5054, 40266, 25917), (5884, 10164, 31837), (5902, 35242, 37585), (7686, 10178, 550), (11227, 31788, 1385), (12609, 37356, 9955), (12616, 37438, 9956), (17502, 35004, 31786), (18443, 37560, 11248), (30503, 37534, 11249)
Points associated with the power curve: X(40297)-X(40305)
This preamble is based on notes contributed by Suren, November 4, 2020.
In the plane of a triangle ABC, the locus of a point at : bt : ct (barycentrics [or trilinears]) as t varies through the real numbers is the power curve, PC(ABC), of ABC. (The term is introduced in Clark Kimberling, "Major Centers of Triangles," American Math. Monthly 104 (1997), 431-438.) Note that PC(ABC) passes through X(i) for i = 1,2,6,31,75,76, and that eliminating t shows that PC(ABC) is given by the equations
(log x)/(log a) = (log y)/(log b) = (log z)/(log c).
(Here, "log" signifies the natural logarithm, but equivalent equations result under change of base for "log".) Centers X(40297)-X(40305) involve the line tangent to PC at X(1), X(2), and X(6).
In general, the line tangent to the power curve at a point at : bt : ct has the direction (i.e., a point on the infinity line) given by
(a*c)t log(a/c) + (a*b)t log(a/b) : : ,
and the trilinear pole of that point is the point at log(c/b) : bt log(a/c) : ct log(b/a).
X(40297) lies on this line: (30,511)
X(40297) = isogonal conjugate of X(40303)
X(40298) lies on this line: (30,511)
X(40298) = isogonal conjugate of X(40304)
X(40299) = isogonal conjugate of X(40304)
X(40301) lies on the Steiner circumellipse and these lines: {99, 40302}, {190, 40300}
X(40301) = isotomic conjugate of X(40327)
X(40301) = isotomic conjugate of the isogonal conjugate of X(40302)
X(40301) = X(40327)-cross conjugate of X(2)
X(40301) = X(31)-isoconjugate of X(40327)
X(40301) = cevapoint of X(2) and X(40327)
X(40301) = trilinear pole of line {2, 40298}
X(40301) = barycentric product X(i)*X(j) for these {i,j}: {75, 40300}, {76, 40302}
X(40301) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 40327}, {40300, 1}, {40302, 6}
X(40302) lies on the circumcircle and these lines: {}
X(40303) lies on the circumcircle and these lines: {}
X(40303) = isogonal conjugate of X(40297)
X(40304) lies on the circumcircle and these lines: {}
X(40304) = isogonal conjugate of X(40298)
X(40305) lies on the circumcircle and these lines: {}
X(40305) = isogonal conjugate of X(40299)
Points on Vu orthogonal conics: X(40306)-X(40315)
This preamble is based on notes contributed by Vu Thanh Tung, November 5, 2020.
In the plane of a triangle ABC, let P and U be points. Let L be the line through P perpendicular to line AU, and let A1 = L∩BC. Define B1 and C1 cyclically. Let L' be the line through U perpendicular to line AP. and A2 = L'∩BC. Define B2 and C2 cyclically. The six points A1, B1, C1, A2, B2, C2 lie on a conic, here named the Vu orthogonal conic of P and U, denoted by VOC(P,U).
Let V(P,U) denote the center, and T(P,U) the perspector, of VOC(P,U). Note that VOC(U,P) = VOC(P,U), V(U,P) = V(P,U), and T(U,P) = T(P,U).
See Vu Orthogonal Conic.
Barycentrics (2*a - b)*(2*a - c)*(b - c)*(9*a^4 - 15*a^3*b - 5*a^2*b^2 + a*b^3 + 6*b^4 - 15*a^3*c + 44*a^2*b*c - 3*a*b^2*c - 20*b^3*c - 5*a^2*c^2 - 3*a*b*c^2 + 20*b^2*c^2 + a*c^3 - 20*b*c^3 + 6*c^4) : :
X(40316) lies on theser lines: {2, 6}, {206, 32220}, {895, 23300}, {1351, 37197}, {1353, 34148}, {1885, 3564}, {5889, 31829}, {6391, 11442}, {6467, 12058}, {6776, 30552}, {7507, 14914}, {14516, 34382}, {15116, 39125}, {15531, 26926}, {34622, 39899}
X(40316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 69, 26156}, {193, 20080, 6515}, {1992, 28408, 6}, {6515, 15066, 3580}
X(40317 lies on these lines: on lines {25, 40316}, {66, 69}, {110, 193}, {524, 20987}, {1992, 19122}, {3580, 6391}, {3618, 5486}, {3620, 23293}, {5059, 5921}, {5181, 28408}, {6338, 9146}, {6467, 18911}, {8263, 26206}, {10602, 26156}, {11416, 28419}, {11441, 34380}, {11449, 14912}, {11898, 14516}, {14913, 27365}, {15107, 20080}
X(40317) = reflection of X(193) in X(1974)
X(40317) = {X(69),X(12272)}-harmonic conjugate of X(11442)
X(40318) lies on these lines: {2, 6}, {22, 6467}, {23, 9924}, {24, 34382}, {25, 6391}, {74, 38263}, {110, 19118}, {155, 6622}, {235, 3564}, {439, 6461}, {511, 1204}, {648, 8745}, {895, 32262}, {1176, 32621}, {1351, 1593}, {1353, 6823}, {1609, 4558}, {1843, 32127}, {1974, 8681}, {1995, 14913}, {2207, 6392}, {2393, 35219}, {2854, 20987}, {2916, 8547}, {3003, 9723}, {3053, 5866}, {3060, 12167}, {3089, 17836}, {3092, 12222}, {3093, 12221}, {3167, 19122}, {3448, 32276}, {5013, 34883}, {5050, 34148}, {5093, 11459}, {5157, 22829}, {6776, 37201}, {6800, 15531}, {7387, 12283}, {7391, 15583}, {7494, 17040}, {7754, 8743}, {9544, 19132}, {9707, 19154}, {10602, 12220}, {10607, 35296}, {10996, 14912}, {11456, 39899}, {11477, 12086}, {11482, 15801}, {12310, 32248}, {15073, 37488}, {15262, 32001}, {16196, 34380}, {18931, 37498}, {19131, 32284}, {22241, 30435}, {33748, 37514}
X(40318) = reflection of X(20806) in X(6)
X(40318) = X(63)-isoconjugate of X(15591)
X(40318) = crosssum of X(647) and X(6388)
X(40318) = polar conjugate of isogonal conjugate of X(41619)
X(40318) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 15591}, {15261, 6391}
X(40318) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 69, 26206}, {6, 193, 1993}, {25, 6391, 12272}, {69, 193, 40316}, {69, 26206, 15066}, {193, 37784, 6}, {1351, 8548, 39588}, {1993, 3580, 15066}, {3580, 40316, 69}, {10602, 37491, 12220}, {15531, 19121, 19459}, {19118, 19588, 110}, {19121, 19459, 6800}
X(40319) lies on the cubic K1164 and these lines: {3, 6391}, {20, 98}, {25, 1611}, {32, 11326}, {184, 682}, {187, 2353}, {237, 33581}, {1402, 38252}, {1799, 6340}, {1885, 5203}, {3425, 13335}, {3455, 5206}, {5023, 9924}, {5139, 15591}, {8408, 21642}, {8420, 21643}, {8884, 34208}, {9292, 9306}, {10316, 14908}, {23099, 39201}, {27364, 34449}, {30739, 40102}
X(40319) = isogonal conjugate of the anticomplement of X(22401)
X(40319) = isogonal conjugate of the isotomic conjugate of X(6391)
X(40319) = isogonal conjugate of the polar conjugate of X(8770)
X(40319) = X(i)-cross conjugate of X(j) for these (i,j): {577, 184}, {1084, 647}
X(40319) = X(i)-isoconjugate of X(j) for these (i,j): {4, 18156}, {63, 21447}, {75, 6353}, {92, 193}, {158, 6337}, {264, 1707}, {286, 4028}, {318, 17081}, {561, 19118}, {811, 3566}, {1969, 3053}, {3798, 6335}, {5139, 24037}, {6521, 10607}, {17876, 18020}
X(40319) = crosspoint of X(6391) and X(8770)
X(40319) = crosssum of X(i) and X(j) for these (i,j): {4, 6392}, {193, 6353}
X(40319) = barycentric product X(i)*X(j) for these {i,j}: {3, 8770}, {6, 6391}, {32, 6340}, {48, 8769}, {63, 38252}, {184, 2996}, {394, 14248}, {577, 34208}, {647, 3565}, {3049, 35136}, {14533, 27364}
X(40319) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 21447}, {32, 6353}, {48, 18156}, {184, 193}, {577, 6337}, {1084, 5139}, {1501, 19118}, {2200, 4028}, {2996, 18022}, {3049, 3566}, {3565, 6331}, {6340, 1502}, {6391, 76}, {8769, 1969}, {8770, 264}, {9247, 1707}, {14248, 2052}, {14575, 3053}, {14585, 3167}, {23200, 32459}, {23606, 10607}, {34208, 18027}, {38252, 92}
X(40320) lies on the cubic K1164 and these lines: {3, 6}, {112, 3542}, {115, 31725}, {206, 682}, {230, 235}, {237, 1660}, {439, 4558}, {468, 17409}, {1611, 36417}, {1627, 7493}, {1656, 18373}, {1885, 10311}, {7735, 37201}, {7755, 19220}, {8770, 21313}, {10313, 30552}, {11326, 19136}, {14908, 20960}, {14910, 37460}, {34481, 37973}
X(40320) = X(6353)-Ceva conjugate of X(1974)
X(40320) = X(304)-isoconjugate of X(15591)
X(40320) = polar conjugate of isotomic conjugate of X(41619)
X(40320) = barycentric product X(6353)*X(15261)
X(40320) = barycentric quotient X(i)/X(j) for these {i,j}: {1974, 15591}, {15261, 6340}
X(40320) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 187, 10316}, {32, 3053, 571}, {571, 3003, 5063}
X(40321) lies on the cubic K1164 and these lines: {3, 69}, {25, 15591}, {154, 5023}, {187, 20993}, {237, 1661}, {1593, 9756}, {1974, 3053}, {2996, 33974}, {3515, 14900}, {10602, 22401}
X(40321) = X(6353)-Ceva conjugate of X(6)
X(40321) = crosssum of X(525) and X(5139)
X(40321) = crossdifference of every pair of points on line {2489, 14341}
X(40321) = {X(3),X(682)}-harmonic conjugate of X(19459)
X(40322) lies on the cubics K1047 and K1164, and also on these lines: {6, 6337}, {32, 3167}, {1498, 9431}, {1611, 2207}, {1974, 3053}, {2129, 21775}, {3224, 17811}, {5013, 39238}, {5023, 6091}
X(40322) = isogonal conjugate of X(6392)
X(40322) = isogonal conjugate of the anticomplement of X(3926)
X(40322) = isogonal conjugate of the isotomic conjugate of X(6339)
X(40322) = isotomic conjugate of the polar conjugate of X(15369)
X(40322) = X(30558)-Ceva conjugate of X(3)
X(40322) = X(394)-cross conjugate of X(6)
X(40322) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6392}, {2, 33781}, {4, 2128}, {6, 33787}, {19, 19583}, {75, 1611}, {92, 19588}, {158, 6461}, {811, 2519}, {1096, 6338}
X(40322) = cevapoint of X(9427) and X(39201)
X(40322) = crosspoint of X(8770) and X(39128)
X(40322) = crosssum of X(i) and X(j) for these (i,j): {193, 18287}, {1611, 19588}, {6462, 6463}
X(40322) = barycentric product X(i)*X(j) for these {i,j}: {6, 6339}, {63, 2129}, {69, 15369}, {8770, 30558}
X(40322) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 33787}, {3, 19583}, {6, 6392}, {31, 33781}, {32, 1611}, {48, 2128}, {184, 19588}, {394, 6338}, {577, 6461}, {2129, 92}, {3049, 2519}, {6339, 76}, {15369, 4}
X(40323) lies on the conic {{A,B,C,X(2)X(6)}}, the cubic K1164, and on these lines: {6, 6387}, {25, 15591}, {30, 36616}, {111, 1370}, {468, 40144}, {1368, 8770}, {1660, 1976}, {2987, 37669}, {3291, 13854}, {8749, 38282}, {18928, 30535}, {21448, 31255}
X(40323) = isotomic conjugate of the polar conjugate of X(15591)
X(40323) = X(i)-cross conjugate of X(j) for these (i,j): {5139, 523}, {22401, 6}
X(40323) = cevapoint of X(647) and X(6388)
X(40323) = barycentric product X(69)*X(15591)
X(40323) = barycentric quotient X(15591)/X(4)
X(40324) lies on the cubic K1164 and these lines: {25, 19583}, {69, 15369}, {1611, 36417}, {1974, 8780}, {5020, 15261}
X(40325) = isogonal conjugate of the anticomplement of X(6391)
X(40325) = trilinear pole of line {2519, 20186}
X(40325) lies on the cubic K1165 and these lines: {4, 69}, {25, 1611}, {51, 460}, {132, 235}, {232, 11325}, {427, 30749}, {682, 1196}, {1974, 2207}, {2386, 3767}, {2489, 23099}, {2971, 3199}, {2996, 12272}, {3089, 9752}, {3853, 16983}, {3917, 7784}, {5254, 6467}, {5395, 5640}, {6392, 8681}, {6525, 6620}, {8754, 27376}, {9822, 32971}, {10151, 11397}, {11574, 32974}, {12220, 32982}
X(40325) = isotomic conjugate of the isogonal conjugate of X(3080)
X(40325) = polar conjugate of the isotomic conjugate of X(1196)
X(40325) = orthic isogonal conjugate of X(5254)
X(40325) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 5254}, {107, 2489}
X(40325) = X(255)-isoconjugate of X(683)
X(40325) = crosspoint of X(4) and X(2207)
X(40325) = crosssum of X(3) and X(3926)
X(40325) = crossdifference of every pair of points on line {3049, 4143}
X(40325) = barycentric product X(i)*X(j) for these {i,j}: {4, 1196}, {19, 17872}, {25, 5254}, {76, 3080}, {112, 12075}, {393, 6467}, {682, 2052}, {1096, 18671}, {1368, 2207}, {1824, 16716}, {6524, 22401}
X(40325) = barycentric quotient X(i)/X(j) for these {i,j}: {393, 683}, {682, 394}, {1196, 69}, {3080, 6}, {5254, 305}, {6467, 3926}, {12075, 3267}, {17872, 304}, {22401, 4176}
X(40325) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2971, 27369, 3199}, {6291, 6406, 12294}
X(40326) lies on the cubic K1165 and these lines: {2, 6}, {4, 8770}, {25, 15591}, {30, 34481}, {32, 6677}, {111, 34603}, {126, 19568}, {187, 10154}, {427, 3291}, {428, 16317}, {468, 17409}, {574, 7734}, {1194, 9607}, {1196, 1368}, {1513, 2883}, {1691, 10192}, {2056, 8550}, {3053, 6353}, {3767, 30771}, {3787, 6388}, {5020, 7745}, {5023, 10565}, {5475, 10128}, {6340, 6392}, {6393, 35294}, {6791, 21969}, {8889, 13881}, {9729, 37451}, {31255, 40126}, {37990, 39576}
X(40326) = orthic-isogonal conjugate of X(6467)
X(40326) = X(4)-Ceva conjugate of X(6467)
X(40326) = crosspoint of X(4) and X(21447)
X(40326) = barycentric product X(i)*X(j) for these {i,j}: {193, 5254}, {1368, 6353}, {17872, 18156}, {21447, 22401}
X(40326) = barycentric quotient X(i)/X(j) for these {i,j}: {1196, 8770}, {1368, 6340}, {5254, 2996}, {6467, 6391}, {17872, 8769}
X(40326) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1611, 230}, {1196, 1368, 5254}
See the preamble just before X(40297). For symbolic substitutions SS(# → #), see X(3221).
X(40327) lies on this line: X(30)X(511)
X(40327) = isotomic conjugate of X(40301)
Osiris points: X(40328)-X(40336)
This preamble and centers X(40328)-X(40336) were contributed by César Eliud Lozada, November 9, 2020.
Let ABC be a triangle, P a point and Q the isotomic conjugate of P. Denote by A' the centroid of the quadrangle BCPQ and define B' and C'. cyclically. Then AA', BB', CC' concur at a point O(P)=O(Q), here named the Osiris point of P.
For P=x:y:z (barycentrics), O(P) = (y^2+5*y*z+z^2)*x+2*(y+z)*(x^2+y*z) : :
The appearance of (i, j) in the following list means that the Osiris point of X(i) is X(j):
(1, 40328), (2, 2), (3, 40329), (4, 40330), (5, 40331), (6, 40332), (7, 40333), (8, 40333), (13, 40334), (14, 40335), (69, 40330), (75, 40328), (76, 40332), (95, 40331), (98, 40336), (99, 523), (190, 514), (264, 40329), (290, 511), (298, 40334), (299, 40335), (325, 40336), (648, 525), (664, 522), (666, 918), (668, 513), (670, 512), (671, 524), (886, 888), (889, 891), (892, 690), (903, 519), (1121, 527), (1494, 30), (2481, 518), (2966, 2799), (3225, 698), (3226, 726), (3227, 536), (3228, 538), (4555, 900), (4562, 812), (4569, 3900), (4577, 826), (4586, 824), (4597, 4777), (5641, 542), (6189, 3414), (6190, 3413), (6540, 4977), (6606, 6362), (6635, 6550), (6648, 3910), (11117, 532), (11118, 533), (14616, 758), (14728, 33906), (14970, 732), (15164, 2574), (15165, 2575), (16077, 9033), (18025, 516), (18026, 521), (18816, 517), (18821, 528), (18822, 537), (18823, 543), (18824, 696), (18826, 714), (18827, 740), (18828, 782), (18829, 804), (18830, 4083), (18831, 6368), (23895, 23870), (23896, 23871), (32036, 23872), (32037, 23873), (32038, 23880), (32039, 23886), (32041, 4762), (32042, 4802), (34393, 515), (35136, 3566), (35137, 7927), (35138, 3906), (35139, 526), (35140, 1503), (35141, 17768), (35142, 3564), (35143, 35101), (35144, 35102), (35145, 8680), (35146, 5969), (35147, 2787), (35148, 2786), (35149, 2792), (35150, 2784), (35151, 2783), (35152, 2795), (35153, 2796), (35154, 2785), (35155, 35103), (35156, 8674), (35157, 6366), (35158, 5845), (35159, 35104), (35160, 5853), (35162, 17770), (35164, 2801), (35168, 545), (35170, 4715), (35171, 3887), (35172, 9055), (35174, 3738), (35175, 2802), (35179, 1499), (35181, 4160), (39626, 39624)
If P or Q lie on the cubic K953, then its Osiris point lies on the Euler line of ABC.
The mapping O takes certain cubics onto lines: O(K296) = X(1)X(2), O(K185) = X(2)X(6), O(K953) = X(2)X(3). (Peter Moses, November 10, 2020)
X(40328) lies on these lines: {1, 3696}, {2, 38}, {7, 24697}, {10, 4684}, {36, 19287}, {37, 3624}, {75, 1125}, {86, 16825}, {142, 32784}, {145, 4732}, {192, 5550}, {238, 10436}, {312, 25501}, {496, 21926}, {518, 1698}, {631, 29054}, {726, 4687}, {740, 3616}, {742, 4798}, {872, 17749}, {1001, 4436}, {1213, 25557}, {1699, 30271}, {1757, 17259}, {1921, 31997}, {3210, 10180}, {3242, 36531}, {3636, 4709}, {3751, 16832}, {3773, 17244}, {3775, 29576}, {3790, 29581}, {3797, 29612}, {3826, 29659}, {3836, 27147}, {3976, 19858}, {4026, 34824}, {4032, 7288}, {4038, 5271}, {4169, 19963}, {4357, 39580}, {4359, 17592}, {4384, 4649}, {4389, 25354}, {4393, 5625}, {4441, 30571}, {4472, 24357}, {4648, 32846}, {4655, 26806}, {4664, 19883}, {4670, 16468}, {4675, 33082}, {4688, 15569}, {4698, 34595}, {4704, 28516}, {4758, 4989}, {4968, 29982}, {4974, 17379}, {5251, 27471}, {5257, 24231}, {5263, 24331}, {5333, 17017}, {5904, 13476}, {6536, 33146}, {7201, 11375}, {10165, 30273}, {10453, 27798}, {11230, 20430}, {14005, 28082}, {16408, 34247}, {16476, 17175}, {16478, 25526}, {16610, 29825}, {16826, 27474}, {17245, 29674}, {17260, 32935}, {17278, 29633}, {17303, 29637}, {17331, 17771}, {17368, 31289}, {17391, 17772}, {17398, 29646}, {18157, 33945}, {19701, 29821}, {19732, 32913}, {19808, 29642}, {19822, 33158}, {21020, 29814}, {24174, 24778}, {24199, 33149}, {24369, 24440}, {25507, 29644}, {26102, 31993}, {26115, 27311}, {26363, 28755}, {26627, 32917}, {26724, 29647}, {27475, 29604}, {29981, 31339}, {31336, 31347}, {33076, 39581}
X(40328) = midpoint of X(3616) and X(4699)
X(40328) = reflection of X(i) in X(j) for these (i, j): (1698, 31238), (4687, 19862)
X(40328) = intersection, other than A,B,C, of conics {{A, B, C, X(291), X(10013)}} and {{A, B, C, X(335), X(39711)}}
X(40328) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 24325, 984), (2, 24349, 3842), (984, 24325, 31178), (1698, 20195, 31252), (3842, 24325, 24349), (3842, 24349, 984)
X(40329) lies on these lines: {2, 1972}, {3, 14767}, {140, 264}, {216, 3526}, {233, 40107}, {511, 1656}, {631, 32428}, {3164, 3525}
X(40330) lies on these lines: {2, 98}, {3, 3619}, {4, 141}, {5, 69}, {6, 3090}, {10, 39898}, {20, 3818}, {66, 7383}, {113, 32247}, {140, 18440}, {159, 7509}, {183, 9752}, {193, 5056}, {235, 11382}, {262, 14994}, {343, 3066}, {376, 21358}, {381, 21356}, {428, 33522}, {487, 37343}, {488, 37342}, {511, 3091}, {518, 5818}, {524, 5071}, {546, 33878}, {547, 1353}, {567, 6193}, {576, 15022}, {590, 39876}, {599, 3545}, {611, 10588}, {613, 10589}, {615, 39875}, {631, 1503}, {632, 12017}, {639, 10514}, {640, 10515}, {895, 23515}, {1125, 39885}, {1176, 10539}, {1370, 21766}, {1469, 10590}, {1614, 5157}, {1656, 3564}, {1843, 11793}, {1853, 5646}, {1992, 5055}, {1995, 37488}, {2080, 3785}, {2854, 15081}, {3056, 10591}, {3085, 12589}, {3086, 12588}, {3088, 37480}, {3098, 3146}, {3167, 11548}, {3313, 7999}, {3316, 13910}, {3317, 13972}, {3416, 5603}, {3522, 29012}, {3523, 18553}, {3524, 20582}, {3525, 5085}, {3528, 21167}, {3529, 31884}, {3544, 3631}, {3589, 5067}, {3624, 39870}, {3628, 5050}, {3630, 5102}, {3751, 10175}, {3819, 7396}, {3832, 31670}, {3839, 25561}, {3844, 5657}, {3851, 21850}, {3917, 7378}, {4259, 6984}, {4413, 39877}, {4648, 7380}, {4869, 7407}, {5052, 31415}, {5068, 19130}, {5070, 38110}, {5072, 38136}, {5079, 5093}, {5084, 26543}, {5092, 10303}, {5094, 39871}, {5181, 14644}, {5432, 39892}, {5433, 39891}, {5476, 11160}, {5544, 18928}, {5550, 38029}, {5562, 9822}, {5590, 6813}, {5591, 6811}, {5596, 7558}, {5714, 24471}, {5800, 6854}, {5820, 6983}, {5846, 10595}, {5847, 8227}, {6090, 37454}, {6214, 11314}, {6215, 11313}, {6248, 32974}, {6292, 8721}, {6403, 29959}, {6515, 37990}, {6530, 32000}, {6623, 12294}, {6698, 14982}, {6759, 20079}, {6803, 18913}, {6815, 26156}, {6843, 10477}, {6920, 36740}, {6933, 15988}, {6946, 36741}, {6997, 37636}, {7379, 17232}, {7385, 17238}, {7395, 18945}, {7400, 15812}, {7401, 37489}, {7404, 13352}, {7405, 11411}, {7410, 17327}, {7484, 32064}, {7486, 15516}, {7499, 11206}, {7512, 20987}, {7528, 37494}, {7539, 11427}, {7697, 10008}, {7709, 10007}, {7795, 18860}, {7800, 8722}, {7808, 39872}, {7914, 39882}, {7998, 31099}, {8263, 16072}, {8889, 17811}, {9753, 15589}, {9863, 16898}, {9967, 10170}, {9969, 11412}, {10109, 14848}, {10272, 32306}, {10446, 36671}, {10565, 32237}, {10594, 37485}, {10752, 32257}, {10753, 36519}, {10754, 23514}, {10755, 23513}, {10762, 36520}, {11061, 14643}, {11257, 33202}, {11284, 37643}, {11387, 15644}, {11433, 37439}, {11459, 19161}, {11482, 12812}, {11645, 15692}, {12140, 35485}, {12215, 32829}, {12319, 14926}, {12383, 32274}, {12900, 32275}, {13862, 16990}, {14001, 39647}, {14913, 15073}, {15058, 34146}, {15184, 39886}, {15577, 35921}, {16986, 37182}, {17578, 29317}, {17792, 31418}, {17825, 18950}, {18141, 37360}, {19145, 32785}, {19146, 32786}, {20304, 25320}, {21851, 40247}, {22165, 38072}, {24220, 36673}, {24273, 35925}, {24953, 39890}, {26118, 33172}, {26363, 39903}, {26364, 39902}, {26468, 32488}, {26469, 32489}, {31742, 34512}, {32152, 32981}, {32217, 37943}, {32255, 38724}, {32815, 37242}, {32956, 39646}, {33198, 36998}, {34229, 37071}, {35283, 37638}, {37174, 39530}, {38118, 39878}
X(40330) = midpoint of X(3091) and X(3620)
X(40330) = reflection of X(i) in X(j) for these (i, j): (631, 3763), (3618, 1656), (12017, 632)
X(40300) = isogonal conjugate of X(40338)
X(40300) = isotomic conjugate of X(40339)
X(40330) = X(6)-isoconjugate of X(40327)
X(40330) = barycentric quotient X(6)/X(40338)
X(40330) = trilinear product X(i)*X(j) for these {i,j}: {2, 40302}, {6, 40301}
X(40330) = trilinear quotient X(i)/X(j) for these (i,j): (1, 40338), (40301, 2), (40302, 6)
X(40330) = intersection, other than A,B,C, of conics {{A, B, C, X(98), X(8797)}} and {{A, B, C, X(287), X(18840)}}
X(40330) = X(3091)-of-1st Brocard triangle
X(40330) = X(3620)-of-McCay triangle
X(40330) = X(6) of cross-triangle of Euler and anti-Euler triangles
X(40330) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1352, 6776), (2, 5921, 182), (3, 39884, 14927), (4, 141, 10519), (5, 69, 14853), (140, 18440, 25406), (141, 10516, 4), (182, 1352, 5921), (182, 5921, 6776), (193, 5056, 14561), (1352, 6776, 11180), (1352, 24206, 2), (3525, 39874, 5085), (3589, 15069, 14912), (5055, 11898, 18583), (5067, 14912, 3589), (5085, 34573, 3525), (11178, 24206, 1352), (11898, 18583, 1992), (14561, 34507, 193), (32257, 36518, 10752)
X(40331) lies on these lines: {2, 35311}, {5, 6709}, {95, 3628}, {233, 6749}, {632, 32428}, {5070, 17035}
X(40332) lies on these lines: {2, 694}, {6, 3934}, {76, 3589}, {83, 8177}, {141, 7752}, {182, 7697}, {183, 12212}, {511, 1656}, {597, 32451}, {599, 5052}, {698, 7786}, {732, 3618}, {1350, 15819}, {1691, 7770}, {1975, 12055}, {2021, 33237}, {2076, 7815}, {3095, 7822}, {3096, 5103}, {3619, 32999}, {3734, 5116}, {5017, 15271}, {5031, 16921}, {5085, 6248}, {5207, 33020}, {5480, 22712}, {6292, 9821}, {6704, 8149}, {7820, 11171}, {10168, 32429}, {10485, 39141}, {10516, 13354}, {12263, 38047}, {13910, 19089}, {13972, 19090}, {20582, 22486}, {24206, 36519}, {33249, 34573}
X(40332) = midpoint of X(3618) and X(31276)
X(40332) = reflection of X(3763) in X(31239)
X(40332) = X(7786)-of-1st Brocard triangle
X(40332) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 24256, 3094), (76, 3589, 13331), (10007, 18906, 3094), (10007, 24256, 18906)
X(40333) lies on these lines: {1, 12630}, {2, 11}, {3, 38149}, {5, 35514}, {7, 10}, {8, 142}, {9, 5128}, {20, 5251}, {75, 39570}, {140, 38170}, {141, 38185}, {144, 5880}, {145, 15570}, {355, 21151}, {391, 4645}, {392, 7673}, {405, 7676}, {442, 7679}, {443, 956}, {474, 7677}, {480, 27525}, {516, 1698}, {518, 3617}, {942, 34784}, {944, 38122}, {954, 9709}, {962, 38150}, {971, 5818}, {984, 4346}, {1125, 8236}, {1156, 34122}, {1320, 38205}, {1482, 38171}, {1699, 36835}, {1738, 3672}, {1890, 7378}, {2345, 3823}, {2346, 5687}, {2551, 37161}, {2951, 19925}, {3008, 4344}, {3059, 3812}, {3062, 38158}, {3146, 11495}, {3241, 38093}, {3523, 19854}, {3525, 38031}, {3616, 5853}, {3624, 30331}, {3626, 38054}, {3634, 30332}, {3654, 38073}, {3679, 5542}, {3696, 27475}, {3717, 31995}, {3753, 7672}, {3755, 5308}, {3832, 34501}, {3886, 29627}, {3932, 4461}, {3945, 4649}, {4000, 39587}, {4187, 7678}, {4197, 7080}, {4294, 17554}, {4307, 16468}, {4312, 6172}, {4323, 12447}, {4454, 27549}, {4470, 5845}, {4566, 10004}, {4669, 38024}, {4678, 25557}, {4731, 8581}, {4745, 38094}, {4999, 38203}, {5056, 38037}, {5070, 38043}, {5082, 17529}, {5187, 15254}, {5220, 20059}, {5226, 8580}, {5260, 37435}, {5265, 17580}, {5316, 9779}, {5435, 12573}, {5439, 11025}, {5550, 38316}, {5587, 36991}, {5657, 5805}, {5690, 38107}, {5698, 6871}, {5750, 5838}, {5759, 6843}, {5779, 38042}, {5784, 40269}, {5790, 31657}, {5817, 9956}, {5819, 17303}, {6042, 16819}, {6067, 9710}, {6173, 24393}, {6361, 18482}, {6601, 12632}, {6666, 6919}, {6844, 31658}, {6856, 8543}, {6904, 26060}, {6908, 18491}, {6984, 21168}, {7308, 9812}, {8583, 18220}, {9776, 25006}, {10005, 24349}, {10175, 11372}, {10394, 15587}, {10591, 38059}, {11362, 38036}, {12245, 20330}, {12730, 34123}, {14543, 24342}, {14986, 17582}, {15717, 24953}, {19860, 30284}, {20007, 28629}, {21931, 29674}, {22754, 37462}, {24599, 38186}
X(40333) = reflection of X(i) in X(j) for these (i, j): (3616, 20195), (11025, 5439), (18230, 1698)
X(40333) = intersection, other than A,B,C, of conics {{A, B, C, X(55), X(14626)}} and {{A, B, C, X(105), X(10390)}}
X(40333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 38121, 35514), (7, 10, 5686), (8, 142, 11038), (10, 4208, 5261), (10, 25590, 5772), (10, 38052, 7), (142, 38200, 8), (984, 7613, 4346), (5177, 9780, 8165), (5880, 38057, 144), (17580, 19843, 5265), (17582, 31419, 14986)
X(40334) lies on these lines: {2, 14}, {3, 36992}, {5, 14538}, {16, 625}, {17, 69}, {18, 3589}, {20, 33387}, {30, 36770}, {61, 7886}, {62, 302}, {140, 20428}, {141, 16966}, {298, 6669}, {303, 635}, {316, 6672}, {325, 22511}, {381, 36755}, {396, 21359}, {511, 1656}, {524, 16960}, {616, 33560}, {618, 36969}, {620, 23004}, {628, 6673}, {629, 5237}, {1975, 16630}, {3090, 7684}, {3104, 7887}, {3105, 7862}, {3106, 7844}, {3525, 36993}, {3526, 13350}, {3618, 16961}, {3624, 11707}, {5070, 5611}, {5238, 11309}, {5318, 5463}, {5395, 10187}, {6722, 22510}, {7778, 25167}, {7808, 11311}, {10646, 11303}, {10653, 31705}, {11133, 22846}, {11301, 36970}, {11308, 30560}, {11310, 35229}, {11542, 22489}, {13449, 21159}, {16239, 33386}, {16242, 37352}, {16809, 37340}, {19106, 31693}, {19107, 37172}, {22691, 23000}, {22693, 37071}, {23005, 33228}, {23006, 38412}, {33416, 37341}, {34509, 34540}, {36968, 37170}
X(40334) = reflection of X(40335) in X(31275)
X(40334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 621, 6671), (2, 623, 15), (140, 20428, 21158), (298, 6669, 16267), (316, 6672, 39554), (621, 6671, 15), (623, 6671, 621), (1656, 3763, 40335)
X(40335) lies on these lines: {2, 13}, {3, 36994}, {5, 14539}, {15, 625}, {17, 3589}, {18, 69}, {20, 33386}, {61, 303}, {62, 7886}, {140, 20429}, {141, 16967}, {299, 6670}, {302, 636}, {316, 6671}, {325, 22510}, {381, 36756}, {395, 21360}, {511, 1656}, {524, 16961}, {617, 33561}, {619, 36970}, {620, 23005}, {627, 6674}, {630, 5238}, {1975, 16631}, {3090, 7685}, {3104, 7862}, {3105, 7887}, {3107, 7844}, {3525, 36995}, {3526, 13349}, {3618, 16960}, {3624, 11708}, {5070, 5615}, {5237, 11310}, {5321, 5464}, {5395, 10188}, {6722, 22511}, {7778, 25157}, {7808, 11312}, {10645, 11304}, {10654, 31706}, {11132, 22891}, {11302, 36969}, {11307, 30559}, {11309, 35230}, {11543, 22490}, {13449, 21158}, {16239, 33387}, {16241, 37351}, {16808, 37341}, {19106, 37173}, {19107, 31694}, {22692, 23009}, {22694, 37071}, {23004, 33228}, {33417, 37340}, {34508, 34541}, {36967, 37171}
X(40335) = reflection of X(40334) in X(31275)
X(40335) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 622, 6672), (2, 624, 16), (140, 20429, 21159), (299, 6670, 16268), (316, 6671, 39555), (622, 6672, 16), (624, 6672, 622), (1656, 3763, 40334)
X(40336) lies on these lines: {2, 3}, {98, 13196}, {99, 10256}, {182, 37647}, {230, 5111}, {325, 5965}, {538, 38740}, {625, 38737}, {1007, 9755}, {1350, 9754}, {2794, 31275}, {3054, 22712}, {3564, 7925}, {6390, 14651}, {6722, 18860}, {7607, 13468}, {7612, 37668}, {16984, 18583}
X(40336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3523, 33253, 3), (5999, 10011, 1513), (6039, 6040, 3529)
X(40337) lies on Feuerbach circumhyperbola of the orthic triangle, the cubic K1165, and on these lines: {4, 12271}, {6, 1196}, {185, 3564}, {511, 5895}, {520, 38359}, {1368, 6467}, {1858, 34381}, {2854, 15583}, {3574, 38136}, {6193, 9730}, {6403, 15741}, {9825, 21651}, {10110, 14914}, {12166, 13352}, {13202, 14984}, {13754, 20080}, {14091, 15143}, {14961, 19597}
X(40337) = reflection of X(6391) in X(14913)
X(40337) = orthic-isogonal conjugate of X(1368)
X(40337) = X(4)-Ceva conjugate of X(1368)
X(40337) = barycentric product X(1368)*X(40318)
X(40337) = barycentric quotient X(i)/X(j) for these {i,j}: {1196, 15591}, {6467, 40323}
X(40338) lies on the line {44, 513}
X(40338) = isogonal conjugate of X(40300)
X(40338) = crossdifference of every pair of points on line {X(1), X(40297)}
X(40338) = crosspoint of X(1) and X(40300)
X(40338) = X(i)-isoconjugate-of-X(j) for these {i,j}: {1, 40300}, {2, 40302}, {6, 40301}
X(40338) = X(i)-reciprocal conjugate of-X(j) for these (i,j): (1, 40301), (31, 40302)
X(40338) = X(i)-Zayin conjugate of-X(j) for these (i,j): (9, 40302), (43, 40301)
X(40338) = trilinear SS(a → log(b/c))
X(40338) = barycentric product X(i)*X(j) for these {i, j}: {1, 40327}, {6, 40339}
X(40338) = barycentric quotient X(i)/X(j) for these (i, j): (1, 40301), (31, 40302)
X(40338) = trilinear product X(i)*X(j) for these {i j}: {6, 40327}, {31, 40339}
X(40338) = trilinear quotient X(i)/X(j) for these (i, j): (1, 40300), (2, 40301), (6, 40302), (6, 40300)
X(40339) lies on the line {514, 693}
X(40339) = isotomic conjugate of X(40300)
X(40339) = barycentric product X(i)*X(j) for these {i, j}: {75, 40327}, {76, 40338}
X(40339) = barycentric quotient X(i)/X(j) for these (i, j): (1, 40302), (75, 40301)
X(40339) = trilinear product X(i)*X(j) for these {i, j}: {2, 40327}, {75, 40338}
X(40339) = trilinear quotient X(i)/X(j) for these (i, j): (2, 40302), (75, 40300), (76, 40301), (40338, 31)
X(40339) = X(i)-isoconjugate-of-X(j) for these {i,j}: {6, 40302}, {31, 40300}, {32, 40301}
X(40339) = X(i)-reciprocal conjugate of-X(j) for these (i,j): (1, 40302), (75, 40301)
X(40340) lies on these lines: {2, 10748}, {3, 10734}, {4, 38623}, {5, 126}, {30, 38803}, {111, 1656}, {140, 23699}, {381, 1296}, {382, 38716}, {543, 547}, {632, 38804}, {2854, 16511}, {3048, 18350}, {3090, 14360}, {3091, 22338}, {3146, 38798}, {3325, 7951}, {3526, 38698}, {3627, 38805}, {3628, 6719}, {3818, 14688}, {3851, 38593}, {5055, 10717}, {5072, 38688}, {5079, 38675}, {5790, 10704}, {6019, 7741}, {6593, 36832}, {7486, 20099}, {7514, 14657}, {9172, 15699}, {10779, 38752}, {11230, 11721}, {11835, 23261}, {11836, 23251}, {12811, 38801}, {14561, 36883}, {28662, 38317}
X(40340) = midpoint of X(i) and X(j) for these {i,j}: {4, 38623}, {5, 126}, {3627, 38805}, {3818, 14688}, {6593, 36832}, {10748, 14650}
X(40340) = reflection of X(6719) in X(3628)
X(40340) = complement of X(14650)
X(40340) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10748, 14650}, {2, 14654, 38806}, {3090, 14360, 38796}, {10748, 38806, 14654}, {14654, 38806, 14650}
Let LA be the reflection of line BC in A, and define LB and LC cyclically. Let A' = LB∩LC, and define B' and C' cyclically. A' is also the reflection of A in the A-vertex of the anticomplementary triangle. A'B'C' is homothetic to, and 5 times the size, of ABC. X(40341) = X(6)-of-A'B'C'. (Randy Hutson, December 18, 2020)
X(40341) lies on these lines: {1, 17253}, {2, 6}, {3, 5965}, {5, 5102}, {7, 4371}, {8, 7222}, {9, 17311}, {20, 16775}, {32, 33242}, {37, 29602}, {45, 4416}, {53, 32001}, {67, 6391}, {110, 16176}, {144, 3943}, {145, 17246}, {159, 2930}, {182, 15720}, {190, 17309}, {239, 7232}, {315, 33229}, {316, 34505}, {319, 4363}, {320, 4361}, {338, 14615}, {340, 9308}, {381, 7845}, {382, 511}, {487, 6410}, {488, 6409}, {518, 3632}, {519, 17276}, {527, 17299}, {542, 15681}, {546, 1352}, {550, 1350}, {576, 5079}, {594, 4644}, {623, 33465}, {624, 33464}, {625, 5111}, {631, 12007}, {633, 5340}, {634, 5339}, {637, 23251}, {638, 23261}, {698, 33256}, {732, 33234}, {742, 3644}, {894, 4445}, {1030, 21518}, {1086, 4402}, {1100, 17272}, {1351, 3851}, {1353, 14869}, {1384, 7801}, {1449, 17237}, {1503, 3529}, {1634, 22152}, {1656, 5097}, {1743, 17231}, {1853, 34777}, {1975, 7893}, {2076, 33235}, {2345, 7277}, {2482, 15655}, {2525, 30511}, {2549, 14929}, {2854, 12220}, {2916, 19588}, {2979, 17710}, {3053, 3793}, {3094, 32450}, {3098, 15688}, {3242, 3244}, {3284, 20208}, {3313, 8681}, {3416, 3626}, {3526, 39561}, {3528, 6776}, {3530, 5085}, {3544, 14853}, {3636, 38315}, {3664, 17275}, {3686, 4675}, {3729, 4715}, {3758, 17287}, {3759, 17288}, {3770, 34282}, {3779, 9038}, {3785, 15815}, {3818, 14269}, {3855, 5480}, {3875, 4725}, {3879, 4643}, {3882, 5036}, {3886, 28570}, {3912, 16885}, {3917, 32366}, {3926, 5023}, {3964, 8553}, {4000, 4969}, {4034, 4688}, {4042, 32949}, {4053, 18161}, {4265, 19535}, {4357, 16884}, {4360, 4741}, {4384, 17376}, {4393, 17273}, {4398, 20016}, {4414, 4938}, {4419, 17388}, {4667, 17303}, {4670, 17270}, {4681, 29605}, {4690, 10436}, {4700, 21255}, {4852, 17274}, {4859, 31138}, {5008, 33237}, {5013, 7758}, {5024, 7810}, {5028, 33241}, {5033, 12151}, {5050, 40107}, {5092, 15700}, {5093, 24206}, {5096, 19537}, {5124, 21524}, {5207, 14062}, {5210, 6390}, {5220, 32846}, {5286, 33232}, {5486, 34817}, {5621, 12901}, {5695, 17770}, {5846, 20050}, {5848, 6154}, {5921, 29181}, {6179, 7881}, {6467, 9027}, {6542, 17262}, {6646, 17318}, {6697, 11216}, {6748, 32000}, {7321, 29617}, {7703, 23061}, {7716, 10301}, {7750, 33253}, {7754, 7768}, {7760, 7879}, {7761, 22253}, {7770, 7877}, {7773, 7946}, {7775, 18584}, {7780, 7916}, {7789, 22331}, {7793, 13196}, {7794, 30435}, {7796, 35006}, {7798, 7848}, {7805, 7866}, {7811, 31859}, {7820, 21309}, {7841, 7850}, {7851, 7939}, {7854, 7890}, {7871, 33233}, {7887, 7917}, {7894, 32027}, {7895, 32954}, {7905, 11285}, {7908, 11288}, {8266, 20794}, {8550, 10299}, {8588, 39785}, {8589, 11165}, {8716, 14907}, {9019, 12272}, {9035, 39232}, {9053, 20054}, {9054, 25304}, {9306, 21970}, {9466, 15484}, {9939, 11742}, {9971, 14913}, {10300, 15812}, {10387, 39873}, {10452, 21769}, {10488, 14928}, {10541, 14912}, {11179, 17504}, {11225, 16419}, {11482, 38317}, {11646, 14645}, {11737, 38072}, {12017, 15707}, {12088, 15580}, {12215, 33276}, {12383, 17835}, {13142, 33537}, {13330, 14994}, {14042, 18906}, {14561, 35018}, {15526, 15905}, {15687, 31670}, {16496, 28538}, {16666, 17306}, {16667, 17384}, {16668, 29598}, {16669, 17284}, {16670, 17357}, {16672, 17257}, {16674, 29574}, {16675, 17316}, {16808, 22493}, {16809, 22494}, {16814, 29573}, {16826, 17328}, {16834, 17235}, {16866, 37492}, {17120, 17228}, {17121, 17227}, {17233, 20072}, {17249, 29584}, {17252, 17394}, {17254, 17393}, {17256, 17391}, {17258, 17389}, {17260, 17387}, {17261, 17386}, {17267, 17296}, {17269, 17295}, {17294, 17351}, {17298, 17348}, {17310, 17336}, {17312, 17335}, {17314, 17334}, {17315, 17333}, {17317, 17331}, {17319, 17329}, {17340, 29616}, {17571, 36740}, {17573, 36741}, {17813, 23300}, {18358, 20423}, {20477, 39352}, {20850, 20987}, {21241, 32853}, {21242, 32946}, {22034, 34371}, {22892, 38412}, {32113, 37897}, {32234, 33851}, {35482, 39588}, {37900, 40317}, {39710, 39720}
X(40341) = midpoint of X(69) and X(20080)
X(40341) = reflection of X(i) in X(j) for these {i,j}: {6, 69}, {69, 3630}, {193, 141}, {599, 15533}, {1351, 34507}, {1992, 22165}, {2549, 14929}, {3629, 3631}, {3729, 17372}, {3875, 17345}, {6144, 6}, {7798, 7848}, {11008, 3629}, {11477, 1352}, {13330, 14994}, {15069, 11898}, {15533, 11160}, {15534, 599}, {16176, 110}, {22253, 7761}, {25336, 2930}, {32234, 33851}, {36990, 15069}, {39899, 3098}
X(40341) = complement of X(11008)
X(40341) = anticomplement of X(3629)
X(40341) = isotomic conjugate of the isogonal conjugate of X(5206)
X(40341) = isotomic conjugate of the polar conjugate of X(37453)
X(40341) = X(5206)-cross conjugate of X(37453)
X(40341) = barycentric product X(i)*X(j) for these {i,j}: {69, 37453}, {76, 5206}
X(40341) = barycentric quotient X(i)/X(j) for these {i,j}: {5206, 6}, {37453, 4}
X(40341) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17344, 17253}, {2, 69, 3631}, {2, 3629, 6}, {2, 11008, 3629}, {6, 69, 599}, {6, 599, 3763}, {6, 6144, 15534}, {6, 15533, 69}, {6, 21358, 3589}, {7, 17362, 17119}, {8, 17365, 17118}, {9, 17374, 17311}, {44, 17296, 17267}, {69, 193, 141}, {69, 1992, 3620}, {69, 3620, 22165}, {69, 3630, 15533}, {69, 6144, 3763}, {69, 11008, 2}, {69, 11160, 3630}, {86, 17343, 17251}, {110, 16176, 25331}, {141, 193, 6}, {141, 3629, 6329}, {141, 6329, 2}, {141, 32455, 3618}, {183, 7779, 9766}, {183, 9766, 31489}, {190, 17373, 17309}, {193, 3618, 32455}, {239, 17361, 7232}, {298, 5859, 16644}, {299, 5858, 16645}, {319, 17364, 4363}, {320, 17363, 4361}, {325, 8667, 37637}, {385, 7788, 7778}, {491, 492, 37647}, {491, 591, 8252}, {492, 1991, 8253}, {599, 6144, 6}, {894, 17360, 4445}, {1100, 17272, 17325}, {1270, 5861, 590}, {1271, 5860, 615}, {1351, 34507, 10516}, {1654, 17378, 15668}, {1992, 3589, 6}, {1992, 3620, 3589}, {1992, 22165, 21358}, {3589, 3620, 21358}, {3589, 22165, 3620}, {3618, 32455, 6}, {3629, 3631, 2}, {3630, 20080, 6}, {3631, 6329, 141}, {3631, 11008, 6}, {3758, 17287, 17293}, {3759, 17288, 17290}, {3763, 15534, 6}, {3815, 15589, 8556}, {3879, 4643, 16777}, {3933, 14023, 3053}, {4034, 4888, 4688}, {4360, 4741, 17255}, {4393, 17273, 17323}, {4416, 4851, 45}, {4644, 32099, 594}, {4869, 37654, 17337}, {5839, 21296, 1086}, {6189, 6190, 7925}, {6542, 17347, 17262}, {6646, 17377, 17318}, {7751, 7776, 13881}, {7751, 7882, 7776}, {7754, 7768, 7784}, {7758, 7767, 5013}, {7774, 37671, 15271}, {7798, 7848, 11287}, {7805, 7896, 7866}, {7826, 7855, 3}, {7845, 17131, 381}, {7854, 7890, 9605}, {7946, 17129, 7773}, {8177, 39099, 6}, {11160, 20080, 69}, {15533, 20080, 6144}, {17257, 17390, 16672}, {17271, 17379, 17327}, {17277, 17375, 17313}, {17295, 17350, 17269}, {17297, 17349, 17265}, {17300, 17346, 17259}, {17316, 17332, 16675}, {17319, 17329, 24441}, {21358, 22165, 599}, {22844, 22845, 3}
X(40342) lies on these lines: {2, 67}, {110, 16176}, {382, 9970}, {524, 32267}, {542, 546}, {550, 2781}, {1112, 1843}, {3529, 32233}, {3632, 32278}, {3851, 32274}, {5079, 32306}, {5965, 25338}, {6053, 37984}, {6329, 15118}, {8550, 12162}, {9019, 37900}, {10299, 32247}, {12824, 32299}, {15303, 25328}, {15462, 15720}, {15687, 32271}, {15808, 32238}, {16534, 31831}, {20050, 32298}, {25321, 32255}
X(40342) = midpoint of X(i) and X(j) for these {i,j}: {3629, 24981}, {6593, 11061}
X(40342) = reflection of X(6698) in X(6593)
X(40342) = {X(11061),X(34319)}-harmonic conjugate of X(6593)
X(40343) lies on these lines: {67, 524}, {111, 5189}, {126, 13574}, {625, 691}, {8877, 31101}, {10989, 15398}
X(40343) ={X(858),X(34320)}-harmonic conjugate of X(15899)
X(40344) lies on these lines: on lines {2, 187}, {3, 7849}, {30, 3934}, {39, 7811}, {141, 8703}, {183, 11648}, {376, 7800}, {381, 7815}, {385, 39593}, {512, 3819}, {524, 8358}, {538, 7810}, {543, 8354}, {549, 626}, {574, 7788}, {620, 12100}, {754, 8359}, {1078, 7861}, {2896, 7799}, {3096, 15513}, {3314, 8589}, {3524, 3788}, {3534, 3734}, {3631, 14148}, {3642, 36755}, {3643, 36756}, {3785, 7739}, {3830, 15271}, {4045, 5306}, {5007, 33021}, {5013, 7882}, {5023, 7914}, {5054, 7784}, {5055, 7825}, {5077, 8556}, {5206, 7915}, {5309, 7780}, {6292, 6661}, {6655, 39563}, {6683, 7750}, {7746, 33251}, {7748, 33263}, {7759, 32990}, {7767, 32450}, {7768, 31652}, {7778, 15693}, {7789, 34200}, {7793, 7884}, {7795, 10304}, {7801, 33008}, {7802, 31239}, {7809, 7824}, {7817, 11287}, {7821, 7936}, {7822, 33255}, {7833, 9466}, {7841, 18362}, {7843, 11285}, {7847, 19570}, {7854, 32833}, {7862, 15694}, {7868, 8588}, {7874, 7928}, {7876, 35007}, {7879, 15515}, {7883, 33273}, {7886, 7935}, {7896, 15815}, {7910, 39565}, {7911, 38223}, {7922, 33022}, {8353, 32479}, {9774, 15698}, {9830, 36521}, {10033, 11001}, {10130, 10989}, {13586, 31168}, {15759, 32459}, {32828, 38259}, {32832, 33278}, {33184, 34506}
X(40344) = midpoint of X(i) and X(j) for these {i,j}: {39, 7811}, {549, 34510}, {7750, 7753}, {7810, 8356}, {7833, 9466}, {11057, 14537}
X(40344) = reflection of X(7753) in X(6683)
X(40344) = complement of X(14537)
X(40344) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11057, 14537}, {2, 14976, 598}, {3, 7865, 7880}, {2896, 37512, 7895}, {5077, 8556, 18546}, {7865, 7880, 7849}, {7936, 33004, 7821}
Points on the tangential power curve: X(40345)-X(40346)
This preamble is contributed by Clark Kimberling, November 11, 2020.
Let PC(ABC) by the power curve; i.e., the locus of the point at : bt : ct (barycentrics) as t varies through the real numbers. If P = at : bt : ct for fixed t, then the isotomic conjugate of P is the point P' = a-t : b-t : c-t. Equations for the lines tangent to PC(ABC) at P and P' are found using Suren's points on the line at infinity; see the preamble just before X(40296). If P is not the centroid of ABC, then the tangent lines are distinct, and they meet in the point
P'' = at(b2t - c2t)/(log b - log c) : bt(c2t - a2t)/(log c - log a) : ct(a2t - b2t)/(log a - log b)
The locus of P'' as t varies through the positive real numbers is here named the (barycentric) tangential power curve.
The corresponding normal lines at P and P' meet in a point whose locus is the normal power curve.
The trilinear tangential and normal power curves are defined in the same manner using trilinear coordindates throughout, using isogonal conjugates instead of isotomic.
X(40345) lies on these lines: {1, 40297}, {759, 40302}, {897, 40300}, {18827, 40301}
X(40345) = barycentric product X(i)*X(j) for these {i, j}: {83, 40346}, {523, 40300}, {661, 40301}, {1577, 40302}
X(40345) = barycentric quotient X(i)/X(j) for these (i, j): (512, 40338), (523, 40339), (661, 40327)
X(40345) = trilinear product X(i)*X(j) for these {i, j}: {82, 40346}, {512, 40301}, {523, 40302}, {661, 40300}
X(40345) = trilinear quotient X(i)/X(j) for these (i, j): (523, 40327), (661, 40338), (1577, 40339)
X(40345) = X(i)-isoconjugate-of-X(j) for these {i,j}: {110, 40327}, {163, 40339}, {662, 40338}
X(40345) = X(i)-reciprocal conjugate of-X(j) for these (i,j): (512, 40338), (523, 40339), (661, 40327)
X(40345) = X(661)-Zayin conjugate of-X(40338)
X(40346) lies on these lines: {6, 40299}, {755, 40302}, {14970, 40301}
X(40346) = barycentric product X(i)*X(j) for these {i, j}: {38, 40345}, {826, 40302}
X(40346) = barycentric quotient X(2084)/X(40338)
X(40346) = trilinear product X(i)*X(j) for these {i, j}: {39, 40345}, {2084, 40301}
X(40346) = trilinear quotient X(826)/X(40339)
X(40346) = X(827)-isoconjugate-of-X(40339)
X(40347) lies on the conic {{A,B,C,X(2),X(6)}, the cubics K478 and K1166, and these lines: {6, 5181}, {25, 1560}, {111, 858}, {112, 40326}, {115, 8770}, {230, 8749}, {393, 2493}, {1611, 40144}, {1976, 10836}, {2987, 11064}, {3291, 8791}, {6339, 28419}, {6587, 14998}, {9606, 39389}, {13881, 21448}, {14772, 14948}, {30535, 37648}, {34609, 36616}
X(40347) = isogonal conjugate of X(37784)
X(40347) = isotomic conjugate of X(37803)
X(40347) = X(i)-cross conjugate of X(j) for these (i,j): {14908, 67}, {14961, 6}, {21639, 4}
X(40347) = X(i)-isoconjugate of X(j) for these (i,j): {1, 37784}, {19, 5866}, {31, 37803}, {63, 37777}, {2349, 20772}
X(40347) = cevapoint of X(647) and X(1648)
X(40347) = trilinear pole of line {512, 6467}
X(40347) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 37803}, {3, 5866}, {6, 37784}, {25, 37777}, {1495, 20772}, {14908, 39169}
X(40348) lies on the cubic K1166 and these lines: {20, 68}, {25, 53}, {5392, 34608}, {7386, 37802}, {11181, 30739}, {12362, 34853}
X(40348) = X(47)-isoconjugate of X(36889)
X(40348) = barycentric product X(i)*X(j) for these {i,j}: {68, 40138}, {376, 2165}, {925, 9209}, {5392, 26864}
X(40348) = barycentric quotient X(i)/X(j) for these {i,j}: {376, 7763}, {2165, 36889}, {9209, 6563}, {26864, 1993}, {40138, 317}
X(40349) lies on these lines: {3, 6}, {112, 37948}, {115, 10257}, {230, 16976}, {232, 2071}, {441, 32459}, {625, 35923}, {647, 22089}, {3199, 12084}, {3289, 21663}, {3548, 7748}, {5866, 36212}, {6390, 15526}, {6640, 39565}, {6644, 33843}, {7386, 39602}, {7746, 15075}, {7756, 11585}, {7816, 28407}, {9155, 34147}, {10311, 15078}, {10313, 37941}, {11598, 11672}, {13509, 15035}, {14581, 34152}, {15013, 32456}, {23967, 39020}, {35067, 39008}
X(40349) = isogonal conjugate of the polar conjugate of X(5159)
X(40349) = isotomic conjugate of the polar conjugate of X(21639)
X(40349) = X(40347)-complementary conjugate of X(20305)
X(40349) = X(5159)-Ceva conjugate of X(21639)
X(40349) = crosssum of X(6) and X(37777)
X(40349) = crossdifference of every pair of points on line {523, 6353}
X(40349) = barycentric product X(i)*X(j) for these {i,j}: {3, 5159}, {69, 21639}
X(40349) = barycentric quotient X(i)/X(j) for these {i,j}: {5159, 264}, {21639, 4}
X(40349) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 574, 216}, {3, 10316, 15513}, {3, 14961, 187}, {3, 15905, 5210}, {3, 23115, 5206}, {187, 14961, 3284}, {574, 5065, 5013}, {15166, 15167, 22401}
X(40350) is the intersection of the tangents to the Moses-Lemoine conic at X(111) and X(1194). (Randy Hutson, December 18, 2020)
X(40350) lies on these lines: {2, 7748}, {4, 15820}, {22, 15513}, {23, 111}, {25, 32}, {39, 1995}, {50, 37972}, {110, 1570}, {115, 468}, {148, 37803}, {230, 37897}, {232, 15262}, {511, 9225}, {574, 11284}, {625, 7665}, {858, 10418}, {1194, 5041}, {1495, 1692}, {1503, 6388}, {1611, 20850}, {1691, 32237}, {2056, 21849}, {2079, 37928}, {2393, 32740}, {2489, 8651}, {2493, 3284}, {2502, 3292}, {2549, 40132}, {3066, 5034}, {3117, 34098}, {3767, 4232}, {3832, 15880}, {3934, 26257}, {4239, 16589}, {5007, 9465}, {5013, 5020}, {5023, 8770}, {5028, 35259}, {5038, 5943}, {5052, 34417}, {5106, 18860}, {5189, 39602}, {5309, 26255}, {5913, 37900}, {6688, 10329}, {6781, 16317}, {7398, 31404}, {7453, 21838}, {7492, 39576}, {7493, 7746}, {7664, 31275}, {7747, 10301}, {7756, 30739}, {8585, 8589}, {8588, 21448}, {8854, 12962}, {8855, 12969}, {13192, 23061}, {15822, 26235}, {16042, 31652}, {16055, 30749}, {16306, 18487}, {16320, 23991}, {17129, 33651}, {19577, 32457}, {26864, 39764}, {35265, 39024}
X(40350) = polar conjugate of the isotomic conjugate of X(21639)
X(40350) = crosspoint of X(25) and X(111)
X(40350) = crosssum of X(i) and X(j) for these (i,j): {69, 524}, {394, 5866}, {1648, 3566}
X(40350) = crossdifference of every pair of points on line {1649, 3265}
X(40350) = barycentric product X(i)*X(j) for these {i,j}: {4, 21639}, {25, 5159}
X(40350) = barycentric quotient X(i)/X(j) for these {i,j}: {5159, 305}, {21639, 69}
X(40350) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 111, 3291}, {23, 3291, 187}, {25, 34481, 1196}, {1495, 3124, 1692}, {2502, 20977, 3292}, {3292, 20977, 5107}
X(40351) lies on these lines: {251, 8749}, {699, 1304}, {1084, 36417}, {3407, 16080}
X(40351) = X(i)-isoconjugate of X(j) for these (i,j): {304, 3260}, {305, 14206}, {561, 11064}, {1928, 3284}, {2173, 40050}, {2631, 4609}, {4602, 9033}
X(40351) = barycentric product X(i)*X(j) for these {i,j}: {32, 8749}, {74, 1974}, {512, 32715}, {560, 36119}, {669, 1304}, {798, 36131}, {1501, 16080}, {1973, 2159}, {2207, 18877}, {2489, 32640}, {3049, 32695}, {9426, 16077}, {14574, 18808}, {14601, 35908}, {14919, 36417}, {22455, 34416}
X(40351) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 40050}, {1304, 4609}, {1501, 11064}, {1974, 3260}, {8749, 1502}, {9233, 3284}, {9426, 9033}, {23216, 1650}, {32715, 670}, {36119, 1928}, {36131, 4602}
X(40352) lies on the cubics K594 and K1171, and on these lines: {3, 74}, {6, 32738}, {25, 8749}, {30, 2986}, {98, 468}, {154, 2351}, {184, 1576}, {228, 692}, {235, 8884}, {237, 14908}, {265, 34104}, {351, 878}, {974, 14703}, {1112, 14673}, {1177, 14380}, {1399, 1410}, {1402, 14975}, {1492, 2349}, {1494, 1799}, {1495, 3003}, {1624, 13198}, {1632, 36178}, {1660, 3135}, {1885, 10152}, {2200, 32739}, {2394, 9147}, {2491, 32740}, {3425, 35908}, {3542, 34449}, {4630, 10547}, {6795, 36789}, {7493, 36875}, {8644, 32741}, {8651, 39840}, {9140, 30510}, {9407, 32715}, {11402, 15291}, {11799, 34150}, {13558, 15647}, {14177, 36311}, {14181, 36308}, {14567, 14600}, {14989, 18325}, {15270, 40319}, {15627, 32736}, {17938, 17970}, {32695, 32725}
X(40352) = isogonal conjugate of X(3260)
X(40352) = isogonal conjugate of the anticomplement of X(3003)
X(40352) = isogonal conjugate of the isotomic conjugate of X(74)
X(40352) = isogonal conjugate of the polar conjugate of X(8749)
X(40352) = polar conjugate of the isotomic conjugate of X(18877)
X(40352) = X(i)-Ceva conjugate of X(j) for these (i,j): {74, 18877}, {1304, 2433}, {10419, 6}
X(40352) = X(i)-cross conjugate of X(j) for these (i,j): {9407, 32}, {14270, 1576}
X(40352) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3260}, {2, 14206}, {30, 75}, {69, 1784}, {76, 2173}, {85, 7359}, {92, 11064}, {99, 36035}, {304, 1990}, {312, 6357}, {321, 18653}, {328, 35201}, {525, 24001}, {561, 1495}, {668, 11125}, {799, 1637}, {811, 9033}, {1099, 1494}, {1502, 9406}, {1577, 2407}, {1650, 23999}, {1733, 36891}, {1928, 9407}, {1969, 3284}, {1978, 14399}, {2166, 6148}, {2349, 36789}, {2420, 20948}, {2631, 6331}, {3163, 33805}, {4240, 14208}, {4554, 14400}, {4602, 14398}, {5664, 32680}, {6739, 14616}, {9214, 14210}
X(40352) = cevapoint of X(i) and X(j) for these (i,j): {32, 9407}, {14575, 19627}, {20975, 21731}, {34394, 34395}
X(40352) = crosspoint of X(i) and X(j) for these (i,j): {6, 34178}, {74, 8749}, {1989, 11744}
X(40352) = crosssum of X(i) and X(j) for these (i,j): {2, 146}, {30, 11064}, {69, 1272}, {323, 2071}, {23097, 36789}
X(40352) = trilinear pole of line {32, 3049}
X(40352) = crossdifference of every pair of points on line {1637, 5664}
X(40352) = barycentric product of circumcircle intercepts of line X(6)X(647)
X(40352) = barycentric product X(i)*X(j) for these {i,j}: {1, 2159}, {3, 8749}, {4, 18877}, {6, 74}, {19, 35200}, {25, 14919}, {31, 2349}, {32, 1494}, {48, 36119}, {50, 5627}, {56, 15627}, {64, 15291}, {110, 2433}, {111, 9717}, {112, 14380}, {184, 16080}, {186, 11079}, {187, 9139}, {248, 35908}, {520, 32695}, {523, 32640}, {525, 32715}, {560, 33805}, {647, 1304}, {656, 36131}, {661, 36034}, {1576, 2394}, {1976, 35910}, {1989, 14385}, {2088, 15395}, {2623, 36831}, {2715, 32112}, {3003, 10419}, {3049, 16077}, {3470, 14579}, {5158, 22455}, {8675, 32681}, {8739, 39377}, {8740, 39378}, {9404, 36064}, {9407, 31621}, {9409, 34568}, {10152, 14642}, {12079, 23357}, {14264, 14910}, {14270, 39290}, {15459, 39201}, {18808, 32661}, {32654, 36875}, {32740, 36890}, {34178, 36896}, {34394, 36308}, {34395, 36311}
X(40352) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3260}, {31, 14206}, {32, 30}, {50, 6148}, {74, 76}, {184, 11064}, {217, 1568}, {560, 2173}, {669, 1637}, {798, 36035}, {1304, 6331}, {1397, 6357}, {1494, 1502}, {1495, 36789}, {1501, 1495}, {1576, 2407}, {1917, 9406}, {1919, 11125}, {1973, 1784}, {1974, 1990}, {1980, 14399}, {2159, 75}, {2175, 7359}, {2206, 18653}, {2349, 561}, {2433, 850}, {3049, 9033}, {5627, 20573}, {8749, 264}, {9139, 18023}, {9233, 9407}, {9406, 1099}, {9407, 3163}, {9408, 23097}, {9426, 14398}, {9717, 3266}, {11060, 14254}, {11079, 328}, {12079, 23962}, {14270, 5664}, {14380, 3267}, {14385, 7799}, {14567, 5642}, {14574, 2420}, {14575, 3284}, {14581, 34334}, {14600, 35912}, {14601, 35906}, {14919, 305}, {15291, 14615}, {15627, 3596}, {16080, 18022}, {18877, 69}, {19627, 1511}, {32640, 99}, {32654, 36891}, {32676, 24001}, {32695, 6528}, {32715, 648}, {32740, 9214}, {33805, 1928}, {34397, 14920}, {34416, 18487}, {35200, 304}, {36034, 799}, {36119, 1969}, {36131, 811}
X(40353) lies on the cubic K1171 and these lines: {6, 11074}, {50, 18877}, {74, 3003}, {323, 3284}, {2433, 2436}, {5063, 14385}, {5627, 6128}, {8749, 14581}, {9407, 32715}, {34568, 35906}
X(40353) = isogonal conjugate of X(36789)
X(40353) = X(3049)-cross conjugate of X(32715)
X(40353) = X(i)-isoconjugate of X(j) for these (i,j): {1, 36789}, {2, 1099}, {30, 14206}, {63, 34334}, {75, 3163}, {85, 6062}, {92, 16163}, {304, 16240}, {312, 1354}, {561, 9408}, {811, 14401}, {1553, 36102}, {1577, 3233}, {1784, 11064}, {2173, 3260}, {2349, 23097}, {2407, 36035}, {3081, 33805}, {9033, 24001}, {18750, 38956}, {23999, 39008}
X(40353) = crosssum of X(3163) and X(16163)
X(40353) = crossdifference of every pair of points on line {1553, 23097}
X(40353) = barycentric product X(i)*X(j) for these {i,j}: {32, 31621}, {74, 74}, {647, 34568}, {1304, 14380}, {2159, 2349}, {2394, 32640}, {5627, 14385}, {8749, 14919}, {9139, 9717}, {10419, 14264}, {16080, 18877}, {32715, 34767}, {35200, 36119}
X(40353) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 36789}, {25, 34334}, {31, 1099}, {32, 3163}, {74, 3260}, {184, 16163}, {1397, 1354}, {1495, 23097}, {1501, 9408}, {1576, 3233}, {1974, 16240}, {2159, 14206}, {2175, 6062}, {3049, 14401}, {9407, 3081}, {14385, 6148}, {18877, 11064}, {31621, 1502}, {32640, 2407}, {32715, 4240}, {33581, 38956}, {34568, 6331}, {36131, 24001}
X(40353) = {X(74),X(36896)}-harmonic conjugate of X(3003)
X(40354) lies on the cubic K1171 and these lines: {6, 74}, {83, 16080}, {113, 6103}, {729, 1304}, {1300, 1990}, {1494, 6661}, {2159, 2281}, {2207, 3124}, {2211, 32715}, {2420, 5504}, {3225, 16077}, {6531, 20031}, {11060, 14581}, {18268, 36131}, {32640, 32654}
X(40354) = isogonal conjugate of the isotomic conjugate of X(8749)
X(40354) = X(i)-isoconjugate of X(j) for these (i,j): {30, 304}, {63, 3260}, {69, 14206}, {75, 11064}, {305, 2173}, {561, 3284}, {670, 2631}, {799, 9033}, {1784, 3926}, {2407, 14208}, {3265, 24001}, {3718, 6357}, {4563, 36035}, {4572, 14395}, {4602, 9409}, {7182, 7359}, {9406, 40050}, {16163, 33805}, {18653, 20336}
X(40354) = trilinear pole of line {669, 1974}
X(40354) = barycentric product X(i)*X(j) for these {i,j}: {6, 8749}, {19, 2159}, {25, 74}, {31, 36119}, {32, 16080}, {112, 2433}, {393, 18877}, {512, 1304}, {523, 32715}, {608, 15627}, {647, 32695}, {661, 36131}, {669, 16077}, {1096, 35200}, {1494, 1974}, {1576, 18808}, {1973, 2349}, {1976, 35908}, {2207, 14919}, {2501, 32640}, {3049, 15459}, {5627, 34397}, {8753, 9717}, {10152, 33581}, {14380, 32713}, {14385, 18384}, {14398, 34568}, {22455, 34417}, {32112, 32696}
X(40354) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 3260}, {32, 11064}, {74, 305}, {669, 9033}, {1304, 670}, {1494, 40050}, {1501, 3284}, {1924, 2631}, {1973, 14206}, {1974, 30}, {2159, 304}, {2433, 3267}, {8749, 76}, {9407, 16163}, {9426, 9409}, {14581, 36789}, {14601, 35912}, {16077, 4609}, {16080, 1502}, {18877, 3926}, {32640, 4563}, {32695, 6331}, {32715, 99}, {34397, 6148}, {34416, 1531}, {36119, 561}, {36131, 799}, {36417, 1990}
X(40355) lies on the cubicx K497 and K1171, and on these lines: {30, 74}, {462, 14372}, {463, 14373}, {1495, 3003}, {1511, 10419}, {4550, 39170}, {8749, 34397}, {9139, 15395}, {11060, 14581}, {11074, 11080}, {14254, 34289}
X(40355) = reflection of X(14560) in X(15295)
X(40355) = isogonal conjugate of X(6148)
X(40355) = isogonal conjugate of the anticomplement of X(6128)
X(40355) = isogonal conjugate of the isotomic conjugate of X(5627)
X(40355) = polar conjugate of the isotomic conjugate of X(11079)
X(40355) = X(i)-Ceva conjugate of X(j) for these (i,j): {74, 11074}, {5627, 11079}
X(40355) = X(i)-cross conjugate of X(j) for these (i,j): {32, 8749}, {512, 14560}, {3124, 2433}, {20975, 15475}
X(40355) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6148}, {63, 14920}, {69, 35201}, {75, 1511}, {304, 39176}, {323, 14206}, {662, 5664}, {2173, 7799}, {2407, 32679}, {3258, 24041}, {3260, 6149}, {8552, 24001}, {10411, 36035}
X(40355) = cevapoint of X(3457) and X(3458)
X(40355) = crosssum of X(3258) and X(5664)
X(40355) = trilinear pole of line {11060, 14398}
X(40355) = barycentric product X(i)*X(j) for these {i,j}: {4, 11079}, {6, 5627}, {74, 1989}, {115, 15395}, {265, 8749}, {476, 2433}, {512, 39290}, {1138, 11074}, {1304, 14582}, {1494, 11060}, {2159, 2166}, {2394, 14560}, {3457, 36311}, {3458, 36308}, {3470, 11071}, {6344, 18877}, {8737, 39378}, {8738, 39377}, {10412, 32640}, {14592, 32715}, {14919, 18384}, {18808, 32662}
X(40355) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 6148}, {25, 14920}, {32, 1511}, {74, 7799}, {512, 5664}, {1973, 35201}, {1974, 39176}, {1989, 3260}, {2433, 3268}, {3124, 3258}, {5627, 76}, {8749, 340}, {11060, 30}, {11074, 1272}, {11079, 69}, {14560, 2407}, {14583, 36789}, {15395, 4590}, {32640, 10411}, {32715, 14590}, {39290, 670}
X(40355) lies on the cubic K1171 and these lines: {1511, 3163}, {14270, 14398}, {14581, 34397}
X(40356) = isogonal conjugate of the isotomic conjugate of X(11070)
X(40356) = X(32)-cross conjugate of X(14581)
X(40356) = X(i)-isoconjugate of X(j) for these (i,j): {399, 33805}, {1272, 2349}
X(40356) = barycentric product X(i)*X(j) for these {i,j}: {6, 11070}, {25, 20123}, {1138, 1495}
X(40356) = barycentric quotient X(i)/X(j) for these {i,j}: {1495, 1272}, {9407, 399}, {11070, 76}, {14398, 14566}, {20123, 305}
X(40357) lies on the cubic K644 and these lines: {2, 19615}, {4, 251}, {6, 18018}, {83, 26209}, {8793, 17407}
X(40357) = X(83)-Ceva conjugate of X(40404)
X(40357) = X(3162)-cross conjugate of X(8793)
X(40357) = X(i)-isoconjugate of X(j) for these (i,j): {2172, 39129}, {20883, 39172}, {23208, 39733}
X(40357) = cevapoint of X(3162) and X(17407)
X(40357) = barycentric product X(i)*X(j) for these {i,j}: {1370, 16277}, {1799, 17407}, {8793, 18018}
X(40357) = barycentric quotient X(i)/X(j) for these {i,j}: {66, 39129}, {159, 3313}, {8793, 22}, {10547, 39172}, {16277, 13575}, {17407, 427}
X(40358) lies on the cubics K555 and K644, and on these lines: {2, 2138}, {22, 39172}, {25, 39417}, {83, 26209}, {1176, 19153}, {20806, 36414}
X(40358) = polar conjugate of the isogonal conjugate of X(39172)
X(40358) = X(40009)-Ceva conjugate of X(34207)
X(40358) = X(i)-cross conjugate of X(j) for these (i,j): {6, 8743}, {2485, 39417}, {17409, 22}
X(40358) = X(i)-isoconjugate of X(j) for these (i,j): {63, 17407}, {66, 18596}, {1370, 2156}, {2353, 21582}
X(40358) = barycentric product X(i)*X(j) for these {i,j}: {22, 13575}, {206, 40009}, {264, 39172}, {315, 34207}, {2172, 39733}, {34254, 40144}
X(40358) = barycentric quotient X(i)/X(j) for these {i,j}: {22, 1370}, {25, 17407}, {206, 159}, {1760, 21582}, {2172, 18596}, {10316, 23115}, {13575, 18018}, {17409, 3162}, {20806, 28419}, {34207, 66}, {39172, 3}, {39417, 1289}, {40144, 13854}
Ceva-conjugates associated with the power curve: X(40359)-X(40375)
This preamble is contributed by Clark Kimberling and Peter Moses, November 17, 2020.
Let P(t) = at : bt : ct, on the power curve, as in the preambles just before X(40297) and X(40345). The P(t)-Ceva conjugate of P(u), denoted by P(t)©P(u) is given by
au(-au-t + bu-t + cu-t) : bu(au-t - bu-t + cu-t) : cu(au-t + bu-t - cu-t),
P(t)©P(u) is the perspector of the cevian triangle of P(t) and the anticevian triangle of P(u).
The appearance of (i,j,k) in the following list means that P(t)©P(u) = X(k):
(-9,-1,33807), (-8,-8,40359), (-8,-6,40360), (-8,-2,40361), (-8,0,33797), (-7,-1,33806), (-7,1,33791), (-6,-6,40362), (-6,-4,40050), (-6,-2,40073), (-6,-1,21585), (-6,0,33796), (-6,2,33802), (-5,-5,1928), (-5,-4,40363), (-5,-3,40364), (-5,-2,40365), (-5,-1,20641), (-5,0,21275), (-5,1,33790), (-4,-4,1502), (-4,-3,28659), (-4,-2,305), (-4,-1,20444), (-4,0,315), (-4,1,21366), (-4,2,33801), (-4,4,40366), (-3,-3,561), (-3,-2,3596), (-3,-1,304), (-3,0,6327), (3,1,1760), (-3,2,23849), (-2,-3,40367), (-2,-2,76), (-2,-1,312), (-2,0,69), (-2,1,1759), (-2,2,22), (-2,4,18796), (-1,-3,18837), (-1,-2,6382), (-1,1,75), (-1,0,8), (-1,1,63), (-1,2,1631), (-1,3,2172), (0,-2,6374), (0,-1,6376), (0,0,2), (0,1,9), (0,2,3), (0,3,32664), (0,4,206), (0,6,,40368), (0,8,,40369), (1,1,17149), (1,0,192), (1,1,1), (1,2,55), (1,3,48), (1,4,,40370), (1,5,17), (2,-2,19562), (2,0,194), (2,1,43), (2,2,6), (2,3,41), (2,4,184), (2,5,40371), (2,6,20968), (3,-1,33788), (3,0,17486), (3,1,1740), (3,2,2176), (3,3,31), (3,4,2175), (3,5,9247), (4,0,8264), (4,2,1613), (4,3,2209), (4,4,32), (4,5,9447), (4,6,14575), (4,8,2,(5,1,33782), (5,2,21776), (5,5,560), (5,6,9448), (6,2,33786), (6,6,1501), (6,8,40373), (7,1,33783), (7,7,1917), (8,8,9233)
A few more: (0,1/2 40374), (1/2,1/2,366), (1/2,1,364), (1/2,3/2,4166), (1/2,2,20469), (1,1/2,40375)
For fixed t = t0 and variable u, the locus of P(t0)©P(u) is here named the P(t0)©P(u)-Ceva power curve. For fixed variable t and fixed u = u0, the locus of P(t)©P(u0) is here named the P(t)©P(u0)-Ceva power curve.
X(40359) lies on these lines: {6, 38812}, {76, 14820}, {561, 23626}, {626, 1502}, {4609, 7796}, {8149, 14603}, {9065, 23849}
X(40359) = isotomic conjugate of X(9233)
X(40359) = polar conjugate of isogonal conjugate of X(40360)
X(40359) = complement of X(40381)
X(40359) = anticomplement of X(40376)
X(40359) = barycentric square of X(1502)
X(40360) lies on these lines: {194, 14603}, {305, 20819}, {670, 12220}, {1502, 3314}, {4609, 40073}, {6374, 23642}, {8264, 35528}
X(40360) = isogonal conjugate of polar conjugate of X(40359)
X(40360) = isotomic conjugate of isogonal conjugate of X(40050)
X(40360) = barycentric quotient X(69)/X(1501)
X(40361) lies on these lines: {32, 76}, {305, 7871}, {3001, 40073}, {4174, 33806}, {7752, 40074}, {7855, 8024}
X(40361) = barycentric product X(76)*X(33796)
X(40362) lies on these lines: {1, 35529}, {2, 14603}, {6, 35530}, {22, 689}, {75, 35527}, {76, 19562}, {305, 4609}, {308, 1239}, {561, 2887}, {670, 2979}, {1235, 5117}, {1502, 3314}, {1928, 35523}, {3124, 40162}, {6374, 8041}, {6386, 32862}, {8039, 23962}, {10010, 39998}, {18018, 40073}, {20023, 20024}, {33802, 38842}
X(40362) = isogonal conjugate of X(9233)
X(40362) = isotomic conjugate of X(1501)
X(40362) = complement of X(40382)
X(40362) = anticomplement of X(40377)
X(40362) = barycentric square of X(561)
X(40363) lies on these lines: {76, 3782}, {305, 6386}, {312, 20684}, {313, 561}, {704, 33782}, {871, 40033}, {1211, 6382}, {1928, 40050}, {1978, 4417}, {3596, 3703}, {5224, 40087}, {6376, 7034}, {17149, 35539}, {28659, 30713}
X(40363) = isogonal conjugate of X(41280)
X(40363) = isotomic conjugate of X(1397)
X(40363) = cevapoint of X(75) and X(21594)
X(40363) = trilinear product X(i)*X(j) for these {i, j}: {2, 28659}, {8, 561}, {9, 1502}, {10, 40072}
X(40363) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 1917}, {31, 1397}, {32, 604}, {34, 14575}, {56, 560}, {57, 1501}
X(40363) = barycentric product X(8)*X(1502)
X(40364) lies on these lines: {38, 75}, {192, 35545}, {304, 18671}, {305, 20336}, {326, 336}, {349, 1502}, {720, 21776}, {799, 1760}, {1102, 3403}, {1920, 2345}, {1921, 4000}, {1928, 1969}, {2643, 18069}, {4602, 33805}, {9239, 18837}, {18068, 33781}, {18833, 23051}, {20641, 21582}, {20915, 20944}, {40050, 40071}
X(40364) = isogonal conjugate of polar conjugate of X(1928)
X(40364) = isotomic conjugate of X(1973)
X(40364) = polar conjugate of trilinear square of X(25)
X(40364) = barycentric product X(69)*X(561)
X(40365) lies on these lines: {1, 76}, {305, 3006}, {310, 29829}, {1492, 18796}, {1932, 4172}, {3596, 6757}, {3616, 30893}, {4153, 20444}, {6374, 35541}, {6382, 35546}, {8024, 29832}, {17143, 36500}, {18152, 29830}, {19562, 35529}, {26230, 40022}, {29831, 39998}, {32773, 33940}, {33108, 33933}, {35517, 40071}, {35552, 40073}
X(40365) = isotomic conjugate of X(7087)
X(40365) = barycentric product X(76)*X(6327)
X(40366) lies on these lines: {2, 66}, {110, 34254}, {184, 1180}, {315, 39466}, {2001, 18796}, {2909, 5012}, {4630, 36414}, {28710, 37183}
X(40366) = barycentric product X(32)*X(33797)
X(40367) lies on these lines: {76, 21138}, {561, 21140}, {700, 33788}, {1502, 1928}, {1921, 10010}, {1925, 4485}, {3596, 14603}, {7034, 33938}, {18837, 35538}
X(40367) = isotomic conjugate of isogonal conjugate of X(6382)
X(40367) = barycentric product X(192)*X(1502)
X(40368) lies on these lines: {31, 40145}, {51, 5007}, {1501, 19556}, {1576, 2979}, {5133, 7792}, {6327, 34069}
X(40368) = centroid of X(31) and its extraversions
X(40368) = barycentric product X(1501)*X(33796)
X(40369) lies on these lines: {32, 39466}, {315, 4630}, {6680, 6697}, {10316, 14574}
X(40369) = barycentric product X(9233)*X(33797)
X(40370) lies on these lines: {1, 7096}, {32, 1917}, {76, 1492}, {110, 34016}, {184, 1475}, {206, 942}, {215, 3202}, {692, 3730}, {766, 2172}, {1631, 20739}, {1932, 4116}, {1974, 2333}, {2242, 18759}, {8618, 9247}, {14963, 23849}, {22164, 35327}
X(40370) = barycentric product X(32)*X(6327)
X(40371) lies on these lines: {6, 7087}, {75, 825}, {560, 9233}, {2260, 4275}, {9247, 22363}, {9407, 9449}, {15624, 32739}, {20444, 38840}
X(40371) = isogonal conjugate of isotomic conjugate of X(32664)
X(40371) = barycentric product X(560)*X(6327)
X(40372) lies on these lines: {2, 4630}, {32, 39466}, {184, 14574}, {206, 36414}, {8023, 9233}, {19556, 33728}, {20968, 22075}
X(40372) = barycentric product X(315)*X(9233)
X(40373) lies on these lines: {32, 2909}, {184, 4173}, {1974, 14573}, {1976, 10312}, {3202, 19627}, {3492, 35924}, {9247, 22364}, {9418, 20968}, {9967, 21637}, {14575, 14585}, {19558, 20960}
X(40373) = isogonal conjugate of polar conjugate of X(1501)
X(40373) = isotomic conjugate of polar conjugate of X(9233)
X(40373) = barycentric product X(69)*X(9233)
X(40374) lies on these lines: {1, 366}, {2, 4182}, {7, 20527}
X(40374) = barycentric product X(366)*X(20534)
X(40375) lies on these lines: {1, 366}, {43, 365}, {87, 20664}, {238, 20673}
Complements and anticomplements associated with the power curve: X(40376)-X(40383)
This preamble is contributed by Clark Kimberling and Peter Moses, November 19, 2020.
Suppose that P(t) = at : bt : ct (barycentrics) is a point on the power curve. The complement of P(t) is the point bt + ct : ct + at : at + bt. The anticomplement of P(t) is the point -at + bt + ct : at - bt + ct : at + bt - ct.
The appearance of (i,j) in the following list means that the (complement of X(i)) = X(j):
(-8,40376), (-6,40377), (-4,8265), (-3,16584), (-2,39), (-1,37), (-1/2,40378), (0,2), (1/2,20527), (1,10), (3/2,20334), (2,141), (5/2,20543), (3,2887), (4,626), (5,21235), (6,40379), (8,40380)
The appearance of (i,j) in the following list means that the (anticomplement of X(i)) = X(j):
(-8,40381), (-6,40382), (-4,8264), (-3,17486), (-2,194), (-1,192), (-1/2,40383), (0,2), (1/2,20534), (1,8), (3/2,20346), (2,69), (5/2,20555), (3,6327), (4,315), (5,21275), (6,33796), (8,33797)
X(40376) lies on these lines: {2, 40359}, {32, 14946}, {6680, 8265}, {9233, 40369}
X(40376) = complement of X(40359)
X(40376) = barycentric product X(9233)*X(40380)
X(40377) lies on these lines: {2, 14603}, {6, 23173}, {31, 14945}, {39, 4074}, {51, 1084}, {427, 35971}, {1194, 7792}, {1501, 19556}, {1915, 9468}, {6679, 16584}
X(40377) = complement of X(40362)
X(40377) = barycentric product X(1501)*X(40379)
X(40378) lies on these lines: {1, 366}, {2, 18297}, {6, 20743}, {28, 20779}, {57, 364}, {81, 2069}, {20357, 20682}
X(40378) = complement of X(18297)
X(40378) = barycentric product X(366)*X(20527)
X(40379) lies on these lines: {2, 1501}, {51, 5103}, {116, 35972}, {141, 427}, {184, 30747}, {316, 33301}, {458, 7784}, {625, 5943}, {626, 2387}, {698, 4121}, {746, 4177}, {779, 37845}, {1853, 7778}, {2076, 16275}, {3096, 11338}, {3763, 11324}, {3981, 5025}, {4048, 11550}, {5133, 24256}, {8024, 16893}, {8041, 31107}, {8878, 12212}, {16584, 30877}
X(40379) = isogonal conjugate of X(38829)
X(40379) = complement of X(1501)
X(40379) = barycentric product X(141)*X(5025)
X(40380) lies on these lines: {2, 9233}, {141, 21536}, {626, 3852}, {1502, 15449}
X(40380) = complement of X(9233)
X(40381) lies on these lines: {32, 8264}, {194, 1186}, {16985, 40366}, {19566, 31981}
X(40381) = anticomplement of X(40359)
X(40382) lies on these lines: {2, 14603}, {31, 17486}, {2998, 33798}, {7766, 8264}, {20064, 39347}
X(40382) = anticomplement of X(40362)
X(40383) lies on these lines: {2, 18297}, {192, 366}, {239, 364}, {330, 367}, {2068, 17350}, {2069, 4393}
X(40383) = anticomplement of X(18297)
X(40384) lies on the cubic K1172 and these lines: {2, 39290}, {6, 34568}, {15, 39378}, {16, 39377}, {74, 186}, {323, 3284}, {842, 40355}, {1138, 3258}, {1494, 3580}, {1990, 14165}, {2349, 18593}, {2394, 2411}, {3431, 14385}, {3470, 15032}, {7799, 11064}, {8431, 15404}, {9139, 9213}, {9717, 14355}, {11430, 38933}, {14264, 14685}, {36210, 36311}, {36211, 36308}
X(40384) = isogonal conjugate of X(3163)
X(40384) = isotomic conjugate of X(36789)
X(40384) = polar conjugate of X(34334)
X(40384) = isogonal conjugate of the complement of X(1494)
X(40384) = isotomic conjugate of the isogonal conjugate of X(40353)
X(40384) = isogonal conjugate of the isotomic conjugate of X(31621)
X(40384) = X(i)-cross conjugate of X(j) for these (i,j): {6, 74}, {647, 1304}, {974, 69}, {3269, 14380}, {11079, 10419}, {14264, 1494}
X(40384) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3163}, {6, 1099}, {9, 1354}, {19, 16163}, {30, 2173}, {31, 36789}, {48, 34334}, {57, 6062}, {63, 16240}, {75, 9408}, {162, 14401}, {610, 38956}, {661, 3233}, {1495, 14206}, {1553, 36151}, {1784, 3284}, {2159, 23097}, {2349, 3081}, {2420, 36035}, {2631, 4240}, {3260, 9406}, {9409, 24001}, {24000, 39008}
X(40384) = cevapoint of X(i) and X(j) for these (i,j): {6, 74}, {3269, 14380}, {14385, 18877}
X(40384) = X(40384) = crosssum of X(i) and X(j) for these (i,j): {30, 34582}, {3081, 36435}, {14401, 39008}
X(40384) = trilinear pole of line {74, 526} (the tangent to the circumcircle at X(74))
X(40384) = crossdifference of every pair of points on line {3081, 14401}
X(40384) = barycentric square of X(2349)
X(40384) = barycentric product X(i)*X(j) for these {i,j}: {6, 31621}, {74, 1494}, {76, 40353}, {525, 34568}, {1304, 34767}, {2159, 33805}, {2349, 2349}, {9139, 36890}, {14380, 16077}, {14919, 16080}
X(40384) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1099}, {2, 36789}, {3, 16163}, {4, 34334}, {6, 3163}, {25, 16240}, {30, 23097}, {32, 9408}, {55, 6062}, {56, 1354}, {64, 38956}, {74, 30}, {110, 3233}, {647, 14401}, {1304, 4240}, {1494, 3260}, {1495, 3081}, {2159, 2173}, {2349, 14206}, {2433, 1637}, {3269, 39008}, {3470, 10272}, {5627, 14254}, {5663, 1553}, {8749, 1990}, {9139, 9214}, {9408, 36435}, {9717, 5642}, {10419, 15454}, {14264, 113}, {14380, 9033}, {14385, 1511}, {14919, 11064}, {15627, 7359}, {18877, 3284}, {31621, 76}, {32640, 2420}, {32715, 23347}, {34568, 648}, {36119, 1784}, {40352, 1495}, {40353, 6}, {40354, 14581}, {40355, 14583}
X(40385) lies on the cubic K1172 and these lines: {4, 6128}, {1302, 3163}, {1494, 3580}, {18877, 32681}
X(40385) = barycentric product X(74)*X(39263)
X(40385) = barycentric quotient X(i)/X(j) for these {i,j}: {26864, 10564}, {39263, 3260}
X(40386) lies on the cubic K1172 and these lines: {4, 3426}, {1495, 9064}, {3580, 11070}, {9140, 18554}
X(40385) = barycentric product X(12112)*X(36889)
X(40385) = barycentric quotient X(i)/X(j) for these {i,j}: {3426, 18317}, {12112, 376}
X(40387) lies on the cubic K1172 and these lines: {2, 74}, {1300, 1990}, {15472, 32738}, {36789, 39263}
X(40388) lies on the cubic K1172 and these lines: {6, 38936}, {186, 3003}, {340, 687}, {1300, 1990}, {2501, 14222}, {3284, 10420}, {5962, 18877}, {11079, 32710}, {15454, 40138}
X(40388) = isogonal conjugate of the complement of X(2986)
X(40388) = polar conjugate of the isotomic conjugate of X(10419)
X(40388) = X(i)-cross conjugate of X(j) for these (i,j): {6, 8749}, {25, 1300}, {512, 10420}, {2501, 32695}
X(40388) = X(i)-isoconjugate of X(j) for these (i,j): {63, 113}, {1725, 11064}, {2315, 3260}, {13754, 14206}
X(40388) = https://en.wikipedia.org/wiki/Aslackby_and_Laughton#/media/File:St.James'_church,_Aslackby,_Lincs._-_geograph.org.uk_-_90690.jpg of X(i) and X(j) for these (i,j): {6, 14910}, {25, 40354}
X(40388) = trilinear pole of line {21731, 40352}
X(40388) = barycentric product X(i)*X(j) for these {i,j}: {4, 10419}, {74, 1300}, {403, 39379}, {687, 2433}, {1304, 15328}, {2394, 32708}, {2986, 8749}, {5627, 38936}, {10420, 18808}, {10421, 35373}, {14910, 16080}, {15421, 32695}, {36053, 36119}
X(40388) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 113}, {1300, 3260}, {2433, 6334}, {8749, 3580}, {10419, 69}, {14910, 11064}, {32695, 16237}, {32708, 2407}, {32715, 15329}, {38936, 6148}, {40352, 13754}, {40354, 3003}, {40355, 39170}
X(40389) lies on the cubic K1172 and these lines: {2, 39290}, {6, 5627}, {74, 1989}, {3470, 11079}, {14582, 18808}
X(40389) = X(16080)-Ceva conjugate of X(5627)
X(40389) = crosspoint of X(10421) and X(16080)
X(40389) = barycentric product X(i)*X(j) for these {i,j}: {265, 10421}, {5627, 12383}
X(40389) = barycentric quotient X(i)/X(j) for these {i,j}: {10421, 340}, {12383, 6148}, {40355, 35372}
X(40390) lies on the cubic K1172 and these lines: {4, 18781}, {74, 35373}, {186, 35372}, {1990, 3580}, {34834, 39176}
X(40390) = X(6)-cross conjugate of X(186)
X(40390) = X(32678)-isoconjugate of X(38401)
X(40390) = cevapoint of X(6) and X(35372)
X(40390) = barycentric product X(340)*X(35372)
X(40390) = barycentric quotient X(i)/X(j) for these {i,j}: {186, 12383}, {526, 38401}, {35372, 265}, {35373, 12028}
X(40391) lies on the cubic K1172 and these lines: {4, 5627}, {6, 34568}, {11070, 16080}
X(40391) = X(2173)-isoconjugate of X(20123)
X(40391) = barycentric product X(14566)*X(34568)
X(40391) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 20123}, {399, 16163}, {8749, 11070}, {40354, 40356}
X(40392) lies on the cubic K1172 and these lines: {2, 5627}, {6, 38936}, {74, 35373}
X(40393) lies on the Kiepert circumhyperbola and these lines: {2, 571}, {4, 569}, {5, 96}, {6, 5392}, {10, 2216}, {22, 262}, {76, 1993}, {94, 34545}, {98, 5133}, {275, 467}, {311, 1994}, {648, 9381}, {1176, 30505}, {2052, 5422}, {2986, 23292}, {6504, 11427}, {7494, 14494}, {7495, 7608}, {7500, 14484}, {7503, 13599}, {9221, 35921}, {10601, 34289}, {14492, 34603}, {37765, 39284}
X(40393) = isogonal conjugate of X(570)
X(40393) = isotomic conjugate of X(37636)
X(40393) = polar conjugate of X(1594)
X(40393) = isogonal conjugate of the complement of X(311)
X(40393) = isotomic conjugate of the anticomplement of X(37649)
X(40393) = isotomic conjugate of the complement of X(1994)
X(40393) = isotomic conjugate of the polar conjugate of X(1179)
X(40393) = X(i)-cross conjugate of X(j) for these (i,j): {6, 1166}, {1510, 99}, {2623, 110}, {5576, 264}, {13353, 95}, {16040, 107}, {18314, 648}, {37649, 2}
X(40393) = X(i)-isoconjugate of X(j) for these (i,j): {1, 570}, {19, 1216}, {31, 37636}, {42, 16698}, {48, 1594}, {92, 23195}, {1209, 2148}, {1238, 1973}, {4020, 10550}
X(40393) = cevapoint of X(i) and X(j) for these (i,j): {2, 1994}, {5, 6}, {216, 34951}
X(40393) = trilinear pole of line {523, 2070} (the polar of X(5) wrt the circumcircle)
X(40393) = barycentric product X(i)*X(j) for these {i,j}: {69, 1179}, {75, 2216}, {311, 1166}
X(40393) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 37636}, {3, 1216}, {4, 1594}, {5, 1209}, {6, 570}, {69, 1238}, {81, 16698}, {184, 23195}, {311, 1225}, {1166, 54}, {1179, 4}, {2216, 1}, {3518, 6152}, {13621, 6153}, {32085, 10550}
X(40394) lies on these lines: {6, 28654}, {8, 595}, {10, 2206}, {92, 26223}, {257, 3219}, {312, 3187}, {333, 32025}, {835, 20966}, {894, 30690}, {1220, 5176}, {2994, 26065}, {3920, 4518}, {4997, 29833}, {5260, 31359}, {18359, 27064}
X(40394) = isotomic conjugate of X(17184)
X(40394) = isogonal conjugate of the complement of X(313)
X(40394) = isotomic conjugate of the anticomplement of X(5294)
X(40394) = X(i)-cross conjugate of X(j) for these (i,j): {6, 3453}, {3050, 101}, {4129, 190}, {5294, 2}, {7252, 100}, {24083, 4632}
X(40394) = X(i)-isoconjugate of X(j) for these (i,j): {6, 3670}, {19, 11573}, {28, 22073}, {31, 17184}, {42, 18601}, {58, 4016}, {81, 20966}, {92, 23197}, {163, 21121}, {649, 3909}, {849, 20654}, {1333, 3454}, {2206, 20896}
X(40394) = cevapoint of X(i) and X(j) for these (i,j): {6, 10}, {9, 3293}, {220, 4097}
X(40394) = trilinear pole of line {522, 1324} (the polar of X(10) wrt the circumcircle)
X(40394) = barycentric product X(313)*X(3453)
X(40394) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3670}, {2, 17184}, {3, 11573}, {10, 3454}, {37, 4016}, {42, 20966}, {71, 22073}, {81, 18601}, {100, 3909}, {184, 23197}, {321, 20896}, {523, 21121}, {594, 20654}, {3453, 58}
X(40395) lies on the Kiepert circumhyperbola and these lines: {2, 7054}, {4, 1175}, {6, 36419}, {10, 29}, {27, 226}, {28, 228}, {76, 7058}, {81, 1446}, {98, 37362}, {107, 1859}, {270, 580}, {321, 2287}, {447, 5294}, {469, 1751}, {1172, 2982}, {2052, 36421}, {2326, 37279}, {3149, 13599}, {5397, 37381}, {5466, 14775}, {5736, 40214}, {17758, 37389}, {26023, 32014}
X(40395) = isogonal conjugate of X(18591)
X(40395) = isogonal conjugate of the complement of X(286)
X(40395) = isotomic conjugate of isogonal conjugate of X(40570)
X(40395) = isotomic conjugate of complement of X(40571)
X(40395) = polar conjugate of X(442)
X(40395) = polar conjugate of the isogonal conjugate of X(1175)
X(40395) = X(i)-cross conjugate of X(j) for these (i,j): {6, 943}, {650, 107}, {15313, 99}, {17796, 39439}, {17924, 648}, {21007, 112}
X(40395) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18591}, {3, 2294}, {9, 39791}, {10, 14597}, {37, 4303}, {42, 18607}, {48, 442}, {71, 942}, {72, 2260}, {226, 23207}, {228, 5249}, {255, 1865}, {906, 23752}, {1214, 14547}, {1234, 9247}, {1409, 6734}, {1437, 21675}, {1838, 3990}, {1841, 3682}, {1859, 40152}, {8021, 37755}
X(40395) = cevapoint of X(i) and X(j) for these (i,j): {4, 1172}, {6, 28}, {284, 580}
X(40395) = trilinear pole of line {523, 2074} (the polar of X(28) wrt the circumcircle)
X(40395) = barycentric product X(i)*X(j) for these {i,j}: {99, 14775}, {264, 1175}, {286, 943}, {2982, 31623}
X(40395) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 442}, {6, 18591}, {19, 2294}, {27, 5249}, {28, 942}, {29, 6734}, {56, 39791}, {58, 4303}, {81, 18607}, {264, 1234}, {393, 1865}, {943, 72}, {1175, 3}, {1333, 14597}, {1474, 2260}, {1794, 3682}, {1826, 21675}, {2194, 23207}, {2259, 71}, {2299, 14547}, {2982, 1214}, {5317, 1841}, {7649, 23752}, {8747, 1838}, {11107, 31938}, {13739, 39772}, {14775, 523}, {15439, 23067}, {30733, 14054}, {31902, 3824}
X(40396) lies on the Feuerbach circumhyperbola and these lines: {1, 947}, {4, 221}, {6, 7003}, {7, 412}, {8, 7078}, {9, 17916}, {33, 84}, {34, 3577}, {65, 36121}, {79, 1785}, {104, 6198}, {108, 3075}, {318, 3562}, {1172, 2182}, {1389, 1870}, {1476, 15500}, {1771, 7412}, {1838, 15909}, {1896, 3194}, {2000, 3561}, {2956, 3062}, {5706, 7149}, {18283, 34046}, {23710, 34485}
X(40396) = isogonal conjugate of X(17102)
X(40396) = isogonal conjugate of the complement of X(318)
X(40396) = X(i)-cross conjugate of X(j) for these (i,j): {1459, 108}, {1887, 4}
X(40396) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17102}, {2, 22063}, {3, 946}, {63, 2262}, {222, 20262}, {603, 23528}, {1804, 1856}
X(40396) = cevapoint of X(i) and X(j) for these (i,j): {1, 1771}, {6, 33}, {19, 3195}
X(40396) = trilinear pole of line {650, 39199} (the polar of X(33) wrt the circumcircle)
X(40396) = barycentric product X(92)*X(947)
X(40396) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 17102}, {19, 946}, {25, 2262}, {31, 22063}, {33, 20262}, {281, 23528}, {947, 63}
X(40396) = {X(33),X(603)}-harmonic conjugate of X(38870)
X(40397) lies on these lines: {4, 2192}, {6, 196}, {34, 40}, {48, 223}, {208, 937}, {219, 278}, {222, 14256}, {1396, 1465}, {1427, 14578}, {1875, 2194}
X(40397) = isogonal conjugate of the complement of X(273)
X(40397) = X(i)-cross conjugate of X(j) for these (i,j): {6, 1167}, {649, 108}
X(40397) = X(i)-isoconjugate of X(j) for these (i,j): {9, 1071}, {63, 1864}, {78, 1108}, {212, 17862}, {219, 1210}, {268, 6260}, {283, 21933}, {312, 23204}, {333, 3611}, {3692, 37566}
X(40397) = cevapoint of X(i) and X(j) for these (i,j): {6, 34}, {208, 608}
X(40397) = trilinear pole of line {1946, 6129} (the polar of X(34) wrt the circumcircle)
X(40397) = barycentric product X(273)*X(1167)
X(40397) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 1864}, {34, 1210}, {56, 1071}, {208, 6260}, {273, 1226}, {278, 17862}, {608, 1108}, {1167, 78}, {1397, 23204}, {1398, 37566}, {1402, 3611}, {1875, 1532}, {1880, 21933}
X(40398) lies on these lines: {6, 7794}, {58, 518}, {81, 3912}, {241, 1412}, {593, 18206}, {741, 22116}, {831, 20969}, {1396, 5236}, {1509, 18157}, {4251, 39957}, {5276, 17758}
X(40398) = isogonal conjugate of X(16600)
X(40398) = isogonal conjugate of the complement of X(1930)
X(40398) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16600}, {6, 4972}, {10, 5299}, {37, 7191}, {42, 16706}, {65, 33950}, {82, 17456}, {83, 20969}, {92, 23203}, {213, 33940}, {251, 21249}, {512, 33951}, {692, 27712}, {1400, 4514}, {1500, 33955}, {1826, 7293}, {4628, 21125}, {18098, 18183}, {22077, 32085}
X(40398) = cevapoint of X(6) and X(38)
X(40398) = trilinear pole of line {2254, 3733} (the polar of X(38) wrt the circumcircle)
X(40398) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4972}, {6, 16600}, {21, 4514}, {38, 21249}, {39, 17456}, {58, 7191}, {81, 16706}, {86, 33940}, {141, 21425}, {184, 23203}, {284, 33950}, {514, 27712}, {662, 33951}, {757, 33955}, {1333, 5299}, {1437, 7293}, {1964, 20969}, {2530, 21125}, {3954, 21037}, {4020, 22077}, {16696, 17192}, {17187, 18183}
X(40399) lies on the circumconic {{A,B,C,X(1),X(2}} and these lines: {1, 1167}, {2, 2256}, {28, 517}, {40, 2208}, {57, 2289}, {63, 1422}, {105, 17642}, {219, 278}, {279, 394}, {291, 25941}, {321, 16082}, {525, 2401}, {957, 4245}, {1123, 1377}, {1214, 34051}, {1336, 1378}, {2006, 3452}, {2192, 17784}, {2810, 16100}, {3219, 34056}, {15474, 33146}, {17658, 36122}, {25243, 35058}, {26591, 30710}, {26637, 39747}, {35057, 35348}
X(40399) = isogonal conjugate of X(1108)
X(40399) = isotomic conjugate of X(17862)
X(40399) = isogonal conjugate of the complement of X(322)
X(40399) = isotomic conjugate of the anticomplement of X(25091)
X(40399) = X(i)-cross conjugate of X(j) for these (i,j): {652, 100}, {14837, 651}, {25091, 2}
X(40399) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1108}, {6, 1210}, {9, 37566}, {19, 1071}, {27, 3611}, {31, 17862}, {32, 1226}, {57, 1864}, {58, 21933}, {92, 23204}, {909, 1532}, {1436, 6260}, {8602, 18239}
X(40399) = cevapoint of X(i) and X(j) for these (i,j): {1, 219}, {6, 40}, {9, 5687}
X(40399) = trilinear pole of line {513, 2077} (the polar of X(40) wrt the circumcircle)
X(40399) = barycentric product X(75)*X(1167)
X(40399) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1210}, {2, 17862}, {3, 1071}, {6, 1108}, {37, 21933}, {40, 6260}, {55, 1864}, {56, 37566}, {75, 1226}, {184, 23204}, {228, 3611}, {517, 1532}, {1167, 1}, {10310, 18239}, {11012, 40249}
X(40400) lies on these lines: {6, 644}, {9, 38266}, {31, 678}, {44, 5548}, {81, 645}, {100, 20972}, {101, 604}, {294, 23836}, {608, 1783}, {651, 1407}, {666, 1462}, {739, 6079}, {1333, 1811}, {1635, 2316}, {5549, 28607}, {16671, 28615}
X(40400) = isogonal conjugate of X(16610)
X(40400) = isogonal conjugate of the complement of X(4358)
X(40400) = isogonal conjugate of the isotomic conjugate of X(36805)
X(40400) = polar conjugate of the isotomic conjugate of X(1811)
X(40400) = X(36805)-Ceva conjugate of X(1811)
X(40400) = X(i)-cross conjugate of X(j) for these (i,j): {1960, 100}, {3689, 1}, {21786, 101}
X(40400) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16610}, {2, 1149}, {6, 1266}, {42, 16711}, {57, 3880}, {63, 1878}, {81, 4695}, {88, 17460}, {92, 23205}, {101, 4927}, {106, 16594}, {190, 6085}, {514, 23832}, {901, 21129}, {903, 20972}, {1797, 5151}, {1978, 8660}, {3669, 23705}, {4358, 17109}, {6336, 22082}, {9456, 20900}
X(40400) = cevapoint of X(i) and X(j) for these (i,j): {6, 44}, {650, 2087}
X(40400) = trilinear pole of line {55, 667} (the polar of X(44) wrt the circumcircle)
X(40400) = crossdifference of every pair of points on line {6018, 6085}
X(40400) = barycentric product of circumcircle intercepts of line X(8)X(513)
X(40400) = barycentric product X(i)*X(j) for these {i,j}: {1, 1120}, {4, 1811}, {6, 36805}, {8, 8686}, {100, 23836}, {513, 6079}, {3699, 37627}
X(40400) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1266}, {6, 16610}, {25, 1878}, {31, 1149}, {42, 4695}, {44, 16594}, {55, 3880}, {81, 16711}, {184, 23205}, {513, 4927}, {519, 20900}, {667, 6085}, {692, 23832}, {902, 17460}, {1120, 75}, {1635, 21129}, {1811, 69}, {1980, 8660}, {2251, 20972}, {3939, 23705}, {6079, 668}, {8686, 7}, {21805, 21041}, {23202, 22082}, {23836, 693}, {36805, 76}, {37627, 3676}
X(40401) lies on these lines: {1, 9456}, {6, 519}, {9, 609}, {31, 44}, {33, 2203}, {37, 604}, {45, 993}, {81, 312}, {100, 751}, {226, 1407}, {513, 750}, {608, 1826}, {739, 5276}, {940, 4795}, {1100, 38266}, {1743, 28615}, {2177, 39974}, {2221, 4383}, {2276, 17961}, {2295, 14584}, {2718, 32686}, {4945, 37633}, {14621, 17790}, {16885, 34819}
X(40401) = isogonal conjugate of X(4850)
X(40401) = isotomic conjugate of X(33934)
X(40401) = isogonal conjugate of the anticomplement of X(30818)
X(40401) = isogonal conjugate of the complement of X(4671)
X(40401) = X(4775)-cross conjugate of X(100)
X(40401) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4850}, {2, 995}, {6, 4389}, {7, 4266}, {31, 33934}, {42, 16712}, {56, 5233}, {57, 3877}, {58, 26580}, {81, 4424}, {89, 17461}, {92, 23206}, {190, 9002}, {306, 4247}, {901, 23888}, {4588, 21130}, {17196, 28658}, {20973, 39704}
X(40401) = cevapoint of X(6) and X(45)
X(40401) = crosssum of X(995) and X(4266)
X(40401) = trilinear pole of line {667, 1635} (the polar of X(45) wrt the circumcircle)
X(40401) = barycentric product X(i)*X(j) for these {i,j}: {1, 996}, {513, 9059}, {900, 36091}, {3762, 32686}
X(40401) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4389}, {2, 33934}, {6, 4850}, {9, 5233}, {31, 995}, {37, 26580}, {41, 4266}, {42, 4424}, {55, 3877}, {81, 16712}, {184, 23206}, {667, 9002}, {996, 75}, {1635, 23888}, {2177, 17461}, {2203, 4247}, {4653, 17196}, {4893, 21130}, {9059, 668}, {32686, 3257}, {36091, 4555}
X(40402) lies on these lines: {4, 577}, {6, 1093}, {53, 1970}, {184, 393}, {216, 436}, {264, 394}, {1217, 13346}, {1352, 18855}, {1826, 4055}, {3087, 6526}, {6748, 18877}
X(40402) = isogonal conjugate of the complement of X(324)
X(40402) = X(i)-cross conjugate of X(j) for these (i,j): {2623, 112}, {15451, 107}
X(40402) = X(i)-isoconjugate of X(j) for these (i,j): {63, 389}, {2169, 34836}
X(40402) = cevapoint of X(i) and X(j) for these (i,j): {4, 436}, {6, 53}, {25, 217}
X(40402) = trilinear pole of line {2501, 39201} (the polar of X(53) wrt the circumcircle)
X(40402) = polar conjugate of isotomic conjugate of X(40448)
X(40402) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 389}, {53, 34836}, {8882, 19170}, {14569, 6750}
X(40403) lies on these lines: {6, 3926}, {58, 1792}, {63, 1973}, {81, 7123}, {284, 30676}, {333, 1396}, {1098, 30733}, {1172, 30688}, {1310, 23620}, {1412, 1708}, {1509, 2303}, {2287, 17206}
X(40403) = isogonal conjugate of X(16583)
X(40403) = isogonal conjugate of the complement of X(304)
X(40403) = X(i)-cross conjugate of X(j) for these (i,j): {6586, 100}, {21789, 99}
X(40403) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16583}, {4, 23620}, {6, 3914}, {10, 16502}, {19, 17441}, {25, 18589}, {37, 614}, {42, 4000}, {65, 2082}, {69, 8020}, {71, 1851}, {75, 21750}, {86, 21813}, {92, 22363}, {210, 28017}, {213, 3673}, {225, 7124}, {226, 7083}, {393, 22057}, {497, 1400}, {512, 3732}, {661, 1633}, {872, 16750}, {1020, 17115}, {1040, 1880}, {1042, 6554}, {1245, 5286}, {1334, 7195}, {1427, 4319}, {1473, 1826}, {1474, 21015}, {1824, 7289}, {1843, 18084}, {1973, 20235}, {2171, 5324}, {2333, 17170}, {3668, 30706}, {3949, 4211}, {8750, 21107}
X(40403) = cevapoint of X(i) and X(j) for these (i,j): {6, 63}, {81, 2287}
X(40403) = crosssum of X(21750) and X(22363)
X(40403) = trilinear pole of line {3733, 8646} (the polar of X(63) wrt the circumcircle)
X(40403) = barycentric product X(i)*X(j) for these {i,j}: {21, 8817}, {81, 30701}, {274, 7123}, {310, 7084}, {314, 1037}, {332, 1041}, {333, 7131}, {2287, 30705}, {7253, 8269}
X(40403) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3914}, {3, 17441}, {6, 16583}, {21, 497}, {28, 1851}, {32, 21750}, {48, 23620}, {58, 614}, {60, 5324}, {63, 18589}, {69, 20235}, {72, 21015}, {81, 4000}, {86, 3673}, {110, 1633}, {184, 22363}, {213, 21813}, {255, 22057}, {283, 1040}, {284, 2082}, {662, 3732}, {905, 21107}, {1014, 7195}, {1037, 65}, {1041, 225}, {1333, 16502}, {1412, 28017}, {1437, 1473}, {1444, 17170}, {1509, 16750}, {1790, 7289}, {1812, 27509}, {1973, 8020}, {2193, 7124}, {2194, 7083}, {2287, 6554}, {2303, 5286}, {2328, 4319}, {4183, 1863}, {7084, 42}, {7123, 37}, {7131, 226}, {8269, 4566}, {8817, 1441}, {14935, 4516}, {16728, 17060}, {21789, 17115}, {30701, 321}, {30705, 1446}, {34055, 18084}
X(40404) lies on the cubic K644 and these lines: {2, 66}, {6, 18018}, {69, 10316}, {83, 264}, {95, 7832}, {251, 13575}, {253, 10548}, {305, 20806}, {1289, 1843}, {2353, 31360}, {2419, 4580}, {3589, 37801}, {3618, 13854}, {6330, 32085}, {6340, 28708}, {9229, 10333}, {10547, 26926}, {18024, 31636}, {20563, 28695}, {27372, 28723}
X(40404) = isogonal conjugate of X(40938)
X(40404) = isogonal conjugate of the complement of X(18018)
X(40404) = isotomic conjugate of the polar conjugate of X(16277)
X(40404) = polar conjugate of X(41375)
X(40404) = X(i)-cross conjugate of X(j) for these (i,j): {6, 1176}, {647, 1289}, {10547, 1799}, {26926, 69}
X(40404) = cevapoint of X(6) and X(66)
X(40404) = trilinear pole of the polar of X(66) wrt the circumcircle
X(40404) = X(i)-isoconjugate of X(j) for these (i,j): {19, 3313}, {22, 17442}, {38, 8743}, {42, 16715}, {63, 27373}, {92, 23208}, {206, 20883}, {427, 2172}, {1235, 17453}, {1760, 1843}, {1930, 17409}, {1964, 17907}, {16747, 21034}, {19595, 19616}, {20641, 27369}, {23881, 32676}
X(40404) = barycentric product X(i)*X(j) for these {i,j}: {66, 1799}, {69, 16277}, {83, 14376}, {1176, 18018}
X(40404) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 3313}, {25, 27373}, {66, 427}, {81, 16715}, {83, 17907}, {184, 23208}, {251, 8743}, {525, 23881}, {1176, 22}, {1799, 315}, {2156, 17442}, {2353, 1843}, {4580, 33294}, {9076, 11605}, {10547, 206}, {13854, 27376}, {14376, 141}, {16277, 4}, {18018, 1235}, {28724, 20806}, {34055, 1760}, {40146, 27369}
X(40405) lies on these lines: {32, 193}, {69, 1974}, {76, 683}, {99, 6467}, {141, 32740}, {305, 40318}, {1918, 4028}, {1975, 6391}, {3618, 39238}, {6337, 17040}, {6394, 14601}, {6531, 9230}, {12272, 16276}, {22468, 35140}
X(40405) = isogonal conjugate of X(1196)
X(40405) = isotomic conjugate of X(5254)
X(40405) = isogonal conjugate of the complement of X(305)
X(40405) = isotomic conjugate of the anticomplement of X(7789)
X(40405) = isotomic conjugate of the complement of X(1975)
X(40405) = isogonal conjugate of the polar conjugate of X(683)
X(40405) = X(i)-cross conjugate of X(j) for these (i,j): {647, 99}, {7789, 2}
X(40405) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1196}, {6, 17872}, {19, 6467}, {25, 18671}, {31, 5254}, {42, 16716}, {63, 40325}, {92, 682}, {163, 12075}, {304, 3080}, {1096, 22401}, {1368, 1973}, {1974, 21406}, {38252, 40326}
X(40405) = cevapoint of X(i) and X(j) for these (i,j): {2, 1975}, {6, 69}, {394, 6337}
X(40405) = trilinear pole of line {669, 3265} (the polar of X(69) wrt the circumcircle)
X(40405) = barycentric product X(3)*X(683)
X(40405) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17872}, {2, 5254}, {3, 6467}, {6, 1196}, {25, 40325}, {63, 18671}, {69, 1368}, {81, 16716}, {184, 682}, {193, 40326}, {304, 21406}, {394, 22401}, {523, 12075}, {683, 264}, {1974, 3080}, {17206, 18648}
X(40406) lies on these lines: {6, 17776}, {31, 3811}, {72, 2203}, {321, 5317}, {604, 1708}, {608, 5739}, {1333, 3998}, {1462, 4359}, {3693, 28615}, {4976, 24115}, {9456, 25091}
X(40406) = isogonal conjugate of X(40941)
X(40406) = isogonal conjugate of the complement of X(20336)
X(40406) = X(647)-cross conjugate of X(100)
X(40406) = X(i)-isoconjugate of X(j) for these (i,j): {6, 23537}, {19, 18732}, {25, 18651}, {28, 18674}, {1474, 21530}
X(40406) = cevapoint of X(i) and X(j) for these (i,j): {6, 72}, {37, 5687}, {213, 12329}, {3990, 11517}
X(40406) = trilinear pole of line {667, 15313} (the polar of X(72) wrt the circumcircle)
X(40406) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 23537}, {3, 18732}, {63, 18651}, {71, 18674}, {72, 21530}, {3949, 21678}
X(40407) lies on these lines: {1, 7008}, {6, 7011}, {9, 16577}, {19, 223}, {55, 581}, {73, 2299}, {222, 1436}, {226, 8748}, {284, 2003}, {333, 17095}, {1427, 2160}
X(40407) = isogonal conjugate of X(40942)
X(40407) = isogonal conjugate of the complement of X(307)
X(40407) = X(647)-cross conjugate of X(109)
X(40407) = X(i)-isoconjugate of X(j) for these (i,j): {6, 23661}, {9, 4292}, {21, 1901}, {29, 18675}, {33, 18652}, {650, 14544}, {1172, 18641}
X(40407) = cevapoint of X(i) and X(j) for these (i,j): {6, 73}, {48, 1399}, {221, 1400}
X(40407) = crosssum of X(1901) and X(18675)
X(40407) = trilinear pole of line {663, 39199} (the polar of X(73) wrt the circumcircle)
X(40407) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 23661}, {56, 4292}, {73, 18641}, {109, 14544}, {222, 18652}, {1400, 1901}, {1409, 18675}
X(40408) lies on these lines: {6, 1509}, {32, 593}, {58, 1918}, {81, 213}, {99, 20963}, {741, 8708}, {757, 4251}, {981, 7760}, {1396, 31919}, {1974, 17562}, {2207, 36419}, {2238, 32014}, {3997, 32004}, {20970, 37128}
X(40408) = isogonal conjugate of X(16589)
X(40408) = isogonal conjugate of the anticomplement of X(36812)
X(40408) = isogonal conjugate of the complement of X(274)
X(40408) = X(i)-cross conjugate of X(j) for these (i,j): {667, 99}, {21007, 110}, {21788, 741}
X(40408) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16589}, {2, 2667}, {6, 21020}, {9, 39793}, {10, 20963}, {37, 3720}, {42, 3739}, {57, 4111}, {65, 3691}, {75, 21753}, {81, 21699}, {86, 21820}, {92, 22369}, {213, 20888}, {661, 4436}, {756, 18166}, {872, 16748}, {1018, 6372}, {1334, 4059}, {1400, 3706}, {1500, 17175}, {1826, 22060}, {18089, 21035}
X(40408) = cevapoint of X(i) and X(j) for these (i,j): {6, 81}, {58, 4251}
X(40408) = crosssum of X(i) and X(j) for these (i,j): {21699, 21820}, {21753, 22369}
X(40408) = trilinear pole of line {669, 2106} (the polar of X(81) wrt the circumcircle)
X(40408) = barycentric product X(i)*X(j) for these {i,j}: {81, 32009}, {7192, 8708}
X(40408) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 21020}, {6, 16589}, {21, 3706}, {31, 2667}, {32, 21753}, {42, 21699}, {55, 4111}, {56, 39793}, {58, 3720}, {81, 3739}, {86, 20888}, {110, 4436}, {184, 22369}, {213, 21820}, {284, 3691}, {593, 18166}, {757, 17175}, {1014, 4059}, {1333, 20963}, {1437, 22060}, {1509, 16748}, {3733, 6372}, {8708, 3952}, {16948, 4891}, {32009, 321}
X(40408) = {X(81),X(213)}-harmonic conjugate of X(33770)
X(40409) lies on these lines: {6, 7304}, {32, 1509}, {81, 21759}, {86, 171}, {87, 1178}, {99, 2309}, {213, 274}, {1434, 7175}, {2663, 18787}, {9468, 37128}, {28369, 40017}
X(40409) = isogonal conjugate of X(21838)
X(40409) = isotomic conjugate of X(21024)
X(40409) = isogonal conjugate of the complement of X(310)
X(40409) = isotomic conjugate of the complement of X(33296)
X(40409) = X(i)-cross conjugate of X(j) for these (i,j): {649, 99}, {16737, 4573}, {18278, 741}, {21791, 110}
X(40409) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21838}, {6, 3728}, {9, 39780}, {10, 1197}, {31, 21024}, {37, 2309}, {42, 1107}, {58, 22206}, {81, 21700}, {92, 23212}, {213, 3741}, {872, 16738}, {893, 27880}, {1333, 21713}, {1500, 18169}, {1824, 22065}, {1826, 22389}, {1918, 20891}, {18091, 21814}
X(40409) = cevapoint of X(i) and X(j) for these (i,j): {2, 33296}, {6, 86}, {81, 17103}, {274, 34020}
X(40409) = trilinear pole of line {669, 4367} (the polar of X(86) wrt the circumcircle)
X(40409) = barycentric product X(i)*X(j) for these {i,j}: {81, 1221}, {274, 1258}
X(40409) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3728}, {2, 21024}, {6, 21838}, {10, 21713}, {37, 22206}, {42, 21700}, {56, 39780}, {58, 2309}, {81, 1107}, {86, 3741}, {171, 27880}, {184, 23212}, {274, 20891}, {757, 18169}, {1221, 321}, {1258, 37}, {1333, 1197}, {1434, 30097}, {1437, 22389}, {1509, 16738}, {1790, 22065}
X(40410) lies on these lines: {2, 10979}, {4, 36948}, {5, 95}, {69, 576}, {233, 648}, {253, 7486}, {261, 39280}, {264, 1656}, {287, 3589}, {288, 14389}, {305, 7539}, {307, 7321}, {311, 1487}, {316, 14788}, {317, 5056}, {340, 35018}, {547, 1494}, {1232, 26862}, {1441, 7504}, {1799, 37439}, {1972, 14767}, {5067, 8797}, {5070, 20477}, {7569, 20563}, {7570, 18019}, {7571, 18018}, {7887, 31360}, {9229, 32967}, {11090, 32807}, {14977, 39183}, {30786, 37454}, {32223, 38833}
X(40410) = isogonal conjugate of X(13366)
X(40410) = isotomic conjugate of X(140)
X(40410) = polar conjugate of X(6748)
X(40410) = isotomic conjugate of the anticomplement of X(3628)
X(40410) = isotomic conjugate of the complement of X(5)
X(40410) = isotomic conjugate of the isogonal conjugate of X(1173)
X(40410) = isotomic conjugate of the polar conjugate of X(39284)
X(40410) = polar conjugate of the isogonal conjugate of X(31626)
X(40410) = X(i)-Ceva conjugate of X(j) for these (i,j): {31617, 31626}, {39289, 1173}
X(40410) = X(i)-cross conjugate of X(j) for these (i,j): {2, 31617}, {5, 31610}, {1173, 39284}, {3628, 2}, {6368, 648}, {23061, 671}
X(40410) = X(i)-isoconjugate of X(j) for these (i,j): {1, 13366}, {6, 17438}, {19, 22052}, {31, 140}, {32, 20879}, {48, 6748}, {213, 17168}, {233, 2148}, {560, 1232}, {661, 35324}, {692, 21103}, {810, 35311}, {1333, 21012}, {2190, 32078}
X(40410) = cevapoint of X(i) and X(j) for these (i,j): {2, 5}, {3, 1994}, {302, 303}, {1173, 31626}
X(40410) = trilinear pole of line {525, 15340}
X(40410) = barycentric product X(i)*X(j) for these {i,j}: {5, 31617}, {69, 39284}, {76, 1173}, {95, 31610}, {99, 39183}, {141, 39289}, {264, 31626}, {288, 311}, {305, 33631}, {343, 39286}, {525, 33513}, {1487, 7769}, {6331, 39180}
X(40410) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17438}, {2, 140}, {3, 22052}, {4, 6748}, {5, 233}, {6, 13366}, {10, 21012}, {75, 20879}, {76, 1232}, {86, 17168}, {110, 35324}, {140, 36422}, {216, 32078}, {288, 54}, {324, 14978}, {514, 21103}, {648, 35311}, {1173, 6}, {1487, 2963}, {1994, 1493}, {6368, 35441}, {20574, 14533}, {31610, 5}, {31617, 95}, {31626, 3}, {33513, 648}, {33631, 25}, {34545, 36153}, {35360, 35318}, {36412, 3078}, {39180, 647}, {39181, 23286}, {39183, 523}, {39284, 4}, {39286, 275}, {39289, 83}
X(40410) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 31610, 31626}, {31610, 31626, 39284}
X(40411) lies on these lines: {2, 2207}, {19, 304}, {27, 19799}, {28, 1043}, {232, 33828}, {264, 17682}, {274, 2322}, {333, 1396}, {475, 17277}, {1968, 33821}, {7058, 14013}, {7131, 16054}, {14829, 37382}, {17680, 27376}, {17907, 33833}, {27109, 35974}
X(40411) = isogonal conjugate of X(23620)
X(40411) = isotomic conjugate of X(18589)
X(40411) = polar conjugate of X(3914)
X(40411) = isotomic conjugate of the complement of X(19)
X(40411) = X(i)-cross conjugate of X(j) for these (i,j): {4228, 86}, {7192, 648}, {21300, 6528}, {21302, 18026}, {26153, 76}
X(40411) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23620}, {2, 22363}, {3, 16583}, {6, 17441}, {19, 22057}, {31, 18589}, {32, 20235}, {37, 1473}, {42, 7289}, {48, 3914}, {65, 7124}, {69, 21750}, {71, 614}, {72, 16502}, {73, 2082}, {213, 17170}, {228, 4000}, {326, 8020}, {497, 1409}, {647, 1633}, {692, 21107}, {810, 3732}, {1040, 1400}, {1214, 7083}, {1333, 21015}, {1402, 27509}, {1410, 6554}, {1439, 30706}, {1444, 21813}, {1851, 3990}, {1964, 18084}, {2197, 5324}, {2200, 3673}, {2281, 7386}, {2318, 28017}
X(40411) = cevapoint of X(i) and X(j) for these (i,j): {2, 19}, {27, 2322}, {3730, 3811}
X(40411) = trilinear pole of line {7253, 14954}
X(40411) = barycentric product X(i)*X(j) for these {i,j}: {27, 30701}, {29, 8817}, {314, 1041}, {2322, 30705}, {7131, 31623}
X(40411) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17441}, {2, 18589}, {3, 22057}, {4, 3914}, {6, 23620}, {10, 21015}, {19, 16583}, {21, 1040}, {27, 4000}, {28, 614}, {29, 497}, {31, 22363}, {58, 1473}, {75, 20235}, {81, 7289}, {83, 18084}, {86, 17170}, {162, 1633}, {270, 5324}, {284, 7124}, {286, 3673}, {333, 27509}, {514, 21107}, {648, 3732}, {1010, 7386}, {1037, 73}, {1041, 65}, {1172, 2082}, {1396, 28017}, {1474, 16502}, {1973, 21750}, {2207, 8020}, {2299, 7083}, {2322, 6554}, {2332, 30706}, {2333, 21813}, {4183, 4319}, {7084, 228}, {7123, 71}, {7131, 1214}, {8747, 1851}, {8817, 307}, {30701, 306}
X(40412) lies on these lines: {2, 7054}, {21, 286}, {69, 261}, {81, 3990}, {85, 1789}, {86, 283}, {95, 7483}, {253, 17558}, {264, 405}, {287, 25536}, {305, 16992}, {306, 319}, {314, 943}, {757, 14828}, {1494, 15670}, {1793, 14616}, {1799, 37664}, {2982, 37870}, {5084, 8797}, {9229, 33047}, {17561, 36889}, {20291, 37369}
X(40412) = isogonal conjugate of X(40952)
X(40412) = isotomic conjugate of X(442)
X(40412) = polar conjugate of X(1865)
X(40412) = isotomic conjugate of the anticomplement of X(6675)
X(40412) = isotomic conjugate of the complement of X(21)
X(40412) = isotomic conjugate of the isogonal conjugate of X(1175)
X(40412) = X(i)-cross conjugate of X(j) for these (i,j): {521, 648}, {693, 99}, {6675, 2}, {22160, 110}
X(40412) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2294}, {19, 18591}, {31, 442}, {33, 39791}, {37, 2260}, {42, 942}, {48, 1865}, {65, 14547}, {71, 1841}, {73, 1859}, {213, 5249}, {225, 23207}, {228, 1838}, {560, 1234}, {692, 23752}, {1020, 33525}, {1254, 8021}, {1333, 21675}, {1402, 6734}, {1824, 4303}, {1826, 14597}, {2333, 18607}
X(40412) = cevapoint of X(i) and X(j) for these (i,j): {2, 21}, {3, 81}, {2328, 4251}
X(40412) = trilinear pole of line {448, 525}
X(40412) = barycentric product X(i)*X(j) for these {i,j}: {76, 1175}, {274, 943}, {310, 2259}, {314, 2982}, {4563, 14775}
X(40412) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2294}, {2, 442}, {3, 18591}, {4, 1865}, {10, 21675}, {27, 1838}, {28, 1841}, {58, 2260}, {76, 1234}, {81, 942}, {86, 5249}, {222, 39791}, {284, 14547}, {333, 6734}, {514, 23752}, {943, 37}, {1172, 1859}, {1175, 6}, {1437, 14597}, {1444, 18607}, {1790, 4303}, {1794, 71}, {2193, 23207}, {2259, 42}, {2982, 65}, {5333, 3824}, {7054, 8021}, {14775, 2501}, {15439, 4559}, {21789, 33525}, {35320, 35307}, {36048, 1020}, {40214, 500}
X(40413) lies on these lines: {2, 1968}, {4, 6340}, {25, 305}, {69, 1974}, {95, 6676}, {183, 40032}, {232, 9229}, {264, 5020}, {287, 1915}, {427, 30786}, {468, 1799}, {648, 1196}, {1078, 38282}, {1995, 18018}, {8770, 9308}, {13595, 18019}, {37962, 39998}
X(40413) = isogonal conjugate of X(6467)
X(40413) = isotomic conjugate of X(1368)
X(40413) = polar conjugate of X(5254)
X(40413) = isogonal conjugate of the anticomplement of X(14913)
X(40413) = isogonal conjugate of the complement of X(12272)
X(40413) = isotomic conjugate of the anticomplement of X(6677)
X(40413) = isotomic conjugate of the complement of X(25)
X(40413) = isogonal conjugate of the isotomic conjugate of X(683)
X(40413) = X(i)-cross conjugate of X(j) for these (i,j): {512, 648}, {6677, 2}, {11326, 6}, {26156, 76}, {32529, 3225}
X(40413) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6467}, {3, 17872}, {6, 18671}, {19, 22401}, {31, 1368}, {32, 21406}, {48, 5254}, {63, 1196}, {71, 16716}, {75, 682}, {213, 18648}, {326, 40325}, {4575, 12075}
X(40413) = cevapoint of X(i) and X(j) for these (i,j): {2, 25}, {3, 193}, {4, 9308}
X(40413) = trilinear pole of line {525, 2451}
X(40413) = barycentric product X(6)*X(683)
X(40413) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18671}, {2, 1368}, {3, 22401}, {4, 5254}, {6, 6467}, {19, 17872}, {25, 1196}, {28, 16716}, {32, 682}, {75, 21406}, {86, 18648}, {683, 76}, {2207, 40325}, {2501, 12075}, {6353, 40326}, {36417, 3080}, {40318, 40337}
X(40414) lies on these lines: {2, 36419}, {27, 306}, {69, 7058}, {95, 7536}, {264, 7522}, {286, 2064}, {307, 333}, {447, 20106}, {1441, 31623}, {29163, 39438}
X(40414) = isotomic conjugate of X(440)
X(40414) = polar conjugate of X(1834)
X(40414) = isotomic conjugate of the anticomplement of X(6678)
X(40414) = isotomic conjugate of the complement of X(27)
X(40414) = X(i)-cross conjugate of X(j) for these (i,j): {514, 648}, {6678, 2}, {13442, 7}, {20293, 6528}, {20294, 99}, {25015, 75}, {26167, 76}, {37113, 86}
X(40414) = X(i)-isoconjugate of X(j) for these (i,j): {6, 18673}, {31, 440}, {48, 1834}, {71, 1104}, {73, 2264}, {213, 18650}, {810, 14543}, {950, 1409}, {1333, 21671}, {1842, 3990}, {2200, 17863}
X(40414) = cevapoint of X(i) and X(j) for these (i,j): {2, 27}, {4, 2322}, {333, 18134}
X(40414) = trilinear pole of line {447, 525}
X(40414) = barycentric product X(286)*X(1257)
X(40414) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18673}, {2, 440}, {4, 1834}, {10, 21671}, {28, 1104}, {29, 950}, {86, 18650}, {286, 17863}, {648, 14543}, {951, 73}, {1172, 2264}, {1257, 72}, {2983, 71}, {8747, 1842}, {17925, 29162}, {29163, 4574}
X(40415) lies on these lines: {2, 1501}, {21, 32010}, {31, 561}, {81, 4621}, {86, 7179}, {171, 334}, {238, 7018}, {261, 7305}, {286, 14006}, {314, 983}, {333, 3661}, {701, 9063}, {3736, 7303}, {4586, 16584}, {7132, 37870}, {7307, 18021}, {7369, 30657}, {17126, 30636}, {17127, 30635}
X(40415) = isogonal conjugate of X(3778)
X(40415) = isotomic conjugate of X(2887)
X(40415) = isotomic conjugate of the anticomplement of X(6679)
X(40415) = isotomic conjugate of the complement of X(31)
X(40415) = isotomic conjugate of the isogonal conjugate of X(38813)
X(40415) = X(i)-cross conjugate of X(j) for these (i,j): {788, 4586}, {6679, 2}, {17217, 99}, {17743, 38810}, {20561, 3226}, {21298, 671}, {21300, 648}, {21301, 190}, {21304, 668}, {21305, 670}, {24995, 75}, {26176, 76}
X(40415) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3778}, {2, 16584}, {6, 3721}, {7, 4531}, {10, 7032}, {19, 20727}, {31, 2887}, {32, 20234}, {37, 2275}, {41, 16888}, {42, 982}, {57, 20684}, {58, 7237}, {65, 3056}, {76, 21751}, {181, 3794}, {210, 7248}, {213, 3662}, {225, 20753}, {226, 20665}, {264, 22364}, {274, 21815}, {292, 18904}, {512, 3888}, {561, 8022}, {604, 4136}, {649, 7239}, {692, 3801}, {722, 14945}, {789, 17415}, {798, 33946}, {872, 33947}, {893, 18905}, {1042, 4073}, {1333, 16886}, {1400, 3061}, {1402, 3705}, {1824, 3784}, {1918, 33930}, {1964, 16889}, {2295, 3863}, {3777, 4557}, {3865, 20964}, {16606, 20284}, {21759, 33890}
X(40415) = cevapoint of X(i) and X(j) for these (i,j): {2, 31}, {21, 27644}, {81, 13588}, {983, 17743}
X(40415) = crosssum of X(4531) and X(16584)
X(40415) = trilinear pole of line {824, 4560}
X(40415) = barycentric product X(i)*X(j) for these {i,j}: {1, 38810}, {42, 7307}, {76, 38813}, {81, 7033}, {86, 17743}, {190, 7255}, {274, 983}, {314, 7132}, {321, 7305}, {824, 33514}, {1333, 7034}, {3114, 3736}, {3407, 30966}, {4621, 7192}, {7096, 38840}, {14124, 16584}
X(40415) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3721}, {2, 2887}, {3, 20727}, {6, 3778}, {7, 16888}, {8, 4136}, {10, 16886}, {21, 3061}, {31, 16584}, {37, 7237}, {41, 4531}, {55, 20684}, {58, 2275}, {75, 20234}, {81, 982}, {83, 16889}, {86, 3662}, {99, 33946}, {100, 7239}, {171, 18905}, {238, 18904}, {274, 33930}, {284, 3056}, {333, 3705}, {514, 3801}, {560, 21751}, {662, 3888}, {983, 37}, {1019, 3777}, {1178, 3863}, {1333, 7032}, {1412, 7248}, {1434, 7185}, {1501, 8022}, {1509, 33947}, {1790, 3784}, {1918, 21815}, {2185, 3794}, {2193, 20753}, {2194, 20665}, {2287, 4073}, {3736, 3094}, {4273, 4787}, {4560, 3810}, {4621, 3952}, {7033, 321}, {7034, 27801}, {7132, 65}, {7192, 3776}, {7255, 514}, {7305, 81}, {7307, 310}, {8685, 4559}, {9247, 22364}, {17103, 7187}, {17743, 10}, {30966, 3314}, {31909, 5117}, {33295, 33891}, {33296, 33890}, {33514, 4586}, {38810, 75}, {38813, 6}, {38832, 20284}, {38837, 21776}, {38840, 20444}, {40214, 7186}
X(40415) = {X(31),X(561)}-harmonic conjugate of X(33767)
X(40416) lies on these lines: {2, 9233}, {32, 710}, {83, 3613}, {141, 1078}, {385, 1627}, {427, 7792}, {1031, 10583}, {1084, 36432}, {4577, 8265}, {18105, 35222}, {30167, 38847}
X(40416) = isogonal conjugate of X(20859)
X(40416) = isotomic conjugate of X(626)
X(40416) = isogonal conjugate of the anticomplement of X(4074)
X(40416) = isotomic conjugate of the anticomplement of X(6680)
X(40416) = isotomic conjugate of the complement of X(32)
X(40416) = isotomic conjugate of the isogonal conjugate of X(38826)
X(40416) = isogonal conjugate of the isotomic conjugate of X(38830)
X(40416) = X(3115)-Ceva conjugate of X(38830)
X(40416) = X(i)-cross conjugate of X(j) for these (i,j): {688, 4577}, {6680, 2}, {14295, 2966}, {21304, 190}, {28759, 4554}
X(40416) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20859}, {2, 2085}, {6, 4118}, {10, 16717}, {19, 20819}, {31, 626}, {32, 20627}, {41, 7217}, {42, 18167}, {75, 8265}, {92, 4173}, {213, 16891}, {604, 4178}, {692, 21110}, {1333, 16894}, {1917, 8039}, {1928, 8023}, {1964, 16890}, {1969, 23209}, {1973, 4121}, {3112, 3118}
X(40416) = cevapoint of X(i) and X(j) for these (i,j): {2, 32}, {4027, 8623}
X(40416) = crosssum of X(4173) and X(8265)
X(40416) = trilinear pole of line {826, 5027}
X(40416) = barycentric product X(i)*X(j) for these {i,j}: {1, 38847}, {6, 38830}, {39, 3115}, {76, 38826}, {826, 33515}, {2353, 38842}
X(40416) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4118}, {2, 626}, {3, 20819}, {6, 20859}, {7, 7217}, {8, 4178}, {10, 16894}, {31, 2085}, {32, 8265}, {69, 4121}, {75, 20627}, {81, 18167}, {83, 16890}, {86, 16891}, {141, 16893}, {184, 4173}, {514, 21110}, {1333, 16717}, {1502, 8039}, {3051, 3118}, {3115, 308}, {9233, 8023}, {14575, 23209}, {16985, 710}, {33515, 4577}, {38826, 6}, {38830, 76}, {38838, 33786}, {38842, 40073}, {38847, 75}
X(40416) = {X(32),X(1502)}-harmonic conjugate of X(33768)
X(40417) lies on these lines: {8, 1804}, {40, 309}, {63, 7101}, {69, 7080}, {75, 7013}, {307, 34393}, {322, 7182}, {332, 947}, {345, 5744}, {3718, 33932}, {8822, 35516}
X(40417) = isotomic conjugate of X(946)
X(40417) = isotomic conjugate of the anticomplement of X(6684)
X(40417) = isotomic conjugate of the complement of X(40)
X(40417) = isotomic conjugate of the isogonal conjugate of X(947)
X(40417) = X(i)-cross conjugate of X(j) for these (i,j): {4131, 664}, {4397, 190}, {6684, 2}
X(40417) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2262}, {19, 22063}, {25, 17102}, {31, 946}, {603, 1856}, {604, 20262}, {1397, 23528}
X(40417) = cevapoint of X(i) and X(j) for these (i,j): {2, 40}, {8, 63}, {200, 3730}, {37558, 40152}
X(40417) = trilinear pole of line {6332, 17496}
X(40417) = barycentric product X(76)*X(947)
X(40417) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2262}, {2, 946}, {3, 22063}, {8, 20262}, {63, 17102}, {281, 1856}, {312, 23528}, {947, 6}
X(40418) lies on the circumconic {{A,B,C,X(2),X(7)}} and these lines: {1, 6384}, {2, 1258}, {7, 1403}, {27, 7119}, {42, 310}, {43, 75}, {65, 7249}, {86, 171}, {190, 21838}, {192, 39967}, {335, 3666}, {350, 1240}, {727, 33682}, {893, 894}, {1911, 2668}, {2162, 17379}, {3210, 27494}, {3502, 40038}, {3720, 31002}, {5936, 26038}, {9315, 27498}, {16712, 24215}, {17234, 27264}, {18170, 23460}, {24512, 39746}, {26102, 40027}, {27483, 31993}, {29822, 33947}, {35916, 40164}
X(40418) = isogonal conjugate of X(2309)
X(40418) = isotomic conjugate of X(3741)
X(40418) = isotomic conjugate of the anticomplement of X(6685)
X(40418) = isotomic conjugate of the complement of X(42)
X(40418) = X(i)-cross conjugate of X(j) for these (i,j): {512, 190}, {4374, 664}, {6685, 2}, {17159, 99}, {17217, 668}, {24533, 4598}, {24782, 658}, {28758, 4554}, {29487, 799}
X(40418) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2309}, {2, 1197}, {4, 22389}, {6, 1107}, {19, 22065}, {21, 39780}, {31, 3741}, {32, 20891}, {41, 30097}, {42, 18169}, {58, 3728}, {81, 21838}, {213, 16738}, {286, 23212}, {593, 22206}, {757, 21700}, {849, 21713}, {983, 23473}, {1178, 27880}, {1333, 21024}, {1964, 18091}
X(40418) = cevapoint of X(i) and X(j) for these (i,j): {1, 894}, {2, 42}, {10, 192}
X(40418) = trilinear pole of line {514, 19565}
X(40418) = barycentric product X(i)*X(j) for these {i,j}: {1, 1221}, {75, 1258}
X(40418) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1107}, {2, 3741}, {3, 22065}, {6, 2309}, {7, 30097}, {10, 21024}, {31, 1197}, {37, 3728}, {42, 21838}, {48, 22389}, {75, 20891}, {81, 18169}, {83, 18091}, {86, 16738}, {594, 21713}, {756, 22206}, {1221, 75}, {1258, 1}, {1400, 39780}, {1500, 21700}, {2200, 23212}, {2275, 23473}, {2295, 27880}
X(40419) lies on these lines: {2, 14827}, {55, 6063}, {100, 40216}, {171, 3664}, {666, 16588}, {693, 1621}, {1001, 32023}, {2223, 7176}, {2329, 3912}, {3263, 7081}, {3449, 29839}, {4219, 7009}, {4998, 5432}, {5218, 8817}, {5253, 32021}, {7196, 15931}, {31637, 39712}
X(40419) = isogonal conjugate of X(21746)
X(40419) = isotomic conjugate of X(2886)
X(40419) = isotomic conjugate of the anticomplement of X(6690)
X(40419) = isotomic conjugate of the complement of X(55)
X(40419) = isotomic conjugate of the isogonal conjugate of X(3449)
X(40419) = X(i)-cross conjugate of X(j) for these (i,j): {926, 666}, {4374, 99}, {6690, 2}, {21302, 190}
X(40419) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21746}, {6, 17451}, {19, 22070}, {31, 2886}, {32, 20236}, {42, 18165}, {57, 16588}, {58, 21804}, {85, 9449}, {273, 22368}, {692, 21118}, {1333, 21029}, {1400, 16699}, {1434, 21819}, {1964, 18088}
X(40419) = cevapoint of X(i) and X(j) for these (i,j): {2, 55}, {11, 17494}, {385, 8299}
X(40419) = trilinear pole of line {918, 3287}
X(40419) = barycentric product X(76)*X(3449)
X(40419) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17451}, {2, 2886}, {3, 22070}, {6, 21746}, {10, 21029}, {21, 16699}, {37, 21804}, {55, 16588}, {75, 20236}, {81, 18165}, {83, 18088}, {514, 21118}, {2175, 9449}, {3449, 6}
X(40420) lies on these lines: {1, 26720}, {2, 1407}, {7, 1997}, {8, 56}, {29, 1877}, {57, 312}, {85, 738}, {92, 1435}, {171, 1416}, {189, 6612}, {226, 4997}, {241, 257}, {333, 1412}, {345, 8828}, {664, 3752}, {1121, 6613}, {1150, 30711}, {1220, 8582}, {1427, 27002}, {1434, 28660}, {1477, 8706}, {3699, 17625}, {4518, 8581}, {5226, 38255}, {5745, 32008}, {7020, 37278}, {7153, 27424}, {7196, 18031}, {8056, 9312}, {8583, 31225}, {9364, 32942}, {17283, 28774}, {17862, 18359}, {20205, 31640}, {26125, 37682}, {30608, 31231}
X(40420) = isogonal conjugate of X(2347)
X(40420) = isotomic conjugate of X(3452)
X(40420) = isotomic conjugate of the anticomplement of X(6692)
X(40420) = isotomic conjugate of the complement of X(57)
X(40420) = isotomic conjugate of the isogonal conjugate of X(3451)
X(40420) = X(i)-cross conjugate of X(j) for these (i,j): {2, 32017}, {513, 664}, {4462, 190}, {5176, 903}, {5253, 86}, {6692, 2}, {10106, 7}, {20293, 18026}, {21302, 4569}, {23617, 1222}, {24982, 75}, {32850, 35160}
X(40420) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2347}, {6, 3057}, {8, 20228}, {9, 1201}, {19, 22072}, {21, 21796}, {31, 3452}, {32, 20895}, {41, 3663}, {42, 18163}, {55, 3752}, {58, 21809}, {101, 6615}, {213, 17183}, {219, 1828}, {220, 1122}, {281, 22344}, {284, 4642}, {604, 6736}, {644, 6363}, {650, 23845}, {663, 21362}, {667, 25268}, {692, 21120}, {1333, 21031}, {1946, 17906}, {1964, 18086}, {2175, 26563}, {2194, 4415}, {3063, 21272}, {12640, 38266}, {14284, 34080}, {18344, 23113}
X(40420) = cevapoint of X(i) and X(j) for these (i,j): {2, 57}, {7, 9312}, {9, 145}, {1400, 37558}, {1476, 23617}
X(40420) = trilinear pole of line {522, 4318}
X(40420) = barycentric product X(i)*X(j) for these {i,j}: {7, 1222}, {57, 32017}, {75, 1476}, {76, 3451}, {85, 23617}, {522, 6613}, {1088, 1261}, {3676, 8706}
X(40420) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3057}, {2, 3452}, {3, 22072}, {6, 2347}, {7, 3663}, {8, 6736}, {10, 21031}, {34, 1828}, {37, 21809}, {56, 1201}, {57, 3752}, {65, 4642}, {75, 20895}, {81, 18163}, {83, 18086}, {85, 26563}, {86, 17183}, {109, 23845}, {145, 12640}, {190, 25268}, {226, 4415}, {269, 1122}, {513, 6615}, {514, 21120}, {603, 22344}, {604, 20228}, {651, 21362}, {653, 17906}, {664, 21272}, {1222, 8}, {1261, 200}, {1400, 21796}, {1434, 18600}, {1476, 1}, {1813, 23113}, {3451, 6}, {3667, 14284}, {4369, 28006}, {4554, 21580}, {6613, 664}, {7153, 27499}, {8706, 3699}, {23617, 9}, {32017, 312}
X(40420) = {X(57),X(30567)}-harmonic conjugate of X(39126)
X(40421) lies on these lines: {3, 16097}, {66, 315}, {76, 5523}, {264, 40009}, {305, 858}, {683, 11185}, {1236, 40050}, {1241, 13854}, {2353, 38907}, {7763, 14376}, {11056, 37801}, {16277, 33651}, {21017, 40071}
X(40421) = isogonal conjugate of X(20968)
X(40421) = isotomic conjugate of X(206)
X(40421) = polar conjugate of X(17409)
X(40421) = isotomic conjugate of the anticomplement of X(6697)
X(40421) = isotomic conjugate of the complement of X(66)
X(40421) = isotomic conjugate of the isogonal conjugate of X(18018)
X(40421) = X(i)-cross conjugate of X(j) for these (i,j): {2, 1502}, {1235, 76}, {6697, 2}, {21407, 75}
X(40421) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20968}, {6, 17453}, {19, 22075}, {22, 560}, {31, 206}, {32, 2172}, {41, 7251}, {48, 17409}, {75, 40372}, {213, 17186}, {315, 1917}, {604, 4548}, {692, 21122}, {1333, 21034}, {1501, 1760}, {1924, 4611}, {1973, 10316}, {7210, 9448}, {8743, 9247}, {9233, 20641}, {9417, 11610}
X(40421) = cevapoint of X(i) and X(j) for these (i,j): {2, 66}, {75, 21583}, {23285, 36793}
X(40421) = trilinear pole of line {3267, 23881}
X(40421) = barycentric product X(i)*X(j) for these {i,j}: {66, 1502}, {76, 18018}, {1928, 2156}, {2353, 40362}, {13854, 40050}, {14376, 18022}, {18024, 34138}, {40146, 40359}
X(40421) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17453}, {2, 206}, {3, 22075}, {4, 17409}, {6, 20968}, {7, 7251}, {8, 4548}, {10, 21034}, {32, 40372}, {66, 32}, {69, 10316}, {75, 2172}, {76, 22}, {86, 17186}, {141, 23208}, {264, 8743}, {290, 11610}, {305, 20806}, {313, 4456}, {315, 36414}, {339, 38356}, {514, 21122}, {561, 1760}, {670, 4611}, {850, 2485}, {1502, 315}, {1928, 20641}, {2156, 560}, {2353, 1501}, {3267, 8673}, {8024, 3313}, {13854, 1974}, {14376, 184}, {18018, 6}, {18022, 17907}, {18024, 31636}, {20567, 7210}, {27801, 4463}, {28659, 4123}, {34138, 237}, {37801, 18374}, {40050, 34254}, {40146, 9233}, {40362, 40073}
X(40422) lies on these lines: {8, 264}, {69, 6063}, {72, 286}, {75, 78}, {271, 309}, {312, 3305}, {314, 943}, {319, 349}, {321, 2287}, {668, 1234}, {1265, 3596}, {1809, 18816}, {2893, 21403}, {2982, 30710}, {2997, 3876}, {5564, 20566}, {31643, 39765}
X(40422) = isotomic conjugate of X(942)
X(40422) = polar conjugate of X(1841)
X(40422) = isotomic conjugate of the anticomplement of X(5044)
X(40422) = isotomic conjugate of the complement of X(72)
X(40422) = isotomic conjugate of the isogonal conjugate of X(943)
X(40422) = X(i)-cross conjugate of X(j) for these (i,j): {850, 668}, {5044, 2}, {7253, 190}, {23683, 18026}
X(40422) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2260}, {19, 14597}, {25, 4303}, {31, 942}, {32, 5249}, {34, 23207}, {48, 1841}, {56, 14547}, {184, 1838}, {442, 2206}, {500, 6186}, {603, 1859}, {1042, 8021}, {1333, 2294}, {1397, 6734}, {1461, 33525}, {1474, 18591}, {1576, 23752}, {1973, 18607}, {2299, 39791}
X(40422) = cevapoint of X(i) and X(j) for these (i,j): {2, 72}, {8, 321}, {75, 319}, {200, 3294}
X(40422) = trilinear pole of line {4391, 17494}
X(40422) = barycentric product X(i)*X(j) for these {i,j}: {76, 943}, {561, 2259}, {1175, 27801}, {1794, 1969}, {2982, 3596}
X(40422) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2260}, {2, 942}, {3, 14597}, {4, 1841}, {9, 14547}, {10, 2294}, {63, 4303}, {69, 18607}, {72, 18591}, {75, 5249}, {92, 1838}, {219, 23207}, {281, 1859}, {312, 6734}, {319, 16585}, {321, 442}, {943, 6}, {1089, 21675}, {1175, 1333}, {1214, 39791}, {1577, 23752}, {1794, 48}, {2259, 31}, {2287, 8021}, {2982, 56}, {3219, 500}, {3900, 33525}, {14775, 6591}, {15439, 1415}, {17776, 14054}, {27801, 1234}, {28605, 3824}, {33116, 39772}, {36048, 1461}
X(40423) lies on these lines: {2, 40353}, {69, 39379}, {74, 3260}, {264, 38937}, {298, 36311}, {299, 36308}, {340, 687}, {1494, 7799}, {5627, 6148}, {12028, 31621}
X(40423) = isotomic conjugate of X(113)
X(40423) = isotomic conjugate of the anticomplement of X(6699)
X(40423) = isotomic conjugate of the complement of X(74)
X(40423) = isotomic conjugate of the isogonal conjugate of X(10419)
X(40423) = X(i)-cross conjugate of X(j) for these (i,j): {69, 1494}, {850, 16077}, {6699, 2}, {15454, 2986}
X(40423) = X(i)-isoconjugate of X(j) for these (i,j): {31, 113}, {1495, 1725}, {1990, 2315}, {2173, 3003}, {3580, 9406}
X(40423) = cevapoint of X(i) and X(j) for these (i,j): {2, 74}, {525, 12079}, {2986, 15454}, {16080, 38937}
X(40423) = trilinear pole of line {2394, 2986}
X(40423) = barycentric product X(i)*X(j) for these {i,j}: {76, 10419}, {305, 40388}, {687, 34767}, {1494, 2986}, {2394, 18878}, {15421, 16077}, {15454, 31621}, {33805, 36053}
X(40423) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 113}, {74, 3003}, {687, 4240}, {1300, 1990}, {1494, 3580}, {2349, 1725}, {2433, 21731}, {2986, 30}, {3580, 34104}, {5504, 3284}, {10419, 6}, {10420, 2420}, {14380, 686}, {14910, 1495}, {14919, 13754}, {15328, 1637}, {15421, 9033}, {15454, 3163}, {16077, 16237}, {16080, 403}, {18878, 2407}, {32708, 23347}, {34767, 6334}, {35200, 2315}, {36053, 2173}, {38936, 39176}, {39379, 14910}, {40384, 14264}, {40388, 25}
X(40424) lies on the circumconic {{A,B,C,X(2),X(7)}} and these lines: {2, 2256}, {7, 404}, {27, 908}, {69, 1440}, {75, 936}, {78, 273}, {86, 1167}, {326, 1088}, {329, 1436}, {965, 27282}, {5736, 30712}, {18815, 20895}
X(40424) = isogonal conjugate of X(40958)
X(40424) = isotomic conjugate of X(1210)
X(40424) = isotomic conjugate of the anticomplement of X(6700)
X(40424) = isotomic conjugate of the complement of X(78)
X(40424) = isotomic conjugate of the isogonal conjugate of X(1167)
X(40424) = trilinear pole of line X(514)X(40863)
X(40424) = X(i)-cross conjugate of X(j) for these (i,j): {521, 190}, {6700, 2}, {17896, 664}
X(40424) = X(i)-isoconjugate of X(j) for these (i,j): {4, 23204}, {6, 1108}, {25, 1071}, {28, 3611}, {31, 1210}, {32, 17862}, {55, 37566}, {56, 1864}, {560, 1226}, {1333, 21933}, {1532, 34858}, {2208, 6260}
X(40424) = cevapoint of X(i) and X(j) for these (i,j): {1, 329}, {2, 78}
X(40424) = barycentric product X(76)*X(1167)
X(40424) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1108}, {2, 1210}, {9, 1864}, {10, 21933}, {48, 23204}, {57, 37566}, {63, 1071}, {71, 3611}, {75, 17862}, {76, 1226}, {329, 6260}, {908, 1532}, {1167, 6}
X(40425) lies on these lines: {83, 141}, {251, 16988}, {308, 3108}, {427, 32085}, {1502, 7808}, {3589, 4577}, {7859, 38946}, {7953, 39427}, {14970, 18092}, {15523, 17285}
X(40425) = isogonal conjugate of X(11205)
X(40425) = isotomic conjugate of X(6292)
X(40425) = isotomic conjugate of the anticomplement of X(6704)
X(40425) = isotomic conjugate of the complement of X(83)
X(40425) = X(i)-cross conjugate of X(j) for these (i,j): {2, 10159}, {523, 4577}, {6704, 2}, {7779, 14970}
X(40425) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11205}, {6, 17457}, {19, 22078}, {31, 6292}, {32, 20898}, {38, 5007}, {39, 17469}, {58, 21817}, {213, 17193}, {428, 4020}, {688, 18062}, {692, 21126}, {1333, 21038}, {1923, 39998}, {1964, 3589}, {2084, 10330}, {17187, 21802}, {17200, 21814}, {17442, 22352}
X(40425) = cevapoint of X(i) and X(j) for these (i,j): {2, 83}, {251, 14247}, {3108, 10159}
X(40425) = trilinear pole of line {826, 14318}
X(40425) = barycentric product X(i)*X(j) for these {i,j}: {83, 10159}, {308, 3108}, {4577, 31065}
X(40425) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17457}, {2, 6292}, {3, 22078}, {6, 11205}, {10, 21038}, {37, 21817}, {75, 20898}, {82, 17469}, {83, 3589}, {86, 17193}, {251, 5007}, {308, 39998}, {427, 28666}, {514, 21126}, {1176, 22352}, {1799, 7767}, {3108, 39}, {4577, 10330}, {4593, 18062}, {7953, 1634}, {10159, 141}, {18098, 21802}, {18105, 8664}, {31065, 826}, {31067, 2528}, {31068, 7813}, {32085, 428}, {35137, 4576}, {39668, 39784}
X(40425) = {X(3589),X(40000)}-harmonic conjugate of X(4577)
X(40426) lies on these lines: {89, 4671}, {996, 1150}, {3306, 23598}, {3758, 30607}, {4597, 4850}, {4945, 37633}, {5219, 30588}, {5235, 30608}, {9059, 39428}, {29908, 30818}
X(40426) = isogonal conjugate of X(20973)
X(40426) = isotomic conjugate of the complement of X(89)
X(40426) = X(513)-cross conjugate of X(4597)
X(40426) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20973}, {6, 17461}, {19, 22083}, {45, 995}, {213, 17196}, {692, 21130}, {1333, 21042}, {1405, 3877}, {2099, 4266}, {2177, 4850}, {4273, 4424}, {4752, 9002}
X(40426) = cevapoint of X(2) and X(89)
X(40426) = trilinear pole of line {4777, 29908}
X(40426) = barycentric product X(996)*X(39704)
X(40426) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17461}, {3, 22083}, {6, 20973}, {10, 21042}, {86, 17196}, {89, 4850}, {514, 21130}, {996, 3679}, {2163, 995}, {2320, 3877}, {2364, 4266}, {9059, 4767}, {20569, 33934}, {30588, 26580}, {30608, 5233}, {39704, 4389}
X(40427) lies on these lines: {94, 323}, {186, 476}, {264, 39290}, {2411, 15421}, {3431, 15454}, {3580, 35139}, {7799, 20573}, {10420, 39430}, {14165, 18883}, {14254, 34289}
X(40427) = isotomic conjugate of X(34834)
X(40427) = polar conjugate of X(1986)
X(40427) = isotomic conjugate of the complement of X(94)
X(40427) = polar conjugate of the isogonal conjugate of X(12028)
X(40427) = X(i)-cross conjugate of X(j) for these (i,j): {2, 2986}, {523, 35139}
X(40427) = X(i)-isoconjugate of X(j) for these (i,j): {31, 34834}, {48, 1986}, {50, 1725}, {186, 2315}, {2624, 15329}, {3003, 6149}
X(40427) = cevapoint of X(i) and X(j) for these (i,j): {2, 94}, {338, 14592}, {1989, 14254}
X(40427) = trilinear pole of line {265, 526}
X(40427) = barycentric product X(i)*X(j) for these {i,j}: {94, 2986}, {264, 12028}, {328, 1300}, {687, 14592}, {1494, 39375}, {5504, 18817}, {10412, 18878}, {14910, 20573}, {15328, 35139}
X(40427) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 34834}, {4, 1986}, {94, 3580}, {265, 13754}, {476, 15329}, {687, 14590}, {1300, 186}, {1989, 3003}, {2166, 1725}, {2970, 16221}, {2986, 323}, {5504, 22115}, {5627, 14264}, {6344, 403}, {10419, 14385}, {12028, 3}, {14254, 113}, {14582, 686}, {14592, 6334}, {14910, 50}, {15328, 526}, {15421, 8552}, {15454, 1511}, {15475, 21731}, {18878, 10411}, {32708, 14591}, {35361, 2081}, {36053, 6149}, {38936, 3043}, {39170, 34333}, {39375, 30}
X(40428) lies on thje cubic K776 and these lines: {98, 325}, {183, 36897}, {230, 297}, {290, 19599}, {327, 14382}, {385, 2987}, {3563, 22456}, {5641, 6055}, {5967, 34803}, {9154, 34229}, {14253, 14265}
X(40428) = isotomic conjugate of X(114)
X(40428) = isotomic conjugate of the anticomplement of X(6036)
X(40428) = isotomic conjugate of the complement of X(98)
X(40428) = isotomic conjugate of the isogonal conjugate of X(2065)
X(40428) = X(i)-cross conjugate of X(j) for these (i,j): {2, 8781}, {69, 290}, {523, 2966}, {6036, 2}, {34157, 2987}
X(40428) = X(i)-isoconjugate of X(j) for these (i,j): {6, 17462}, {31, 114}, {230, 1755}, {237, 1733}, {511, 8772}, {1692, 1959}
X(40428) = cevapoint of X(i) and X(j) for these (i,j): {2, 98}, {647, 15630}, {2987, 34157}
X(40428) = trilinear pole of line {287, 2395}
X(40428) = barycentric product X(i)*X(j) for these {i,j}: {76, 2065}, {98, 8781}, {287, 35142}, {290, 2987}, {1821, 8773}, {18024, 32654}
X(40428) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17462}, {2, 114}, {98, 230}, {287, 3564}, {1821, 1733}, {1910, 8772}, {1976, 1692}, {2065, 6}, {2966, 4226}, {2987, 511}, {3563, 232}, {5967, 5477}, {6531, 460}, {8773, 1959}, {8781, 325}, {10425, 2421}, {32654, 237}, {32697, 4230}, {34157, 11672}, {34536, 14265}, {35142, 297}, {35364, 3569}, {36051, 1755}
X(40429) lies on these lines: {2, 33799}, {99, 31644}, {115, 4590}, {468, 30716}, {523, 14061}, {524, 5103}, {671, 9164}, {892, 23991}, {3266, 7925}, {3618, 5967}, {5461, 14728}, {31372, 35087}
X(40429) = isogonal conjugate of X(20976)
X(40429) = isotomic conjugate of X(620)
X(40429) = isotomic conjugate of the anticomplement of X(6722)
X(40429) = isotomic conjugate of the complement of X(115)
X(40429) = X(i)-cross conjugate of X(j) for these (i,j): {5468, 671}, {6722, 2}, {33919, 892}
X(40429) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20976}, {6, 17467}, {19, 22085}, {31, 620}, {32, 20903}, {163, 11123}, {213, 17199}, {692, 21135}, {798, 14588}, {1101, 23991}, {1333, 21047}, {33906, 36142}
X(40429) = cevapoint of X(i) and X(j) for these (i,j): {2, 115}, {523, 31644}
X(40429) = trilinear pole of line {148, 690}
X(40429) = barycentric product X(690)*X(14728)
X(40429) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17467}, {2, 620}, {3, 22085}, {6, 20976}, {10, 21047}, {75, 20903}, {86, 17199}, {99, 14588}, {115, 23991}, {514, 21135}, {523, 11123}, {690, 33906}, {14728, 892}
X(40430) lies on these lines: {1, 1098}, {10, 1043}, {19, 2326}, {21, 65}, {29, 225}, {37, 2287}, {75, 10448}, {81, 31503}, {86, 3668}, {158, 1982}, {267, 5426}, {409, 662}, {757, 969}, {759, 35016}, {994, 5248}, {1010, 23604}, {1125, 5620}, {1621, 34434}, {2185, 2217}, {2975, 13476}, {3612, 11116}, {3615, 3616}, {6740, 26095}, {7259, 16601}, {10543, 19642}, {11115, 25536}, {35991, 37600}
X(40430) = isogonal conjugate of X(2650)
X(40430) = isotomic conjugate of X(18698)
X(40430) = isotomic conjugate of the anticomplement of X(25081)
X(40430) = isotomic conjugate of the complement of X(25255)
X(40430) = X(i)-cross conjugate of X(j) for these (i,j): {1, 17097}, {650, 662}, {1758, 37142}, {21189, 162}, {21390, 799}, {25081, 2}
X(40430) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2650}, {3, 407}, {6, 17056}, {31, 18698}, {42, 3664}, {56, 21677}, {57, 21811}, {58, 21674}, {65, 2646}, {101, 23755}, {225, 22361}, {226, 21748}, {512, 17136}, {649, 22003}, {1042, 6737}, {1400, 5745}, {4588, 30604}, {15232, 37836}
X(40430) = cevapoint of X(i) and X(j) for these (i,j): {1, 21}, {2, 25255}
X(40430) = trilinear pole of line {661, 1021}
X(40430) = barycentric product X(333)*X(17097)
X(40430) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17056}, {2, 18698}, {6, 2650}, {9, 21677}, {19, 407}, {21, 5745}, {37, 21674}, {55, 21811}, {81, 3664}, {100, 22003}, {284, 2646}, {513, 23755}, {662, 17136}, {2193, 22361}, {2194, 21748}, {2287, 6737}, {4893, 30604}, {17097, 226}
X(40430) = {X(409),X(2646)}-harmonic conjugate of X(662)
X(40431) lies on these lines: {1, 2326}, {21, 1214}, {27, 306}, {28, 72}, {29, 226}, {63, 1098}, {162, 1104}, {270, 3868}, {1426, 4183}, {5436, 11107}
X(40431) = isogonal conjugate of X(18673)
X(40431) = X(i)-cross conjugate of X(j) for these (i,j): {1, 1257}, {513, 162}
X(40431) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18673}, {3, 1834}, {6, 440}, {42, 18650}, {58, 21671}, {72, 1104}, {73, 950}, {228, 17863}, {647, 14543}, {1214, 2264}, {1842, 3682}, {4574, 29162}
X(40431) = cevapoint of X(i) and X(j) for these (i,j): {1, 28}, {19, 4183}, {21, 3868}
X(40431) = trilinear pole of line {656, 1021}
X(40431) = barycentric product X(i)*X(j) for these {i,j}: {1, 40414}, {27, 1257}, {286, 2983}, {951, 31623}
X(40431) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 440}, {6, 18673}, {19, 1834}, {27, 17863}, {37, 21671}, {81, 18650}, {162, 14543}, {951, 1214}, {1172, 950}, {1257, 306}, {1474, 1104}, {2299, 2264}, {2983, 72}, {5317, 1842}, {40414, 75}
X(40432) lies on these lines: {1, 1581}, {6, 24519}, {21, 238}, {27, 7249}, {37, 27954}, {39, 83}, {56, 2363}, {58, 3865}, {81, 1429}, {82, 16689}, {86, 16744}, {239, 257}, {261, 40099}, {274, 33891}, {330, 8033}, {404, 27665}, {662, 21008}, {694, 39971}, {799, 21226}, {805, 3110}, {882, 24286}, {964, 27642}, {1015, 1509}, {1016, 1500}, {1201, 2106}, {1244, 36214}, {1431, 5331}, {2185, 7303}, {2275, 14621}, {2276, 17743}, {3571, 9424}, {3752, 24378}, {3905, 28606}, {4850, 24595}, {5209, 26959}, {6625, 16592}, {7018, 19786}, {7257, 26752}, {7260, 16722}, {16591, 17084}, {16705, 16738}, {16975, 34016}, {17448, 17731}, {18140, 25530}, {18600, 26802}, {18829, 35172}, {19281, 24598}, {24555, 37228}, {24617, 37233}, {25520, 29983}, {26978, 27189}, {27368, 32921}
X(40432) = isogonal conjugate of X(2295)
X(40432) = isotomic conjugate of X(3963)
X(40432) = isogonal conjugate of the complement of X(17152)
X(40432) = X(7303)-Ceva conjugate of X(1178)
X(40432) = X(i)-cross conjugate of X(j) for these (i,j): {256, 32010}, {893, 1178}, {3271, 7192}, {6377, 3733}, {18169, 86}, {29545, 190}, {29821, 757}, {33295, 37128}
X(40432) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2295}, {2, 20964}, {3, 1840}, {4, 22061}, {6, 1215}, {10, 172}, {25, 4019}, {31, 3963}, {32, 1237}, {37, 171}, {39, 18099}, {42, 894}, {55, 4032}, {56, 4095}, {58, 21021}, {65, 2329}, {71, 7009}, {72, 7119}, {81, 21803}, {82, 16587}, {101, 2533}, {109, 4140}, {181, 27958}, {190, 7234}, {210, 7175}, {213, 1909}, {226, 2330}, {284, 7211}, {292, 4039}, {321, 7122}, {512, 18047}, {661, 4579}, {765, 16592}, {804, 813}, {872, 8033}, {983, 18905}, {1016, 4128}, {1018, 4367}, {1020, 4477}, {1258, 27880}, {1334, 7176}, {1400, 7081}, {1402, 17787}, {1500, 17103}, {1826, 3955}, {1918, 1920}, {2197, 14006}, {2238, 18787}, {3112, 21752}, {3287, 4551}, {3709, 6649}, {3747, 30669}, {3907, 4559}, {3952, 20981}, {4368, 30657}, {4369, 4557}, {4447, 18785}, {4562, 5027}, {4567, 21725}, {4600, 21823}, {7035, 21755}, {17752, 23493}
X(40432) = cevapoint of X(i) and X(j) for these (i,j): {1, 39}, {256, 893}, {1015, 1019}
X(40432) = crosssum of X(i) and X(j) for these (i,j): {7234, 21755}, {16587, 21752}, {20691, 21879}
X(40432) = trilinear pole of line {659, 3737}
X(40432) = barycentric product X(i)*X(j) for these {i,j}: {1, 32010}, {10, 7303}, {21, 7249}, {28, 7019}, {58, 7018}, {75, 1178}, {81, 257}, {86, 256}, {274, 893}, {286, 7015}, {310, 904}, {314, 1431}, {333, 1432}, {513, 4594}, {514, 4603}, {649, 7260}, {659, 18829}, {694, 30940}, {805, 3766}, {812, 37134}, {1014, 4451}, {1019, 27805}, {1581, 33295}, {1934, 5009}, {3863, 38810}, {3865, 40415}, {3903, 7192}, {4560, 37137}, {6385, 7104}, {17493, 37128}, {18155, 29055}, {18786, 18827}, {27447, 27644}, {39292, 39786}
X(40432) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1215}, {2, 3963}, {6, 2295}, {9, 4095}, {19, 1840}, {21, 7081}, {28, 7009}, {31, 20964}, {37, 21021}, {39, 16587}, {42, 21803}, {48, 22061}, {57, 4032}, {58, 171}, {63, 4019}, {65, 7211}, {75, 1237}, {81, 894}, {82, 18099}, {86, 1909}, {110, 4579}, {238, 4039}, {256, 10}, {257, 321}, {270, 14006}, {274, 1920}, {284, 2329}, {333, 17787}, {513, 2533}, {650, 4140}, {659, 804}, {662, 18047}, {667, 7234}, {741, 18787}, {757, 17103}, {805, 660}, {893, 37}, {904, 42}, {1014, 7176}, {1015, 16592}, {1019, 4369}, {1021, 4529}, {1178, 1}, {1333, 172}, {1412, 7175}, {1414, 6649}, {1431, 65}, {1432, 226}, {1434, 7196}, {1437, 3955}, {1474, 7119}, {1509, 8033}, {1977, 21755}, {2185, 27958}, {2194, 2330}, {2206, 7122}, {2275, 18905}, {2309, 27880}, {3051, 21752}, {3121, 21823}, {3122, 21725}, {3248, 4128}, {3286, 4447}, {3666, 27697}, {3733, 4367}, {3737, 3907}, {3766, 14295}, {3863, 3721}, {3865, 2887}, {3903, 3952}, {4267, 18235}, {4451, 3701}, {4594, 668}, {4603, 190}, {4833, 4774}, {4960, 4842}, {5009, 1580}, {7015, 72}, {7018, 313}, {7019, 20336}, {7104, 213}, {7116, 71}, {7192, 4374}, {7249, 1441}, {7252, 3287}, {7260, 1978}, {7303, 86}, {8300, 4154}, {16695, 24533}, {16696, 16720}, {16702, 7267}, {16726, 7200}, {17302, 27966}, {17493, 3948}, {17938, 34067}, {18166, 4754}, {18191, 4459}, {18786, 740}, {18829, 4583}, {20775, 22367}, {21789, 4477}, {21814, 21818}, {22096, 22373}, {27644, 17752}, {27805, 4033}, {29055, 4551}, {30670, 4613}, {30940, 3978}, {32010, 75}, {33295, 1966}, {37128, 30669}, {37134, 4562}, {37137, 4552}, {38814, 27954}, {39179, 18111}, {39915, 27890}, {40153, 28369}
X(40432) =
{X(2275),X(17103)}-harmonic conjugate of X(37128)
X(40433) lies on the conic {{A,B,C,X(1),X(6)}} and these lines: {1, 872}, {2, 10013}, {6, 1621}, {37, 25426}, {42, 86}, {56, 5132}, {58, 1918}, {100, 18166}, {106, 8708}, {190, 2663}, {238, 1126}, {269, 33765}, {292, 1100}, {870, 4360}, {1001, 2334}, {1411, 17015}, {1449, 2279}, {1911, 30593}, {2191, 5256}, {2309, 37129}, {3240, 15668}, {3736, 39949}, {3979, 39977}, {4393, 20140}, {4651, 25508}, {17259, 29814}, {27164, 29822}
X(40433) = isogonal conjugate of X(3720)
X(40433) = isotomic conjugate of X(20888)
X(40433) = isogonal conjugate of the complement of X(4651)
X(40433) = isotomic conjugate of the anticomplement of X(25092)
X(40433) = isotomic conjugate of the complement of X(25264)
X(40433) = X(i)-cross conjugate of X(j) for these (i,j): {798, 190}, {1019, 100}, {21763, 4598}, {25092, 2}, {28840, 37138}
X(40433) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3720}, {2, 20963}, {4, 22060}, {6, 3739}, {21, 39793}, {31, 20888}, {37, 18166}, {39, 18089}, {42, 17175}, {55, 4059}, {56, 3706}, {57, 3691}, {58, 21020}, {81, 16589}, {86, 2667}, {100, 6372}, {213, 16748}, {274, 21753}, {286, 22369}, {513, 4436}, {757, 21699}, {893, 4754}, {1014, 4111}, {1509, 21820}, {2350, 29773}, {3445, 4891}
X(40433) = cevapoint of X(i) and X(j) for these (i,j): {1, 42}, {2, 25264}, {9, 4097}, {10, 32925}
X(40433) = crosssum of X(2667) and X(16589)
X(40433) = trilinear pole of line {649, 2664}
X(40433) = barycentric product X(i)*X(j) for these {i,j}: {1, 32009}, {10, 40408}, {514, 8708}
X(40433) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3739}, {2, 20888}, {6, 3720}, {9, 3706}, {31, 20963}, {37, 21020}, {42, 16589}, {48, 22060}, {55, 3691}, {57, 4059}, {58, 18166}, {81, 17175}, {82, 18089}, {86, 16748}, {101, 4436}, {171, 4754}, {213, 2667}, {649, 6372}, {872, 21820}, {1334, 4111}, {1400, 39793}, {1500, 21699}, {1621, 29773}, {1743, 4891}, {1918, 21753}, {2200, 22369}, {8708, 190}, {32009, 75}, {40408, 86}
X(40433) = {X(2663),X(2667)}-harmonic conjugate of X(190)
X(40434) lies on the conic {{A,B,C,X(1),X(2)} and these lines: {1, 4015}, {2, 3943}, {28, 1900}, {37, 88}, {44, 81}, {45, 89}, {57, 16676}, {105, 5297}, {274, 4358}, {291, 30950}, {330, 29595}, {519, 24857}, {551, 4767}, {661, 1022}, {899, 30571}, {1150, 26071}, {1224, 19862}, {1255, 17012}, {1390, 7292}, {3227, 16826}, {3666, 39962}, {3912, 34914}, {4789, 31992}, {4850, 39963}, {4945, 30588}, {5287, 39948}, {5333, 39747}, {8056, 28606}, {11010, 27784}, {16666, 35595}, {16815, 32009}, {16816, 39738}, {16831, 36871}, {17013, 27789}, {17022, 39980}, {17023, 34892}, {17595, 26745}, {21907, 37691}, {25417, 32911}, {29007, 34051}, {29571, 34578}, {31035, 39706}, {33761, 37520}
X(40434) = isogonal conjugate of X(16666)
X(40434) = isotomic conjugate of X(24589)
X(40434) = isogonal conjugate of the complement of X(17360)
X(40434) = isotomic conjugate of the complement of X(31035)
X(40434) = X(i)-cross conjugate of X(j) for these (i,j): {4893, 100}, {5049, 7}
X(40434) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16666}, {2, 21747}, {4, 22357}, {6, 551}, {31, 24589}, {42, 26860}, {55, 4031}, {56, 3707}, {81, 21806}, {101, 28209}, {604, 3902}, {649, 4781}, {901, 14435}, {1333, 4714}, {2163, 16590}, {2364, 39782}, {3939, 30722}, {4793, 28607}, {21754, 39704}
X(40434) = cevapoint of X(i) and X(j) for these (i,j): {1, 45}, {2, 31035}, {6, 5010}
X(40434) = trilinear pole of line {513, 3245}
X(40434) = barycentric product X(i)*X(j) for these {i,j}: {81, 27797}, {693, 28210}
X(40434) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 551}, {2, 24589}, {6, 16666}, {8, 3902}, {9, 3707}, {10, 4714}, {31, 21747}, {42, 21806}, {45, 16590}, {48, 22357}, {57, 4031}, {81, 26860}, {100, 4781}, {513, 28209}, {644, 30727}, {984, 4407}, {1635, 14435}, {2099, 39782}, {3669, 30722}, {3679, 4793}, {27797, 321}, {28210, 100}
X(40435) lies on these lines: {2, 219}, {8, 405}, {9, 92}, {10, 29}, {27, 71}, {48, 7573}, {63, 85}, {100, 8021}, {189, 268}, {220, 27287}, {306, 319}, {312, 3305}, {469, 26063}, {664, 16585}, {756, 26000}, {1073, 6349}, {1175, 33078}, {1220, 5294}, {1311, 15439}, {1441, 3219}, {1762, 21231}, {1796, 18653}, {1815, 18652}, {1952, 25091}, {2983, 17923}, {3757, 4518}, {4102, 17264}, {4552, 39770}, {5235, 25515}, {5657, 7497}, {5745, 34234}, {6998, 26885}, {14829, 30608}, {14942, 25006}, {18359, 27065}, {19607, 32779}, {19810, 28660}, {19860, 31359}, {20305, 30841}, {25255, 33761}, {25935, 32008}, {28980, 33066}
X(40435) = isogonal conjugate of X(2260)
X(40435) = isotomic conjugate of X(5249)
X(40435) = polar conjugate of X(1838)
X(40435) = isotomic conjugate of the complement of X(3219)
X(40435) = isotomic conjugate of the isogonal conjugate of X(2259)
X(40435) = polar conjugate of the isogonal conjugate of X(1794)
X(40435) = X(40412)-Ceva conjugate of X(943)
X(40435) = X(i)-cross conjugate of X(j) for these (i,j): {1021, 100}, {1577, 190}, {5259, 86}, {8611, 1897}, {24084, 4632}, {26017, 37206}, {35057, 664}
X(40435) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2260}, {3, 1841}, {4, 14597}, {6, 942}, {19, 4303}, {25, 18607}, {28, 18591}, {31, 5249}, {48, 1838}, {57, 14547}, {58, 2294}, {163, 23752}, {222, 1859}, {278, 23207}, {442, 1333}, {500, 2160}, {604, 6734}, {849, 21675}, {934, 33525}, {1172, 39791}, {1427, 8021}, {1437, 1865}, {2982, 37993}, {3824, 34819}, {6186, 16585}, {23595, 32656}
X(40435) = cevapoint of X(i) and X(j) for these (i,j): {1, 71}, {2, 3219}, {9, 10}, {1794, 2259}
X(40435) = trilinear pole of line {522, 3465}
X(40435) = barycentric product X(i)*X(j) for these {i,j}: {10, 40412}, {75, 943}, {76, 2259}, {264, 1794}, {306, 40395}, {312, 2982}, {313, 1175}, {4397, 36048}, {4561, 14775}, {15439, 35519}
X(40435) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 942}, {2, 5249}, {3, 4303}, {4, 1838}, {6, 2260}, {8, 6734}, {10, 442}, {19, 1841}, {33, 1859}, {35, 500}, {37, 2294}, {48, 14597}, {55, 14547}, {63, 18607}, {71, 18591}, {73, 39791}, {212, 23207}, {313, 1234}, {523, 23752}, {594, 21675}, {657, 33525}, {943, 1}, {1175, 58}, {1698, 3824}, {1794, 3}, {1826, 1865}, {2259, 6}, {2328, 8021}, {2982, 57}, {3219, 16585}, {3811, 14054}, {4420, 31938}, {6198, 1844}, {14547, 37993}, {14775, 7649}, {15439, 109}, {17924, 23595}, {32651, 1461}, {34772, 39772}, {36048, 934}, {40395, 27}, {40412, 86}
X(40436) lies on the conic {{A,B,C,X(1),X(6)}} and on these lines: {1, 4438}, {6, 26690}, {8, 1411}, {34, 78}, {56, 1259}, {58, 22836}, {106, 3976}, {269, 320}, {447, 1043}, {976, 1220}, {977, 1193}, {998, 3811}, {1027, 3810}, {1098, 5692}, {1222, 3938}, {1431, 4259}, {1438, 3061}, {1474, 2327}, {2191, 19861}, {3445, 17597}, {7253, 25253}, {7259, 25087}
X(40436) = isogonal conjugate of X(3924)
X(40436) =isotomic conjugate of X(17861)
X(40436) =isotomic conjugate of the anticomplement of X(25078)
X(40436) =isotomic conjugate of the complement of X(25252)
X(40436) =X(i)-cross conjugate of X(j) for these (i,j): {652, 190}, {16612, 662}, {21189, 100}, {25078, 2}
X(40436) =X(i)-isoconjugate of X(j) for these (i,j): {1, 3924}, {6, 3772}, {9, 36570}, {19, 26934}, {31, 17861}, {42, 17189}, {56, 1837}, {58, 21935}, {213, 16749}
X(40436) =cevapoint of X(i) and X(j) for these (i,j): {1, 78}, {2, 25252}, {42, 21078}
X(40436) =trilinear pole of line {649, 6003}
X(40436) =barycentric product X(i)*X(j) for these {i,j}: {9, 34399}, {63, 34406}
X(40436) =barycentric quotient X(i)/X(j) for these {i,j}: {1, 3772}, {2, 17861}, {3, 26934}, {6, 3924}, {9, 1837}, {37, 21935}, {56, 36570}, {81, 17189}, {86, 16749}, {34399, 85}, {34406, 92}
X(40437) lies on these lines: {1, 14628}, {2, 36590}, {11, 953}, {36, 80}, {54, 10950}, {59, 952}, {60, 3109}, {514, 1168}, {517, 655}, {519, 2323}, {859, 24624}, {860, 1309}, {1317, 1391}, {1318, 1387}, {1319, 14204}, {1411, 1870}, {1443, 17895}, {1807, 4358}, {1837, 3417}, {6740, 16704}, {6830, 39270}, {6882, 38954}, {10428, 37222}, {14266, 14584}, {18359, 38460}, {32899, 37718}, {34079, 37168}, {36909, 36915}
X(40437) = isogonal conjugate of X(34586)
X(40437) = isogonal conjugate of the complement of X(38955)
X(40437) = X(i)-cross conjugate of X(j) for these (i,j): {1, 104}, {6, 24624}, {523, 1309}, {650, 655}, {2605, 2720}, {14584, 80}
X(40437) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34586}, {3, 1845}, {6, 16586}, {36, 517}, {214, 14260}, {654, 24029}, {758, 859}, {908, 7113}, {1145, 16944}, {1457, 4511}, {1465, 2323}, {1870, 22350}, {1983, 10015}, {2183, 3218}, {2361, 22464}, {2397, 21758}, {2427, 3960}, {3310, 4585}, {3724, 17139}, {3738, 23981}, {4242, 8677}, {7128, 38353}, {11570, 39173}, {14571, 22128}, {15906, 39166}
X(40437) = cevapoint of X(i) and X(j) for these (i,j): {1, 80}, {36944, 38955}
X(40437) = trilinear pole of line {654, 900}
X(40437) = barycentric product X(i)*X(j) for these {i,j}: {80, 34234}, {104, 18359}, {909, 20566}, {1411, 36795}, {1807, 16082}, {2161, 18816}, {2250, 14616}, {24624, 38955}, {36590, 40218}
X(40437) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16586}, {6, 34586}, {19, 1845}, {80, 908}, {104, 3218}, {909, 36}, {1411, 1465}, {1795, 22128}, {2006, 22464}, {2161, 517}, {2222, 24029}, {2250, 758}, {2342, 2323}, {2401, 4453}, {3270, 38353}, {6187, 2183}, {10428, 40215}, {18359, 3262}, {18816, 20924}, {24624, 17139}, {32675, 23981}, {34051, 1443}, {34079, 859}, {34234, 320}, {34857, 21801}, {34858, 7113}, {36037, 4585}, {36123, 17923}, {36910, 6735}, {36921, 27757}, {38955, 3936}
X(40438) lies on these lines: {1, 757}, {6, 24944}, {10, 86}, {31, 39737}, {37, 81}, {65, 1014}, {75, 873}, {99, 30593}, {171, 38836}, {225, 7282}, {314, 32018}, {320, 34920}, {596, 1509}, {662, 1100}, {741, 2667}, {759, 6578}, {940, 24530}, {1414, 7269}, {1444, 31503}, {1931, 3723}, {2166, 14616}, {2185, 2214}, {2363, 20360}, {3664, 5620}, {3875, 39711}, {4038, 17322}, {4596, 4674}, {4629, 18785}, {4663, 32635}, {6539, 8025}, {10436, 39708}, {17103, 17393}, {17394, 31359}, {18166, 37128}, {20090, 31064}, {25417, 40214}, {26860, 31011}
X(40438) = reflection of X(662) in X(39042)
X(40438) = isogonal conjugate of X(1962)
X(40438) = isotomic conjugate of X(4647)
X(40438) = isogonal conjugate of the anticomplement of X(27798)
X(40438) = isogonal conjugate of the complement of X(17163)
X(40438) = isotomic conjugate of the anticomplement of X(3743)
X(40438) = X(i)-cross conjugate of X(j) for these (i,j): {1, 1255}, {484, 24624}, {513, 662}, {1126, 1171}, {1255, 32014}, {1734, 162}, {1757, 37128}, {3743, 2}, {4063, 799}
X(40438) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1962}, {2, 20970}, {3, 430}, {4, 22080}, {6, 1213}, {10, 2308}, {19, 3958}, {31, 4647}, {32, 1230}, {37, 1100}, {42, 1125}, {55, 3649}, {56, 4046}, {58, 8013}, {65, 3683}, {71, 1839}, {72, 2355}, {81, 21816}, {99, 8663}, {100, 4983}, {101, 4988}, {110, 6367}, {210, 32636}, {213, 4359}, {512, 4427}, {523, 35327}, {553, 1334}, {649, 4115}, {661, 35342}, {692, 30591}, {762, 30581}, {872, 16709}, {1018, 4979}, {1126, 8040}, {1269, 1918}, {1400, 3686}, {1402, 3702}, {1500, 8025}, {1824, 3916}, {1826, 22054}, {2333, 4001}, {3690, 31900}, {3700, 36075}, {4065, 40148}, {4557, 4977}, {4559, 4976}, {4822, 35339}, {4970, 23493}, {4973, 34857}, {7180, 30729}, {8818, 17454}
X(40438) = cevapoint of X(i) and X(j) for these (i,j): {1, 81}, {6, 4068}, {58, 40214}, {63, 14868}, {86, 4360}, {1126, 1255}
X(40438) = trilinear pole of line {661, 1019}
X(40438) = barycentric product X(i)*X(j) for these {i,j}: {1, 32014}, {58, 32018}, {75, 1171}, {81, 1268}, {86, 1255}, {274, 1126}, {286, 1796}, {310, 28615}, {513, 4632}, {514, 4596}, {662, 4608}, {693, 4629}, {757, 6539}, {763, 6538}, {1014, 4102}, {1019, 6540}, {1434, 32635}, {1577, 6578}, {7192, 37212}, {7199, 8701}, {30581, 30594}, {30582, 30593}
X(40438) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1213}, {2, 4647}, {3, 3958}, {6, 1962}, {9, 4046}, {19, 430}, {21, 3686}, {28, 1839}, {31, 20970}, {37, 8013}, {42, 21816}, {48, 22080}, {57, 3649}, {58, 1100}, {75, 1230}, {81, 1125}, {86, 4359}, {100, 4115}, {110, 35342}, {163, 35327}, {274, 1269}, {284, 3683}, {333, 3702}, {513, 4988}, {514, 30591}, {643, 30729}, {649, 4983}, {661, 6367}, {662, 4427}, {757, 8025}, {763, 30593}, {798, 8663}, {1014, 553}, {1019, 4977}, {1021, 4990}, {1100, 8040}, {1126, 37}, {1171, 1}, {1255, 10}, {1268, 321}, {1333, 2308}, {1412, 32636}, {1437, 22054}, {1444, 4001}, {1474, 2355}, {1509, 16709}, {1790, 3916}, {1796, 72}, {3733, 4979}, {3737, 4976}, {4102, 3701}, {4184, 17746}, {4560, 4985}, {4596, 190}, {4608, 1577}, {4627, 35339}, {4629, 100}, {4632, 668}, {5235, 4717}, {6539, 1089}, {6540, 4033}, {6578, 662}, {7192, 4978}, {7203, 30724}, {8025, 6533}, {8701, 1018}, {16704, 4975}, {16948, 4856}, {17104, 17454}, {18197, 4992}, {18206, 4966}, {27644, 4970}, {28615, 42}, {30582, 6538}, {31010, 4036}, {31011, 3992}, {32014, 75}, {32018, 313}, {32635, 2321}, {32911, 4065}, {33635, 210}, {37212, 3952}, {38836, 21879}, {40214, 3647}
X(40438) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 81, 33766}, {81, 1255, 1171}, {86, 1268, 32014}, {86, 32004, 319}, {1100, 1963, 662}
X(40439) lies on these lines: {1, 873}, {31, 757}, {42, 86}, {81, 213}, {274, 3896}, {741, 5625}, {799, 2107}, {1014, 1402}, {1206, 2106}, {1509, 1621}, {1962, 18827}, {1973, 31904}, {8025, 37128}, {8033, 29814}, {10013, 34022}, {10458, 23493}, {17450, 32010}, {32004, 32864}
X(40439) = isogonal conjugate of X(2667)
X(40439) = isotomic conjugate of X(21020)
X(40439) = isotomic conjugate of the anticomplement of X(10180)
X(40439) = isotomic conjugate of the complement of X(27804)
X(40439) = X(i)-cross conjugate of X(j) for these (i,j): {649, 799}, {2664, 37128}, {4040, 662}, {10180, 2}
X(40439) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2667}, {2, 21753}, {4, 22369}, {6, 16589}, {31, 21020}, {37, 20963}, {42, 3720}, {55, 39793}, {56, 4111}, {58, 21699}, {81, 21820}, {213, 3739}, {512, 4436}, {872, 17175}, {1400, 3691}, {1402, 3706}, {1500, 18166}, {1824, 22060}, {1918, 20888}, {4557, 6372}, {7109, 16748}, {18089, 21814}
X(40439) = cevapoint of X(i) and X(j) for these (i,j): {1, 86}, {2, 27804}, {81, 1621}, {274, 34022}
X(40439) = trilinear pole of line {798, 1019}
X(40439) = barycentric product X(i)*X(j) for these {i,j}: {75, 40408}, {86, 32009}, {7199, 8708}
X(40439) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16589}, {2, 21020}, {6, 2667}, {9, 4111}, {21, 3691}, {31, 21753}, {37, 21699}, {42, 21820}, {48, 22369}, {57, 39793}, {58, 20963}, {81, 3720}, {86, 3739}, {274, 20888}, {333, 3706}, {662, 4436}, {757, 18166}, {873, 16748}, {1019, 6372}, {1434, 4059}, {1509, 17175}, {1790, 22060}, {8708, 1018}, {17103, 4754}, {32009, 10}, {40408, 1}
X(40439) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 86, 33779}, {2668, 3720, 799}
X(40440) lies on these lines: {48, 92}, {73, 8795}, {75, 255}, {95, 404}, {275, 321}, {276, 313}, {326, 561}, {823, 1953}, {1821, 2148}, {1955, 2169}, {1964, 36120}, {1969, 20571}, {14616, 18831}, {17858, 35200}
X(40440) = polar conjugate of X(1953)
X(40440) = isotomic conjugate of the isogonal conjugate of X(2190)
X(40440) = polar conjugate of the isogonal conjugate of X(2167)
X(40440) = X(i)-cross conjugate of X(j) for these (i,j): {1, 2167}, {656, 823}, {1955, 1821}, {17859, 75}, {21173, 653}
X(40440) = X(i)-isoconjugate of X(j) for these (i,j): {2, 217}, {3, 51}, {4, 418}, {5, 184}, {6, 216}, {22, 27372}, {25, 5562}, {32, 343}, {48, 1953}, {52, 2351}, {53, 577}, {55, 30493}, {63, 2179}, {110, 15451}, {112, 17434}, {154, 8798}, {212, 1393}, {213, 16697}, {228, 18180}, {255, 2181}, {311, 14575}, {324, 14585}, {394, 3199}, {512, 23181}, {560, 18695}, {603, 7069}, {647, 1625}, {810, 2617}, {933, 34983}, {1092, 14569}, {1173, 32078}, {1437, 21807}, {1501, 28706}, {1568, 40352}, {1576, 6368}, {1799, 27374}, {1820, 2180}, {2081, 32662}, {2200, 17167}, {3049, 14570}, {3078, 20574}, {3527, 26907}, {9247, 14213}, {9409, 36831}, {12077, 32661}, {13450, 23606}, {14391, 32640}, {14533, 36412}, {14587, 24862}, {17500, 20775}, {17810, 31504}, {21102, 32656}, {35360, 39201}
X(40440) = cevapoint of X(i) and X(j) for these (i,j): {1, 92}, {4, 18676}, {2167, 2190}
X(40440) = trilinear pole of line {822, 1577}
X(40440) = barycentric product X(i)*X(j) for these {i,j}: {1, 276}, {19, 34384}, {54, 1969}, {63, 8795}, {75, 275}, {76, 2190}, {92, 95}, {158, 34386}, {264, 2167}, {304, 8884}, {326, 8794}, {561, 8882}, {811, 15412}, {933, 20948}, {1577, 18831}, {1748, 34385}, {2148, 18022}, {2169, 18027}, {2616, 6331}, {14208, 16813}, {15414, 36126}, {20879, 39286}, {20883, 39287}
X(40440) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 216}, {4, 1953}, {19, 51}, {24, 2180}, {25, 2179}, {27, 18180}, {31, 217}, {48, 418}, {54, 48}, {57, 30493}, {63, 5562}, {75, 343}, {76, 18695}, {86, 16697}, {92, 5}, {95, 63}, {96, 1820}, {97, 255}, {158, 53}, {162, 1625}, {186, 2290}, {264, 14213}, {275, 1}, {276, 75}, {278, 1393}, {281, 7069}, {286, 17167}, {324, 1087}, {393, 2181}, {561, 28706}, {648, 2617}, {656, 17434}, {661, 15451}, {662, 23181}, {811, 14570}, {823, 35360}, {933, 163}, {1096, 3199}, {1309, 35321}, {1577, 6368}, {1748, 52}, {1826, 21807}, {1969, 311}, {2083, 6751}, {2148, 184}, {2156, 27372}, {2167, 3}, {2168, 2351}, {2169, 577}, {2184, 8798}, {2190, 6}, {2616, 647}, {2623, 810}, {4993, 18477}, {6520, 14569}, {6521, 13450}, {8794, 158}, {8795, 92}, {8882, 31}, {8884, 19}, {8901, 3708}, {14206, 1568}, {14618, 2618}, {15412, 656}, {16030, 4020}, {16813, 162}, {17438, 32078}, {17924, 21102}, {18315, 4575}, {18831, 662}, {19166, 6508}, {19174, 17442}, {19180, 820}, {19189, 1755}, {19210, 4100}, {20902, 35442}, {21449, 1954}, {23286, 822}, {24006, 12077}, {34384, 304}, {34386, 326}, {35196, 2193}, {36035, 14391}, {36134, 32661}, {38808, 610}, {39177, 23189}, {39287, 34055}
X(40440) = {X(1953),X(9252)}-harmonic conjugate of X(823)
X(40441) lies on the Jerabek circumhyperbola and these lines: {2, 70}, {3, 19362}, {4, 569}, {5, 6145}, {6, 26}, {23, 1173}, {49, 343}, {52, 54}, {64, 7526}, {65, 2216}, {66, 182}, {67, 140}, {68, 184}, {69, 1147}, {72, 24301}, {74, 11562}, {110, 1209}, {265, 6146}, {578, 14542}, {895, 12235}, {973, 2070}, {1176, 9967}, {1177, 34155}, {1181, 34801}, {1614, 16000}, {2917, 5944}, {3431, 34148}, {3521, 18563}, {3527, 7517}, {3532, 32210}, {4846, 10984}, {5462, 19128}, {5504, 13367}, {5576, 13353}, {5622, 18125}, {5900, 6699}, {6293, 18570}, {6391, 9937}, {6413, 10898}, {6414, 10897}, {6759, 38443}, {6776, 18124}, {7525, 19151}, {7527, 16835}, {7556, 13472}, {8795, 37127}, {9706, 11271}, {9908, 19125}, {9970, 34437}, {9977, 10282}, {10610, 12228}, {10634, 32586}, {10635, 32585}, {12359, 19129}, {14528, 17834}, {15316, 19357}, {15761, 22466}, {18400, 18428}, {18532, 35603}, {19506, 32364}, {22115, 34483}, {22334, 31861}, {34114, 34438}, {34117, 34207}
X(40441) = midpoint of X(3) and X(19362)
X(40441) = isogonal conjugate of X(1594)
X(40441) = isogonal conjugate of the anticomplement of X(7542)
X(40441) = isogonal conjugate of the complement of X(7488)
X(40441) = isogonal conjugate of the polar conjugate of X(40393)
X(40441) = X(6368)-cross conjugate of X(110)
X(40441) = X(2949)-of-orthic-triangle if ABC is acute
X(40441) = cevapoint of X(i) and X(j) for these (i,j): {3, 49}, {52, 34116}, {184, 216}
X(40441) = trilinear pole of line {647, 9380}
X(40441) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1594}, {19, 37636}, {38, 10550}, {92, 570}, {158, 1216}, {1096, 1238}, {1209, 2190}, {1826, 16698}, {2962, 6152}
X(40441) = barycentric product X(i)*X(j) for these {i,j}: {3, 40393}, {63, 2216}, {343, 1166}, {394, 1179}
X(40441) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 37636}, {6, 1594}, {184, 570}, {216, 1209}, {251, 10550}, {343, 1225}, {394, 1238}, {577, 1216}, {1166, 275}, {1179, 2052}, {1437, 16698}, {2216, 92}, {2965, 6152}, {14585, 23195}, {40393, 264}
X(40442) lies on the conic {{A,B,C,X(1),X(3)}} and these lines: {1, 411}, {2, 10570}, {3, 1425}, {29, 225}, {73, 283}, {78, 201}, {102, 10902}, {109, 40081}, {219, 2197}, {284, 1400}, {307, 332}, {945, 10267}, {947, 11012}, {1036, 37579}, {1037, 26357}, {1758, 9398}, {1794, 22350}, {1795, 4303}, {1807, 33597}, {1813, 17973}, {3422, 36152}, {3478, 11510}, {10571, 20846}, {35979, 37558}
X(40442) = isogonal conjugate of X(40950)
X(40442) = X(i)-cross conjugate of X(j) for these (i,j): {647, 1813}, {23090, 651}
X(40442) = X(i)-isoconjugate of X(j) for these (i,j): {4, 2646}, {19, 5745}, {21, 407}, {27, 21811}, {28, 21677}, {29, 2650}, {33, 3664}, {34, 6737}, {92, 21748}, {158, 22361}, {270, 21674}, {1172, 17056}, {2299, 18698}, {17136, 18344}
X(40442) = cevapoint of X(3) and X(73)
X(40442) = crosssum of X(407) and X(2650)
X(40442) = trilinear pole of line {652, 17975}
X(40442) = barycentric product X(63)*X(17097)
X(40442) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 5745}, {48, 2646}, {71, 21677}, {73, 17056}, {184, 21748}, {219, 6737}, {222, 3664}, {228, 21811}, {577, 22361}, {1214, 18698}, {1400, 407}, {1409, 2650}, {1813, 17136}, {2197, 21674}, {17097, 92}, {23067, 22003}
X(40443) lies on these lines: {3, 7056}, {7, 55}, {63, 1802}, {69, 1260}, {77, 212}, {81, 241}, {85, 1621}, {189, 7367}, {286, 4183}, {1174, 1708}, {1214, 1814}, {3219, 6605}, {6606, 18816}, {7084, 10482}
X(40443) = isogonal conjugate of X(1827)
X(40443) = isotomic conjugate of the polar conjugate of X(1170)
X(40443) = isogonal conjugate of the polar conjugate of X(31618)
X(40443) = X(31618)-Ceva conjugate of X(1170)
X(40443) = X(22160)-cross conjugate of X(1813)
X(40443) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1827}, {4, 2293}, {6, 1855}, {19, 1212}, {25, 4847}, {27, 21795}, {28, 21039}, {33, 354}, {34, 3059}, {92, 20229}, {108, 6608}, {142, 607}, {158, 22079}, {278, 8012}, {281, 1475}, {653, 10581}, {1172, 21808}, {1229, 1973}, {1418, 7079}, {1783, 21127}, {1824, 17194}, {1847, 8551}, {1857, 22053}, {1897, 2488}, {2212, 20880}, {2299, 3925}, {2333, 16713}, {3064, 35326}, {6362, 8750}, {6591, 35341}, {6607, 36118}, {7071, 10481}, {18344, 35338}
X(40443) = cevapoint of X(3) and X(77)
X(40443) = trilinear pole of line {905, 23146}
X(40443) = barycentric product X(i)*X(j) for these {i,j}: {3, 31618}, {63, 21453}, {69, 1170}, {75, 1803}, {77, 32008}, {78, 10509}, {348, 2346}, {905, 6606}, {1174, 7182}, {6605, 7056}
X(40443) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1855}, {3, 1212}, {6, 1827}, {48, 2293}, {63, 4847}, {69, 1229}, {71, 21039}, {73, 21808}, {77, 142}, {184, 20229}, {212, 8012}, {219, 3059}, {222, 354}, {228, 21795}, {348, 20880}, {577, 22079}, {603, 1475}, {652, 6608}, {905, 6362}, {1170, 4}, {1174, 33}, {1214, 3925}, {1331, 35341}, {1444, 16713}, {1459, 21127}, {1790, 17194}, {1803, 1}, {1813, 35338}, {1946, 10581}, {2346, 281}, {6605, 7046}, {6606, 6335}, {7053, 1418}, {7125, 22053}, {7177, 10481}, {7182, 1233}, {10482, 7079}, {10509, 273}, {21453, 92}, {22383, 2488}, {23067, 35310}, {23144, 15185}, {31618, 264}, {32008, 318}, {36059, 35326}
X(40444) lies on these lines: {2, 268}, {4, 1260}, {27, 908}, {63, 1847}, {92, 3692}, {219, 278}, {342, 1767}, {1167, 1785}, {1864, 1897}, {7151, 7952}, {9612, 37278}, {11109, 27287}
X(40444) = isogonal conjugate of isotomic conjugate of polar conjugate of X(40958)
X(40444) = polar conjugate of X(1210)
X(40444) = polar conjugate of the isogonal conjugate of X(1167)
X(40444) = X(650)-cross conjugate of X(1897)
X(40444) = X(i)-isoconjugate of X(j) for these (i,j): {2, 23204}, {3, 1108}, {6, 1071}, {48, 1210}, {81, 3611}, {184, 17862}, {219, 37566}, {222, 1864}, {1226, 9247}, {1437, 21933}, {1532, 14578}
X(40444) = cevapoint of X(i) and X(j) for these (i,j): {4, 9}, {19, 7952}, {71, 3191}, {278, 1767}
X(40444) = trilinear pole of line {7649, 8058}
X(40444) = barycentric product X(i)*X(j) for these {i,j}: {92, 40399}, {264, 1167}, {312, 40397}
X(40444) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1071}, {4, 1210}, {19, 1108}, {31, 23204}, {33, 1864}, {34, 37566}, {42, 3611}, {92, 17862}, {264, 1226}, {1167, 3}, {1785, 1532}, {1826, 21933}, {7952, 6260}, {40397, 57}, {40399, 63}
X(40445) lies on these lines: {4, 346}, {8, 278}, {10, 2322}, {27, 306}, {29, 40161}, {75, 1847}, {92, 341}, {280, 377}, {318, 6358}, {917, 29163}, {951, 10106}, {1834, 1897}, {3692, 11471}, {5016, 37279}, {6559, 36124}
X(40445) = isotomic conjugate of X(18650)
X(40445) = polar conjugate of X(40940)
X(40445) = polar conjugate of the isogonal conjugate of X(2983)
X(40445) = X(i)-cross conjugate of X(j) for these (i,j): {523, 1897}, {17926, 6335}
X(40445) = X(i)-isoconjugate of X(j) for these (i,j): {3, 1104}, {31, 18650}, {58, 18673}, {184, 17863}, {222, 2264}, {255, 1842}, {440, 1333}, {603, 950}, {849, 21671}, {906, 29162}, {1437, 1834}, {14543, 22383}
X(40445) = cevapoint of X(i) and X(j) for these (i,j): {1, 1782}, {4, 10}, {71, 3190}, {1826, 7046}
X(40445) = trilinear pole of line {3239, 4064}
X(40445) = barycentric product X(i)*X(j) for these {i,j}: {10, 40414}, {92, 1257}, {264, 2983}, {951, 7017}
X(40445) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 18650}, {10, 440}, {19, 1104}, {33, 2264}, {37, 18673}, {92, 17863}, {281, 950}, {393, 1842}, {594, 21671}, {951, 222}, {1257, 63}, {1826, 1834}, {1897, 14543}, {2983, 3}, {7649, 29162}, {29163, 1331}, {40414, 86}
X(40446) lies on these lines: {4, 496}, {29, 1877}, {34, 318}, {281, 608}, {653, 1828}, {1261, 4200}, {2316, 4848}, {3451, 8748}, {4318, 4696}
X(40446) = isogonal conjugate of X(22072)
X(40446) = polar conjugate of X(3452)
X(40446) = polar conjugate of the isotomic conjugate of X(40420)
X(40446) = polar conjugate of the isogonal conjugate of X(3451)
X(40446) = X(i)-cross conjugate of X(j) for these (i,j): {3451, 40420}, {6591, 653}
X(40446) = X(i)-isoconjugate of X(j) for these (i,j): {1, 22072}, {3, 3057}, {8, 22344}, {48, 3452}, {63, 2347}, {71, 18163}, {78, 1201}, {184, 20895}, {212, 3663}, {219, 3752}, {228, 17183}, {283, 4642}, {345, 20228}, {521, 23845}, {603, 6736}, {650, 23113}, {652, 21362}, {906, 21120}, {1122, 1260}, {1259, 1828}, {1331, 6615}, {1437, 21031}, {1790, 21809}, {1812, 21796}, {1946, 21272}, {2193, 4415}, {4020, 18086}, {4571, 6363}, {17906, 36054}, {22383, 25268}
X(40446) = cevapoint of X(i) and X(j) for these (i,j): {1, 1788}, {4, 34}
X(40446) = barycentric product X(i)*X(j) for these {i,j}: {4, 40420}, {34, 32017}, {92, 1476}, {264, 3451}, {273, 23617}, {278, 1222}, {1261, 1847}, {3064, 6613}
X(40446) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 3452}, {6, 22072}, {19, 3057}, {25, 2347}, {27, 17183}, {28, 18163}, {34, 3752}, {92, 20895}, {108, 21362}, {109, 23113}, {225, 4415}, {273, 26563}, {278, 3663}, {281, 6736}, {604, 22344}, {608, 1201}, {653, 21272}, {1222, 345}, {1261, 3692}, {1395, 20228}, {1435, 1122}, {1476, 63}, {1824, 21809}, {1826, 21031}, {1880, 4642}, {1897, 25268}, {3451, 3}, {6591, 6615}, {7649, 21120}, {18026, 21580}, {23617, 78}, {32017, 3718}, {32085, 18086}, {32674, 23845}, {36127, 17906}, {40420, 69}
X(40447) lies on these lines: {2, 331}, {4, 3690}, {9, 92}, {29, 3191}, {200, 318}, {264, 17776}, {281, 2052}, {286, 3219}, {321, 2287}, {346, 7017}, {445, 18026}, {943, 1896}, {2982, 16082}, {15439, 39429}
X(40447) = isogonal conjugate of X(14597)
X(40447) = isotomic conjugate of X(18607)
X(40447) = polar conjugate of X(942)
X(40447) = polar conjugate of the isogonal conjugate of X(943)
X(40447) = X(i)-cross conjugate of X(j) for these (i,j): {14618, 6335}, {17926, 1897}
X(40447) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14597}, {3, 2260}, {6, 4303}, {31, 18607}, {48, 942}, {57, 23207}, {58, 18591}, {184, 5249}, {222, 14547}, {255, 1841}, {284, 39791}, {577, 1838}, {1437, 2294}, {1859, 7125}, {23752, 32661}
X(40447) = cevapoint of X(i) and X(j) for these (i,j): {4, 37}, {9, 3191}, {321, 17776}
X(40447) = trilinear pole of line {3900, 4036}
X(40447) = barycentric product X(i)*X(j) for these {i,j}: {264, 943}, {321, 40395}, {668, 14775}, {1969, 2259}, {2982, 7017}
X(40447) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4303}, {2, 18607}, {4, 942}, {6, 14597}, {19, 2260}, {33, 14547}, {37, 18591}, {55, 23207}, {65, 39791}, {92, 5249}, {158, 1838}, {318, 6734}, {393, 1841}, {943, 3}, {1175, 1437}, {1794, 255}, {1826, 2294}, {1857, 1859}, {1859, 37993}, {2259, 48}, {2982, 222}, {4183, 8021}, {5174, 39772}, {6198, 500}, {14775, 513}, {15439, 36059}, {24006, 23752}, {40395, 81}, {40412, 1444}
Let A'B'C' be the orthic triangle. Let BA and CA be the orthogonal projections of B' and C' on line BC, resp. Let (OA) be the circle with segment BACA as diameter. Define (OB), (OC) cyclically. X(40448) is the radical center of circles (OA), (OB), (OA). (Randy Hutson, December 18, 2020)
X(40448) lies on the Kiepert circumhyperbola and these lines: {2, 578}, {3, 2052}, {4, 577}, {5, 275}, {6, 13599}, {20, 8796}, {30, 39284}, {76, 3964}, {83, 7399}, {94, 14118}, {95, 9291}, {96, 12022}, {98, 6146}, {140, 16080}, {226, 3075}, {262, 10982}, {321, 7549}, {418, 8884}, {459, 631}, {485, 6809}, {486, 6810}, {671, 34664}, {1093, 6641}, {1181, 13380}, {2394, 38933}, {3525, 38253}, {5392, 7503}, {5562, 9290}, {6504, 6816}, {6831, 40395}, {6905, 22341}, {8613, 8887}, {9381, 34864}, {11414, 20792}, {11538, 34007}, {13160, 40393}, {13322, 19169}, {17928, 34289}, {23239, 40082}, {37334, 37892}
X(40448) = midpoint of X(4) and X(17401)
X(40448) = isogonal conjugate of X(389)
X(40448) = isogonal conjugate of the anticomplement of X(11793)
X(40448) = isogonal conjugate of the complement of X(5562)
X(40448) = isotomic conjugate of the polar conjugate of X(40402)
X(40448) = X(i)-cross conjugate of X(j) for these (i,j): {12241, 4}, {17434, 648}, {23286, 110}, {23290, 925}, {26897, 3}, {34965, 264}
X(40448) = X(i)-isoconjugate of X(j) for these (i,j): {1, 389}, {1953, 19170}, {2148, 34836}, {2169, 6750}
X(40448) = cevapoint of X(i) and X(j) for these (i,j): {3, 5}, {6, 418}, {216, 34985}
X(40448) = trilinear pole of line {523, 32320}
X(40448) = barycentric product X(69)*X(40402)
X(40448) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 34836}, {6, 389}, {53, 6750}, {54, 19170}, {40402, 4}
X(40448) = {X(5),X(2055)}-harmonic conjugate of X(275)
X(40449) lies on the conic {{A,B,C,X(4),X(5)}} and these lines: {2, 16837}, {3, 3613}, {4, 569}, {32, 2165}, {52, 311}, {143, 25043}, {315, 327}, {1141, 1166}, {1487, 31610}, {1625, 7745}, {3843, 17703}, {7401, 8797}, {10412, 20188}, {11816, 15226}, {11818, 34449}, {13450, 30506}, {31724, 38305}
X(40449) = X(512)-cross conjugate of X(1625)
X(40449) = X(i)-isoconjugate of X(j) for these (i,j): {570, 2167}, {1216, 2190}, {1594, 2169}, {2148, 37636}
X(40449) = cevapoint of X(i) and X(j) for these (i,j): {5, 143}, {51, 36412}
X(40449) = crosssum of X(570) and X(23195)
X(40449) = barycentric product X(i)*X(j) for these {i,j}: {5, 40393}, {343, 1179}, {2216, 14213}
X(40449) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 37636}, {51, 570}, {53, 1594}, {216, 1216}, {217, 23195}, {343, 1238}, {1179, 275}, {2216, 2167}, {14577, 6152}, {18180, 16698}, {36412, 1209}, {40393, 95}
X(40450) lies on these lines: {1, 1090}, {11, 59}, {36, 516}, {54, 496}, {60, 37722}, {952, 1391}, {953, 1387}, {2323, 4700}, {3417, 11373}, {3582, 13329}, {4511, 4742}, {24002, 24203}
X(40450) = X(1983)-cross conjugate of X(24624)
X(40450) = X(i)-isoconjugate of X(j) for these (i,j): {2, 21742}, {3, 1830}, {4, 22346}, {6, 16578}, {56, 14740}, {81, 21797}
X(40450) = cevapoint of X(1) and X(11)
X(40450) = trilinear pole of line {654, 1768}
X(40450) = crosspoint of X(1) and X(11) wrt the excentral triangle
X(40450) = intersection of tangents at X(1) and X(11) to the rectangular hyperbola passing through X(1), X(11), and the excenters
X(40450) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16578}, {9, 14740}, {19, 1830}, {31, 21742}, {42, 21797}, {48, 22346}
X(40450) lies on these lines: {10, 106}, {11, 1357}, {80, 1210}, {171, 1416}, {244, 17888}, {291, 3840}, {1015, 1146}, {1261, 4847}, {3663, 4554}, {3976, 39697}, {6736, 31343}, {18191, 34590}, {23617, 32944}
X(40451) = X(i)-isoconjugate of X(j) for these (i,j): {59, 3057}, {100, 23845}, {101, 21362}, {692, 21272}, {765, 1201}, {906, 17906}, {1016, 20228}, {1110, 3663}, {1122, 6065}, {1252, 3752}, {1415, 25268}, {1783, 23113}, {2149, 3452}, {2347, 4564}, {4567, 21796}, {4570, 4642}, {6736, 24027}, {7012, 22072}, {15742, 22344}, {21580, 32739}, {23990, 26563}
X(40451) = cevapoint of X(i) and X(j) for these (i,j): {11, 244}, {1086, 21139}, {1647, 34590}, {2310, 4534}
X(40451) = crosssum of X(1201) and X(23845)
X(40451) = trilinear pole of line {21143, 23764}
X(40451) = barycentric product X(i)*X(j) for these {i,j}: {11, 40420}, {244, 32017}, {1086, 1222}, {1111, 23617}, {1476, 4858}, {3451, 34387}, {6545, 8706}
X(40451) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 3452}, {244, 3752}, {513, 21362}, {514, 21272}, {522, 25268}, {649, 23845}, {693, 21580}, {1015, 1201}, {1086, 3663}, {1111, 26563}, {1146, 6736}, {1222, 1016}, {1459, 23113}, {1476, 4564}, {2170, 3057}, {3120, 4415}, {3122, 21796}, {3125, 4642}, {3248, 20228}, {3271, 2347}, {3451, 59}, {4516, 21809}, {4534, 12640}, {4858, 20895}, {7117, 22072}, {7649, 17906}, {8706, 6632}, {17197, 17183}, {17205, 18600}, {18101, 18086}, {18191, 18163}, {21044, 21031}, {21132, 21120}, {21143, 6363}, {23617, 765}, {32017, 7035}, {40420, 4998}
X(40452) lies on the cubic K1173 and these lines: {1, 849}, {21, 961}, {28, 1791}, {261, 2975}, {314, 16049}, {1043, 5285}, {1169, 17521}, {1220, 5251}, {1610, 7058}, {37265, 37583}
X(40452) = X(i)-isoconjugate of X(j) for these (i,j): {1193, 15232}, {1400, 19608}, {2092, 13478}, {2217, 2292}, {2269, 40160}, {2995, 3725}, {21124, 32653}
X(40452) = cevapoint of X(i) and X(j) for these (i,j): {21, 1610}, {2975, 16049}, {3869, 4225}
X(40452) = barycentric product X(i)*X(j) for these {i,j}: {2363, 4417}, {3869, 14534}, {4225, 30710}, {8707, 16754}
X(40452) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 19608}, {573, 2292}, {961, 40160}, {1169, 2217}, {2298, 15232}, {2363, 13478}, {3185, 2092}, {3869, 1211}, {4225, 3666}, {4417, 18697}, {14534, 2995}, {16754, 3004}, {21078, 20653}, {21189, 21124}, {22134, 22076}, {22276, 21810}
X(40452) = {X(21),X(961)}-harmonic conjugate of X(14534)
X(40453) lies on the cubic K1173 and these lines: {21, 1220}, {58, 961}, {60, 1610}, {261, 2975}, {284, 2298}, {2051, 37399}, {16049, 20028}
X(40453) = X(31)-cross conjugate of X(2298)
X(40453) = X(i)-isoconjugate of X(j) for these (i,j): {572, 1211}, {960, 37558}, {1193, 17751}, {2092, 14829}, {2292, 2975}, {3666, 21061}, {11109, 22076}, {17074, 21033}, {18697, 20986}
X(40453) = barycentric product X(i)*X(j) for these {i,j}: {2051, 2363}, {2298, 20028}, {14534, 34434}
X(40453) = barycentric quotient X(i)/X(j) for these {i,j}: {1169, 2975}, {2051, 18697}, {2298, 17751}, {2363, 14829}, {20028, 20911}, {34434, 1211}
X(40454) lies on the Feuerbach circumhyperbola, the cubic K1173, and these lines: {4, 961}, {8, 197}, {9, 205}, {21, 1798}, {314, 16049}, {1169, 1172}, {1220, 30513}, {2975, 8048}
X(40454) = isogonal conjugate of X(41600)
X(40454) = X(25)-cross conjugate of X(1169)
X(40454) = X(i)-isoconjugate of X(j) for these (i,j): {197, 4357}, {205, 20911}, {478, 3687}, {960, 21147}, {1193, 3436}, {1766, 3666}, {1848, 22132}, {2292, 16049}, {2300, 20928}, {3882, 6588}, {21074, 40153}
X(40454) = barycentric product X(i)*X(j) for these {i,j}: {961, 34277}, {2298, 8048}, {3435, 30710}, {15420, 40097}
X(40454) = barycentric quotient X(i)/X(j) for these {i,j}: {1169, 16049}, {1220, 20928}, {2298, 3436}, {3435, 3666}, {8048, 20911}
X(40455) lies on the cubic K1173 and these lines: {1, 572}, {21, 1220}, {958, 14624}, {1791, 2217}, {2975, 30710}, {4216, 5552}, {4224, 29828}, {16049, 17751}
X(40455) = cevapoint of X(22299) and X(23361)
barycentric product X(i)*X(j) for these {i,j}: {1220, 1764}, {2298, 20245}, {2363, 22020}, {14534, 22299}, {23361, 30710}, {23799, 36147}
barycentric quotient X(i)/X(j) for these {i,j}: {1764, 4357}, {3588, 2292}, {20245, 20911}, {22020, 18697}, {22299, 1211}, {23361, 3666}, {23799, 4509}
X(40456) lies on the cubic K1173 and these lines: {1, 1437}, {21, 572}, {58, 961}, {859, 1724}, {1764, 16049}, {1791, 21061}, {4225, 21363}
X(40457) lies on the curves K1173 and Q066, and on these lines: {2, 14257}, {4, 34277}, {63, 12089}, {78, 1766}, {345, 3436}, {1610, 1812}, {17408, 39167}, {34188, 39990}, {34259, 34263}
X(40457) = isotomic conjugate of the anticomplement of X(1880)
X(40457) = X(i)-cross conjugate of X(j) for these (i,j): {1880, 2}, {2217, 1}
X(40457) = X(i)-isoconjugate of X(j) for these (i,j): {21, 12089}, {1400, 28944}
X(40457) = cevapoint of X(i) and X(j) for these (i,j): {123, 523}, {512, 35072}, {513, 34588}
X(40457) = trilinear pole of line {521, 6588}
X(40457) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 28944}, {1400, 12089}
The 1st and 2nd Moses points are the incircle-inverses of the 1st and 2nd Brocard points. See P(195) in Bicentric Pairs.
X(40458) lies on these lines: {1, 813}, {354, 15615}, {3333, 12032}, {9320, 14760}, {18240, 37998}
X(40458) = midpoint of PU(195)
X(40459) lies on these lines: {1, 4444}, {10, 27929}, {30, 511}, {98, 12032}, {99, 813}, {115, 4129}, {148, 39362}, {239, 661}, {350, 1577}, {671, 18822}, {1575, 9321}, {2482, 35123}, {3008, 25666}, {3023, 15615}, {3912, 4369}, {4107, 24290}, {4367, 8299}, {4375, 6161}, {4560, 17759}, {4761, 32847}, {5216, 38481}, {6542, 7192}, {13178, 13576}, {17266, 24924}, {17310, 31148}, {20016, 31290}, {23596, 24286}, {24281, 24289}, {27321, 27527}, {30225, 36216}, {34342, 34343}, {34362, 34363}, {35352, 38348}, {36230, 36232}, {36234, 36235}
X(40459) = crossdifference of every pair of points on line {6, 25817}
X(40459) = ideal point of PU(195)
X(40459) = barycentric quotient X(2823)/X(21285)
X(40460) lies on these lines: {1, 39}, {528, 5572}, {938, 13576}, {3022, 24203}, {3271, 3732}, {3673, 39789}, {3753, 14523}, {3887, 14760}, {5728, 18413}, {11019, 17761}
X(40460) = crosssum of X(55) and X(21320)
X(40460) = bicentric sum of PU(195)
X(40461) lies on these lines: {6, 25817}, {220, 3570}, {1901, 2238}
X(40461) = crossdifference of PU(195)
Centers and perspectors of cevapoint conics: X(40462)-X(40529)
This preamble is contributed by Clark Kimberling and Peter Moses, November 30, 2020.
In the plane of a triangle ABC, let L be the line u x + v y + w z = 0, and let U be the point u : v : w, this being the isotomic conjugate of the trilinear pole of L. Let P = p : q : r be a point. The (U,P)-cevapoint conic, introduced here as the locus of X such that the cevapoint of P and X is on the line LU is given by
u (q x + p y)(r x + p z) + v (r y + q z)(p y + q x) + w (p z + r x)(q z + r y) = 0.
The center of the conic is the point
p*(p^2*(p - q - r) u^2 + q^2 (p - q + r) v^2 + r^2 (p + q - r) w^2 - 2 p q r v w + 2 p r (p - r) w u + 2 p q (p - q) u v) : : ,
and the perspector, by
p/(-p u + q r + r w) : q/(p u - q v + r w) : r/(p u + q v - r w).
For every point U, the (U,P)-cevapoint conic passes through the vertices of the anticevian triangle of P.
The appearance of (i,j,k) in the following list means that the center of the (X(i),X(j))-cevapoint conic is X(k):
(1,1,15487), (1,2,7), (1,37,10), (1,514,693), (1,661,523), (1,1577,850), (1,3239,4397), (2,2,2), (6,6,14713), (2,1,40), (2,6,159), (2,37,22271), (2,512,512), (2,513,513), (2,514,514), (2,522,522), (2,523,523), (2,900,900), (75,1,3973), (75,6,15494), (75,513,649), (75,649,667), (75,661,512), (75,798,669), (75,822,39201), (115,523,6722), (264,3,38292), (76,6,5023), (274,37,21868), (190,514,1086), (6,2,4), (6,514,522), (6,523,850), (10,1,36808), (10,2,75), (10,514,7192), (10,649,3733), (514,1,100), (514,2,190), (514,6,14723), (514,8,3699), (514,10,3952), (514,42,4557), (514,200,4578), (514,519,17780), (514,1125,4427), (514,1647,900)
The appearance of {i, {j(1),j(2),...}} in the following list means that the (X(1),X(i))-cevapoint conic passes through the points X(j1), X(j2),... :
{1, {2640,5540,16550,16559,16560,16561,16562,16563}}
{2, {149,4440,20355,20533,21220,21221,30578,37781}}
{6, {2932,20871,20999,21004,23402,23860}}
{10, {21090,21100,22029,22031,22035}}
{37, {20716,21888,22306,22308,22313,22321}}
{513, {650,905,6588,14079}}
{514, {514,522,14078,14837,20516,21192,21198,21199}}
{522, {514,3239,4521,14331}}
{523, {661,1577,3700,14086,21051}}
{650, {513,521,11934,14298}}
{661, {523,656,661,6587,13636,13722,14086,17431,17432,23301,31946}}
{1577, {523,525,1577,14086,14566,17898,18310,20910}}
{3239, {522,3239,8058,14302}}
The appearance of {i, {j(1),j(2),...}} in the following list means that the (X(2),X(i))-cevapoint conic passes through the points X(j1), X(j2),... :
{1, {1054,1282,1768,2100,2101,2448,2449,2948,3464,5539,5540,5541,9860,9904,12408,13174,13221,13513,20114,20375,21381,34196,34464,39156}}
{2, {148,4440,8591,9263,17487,25054,39345,39346,39347,39348,39349,39350,39351,39352,39353,39354,39355,39356,39357,39358,39359,39360,39361,39362,39363,39364,39365,39366,39367,39368}}
{6,{2930,7669,10117,15588,16686,20468,20998,20999,23858}}
{37, {20694,21889,21893,22313,22323}}
{512, {512,647,661,2519,14090}}
{513, {513,650,6129,6728,14079,17427,31947,33646}}
{514, {514,3835,7658,14078,21196,25381}}
{522, {522,4521,6728,6730}}
{523, {523,656,661,6587,13636,13722,14086,17431,17432,23301,31946}}
{661, {512,523,4041,21834,22226}}
{900, {900,1647,6544,23757}}
{1647, {900,6550,14442,24131}}
The appearance of {i, {j(1),j(2),...}} in the following list means that the (X(75),X(i))-cevapoint conic passes through the points X(j1), X(j2),...:
{1, {1054,2629,2636,2640,9324,9355,9359,39335,39336,39337,39338,39339,39340,39341,39342,39343,39344}}
{6, {3196,9259,9509,16686,20672,21004,21783}}
{512, {661,798,3709,14090}}
{513, {513,4083,9269,14079}}
{514, {3835,14078,21191,21195}}
{523, {9276,14086,21051,31946}}
{649, {649,663,6729,14088}}
{661, {512,647,661,2519,14090}}
{798, {512,798,810,3221,14090}}
{822, {647,810,822,2524}}
The appearance of {i, {j(1),j(2),...}} in the following list means that the (X(6),X(i))-cevapoint conic passes through the points X(j1), X(j2),...:
{1, {16560,16565,20601,21381,21382,39335}}
{2, {146,147,148,149,150,151,152,153,3448,11671,12384,13219,13510,14360,14731,14732,14807,14808,20344,21290,33650,34186,34188,34193,34547,34548,34549,34550}}
{6, {2936,7669,16873,23402,39857}}
{10, {20496,21091,21093,22031,22032}}
{37, {21889,22308,22309,22310}}
{75, {18151,18159,20937,20951}}
{514, {522,4025,14078,20518,21186,21187,21196,21197}}
{523, {523,525,1577,14086,14566,17898,18310,20910}}
{525, {523,3265,8057,38401}}
{690, {1649,14417,18311,21906}}
{693, {693,4391,14080,17896}}
The appearance of {i, {j(1),j(2),...}} in the following list means that the (X(10),X(i))-cevapoint conic passes through the points X(j1), X(j2),...:
{1, {5540,9359,16554,24578}}
{2, {4440,17154,21224,30579,33888}}
{6, {8301,9259,20999,23392,23404}}
{513, {514,649,650,4083,6589,14079}}
{514, {513,514,905,14078,14079,21172,21191,21194}}
{522, {650,4521,14837,20317}}
{649, {513,649,1459,14079,14088}}
The appearance of {i, {j(1),j(2),...}} in the following list means that the (X(514),X(i))-cevapoint conic passes through the points X(j1), X(j2),...:
{1, {1,9,40,188,191,366,1045,1050,1490,2136,2949,2950,2951,3174,3307,3308,3646,5506,5528,5541,6326,12658,12660,13144,13146,16009,16550,16558,18598,24578,25427,32632,38004,39131}}
{2, {2,144,192,366,1654,3151,4182,17487,17488,20533,24313,24314,27484,31308,33888,37881}}
{3, {6,3157,7078,22133}}
{6, {3,55,197,199,8301,11505,11506,12335,18755,20871,20996,23858,23859,36943}}
{8, {8,188,3161,6731,8834,19582,30412,30413,39800}}
{9, {1,200,3158,7070}}
{10, {10,37,72,3159,8804,20722,21080,21083,22271,22299,22306,22307,39131}}
{11, {522,523,650,17420}}
{37, {10,42,210,20691,20700,22276,28600}}
{42, {37,42,71,3198,3588,21858,21877,21880}}
{44, {214,678,1960,3689}}
{55, {6,219,5452,7074}}
{115, {523,6367,12069,12071}}
{200, {9,200,2324,4182,6731,24771}}
{512, {1015,1084,3122,14090,16613}}
{513, {244,1015,3756,14079}}
{514, {1086,4904,14078,17761,24185}}
{518, {1575,2254,3693,6184,8299}}
{519, {519,900,1145,4370,34587,36945}}
{521, {2968,7004,34588,35072}}
{522, {11,1146,3036,34589}}
{523, {11,115,3120,8286,14086,23938}}
{650, {11,2310,3271,38375}}
{740, {2238,4010,10026,17793,20723,35068}}
{900, {519,1647,34590,35092}}
{1125, {1125,1213,3650,4065}}
{1279, {659,2348,2976,39048}}
{1647, {900,1647,6544,23757}}
The appearance of {i, {j(1),j(2),...}} in the following list means that the (X(i),X(i))-cevapoint conic passes through the points X(j1), X(j2),... :
{1, {2640,5540,16550,16559,16560,16561,16562,16563}}
{2, {148,4440,8591,9263,17487,25054,39345,39346,39347,39348,39349,39350,39351,39352,39353,39354,39355,39356,39357,39358,39359,39360,39361,39362,39363,39364,39365,39366,39367,39368}}
{6, {2936,7669,16873,23402,39857}}
{514, {1086,4904,14078,17761,24185}}
{523, {115,5461,6128,7668,14086,39022,39023}}
{525, {127,2454,2455,15526}}
Let X*(i) denote the isotomic conjugate of X(i). The appearance of {i, {j(1),j(2),...}} in the following list means that the (X*(i),X(i))-cevapoint conic passes through the points X(j1), X(j2),...:
{1, {1054,2629,2636,2640,9324,9355,9359,39335,39336,39337,39338,39339,39340,39341,39342,39343,39344}}
{2, {148,4440,8591,9263,17487,25054,39345,39346,39347,39348,39349,39350,39351,39352,39353,39354,39355,39356,39357,39358,39359,39360,39361,39362,39363,39364,39365,39366,39367,39368}}
{3, {20795,22143,22148,22158,23081,23180}}
{6, {1979,9259,9412,9431,20998,21781}}
{37, {21885,21888,21893,21899}}
{514, {14078,21200,21204,21211}}
Let X^2(i) denote the barycentric square of X(i). The appearance of {i, {j(1),j(2),...}} in the following list means that the (X^2(i),X(i))-cevapoint conic passes through the points X(j1), X(j2),...:
{1, {16560,16565,20601,21381,21382,39335}}
{2, {148,4440,8591,9263,17487,25054,39345,39346,39347,39348,39349,39350,39351,39352,39353,39354,39355,39356,39357,39358,39359,39360,39361,39362,39363,39364,39365,39366,39367,39368}}
{30, {2,402,23583,24975}}
{512, {2,3589,4698,6375,6387,6677,6685,6719,14090,15895,15896,34236}}
{513, {2,1125,6692,6703,6714,14079,16604,28600,36812}}
{514, {2,142,3739,4859,6678,6707,14078,15497,27478,31312,31351,31380}}
{520, {2,140,3788,20203,34841}}
{521, {2,5745,6675,6700}}
{522, {2,10,6706,6708,20205,21198,23058}}
{523, {2,5,2023,3413,3414,3634,3934,5461,6036,6118,6119,6669,6670,6673,6674,6704,9478,9756,13881,14086,14566,14762,16509,22847,22893,36597,37691,39143}}
{525, {2,141,6709,14767,18310,20106,20208}}
{526, {2,6671,6672,11064,16760}}
{690, {2,523,524,16511,37911}}
{812, {2,3008,4369,20530,27800}}
{900, {2,514,519,34024,35466}}
{924, {2,6689,16238,23292}}
{1510, {2,6694,6695,37649}}
X(40462) lies on these lines: {1, 11334}, {21, 1626}, {100, 1610}, {1001, 23850}, {1324, 3913}, {3736, 7087}
X(40463) lies on these lines: {37, 42}, {244, 21877}, {321, 1930}, {2205, 3722}, {3294, 3681}, {3936, 22009}, {3954, 21820}, {3994, 22039}, {3995, 40007}, {4043, 18138}, {21020, 21808}, {22000, 24071}, {22021, 24067}, {30821, 31993}, {35892, 36808}
X(40464) lies on these lines: {514, 16604}, {650, 29226}, {663, 1575}, {812, 14838}, {978, 21791}, {4147, 17448}, {25127, 31286}
X(40465) lies on these lines: {9, 3900}, {1212, 1734}
X(40466) lies on these lines: {3907, 23905}, {4129, 28840}, {4151, 6537}, {21052, 23897}
X(40467) lies on these lines: {55, 21173}, {65, 32475}, {513, 4162}, {521, 4086}, {522, 3057}, {1459, 2646}, {1837, 20293}, {17606, 20316}
X(40468) lies on these lines: {2, 32094}, {1086, 6545}, {3452, 24198}, {6546, 6547}, {24232, 33117}
X(40469) lies on these lines: {2, 14588}, {115, 8029}, {1648, 10189}, {11123, 23991}
X(40470) lies on these lines: {15526, 23616}
X(40471) lies on these lines: {38, 7192}, {244, 4369}, {512, 4895}, {513, 21350}, {523, 2254}, {661, 756}, {984, 31290}, {4132, 4784}, {4151, 4467}, {4642, 4761}, {4988, 21727}, {24325, 26822}, {28758, 31264}
X(40472) lies on these lines: {514, 20042}, {764, 1647}, {900, 4088}, {6546, 17780}
X(40473) lies on these lines: {14838, 14991}
X(40474) lies on these lines: {2, 21390}, {142, 513}, {649, 25604}, {812, 14838}, {2254, 3667}, {3008, 3063}, {3664, 20980}, {3912, 20906}, {4049, 17758}, {4129, 21188}, {4667, 39521}, {4775, 17050}, {4776, 5249}, {17234, 20949}, {17278, 21007}, {20516, 21200}, {21099, 27485}, {21348, 29571}, {21617, 24002}, {23696, 24220}, {23828, 27147}, {30835, 33864}
X(40475) lies on these lines: {661, 5949}, {2610, 14321}
X(40476) lies on these lines: {2, 1726}, {20, 10005}, {35, 984}, {75, 16551}, {1782, 2550}, {4859, 16560}, {21368, 25728}
X(40477) lies on these lines: {2, 648}, {542, 547}, {549, 6720}, {2799, 22247}
X(40478) lies on these lines: {2, 670}, {804, 6722}, {2882, 6680}, {3589, 34383}, {5969, 6683}, {22110, 32530}
X(40479) lies on these lines: {2, 668}, {10, 24739}, {39, 30963}, {291, 3624}, {537, 4698}, {538, 20530}, {1001, 8671}, {1125, 6683}, {2787, 6667}, {2810, 3589}, {3816, 4045}, {3825, 7861}, {3934, 16604}, {6680, 6691}, {7786, 20671}, {7808, 25524}, {7834, 10200}, {17290, 24497}, {17793, 19862}, {22247, 35103}, {24508, 27191}, {31239, 31997}, {32020, 39736}
X(40480) lies on these lines: {2, 45}, {10, 9041}, {44, 7238}, {75, 29629}, {140, 29243}, {141, 4384}, {142, 3589}, {239, 28337}, {320, 29607}, {335, 4751}, {524, 3008}, {527, 6687}, {528, 1125}, {536, 17067}, {537, 3634}, {549, 24827}, {583, 29749}, {594, 17283}, {597, 4675}, {673, 15668}, {900, 6667}, {1213, 17291}, {1656, 24828}, {1738, 4702}, {2325, 28297}, {2786, 6722}, {2796, 19878}, {3090, 24813}, {3526, 24833}, {3533, 24817}, {3619, 32029}, {3624, 24715}, {3629, 17298}, {3631, 17348}, {3662, 17329}, {3664, 6329}, {3739, 9055}, {3763, 4437}, {3823, 9053}, {3826, 36480}, {3836, 5846}, {3912, 4395}, {3932, 31252}, {3943, 17266}, {3946, 29606}, {4000, 17243}, {4014, 16482}, {4360, 29589}, {4361, 29616}, {4393, 17234}, {4399, 17231}, {4402, 17309}, {4405, 17294}, {4432, 19862}, {4643, 31183}, {4644, 31189}, {4657, 16593}, {4659, 4859}, {4665, 17284}, {4688, 29596}, {4708, 31211}, {4748, 17259}, {4759, 17768}, {4767, 33148}, {4781, 24542}, {4871, 17070}, {4969, 17297}, {5222, 17313}, {5437, 16560}, {6547, 6633}, {6666, 17235}, {6707, 17384}, {7227, 17357}, {7228, 17353}, {7232, 37650}, {8252, 24843}, {8253, 24842}, {9780, 24841}, {16419, 24822}, {16706, 16826}, {17119, 29579}, {17227, 17330}, {17232, 17362}, {17241, 17388}, {17244, 17395}, {17246, 17263}, {17255, 18230}, {17293, 36807}, {17320, 29626}, {17334, 17338}, {17340, 17341}, {17352, 17365}, {17367, 17392}, {17370, 17398}, {17376, 32455}, {17382, 29571}, {17394, 32096}, {17399, 29581}, {17724, 17780}, {17755, 31238}, {19872, 24821}, {24593, 35466}, {24690, 31199}, {24691, 31200}, {24818, 32786}, {24819, 32785}, {26982, 27159}, {29598, 36834}, {29853, 34612}
X(40480) = complement of X(4422)
X(40481) lies on these lines: {2, 6528}, {2797, 6722}, {3526, 14941}
X(40482) lies on these lines: {2, 18026}, {140, 2808}, {2798, 6722}
X(40483) lies on these lines: {2, 664}, {116, 5845}, {528, 3828}, {952, 6710}, {1213, 23674}, {1565, 31273}, {2785, 6722}, {3015, 6707}, {3039, 24318}, {3634, 28850}, {5834, 30808}, {6366, 6667}, {9317, 31192}, {9780, 14942}, {21044, 26007}
X(40484) lies on these lines: {2, 648}, {5, 9530}, {140, 542}, {287, 3619}, {2799, 6722}, {3763, 15595}, {6723, 9033}
X(40485) lies on this line: {2, 18334}
X(40486) lies on these lines: {2, 892}, {99, 23991}, {523, 6722}, {524, 22244}, {7804, 18122}, {9182, 31274}
X(40487) lies on these lines: {2, 4562}, {350, 29607}, {3008, 20530}, {17278, 36232}
X(40488) lies on these lines: {2, 4555}, {190, 6547}, {519, 6687}, {3008, 22247}, {4384, 36230}, {4409, 32106}, {6722, 25666}, {25031, 31285}, {29629, 35957}
X(40489) lies on this line: {2, 39013}
X(40490) lies on this line: {2, 39018}
X(40491) lies on these lines: {10, 15281}, {313, 22008}, {321, 908}, {3947, 15282}, {20245, 21061}
X(40492) lies on these lines: {321, 22271}, {1233, 22275}, {21867, 31993}, {21883, 21889}
X(40493) lies on these lines: {75, 354}, {76, 85}, {210, 16284}, {305, 17786}, {322, 325}, {345, 7196}, {561, 20923}, {1088, 3693}, {1214, 31627}, {1909, 3974}, {4847, 4967}, {6374, 30048}, {10030, 18141}, {17026, 19804}, {17241, 18045}, {18142, 20942}, {18157, 40072}, {18743, 20448}, {20646, 20946}, {20930, 20945}, {24524, 30615}, {27538, 30806}, {30988, 33116}
X(40494) lies on these lines: {3, 520}, {523, 2072}, {2972, 12079}, {34333, 36169}
X(40495) lies on these lines: {75, 1734}, {76, 4391}, {99, 2864}, {274, 905}, {667, 7255}, {670, 35156}, {693, 784}, {772, 2084}, {824, 1577}, {826, 850}, {3122, 24238}, {3126, 33933}, {3900, 17143}, {4077, 23877}, {4142, 20518}, {4705, 20906}, {8714, 20888}, {15413, 17924}, {16992, 22160}, {17072, 20907}, {17496, 34284}, {20909, 35560}, {21056, 35554}, {21438, 24290}, {23100, 23596}, {23685, 33935}
X(40495) = isotomic conjugate of X(692)
X(40495) = polar conjugate of isogonal conjugate of X(15413)
X(40495) = polar conjugate of barycentric product of circumcircle intercepts of Stevanovic circle
X(40495) = complement of polar conjugate of isogonal conjugate of X(23191)
X(40495) = anticomplement of polar conjugate of isogonal conjugate of X(23228)
X(40495) = crossdifference of every pair of points on line X(560)X(1501)
X(40495) = trilinear pole of line X(16732)X(17878)
X(40496) lies on these lines: {1, 7428}, {55, 14753}, {56, 34281}, {58, 23383}, {333, 1610}, {978, 20470}, {3679, 39578}, {8053, 37296}, {11194, 15654}
X(40497) lies on this line: {14838, 23058}
X(40498) lies on this line: {1331, 22154}
X(40499) lies on these lines: {1, 17048}, {8, 27010}, {100, 3903}, {101, 692}, {512, 8671}, {522, 4568}, {644, 663}, {660, 932}, {668, 3907}, {831, 29067}, {874, 4561}, {997, 32941}, {1026, 4595}, {1293, 28528}, {1310, 29052}, {2605, 3908}, {2705, 28486}, {3009, 19589}, {3810, 33946}, {4069, 30728}, {4073, 20753}, {8691, 29187}, {14714, 28071}, {28552, 28564}
X(40500) lies on these lines: {522, 4546}, {523, 1459}, {650, 28161}, {900, 21119}, {1638, 14353}, {17420, 24457}, {21106, 28179}
X(40501) lies on these lines: {10, 20529}, {100, 17943}, {210, 21890}, {1018, 4705}, {2533, 21272}, {3293, 8298}, {3699, 3799}, {3939, 21891}, {4103, 4155}, {4553, 17934}, {21295, 21604}, {21383, 23861}, {21725, 21888}
X(40502) lies on these lines: {523, 2487}, {690, 31290}, {4024, 4705}
X(40503) lies on these lines: {519, 1279}, {1086, 6550}
X(40504) lies on these lines: {1, 5132}, {10, 15281}, {37, 40147}, {42, 13476}, {75, 3681}, {517, 4698}, {518, 596}, {759, 6577}, {969, 22282}, {2214, 2280}, {2218, 21059}, {3739, 22325}, {4850, 39739}, {9278, 21863}, {19874, 22299}, {22279, 39712}, {22293, 40005}
X(40505) lies on these lines: {354, 1122}, {497, 17183}, {1201, 1279}, {1827, 1828}, {2347, 2348}, {3057, 3059}, {3271, 6067}, {7083, 26357}, {8605, 11246}, {9309, 24477}
X(40506) lies on this line: {5055, 35912}
X(40507) lies on this line: {2, 31646}
X(40508) lies on these lines: {2, 31645}, {536, 20688}, {1015, 36957}, {27195, 31625}
X(40509) lies on these lines: {2, 31647}, {519, 3836}, {1000, 25031}, {1016, 27191}, {1086, 36954}, {3008, 16704}, {3912, 31011}, {4358, 20432}, {17305, 32013}
X(40510) lies on these lines: {2, 31648}, {1146, 36956}, {1275, 31640}
X(40511) lies on these lines: {2, 31644}, {115, 36953}, {325, 31068}, {523, 6722}, {524, 1570}, {3589, 5967}, {4045, 15464}, {4590, 14061}, {5461, 9164}
X(40512) lies on this line: {140, 35912}
X(40513) lies on these lines: {543, 23991}, {1641, 22247}, {6722, 8371}
X(40514) lies on this line: {545, 6547}
X(40515) lies on these lines: {2, 2140}, {10, 15281}, {37, 17758}, {76, 4043}, {98, 6577}, {101, 29775}, {213, 17761}, {218, 1751}, {226, 20616}, {321, 4006}, {1001, 22006}, {3293, 13576}, {3912, 22010}, {4049, 22046}, {4079, 23100}, {5134, 6625}, {17152, 29773}, {22018, 24072}, {22020, 34258}
X(40516) lies on these lines: {8, 22271}, {55, 5283}, {76, 22275}, {13576, 22300}
X(40517) lies on these lines: {3, 36880}, {39, 597}, {83, 31128}, {126, 1506}, {574, 34161}, {1649, 3005}, {6680, 7664}, {7794, 23992}, {7813, 21906}, {7820, 14357}
X(40518) lies on these lines: {651, 1625}, {1813, 22154}
X(40519) lies on these lines: {3, 596}, {35, 39949}, {55, 40148}, {100, 1634}, {190, 4057}, {692, 8671}, {3733, 4553}, {4436, 4613}, {4557, 21003}, {8053, 37586}, {8683, 23703}, {23344, 36075}
X(40520) lies on these lines: {}
X(40521) lies on these lines: {10, 2486}, {37, 3122}, {72, 7206}, {100, 8701}, {190, 513}, {210, 6535}, {518, 4439}, {594, 4092}, {644, 692}, {651, 3908}, {674, 2325}, {756, 2643}, {765, 8702}, {872, 4094}, {1018, 4069}, {1023, 35327}, {1026, 4436}, {1084, 1500}, {1215, 21254}, {2321, 22271}, {2511, 21859}, {3271, 4370}, {3294, 22328}, {3678, 4535}, {3688, 17340}, {3690, 6057}, {3710, 22299}, {3882, 23343}, {3900, 3939}, {3932, 20718}, {3943, 20683}, {3950, 22277}, {3952, 4010}, {3967, 4377}, {3985, 20723}, {4009, 38472}, {4015, 6538}, {4043, 22289}, {4072, 22312}, {4082, 22276}, {4103, 4155}, {4422, 14839}, {4473, 16482}, {4505, 33948}, {4517, 17281}, {4605, 6370}, {4712, 17463}, {6386, 36863}, {13476, 17243}, {17142, 29396}, {20691, 21900}, {20713, 20714}, {20715, 21864}, {21070, 22292}, {21071, 22293}, {21096, 22317}, {22280, 30730}, {35309, 35310}
X(40522) lies on these lines: {42, 678}, {214, 39697}, {662, 28210}, {667, 4557}
X(40523) lies on these lines: {}
X(40524) lies on this line: {190, 12078}
X(40525) lies on these lines: {190, 21838}, {1015, 9427}, {1084, 1086}, {1258, 17946}, {3125, 21823}, {9468, 37128}
X(40526) lies on these lines: {37, 142}, {513, 4557}, {4552, 24002}
X(40527) lies on these lines: {1086, 16596}, {1167, 17102}, {1214, 34051}, {3942, 39006}, {18191, 35014}, {36100, 40397}
X(40528) lies on these lines: {11, 1357}, {190, 1222}, {210, 1261}, {1156, 1476}, {2310, 3248}, {2330, 14100}, {3119, 38991}, {3271, 4081}, {17604, 40420}, {20359, 32017}
X(40529) lies on these lines: {1086, 1213}
Centers and perspectors of 1st Ceva conics: X(40530)-X(40564)
This preamble is contributed by Clark Kimberling and Peter Moses, November 30, 2020.
In the plane of a triangle ABC, let L be the line u x + v y + w z = 0, and let U be the point u : v : w, this being the isotomic conjugate of the trilinear pole of L. Let P = p : q : r be a point. The 1st (U,P)-Ceva conic, introduced here as the locus of X such that the P-Ceva conjugate of X is on the line L, is given by
u p (-p/x + q/y + r/z) + v q (p/x - q/y + r/z) + w r (p/x + q/y - r/z) = 0.
The center of the conic is the point
p (-p q^2 u v - 3 p q r u v + p q^2 v^2 - q^2 r v^2 - 3 p q r u w - p r^2 u w - 2 p q r v w - 3 q^2 r v w - 3 q r^2 v w + p r^2 w^2 - q r^2 w^2) : :
If U = X(2), then the center of the 1st (U,P)-Ceva conic is the complement of the complement of P, which is also the centroid of {A,B,C,P}, and also the center of the bicevian conic of X(2) and P. (Randy Hutson, December 18, 2020)
The appearance of (i,j,k) in the following list means that the center of the 1st (X(i),X(j))-Ceva conic is X(k):
(2,1,1125), (2,2,2), (2,3,140), (2,4,5), (2,5,3628), (2,6,3589), (2,7,142), (2,8,10), (2,10,3634), (2,25,6677), (2,54,6689), (2,56,6691), (2,57,6692), (2,58,6693), (2,63,5745), (2,69,141), (2,74,6699), (2,75,3739), (2,76,3934), (2,81,6703), (2,85,6706), (2,86,6707), (2,92,6708), (2,98,6036), (2,99,620), (2,100,3035), (2,101,6710), (2,105,6714), (2,107,6716), (2,108,6717), (2,109,6718), (2,110,5972), (2,111,6719), (2,112,6720), (2,190,4422), (2,264,14767), (2,476,22104), (2,511,511), (2,512,512), (2,513,513), (2,514,514), (2,517,517), (2,518,518), (2,522,522), (2,523,523), (2,525,525), (2,648,23583), (2,651,36949), (2,664,17044), (2,668,27076), (2,670,36950), (2,690,690), (2,693,4885), (2,805,22103), (2,842,16760), (2,850,30476), (2,901,22102), (2,925,34844), (2,930,13372), (2,1303,34839), (2,1897,15252), (1,2,3739), (1,75,10), (1,85,40216), (75,1,37), (75,2,1125), (75,6,14751), (75,57,1), (75,99,14750), (75,190,14752), (75,513,4979), (75,1029,8143), (7,7,5452), (264,3,216), (69,4,6), (76,6,39), (8,7,1), (7,8,9), (298,13,396), (299,14,395), (274,37,16589), (34387,59,13006), (4,69,3), (6,76,141), (523,99,523), (693,100,650), (850,110,647), (514,190,514), (338,249,34990), (3,264,5), (37,274,3739), (99,523,115), (599,598,597), (525,648,525), (513,668,513), (1111,765,24036), (1086,1016,4422), (23994,1101,23993), (23989,1252,23988), (1146,1275,17044), (32,1502,626), (594,1509,17045), (10,2,6707), (514,1,14752), (514,2,4422), (514,4,14774), (514,6,14780), (514,7,14759), (514,8,14740), (514,264,14771), (514,664,17494), (514,668,31290), (514,903,39349), (514,1897,522),
The appearance of {i, {j(1),j(2),...}} in the following list means that the 1st (X(2),X(i))-Ceva conic passes through the points X(j1), X(j2),... :
{1, {11,214,244,1015,8054,8299,10494,14714,17417,17419,17421,17761,17793,34586,34587,34588,34589,34590,34591,34592,34593,38978,38979,38980,38981,38982,38983,38984,38985,38986,39046}
{2, {115,1015,1084,1086,1146,2454,2455,2482,3163,4370,5997,6184,11672,13466,15166,15167,15449,15525,15526,15527,17416,17429,18334,20532,23967,23972,23976,23980,23986,23992,35066,35067,35068,35069,35070,35071,35072,35073,35074,35075,35076,35077,35078,35079,35080,35081,35082,35083,35084,35085,35086,35087,35088,35089,35090,35091,35092,35093,35094,35095,35110,35111,35112,35113,35114,35115,35116,35117,35118,35119,35120,35121,35122,35123,35124,35125,35126,35127,35128,35129,35130,35131,35132,35133,35134,35135,35508,35509,39008,39009,39010,39011,39012,39013,39014,39015,39016,39017,39018,39019,39020,39021,39022,39023,39206,39207,39208,39209}
{3, {125,1511,2972,17423,34467,35071,38983,38999,39000,39001,39002,39003,39004,39005,39006,39007,39071}
{4, {11,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,1312,1313,1560,1566,2039,2040,2679,3258,3259,5099,5139,5190,5509,5510,5511,5512,5513,5514,5515,5516,5517,5518,5519,5520,5521,5522,5950,5952,5993,6092,9151,9152,9193,10017,11569,11792,12494,12624,13141,13234,13249,13499,13517,13612,13613,13870,13871,13872,13994,13999,14103,14672,15169,15241,15607,15608,15609,15610,15611,15612,15613,15614,16177,16178,16188,16221,16938,18402,18809,20033,20389,20551,20619,20620,20621,20622,20623,20625,21662,22474,25640,25641,25642,31653,31654,31655,31841,31842,31843,31844,31845,33330,33331,33333,33504,34111,34113,35579,35580,35581,35582,35583,35584,35585,35586,35587,35588,35589,35590,35591,35592,35593,35594,35967,35968,35969,35970,35971,35972,36471,36472,38957,38958,38959,38960,38961,38962,38963,38964,38965,38966,38967,38968,38969,38970,38971,38972,38973,38974,38975,38976,38977,39535,40357,40358}
{5, {137,2972,6592,8902,17433,35442,39019}
{6, {125,1084,3124,6593,7668,8054,15450,17413,36213,38987,38988,38989,38990,38991,38992,38993,38994,38995,38996,38997,38998,39067,39068,39075,39079,39080}
{7, {11,1086,8287,10427,13609,16591,16592,16593,16594,16595,16596,16597,20343,21623,26932,34846,38989,39007,39063}
{8, {11,1145,1146,2968,3756,4904,6739,6741,7358,8286,16613,38992,39004,39050}
{10, {115,244,3120,6741,21709,24185}
{19, {244,5521,14936,17463,38991,39069,39070}
{25, {1084,5139,17423,20975,39025,39072}
{54, {125,8901,11597,17433,38984,39013,39027,39045,39233}
{56, {3259,8054,20982,34467,39015,39025}
{57, {1015,2170,5514,19593,24237,38991,39006,39048}
{58, {124,8054,18191,39006,39016,39029}
{59, {15608,38984,38989,39004,39017,39026}
{63, {6506,26932,31653,34591,35072,39006}
{69, {125,5181,6388,7358,15526,15595,17421,26932}
{74, {3,125,2088,3134,39174,39987}
{75, {244,1086,2968,4858,5515,6377,16586,17755,38995,39040}
{76, {115,339,3124,5976,7664,21208,36901,39000}
{81, {1015,3125,5517,17197,19557,26932}
{85, {1111,1146,3119,36905,38959,38980}
{86, {1086,3120,6627,6651,8054,16726,38960}
{92, {1146,4858,5190,16596,34591,39039}
{98, {3,115,868,17423,34156,34810,38997,39078}
{99, {2,3,39,114,618,619,629,630,641,642,1125,1649,2482,3413,3414,3666,5664,5745,5976,6292,6337,6503,6509,6626,7710,8290,8299,8786,10291,10335,11147,11165,13701,13821,13882,13934,14713,15349,15810,15814,15819,15850,22848,22892,27929,30471,30472,33364,33365,33614,33615,33616,33617,33618,33619,33620,33621,34452,34834,34835,38998,39090,39091,39094,39096,39098,39100,39102,40125}
{100, {1,3,9,10,119,142,214,442,600,1145,2092,3126,3307,3308,3647,5507,6184,6260,6594,6600,10427,10472,11517,11530,12631,12639,12640,12864,13089,15346,15347,15348,17057,17060,18258,18642,19557,19584,22754,34261,35204,39041,39048}
{101, {3,118,354,2140,3136,3789,5452,20970,32664,39029,39046}
{105, {3,1015,3140,3675,5511,34160,39025}
{107, {3,4,133,800,1249,3184,6523,14363,15259,16253,20208,23976,33549,33580}
{108, {3,56,429,12610,25640,36103}
{109, {3,65,117,478,3142,3454,24220,34281,36033,39037,39070}
{110, {3,5,6,113,141,206,942,960,1147,1209,1493,1511,2574,2575,2883,4550,5181,6593,8542,10639,10640,10960,10962,11597,11598,11672,15116,15748,16254,17713,19576,19602,21905,22333,22966,32391,33537,33556,34116,34472,34586,34830,34831,37836,37890,39072,39083,39084}
{111, {3,1084,3143,5512,21906,34158}
{112, {3,32,132,427,3162,21248,22391,39045,39071,39086}
{162, {9,1104,36033,36103,39038,39039}
{190, {2,9,37,440,1213,3161,4370,5513,6544,6651,15487,16590,16593,17755,21838,24771,27481,31336,36911,38015,39056,39059,40181}
{264, {136,338,2972,14920,15526,34834,36901,38987}
{291, {10,1015,5518,22116,27846,38995}
{476, {3,30,523,3003,6663,14993,15295,23967,25641,31378,39170}
{511, {511,2679,38987,39000,39009,39073}
{512, {512,2679,3005,21905,23301,38978,38988,39001,39010}
{513, {513,661,3259,3835,6615,14434,17115,27854,31946,38979,38989,39002,39011}
{514, {514,650,661,1566,4521,4988,6544,27929,35092,38980,38990,39003}
{517, {517,3259,33646,35014,38981,39004}
{518, {518,5519,17435,38980,38989,39012,39077}
{522, {522,650,656,6129,6608,6615,7658,10017,23757,35091,38981}
{523, {523,647,1649,3005,3258,4988,8562,13636,13722,17433,17436,21196,23992,31945,31947,35443,35444,38982,38987,39005}
{525, {525,647,6587,14401,17434,33504,35441,39000,39008}
{644, {1,220,1040,4847,5452,24152,24153,24181,24771}
{648, {2,6,216,233,1196,1249,1560,3162,3163,8105,8106,8968,14091,14401,15595,18311,32750,37891,37895,39034,39078,39081,40179}
{651, {6,9,223,226,478,1211,5452,13388,13389,18591,20262,20623,23980,39032,39049,39050,39055,39063}
{653, {9,57,281,1108,1214,1249,1901,23986,39033}
{655, {9,216,650,2245,3911,8609}
{658, {7,9,3160,17113,23058,23972,40133}
{660, {9,141,513,518,2238,3789,9470,20335,36906}
{662, {9,1100,5249,5949,6505,32664,34544,35069,39040,39042,39043,39069}
{664, {1,2,223,1212,1214,2582,2583,3160,3752,6505,16585,16586,17056,18641,31534,31535,35110,36905,39035,39046,39047,39066}
{666, {2,650,2238,3008,3290,5375,5452,16588,27942,35113}
{668, {2,10,120,1211,3452,3789,6376,6552,6554,13466,14434,16589,16594,17793,21530,28651,36912,39028}
{670, {2,126,141,1368,3739,3741,6338,6374,6389,10472,20339,21246,21248,27854,32746,34021,35073,39080}
{677, {6,518,521,6600,16608,39026}
{685, {206,232,523,1249,1503,6389,7710,36899,39085}
{687, {577,1249,2501,3003,14918,36830}
{690, {690,1648,1649,11053,21905,35582}
{691, {3,187,858,3005,15477,15899,16188,36830,39169}
{693, {514,522,905,1577,3126,15612,35094}
{789, {3,3821,6376,6651,26601,37596}
{799, {9,1107,4357,6376,6626,34021,35068,39044,39057}
{805, {3,511,512,626,8623,9467,21531,33330,39088,39092}
{835, {3,37,958,4205,4657,37592}
{842, {3,5099,18334,36189,38987,39233}
{850, {523,525,2485,5664,18311,18314,21187,23285,35088,38971}
{874, {740,812,1966,6651,8299,26582,39028}
{876, {244,661,665,3005,3837,4369,9508,24003}
{879, {125,647,5972,6130,24284,30476}
{885, {11,650,676,3035,3716,4885,17115}
{889, {2,513,536,2229,4871,9296}
{892, {2,523,524,3291,5159,8542,9165,15899,23991,31655,31998,35087,39061}
{901, {3,513,517,1329,2245,31841,39026}
{925, {3,131,216,6389,10600,24245,24246,31377,33553,34833,34851,34853,35067,37565,37864}
{927, {3,241,514,516,857,3160,6554,33331,35093}
{930, {3,128,140,570,6592,8562,15345,17707,21975,23702,34828,39171}
{934, {3,57,223,946,3452,6609,20205,36908}
{1296, {3,126,574,10354,30739,39027}
{1303, {3,129,389,3819,21243,34850}
{1304, {3,403,12096,14385,18809,36896,40135}
{1309, {3,515,522,860,7952,36944,39535}
{1576, {51,206,22391,34452,34845,40368}
{1633, {614,1486,15487,15497,18589,40125}
{1783, {10,614,3162,5452,7079,20621,36103,40181}
{1897, {1,37,1249,1834,2588,2589,4000,7952,17102,18643,20619,23050,23757,23972,36103}
{1978, {37,75,3061,6374,6376,16604,18277,19584,20532,21024}
The appearance of {i, {j(1),j(2),...}
in the following list means that the 1st (X(1),X(i))-Ceva conic passes through the points X(j1), X(j2),... :
{2, {244,1086,2968,4858,5515,6377,16586,17755,38995,39040}
{75, {244,1099,1109,1111,4712,4736,4738,10504,17879,23996,24010,24014,24023,24026,24028,24031,24034,24038}
{76, {1086,1111,1227,3123,21208,34387}
{85, {1111,4858,17880,17886,20443,20900}
{92, {1109,4858,20431,20639,20901,20902,21427}
{99, {8,1125,1631,4736,4996,23928}
{100, {63,142,1631,1962,22271,27474}
{190, {2,8,63,321,1281,2292,3413,3414,3578,4712,17741,20880,21129,33890}
{304, {17875,17876,17877,17878,17879,17880,17881,20902}
{514, {514,523,20504,20906,21120,21124,21129,21130}
{651, {63,226,2650,20896,21147,22130}
{662, {1,63,1930,2172,2582,2583,3687,5249,14213,16586,17746,17866,19572,19600,23996,38822}
{664, {1,8,347,1441,17797,18697,20504,21147,23528,23555,23668,23669,24028}
{668, {8,10,75,3728,4647,4738,4793,11677,22271,28616}
{789, {75,1281,1631,3778,3821,17797,26234}
{799, {38,63,75,1227,4357,4359,17755,20898,24038}
{811, {1,75,1099,1895,2588,2589,6734,17863,17872,17875,23537,23661,23665}
{927, {347,516,523,1631,5002,5003,11677}
{1577, {656,1577,8061,21124,21192,30591}
{1978, {75,321,6382,18697,20431,20895,20900,21020,27474}
The appearance of {i, {j(1),j(2),...}
in the following list means that the 1st (X(75),X(i))-Ceva conic passes through the points X(j1), X(j2),... :
{1, {244,678,2310,2632,2638,2643,3248,4094,4117,10501,23063,24012}
{2, {11,214,244,1015,8054,8299,10494,14714,17417,17419,17421,17761,17793,34586,34587,34588,34589,34590,34591,34592,34593,38978,38979,38980,38981,38982,38983,38984,38985,38986,39046}
{6, {1015,2170,3248,3270,11998,17455,17475,21762}
{19, {2170,2643,3708,17462,17463,17464,17465,17466,20600,38345}
{57, {244,2170,2446,2447,2611,4128,7004,17460,20366,35065}
{92, {1109,2632,34589,35201,37754,38350}
{99, {55,192,2309,3666,4094,4366,11997,23928,38814,39915}
{100, {1,42,55,678,1962,3158,3251,3795,8298,8299,18673,27787,38349}
{101, {6,37,48,55,354,2294,2590,2591,3725,5638,5639,17454,17455,19561,19586,20284}
{108, {33,55,56,73,204,207}
{109, {31,55,65,221,2067,2292,6502}
{110, {55,202,203,215,501,942,2308,3157,40370}
{163, {31,38,48,563,1953,2260,2269,2578,2579,17453,19578,19603}
{190, {1,37,192,2292,2667,3057,3159,4065,4319,5497,8393,8394,17460,17461,17464,17475,18674,19582,23757,34587,39916}
{513, {512,513,663,3251,4162,4983,38348}
{514, {513,523,650,1459,14284,21104,23752,23757,23758,34590}
{651, {1,6,73,221,500,1201,1419,1480,2293,2574,2575,2650,3157,6126,9502,18675,28369,34586,35197}
{653, {1,65,207,1108,1148,2294,2331,2658,3924,4336}
{658, {1,354,614,20277,31526,40133}
{662, {1,48,214,501,820,1100,1193,1964,2584,2585,2646,17457,17462,38348,38814}
{664, {192,1419,3158,3752,7032,14100,23668,31526}
{666, {6,192,385,518,523,3290,6163,33674}
{668, {2,42,192,3056,3728,17149,19581,19586,28369}
{799, {1,38,1107,3720,17149,17466,17793,18671,20362,21334,21336,39915}
{813, {38,55,649,672,3747,20358,40155}
{901, {15,16,55,512,517,902,1480,17461,39148}
{927, {55,241,6654,9358,21104,31526}
{1018, {37,42,836,1100,2269,3720,4094,17441,17456}
{1020, {37,65,73,1104,2260,2599,2646,2654}
{1029, {11,115,3024,10036,14101,23063}
{1783, {6,42,204,614,2331,8105,8106,21148,22063}
The appearance of {i, {j(1),j(2),...}
in the following list means that the 1st (X(10),X(i))-Ceva conic passes through the points X(j1), X(j2),... :
{2, {1086,3120,6627,6651,8054,16726,38960}
{99, {1,21,86,1125,2309,8053,18650,28627}
{100, {2,42,142,8021,8053,18166,22279}
{190, {1,2,3294,3995,4368,4375,8025,17170,17175,17185,17192,30568}
{662, {2,21,81,1193,1790,5249,17169,17190,17191}
{799, {2,86,3720,4357,17183,17195,17196,18133,18651,31008}
{1414, {7,21,58,4303,4357,10571,12047}
The appearance of {i, {j(1),j(2),...}
in the following list means that the 1st (X(75),X(i))-Ceva conic passes through the points X(j1), X(j2),... :
{1, {1,37,192,2292,2667,3057,3159,4065,4319,5497,8393,8394,17460,17461,17464,17475,18674,19582,23757,34587,39916}
{2, {2,9,37,440,1213,3161,4370,5513,6544,6651,15487,16590,16593,17755,21838,24771,27481,31336,36911,38015,39056,39059,40181}
{4, {46,121,193,1213,2899,2901,3057}
{6, {1,43,194,213,19579,19587,20665,20671,21757,21838,22024,23552,23553,33688,39929}
{7, {2,57,145,3021,3057,3175,8055,16594}
{8, {8,9,40,72,144,1145,3057,3059,3307,3308,3588,3650,6068,12665,12670,12682,16008,18239,21677,31938,36922}
{9, {165,3057,3177,4712,4936,20665,22027,27538}
{10, {10,71,191,1213,1654,2292,21035,21038,21677}
{37, {846,1334,1655,2292,3971,4368,21838}
{42, {42,1045,2667,20681,21035,21080,21838}
{69, {20,63,72,329,440,1763,2582,2583,17170,17742,22001,31547,31548}
{75, {2,8,63,321,1281,2292,3413,3414,3578,4712,17741,20880,21129,33890}
{80, {10,484,513,519,2183,3057,16590,20072,36926}
{85, {7,9,169,3970,17170,17464,20880}
{86, {1,2,3294,3995,4368,4375,8025,17170,17175,17185,17192,30568}
{92, {9,19,5905,18674,20431,22021}
{100, {513,522,649,4057,8640,17494,38349}
{101, {4040,4057,4064,4079,21225,38367}
{141, {2896,3954,16555,17192,17744,22026}
{190, {514,649,3234,3239,4024,4375,6544,24979,31182}
{238, {659,672,2108,4368,17475,30667}
{239, {239,17475,17755,21832,24578,33888}
{264, {4,321,440,1726,3730,17776,22000,34335}
{274, {37,75,16552,17175,20880,22011,25082}
{291, {37,513,672,726,894,1757,9334,9339,17759,21035}
{304, {346,4329,17170,18596,18674,20336,22005}
{306, {71,306,440,3151,8804,18598,18674}
{312, {9,321,329,346,1766,21078}
{314, {312,321,1764,3057,3869,17185,22022}
{319, {2895,3219,3578,3648,17781,31938}
{333, {9,63,573,17185,20665,21061}
{334, {10,3912,4391,4645,17192,20602,20880,31647}
{335, {2,3509,4024,4037,6542,40217}
{350, {726,812,3685,4368,17738,17755,17794}
{514, {4370,4440,5540,14442,17464,22035}
{518, {672,1282,4088,4712,10025,17464,17794,39350}
{519, {519,900,4370,5541,17460,17487}
{664, {514,522,6332,7265,30719,31605,38371}
{668, {513,514,4063,4391,20954,20979}
{673, {2,239,364,649,672,20665}
{740, {4037,4088,4368,13174,17759,39367}
{765, {100,644,1331,3952,4712,17460}
{870, {1,4384,17755,20880,22048,24349}
{903, {2,514,519,3218,17461,24428,31647,32094,36591}
{1016, {190,644,1018,4115,4370,17475,30720}
{1441, {226,440,1762,2475,3219,21677}
{1897, {522,4024,4064,23757,25259,38360}
The appearance of {i, {j(1),j(2),...}
in the following list means that the 1st (X(1),X(i))-Ceva conic passes through the points X(j1), X(j2),... :
{2, {115,1015,1084,1086,1146,2454,2455,2482,3163,4370,5997,6184,11672,13466,15166,15167,15449,15525,15526,15527,17416,17429,18334,20532,23967,23972,23976,23980,23986,23992,35066,35067,35068,35069,35070,35071,35072,35073,35074,35075,35076,35077,35078,35079,35080,35081,35082,35083,35084,35085,35086,35087,35088,35089,35090,35091,35092,35093,35094,35095,35110,35111,35112,35113,35114,35115,35116,35117,35118,35119,35120,35121,35122,35123,35124,35125,35126,35127,35128,35129,35130,35131,35132,35133,35134,35135,35508,35509,39008,39009,39010,39011,39012,39013,39014,39015,39016,39017,39018,39019,39020,39021,39022,39023,39206,39207,39208,39209}
{7, {3022,3271,4904,26932}
{99, {148,2482,7669,12076,14443}
{100, {16560,17060,22308,23402}
{190, {4370,4440,5540,14442,17464,22035}
{513, {9263,13466,14441,22323}
Let X*(i) denote the isotomic conjugate of X(i). The appearance of {i, {j(1),j(2),...}
in the following list means that the 1st (X*(1),X(i))-Ceva conic passes through the points X(j1), X(j2),... :
{1, {244,678,2310,2632,2638,2643,3248,4094,4117,10501,23063,24012}
{2, {115,1015,1084,1086,1146,2454,2455,2482,3163,4370,5997,6184,11672,13466,15166,15167,15449,15525,15526,15527,17416,17429,18334,20532,23967,23972,23976,23980,23986,23992,35066,35067,35068,35069,35070,35071,35072,35073,35074,35075,35076,35077,35078,35079,35080,35081,35082,35083,35084,35085,35086,35087,35088,35089,35090,35091,35092,35093,35094,35095,35110,35111,35112,35113,35114,35115,35116,35117,35118,35119,35120,35121,35122,35123,35124,35125,35126,35127,35128,35129,35130,35131,35132,35133,35134,35135,35508,35509,39008,39009,39010,39011,39012,39013,39014,39015,39016,39017,39018,39019,39020,39021,39022,39023,39206,39207,39208,39209}
{3, {2972,3270,3937,20759,20776,20975,22096,22371,23216}
{4, {125,2969,3270,5095,6754,8754,16240,24862,34980}
{6, {1015,1017,1977,2028,2029,3124,3269,9408,9419,9427,14936,20671,24973,35505,35506,39686,39687,39689}
{7, {11,1314,1315,1317,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,2446,2447,3020,3021,3022,3023,3024,3025,3026,3027,3028,3318,3319,3320,3321,3322,3323,3324,3325,3326,3327,3328,5577,5578,5579,5580,5581,5582,5997,6018,6019,6020,6021,6022,6023,6024,6025,6026,6027,6028,6029,7158,7159,7333,7334,10491,10501,10504,10505,10506,12809,13756,14027,15615,15616,16184,16185,22106,22107,31522,31524,31889,31890,31891,31892,31893,33964,33965,33966,34194,34228,35504}
{8, {11,3271,4081,4092,4152,4542,6062,6068,7062,7063,7065,7067,7068}
{13, {30452,30454,30459,30460,30461,30465,30466,30467}
{14, {30453,30455,30462,30463,30464,30468,30469,30470}
{37, {3121,3125,20690,21821,21833,36197}
{59, {55,56,181,202,203,215,1124,1335,1362,1397,1672,1673,1682,2007,2008,3235,3236,3237,3238,6056,7005,7006,7066,10799,12835,12836,12837,12838,12839,12840,12841,37993,39641,39642}
{69, {125,1565,2968,3937,16163,38554}
{75, {244,1099,1109,1111,4712,4736,4738,10504,17879,23996,24010,24014,24023,24026,24028,24031,24034,24038}
{76, {338,1086,3124,4437,23970,23978,23983,23989,26611,36789,36790,36791,36792,36793}
{99, {523,669,1649,2528,3233,3265,3733,7192,7253,24974,30508,30509}
{100, {513,667,3126,3251,3900,4705,4825}
{110, {512,520,3733,9426,21789,34983}
{190, {514,649,3234,3239,4024,4375,6544,24979,31182}
{249, {6,394,593,1501,1599,1600,7054,8041,11130,11131,35069,36790,39689}
{264, {339,1312,1313,2967,2968,2969,2970,2971,2972,2973,2974,21664,21665,21666,24977,34332,34333,34334,34335,34336,34337,34338,35012,38552}
{274, {3121,16725,16726,16727,16728,16729,16730,16731,16732,16733}
{523, {1649,5489,8029,8034,14443,23099}
{598, {8288,20380,20381,20382,20383,20384,20385,20386,35507}
{648, {525,2501,14401,15639,17925,17926,23090,32320}
{668, {513,693,4036,4397,14434,15632,25142,27855}
{765, {1,31,200,678,756,4712,8300}
{1016, {2,6,346,594,4366,4370,4437,7109,13425,13458}
{1101, {31,255,849,1094,1095,1917,23996}
{1252, {6,32,220,1017,1500,6184}
{1275, {2,220,279,394,1407,6354,6645,13436,13453,26611,35110,39686}
{1502, {115,23962,23965,23974,23989,32458}
{1509, {1086,1977,4366,26844,26846,26856}
X(40530) lines on these lines: {2, 19}, {4, 21160}, {5, 516}, {10, 7535}, {48, 25935}, {142, 24315}, {226, 34176}, {379, 1826}, {515, 15943}, {610, 26130}, {631, 30265}, {857, 1839}, {1125, 9895}, {1376, 1486}, {1441, 8756}, {1731, 24884}, {1788, 2263}, {1838, 25443}, {1842, 25015}, {1861, 4223}, {1953, 26006}, {2173, 18650}, {2182, 25964}, {2264, 18635}, {2822, 38601}, {2876, 9822}, {3589, 3812}, {3668, 3911}, {3739, 5745}, {4319, 5218}, {4698, 6677}, {5338, 26052}, {6642, 6796}, {6692, 14743}, {6711, 20202}, {7392, 11677}, {7522, 8804}, {9028, 16608}, {12047, 25651}, {14213, 28705}, {17073, 31184}, {17259, 26066}, {18594, 24683}, {18634, 24316}, {25514, 34822}, {28258, 34851}
X(40530) = complement of X(18589)
X(40530) = centroid of {A,B,C,X(19)}
X(40530) = center of bicevian conic of X(2) and X(19)
X(40531) lies on these lines: {2, 59}, {513, 36949}, {518, 15325}, {521, 3035}, {6718, 22102}, {21189, 23593}
X(40531) = complement of complement of X(59)
X(40531) = centroid of {A,B,C,X(59)}
X(40531) = center of bicevian conic of X(2) and X(59)
X(40532) lies on these lines: {2, 162}, {5, 25448}, {2806, 3035}, {2846, 6716}, {2850, 5972}, {4422, 15252}, {6679, 6708}, {8062, 24030}
X(40532) = complement of X(34846)
X(40532) = centroid of {A,B,C,X(162)}
X(40532) = center of bicevian conic of X(2) and X(162)
X(40533) lies on these lines: {1, 4595}, {2, 38}, {10, 1015}, {37, 20671}, {75, 32020}, {325, 3836}, {350, 28516}, {668, 1698}, {726, 20530}, {740, 1575}, {812, 3837}, {1086, 36217}, {1125, 6683}, {2023, 5750}, {2108, 4432}, {2787, 6702}, {2810, 6686}, {3035, 6685}, {3097, 30963}, {3227, 19875}, {3248, 18793}, {3634, 25109}, {3756, 3773}, {3821, 25350}, {3828, 33908}, {4368, 20331}, {4472, 25347}, {4672, 17754}, {4974, 37686}, {5248, 8671}, {6714, 31289}, {9263, 9780}, {14829, 16569}, {20457, 24512}, {21238, 39798}, {21337, 24443}, {24508, 24715}, {28850, 34460}
X(40533) = complement of X(17793)
X(40533) = centroid of {A,B,C,X(291)}
X(40533) = center of bicevian conic of X(2) and X(291)
X(40534) lies on these lines: {2, 644}, {9, 1565}, {101, 16593}, {120, 1083}, {218, 28740}, {344, 4561}, {514, 3039}, {518, 11730}, {525, 25095}, {551, 3589}, {918, 3960}, {997, 1807}, {1018, 26007}, {1086, 25600}, {1280, 3616}, {1292, 38386}, {1387, 6666}, {2006, 16594}, {2802, 33970}, {3035, 3887}, {5432, 36639}, {6714, 14839}, {15252, 24003}, {15903, 25072}, {20328, 24333}, {24398, 24795}, {25430, 34892}, {26074, 30857}, {27132, 28961}, {30618, 34847}, {30728, 36807}, {34625, 37650}
X(40534) = complement of X(4904)
X(40534) = centroid of {A,B,C,X(644)}
X(40534) = center of bicevian conic of X(2) and X(644)
X(40535) lies on these lines: {2, 196}, {5, 1158}, {676, 2804}, {1375, 37805}, {2846, 6716}, {5437, 20197}, {6692, 6708}, {14837, 23982}, {17044, 23583}, {17073, 20204}, {31190, 37695}, {36949, 39470}
X(40535) = complement of X(16596)
X(40535) = centroid of {A,B,C,X(653)}
X(40535) = center of bicevian conic of X(2) and X(653)
X(40536) lies on these lines: {2, 655}, {514, 36949}, {516, 6702}, {522, 3035}, {908, 7359}, {3911, 26011}, {10015, 23593}, {14838, 16578}
X(40536) = complement of complement of X(655)
X(40536) = centroid of {A,B,C,X(655)}
X(40536) = center of bicevian conic of X(2) and X(655)
X(40537) lies on these lines: {2, 658}, {142, 5851}, {3035, 6366}, {7658, 15252}
X(40537) = complement of X(13609)
X(40537) = centroid of {A,B,C,X(658)}
X(40537) = center of bicevian conic of X(2) and X(658)
X(40538) lies on these lines: {2, 660}, {9, 39344}, {238, 4447}, {513, 4422}, {518, 3008}, {1083, 36086}, {3035, 31286}, {4369, 24003}, {6005, 36954}, {17338, 36294}, {34807, 36280}
X(40538) = complement of X(38989)
X(40538) = centroid of {A,B,C,X(660)}
X(40538) = center of bicevian conic of X(2) and X(660)
X(40539) lies on these lines: {2, 662}, {141, 31186}, {190, 24636}, {620, 2786}, {645, 25469}, {3035, 5972}, {8286, 25533}, {9034, 36949}, {14838, 16578}, {17044, 23583}, {17359, 24384}, {24617, 24957}, {31201, 35466}
X(40539) = complement of X(8287)
X(40539) = centroid of {A,B,C,X(662)}
X(40539) = center of bicevian conic of X(2) and X(662)
X(40540) lies on these lines: {2, 666}, {514, 6710}, {522, 4422}, {620, 14838}, {997, 36230}, {1566, 34906}, {1944, 23593}, {3008, 34852}, {3814, 5461}, {4763, 22102}, {6547, 24203}, {6554, 35093}, {6714, 15325}, {10025, 29607}, {26685, 34361}
X(40540) = complement of X(35094)
X(40540) = centroid of {A,B,C,X(666)}
X(40540) = center of bicevian conic of X(2) and X(666)
X(40541) lies on these lines: {2, 677}, {521, 36949}, {3239, 15252}, {6712, 22102}, {8062, 23583}
X(40541) = complement of complement of X(677)
X(40541) = centroid of {A,B,C,X(677)}
X(40541) = center of bicevian conic of X(2) and X(677)
X(40542) lies on these lines: {2, 685}, {523, 23583}, {5972, 11595}, {6036, 37911}, {6716, 14341}
X(40542) = complement of complement of X(685)
X(40542) = centroid of {A,B,C,X(685)}
X(40542) = center of bicevian conic of X(2) and X(685)
X(40543) lies on these lines: {2, 687}, {6716, 12068}
X(40543) = complement of complement of X(687)
X(40543) = centroid of {A,B,C,X(687)}
X(40543) = center of bicevian conic of X(2) and X(687)
X(40544) lies on these lines: {2, 691}, {3, 16188}, {4, 38702}, {5, 38611}, {30, 5461}, {115, 7472}, {125, 9181}, {140, 16760}, {187, 858}, {249, 3448}, {316, 30745}, {468, 5140}, {511, 6699}, {512, 5972}, {523, 620}, {538, 16315}, {549, 31379}, {625, 5159}, {631, 842}, {1692, 32220}, {2072, 13449}, {2453, 11288}, {2482, 16092}, {2794, 36170}, {3523, 38704}, {3525, 38679}, {3526, 38582}, {3767, 14659}, {5054, 38583}, {5206, 36187}, {5215, 7426}, {5432, 6027}, {5433, 6023}, {5569, 36194}, {6680, 36157}, {6722, 14120}, {7464, 38227}, {7574, 38225}, {7575, 34837}, {7665, 15398}, {7749, 36165}, {7857, 36182}, {7907, 38526}, {9218, 15059}, {10257, 34841}, {10277, 38230}, {10303, 38680}, {10415, 14360}, {10989, 26613}, {14061, 36174}, {14971, 36196}, {14999, 15357}, {18911, 32761}, {21843, 36163}, {22104, 36597}, {34473, 36173}, {36166, 38737}
X(40544) = complement of X(5099)
X(40544) = centroid of {A,B,C,X(691)}
X(40544) = center of bicevian conic of X(2) and X(691)
X(40545) lies on these lines: {2, 743}, {6710, 27076}
X(40545) = complement of complement of X(789)
X(40545) = centroid of {A,B,C,X(789)}
X(40545) = center of bicevian conic of X(2) and X(789)
X(40546) lies on these lines: {2, 799}, {100, 30996}, {141, 25652}, {620, 2787}, {4369, 24003}, {4422, 36950}, {16613, 25472}, {24384, 25107}, {24505, 27805}, {27008, 27306}
X(40546) = complement of X(16592)
X(40546) = centroid of {A,B,C,X(799)}
X(40546) = center of bicevian conic of X(2) and X(799)
X(40547) lies on these lines: {2, 835}, {4422, 5972}, {4687, 37842}, {6710, 24003}, {6711, 13731}, {6715, 11814}, {6718, 16578}, {6720, 15252}
X(40547) = complement of X(5515)
X(40547) = centroid of {A,B,C,X(835)}
X(40547) = center of bicevian conic of X(2) and X(835)
X(40548) lies on these lines: {2, 874}, {620, 804}, {740, 1125}, {812, 4422}, {1966, 17289}, {4155, 21254}, {4432, 20333}, {17357, 18904}, {24254, 24327}, {27838, 38989}, {28604, 30940}
X(40548) = complement of X(39786)
X(40548) = centroid of {A,B,C,X(874)}
X(40548) = center of bicevian conic of X(2) and X(874)
X(40549) lies on these lines: {2, 876}, {512, 1125}, {513, 4698}, {514, 3634}, {523, 3739}, {665, 3837}, {3005, 27167}, {3766, 30795}, {3812, 4083}, {4151, 6532}, {4367, 16830}, {4784, 29578}, {6372, 23814}, {7180, 25126}, {16826, 38348}, {18004, 23829}, {19948, 19949}, {25380, 30665}
X(40549) = complement of complement of X(876)
X(40549) = centroid of {A,B,C,X(876)}
X(40549) = center of bicevian conic of X(2) and X(876)
X(40550) lies on these lines: {2, 879}, {5, 512}, {140, 525}, {141, 520}, {182, 18312}, {523, 3589}, {526, 6698}, {690, 6036}, {804, 14271}, {826, 6689}, {924, 6697}, {3566, 6696}, {3800, 10280}, {3906, 40108}, {5449, 8673}, {6130, 24284}, {8675, 16511}, {8723, 23105}, {9030, 32154}, {9033, 15118}, {9517, 20304}, {10168, 23878}, {11182, 35364}, {14096, 38354}, {14618, 37124}, {15059, 35909}, {33752, 38317}
X(40550) = complement of X(41167)
X(40550) = complement of complement of X(879)
X(40550) = centroid of {A,B,C,X(879)}
X(40550) = center of bicevian conic of X(2) and X(879)
X(40551) lies on these lines: {2, 885}, {5, 3309}, {10, 3900}, {142, 513}, {514, 1125}, {522, 6666}, {523, 25081}, {667, 4223}, {676, 20516}, {1387, 6366}, {2488, 26017}, {2826, 6713}, {3716, 24285}, {3887, 6702}, {3925, 11193}, {4391, 16823}, {4423, 40166}, {4806, 6701}, {6362, 6675}, {8641, 25009}, {8728, 11247}, {15584, 31287}, {31419, 32195}, {35355, 36848}
X(40551) = complement of X(3126)
X(40551) = centroid of {A,B,C,X(885)}
X(40551) = center of bicevian conic of X(2) and X(885)
X(40552) lies on these lines: {2, 889}, {513, 27076}, {4369, 36950}, {4422, 31286}, {9263, 31625}, {9296, 27195}, {21264, 25382}
X(40552) = complement of X(39011)
X(40552) = centroid of {A,B,C,X(889)}
X(40552) = center of bicevian conic of X(2) and X(889)
X(40553) lies on these lines: {2, 892}, {115, 9182}, {126, 16092}, {148, 4590}, {230, 6719}, {385, 23589}, {523, 620}, {524, 625}, {888, 22103}, {2482, 17948}, {7778, 36207}, {9164, 36521}, {9183, 33915}, {11053, 33921}, {14061, 23991}, {14341, 23583}, {18310, 24975}, {30476, 36950}
X(40553) = complement of X(23992)
X(40553) = centroid of {A,B,C,X(892)}
X(40553) = center of bicevian conic of X(2) and X(892)
X(40553) = crosssum of PU(62)
X(40554) lies on these lines: {2, 927}, {3, 33331}, {101, 14505}, {103, 6074}, {514, 6710}, {516, 6712}, {631, 2724}, {1565, 34805}, {3035, 4885}, {3234, 5845}, {3323, 9318}, {4369, 5972}, {4778, 36956}, {5074, 6699}, {5532, 9317}, {34906, 35094}
X(40554) = complement of X(1566)
X(40554) = centroid of {A,B,C,X(927)}
X(40554) = center of bicevian conic of X(2) and X(927)
X(40555) lies on these lines: {2, 934}, {9, 28344}, {116, 20418}, {142, 6713}, {631, 972}, {1125, 6712}, {1360, 5433}, {3035, 6366}, {6691, 6714}, {6710, 36949}, {7483, 15725}
X(40555) = complement of X(5514)
X(40555) = centroid of {A,B,C,X(934)}
X(40555) = center of bicevian conic of X(2) and X(934)
X(40556) lies on these lines: {2, 1296}, {3, 126}, {4, 38716}, {5, 38623}, {30, 38803}, {111, 631}, {140, 6719}, {141, 14688}, {376, 10734}, {381, 38797}, {382, 38798}, {485, 11836}, {486, 11835}, {543, 549}, {620, 2793}, {1656, 22338}, {2780, 5972}, {2805, 6713}, {2813, 6712}, {2819, 6718}, {2824, 6710}, {2830, 3035}, {2847, 34842}, {2852, 6711}, {2854, 6699}, {3325, 5432}, {3523, 14360}, {3524, 10717}, {3525, 38688}, {3526, 38593}, {3628, 38801}, {5054, 9172}, {5055, 38800}, {5070, 38799}, {5085, 36883}, {5433, 6019}, {5657, 10704}, {6714, 9522}, {6715, 9526}, {6716, 9529}, {6717, 9531}, {9129, 38793}, {10165, 11721}, {10303, 38675}, {10519, 10765}, {10779, 34474}, {12100, 32424}, {14643, 35447}, {14666, 15693}, {15122, 16760}, {16239, 38802}, {17566, 38518}, {18580, 34840}, {37450, 38651}
X(40556) = complement of X(5512)
X(40556) = centroid of {A,B,C,X(1296)}
X(40556) = center of bicevian conic of X(2) and X(1296)
X(40557) lies on these lines: {2, 1304}, {3, 18809}, {4, 38719}, {5, 31379}, {30, 34842}, {122, 31510}, {402, 22104}, {403, 12096}, {468, 12145}, {520, 5972}, {523, 6716}, {631, 2693}, {1552, 3184}, {3526, 38595}, {6000, 6699}, {6036, 37911}, {6677, 16760}, {12068, 34844}, {23583, 31945}, {32417, 38605}
X(40557) = complement of X(16177)
X(40557) = centroid of {A,B,C,X(1304)}
X(40557) = center of bicevian conic of X(2) and X(1304)
X(40558) lies on these lines: {2, 1309}, {3, 39535}, {5, 38617}, {515, 6711}, {522, 6718}, {631, 2734}, {3326, 24410}, {5972, 8062}, {22102, 35013}
X(40558) = complement of X(10017)
X(40558) = centroid of {A,B,C,X(1309)}
X(40558) = center of bicevian conic of X(2) and X(1309)
X(40559) lies on these lines: {2, 1576}, {140, 2781}, {338, 15000}, {420, 39231}, {523, 23583}, {526, 5972}, {620, 9479}, {1316, 34981}, {2871, 3589}, {2881, 6720}, {2882, 6680}
X(40559) = complement of complement of X(1576)
X(40559) = centroid of {A,B,C,X(1576)}
X(40559) = center of bicevian conic of X(2) and X(1576)
X(40560) lies on these lines: {2, 1633}, {11, 16686}, {45, 5432}, {140, 12608}, {190, 26231}, {468, 1155}, {513, 36949}, {523, 16599}, {692, 5848}, {900, 3035}, {1086, 24346}, {1125, 2835}, {2820, 6710}, {2823, 6684}, {2849, 6717}, {3246, 15325}, {3579, 16618}, {3683, 7499}, {3826, 36477}, {4364, 6690}, {4640, 6676}, {5849, 7193}, {6713, 38607}, {12329, 27509}, {21293, 35280}, {23305, 24309}, {23845, 25968}
X(40560) = complement of complement of X(1633)
X(40560) = centroid of {A,B,C,X(1633)}
X(40560) = center of bicevian conic of X(2) and X(1633)
X(40561) lies on these lines: {2, 1783}, {2806, 3035}, {2812, 6710}, {3820, 20204}, {15252, 24003}, {23583, 27076}, {36949, 39470}
X(40561) = complement of complement of X(1783)
X(40561) = centroid of {A,B,C,X(1783)}
X(40561) = center of bicevian conic of X(2) and X(1783)
X(40562) lies on these lines: {2, 1978}, {891, 4928}, {1015, 18149}, {3835, 36951}, {3934, 17760}, {4422, 36950}, {4598, 24502}, {11052, 13006}, {11814, 20333}, {21893, 33908}
X(40562) = complement of X(6377)
X(40562) = centroid of {A,B,C,X(1978)}
X(40562) = center of bicevian conic of X(2) and X(1978)
X(40563) lies on these lines: {141, 40216}, {693, 3741}, {1269, 35544}, {4357, 4972}, {4980, 20888}, {14751, 27800}, {17184, 26582}, {20292, 20347}
X(40564) lies on these lines: {37, 4858}, {72, 3696}, {75, 16574}, {321, 908}, {1089, 15281}, {1214, 6358}, {1229, 21070}, {1441, 4605}, {1577, 20305}, {1838, 1861}, {3262, 22008}, {3588, 29069}, {3613, 30171}, {4404, 20910}, {22018, 26165}
X(40565) lies on the Feuerbach circumhyperbola, the curve Q044, and these lines: {2, 11}, {7, 3514}, {104, 38014}, {516, 32622}, {2801, 39145}, {3513, 7677}
X(40565) = reflection of X(40566) in X(11)
X(40565) = isogonal conjugate of X(3513)
X(40565) = cevapoint of X(1) and X(32622)
X(40565) = barycentric product X(3514)*X(36796)
X(40565) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3513}, {3514, 241}
X(40565) = {X(2),X(390)}-harmonic conjugate of X(40566)
X(40566) lies on the Feuerbach circumhyperbola, the curve Q044, and these lines: {2, 11}, {7, 3513}, {104, 38013}, {516, 32623}, {2801, 39144}, {3514, 7677}
X(40566) = reflection of X(40565) in X(11)
X(40566) = isogonal conjugate of X(3514)
X(40566) = cevapoint of X(1) and X(32623)
X(40566) = barycentric product X(3513)*X(36796)
X(40566) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3514}, {3513, 241}
X(40566) = {X(2),X(390)}-harmonic conjugate of X(40565)
X(40567) lies on the cubic K1175 and these lines: {105, 516}, {518, 677}
X(40568) lies on the cubic K1175 and these lines: {3, 348}, {105, 175}, {1814, 13388}
X(40568) = circumcircle-inverse of X(40569)
X(40568) = X(5089)-isoconjugate of X(7348)
X(40568) = barycentric product X(6203)*X(31637)
X(40568) = barycentric quotient X(i)/X(j) for these {i,j}: {6203, 1861}, {36057, 7348}
X(40569) lies on the cubic K1175 and these lines: {3, 348}, {105, 176}, {1814, 13389}
X(40569) = circumcircle-inverse of X(40568)
X(40569) = X(5089)-isoconjugate of X(7347)
X(40569) = barycentric product X(6204)*X(31637)
X(40569) = barycentric quotient X(i)/X(j) for these {i,j}: {6204, 1861}, {36057, 7347}
X(40570) lies on the conic {{A,B,C,X(2),X(6)}}, the cubic K1174, and on these lines:" {2, 7054}, {6, 1175}, {32, 36420}, {37, 943}, {42, 2259}, {112, 1841}, {1333, 1396}, {1400, 1474}, {1880, 2204}, {2395, 14775}
X(40570) = polar conjugate of X(1234)
X(40570) = isogonal conjugate of the isotomic conjugate of X(40395)
X(40570) = polar conjugate of the isotomic conjugate of X(1175)
X(40570) = X(40395)-Ceva conjugate of X(1175)
X(40570) = X(i)-cross conjugate of X(j) for these (i,j): {3063, 32713}, {6591, 112}
X(40570) = X(i)-isoconjugate of X(j) for these (i,j): {10, 18607}, {48, 1234}, {63, 442}, {69, 2294}, {72, 5249}, {75, 18591}, {306, 942}, {312, 39791}, {313, 14597}, {321, 4303}, {326, 1865}, {349, 23207}, {1214, 6734}, {1231, 14547}, {1332, 23752}, {1444, 21675}, {1838, 3998}, {2260, 20336}
X(40570) = cevapoint of X(i) and X(j) for these (i,j): {25, 2204}, {32, 2203}
X(40570) = barycentric product X(i)*X(j) for these {i,j}: {4, 1175}, {6, 40395}, {25, 40412}, {27, 2259}, {28, 943}, {110, 14775}, {1172, 2982}, {1794, 8747}, {17926, 32651}
X(40570) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 1234}, {25, 442}, {32, 18591}, {943, 20336}, {1175, 69}, {1333, 18607}, {1397, 39791}, {1474, 5249}, {1973, 2294}, {2203, 942}, {2206, 4303}, {2207, 1865}, {2259, 306}, {2299, 6734}, {2333, 21675}, {2982, 1231}, {14775, 850}, {40395, 76}, {40412, 305}
X(40571) lies on the cubics K610 and K1174 and on these lines: {2, 6}, {21, 72}, {27, 5905}, {28, 3868}, {29, 1069}, {58, 78}, {63, 284}, {92, 1172}, {100, 209}, {110, 2203}, {184, 36018}, {218, 16050}, {239, 17866}, {286, 40395}, {307, 2003}, {411, 5752}, {518, 2194}, {579, 37312}, {593, 40403}, {648, 2990}, {651, 1396}, {758, 21376}, {894, 37095}, {912, 4227}, {1029, 13583}, {1043, 20013}, {1170, 39747}, {1210, 27412}, {1333, 3998}, {1412, 1445}, {1441, 2982}, {1444, 4280}, {1778, 27396}, {1780, 3811}, {1790, 18206}, {1817, 3218}, {2206, 32912}, {2328, 3870}, {2651, 26893}, {2893, 27052}, {2911, 17776}, {3060, 7466}, {3149, 12160}, {3152, 20077}, {3194, 5081}, {3434, 5327}, {3564, 37362}, {3666, 4273}, {3759, 19788}, {4001, 24632}, {4184, 7085}, {4215, 20760}, {4228, 5208}, {4558, 18605}, {5320, 10477}, {5358, 20602}, {5810, 6828}, {6915, 15801}, {6986, 34148}, {7538, 20018}, {7754, 11341}, {8822, 20078}, {9965, 14953}, {10974, 35979}, {11115, 20007}, {14054, 30733}, {14868, 37301}, {17188, 26015}, {17189, 26723}, {17498, 23090}, {20043, 20212}, {21997, 26840}
X(40571) = anticomplement of the isotomic conjugate of X(40395)
X(40571) = isotomic conjugate of the polar conjugate of X(30733)
X(40571) = isotomic conjugate of isogonal conjugate of X(41332)
X(40571) = polar conjugate of isogonal conjugate of X(41608)
X(40571) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1175, 4329}, {1474, 2894}, {14775, 21294}, {40395, 6327}
X(40571) = X(i)-Ceva conjugate of X(j) for these (i,j): {286, 21}, {40395, 2}
X(40571) = X(2911)-cross conjugate of X(1780)
X(40571) = X(i)-isoconjugate of X(j) for these (i,j): {6, 23604}, {19, 28787}, {42, 15474}, {65, 39943}, {71, 39267}, {661, 13397}
X(40571) = cevapoint of X(i) and X(j) for these (i,j): {1708, 3173}, {2911, 3811}
X(40571) = crosspoint of X(648) and X(4567)
X(40571) = crosssum of X(647) and X(3125)
X(40571) = barycentric product X(i)*X(j) for these {i,j}: {69, 30733}, {75, 1780}, {81, 17776}, {86, 3811}, {99, 15313}, {274, 2911}, {286, 11517}, {314, 37579}, {333, 1708}, {1043, 4341}, {3173, 31623}, {4570, 17877}, {14054, 40412}
X(40571) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 23604}, {3, 28787}, {28, 39267}, {81, 15474}, {110, 13397}, {284, 39943}, {1708, 226}, {1780, 1}, {2911, 37}, {3173, 1214}, {3215, 73}, {3811, 10}, {4341, 3668}, {11517, 72}, {14054, 442}, {15313, 523}, {17776, 321}, {17877, 21207}, {26217, 33294}, {30733, 4}, {37579, 65}
X(40571) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 284, 27174}, {81, 1812, 26637}, {81, 2287, 2}, {81, 37783, 1812}, {965, 19716, 2}, {5278, 5736, 2}, {5320, 10477, 37325}, {20078, 26830, 8822}
X(40572) lies on the cubic K1174 and these lines: {2, 219}, {4, 2911}, {6, 943}, {35, 71}, {2174, 7430}, {2323, 2983}, {9085, 15439}
X(40572) = X(40395)-Ceva conjugate of X(943)
X(40572) = X(i)-isoconjugate of X(j) for these (i,j): {272, 2294}, {942, 1751}, {2218, 5249}, {2260, 2997}
X(40572) = barycentric product X(i)*X(j) for these {i,j}: {209, 40412}, {943, 3868}, {1794, 5125}, {2259, 18134}, {2982, 27396}, {15439, 20294}
X(40572) = barycentric quotient X(i)/X(j) for these {i,j}: {209, 442}, {579, 5249}, {943, 2997}, {1175, 272}, {2198, 2294}, {2259, 1751}, {2352, 942}, {3190, 6734}, {15439, 1305}
X(40573) lies on the cubic K1174 and these lines: {4, 12}, {6, 278}, {9, 92}, {27, 226}, {57, 1847}, {225, 2299}, {273, 1708}, {333, 349}, {917, 15439}, {1175, 14016}, {1214, 36019}, {1436, 7490}, {1794, 1838}, {1860, 2195}, {2164, 7363}, {2316, 6336}, {2339, 37086}, {6994, 8232}, {14775, 23351}
X(40573) = polar conjugate of X(6734)
X(40573) = X(40395)-Ceva conjugate of X(2982)
X(40573) = X(661)-cross conjugate of X(36127)
X(40573) = X(i)-isoconjugate of X(j) for these (i,j): {2, 23207}, {8, 14597}, {9, 4303}, {21, 18591}, {48, 6734}, {55, 18607}, {63, 14547}, {78, 2260}, {212, 5249}, {219, 942}, {283, 2294}, {394, 1859}, {442, 2193}, {1214, 8021}, {1259, 1841}, {1838, 2289}, {2287, 39791}, {6516, 33525}, {8606, 16585}
X(40573) = cevapoint of X(i) and X(j) for these (i,j): {19, 225}, {34, 1400}, {226, 1708}
X(40573) = trilinear pole of line {663, 7649}
X(40573) = barycentric product X(i)*X(j) for these {i,j}: {92, 2982}, {225, 40412}, {226, 40395}, {273, 943}, {331, 2259}, {664, 14775}
X(40573) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 6734}, {25, 14547}, {31, 23207}, {34, 942}, {56, 4303}, {57, 18607}, {225, 442}, {278, 5249}, {604, 14597}, {608, 2260}, {943, 78}, {1042, 39791}, {1096, 1859}, {1118, 1838}, {1175, 283}, {1400, 18591}, {1794, 1259}, {1880, 2294}, {2259, 219}, {2299, 8021}, {2982, 63}, {6198, 31938}, {8736, 21675}, {14775, 522}, {15439, 1331}, {32651, 1813}, {36048, 6516}, {40395, 333}, {40412, 332}
X(40574) lies on the cubic K1174 and these lines: {4, 580}, {27, 272}, {28, 1612}, {29, 40161}, {92, 1172}, {278, 1474}, {1214, 1305}, {1396, 1847}, {5137, 5146}
X(40574) = isogonal conjugate of the complement of X(2997)
X(40574) = polar conjugate of the isotomic conjugate of X(272)
X(40574) = X(i)-cross conjugate of X(j) for these (i,j): {6, 28}, {513, 1305}
X(40574) = X(i)-isoconjugate of X(j) for these (i,j): {3, 22021}, {63, 209}, {69, 2198}, {71, 3868}, {72, 579}, {73, 27396}, {228, 18134}, {306, 2352}, {1214, 3190}, {3694, 4306}, {3990, 5125}, {4574, 23800}
X(40574) = cevapoint of X(6) and X(2218)
X(40574) = barycentric product X(i)*X(j) for these {i,j}: {4, 272}, {27, 1751}, {28, 2997}, {286, 2218}, {1474, 40011}, {2299, 15467}, {36419, 40161}
X(40574) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 22021}, {25, 209}, {27, 18134}, {28, 3868}, {272, 69}, {1172, 27396}, {1474, 579}, {1751, 306}, {1973, 2198}, {2203, 2352}, {2218, 72}, {2299, 3190}, {2997, 20336}, {8747, 5125}, {40011, 40071}
X(40575) lies on the cubic K1174 and these lines: {4, 18687}, {63, 284}, {226, 13395}
X(40576) lies on these lines: {7, 1037}, {8, 8283}, {56, 528}, {59, 513}, {77, 24309}, {100, 108}, {105, 37771}, {109, 13397}, {934, 1292}, {1376, 4081}, {1486, 37800}, {1804, 11495}, {1813, 35338}, {2222, 9058}, {2961, 4319}, {3939, 24029}, {4236, 4565}, {4331, 37576}, {5723, 16686}, {19850, 37579}, {21147, 35998}
X(40576) = X(4569)-Ceva conjugate of X(651)
X(40576) = X(i)-cross conjugate of X(j) for these (i,j): {11934, 169}, {21185, 4228}
X(40576) = X(i)-isoconjugate of X(j) for these (i,j): {55, 26721}, {514, 40141}, {522, 3433}, {663, 13577}, {7004, 26706}
X(40576) = cevapoint of X(169) and X(11934)
X(40576) = trilinear pole of line {169, 5452}
X(40576) = crossdifference of every pair of points on line {7117, 17435}
X(40576) = barycentric product X(i)*X(j) for these {i,j}: {59, 26546}, {100, 37800}, {108, 28420}, {109, 20927}, {169, 664}, {190, 34036}, {651, 3434}, {1275, 11934}, {1414, 21073}, {1486, 4554}, {4228, 4552}, {4564, 21185}, {4569, 5452}, {4573, 21867}, {6516, 17905}, {18026, 22131}
X(40576) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 26721}, {169, 522}, {651, 13577}, {692, 40141}, {1415, 3433}, {1486, 650}, {3434, 4391}, {4228, 4560}, {5452, 3900}, {7115, 26706}, {11934, 1146}, {20927, 35519}, {21073, 4086}, {21185, 4858}, {21867, 3700}, {22131, 521}, {26546, 34387}, {28420, 35518}, {34036, 514}, {37800, 693}
X(40577) lies on the cubic K578 and these lines: {7, 3446}, {36, 516}, {59, 513}, {100, 522}, {101, 21127}, {105, 3322}, {108, 901}, {109, 1290}, {165, 29374}, {404, 24410}, {484, 1725}, {517, 3100}, {656, 36031}, {927, 24002}, {934, 1308}, {1086, 38863}, {1155, 9358}, {1284, 5172}, {1292, 14733}, {1305, 2722}, {1319, 4318}, {1769, 39026}, {2077, 16869}, {2078, 22464}, {2310, 2957}, {2720, 13397}, {3315, 24201}, {4236, 17942}, {5091, 21746}, {13589, 23981}, {16686, 37771}, {24025, 34464}, {38682, 39756}
X(40577) = reflection of X(i) in X(j) for these {i,j}: {651, 59}, {4318, 1319}
X(40577) = reflection of X(59) in the OI line
X(40577) = X(7)-Ceva conjugate of X(651)
X(40577) = X(11193)-cross conjugate of X(5540)
X(40577) = X(i)-isoconjugate of X(j) for these (i,j): {109, 34896}, {522, 3446}, {663, 8047}
X(40577) = cevapoint of X(i) and X(j) for these (i,j): {513, 38863}, {5540, 11193}
X(40577) = crosspoint of X(7) and X(37771)
X(40577) = trilinear pole of line {1421, 5540}
X(40577) = isogonal conjugate of X(11) wrt the anticevian triangle of X(11)
X(40577) = barycentric product X(i)*X(j) for these {i,j}: {7, 5375}, {100, 37771}, {109, 18151}, {149, 651}, {190, 1421}, {513, 31633}, {664, 5540}, {1275, 11193}, {1414, 21090}, {3669, 11607}, {4554, 16686}, {4564, 21201}, {4573, 21889}, {18026, 22144}
X(40577) = barycentric quotient X(i)/X(j) for these {i,j}: {149, 4391}, {650, 34896}, {651, 8047}, {1415, 3446}, {1421, 514}, {5375, 8}, {5540, 522}, {11193, 1146}, {11607, 646}, {16686, 650}, {18151, 35519}, {21090, 4086}, {21201, 4858}, {21889, 3700}, {22144, 521}, {31633, 668}, {37771, 693}
Centers of 2nd Ceva conics: X(40578)-X(40629)
This preamble is contributed by Clark Kimberling and Peter Moses, December 6, 2020.
In the plane of a triangle ABC, let L be the line u x + v y + w z = 0, and let U be the point u : v : w, this being the trilinear pole of L. Let P = p : q : r be a point. The 2nd (U,P)-Ceva conic is introduced here as the locus of X such that the X-Ceva conjugate of P is on the line L. This conic circumscribes ABC and is given by
p(-u p + v q + w r)/x + q(u p - v q + w r)/y + r(u p + v q - w r)/z = 0.
The center of the conic is the point
p*((p+q+r) p^2 u^2 + (p+q-r) q^2 v^2 + (p-q+r) r^2 w^2 + 2 p q r v w - 2 p r (p+r) w u - 2 p q (p+q) u v) : :
If U = X(2), then the center of the 2nd (U,P)-Ceva conic is the X(2)-Ceva conjugate of P, and the perspector of the 2nd (U,P)-Ceva conic is P. (Randy Hutson, December 18, 2020)
See also X(41889).
X(40578) lies on these lines: {2, 19776}, {3, 5623}, {13, 15}, {14, 39170}, {298, 1494}, {470, 8737}, {476, 36298}, {2153, 37772}, {2992, 3180}, {8014, 37640}, {16645, 18777}
X(40578) = complement of X(19776)
X(40578) = complementary conjugate of complement of X(15)-Ceva conjugate of X(6)
X(40578) = X(2)-Ceva conjugate of X(13)
X(40578) = perspector of circumconic centered at X(13)
X(40579) lies on the cubics K277, K341b, K472 and these lines: {2,19777}, {3,5624}, {13,39170}, {14,16}, {299,1494}, {471,8738}, {476,36299}, {2154,37772}, {2993,3181}, {3642,40580}, {8015,37641}, {11556,42989}, {14583,51270}, {16241,40695}, {16644,18776}, {25641,46465}, {36840,46825}, {37640,52040}
X(40579) = midpoint of X(i) and X(j) for these {i, j}: {14, 45779}, {23896, 36311}
X(40579) = reflection of X(14) in X(10218)
X(40579) = complement of X(19777)
X(40579) = perspector of the circumconic {A, B, C, X(36840), X(39133)}
X(40579) = center of the circumconic {A, B, C, X(476), X(23896)}
X(40579) = intersection, other than A, B, C, of circumconics {A, B, C, X(13), X(15442)} and {A, B, C, X(14), X(617)}
X(40579) = barycentric product X(i)*X(j) for these {i, j}: {14, 617}, {533, 39133}, {622, 46059}
X(40579) = barycentric quotient X(i)/X(j) for these (i, j): (14, 19777), (617, 299)
X(40579) = trilinear product X(i)*X(j) for these {i, j}: {14, 19299}, {617, 2154}
X(40579) = trilinear quotient X(2154)/X(3441)
X(40579) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 36298, 51277), (14, 46074, 15442), (16, 36210, 14), (395, 11085, 14), (395, 11549, 11085), (11549, 47142, 36210), (11582, 16268, 14), (23715, 47482, 51269)
X(40580) lies on these lines: {2, 2992}, {3, 3165}, {5, 13}, {6, 3170}, {15, 1511}, {16, 4550}, {61, 1147}, {110, 36296}, {113, 5668}, {202, 942}, {216, 10639}, {298, 340}, {300, 23896}, {577, 10640}, {2005, 11088}, {5158, 9306}, {5237, 34328}, {5238, 33556}, {10217, 10272}, {11126, 17035}, {15748, 36836}, {22238, 33537}, {30383, 34830}, {32586, 34425}
X(40580) = complement of X(2992)
X(40580) = complementary conjugate of complement of X(3129)
X(40580) = X(2)-Ceva conjugate of X(15)
X(40580) = perspector of circumconic centered at X(15)
X(40580) = crosssum of circumcircle intercepts of inner Napoleon circle
X(40580) = {X(5158),X(9306)}-harmonic conjugate of X(40581)
X(40581) lies on these lines: {2, 2993}, {3, 3166}, {5, 14}, {6, 3171}, {15, 4550}, {16, 1511}, {62, 1147}, {110, 36297}, {113, 5669}, {203, 942}, {216, 10640}, {299, 340}, {301, 23895}, {577, 10639}, {2004, 11083}, {5158, 9306}, {5237, 33556}, {5238, 34327}, {10218, 10272}, {11127, 17035}, {15748, 36843}, {22236, 33537}, {30382, 34830}, {32585, 34424}
X(40581) = complement of X(2993)
X(40581) = complementary conjugate of complement of X(3130)
X(40581) = X(2)-Ceva conjugate of X(16)
X(40581) = perspector of circumconic centered at X(16)
X(40581) = crosssum of circumcircle intercepts of outer Napoleon circle
X(40581) = {X(5158),X(9306)}-harmonic conjugate of X(40580)
X(40582) lies on the hyperbola {{X(2),X(6),X(216),X(233),X(1249)}} and these lines: {6, 2476}, {9, 35193}, {19, 1325}, {21, 270}, {37, 5546}, {60, 2264}, {81, 3664}, {216, 404}, {229, 1781}, {233, 7504}, {281, 13746}, {284, 2170}, {377, 1249}, {403, 15947}, {442, 2906}, {648, 1441}, {662, 1442}, {857, 2905}, {1100, 2303}, {1196, 2670}, {1560, 30770}, {1731, 2150}, {2182, 23059}, {2287, 2323}, {2322, 11103}, {2907, 5051}, {3163, 6175}, {4560, 18311}, {5778, 11441}, {14401, 23090}, {15595, 15988}, {17686, 37891}, {33841, 37895}
X(40582) = X(2)-Ceva conjugate of X(21)
X(40582) = perspector of circumconic centered at X(21)
X(40583) lies on the hyperbola {{X(2),X(6),X(216),X(233),X(1249)}} and these lines: {2, 8792}, {6, 3448}, {23, 8744}, {111, 251}, {112, 6636}, {115, 34482}, {216, 7496}, {233, 6103}, {323, 15595}, {648, 18019}, {1249, 16063}, {1560, 30745}, {3162, 31101}, {3163, 10989}, {5189, 22121}, {7394, 40179}, {7711, 13114}, {18311, 31128}, {31107, 37895}
X(40583) = complement of isogonal conjugate of X(19596)
X(40583) = complementary conjugate of complement of X(19596)
X(40583) = X(2)-Ceva conjugate of X(23)
X(40583) = perspector of circumconic centered at X(23)
X(40584) is the antipode of X(1211) in the hyperbola described at X(36949). (Randy Hutson, December 18, 2020)
X(40584) lies on these lines: {6, 1718}, {9, 1060}, {81, 226}, {758, 1870}, {1015, 16470}, {1211, 36949}, {1415, 2193}, {1983, 26744}, {2245, 6149}, {2610, 3738}, {3013, 8068}, {3284, 23980}, {5299, 9456}, {5526, 16307}, {6703, 26932}, {7110, 20262}, {13006, 18591}, {16548, 22123}, {34544, 34586}, {35069, 35204}
X(40584) = reflection of X(1211) in X(36949)
X(40584) = complementary conjugate of complement of X(20989)
X(40584) = X(2)-Ceva conjugate of X(36)
X(40584) = perspector of circumconic centered at X(36)
X(40585) lies on these lines: {2, 7239}, {38, 8041}, {42, 1100}, {321, 1930}, {3112, 4562}, {3661, 17177}, {4876, 33123}, {5949, 29687}, {19584, 32771}, {22013, 40013}, {24484, 33166}, {25440, 32664}, {31161, 35123}
X(40585) = complement of isogonal conjugate of X(20990)
X(40585) = complement of isotomic conjugate of X(17165)
X(40585) = complement of X(19)-isoconjugate of X(22164)
X(40585) = complementary conjugate of complement of X(20990)
X(40585) = X(2)-Ceva conjugate of X(38)
X(40585) = perspector of circumconic centered at X(38)
X(50586) lies on these lines: {2, 2140}, {9, 3588}, {37, 38}, {42, 213}, {71, 1213}, {101, 4184}, {190, 310}, {220, 1011}, {228, 8012}, {321, 17755}, {430, 2333}, {518, 40463}, {573, 9812}, {649, 4640}, {756, 39258}, {899, 21877}, {902, 2205}, {1001, 36808}, {1018, 4651}, {1386, 14751}, {1400, 39793}, {2183, 16590}, {2225, 3683}, {2238, 21858}, {2328, 32739}, {3006, 22009}, {3159, 17031}, {3161, 10453}, {3207, 19346}, {3219, 6651}, {3230, 23632}, {3501, 26037}, {3736, 38853}, {3995, 17027}, {4024, 22027}, {4115, 22013}, {4210, 24047}, {4253, 29814}, {4370, 31136}, {5513, 30751}, {12514, 15487}, {14752, 21345}, {15830, 38015}, {16552, 17135}, {16593, 30821}, {17149, 17336}, {17208, 27097}, {20966, 21813}, {21879, 21880}
X(40586) = complement of X(8049)
X(40586) = complementary conjugate of complement of X(8053)
X(40586) = X(2)-Ceva conjugate of X(42)
X(40586) = perspector of circumconic centered at X(42)
X(40587) lies on the Feuerbach circumhyperbola of the medial triangle and these lines: {1, 3689}, {2, 1000}, {3, 5836}, {5, 64322}, {8, 442}, {9, 374}, {10, 1482}, {40, 51576}, {45, 4752}, {55, 5426}, {80, 31140}, {100, 2320}, {119, 2886}, {142, 519}, {145, 37462}, {200, 50194}, {210, 25415}, {214, 1376}, {355, 6260}, {392, 51378}, {405, 14923}, {474, 4861}, {514, 996}, {515, 43182}, {518, 1159}, {529, 18541}, {936, 10222}, {940, 49494}, {942, 4853}, {952, 2550}, {956, 3218}, {958, 3647}, {960, 8148}, {993, 51570}, {997, 10247}, {999, 3306}, {1001, 2802}, {1056, 62778}, {1100, 34261}, {1125, 10912}, {1319, 16417}, {1329, 18493}, {1385, 1706}, {1480, 55432}, {1538, 5587}, {1698, 2098}, {2092, 16777}, {2099, 3679}, {2551, 22791}, {2800, 5779}, {3057, 11108}, {3059, 4915}, {3126, 4825}, {3245, 16558}, {3246, 41453}, {3295, 3895}, {3338, 3922}, {3340, 34790}, {3421, 39542}, {3434, 12690}, {3452, 3656}, {3488, 60959}, {3526, 37828}, {3616, 47742}, {3617, 5730}, {3621, 50237}, {3626, 12635}, {3632, 41862}, {3654, 5745}, {3680, 31792}, {3697, 11682}, {3715, 3899}, {3754, 5708}, {3812, 7373}, {3820, 5328}, {3826, 5854}, {3877, 35595}, {3878, 51573}, {3880, 6600}, {3890, 16842}, {3898, 8167}, {3900, 57178}, {3913, 30147}, {3918, 22837}, {3925, 12647}, {3927, 5903}, {4002, 19861}, {4004, 62874}, {4018, 63135}, {4304, 34707}, {4555, 20569}, {4669, 62822}, {4674, 16499}, {4677, 5425}, {4678, 62830}, {4701, 62860}, {4731, 5048}, {5044, 7982}, {5045, 12629}, {5055, 5123}, {5082, 37730}, {5119, 16418}, {5126, 64112}, {5176, 17532}, {5221, 5288}, {5252, 17528}, {5258, 37567}, {5273, 50810}, {5330, 46933}, {5436, 64202}, {5437, 51788}, {5438, 15178}, {5439, 36846}, {5554, 24390}, {5690, 6862}, {5698, 28212}, {5719, 34619}, {5774, 16821}, {5791, 11362}, {5794, 12645}, {5795, 12699}, {5904, 64963}, {5919, 64203}, {6001, 60884}, {6184, 34522}, {6547, 24864}, {6700, 61276}, {6735, 31479}, {6736, 11374}, {6762, 31794}, {6832, 12245}, {6850, 52683}, {6857, 63133}, {6907, 64317}, {6923, 33898}, {6955, 64191}, {6974, 59417}, {7080, 37737}, {7171, 31788}, {7686, 8158}, {7971, 9947}, {7991, 31445}, {8256, 26363}, {8580, 16200}, {8582, 11373}, {8666, 37545}, {9460, 52553}, {9654, 64087}, {9819, 15837}, {9843, 64205}, {9957, 64673}, {10107, 62858}, {10915, 28628}, {11278, 15829}, {11499, 64286}, {12433, 64068}, {12515, 22758}, {12609, 32049}, {12619, 64330}, {12631, 64675}, {12649, 64200}, {12650, 31787}, {12773, 64745}, {13253, 58659}, {14151, 38092}, {14260, 40594}, {15015, 61152}, {15347, 16863}, {15668, 59711}, {16126, 58658}, {16370, 63136}, {16494, 48805}, {16853, 58679}, {17054, 50637}, {17060, 36479}, {17571, 37568}, {17573, 37618}, {17647, 18526}, {18357, 31418}, {18393, 31141}, {18421, 60937}, {18525, 47032}, {19541, 64332}, {19875, 63210}, {20085, 33110}, {21888, 31449}, {24870, 31139}, {24929, 63137}, {25055, 41702}, {25466, 49169}, {25917, 30323}, {26446, 64315}, {26492, 45080}, {26727, 29676}, {28444, 35460}, {30478, 61524}, {30827, 51709}, {31145, 63159}, {31246, 37735}, {31420, 61249}, {31485, 35775}, {34918, 45631}, {35457, 38066}, {37075, 40863}, {37562, 49171}, {37624, 51577}, {37727, 57284}, {37739, 63146}, {38028, 59572}, {41541, 51767}, {44663, 60973}, {48661, 57288}, {48907, 49734}, {49712, 53115}, {50193, 57279}, {50726, 64744}, {50798, 51569}, {53114, 64165}, {53620, 62826}, {56938, 62582}, {58641, 64896}, {59388, 64313}, {61146, 64328}, {61158, 64137}, {63130, 64951}
X(40587) = midpoint of X(i) and X(j) for these {i,j}: {1, 11525}, {8, 11041}, {100, 24297}, {4752, 4792}, {4915, 11529}, {16236, 36922}
X(40587) = reflection of X(i) in X(j) for these {i,j}: {1, 64732}, {3, 64733}, {1000, 64109}, {1482, 64731}, {6767, 54318}, {7966, 1385}, {9708, 9623}, {36867, 14563}, {37727, 64323}, {64322, 5}, {64326, 64318}, {64330, 12619}, {64734, 10}
X(40587) = complement of X(1000)
X(40587) = anticomplement of X(64109)
X(40587) = complement of the isogonal conjugate of X(999)
X(40587) = complement of the isotomic conjugate of X(42697)
X(40587) = medial-isogonal conjugate of X(3820)
X(40587) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 3820}, {6, 5316}, {31, 45}, {48, 6350}, {56, 31397}, {106, 51362}, {999, 10}, {2163, 64109}, {3306, 141}, {3753, 3454}, {3872, 1329}, {4054, 21245}, {7113, 36913}, {17079, 17046}, {17519, 34831}, {20925, 626}, {21183, 21252}, {22129, 18589}, {28808, 21244}, {35281, 513}, {40587, 21251}, {42697, 2887}, {52428, 9}, {55432, 3452}, {56426, 3814}
X(40587) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 45}, {1320, 4867}
X(40587) = X(i)-isoconjugate of X(j) for these (i,j): {1000, 2163}, {28607, 65029}, {34446, 39704}
X(40587) = X(i)-Dao conjugate of X(j) for these (i,j): {45, 2}, {36911, 65029}, {40587, 1000}, {51362, 1145}, {52148, 2320}
X(40587) = crosspoint of X(2) and X(42697)
X(40587) = crosssum of X(6) and X(34446)
X(40587) = barycentric product X(i)*X(j) for these {i,j}: {9, 36595}, {45, 42697}, {88, 36919}, {999, 4671}, {1320, 36914}, {2099, 28808}, {2177, 20925}, {3306, 3679}, {3711, 17079}, {3753, 5235}, {3872, 5219}, {4054, 4653}, {4752, 21183}, {4791, 35281}, {4792, 62621}, {27757, 56426}
X(40587) = barycentric quotient X(i)/X(j) for these {i,j}: {45, 1000}, {999, 89}, {3306, 39704}, {3679, 65029}, {3711, 36916}, {3753, 30588}, {3872, 30608}, {3940, 30680}, {4671, 58029}, {4752, 51564}, {35281, 4604}, {36595, 85}, {36919, 4358}, {42697, 20569}, {52428, 2364}, {55432, 2320}, {62621, 63226}
X(40587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3698, 16408}, {1, 4413, 35272}, {2, 1000, 64109}, {2099, 3679, 3940}, {2099, 3711, 4867}, {2099, 3940, 4930}, {3679, 4867, 3711}, {3679, 5219, 51362}, {3679, 16236, 36922}, {3711, 4867, 3940}, {3753, 3872, 999}, {3754, 12513, 5708}, {3918, 22837, 25524}, {4674, 16499, 17595}, {4677, 5425, 41711}, {10914, 19860, 3295}, {37624, 59691, 51577}
X(40588) is the center of the conic that is the locus of the barycentric product of circumcircle-X(5)-antipodes. (Randy Hutson, December 18, 2020)
X(40588) lies on these lines: {32, 184}, {53, 232}, {206, 22391}, {343, 35319}, {647, 10192}, {1180, 9993}, {2211, 23195}, {3917, 11672}, {5480, 14773}, {6636, 13236}, {34990, 40379}
X(40588) = isogonal conjugate of isotomic conjugate of X(41480)
X(40588) = complement of isogonal conjugate of X(160)
X(40588) = complement of isotomic conjugate of X(2979)
X(40588) = complement of polar conjugate of X(39575)
X(40588) = complementary conjugate of X(34845)
X(40588) = X(2)-Ceva conjugate of X(51)
X(40588) = perspector of circumconic centered at X(51)
Let (OA) be the A-extraversion of the Conway circle (the circle centered at the A-excenter and passing through A, with radius sqrt(ra2 + s2), where ra is the A-exradius). Define (OB) and (OC) cyclically. Let AB be the intersection, other than B, of line BC and (OB). Define BC and CA cyclically. Let AC be the intersection, other than C, of line BC and (OC). Define BA and CB cyclically. AB, AC, BC, BA, CA, CB lie on a common conic, here named the Conway conic, with center X(40589). (Randy Hutson, December 18, 2020)
X(40589) lies on these lines: {2, 8044}, {3, 34440}, {5, 572}, {6, 2248}, {27, 86}, {36, 2150}, {48, 3868}, {60, 2260}, {71, 110}, {101, 21873}, {141, 7536}, {199, 22133}, {229, 2294}, {284, 501}, {319, 662}, {573, 1147}, {579, 17104}, {849, 16470}, {960, 2360}, {1201, 38858}, {1325, 1953}, {1326, 5301}, {1412, 24471}, {1437, 4269}, {1511, 35069}, {1798, 28266}, {1963, 40214}, {2189, 4303}, {2193, 34586}, {2252, 23059}, {4280, 16519}, {4288, 37836}, {5006, 17053}, {7054, 22054}, {18417, 34544}, {21011, 37158}
X(40589) = complement of X(8044)
X(40589) = complementary conjugate of X(34119)
X(40589) = X(2)-Ceva conjugate of X(58)
X(40589) = perspector of circumconic centered at X(58)
X(40590) lies on these lines: {2, 2995}, {3, 478}, {6, 41}, {9, 37694}, {12, 37}, {58, 38864}, {65, 2092}, {71, 4559}, {109, 37508}, {201, 21033}, {216, 2182}, {221, 37499}, {226, 1465}, {313, 4552}, {314, 32038}, {573, 10571}, {608, 36744}, {651, 1444}, {800, 2264}, {828, 18591}, {941, 3485}, {946, 14749}, {980, 10401}, {1030, 1950}, {1211, 1214}, {1319, 17053}, {1399, 2305}, {1409, 2245}, {1415, 2193}, {1441, 27042}, {1457, 2269}, {2285, 4261}, {2321, 21859}, {3185, 3192}, {4417, 17080}, {4551, 21061}, {5257, 5930}, {5433, 28244}, {5723, 28366}, {16578, 21244}, {16584, 21796}, {17321, 37800}, {20623, 38977}, {32431, 38945}, {34042, 40152}, {34528, 35069}, {34586, 37620}
X(40590) = isogonal conjugate of X(19607)
X(40590) = complement of X(2995)
X(40590) = complementary conjugate of complement of X(3185)
X(40590) = crosssum of X(6) and X(2217)
X(40590) = X(2)-Ceva conjugate of X(65)
X(40590) = perspector of circumconic centered at X(65)
X(40590) = trilinear product X(i)*X(j) for these {i,j}: {37, 10571}, {42, 17080}, {65, 573}, {226, 3185}, {1214, 3192}, {1400, 3869}, {1402, 4417}, {1409, 17555}, {2171, 4225}, {4551, 6589}
X(40591) lies on these lines: {12, 42}, {58, 32656}, {72, 17102}, {73, 228}, {201, 2658}, {354, 1193}, {386, 2140}, {2198, 8776}, {3159, 4064}, {3191, 3192}, {3682, 18643}, {3811, 23050}, {3990, 22063}, {20970, 21796}, {22072, 22400}
X(40591) = complement of isogonal conjugate of X(23383)
X(40591) = complement of isotomic conjugate of X(17220)
X(40591) = complementary conjugate of complement of X(23383)
X(40591) = X(2)-Ceva conjugate of X(71)
X(40591) = perspector of circumconic centered at X(71)
X(40592) lies on these lines: {2, 1029}, {3, 32782}, {9, 19620}, {10, 37294}, {21, 36}, {38, 1326}, {39, 1931}, {56, 37032}, {60, 3916}, {63, 37783}, {81, 593}, {86, 26842}, {99, 321}, {100, 8935}, {110, 4640}, {114, 4220}, {191, 501}, {261, 4359}, {333, 19302}, {553, 1014}, {641, 16441}, {642, 16440}, {662, 3219}, {958, 37405}, {993, 1325}, {1030, 2895}, {1214, 4565}, {1386, 33774}, {1649, 3733}, {1790, 34544}, {1817, 5235}, {2352, 5867}, {2482, 31143}, {2886, 5196}, {2975, 15349}, {3434, 35915}, {3616, 37029}, {4184, 8299}, {4560, 5664}, {4972, 35916}, {4999, 37369}, {5260, 35991}, {5739, 6337}, {5976, 26243}, {6292, 21495}, {6505, 35193}, {6509, 37659}, {6626, 19308}, {6763, 15792}, {7279, 26942}, {7354, 37152}, {8290, 31089}, {11102, 16752}, {11104, 24552}, {11165, 16436}, {15819, 19649}, {16948, 37599}, {17103, 19684}, {17147, 19623}, {17512, 19785}, {21566, 33364}, {21567, 33365}, {24617, 26724}, {27958, 32933}, {34834, 35069}
X(40592) = isogonal conjugate of X(21353)
X(40592) = complement of X(1029)
X(40592) = complementary conjugate of complement of X(1030)
X(40592) = X(2)-Ceva conjugate of X(81)
X(40592) = perspector of circumconic centered at X(81)
X(40592) = X{i}-isoconjugate of X(j) for these {i,j}: {1, 21353}, {6, 502}, {10, 3444}, {37, 267}, {42, 1029}
X(40593) lies on these lines: {7, 34019}, {9, 4569}, {75, 4081}, {85, 142}, {87, 7209}, {348, 2275}, {658, 30988}, {927, 24309}, {982, 3663}, {3729, 4554}, {4572, 17786}, {4859, 34018}, {6063, 24199}, {17073, 17095}, {20195, 31618}, {20206, 34863}, {20935, 31526}, {21348, 24002}, {30854, 39063}
X(40593) = isotomic conjugate of X(2)-cross conjugate of X(9)
X(40593) = complement of isogonal conjugate of X(20995)
X(40593) = complement of isotomic conjugate of X(3177)
X(40593) = complement of X(19)-isoconjugate of X(20793)
X(40593) = complementary conjugate of complement of X(20995)
X(40593) = X(2)-Ceva conjugate of X(85)
X(40593) = perspector of circumconic centered at X(85)
X(40594) lies on these lines: {2, 8046}, {9, 19618}, {44, 88}, {80, 519}, {903, 17484}, {3306, 40215}, {3689, 14190}, {3911, 36592}, {3936, 4997}, {4358, 4555}, {4792, 21805}, {5541, 39148}, {6631, 30566}, {31171, 35121}
X(40594) = complement of X(8046)
X(40594) = complementary conjugate of complement of X(3196)
X(40594) = X(2)-Ceva conjugate of X(88)
X(40594) = perspector of circumconic centered at X(88)
X(40594) = center of conic {{A,B,C,PU(50)}}
X(40595) lies on these lines: {44, 517}, {101, 35129}, {106, 5053}, {320, 908}, {901, 2183}, {1320, 21801}, {2245, 17969}, {2265, 5375}, {5548, 22356}, {8752, 8756}, {9326, 40215}
X(40595) = complement of isogonal conjugate of X(23858)
X(40595) = complement of isotomic conjugate of X(21290)
X(40595) = complement of X(19)-isoconjugate of X(23135)
X(40595) = complementary conjugate of complement of X(23858)
X(40595) = X(2)-Ceva conjugate of X(106)
X(40595) = perspector of circumconic centered at X(106)
X(40596) lies on these lines: {2, 13573}, {24, 3447}, {110, 8057}, {112, 2485}, {186, 12096}, {232, 15262}, {250, 4558}, {403, 1503}, {523, 32713}, {924, 32715}, {935, 39417}, {1301, 1304}, {1974, 36191}, {2409, 16237}, {9934, 18809}
X(40596) = complement of X(13573)
X(40596) = complementary conjugate of X(23315)
X(40596) = X(2)-Ceva conjugate of X(112)
X(40596) = perspector of circumconic centered at X(112)
X(40597) lies on these lines: {2, 7224}, {3, 8866}, {6, 982}, {83, 226}, {171, 1691}, {238, 9285}, {385, 39928}, {419, 1215}, {1915, 9284}, {1920, 19574}, {2174, 10026}, {2344, 26098}, {2887, 19557}, {3496, 23150}, {3684, 32861}, {3955, 36213}, {4426, 14823}, {4586, 7018}, {5247, 23447}, {7234, 23865}, {8290, 8857}, {20995, 23143}, {25760, 32664}, {27967, 27976}
X(40597) = complement of X(7224)
X(40597) = complementary conjugate of complement of X(23868)
X(40597) = X(2)-Ceva conjugate of X(171)
X(40597) = perspector of circumconic centered at X(171)
X(40598) lies on these lines: {2, 17448}, {8, 17793}, {10, 3662}, {76, 4740}, {120, 3314}, {192, 4110}, {330, 668}, {1211, 23897}, {1278, 20943}, {1575, 21219}, {3177, 4462}, {3452, 3661}, {3617, 3789}, {3679, 31276}, {3730, 20979}, {4661, 22293}, {5233, 16594}, {6554, 17280}, {7885, 31141}, {7904, 34606}, {14434, 25142}, {16589, 26772}, {17294, 30863}, {17349, 27430}, {17350, 24343}, {18140, 32095}, {25120, 25311}, {25277, 25625}, {29572, 37663}, {30713, 31060}
X(40598) = complement of X(38247)
X(40598) = complementary conjugate of complement of X(16969)
X(40598) = X(2)-Ceva conjugate of X(192)
X(40598) = perspector of circumconic centered at X(192)
X(40599) lies on these lines: {37, 3914}, {41, 55}, {142, 14746}, {209, 39258}, {210, 21795}, {226, 35310}, {345, 28797}, {354, 6184}, {1214, 3991}, {1500, 16584}, {2276, 3720}, {2321, 3693}, {3666, 24175}, {3689, 16588}, {3700, 3971}, {3744, 3997}, {4046, 4515}, {5452, 6600}, {9049, 36808}
X(40599) = complement of isogonal conjugate of X(3941)
X(40599) = complement of isotomic conjugate of X(3873)
X(40599) = complementary conjugate of complement of X(3941)
X(40599) = X(2)-Ceva conjugate of X(210)
X(40599) = perspector of circumconic centered at X(210)
X(40600) lies on these lines: {1, 5132}, {3, 35628}, {9, 3185}, {10, 13731}, {42, 181}, {55, 14749}, {71, 6184}, {100, 314}, {142, 16056}, {171, 18724}, {214, 37620}, {442, 4026}, {572, 16872}, {573, 22301}, {1045, 5143}, {1376, 10472}, {1918, 1964}, {2175, 33718}, {4097, 12640}, {4191, 10473}, {4210, 35614}, {4557, 21061}, {6600, 23853}, {10470, 23361}, {10477, 11517}, {16574, 16678}, {22286, 35552}, {22299, 23846}
X(40600) = complement of isogonal conjugate of X(16678)
X(40600) = complement of isotomic conjugate of X(17137)
X(40600) = complement of polar conjugate of X(17913)
X(40600) = complementary conjugate of complement of X(16678)
X(40600) = complementary conjugate of nine-point-circle pole of antiorthic axis
X(40600) = X(2)-Ceva conjugate of X(213)
X(40600) = perspector of circumconic centered at X(213)
X(40601) lies on these lines: {2, 25053}, {6, 3613}, {51, 1196}, {125, 20965}, {216, 9475}, {237, 2211}, {648, 18024}, {1249, 37190}, {1625, 25046}, {2967, 7467}, {3569, 36213}, {5007, 38997}, {8623, 38987}, {14957, 14965}, {37891, 39931}
X(40601) = complement of isotomic conjugate of X(14957)
X(40601) = X(2)-Ceva conjugate of X(237)
X(40601) = perspector of circumconic centered at X(237)
X(40602) lies on these lines: {5, 580}, {6, 2653}, {21, 7004}, {29, 270}, {58, 942}, {60, 14547}, {73, 110}, {141, 7515}, {162, 1935}, {212, 3876}, {238, 1780}, {411, 23692}, {501, 1511}, {581, 1147}, {960, 2328}, {1064, 38850}, {1451, 37791}, {2360, 37836}, {11107, 24430}, {13739, 37591}
X(40602) = complement of isogonal conjugate of X(3145)
X(40602) = complement of isotomic conjugate of X(2893)
X(40602) = complement of polar conjugate of X(18679)
X(40602) = complementary conjugate of complement of X(3145)
X(40602) = X(2)-Ceva conjugate of X(284)
X(40602) = perspector of circumconic centered at X(284)
X(40603) lies on these lines: {2, 18040}, {10, 38}, {37, 27041}, {42, 17793}, {63, 29511}, {75, 30603}, {81, 668}, {306, 3452}, {313, 321}, {2895, 17790}, {3219, 29508}, {3264, 17184}, {3596, 32782}, {3765, 26035}, {3780, 25298}, {3789, 4651}, {3936, 22020}, {3948, 3969}, {3975, 33157}, {3995, 4033}, {4036, 14434}, {6376, 28606}, {6554, 17776}, {10371, 17751}, {16589, 21827}, {16594, 37662}, {17147, 18133}, {17495, 18136}, {17757, 21530}, {18147, 20017}, {18601, 27102}, {19804, 28651}, {19810, 25280}, {21443, 40563}, {26563, 40071}, {27792, 31025}, {27793, 31993}, {30710, 31247}
X(40603) = complement of X(35058)
X(40603) = complementary conjugate of complement of X(16685)
X(40603) = X(2)-Ceva conjugate of X(321)
X(40603) = perspector of circumconic centered at X(321)
X(40604) lies on these lines: {2, 13582}, {3, 2888}, {23, 114}, {39, 2981}, {50, 323}, {94, 99}, {97, 6509}, {618, 6105}, {619, 6104}, {1125, 4996}, {1994, 4558}, {2482, 35296}, {3518, 14111}, {3628, 10276}, {5664, 24978}, {6337, 37644}, {7492, 7710}, {7496, 15819}, {10272, 14354}, {11063, 37779}, {15850, 16042}, {16023, 22892}, {16024, 22848}, {34545, 34990}
X(40604) = isogonal conjugate of X(11071)
X(40604) = complement of X(13582)
X(40604) = complementary conjugate of complement of X(11063)
X(40604) = X(2)-Ceva conjugate of X(323)
X(40604) = perspector of circumconic centered at X(323)
X(40604) = trilinear product X(i)*X(j) for these {i,j}: {63,2914}, {323,1749}, {662,8562}
X(40605) lies on these lines: {1, 15349}, {2, 5110}, {3, 18134}, {21, 21321}, {86, 3666}, {99, 226}, {114, 7413}, {171, 643}, {261, 284}, {314, 20882}, {345, 27958}, {662, 33116}, {811, 1947}, {1010, 1125}, {1043, 2646}, {1211, 6626}, {1326, 29671}, {1649, 7253}, {1944, 7106}, {2305, 17778}, {2887, 35916}, {3736, 17477}, {3752, 25536}, {5333, 17302}, {5712, 6337}, {5976, 39915}, {8299, 13588}, {11104, 26098}, {15604, 17770}, {16050, 40432}, {17190, 27757}, {18155, 27929}, {18755, 27319}, {19270, 24931}, {19803, 25523}, {24378, 24789}, {27398, 27399}, {33113, 40214}
X(40605) = complement of isogonal conjugate of X(2305)
X(40605) = complement of isotomic conjugate of X(17778)
X(40605) = complement of polar conjugate of X(3144)
X(40605) = complementary conjugate of complement of X(2305)
X(40605) = X(2)-Ceva conjugate of X(333)
X(40605) = perspector of circumconic centered at X(333)
X(40606) lies on these lines: {3, 5452}, {6, 31}, {11, 21856}, {210, 6184}, {226, 241}, {354, 21795}, {650, 10164}, {651, 40443}, {1155, 16588}, {1211, 25066}, {1212, 1855}, {1214, 39063}, {2887, 24036}, {3748, 23653}, {4640, 23988}, {4847, 35310}, {5542, 14746}, {5718, 25074}, {8012, 22053}, {14827, 34879}, {18134, 25082}, {20331, 21954}, {23636, 39258}, {25075, 37663}, {26690, 32773}
X(40606) = complement of isogonal conjugate of X(15624)
X(40606) = complement of isotomic conjugate of X(3681)
X(40606) = complement of polar conjugate of X(17916)
X(40606) = complementary conjugate of complement of X(15624)
X(40606) = X(2)-Ceva conjugate of X(354)
X(40606) = perspector of circumconic centered at X(354)
The 2nd (X(1),X(181))-Ceva conic is also the 2nd (X(2),X(1500))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40607) lies on these lines: {2, 13476}, {9, 4557}, {10, 15281}, {37, 42}, {44, 20964}, {72, 16828}, {75, 3952}, {141, 25323}, {513, 17332}, {518, 1125}, {536, 4096}, {594, 4092}, {740, 4015}, {984, 3216}, {1089, 3696}, {1211, 21249}, {1213, 20683}, {1215, 3739}, {1654, 4553}, {2664, 16696}, {3681, 4687}, {3688, 17330}, {3715, 34247}, {3789, 17279}, {3799, 32025}, {3943, 4111}, {3948, 22289}, {3956, 4732}, {3971, 22316}, {3986, 22312}, {4043, 4651}, {4104, 18589}, {4517, 17275}, {4662, 28581}, {4735, 21892}, {5257, 22277}, {10176, 34587}, {14992, 21830}, {15569, 34790}, {16552, 20990}, {16589, 22292}, {17328, 25279}, {20715, 21873}, {21068, 22276}, {21699, 21803}, {21879, 21897}, {39735, 40216}
X(40607) = complement of X(13476)
X(40607) = complementary conjugate of X(3925)
X(40607) = X(2)-Ceva conjugate of X(1500)
X(40607) = perspector of circumconic centered at X(1500)
The 2nd (X(1),X(512))-Ceva conic is also the 2nd (X(2),X(3709))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40608) lies on these lines: {2, 3903}, {8, 7257}, {10, 4531}, {11, 7063}, {115, 512}, {1111, 4761}, {1146, 3271}, {1966, 32850}, {2170, 4041}, {2642, 2643}, {3023, 3907}, {3056, 23902}, {3753, 4085}, {4111, 4711}, {4128, 16592}, {4433, 19589}, {4705, 20982}, {4807, 17761}, {5976, 14839}, {6741, 18191}, {7234, 22373}, {15864, 37568}, {20359, 23922}
X(40608) = complement of X(3903)
X(40608) = complementary conjugate of X(21051)
X(40608) = excentral-to-ABC barycentric image of X(99)
X(40608) = X(99)com(extouch triangle)
X(40608) = X(2)-Ceva conjugate of X(3709)
X(40608) = perspector of circumconic centered at X(3709)
The 2nd (X(1),X(518))-Ceva conic is also the 2nd (X(2),X(3693))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40609) lies on these lines: {1, 40534}, {2, 1280}, {8, 220}, {10, 4904}, {11, 210}, {120, 518}, {200, 1040}, {341, 27390}, {668, 34018}, {918, 2254}, {1145, 3887}, {1211, 8286}, {1639, 38376}, {2348, 3021}, {3243, 30813}, {3693, 3717}, {3870, 4952}, {4046, 6741}, {4152, 6745}, {4383, 36845}, {4422, 4578}, {4543, 14430}, {4738, 24014}, {4899, 9436}, {4953, 25268}, {5845, 20344}, {8580, 33169}, {9451, 26007}, {10025, 32850}, {10580, 25531}, {11019, 24003}, {16589, 16613}, {16594, 26015}, {21530, 34790}
X(40609) = complement of X(1280)
X(40609) = complementary conjugate of X(3823)
X(40609) = X(2)-Ceva conjugate of X(3693)
X(40609) = perspector of circumconic centered at X(3693)
The 2nd (X(75),X(513))-Ceva conic is also the 2nd (X(2),X(4083))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40610) lies on the Steiner inellipse and these lines: {2, 18830}, {37, 20532}, {39, 14823}, {115, 5518}, {190, 20671}, {192, 23643}, {244, 22227}, {256, 7168}, {1015, 1960}, {1146, 39786}, {1500, 4033}, {2092, 35068}, {3123, 6377}, {3124, 40525}, {3666, 35070}, {4364, 21250}, {6184, 21796}, {9294, 35119}, {17321, 27289}, {20979, 21762}, {21830, 35126}
X(40610) = complement of X(18830)
X(40610) = complementary conjugate of complement of X(8640)
X(40610) = crosspoint of X(2) and X(4083)
X(40610) = crosssum of X(6) and X(932)
X(40610) = barycentric square of X(4083)
X(40610) = X(2)-Ceva conjugate of X(4083)
X(40610) = perspector of circumparabola centered at X(4083)
The 2nd (X(10),X(65))-Ceva conic is also the 2nd (X(2),X(1400))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40611) lies on these lines: {1, 9551}, {2, 10571}, {12, 73}, {42, 10474}, {56, 34281}, {65, 1193}, {109, 4225}, {213, 1042}, {221, 13738}, {664, 28660}, {959, 39797}, {1064, 6831}, {1201, 1402}, {1212, 30456}, {1214, 12089}, {1458, 28350}, {1880, 17442}, {4296, 39035}, {4300, 13734}, {4551, 17751}, {6505, 21147}, {14529, 36033}, {19513, 34586}, {24806, 31339}
X(40611) = complement of isogonal conjugate of X(23361)
X(40611) = complement of isotomic conjugate of X(20245)
X(40611) = complement of X(19)-isoconjugate of X(23131)
X(40611) = complementary conjugate of complement of X(23361)
X(40611) = X(2)-Ceva conjugate of X(1400)
X(40611) = perspector of circumconic centered at X(1400)
The 2nd (X(10),X(320))-Ceva conic is also the 2nd (X(2),X(3218))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40612) lies on these lines: {1, 149}, {2, 21739}, {81, 88}, {223, 27131}, {226, 13582}, {323, 1443}, {651, 1214}, {664, 18359}, {1086, 17011}, {1212, 35595}, {1442, 2006}, {2610, 3960}, {3160, 31018}, {3580, 18644}, {5249, 24145}, {5483, 17021}, {6505, 18625}, {11078, 36933}, {11092, 36932}, {11126, 37773}, {11127, 37772}, {14918, 17923}, {16578, 16585}, {26611, 35110}, {27186, 37771}, {30144, 30991}
X(40612) = isogonal conjugate of X(11075)
X(40612) = complement of X(21739)
X(40612) = complementary conjugate of complement of X(19297)
X(40612) = X(2)-Ceva conjugate of X(3218)
X(40612) = perspector of circumconic centered at X(3218)
X(40612) = trilinear product X(i)*X(j) for these {i,j}: {2,6126}, {484,3218}
The 2nd (X(10),X(517))-Ceva conic is also the 2nd (X(2),X(2183))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40613) lies on these lines: {1, 26095}, {11, 1193}, {37, 22063}, {65, 244}, {73, 38985}, {392, 17102}, {995, 4000}, {997, 23050}, {1015, 2260}, {1104, 8054}, {1149, 34590}, {1191, 23404}, {1361, 1457}, {1459, 11700}, {1769, 14299}, {2646, 38983}, {8299, 14414}, {17757, 22350}, {23757, 34587}
X(40613) = X(2)-Ceva conjugate of X(2183)
X(40613) = perspector of circumconic centered at X(2183)
The 2nd (X(10),X(536))-Ceva conic is also the 2nd (X(2),X(899))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40614) lies on these lines: {2, 1018}, {9, 30942}, {11, 1213}, {37, 244}, {42, 38986}, {190, 31002}, {214, 5029}, {649, 4432}, {672, 4370}, {836, 38985}, {899, 3230}, {1015, 3720}, {1100, 8054}, {1635, 8299}, {2238, 38979}, {3161, 30947}, {3218, 6651}, {3768, 4465}, {4094, 38978}, {4358, 17755}, {5163, 9283}, {6377, 14752}, {6544, 21832}, {17441, 34591}, {17754, 36911}, {21580, 30964}, {21894, 39046}, {27481, 31035}
X(40614) = complement of isotomic conjugate of X(29824)
X(40614) = X(2)-Ceva conjugate of X(899)
X(40614) = perspector of circumconic centered at X(899)
The 2nd (X(514),X(7))-Ceva conic is also the 2nd (X(2),X(3676))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40615) lies on these lines: {2, 37206}, {7, 100}, {11, 1111}, {57, 26007}, {226, 16593}, {1086, 14936}, {1357, 3323}, {1617, 17093}, {3119, 26932}, {3665, 5219}, {3676, 3756}, {3699, 35160}, {4106, 38384}, {4468, 5519}, {4904, 38375}, {5173, 36905}, {5435, 31226}, {17107, 20269}, {17272, 19604}, {17718, 24796}, {20343, 36482}, {21208, 38374}
X(40615) = complement of X(37206)
X(40615) = X(2)-Ceva conjugate of X(3676)
X(40615) = perspector of circumconic centered at X(3676)
The 2nd (X(514),X(20))-Ceva conic is also the 2nd (X(2),X(21172))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40616) lies on these lines: {2, 36118}, {3, 6554}, {101, 38554}, {123, 5514}, {189, 1073}, {268, 281}, {441, 37774}, {1146, 2968}, {1565, 3942}, {2822, 3184}, {4534, 35014}, {13609, 13611}, {15905, 27382}
X(40616) = complement of X(36118)
X(40616) = X(2)-Ceva conjugate of X(21172)
X(40616) = perspector of circumconic centered at X(21172)
The 2nd (X(514),X(57))-Ceva conic is also the 2nd (X(2),X(3669))-Ceva conic.
X(40617) lies on these lines: {2, 27825}, {7, 190}, {11, 1357}, {12, 2885}, {56, 1633}, {57, 21362}, {65, 10427}, {226, 16594}, {553, 36913}, {1086, 1358}, {1122, 14524}, {1477, 3021}, {2976, 3756}, {3649, 16597}, {3937, 38351}, {4675, 17107}, {4859, 19604}, {5435, 31227}, {6173, 24796}, {6557, 8051}, {8287, 10933}, {16603, 20343}, {21454, 30577}
X(40617) = complement of X(27834)
X(40617) = complementary conjugate of X(4816)
X(40617) = X(2)-Ceva conjugate of X(3669)
X(40617) = perspector of circumconic centered at X(3669)
The 2nd (X(514),X(69))-Ceva conic is also the 2nd (X(2),X(4025))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40618) lies on these lines: {2, 1815}, {69, 1331}, {77, 4551}, {116, 17198}, {124, 693}, {125, 1565}, {141, 23988}, {1111, 3120}, {1897, 18025}, {2968, 4025}, {5181, 18650}, {17170, 29579}, {17219, 17421}, {25006, 36905}
X(40618) = isotomic conjugate of isogonal conjugate of X(22084)
X(40618) = isotomic conjugate of polar conjugate of X(116)
X(40618) = isotomic conjugate of X(63)-isoconjugate of X(20974)
X(40618) = complement of isogonal conjugate of X(6586)
X(40618) = complement of isotomic conjugate of X(25259)
X(40618) = complement of trilinear pole of line X(3)X(142)
X(40618) = complementary conjugate of complement of X(6586)
X(40618) = X(2)-Ceva conjugate of X(4025)
X(40618) = perspector of circumconic centered at X(4025)
The 2nd (X(514),X(75))-Ceva conic is also the 2nd (X(2),X(693))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40619) lies on these lines: {2, 40216}, {11, 693}, {75, 3952}, {76, 33089}, {85, 35312}, {100, 2481}, {244, 1111}, {321, 20433}, {339, 2968}, {650, 27009}, {1086, 3124}, {1211, 40563}, {2973, 5521}, {3119, 4858}, {3121, 14296}, {3673, 4850}, {4358, 20435}, {4359, 17755}, {4554, 31272}, {4957, 20906}, {5057, 10030}, {5701, 27190}, {13476, 39735}, {14936, 31150}, {16586, 17866}, {17165, 18142}, {17494, 26846}, {18152, 40094}, {20295, 38390}, {20448, 29824}, {20880, 24589}, {21404, 30566}, {23822, 38995}, {25009, 26565}, {27072, 35310}
X(40619) = complement of isogonal conjugate of X(21007)
X(40619) = complement of isotomic conjugate of X(17494)
X(40619) = complement of trilinear pole of line X(10)X(141)
X(40619) = complement of X(19)-isoconjugate of X(22160)
X(40619) = complementary conjugate of complement of X(21007)
X(40619) = X(2)-Ceva conjugate of X(693)
X(40619) = perspector of circumconic centered at X(693)
The 2nd (X(514),X(86))-Ceva conic is also the 2nd (X(2),X(7192))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40620) lies on these lines: {86, 4427}, {244, 7192}, {274, 27812}, {2669, 17145}, {3120, 17198}, {3121, 16726}, {3952, 18827}, {8025, 17199}, {16700, 39734}, {16887, 27081}, {17169, 37635}, {17175, 29578}
X(40620) = complement of isotomic conjugate of X(31290)
X(40620) = X(2)-Ceva conjugate of X(7192)
X(40620) = perspector of circumconic centered at X(7192)
The 2nd (X(514),X(145))-Ceva conic is also the 2nd (X(2),X(3667))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40621) lies on the Steiner inellipse and these lines: {1, 3039}, {5, 3244}, {6, 644}, {44, 13540}, {115, 2789}, {145, 30720}, {230, 35085}, {346, 24150}, {1086, 1358}, {1107, 35095}, {1108, 23980}, {1146, 2087}, {2885, 3815}, {3554, 23986}, {3756, 4534}, {4521, 5516}, {6184, 12640}, {7735, 23972}, {8609, 35129}, {13466, 29600}, {14759, 16593}, {15637, 31182}, {15993, 35117}, {24918, 35110}
X(40621) = complement of isogonal conjugate of X(8643)
X(40621) = complement of isotomic conjugate of X(3667)
X(40621) = complementary conjugate of complement of X(8643)
X(40621) = crosspoint of X(2) and X(3667)
X(40621) = crosssum of X(6) and X(1293)
X(40621) = barycentric square of X(3667)
X(40621) = X(2)-Ceva conjugate of X(3667)
X(40621) = perspector of circumparabola centered at X(3667)
The 2nd (X(514),X(226))-Ceva conic is also the 2nd (X(2),X(7178))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40622) lies on these lines: {7, 662}, {11, 1365}, {226, 22003}, {1086, 7117}, {1358, 1367}, {3649, 10427}, {4466, 8287}, {7178, 17058}, {11375, 16597}, {16593, 21617}, {16888, 27691}, {20662, 39063}
X(40622) = X(2)-Ceva conjugate of X(7178)
X(40622) = perspector of circumconic centered at X(7178)
The 2nd (X(514),X(238))-Ceva conic is also the 2nd (X(2),X(659))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40623) lies on these lines: {11, 31003}, {244, 649}, {661, 8054}, {663, 38986}, {1015, 4367}, {1279, 1575}, {2238, 4974}, {2295, 12264}, {3230, 17475}, {4366, 17495}, {4375, 27918}, {4583, 35172}, {32922, 33854}
X(40623) = complement of isogonal conjugate of X(21003)
X(40623) = complement of isotomic conjugate of anticomplement of X(659)
X(40623) = complement of X(19)-isoconjugate of X(22155)
X(40623) = complementary conjugate of complement of X(21003)
X(40623) = X(2)-Ceva conjugate of X(659)
X(40623) = perspector of circumconic centered at X(659)
The 2nd (X(514),X(312))-Ceva conic is also the 2nd (X(2),X(4391))-Ceva conic and the isotomic conjugate of line X(1)X(3). (Randy Hutson, December 18, 2020)
X(40624) lies on these lines: {2, 56188}, {8, 4553}, {75, 4552}, {116, 40626}, {244, 17888}, {312, 25268}, {321, 20879}, {338, 1086}, {651, 18816}, {2170, 3904}, {2517, 21252}, {2968, 2972}, {4359, 16586}, {4391, 23978}, {14920, 29833}, {17023, 18690}, {17755, 20891}, {17790, 28813}, {20892, 20895}, {21422, 52882}, {24220, 54121}, {24224, 40619}
X(40624) = complement of X(56188)
X(40624) = complement of the isotomic conjugate of X(17496)
X(40624) = isotomic conjugate of the isogonal conjugate of X(11998)
X(40624) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 4391}, {572, 513}, {604, 21189}, {649, 12}, {667, 37662}, {1919, 21796}, {2975, 3835}, {11998, 124}, {14829, 21260}, {17074, 17072}, {17496, 2887}, {20986, 514}, {21061, 31946}, {21173, 141}, {22118, 20315}, {23187, 18589}, {24237, 21252}, {38344, 123}, {51662, 17052}, {52139, 4129}, {53566, 21253}, {57091, 21244}, {57125, 21246}, {57129, 1193}, {57244, 626}
X(40624) = X(2)-Ceva conjugate of X(4391)
X(40624) = X(i)-isoconjugate of X(j) for these (i,j): {1415, 56194}, {2149, 34434}
X(40624) = X(i)-Dao conjugate of X(j) for these (i,j): {650, 34434}, {1146, 56194}, {1577, 2051}, {4391, 2}, {21189, 573}, {34589, 4559}, {40624, 56188}
X(40624) = barycentric product X(i)*X(j) for these {i,j}: {75, 34589}, {76, 11998}, {312, 24237}, {314, 53566}, {522, 57244}, {693, 57091}, {850, 57125}, {1969, 38344}, {2975, 34387}, {4391, 17496}, {4858, 14829}, {11109, 17880}, {17074, 23978}, {21173, 35519}
X(40624) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 34434}, {522, 56194}, {572, 2149}, {2975, 59}, {4391, 56188}, {4858, 2051}, {11109, 7012}, {11998, 6}, {14829, 4564}, {17074, 1262}, {17197, 53083}, {17496, 651}, {18191, 52150}, {21173, 109}, {23187, 36059}, {24237, 57}, {34387, 54121}, {34589, 1}, {35519, 56252}, {38344, 48}, {43728, 53702}, {51662, 53321}, {52322, 35307}, {53566, 65}, {57091, 100}, {57125, 110}, {57244, 664}
X(40624) = {X(23978),X(26932)}-harmonic conjugate of X(4391)
X(40624) = pole of line {40467, 50518} with respect to the Feuerbach circumhyperbola
X(40624) = pole of line {4391, 21189} with respect to {{A,B,C,X(2),X(7)}}
X(40624) = pole of line {4391, 55187} with respect to the {{A,B,C,X(1),X(2)}}
X(40624) = pole of line {24237, 34589} with respect to the Steiner inellipse
X(40624) = pole of line {37, 1953} with respect to the Mandart parabola
The 2nd (X(514),X(333))-Ceva conic is also the 2nd (X(2),X(4560))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40625) lies on these lines: {21, 4436}, {1654, 17183}, {3120, 23821}, {4552, 14616}, {4560, 4858}, {6740, 25536}, {7192, 24237}, {7200, 16726}, {17182, 31037}, {17185, 27065}, {17197, 21044}, {25268, 28828}
X(40625) = complement of isotomic conjugate of anticomplement of X(4560)
X(40625) = complement of trilinear pole of line X(758)X(942)
X(40625) = X(2)-Ceva conjugate of X(4560)
X(40625) = perspector of circumconic centered at X(4560)
The 2nd (X(514),X(345))-Ceva conic is also the 2nd (X(2),X(6332))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40626) lies on these lines: {63, 5741}, {69, 1813}, {125, 2968}, {141, 23585}, {244, 24031}, {653, 34393}, {3687, 16586}, {4384, 25000}, {4466, 17880}, {4858, 21044}, {5181, 37836}, {6332, 16596}, {6377, 6388}, {7117, 16731}, {27108, 27509}
X(40626) = isotomic conjugate of polar conjugate of X(124)
X(40626) = isotomic conjugate of X(2)-cross conjugate of X(653)
X(40626) = isotomic conjugate of trilinear pole of line X(109)X(23987)
X(40626) = complement of isogonal conjugate of X(6589)
X(40626) = complement of isotomic conjugate of polar conjugate of X(26704)
X(40626) = complement of isotomic conjugate of anticomplement of X(6332)
X(40626) = complement of isotomic conjugate of trilinear pole of line X(124)X(2968)
X(40626) = complement of isotomic conjugate of crossdifference of X(42) and X(184)
X(40626) = complement of isotomic conjugate of Steiner-circumellipse pole of line X(1)X(4)
X(40626) = complement of trilinear pole of line X(3)X(10)
X(40626) = complementary conjugate of complement of X(6589)
X(40626) = X(2)-Ceva conjugate of X(6332)
X(40626) = perspector of circumconic centered at X(6332)
The 2nd (X(514),X(512))-Ceva conic is also the 2nd (X(2),X(3122))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40627) lies on these lines: {512, 798}, {514, 1921}, {649, 16695}, {650, 3250}, {661, 2533}, {772, 20906}, {2084, 4705}, {4151, 21836}, {6372, 21143}, {14825, 27929}, {27469, 30096}
X(40627) = complement of isotomic conjugate of anticomplement of X(3122)
X(40627) = X(2)-Ceva conjugate of X(3122)
X(40627) = perspector of circumconic centered at X(3122)
The 2nd (X(514),X(512))-Ceva conic is also the 2nd (X(2),X(7004))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40628) lies on these lines: {284, 1021}, {514, 3064}, {521, 652}, {647, 18675}, {650, 1459}, {661, 8819}, {1566, 38375}, {4521, 14331}, {4988, 21127}, {20297, 24562}, {20314, 25925}
X(40628) = X(2)-Ceva conjugate of X(7004)
X(40628) = perspector of circumconic centered at X(7004)
The 2nd (X(514),X(527))-Ceva conic is also the 2nd (X(2),X(1638))-Ceva conic. (Randy Hutson, December 18, 2020)
X(40629) lies on these lines: {2, 37131}, {7, 37139}, {11, 514}, {527, 1155}, {650, 1086}, {661, 3942}, {812, 38385}, {908, 16593}, {1639, 35094}, {3218, 24582}, {3259, 6084}, {3321, 3323}, {4465, 16597}, {4521, 26932}, {4643, 9458}, {4988, 16732}, {9318, 17718}, {16594, 30823}, {17484, 31020}, {24499, 33151}, {27929, 38989}, {28534, 39308}, {37757, 37787}
X(40629) = complement of X(37143)
X(40629) = complementary conjugate of complement of X(22108)
X(40629) = X(2)-Ceva conjugate of X(1638)
X(40629) = perspector of circumconic centered at X(1638)
X(40630) lies on the curve X161 and these lines: {2, 14264}, {30, 74}, {125, 32417}, {140, 3470}, {186, 17986}, {403, 16080}, {523, 1138}, {542, 15468}, {549, 14385}, {1494, 7799}, {2394, 15543}, {3233, 12317}, {3524, 36875}, {5054, 9717}, {6070, 20417}, {6699, 14611}, {7471, 16003}, {10257, 14919}, {10295, 10421}, {11539, 39239}, {12068, 14094}, {14480, 15057}, {14568, 38894}, {15054, 36169}, {16319, 40384}, {20379, 36184}, {26879, 38933}, {32836, 36890}
X(40630) = midpoint of X(74) and X(5627)
X(40630) = reflection of X(i) in X(j) for these {i,j}: {5627, 12079}, {14611, 31378}, {31378, 6699}, {34150, 5627}
X(40630) = X(99)-Ceva conjugate of X(2394)
X(40630) = barycentric product X(i)*X(j) for these {i,j}: {1494, 6128}, {2394, 14611}, {6699, 16080}
X(40630) = barycentric quotient X(i)/X(j) for these {i,j}: {6128, 30}, {6699, 11064}, {14611, 2407}
X(40630) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 12079, 34150}, {6070, 20417, 36164}, {36308, 36311, 3580}
Barycentrics (a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)*(2*a^8 - 4*a^6*b^2 + 3*a^4*b^4 - 2*a^2*b^6 + b^8 - 4*a^6*c^2 + 2*a^2*b^4*c^2 - 4*b^6*c^2 + 3*a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :
X(40631) lies on the curve Q161 and these lines: {3, 19553}, {4, 35724}, {5, 23338}, {30, 1141}, {54, 140}, {95, 1238}, {96, 275}, {128, 539}, {186, 523}, {230, 14586}, {403, 933}, {1154, 24147}, {1166, 14788}, {1493, 13856}, {3479, 3480}, {3530, 25042}, {3575, 8883}, {6150, 25150}, {7604, 35018}, {8901, 37938}, {12026, 32744}, {12060, 18400}, {12242, 32904}, {16336, 34837}, {16768, 36966}, {19210, 37452}, {23337, 24573}
X(40631) = midpoint of X(i) and X(j) for these {i,j}: {3, 19553}, {1141, 1157}, {1263, 35729}, {24147, 38618}
X(40631) = reflection of X(i) in X(j) for these {i,j}: {128, 10615}, {16336, 34837}
X(40631) = barycentric product X(i)*X(j) for these {i,j}: {95, 231}, {275, 539}, {13582, 27423}
X(40631) = barycentric quotient X(i)/X(j) for these {i,j}: {231, 5}, {539, 343}, {8882, 2383}, {27423, 37779}
X(40631) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 25044, 36842}, {54, 252, 140}
Points associated with bicevian triangles: X(40632)-X(40661)
This preamble is contributed by Clark Kimberling and Peter Moses, December 8, 2020.
Let P = p : q : r and U = u : v : w be points in the plane of a triangle ABC. Let A'B'C' be the cevian triangle of P and A"B"C" the cevian triangle. Let A* be the midpoint of A' and A", and define B* and C* cyclically. The triangle A*B*C* is here named the (P,U)-bicevian triangle:
A* = 0 : 2 q v + q w + r v : 2 r w + q w + r v
B* = 2 p u + r u + p w : 0 : 2 r w + r u + p w
C* = 2 p u + p v + q u : 2 q v + p v + q u : 0
For example, let DEF be the (X(2),X(4))-bicevian triangle, so that D = 0 : 2 a^2 + b^2 - c^2 : a^2 - b^2 + c^2. The vertices D, E, F lie on the cubics K054 and K124 and on the Moses-Steiner ellipse (see X(6070).
These points lie on the Euler line of DEF:
X(5943) = X(2)-of-DEF
X(8254) = X(3)-of-DEF
X(6153) = X(4)-of-DEF
X(13365) = X(5)-of-DEF
X(40632) = X(20)-of-DEF
The following triangles are perspective to DEF, all with perspector X(5): 3rd and 4th Euler triangles, submedial, infinite altitude, Ehrmann mid-triangle, Gemini 110, 1st and 2nd half-diamonds equilateral triangles, and 1st and 2nd half-diamonds triangles (X(33338).
The circumcircle (M), of DEF, passes through X(i) for i = 125, 137, 11702, 14071, 30480 and has squared radius
(2*(a^2 + b^2 - c^2)^2 - a^2*b^2*(-2 + J^2))*(2*(a^2 - b^2 + c^2)^2 - a^2*c^2*(-2 + J^2))*(2*(-a^2 + b^2 + c^2)^2 - b^2*c^2*(-2 + J^2))/(64*a^2*b^2*c^2*(-2 + J)^2*(2 + J)^2*S^2)
Note that (M) meets the nine-point circle in the points X(125) and X(137).
DEF is the reflection triangle of the medial-of-medial triangle (which is also Gemini triangle 110, the X(2)-midcevian triangle, and the excentral triangle of the submedial triangle, if ABC is acute), and DEF is homothetic to the reflection triangle at X(2). (Randy Hutson, December 18, 2020)
Let D' be the point, other than D, where (M) meets the line BC, and define E' and F' cyclically. Then
Let D' = 0 : (a^2 + 2*b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2) : (a^2 - b^2 + 2*c^2)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4).
The triangle D'E'F', here named the Maia triangle, is perspective to the following triangles, with perspectors as shown:
1st orthosymmedial (see X(6792); perspector X(40633)
infinite altitude; perspector X(54)
orthic axes triangle (see X(25010)); perspector X(275)
Yiu tangents triangle (see X(7495); perspector X(40634)
The Maia triangle is homothetic to the polar triangle of the nine-point circle at X(8901). (Randy Hutson, December 18, 2020)
X(40632) lies on these lines: {5, 15532}, {51, 13423}, {54, 186}, {195, 511}, {548, 1154}, {1209, 5181}, {1216, 11264}, {1885, 11577}, {2888, 11793}, {3519, 13622}, {3574, 11817}, {3819, 21230}, {3917, 12325}, {5446, 22051}, {5462, 13368}, {5907, 32423}, {5943, 6153}, {5965, 11574}, {6000, 12254}, {6467, 18946}, {9920, 19596}, {9969, 11808}, {10110, 12291}, {10203, 22352}, {10274, 19468}, {10610, 16836}, {10619, 10628}, {10625, 12316}, {11271, 15606}, {11430, 32333}, {11692, 15806}, {11695, 12280}, {12307, 13348}, {13382, 32339}, {13598, 20424}, {13754, 36966}, {15073, 23048}, {15801, 16661}, {18368, 33565}, {21849, 32196}
X(40632) = midpoint of X(i) and X(j) for these {i,j}: {5, 15532}, {54, 21660}, {10625, 12316}
X(40632) = reflection of X(i) in X(j) for these {i,j}: {389, 54}, {2888, 11793}, {5446, 22051}, {6153, 8254}, {11808, 12242}, {12307, 13348}, {13368, 5462}, {13433, 11808}, {13598, 20424}, {32339, 13382}
X(40632) = crosspoint of X(54) and X(13418)
X(40632) = crosssum of X(5) and X(13621)
X(40632) = {X(6153),X(8254)}-harmonic conjugate of X(5943)
X(40633) lies on the cubic K055 and these lines: {6, 24}, {32, 14586}, {1141, 3767}, {1157, 3053}, {1992, 18315}, {5013, 25042}, {7604, 31415}, {11815, 35906}, {18907, 36842}
X(40633) = X(13622)-isoconjugate of X(14213)
X(40633) = barycentric product X(54)*X(13595)
X(40633) = barycentric quotient X(13595)/X(311)
X(40633) = {X(32),X(14586)}-harmonic conjugate of X(25044)
X(40634) lies on these lines: {2, 38429}, {5, 23338}, {54, 550}, {98, 275}, {549, 1157}, {1141, 3845}, {1166, 11585}, {1493, 35720}, {2623, 3051}, {3520, 16035}, {3574, 35728}, {6636, 16030}, {8254, 35888}, {10619, 35721}, {12242, 30484}, {14073, 27423}, {14586, 18907}, {33992, 35885}
X(40634) = barycentric quotient X(39454)/X(15031)
X(40634) = pedal homothetic center of X(54) (see X(3066))
X(40634) = {X(25044),X(36842)}-harmonic conjugate of X(5)
X(40635) lies on these lines: {5, 10}, {12, 1829}, {19, 25}, {26, 32613}, {42, 1953}, {48, 5311}, {65, 3772}, {200, 21867}, {206, 10537}, {210, 2262}, {226, 3827}, {312, 3434}, {518, 4362}, {528, 35652}, {674, 9969}, {756, 2183}, {942, 17061}, {1402, 8609}, {1828, 10895}, {1871, 11500}, {1872, 11496}, {1900, 6284}, {2182, 3745}, {2217, 37539}, {2265, 2308}, {2270, 7322}, {2643, 3725}, {2875, 14717}, {2900, 19589}, {3052, 12723}, {3419, 3714}, {3428, 7395}, {3742, 29645}, {3752, 20276}, {4463, 26227}, {4523, 29670}, {5173, 15253}, {5842, 6756}, {5903, 17064}, {6051, 23846}, {6676, 6690}, {7493, 20243}, {7528, 37820}, {7529, 10679}, {7539, 31245}, {8758, 21318}, {9958, 13754}, {10831, 26377}, {11365, 37696}, {11818, 18407}, {13407, 18732}, {15940, 16072}, {17441, 17718}, {20961, 34857}, {21370, 22769}, {24476, 33144}, {24929, 30142}, {25466, 37613}, {37000, 37122}
X(40636) lies on these lines: {1, 3286}, {354, 1418}, {516, 5045}, {674, 11018}, {916, 16216}, {5572, 34830}
X(40637) lies on these lines: {2, 40216}, {37, 39735}, {55, 17494}, {190, 33798}, {192, 4661}, {239, 3219}, {1655, 21217}, {3177, 4430}, {3957, 10025}, {3995, 40007}, {8267, 16684}, {16588, 27009}, {17495, 25249}, {21795, 23989}
X(40638) lies on these lines: {1, 5132}, {31, 32}, {55, 5277}, {100, 1078}, {595, 38887}, {976, 37575}, {1030, 20994}, {1621, 32009}, {3185, 36014}, {3294, 8053}, {3688, 22369}, {4251, 16693}, {4557, 16552}, {5283, 34247}, {23851, 35342}
X(40639) lies on these lines: {5, 13576}, {11, 116}, {442, 8299}, {528, 3584}, {1018, 2886}, {1111, 6362}, {2170, 28473}, {3140, 18101}, {5511, 38959}, {14839, 24390}
X(40640) lies on these lines: {5, 399}, {23, 11557}, {74, 11562}, {110, 389}, {113, 25739}, {125, 32396}, {182, 15100}, {186, 323}, {265, 34545}, {569, 15102}, {1181, 18933}, {1199, 32423}, {1994, 12383}, {3523, 17847}, {5622, 19140}, {5663, 13353}, {6126, 11570}, {6593, 12825}, {6636, 7731}, {7512, 38898}, {7527, 12270}, {7574, 11805}, {7592, 14683}, {7728, 13470}, {9143, 19456}, {10296, 13202}, {10628, 27866}, {10733, 34155}, {11003, 12412}, {11807, 37945}, {12112, 18403}, {12219, 15462}, {12364, 32325}, {13392, 16532}, {14643, 34826}, {14940, 15068}, {15051, 38448}, {15101, 37471}, {18445, 18932}, {33565, 37347}
X(40641) lies on these lines: {30, 5462}, {51, 216}, {5640, 15466}, {14249, 15043}
X(40642) lies on these lines: {2, 11794}, {184, 31296}, {385, 6636}, {401, 1994}, {14570, 33798}
X(40643) lies on these lines: {3, 3202}, {5, 182}, {6, 27375}, {25, 27370}, {32, 184}, {39, 9418}, {49, 2080}, {54, 12110}, {83, 5012}, {98, 1614}, {110, 1078}, {156, 10104}, {567, 18502}, {569, 10358}, {626, 36213}, {1092, 8722}, {1147, 5171}, {1207, 1915}, {1627, 38854}, {1691, 11360}, {1974, 5034}, {3044, 39652}, {3506, 8150}, {3796, 20993}, {4045, 14133}, {5038, 18374}, {5118, 7782}, {7787, 11003}, {7793, 9544}, {7815, 9306}, {10274, 14676}, {10790, 11402}, {10796, 32046}, {10984, 37479}, {11380, 34397}, {12177, 39840}, {14574, 15257}
X(40644) lies on these lines: {3, 102}, {4, 34956}, {57, 1745}, {142, 14058}, {222, 578}, {389, 1465}, {515, 942}, {970, 7352}, {1214, 11793}, {1364, 3468}, {1425, 6905}, {3075, 39791}, {5562, 17080}, {5907, 37565}, {6000, 17102}, {6942, 19368}, {8726, 21228}, {10110, 20122}, {21484, 34032}
X(40645) lies on these lines: {6, 27375}, {51, 217}, {1503, 10110}, {5943, 34850}
X(40646) lies on these lines: {354, 1827}, {971, 12005}, {4860, 7004}, {8679, 9969}, {11028, 13476}
X(40647) lies on these lines: {2, 6241}, {3, 49}, {4, 4846}, {5, 2883}, {6, 12085}, {20, 52}, {23, 8718}, {26, 11438}, {30, 143}, {51, 382}, {54, 2071}, {64, 9818}, {68, 15740}, {74, 11562}, {113, 17854}, {125, 10024}, {140, 5663}, {182, 3357}, {195, 37477}, {217, 14961}, {265, 14861}, {373, 3851}, {376, 5889}, {378, 569}, {381, 11381}, {511, 550}, {541, 25711}, {546, 5943}, {548, 1154}, {549, 5876}, {568, 1657}, {578, 12084}, {631, 5891}, {632, 15060}, {916, 31837}, {974, 6146}, {1038, 6238}, {1040, 7352}, {1192, 14070}, {1199, 7464}, {1209, 12827}, {1368, 22660}, {1385, 2807}, {1425, 18455}, {1498, 6642}, {1503, 31833}, {1511, 22966}, {1568, 37452}, {1593, 36752}, {1614, 22467}, {1656, 15030}, {1899, 9927}, {1986, 16111}, {2393, 34785}, {2772, 20117}, {2777, 11557}, {2979, 3528}, {3060, 3529}, {3090, 15305}, {3091, 12290}, {3146, 3567}, {3270, 18447}, {3516, 37506}, {3518, 15053}, {3519, 13623}, {3520, 5012}, {3521, 18403}, {3522, 11412}, {3523, 11459}, {3524, 11444}, {3525, 15056}, {3526, 18435}, {3530, 3819}, {3534, 6243}, {3543, 9781}, {3545, 11439}, {3546, 5654}, {3547, 18913}, {3549, 26937}, {3581, 13564}, {3627, 5946}, {3767, 15575}, {3830, 16226}, {3832, 11455}, {3843, 32062}, {3845, 15026}, {3850, 13363}, {3853, 10095}, {3855, 11451}, {3861, 13364}, {4297, 31728}, {4550, 7395}, {5020, 12315}, {5050, 12294}, {5066, 32205}, {5068, 11465}, {5073, 12002}, {5133, 18488}, {5422, 35502}, {5448, 11585}, {5449, 15760}, {5650, 15720}, {5878, 34944}, {5893, 9826}, {5944, 15646}, {6101, 8703}, {6153, 11802}, {6225, 18537}, {6240, 11750}, {6285, 37696}, {6293, 10606}, {6467, 10937}, {6560, 12239}, {6561, 12240}, {6583, 15229}, {6593, 20190}, {6644, 6759}, {6689, 6696}, {6776, 12118}, {6800, 32534}, {6823, 12359}, {6842, 34462}, {7355, 37697}, {7387, 9786}, {7401, 12324}, {7488, 32110}, {7503, 13336}, {7506, 26883}, {7514, 37515}, {7516, 13347}, {7542, 20191}, {7550, 15054}, {7592, 11413}, {7722, 15055}, {7723, 38727}, {7728, 16223}, {7998, 10299}, {7999, 15717}, {8717, 11414}, {9306, 32139}, {9707, 15078}, {9820, 14156}, {9822, 39884}, {9937, 17818}, {9967, 25406}, {9969, 11819}, {10019, 12133}, {10112, 11232}, {10115, 17712}, {10116, 18914}, {10263, 15704}, {10264, 34826}, {10282, 37814}, {10323, 37478}, {10539, 11456}, {10564, 15032}, {10610, 10628}, {10619, 16163}, {10620, 13339}, {10627, 33923}, {10938, 14852}, {10996, 11411}, {11017, 12812}, {11250, 11430}, {11402, 12058}, {11424, 36753}, {11440, 35921}, {11457, 18474}, {11472, 11479}, {11645, 38322}, {11807, 34584}, {12083, 37490}, {12086, 15033}, {12100, 31834}, {12103, 13391}, {12121, 21649}, {12160, 37483}, {12161, 13346}, {12174, 18451}, {12228, 13293}, {12233, 23335}, {12254, 12280}, {12292, 23515}, {12370, 22952}, {12825, 38793}, {12901, 13198}, {12918, 16225}, {13202, 16222}, {13353, 14130}, {13366, 18859}, {13371, 18388}, {13399, 37347}, {13417, 20127}, {13419, 31830}, {13434, 13445}, {14216, 18420}, {14531, 15696}, {14627, 35452}, {14677, 38898}, {14864, 34514}, {14869, 40247}, {15041, 18364}, {15061, 21650}, {15062, 35500}, {15063, 17853}, {15067, 15712}, {15087, 37495}, {15123, 15129}, {15138, 32345}, {15681, 21969}, {15738, 20397}, {16238, 16252}, {16266, 37480}, {16270, 36253}, {16868, 26913}, {17834, 35243}, {17856, 36518}, {18390, 18952}, {18570, 32392}, {18916, 37201}, {18925, 27082}, {21312, 36747}, {22584, 38728}, {23128, 39913}, {25739, 34007}, {28150, 31757}, {28164, 31760}, {31730, 31732}, {32068, 40240}, {34224, 38323}, {35237, 39568}, {35477, 39242}, {37198, 37486}, {37374, 39271}, {38730, 39817}, {38741, 39846}, {39805, 39860}, {39831, 39834}
X(40647) = midpoint of X(3) and X(185)
X(40647) = reflection of X(1216) in X(3)
X(40647) = complement of X(12162)
X(40647) = X(20) of X(5)-Brocard triangle
X(40648) lies on these lines: {3, 37806}, {57, 3460}, {5122, 22835}, {9940, 16870}
X(40649) lies on these lines: {3, 595}, {43, 57}, {142, 3840}, {511, 3752}, {519, 942}, {982, 9052}, {1015, 21792}, {2999, 3784}, {3216, 29958}, {3666, 3819}, {3688, 17591}, {3742, 39543}, {3779, 18193}, {3917, 4850}, {3937, 32911}, {4000, 37521}, {4014, 33096}, {4253, 20995}, {5650, 28606}, {5745, 6686}, {5943, 16610}, {6688, 16602}, {6904, 20037}, {9776, 10453}, {10219, 31197}, {11227, 29353}, {12109, 24046}, {17063, 21746}, {33150, 33852}
X(40650) lies on these lines: {2, 586}, {326, 1267}, {3086, 17869}, {38487, 38491}, {38488, 39312}
X(40650) = {X(2),X(40651)}-harmonic conjugate of X(40652)
X(40651) lies on these lines: {2, 586}, {9, 13389}, {63, 10252}, {394, 1124}, {440, 31591}, {1125, 6509}, {1214, 31535}, {1267, 38488}, {37861, 38015}, {38487, 38489}, {39314, 39609}
X(40651) = complement of isogonal conjugate of X(605)
X(40651) = complement of isotomic conjugate of X(3083)
X(40651) = complement of polar conjugate of X(6212)
X(40651) = complement of complement of X(37881)
X(40651) = {X(40650),X(40652)}-harmonic conjugate of X(2)
X(40652) lies on these lines: {2, 586}, {3083, 38488}, {38487, 38495}, {39314, 39610}
X(40652) = {X(2),X(40651)}-harmonic conjugate of X(40650)
X(40653) lies on these lines: {1, 1123}, {2, 30416}, {3, 31595}, {142, 13360}, {6600, 18234}, {38487, 38493}, {39313, 39616}
X(40654) lies on these lines: {3, 37815}, {57, 2957}, {142, 40531}, {516, 5122}, {3667, 13226}
X(40655) lies on these lines: {3, 37816}, {942, 35063}, {3008, 6678}, {5087, 5122}, {5972, 12047}, {6723, 14873}, {28239, 28258}
X(40656) lies on these lines: {3, 1104}, {57, 238}, {142, 3846}, {518, 3771}, {579, 20227}, {614, 37581}, {758, 942}, {1108, 20254}, {1427, 37507}, {2886, 12722}, {3306, 16352}, {3666, 8731}, {3812, 32916}, {3848, 25498}, {3911, 6676}, {4260, 11018}, {4463, 31229}, {5437, 16852}, {5439, 16343}, {8727, 9944}, {11227, 29353}, {11997, 33135}, {12723, 17064}, {16056, 16610}, {17441, 24597}, {19788, 30943}, {28389, 37566}
X(40657) lies on these lines: {3, 36908}, {4, 57}, {77, 3345}, {12436, 20205}, {12572, 20206}, {15803, 34050}, {24604, 26723}
X(40658) lies on these lines: {1, 84}, {3, 12335}, {10, 16252}, {40, 154}, {64, 3576}, {65, 10535}, {108, 15498}, {110, 1295}, {159, 9911}, {165, 17821}, {184, 1902}, {185, 11363}, {515, 2883}, {516, 34782}, {517, 6759}, {518, 19149}, {651, 18239}, {912, 32139}, {944, 5656}, {946, 1386}, {962, 11206}, {971, 8144}, {1062, 9942}, {1103, 7070}, {1108, 3073}, {1125, 6247}, {1201, 28381}, {1319, 7355}, {1385, 6000}, {1482, 32063}, {1702, 17819}, {1703, 17820}, {1829, 26883}, {1853, 8227}, {2393, 31812}, {2646, 6285}, {2777, 11699}, {2781, 31738}, {2829, 5930}, {2917, 9591}, {3057, 26888}, {3100, 12671}, {3197, 6769}, {3357, 13624}, {3428, 37250}, {3556, 22770}, {3579, 10282}, {3612, 10060}, {3616, 12324}, {4297, 15311}, {4663, 34117}, {5603, 34781}, {5706, 7686}, {5731, 6225}, {5878, 18481}, {5886, 14216}, {5893, 31673}, {6198, 12664}, {6254, 11189}, {6684, 10192}, {6696, 10165}, {6700, 20307}, {7957, 10536}, {7968, 12964}, {7969, 12970}, {7987, 9899}, {9538, 9960}, {9583, 19088}, {9626, 10117}, {9833, 12699}, {9955, 18381}, {10076, 37618}, {10246, 12315}, {11202, 31663}, {11230, 20299}, {12162, 24301}, {12330, 38288}, {12571, 23324}, {12688, 38336}, {12702, 14530}, {13374, 37543}, {14529, 31786}, {14925, 31788}, {18400, 22793}, {18493, 34780}, {20323, 32065}, {22802, 28160}, {28146, 34785}, {32380, 40263}, {36851, 38035}
X(40659) lies on these lines: {2, 11025}, {7, 3681}, {8, 1229}, {9, 55}, {10, 141}, {46, 5223}, {65, 38200}, {72, 2550}, {144, 17615}, {219, 28043}, {281, 1827}, {354, 20195}, {390, 3876}, {516, 3678}, {517, 18482}, {527, 9954}, {528, 18254}, {756, 4343}, {960, 5853}, {971, 1158}, {1001, 3811}, {2340, 21039}, {2346, 3935}, {3036, 4711}, {3085, 3697}, {3219, 7676}, {3452, 24389}, {3555, 19855}, {3617, 7672}, {3626, 7686}, {3634, 20116}, {3740, 5572}, {3868, 40333}, {3890, 12630}, {4067, 38201}, {4092, 4111}, {4533, 5698}, {5173, 21617}, {5221, 8581}, {5686, 7080}, {5732, 14872}, {5779, 35448}, {5856, 14740}, {5904, 38052}, {6172, 25722}, {7064, 11997}, {7678, 27131}, {8271, 25878}, {8732, 17625}, {10176, 30331}, {10177, 18230}, {10198, 16216}, {14523, 37650}, {15254, 18233}, {15481, 18232}, {15570, 30143}, {17620, 37787}, {18412, 31434}, {25917, 38316}
X(40660) lies on these lines: {1, 154}, {3, 960}, {4, 2182}, {6, 7713}, {8, 11206}, {9, 37320}, {10, 1503}, {19, 5706}, {20, 12779}, {26, 912}, {28, 65}, {40, 219}, {46, 11347}, {48, 37528}, {57, 221}, {63, 37250}, {64, 165}, {66, 3844}, {72, 2915}, {159, 518}, {161, 8185}, {184, 1829}, {206, 942}, {208, 34032}, {284, 3931}, {355, 9833}, {387, 2264}, {406, 5928}, {515, 34782}, {516, 2883}, {517, 6759}, {611, 1773}, {946, 16252}, {1071, 3220}, {1125, 10192}, {1155, 7355}, {1177, 2836}, {1214, 1782}, {1385, 10282}, {1439, 34043}, {1452, 19349}, {1482, 14530}, {1486, 12710}, {1495, 11363}, {1610, 14110}, {1619, 8193}, {1633, 30267}, {1697, 2192}, {1698, 1853}, {1708, 13737}, {1709, 37046}, {1763, 7078}, {1836, 14018}, {1842, 5721}, {1854, 3601}, {1858, 14017}, {1864, 4222}, {1902, 26883}, {1944, 37088}, {2390, 37582}, {2393, 4663}, {2771, 13289}, {2778, 9934}, {2781, 31737}, {2818, 37623}, {2917, 9626}, {2939, 3198}, {2948, 9591}, {2956, 3182}, {3057, 10535}, {3079, 3176}, {3157, 34371}, {3194, 30456}, {3211, 19149}, {3295, 18621}, {3357, 31663}, {3416, 5596}, {3562, 7291}, {3576, 17821}, {3579, 6000}, {3616, 35260}, {3634, 23332}, {3683, 13726}, {3694, 38868}, {3743, 24929}, {3751, 9924}, {3811, 39600}, {3812, 7535}, {3869, 7520}, {4219, 12688}, {4295, 7490}, {4401, 8676}, {5090, 31383}, {5656, 6361}, {5657, 34781}, {5691, 17845}, {5709, 15509}, {5745, 20306}, {5786, 39585}, {5847, 34774}, {5894, 12512}, {6197, 38860}, {6225, 9778}, {6244, 12335}, {6247, 6684}, {6285, 11190}, {6678, 12609}, {6696, 10164}, {7387, 9928}, {7412, 12664}, {7497, 7686}, {7523, 25917}, {7959, 37551}, {7968, 10534}, {7969, 10533}, {7973, 7991}, {8282, 20224}, {8567, 16192}, {9306, 37613}, {9616, 19088}, {9712, 14454}, {9780, 32064}, {9956, 18381}, {10391, 13730}, {10606, 35242}, {11202, 13624}, {11231, 20299}, {11396, 26864}, {12259, 13383}, {12675, 22654}, {12702, 32063}, {12785, 32359}, {14216, 26446}, {14925, 31786}, {15254, 16290}, {15311, 31730}, {15324, 40117}, {15726, 15951}, {15823, 19262}, {16475, 19132}, {16980, 34750}, {17594, 19764}, {17819, 18991}, {17820, 18992}, {18383, 38140}, {18400, 18480}, {18405, 18492}, {22802, 28146}, {24474, 32379}, {28160, 34785}, {28538, 31166}, {32065, 32636}, {32278, 38885}, {36851, 38047}
X(40661) lies on these lines: {1, 12867}, {2, 39772}, {4, 5692}, {8, 6598}, {9, 21}, {10, 12}, {30, 5777}, {63, 35979}, {165, 191}, {329, 2475}, {405, 10176}, {498, 18397}, {517, 15911}, {518, 11281}, {936, 1708}, {943, 15910}, {950, 960}, {1125, 14054}, {1762, 3430}, {1794, 3465}, {1858, 18249}, {1864, 10543}, {1901, 21873}, {2771, 20417}, {2900, 5250}, {2949, 6905}, {3036, 4662}, {3419, 3878}, {3452, 10395}, {3487, 5904}, {3647, 5217}, {3650, 17653}, {3679, 5715}, {3681, 11523}, {3682, 16577}, {3715, 33857}, {3740, 8261}, {3868, 25525}, {3877, 12625}, {3929, 12528}, {4420, 31660}, {4866, 16126}, {5044, 6675}, {5128, 11684}, {5220, 12059}, {5552, 18231}, {5693, 6908}, {5694, 6907}, {5728, 25917}, {5791, 18389}, {5812, 37230}, {5884, 6889}, {6175, 28609}, {6745, 14454}, {6829, 31870}, {6843, 37625}, {7580, 31803}, {10123, 15587}, {10399, 16845}, {11499, 16139}, {12053, 24389}, {12572, 18254}, {12635, 37224}, {12691, 26878}
X(406652) lies on the curve Q161 and these lines: {30, 146}, {14354, 31378}
midpoint of X(1138) and X(14451)
on Q161
X(40663) lies on the curve Q161 and these lines: {1, 140}, {2, 2099}, {3, 10573}, {4, 37567}, {5, 5903}, {7, 11237}, {8, 56}, {10, 12}, {11, 517}, {21, 14882}, {30, 80}, {35, 5428}, {36, 952}, {40, 1728}, {43, 24806}, {44, 1877}, {46, 355}, {55, 1006}, {57, 3679}, {63, 34606}, {71, 21933}, {73, 3214}, {78, 37828}, {100, 5172}, {109, 2758}, {119, 13141}, {145, 1388}, {165, 5727}, {171, 5724}, {190, 36926}, {201, 1834}, {214, 519}, {227, 21896}, {298, 36929}, {299, 36928}, {329, 31141}, {354, 31397}, {377, 18962}, {388, 3617}, {395, 7052}, {396, 33655}, {429, 1825}, {474, 26437}, {485, 38235}, {495, 5902}, {496, 5697}, {499, 1482}, {515, 1155}, {516, 5183}, {518, 6735}, {523, 656}, {524, 24324}, {527, 38099}, {528, 37787}, {529, 3036}, {549, 37525}, {550, 37572}, {553, 4745}, {594, 1400}, {604, 17362}, {611, 38116}, {631, 34471}, {664, 7181}, {672, 1146}, {855, 23845}, {899, 1457}, {908, 5123}, {912, 37725}, {920, 11826}, {938, 3303}, {942, 10039}, {944, 5204}, {946, 7173}, {950, 37568}, {956, 1470}, {958, 5554}, {960, 24982}, {962, 10896}, {999, 12647}, {1056, 4860}, {1125, 7294}, {1149, 3756}, {1159, 31479}, {1210, 3057}, {1213, 2171}, {1227, 3264}, {1284, 3932}, {1320, 32198}, {1329, 3869}, {1334, 21049}, {1358, 9436}, {1385, 21155}, {1387, 3582}, {1389, 6952}, {1399, 5247}, {1402, 4046}, {1403, 3703}, {1404, 4969}, {1405, 17369}, {1406, 9370}, {1411, 26727}, {1415, 5291}, {1420, 3632}, {1423, 33165}, {1428, 5846}, {1429, 32847}, {1452, 5090}, {1454, 5794}, {1460, 5774}, {1464, 4551}, {1466, 22759}, {1467, 4882}, {1478, 5790}, {1479, 12702}, {1483, 21842}, {1512, 6001}, {1532, 2800}, {1616, 28074}, {1698, 3340}, {1706, 37550}, {1708, 3419}, {1770, 18480}, {1826, 21866}, {1836, 2093}, {1846, 38462}, {1852, 6197}, {1858, 31788}, {1861, 1875}, {1866, 1883}, {1869, 1882}, {1901, 21011}, {1935, 18360}, {1940, 5174}, {2098, 3086}, {2197, 21858}, {2238, 4559}, {2245, 2250}, {2285, 17275}, {2294, 21012}, {2295, 21965}, {2348, 8074}, {2362, 13911}, {2475, 12745}, {2550, 12848}, {2594, 3293}, {2646, 6684}, {2802, 20118}, {2975, 37293}, {3017, 24912}, {3035, 4511}, {3058, 3654}, {3109, 5127}, {3212, 3665}, {3244, 17663}, {3245, 3583}, {3256, 5251}, {3336, 18990}, {3339, 9578}, {3361, 4668}, {3416, 39897}, {3428, 11502}, {3436, 18961}, {3452, 31165}, {3474, 12943}, {3485, 9780}, {3486, 5217}, {3530, 37616}, {3555, 10915}, {3576, 37740}, {3579, 10572}, {3584, 5425}, {3585, 18357}, {3600, 4678}, {3601, 9588}, {3612, 37739}, {3614, 9956}, {3621, 5265}, {3626, 10106}, {3628, 5443}, {3656, 23708}, {3704, 3969}, {3746, 12433}, {3782, 37716}, {3812, 24987}, {3813, 14923}, {3814, 34122}, {3816, 3877}, {3820, 5692}, {3826, 7672}, {3828, 4870}, {3868, 12607}, {3871, 32157}, {3876, 9711}, {3878, 4187}, {3880, 13996}, {3881, 13751}, {3895, 34699}, {3913, 11510}, {3930, 21013}, {3943, 21942}, {4031, 38098}, {4032, 4732}, {4295, 5818}, {4298, 4691}, {4299, 18525}, {4315, 4669}, {4316, 28186}, {4317, 37545}, {4323, 19877}, {4424, 4854}, {4654, 5726}, {4661, 18419}, {4677, 13462}, {4714, 6358}, {4863, 34720}, {4868, 16577}, {4880, 24465}, {4973, 15863}, {4995, 24929}, {5044, 13601}, {5048, 28234}, {5080, 13273}, {5086, 7098}, {5122, 21578}, {5128, 5691}, {5131, 9897}, {5180, 37375}, {5219, 18421}, {5222, 31230}, {5225, 20070}, {5228, 36487}, {5260, 18253}, {5270, 24470}, {5326, 11231}, {5552, 12635}, {5563, 34753}, {5599, 18956}, {5600, 18955}, {5687, 37579}, {5730, 26364}, {5740, 21271}, {5836, 6734}, {5837, 8582}, {5854, 38460}, {5881, 15803}, {5882, 37605}, {5886, 25415}, {5901, 11009}, {5904, 26482}, {5905, 11236}, {5919, 11019}, {6048, 37694}, {6049, 20053}, {6147, 37719}, {6224, 13587}, {6361, 12953}, {6681, 34123}, {6702, 11813}, {6736, 24391}, {6738, 37080}, {6788, 40091}, {6842, 35004}, {6905, 12247}, {6907, 18397}, {6922, 26475}, {7146, 29659}, {7211, 21020}, {7280, 34773}, {7483, 30147}, {7741, 22791}, {7807, 30136}, {7951, 38042}, {7968, 18966}, {7969, 18965}, {7982, 11376}, {7991, 9581}, {8162, 10580}, {8362, 30124}, {8581, 24393}, {8666, 34880}, {9579, 37714}, {9583, 9663}, {9661, 35641}, {9708, 37541}, {9710, 15844}, {10056, 15934}, {10058, 35000}, {10072, 34718}, {10090, 19914}, {10164, 37600}, {10175, 17605}, {10265, 17636}, {10310, 22760}, {10401, 17270}, {10529, 10912}, {10593, 15079}, {10826, 12699}, {10914, 10916}, {10954, 37438}, {10955, 34339}, {10958, 15908}, {11010, 15171}, {11238, 30305}, {11280, 37735}, {11373, 30323}, {11529, 17718}, {11571, 11698}, {11682, 25681}, {11822, 11872}, {11823, 11871}, {13145, 37401}, {13407, 31794}, {13724, 23844}, {13747, 30144}, {13973, 16232}, {14026, 23832}, {14584, 23703}, {15172, 37563}, {15298, 38126}, {15500, 23711}, {15829, 24954}, {15867, 26487}, {16137, 37731}, {16210, 18958}, {16236, 25055}, {16589, 20616}, {17023, 31221}, {17051, 31188}, {17619, 21616}, {17747, 21044}, {17950, 24836}, {18481, 37711}, {18591, 21860}, {18635, 21231}, {18967, 25524}, {18995, 19066}, {18996, 19065}, {19029, 35775}, {19030, 35774}, {19636, 36590}, {19860, 24953}, {20085, 36004}, {21273, 24986}, {21672, 21674}, {21857, 40590}, {21871, 24005}, {21888, 21956}, {23846, 28238}, {23958, 34605}, {24223, 26742}, {24440, 37591}, {24541, 31260}, {24633, 26575}, {25466, 27186}, {25557, 30312}, {26481, 31419}, {26752, 28771}, {28212, 37718}, {30852, 34647}, {32141, 36152}, {36574, 37542}, {37524, 37705}, {37618, 37727}
X(40663) = midpoint of X(i) and X(j) for these {i,j}: {80, 484}, {1319, 36920}, {3218, 5176}, {3245, 3583}, {4316, 37006}, {4973, 15863}, {6905, 12247}, {9897, 36975}, {19914, 22765}
X(40663) = reflection of X(i) in X(j) for these {i,j}: {1, 15325}, {11, 1737}, {80, 11545}, {908, 5123}, {1317, 1319}, {1319, 3911}, {3583, 12019}, {4511, 3035}, {5176, 3036}, {6882, 12619}, {11813, 6702}, {15326, 1155}, {17757, 10}, {21578, 5122}
X(40663) = X(i)-Ceva conjugate of X(j) for these (i,j): {14584, 1317}, {23703, 900}
X(40663) = X(21805)-cross conjugate of X(3943)
X(40663) = X(i)-isoconjugate of X(j) for these (i,j): {21, 106}, {29, 36058}, {58, 1320}, {60, 4674}, {81, 2316}, {88, 284}, {110, 23838}, {283, 36125}, {333, 9456}, {643, 23345}, {650, 4591}, {663, 4622}, {901, 3737}, {903, 2194}, {1019, 5548}, {1022, 5546}, {1043, 1417}, {1172, 1797}, {1333, 4997}, {1812, 8752}, {2150, 4080}, {2193, 6336}, {2341, 40215}, {3063, 4615}, {3257, 7252}, {4560, 32665}, {6740, 16944}, {9268, 18191}, {18155, 32719}, {31623, 32659}
X(40663) = crosspoint of X(i) and X(j) for these (i,j): {10, 38955}, {519, 38462}, {655, 4998}
X(40663) = crosssum of X(i) and X(j) for these (i,j): {58, 859}, {106, 36058}, {654, 3271}, {2194, 4282}
X(40663) = trilinear pole of line {4120, 30572}
X(40663) = crossdifference of every pair of points on line {284, 7252}
X(40663) = barycentric product X(i)*X(j) for these {i,j}: {7, 3943}, {10, 3911}, {12, 16704}, {44, 1441}, {57, 3992}, {65, 4358}, {72, 37790}, {85, 21805}, {190, 30572}, {225, 3977}, {226, 519}, {306, 1877}, {307, 8756}, {313, 1404}, {321, 1319}, {349, 902}, {653, 14429}, {664, 4120}, {758, 14628}, {900, 4552}, {1020, 4768}, {1023, 4077}, {1214, 38462}, {1317, 4080}, {1400, 3264}, {1427, 4723}, {1446, 3689}, {1577, 23703}, {1639, 4566}, {2171, 30939}, {2325, 3668}, {3285, 34388}, {3649, 31011}, {3676, 4169}, {3762, 4551}, {3936, 14584}, {3952, 30725}, {4017, 24004}, {4554, 4730}, {4572, 14407}, {5298, 6539}, {5440, 40149}, {7178, 17780}, {17757, 40218}, {24816, 27809}, {26942, 37168}, {30588, 36920}
X(40663) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 4997}, {12, 4080}, {37, 1320}, {42, 2316}, {44, 21}, {65, 88}, {73, 1797}, {109, 4591}, {225, 6336}, {226, 903}, {519, 333}, {651, 4622}, {661, 23838}, {664, 4615}, {900, 4560}, {902, 284}, {1023, 643}, {1317, 16704}, {1319, 81}, {1400, 106}, {1402, 9456}, {1404, 58}, {1409, 36058}, {1441, 20568}, {1464, 40215}, {1635, 3737}, {1639, 7253}, {1647, 17197}, {1877, 27}, {1880, 36125}, {1960, 7252}, {2087, 18191}, {2171, 4674}, {2251, 2194}, {2325, 1043}, {3264, 28660}, {3285, 60}, {3689, 2287}, {3762, 18155}, {3911, 86}, {3943, 8}, {3952, 4582}, {3977, 332}, {3992, 312}, {4017, 1022}, {4120, 522}, {4169, 3699}, {4358, 314}, {4434, 27958}, {4551, 3257}, {4552, 4555}, {4554, 4634}, {4557, 5548}, {4559, 901}, {4730, 650}, {4783, 3975}, {4819, 391}, {4848, 31227}, {4895, 1021}, {4908, 4720}, {5298, 8025}, {5440, 1812}, {7178, 6548}, {7180, 23345}, {8756, 29}, {14407, 663}, {14429, 6332}, {14584, 24624}, {14628, 14616}, {16609, 27922}, {16704, 261}, {17780, 645}, {21805, 9}, {21821, 3689}, {21942, 6735}, {22086, 23189}, {22356, 283}, {23202, 2193}, {23344, 5546}, {23703, 662}, {24004, 7257}, {30572, 514}, {30725, 7192}, {30731, 7256}, {36920, 5235}, {37790, 286}, {38462, 31623}, {40172, 2341}
X(40663) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5445, 140}, {1, 24914, 5433}, {1, 26446, 5432}, {2, 2099, 15950}, {3, 10573, 10950}, {8, 56, 10944}, {8, 1788, 56}, {8, 5435, 3476}, {10, 65, 12}, {10, 72, 21031}, {10, 3753, 3925}, {10, 3754, 442}, {10, 3822, 38058}, {10, 3919, 3822}, {10, 4848, 65}, {12, 65, 3649}, {35, 37730, 10543}, {40, 1837, 6284}, {46, 355, 7354}, {57, 3679, 5252}, {57, 5252, 5434}, {145, 7288, 1388}, {165, 30286, 5727}, {484, 1727, 12515}, {549, 37728, 37525}, {942, 10039, 15888}, {946, 17606, 7173}, {1145, 12832, 1317}, {1210, 3057, 37722}, {1210, 11362, 3057}, {1317, 5298, 1319}, {1319, 3911, 5298}, {1420, 3632, 37738}, {1478, 36279, 11246}, {1698, 3340, 11375}, {1788, 3476, 5435}, {2093, 5587, 1836}, {2362, 13911, 19028}, {3086, 12245, 2098}, {3212, 33298, 3665}, {3293, 37558, 2594}, {3336, 37710, 18990}, {3339, 9578, 10404}, {3361, 4668, 37709}, {3476, 5435, 56}, {3579, 10572, 15338}, {3584, 5425, 5719}, {3654, 5722, 5119}, {3754, 15556, 65}, {3869, 25005, 1329}, {3911, 36920, 1317}, {4295, 5818, 10895}, {4424, 37715, 4854}, {5119, 5722, 3058}, {5131, 9897, 36975}, {5657, 18391, 55}, {5790, 36279, 1478}, {5837, 8582, 25917}, {5903, 18395, 5}, {6702, 11813, 17533}, {6735, 18838, 10956}, {7280, 37706, 34773}, {7991, 9581, 12701}, {9956, 12047, 3614}, {10056, 15934, 37703}, {11010, 37702, 15171}, {11529, 31434, 17718}, {13973, 16232, 19027}, {18421, 19875, 5219}, {19860, 26066, 24953}, {24633, 26575, 30847}, {38042, 39542, 7951}
X(40664) lies on the curve Q161 and these lines: {3, 1075}, {4, 64}, {30, 5667}, {55, 1148}, {56, 7049}, {107, 6000}, {140, 3462}, {186, 523}, {275, 389}, {324, 15053}, {376, 14361}, {378, 3168}, {395, 36303}, {396, 36302}, {436, 5890}, {450, 13754}, {1093, 1204}, {1249, 3524}, {1294, 11589}, {2052, 11438}, {2071, 35360}, {2322, 21162}, {2777, 34170}, {3357, 14249}, {3484, 16813}, {6524, 18931}, {6760, 38605}, {12096, 23239}, {14379, 15318}, {15045, 37124}, {15312, 39221}, {16080, 34329}, {16226, 36794}, {34109, 38672}, {37127, 37481}
X(40664) = midpoint of X(5667) and X(6761)
X(40664) = reflection of X(i) in X(j) for these {i,j}: {1294, 11589}, {6760, 38605}
X(40664) = X(1294)-Ceva conjugate of X(4)
X(40664) = cevapoint of X(1075) and X(5667)
X(40664) = barycentric product X(i)*X(j) for these {i,j}: {2052, 6760}, {16080, 38605}
X(40664) = barycentric quotient X(i)/X(j) for these {i,j}: {6760, 394}, {38605, 11064}
X(40664) = {X(6523),X(12250)}-harmonic conjugate of X(4)
X(40665) lies on the curve Q161 and these lines: {4, 6}, {17, 6113}, {30, 5668}, {125, 23714}, {140, 8837}, {298, 19772}, {395, 3130}, {396, 36296}, {470, 11243}, {471, 2993}, {523, 14446}, {1495, 23715}, {6000, 6110}, {6111, 18400}, {14634, 35469}
X(40665) = midpoint of X(5668) and X(38943)
X(40665) = reflection of X(40666) in X(1990)
X(40665) = crosspoint of X(13) and X(19775)
X(40665) = crosssum of X(15) and X(11244)
X(40665) = crossdifference of every pair of points on line {61, 520}
X(40666) lies on the curve Q161 and these lines: {4, 6}, {18, 6112}, {30, 5669}, {125, 23715}, {140, 8839}, {299, 19773}, {395, 36297}, {396, 3129}, {470, 2992}, {471, 11244}, {523, 14447}, {1495, 23714}, {6000, 6111}, {6110, 18400}, {14634, 35470}
X(40666) = midpoint of X(5669) and X(38944)
X(40666) = reflection of X(40665) in X(1990)
X(40666) = crosspoint of X(14) and X(19774)
X(40666) = crosssum of X(16) and X(11243)
X(40666) = crossdifference of every pair of points on line {62, 520}
X(40667) lies on the curve Q161 and these lines: {16, 17}, {30, 8172}, {299, 11145}, {395, 11087}, {396, 15802}, {523, 14446}, {524, 32036}, {532, 18803}, {930, 40668}, {11078, 11119}, {19294, 23714}, {23303, 36300}
X(40667) = midpoint of X(8172) and X(11600)
X(40667) = X(2981)-isoconjugate of X(3376)
X(40667) = barycentric product X(i)*X(j) for these {i,j}: {17, 532}, {299, 36304}, {396, 19779}, {11139, 14922}, {14446, 32036}
X(40667) = barycentric quotient X(i)/X(j) for these {i,j}: {17, 11117}, {396, 16771}, {532, 302}, {14446, 23872}, {19294, 11146}, {21461, 2380}, {23714, 473}, {30462, 6671}, {36304, 14}
X(40668) lies on the curve Q161 and these lines: {15, 18}, {30, 8173}, {298, 11146}, {395, 15778}, {396, 11082}, {523, 14447}, {524, 32037}, {533, 18804}, {930, 40667}, {11092, 11120}, {19295, 23715}, {23302, 36301}
X(40668) = midpoint of X(8173) and X(11601)
X(40668) = X(3383)-isoconjugate of X(6151)
X(40668) = barycentric product X(i)*X(j) for these {i,j}: {18, 533}, {298, 36305}, {395, 19778}, {11138, 14921}, {14447, 32037}
X(40668) = barycentric quotient X(i)/X(j) for these {i,j}: {18, 11118}, {395, 16770}, {533, 303}, {14447, 23873}, {19295, 11145}, {21462, 2381}, {23715, 472}, {30459, 6672}, {36305, 13}
X(40669) lies on the curve Q161 and these lines: {4, 5221}, {30, 3464}, {140, 3468}, {226, 14873}, {523, 656}, {3649, 27555}
X(40669) = midpoint of X(3464) and X(34301)
Points associated with the pedal triangle of the centroid: X(40670)-X(40673)
This preamble is contributed by Clark Kimberling and Peter Moses, December 9, 2020.
Let T denote the pedal triangle of X(2); T is perspective to these triangles:
orthocentroidal, with perspector X(1992)
1st Ehrmann, with perspector X(1995)
Artzt, with perspector X(2)
infinite altitude, with persector X(2)
anti-Artzt, with perspector X(2)
Gemini 105 triangle, with perspector X(145)
Gemini 107 triangle, with perspector X(1992)
X(2)-of-T = X(373)
X(3)-of-T = X(597)
X(4)-of-T = X(29959)
X(5)-of-T = X(40670)
X(6)-of-T = X(3363)
X(15)-of-T = X(40671)
X(16)-of-T = X(40672)
X(20)-of-T = X(40673)
X(30)-of-T = X(3854)
X(40670) lies on these lines: {2, 9019}, {5, 2781}, {6, 11451}, {51, 141}, {83, 16175}, {182, 15580}, {373, 597}, {511, 547}, {524, 5943}, {542, 13363}, {575, 32205}, {599, 5640}, {1154, 24206}, {1503, 5892}, {1576, 21513}, {1995, 19127}, {2393, 3589}, {2871, 34236}, {2930, 5643}, {2979, 3763}, {3060, 21358}, {3819, 9969}, {5020, 19153}, {5056, 37473}, {5480, 14845}, {5544, 8547}, {5663, 25561}, {5890, 10516}, {5946, 11178}, {6329, 14913}, {6593, 16042}, {8254, 25555}, {9027, 20583}, {10095, 40107}, {11746, 20113}, {12006, 18553}, {15024, 15069}, {15026, 34507}, {15435, 18950}, {15581, 15805}, {20791, 36990}, {21167, 36987}, {23048, 38317}, {25488, 35370}, {34990, 37338}
X(40670) = midpoint of X(i) and X(j) for these {i,j}: {2, 16776}, {51, 141}, {597, 29959}, {3819, 9969}, {5946, 11178}, {6688, 9822}
X(40670) = reflection of X(i) in X(j) for these {i,j}: {3589, 6688}, {3819, 34573}
X(40670) = {X(373),X(29959)}-harmonic conjugate of X(597)
X(40671) lies on these lines: {2, 13}, {6, 22574}, {14, 8593}, {17, 9116}, {18, 33398}, {115, 597}, {395, 33477}, {396, 543}, {524, 5472}, {542, 31693}, {671, 12154}, {1992, 9112}, {2482, 33475}, {5077, 22513}, {5182, 5470}, {5471, 8787}, {6771, 35303}, {6772, 11159}, {6778, 11161}, {7603, 9115}, {8370, 36251}, {8599, 27551}, {9885, 16644}, {10654, 22576}, {11054, 37786}, {11121, 22487}, {11153, 36764}, {11295, 25154}, {11303, 38664}, {11317, 31710}, {14711, 25183}, {16001, 37340}, {20415, 37341}, {32907, 37352}
X(40671) = reflection of X(6115) in X(5459)
X(40671) = circumcircle-of-inner-Napoleon-triangle-inverse of X(22492)
X(40671) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8595, 618}, {13, 5463, 22492}, {115, 18800, 40672}, {597, 3363, 40672}
X(40672) lies on these lines: {2, 14}, {6, 22573}, {13, 8593}, {17, 33399}, {18, 9114}, {115, 597}, {395, 543}, {396, 33476}, {524, 5471}, {542, 31694}, {671, 12155}, {1992, 9113}, {2482, 33474}, {5077, 22512}, {5182, 5469}, {5472, 8787}, {6774, 35304}, {6775, 11159}, {6777, 11161}, {7603, 9117}, {8370, 36252}, {8599, 27550}, {9886, 16645}, {10653, 22575}, {11054, 37785}, {11122, 22488}, {11296, 25164}, {11304, 38664}, {11317, 31709}, {14711, 25187}, {16002, 37341}, {20416, 37340}, {32909, 37351}
X(40672) = reflection of X(6114) in X(5460)
X(40672) = {circumcircle-of-outer-Napoleon-triangle-inverse of X(22491)}
X(40672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8594, 619}, {14, 5464, 22491}, {115, 18800, 40671}, {597, 3363, 40671}
X(40673) lies on these lines: {2, 8681}, {3, 32284}, {6, 25}, {39, 682}, {52, 15074}, {54, 575}, {69, 3819}, {182, 32127}, {185, 1205}, {193, 2979}, {373, 597}, {376, 511}, {389, 15073}, {524, 3917}, {542, 12022}, {567, 39562}, {569, 8548}, {576, 7592}, {578, 10250}, {599, 5650}, {800, 20775}, {1154, 1353}, {1181, 11470}, {1199, 8537}, {1351, 8717}, {1503, 32062}, {1587, 6291}, {1588, 6406}, {1993, 11511}, {1994, 11416}, {2386, 7739}, {3060, 5032}, {3148, 33871}, {3284, 34396}, {3313, 3629}, {3398, 22143}, {3564, 5891}, {3618, 6688}, {4558, 13335}, {4663, 16980}, {5012, 37784}, {5013, 40321}, {5050, 5892}, {5097, 37925}, {5254, 8754}, {5286, 40325}, {5422, 9813}, {5446, 11482}, {5486, 35371}, {5622, 11430}, {5943, 11188}, {6000, 6776}, {6248, 25051}, {7827, 16175}, {7998, 11160}, {8263, 32114}, {8538, 12161}, {8546, 19127}, {8549, 11424}, {8584, 9019}, {8705, 20583}, {9730, 14984}, {9822, 11451}, {10510, 15135}, {10765, 30534}, {11423, 22330}, {11427, 18919}, {11443, 27365}, {11455, 39874}, {11596, 32467}, {12007, 19161}, {14644, 25561}, {14845, 18583}, {14853, 23048}, {15087, 18449}, {15118, 32260}, {15121, 19510}, {17710, 32455}, {18435, 39899}, {18553, 32255}, {18912, 34507}, {18935, 32064}, {19126, 40318}, {22112, 38396}, {22151, 34986}, {26879, 40107}, {32245, 34470}, {34854, 40138}
X(40673) = midpoint of X(i) and X(j) for these {i,j}: {2, 15531}, {51, 6467}, {193, 2979}, {11455, 39874}, {18435, 39899}
X(40673) = reflection of X(i) in X(j) for these {i,j}: {51, 6}, {69, 3819}, {1843, 51}, {2979, 11574}, {11188, 5943}, {14913, 6688}, {29959, 597}
X(40673) = isogonal conjugate of the isotomic conjugate of X(30739)
X(40673) = X(30247)-Ceva conjugate of X(647)
X(40673) = crosspoint of X(i) and X(j) for these (i,j): {4, 21448}, {6, 5486}, {25, 36878}
X(40673) = crosssum of X(i) and X(j) for these (i,j): {2, 1995}, {3, 1992}
X(40673) = barycentric product X(6)*X(30739)
X(40673) = barycentric quotient X(30739)/X(76)
X(40673) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 6467, 1843}, {6, 10602, 8541}, {6, 19459, 1974}, {6, 32366, 6467}, {6, 32621, 184}, {597, 29959, 373}, {13366, 21639, 6}, {22829, 32366, 6}
Points associated with midcevian triangles: X(40674)-X(40696)
This preamble is contributed by Clark Kimberling and Peter Moses, December 9, 2020.
Let U = u : v : w be a point in the plane of a triangle ABC. Let A'B'C' be the cevian triangle of U, and let A'' be the midpoint of the segment AA'. Define B'' and C'' cyclically, so that
A'' = v + w : v : w
B'' = u : w + u : w
C'' = u : v : u + v.
The triangle A''B''C'' is here named the U-midcevian triangle. Examples include
X(1)-midcevian triangle = Gemini triangle 15
X(2)-midcevian triangle = Gemini triangle 110
X(4)-midcevian triangle = half-altitude triangle
X(7)-midcevian triangle = 1st Zaniah triangle
X(8)-midcevian triangle = 2nd Zaniah triangle
X(69)-midcevian triangle = orthic-of-medial triangle = anti-6th-mixtilinear = anticomplement of submedial triangle; see X(11363)
X(75)-midcevian triangle = Gemini triangle 16 = complement of incentral triangle = n(Incentral)*n(Medial) (ETC preamble before X(3739))
X(523)-midcevian triangle = anticevian triangle of X(523) = Schroeter triangle (ETC X(8286) = diagonal triangle of Feuerbach quadrangle of ABC (ETC X(10276)
In general, the U-midcevian triangle is perspective to the following triangles:
ABC, with perspector U
medial triangle, with perspector u v + u w : :
Wasat triangle (see X(21616)), with perspector a u (b + c) - (b v - c w)(b - c) : :
Gemini 7 triangle, with perspector a u (a - b - c) - (b - c)((a - b + c) v + (a + b - c) w) : :
Let T(U) denote the midcevian triangle of U, and let C(U) denote the cevian triangle of U.
The locus of a point X such that T(U) is perspective to C(X) is the cubic pK(X(2),U*), where U* = isotomic conjugate of U.
The locus of X such that T(U) is perspective to the anticevian triangle of X is the cubic pK(u*(v + w) : : , -u + v + w : :). For example, if U = X(3), then the cubic is K044.
The locus of X such that T(X(1)) is perspective to C(X) is the cubic K034.
The locus of X such that T(X(3)) is perspective to C(X) is the cubic K045.
The locus of X such that T(X(4)) is perspective to C(X) is the cubic K007.
The locus of X such that T(X(6)) is perspective to C(X) is the cubic K141.
The locus of X such that T(X(7)) is perspective to C(X) is the cubic K200.
The locus of X such that T(X(8)) is perspective to C(X) is the cubic K1078.
The locus of X such that T(X13)) is perspective to C(X) is the cubic K264a.
The locus of X such that T(X(14)) is perspective to C(X) is the cubic K264b.
X(40674) lies on these lines: {3, 251}, {25, 32078}, {112, 7485}, {216, 1194}, {1368, 6032}, {2548, 7386}, {7499, 22240}, {8879, 39575}, {10691, 15302}, {14570, 40022}, {17409, 37126}
X(40675) lies on these lines: {2, 3183}, {3, 64}, {4, 20208}, {5, 6525}, {30, 35711}, {590, 22838}, {615, 22839}, {1033, 7395}, {1368, 17830}, {2130, 39268}, {2972, 3516}, {3348, 15394}, {3851, 10745}, {5020, 18288}, {5562, 15905}, {10319, 17831}, {12164, 23163}, {17928, 34993}, {18017, 18405}, {20410, 38689}, {26937, 37072}
X(40676) lies on these lines: {112, 37126}, {1297, 7499}, {10749, 12362}, {12145, 21284}
X(40677) lies on these lines: {2, 1726}, {10, 21243}, {48, 20268}, {142, 6678}, {212, 29307}, {226, 1465}, {321, 21429}, {379, 2140}, {908, 33113}, {946, 4314}, {1751, 24789}, {1848, 24220}, {2339, 25527}, {3452, 4422}, {6260, 16388}, {13478, 37695}, {14213, 21072}, {21375, 28776}, {24618, 26724}
X(40678) lies on these lines: {2, 254}, {3, 34428}, {5, 8800}, {6, 1147}, {24, 12095}, {136, 11585}, {1594, 16172}, {2383, 7488}, {3133, 14576}, {6504, 7401}, {9818, 15827}, {40674, 40678}
X(40678) = complement of X(40698)
X(40679) lies on these lines: {2, 1068}, {3, 31}, {3144, 17080}
X(40680) lies on these lines: {2, 216}, {3, 69}, {4, 20477}, {6, 34828}, {20, 317}, {76, 7400}, {83, 28717}, {95, 253}, {141, 36751}, {157, 5596}, {183, 7494}, {193, 577}, {286, 6847}, {309, 17095}, {311, 3547}, {322, 6350}, {325, 7386}, {339, 1272}, {340, 3522}, {376, 32001}, {401, 3087}, {441, 3618}, {464, 4417}, {491, 1590}, {492, 1589}, {524, 36748}, {590, 19439}, {615, 19438}, {631, 32000}, {1007, 1368}, {1232, 32836}, {1235, 7383}, {1494, 15692}, {1656, 8797}, {1975, 10996}, {1976, 6394}, {1992, 15905}, {3146, 32002}, {3260, 3546}, {3537, 32817}, {3538, 32818}, {3548, 32839}, {3549, 32838}, {3619, 20208}, {3620, 10979}, {4648, 21940}, {5054, 36889}, {5224, 25876}, {6146, 10608}, {6349, 19804}, {6617, 18928}, {6639, 32883}, {6640, 32884}, {6641, 14826}, {6643, 32816}, {6676, 34229}, {7763, 14615}, {7782, 22468}, {7803, 28425}, {8573, 11433}, {10565, 26880}, {11206, 33582}, {12362, 32006}, {14555, 21482}, {14853, 30258}, {15705, 35510}, {17102, 17321}, {17234, 25932}, {18531, 32827}, {18589, 29965}, {20080, 22052}, {20563, 34853}, {27377, 35941}, {30771, 34803}
X(40680) = isogonal conjugate of polar conjugate of trilinear product of vertices of anti-Atik triangle
X(40680) = isotomic conjugate of X(1217)
X(40681) lies on these lines: {2, 216}, {3, 1176}, {566, 34828}, {570, 37188}, {3618, 28696}, {6643, 26870}, {7485, 35211}, {11174, 28701}, {26216, 36794}, {34990, 36751}
X(40682) lies on these lines: {3, 13}, {5, 31687}, {30, 35714}, {115, 577}, {216, 5472}, {465, 5459}, {466, 530}, {590, 31689}, {615, 31692}, {1368, 6108}, {2058, 18403}, {3129, 12142}, {3165, 5972}, {6115, 6676}, {12362, 36251}
X(40682) = {X(577),X(18531)}-harmonic conjugate of X(40683)
X(40683) lies on these lines: {3, 14}, {5, 31688}, {30, 35715}, {115, 577}, {216, 5471}, {465, 531}, {466, 5460}, {590, 31691}, {615, 31690}, {1368, 6109}, {2059, 18403}, {3130, 12141}, {3166, 5972}, {6114, 6676}, {12362, 36252}
X(40683) = {X(577),X(18531)}-harmonic conjugate of X(40682)
X(40684) lies on these lines: {2, 216}, {4, 1216}, {5, 6662}, {92, 27131}, {97, 276}, {140, 14978}, {141, 467}, {275, 323}, {297, 14129}, {311, 394}, {338, 14920}, {340, 15108}, {343, 3260}, {458, 1235}, {511, 30506}, {648, 34545}, {850, 38240}, {1075, 15028}, {1093, 5056}, {1232, 6748}, {1629, 6636}, {1656, 13450}, {1896, 37162}, {1947, 27003}, {1948, 27065}, {1994, 36794}, {2972, 11197}, {3108, 16081}, {3168, 11451}, {3266, 18022}, {3917, 39530}, {5012, 37124}, {5066, 34334}, {5068, 14249}, {5392, 37645}, {5422, 9308}, {5943, 35360}, {6194, 6995}, {6515, 6819}, {6530, 37990}, {6531, 34945}, {6747, 24206}, {7485, 33971}, {8884, 37126}, {13366, 35311}, {14566, 14618}, {14768, 35325}, {14918, 37636}, {15526, 34836}, {18026, 26842}, {20477, 37068}, {32142, 35719}, {34289, 38253}
X(40684) = isotomic conjugate of X(31626)
X(40684) = polar conjugate of X(1173)
X(40684) = crosspoint of [polar conjugate of X(61)] and [polar conjugate of X(62)]
X(40685) lies on these lines: {2, 399}, {3, 11801}, {5, 74}, {30, 6699}, {67, 38110}, {110, 632}, {113, 547}, {125, 128}, {141, 9976}, {146, 5055}, {265, 549}, {323, 10821}, {381, 14677}, {389, 30531}, {427, 11566}, {541, 10109}, {542, 10124}, {546, 12041}, {548, 10113}, {550, 14644}, {631, 34153}, {1216, 13358}, {1539, 5066}, {2771, 3634}, {2777, 3850}, {2914, 6143}, {2929, 11250}, {3054, 14901}, {3090, 10620}, {3091, 15041}, {3448, 3526}, {3523, 12902}, {3525, 32609}, {3530, 17702}, {3533, 14683}, {3545, 38790}, {3564, 6698}, {3581, 37938}, {3589, 25556}, {3620, 39562}, {3627, 15055}, {3628, 5663}, {3845, 20127}, {3851, 12244}, {3853, 16111}, {3857, 15021}, {3858, 10721}, {3861, 34584}, {5054, 12383}, {5056, 38789}, {5159, 12358}, {5498, 11430}, {5844, 11735}, {5892, 11561}, {5972, 16239}, {6000, 15350}, {7486, 15046}, {7984, 38112}, {8703, 10733}, {8994, 13979}, {9140, 11539}, {10065, 10593}, {10081, 10592}, {10114, 25401}, {10224, 11438}, {10303, 15040}, {10627, 11800}, {10628, 12006}, {11231, 13605}, {11487, 19348}, {11557, 13363}, {11591, 11806}, {11699, 19862}, {11709, 18357}, {11749, 14993}, {11807, 13364}, {12100, 16163}, {12103, 12295}, {12108, 36253}, {12121, 15712}, {12133, 37942}, {12140, 37935}, {12227, 34331}, {12270, 40280}, {12375, 32789}, {12376, 32790}, {12812, 36518}, {13211, 38028}, {13289, 23332}, {13413, 32743}, {13417, 15026}, {13418, 21230}, {13915, 13969}, {14805, 26913}, {14869, 15027}, {15025, 15704}, {15032, 15806}, {15067, 21649}, {15101, 16223}, {15118, 34380}, {15357, 34127}, {15699, 20126}, {16881, 32144}, {18281, 37643}, {18377, 37487}, {20417, 35018}, {21167, 32273}, {21315, 36164}, {22251, 23236}, {23302, 36208}, {23303, 36209}, {23306, 33533}, {32226, 36153}
X(40685) = complement of X(10272)
X(40686) lies on these lines: {2, 1498}, {3, 161}, {4, 1192}, {5, 64}, {6, 3541}, {20, 18405}, {24, 35217}, {30, 8567}, {66, 5085}, {68, 37497}, {74, 7547}, {125, 1593}, {140, 154}, {155, 18281}, {185, 5094}, {221, 498}, {378, 23294}, {381, 3357}, {382, 23325}, {427, 9786}, {485, 19087}, {486, 19088}, {499, 2192}, {546, 20427}, {549, 9833}, {578, 26944}, {599, 8549}, {631, 1503}, {1075, 15274}, {1092, 15069}, {1181, 37119}, {1204, 7507}, {1350, 23300}, {1352, 16196}, {1587, 13980}, {1588, 8991}, {1594, 10605}, {1595, 17810}, {1620, 18533}, {1656, 6000}, {1657, 11204}, {1698, 6001}, {1737, 1854}, {1899, 11425}, {2777, 3843}, {2781, 3567}, {2883, 3090}, {3088, 13567}, {3091, 15311}, {3146, 23324}, {3147, 16655}, {3515, 11550}, {3520, 18396}, {3523, 32064}, {3525, 10192}, {3526, 6759}, {3534, 34786}, {3538, 36851}, {3542, 15811}, {3545, 5893}, {3546, 11487}, {3548, 17814}, {3575, 37487}, {3614, 12940}, {3624, 40658}, {3851, 22802}, {5054, 10282}, {5055, 13093}, {5056, 6225}, {5067, 5656}, {5068, 15105}, {5070, 12315}, {5073, 18376}, {5418, 17819}, {5420, 17820}, {5449, 12085}, {5587, 12262}, {5654, 32144}, {5663, 31283}, {5886, 7973}, {5890, 12300}, {5907, 30771}, {6143, 11456}, {6293, 9730}, {6353, 16621}, {6624, 35711}, {6640, 18451}, {6697, 10516}, {7173, 12950}, {7378, 11745}, {7401, 34944}, {7404, 17825}, {7506, 10117}, {7512, 15578}, {7529, 18488}, {7552, 20391}, {7566, 15053}, {7729, 12162}, {7741, 10060}, {7951, 10076}, {7988, 9899}, {8252, 12970}, {8253, 12964}, {8254, 17824}, {8889, 12233}, {9934, 34128}, {10175, 12779}, {10249, 11457}, {10264, 12161}, {10303, 11206}, {10519, 15583}, {10574, 31236}, {10620, 32743}, {10625, 34751}, {10982, 26879}, {11202, 14864}, {11250, 12293}, {11410, 21659}, {11411, 37672}, {11413, 23293}, {11424, 26869}, {11439, 15059}, {11442, 35602}, {11468, 35480}, {11477, 23327}, {11572, 37196}, {11598, 14644}, {11744, 23515}, {12084, 13561}, {12111, 30744}, {12163, 13371}, {12173, 21663}, {12174, 13399}, {12241, 23291}, {12325, 40341}, {12359, 37498}, {12902, 25564}, {13293, 38724}, {13568, 18931}, {14070, 20191}, {14528, 31804}, {14530, 15694}, {15030, 31978}, {15041, 19506}, {15058, 31282}, {15063, 15113}, {15116, 16010}, {15126, 15138}, {15131, 16003}, {15238, 20208}, {15559, 20300}, {15873, 37643}, {16195, 29012}, {16266, 17823}, {17809, 18914}, {17834, 23335}, {17835, 23315}, {18909, 23292}, {19843, 20307}, {20376, 32337}, {23336, 32140}, {25739, 35477}, {26883, 37453}, {26917, 35502}, {31074, 32351}, {31423, 40660}, {31489, 32445}, {36201, 38729}
X(40687) lies on these lines: {2, 21361}, {10, 3819}, {57, 24179}, {81, 24618}, {142, 6678}, {226, 4896}, {946, 15325}, {1746, 17074}, {1764, 17077}, {2051, 3911}, {2140, 9776}, {3218, 22000}, {3452, 17332}, {3752, 17197}, {4416, 30006}, {5435, 10478}, {11019, 39543}, {14829, 22020}, {16551, 28951}, {17167, 27003}, {17182, 24627}, {17761, 24177}, {22019, 32939}, {28748, 29529}, {30035, 30567}, {30097, 39595}
X(40688) lies on these lines: {1, 34612}, {2, 45}, {7, 4383}, {11, 17063}, {12, 24174}, {38, 3826}, {42, 25557}, {57, 1723}, {63, 17278}, {65, 24178}, {81, 17366}, {141, 4359}, {142, 3666}, {210, 24231}, {222, 5723}, {226, 16610}, {238, 11246}, {241, 24181}, {244, 2886}, {277, 2982}, {306, 3834}, {321, 7263}, {354, 1738}, {377, 17054}, {442, 24046}, {443, 37549}, {474, 24159}, {495, 1739}, {497, 7613}, {537, 4126}, {553, 3008}, {594, 33172}, {614, 5880}, {748, 17768}, {750, 17061}, {908, 16602}, {940, 4000}, {978, 3649}, {982, 3925}, {1054, 5432}, {1211, 3662}, {1266, 3175}, {1376, 17724}, {1407, 37800}, {1427, 30379}, {1647, 3829}, {1714, 5708}, {1722, 10404}, {1724, 24470}, {1836, 5272}, {1999, 37756}, {2185, 24617}, {2550, 17597}, {2999, 6173}, {3035, 33127}, {3058, 24715}, {3120, 3816}, {3187, 4395}, {3210, 17234}, {3216, 6147}, {3218, 26724}, {3219, 17337}, {3305, 17276}, {3306, 3772}, {3315, 33110}, {3474, 16020}, {3616, 19336}, {3670, 8728}, {3677, 38052}, {3703, 3836}, {3712, 29642}, {3742, 3914}, {3752, 5249}, {3755, 4883}, {3756, 9335}, {3763, 19822}, {3812, 23536}, {3822, 24168}, {3841, 24167}, {3929, 31183}, {3932, 17155}, {3946, 37595}, {3953, 31419}, {3999, 4847}, {4001, 17348}, {4023, 33064}, {4026, 33125}, {4028, 4706}, {4046, 33087}, {4310, 26040}, {4413, 33144}, {4417, 24620}, {4423, 24248}, {4648, 20182}, {4654, 23511}, {4675, 5256}, {4850, 17056}, {4854, 26102}, {4860, 33137}, {4862, 7308}, {4886, 17288}, {4966, 32860}, {4995, 29675}, {5121, 17605}, {5219, 8056}, {5241, 27184}, {5284, 33102}, {5287, 17301}, {5294, 17356}, {5433, 24161}, {5435, 6354}, {5437, 17720}, {5439, 23537}, {5440, 26728}, {5573, 17721}, {5721, 10202}, {5739, 7232}, {5743, 17184}, {5836, 23675}, {5905, 37679}, {6154, 17715}, {6703, 26627}, {7228, 26223}, {7238, 32859}, {7292, 20292}, {7321, 27064}, {7336, 34583}, {9342, 33153}, {9352, 29681}, {9965, 37650}, {10589, 38357}, {11112, 30117}, {11375, 11512}, {12436, 37539}, {13747, 24160}, {15888, 24440}, {16569, 33103}, {16736, 17167}, {16752, 40153}, {16753, 17173}, {16823, 33068}, {16885, 20078}, {17011, 17392}, {17019, 17395}, {17050, 37596}, {17064, 17728}, {17067, 37520}, {17070, 29662}, {17074, 37771}, {17122, 17602}, {17123, 32857}, {17124, 33143}, {17125, 33098}, {17147, 17243}, {17165, 24988}, {17245, 28606}, {17265, 17776}, {17277, 26840}, {17282, 32777}, {17291, 19808}, {17292, 19797}, {17293, 19825}, {17334, 27065}, {17362, 32863}, {17365, 26842}, {17483, 37680}, {17484, 37687}, {17490, 18134}, {17495, 18139}, {17775, 31019}, {18201, 33138}, {18635, 19788}, {19512, 21375}, {19785, 37674}, {20255, 20913}, {21342, 25006}, {21949, 26015}, {24169, 24325}, {24199, 31993}, {24200, 29653}, {24443, 25466}, {24693, 29652}, {24779, 37543}, {24911, 25448}, {25351, 29673}, {25502, 33154}, {26007, 36538}, {27003, 33129}, {28244, 30007}, {29851, 32845}, {30950, 33145}, {31151, 32866}, {31252, 33164}, {33150, 37633}
X(40689) lies on these lines: {3, 3589}, {25, 39}, {32, 39653}, {159, 9605}, {1486, 25066}, {1576, 30435}, {1598, 8721}, {1995, 3926}, {5020, 7795}, {7506, 10983}, {7772, 19459}, {7800, 37491}, {7822, 11284}, {8362, 37485}, {9914, 40053}, {9969, 23115}, {11414, 37479}, {27802, 37592}
X(40689) = eigencenter of Ara triangle
X(40690) lies on these lines: {1, 5074}, {2, 1759}, {10, 626}, {31, 20267}, {41, 4056}, {46, 30742}, {65, 116}, {101, 4911}, {142, 3647}, {226, 241}, {315, 30108}, {519, 4950}, {758, 17046}, {908, 29596}, {946, 15251}, {1125, 25497}, {1155, 24784}, {1770, 17729}, {1836, 14377}, {1930, 4153}, {2051, 36907}, {2140, 12047}, {3120, 24790}, {3585, 9317}, {3673, 24045}, {3674, 5179}, {3730, 7179}, {3741, 30954}, {3825, 17048}, {3835, 21201}, {3878, 17062}, {3997, 24211}, {4129, 34959}, {4251, 4872}, {4253, 17181}, {4797, 6680}, {4920, 16600}, {5011, 33867}, {5030, 17095}, {5757, 24220}, {7272, 9310}, {12609, 39580}, {16549, 33864}, {17044, 18990}, {17198, 39950}, {17266, 31053}, {17605, 24774}, {17671, 33949}, {17736, 28734}, {17745, 24712}, {18589, 37565}, {21258, 39542}, {29578, 31019}
X(40690) = complement of X(1759)
X(40691) lies on these lines: {6, 3926}, {39, 6389}, {4558, 32973}, {5489, 34291}, {7736, 26226}, {26218, 37665}
X(40692) lies on these lines: {6, 28724}, {39, 28696}, {7789, 28710}
X(40693) lies on these lines: {2, 17}, {3, 396}, {4, 13}, {5, 6}, {14, 3091}, {15, 20}, {16, 631}, {18, 3090}, {30, 5340}, {32, 5472}, {69, 635}, {115, 22509}, {140, 16644}, {141, 11311}, {156, 11137}, {193, 623}, {194, 628}, {202, 3086}, {203, 388}, {299, 11289}, {303, 7763}, {371, 2041}, {372, 2042}, {376, 5238}, {381, 398}, {382, 5318}, {395, 1656}, {497, 7005}, {498, 7127}, {524, 11305}, {530, 37172}, {533, 37170}, {546, 5339}, {548, 11480}, {549, 36843}, {550, 36836}, {568, 11624}, {576, 20415}, {597, 11306}, {617, 16529}, {618, 36763}, {622, 7787}, {624, 3618}, {633, 3180}, {1075, 36302}, {1249, 6117}, {1250, 31452}, {1478, 2307}, {1587, 3365}, {1588, 3364}, {1992, 5459}, {2043, 35822}, {2044, 35823}, {2045, 8960}, {2912, 3457}, {3068, 3389}, {3069, 3390}, {3085, 7006}, {3087, 6116}, {3104, 22691}, {3105, 12251}, {3146, 5344}, {3181, 22511}, {3201, 9545}, {3205, 9544}, {3411, 5067}, {3448, 36208}, {3522, 5352}, {3523, 5237}, {3524, 5351}, {3525, 16242}, {3526, 11486}, {3528, 10645}, {3529, 36967}, {3530, 11481}, {3542, 8739}, {3543, 5366}, {3589, 11312}, {3594, 35738}, {3628, 16645}, {3643, 6694}, {3830, 5350}, {3832, 5334}, {3839, 5343}, {3843, 5321}, {3855, 16809}, {4197, 5362}, {4309, 10638}, {4317, 7051}, {5007, 37825}, {5056, 37835}, {5070, 23303}, {5071, 16268}, {5286, 6783}, {5309, 37824}, {5353, 37719}, {5357, 37720}, {5613, 7772}, {5617, 7755}, {5859, 37352}, {5862, 21359}, {5984, 6778}, {6107, 18912}, {6114, 37665}, {6115, 7735}, {6243, 36978}, {6515, 33529}, {6772, 16001}, {6773, 22510}, {6776, 7684}, {6782, 36771}, {7486, 16967}, {7753, 16627}, {7765, 22907}, {8259, 16629}, {8742, 36612}, {8838, 37644}, {8930, 21467}, {9763, 34511}, {9833, 11243}, {10573, 33655}, {10611, 16626}, {10641, 37122}, {10646, 15717}, {10677, 11271}, {11080, 11555}, {11134, 32046}, {11298, 33458}, {11303, 37786}, {11304, 22492}, {12155, 32985}, {14138, 21158}, {16628, 16634}, {16630, 22491}, {17578, 19107}, {18586, 32788}, {18587, 32787}, {19106, 33703}, {20416, 22234}, {22114, 22846}, {22237, 33607}, {30328, 39153}, {33417, 34755}, {36995, 39555}
X(40693) = {X(5),X(6)}-harmonic conjugate of X(40694)
X(40694) lies on these lines: {2, 18}, {3, 395}, {4, 14}, {5, 6}, {13, 3091}, {15, 631}, {16, 20}, {17, 3090}, {30, 5339}, {32, 5471}, {69, 636}, {115, 22507}, {140, 16645}, {141, 11312}, {156, 11134}, {193, 624}, {194, 627}, {202, 388}, {203, 3086}, {298, 11290}, {302, 7763}, {371, 2042}, {372, 2041}, {376, 5237}, {381, 397}, {382, 5321}, {396, 1656}, {497, 7006}, {499, 2307}, {524, 11306}, {531, 37173}, {532, 37171}, {546, 5340}, {548, 11481}, {549, 36836}, {550, 36843}, {568, 11626}, {576, 20416}, {597, 11305}, {616, 16530}, {621, 7787}, {623, 3618}, {634, 3181}, {1075, 36303}, {1249, 6116}, {1250, 4309}, {1479, 7127}, {1587, 3390}, {1588, 3389}, {1992, 5460}, {2043, 35823}, {2044, 35822}, {2046, 8960}, {2913, 3458}, {3068, 3364}, {3069, 3365}, {3085, 7005}, {3087, 6117}, {3104, 12251}, {3105, 22692}, {3146, 5343}, {3180, 22510}, {3200, 9545}, {3206, 9544}, {3412, 5067}, {3448, 36209}, {3522, 5351}, {3523, 5238}, {3524, 5352}, {3525, 16241}, {3526, 11485}, {3528, 10646}, {3529, 36968}, {3530, 11480}, {3542, 8740}, {3543, 5365}, {3589, 11311}, {3592, 35738}, {3628, 16644}, {3642, 6695}, {3830, 5349}, {3832, 5335}, {3839, 5344}, {3843, 5318}, {3855, 16808}, {4197, 5367}, {4317, 19373}, {5007, 37824}, {5056, 37832}, {5070, 23302}, {5071, 16267}, {5286, 6782}, {5309, 37825}, {5353, 37720}, {5357, 37719}, {5613, 7755}, {5617, 7772}, {5858, 37351}, {5863, 21360}, {5984, 6777}, {6106, 18912}, {6114, 7735}, {6115, 37665}, {6243, 36980}, {6515, 33530}, {6770, 22511}, {6775, 16002}, {6776, 7685}, {7052, 10573}, {7486, 16966}, {7753, 16626}, {7765, 22861}, {8260, 16628}, {8741, 36612}, {8836, 37644}, {8929, 21466}, {9761, 34511}, {9833, 11244}, {10612, 16627}, {10638, 31452}, {10642, 37122}, {10645, 15717}, {10678, 11271}, {11085, 11556}, {11137, 32046}, {11297, 33459}, {11303, 22491}, {11304, 37785}, {12154, 32985}, {14136, 36765}, {14139, 21159}, {16629, 16635}, {16631, 22492}, {17578, 19106}, {18586, 32787}, {18587, 32788}, {19107, 33703}, {20415, 22234}, {22113, 22891}, {22235, 33606}, {30327, 39152}, {33416, 34754}, {36993, 39554}
X(40694) = {X(5),X(6)}-harmonic conjugate of X(40693)
X(40695) lies on these lines: {2, 94}, {6, 2981}, {15, 1511}, {16, 11083}, {39, 395}, {50, 11146}, {216, 23302}, {396, 3003}, {470, 11062}, {570, 23303}, {1576, 3131}, {2058, 37848}, {3104, 36980}, {3106, 11626}, {5663, 30260}, {6593, 38431}, {8562, 23284}, {11142, 37776}, {11489, 13351}, {13337, 37641}, {16644, 18573}
X(40695) = isogonal conjugate of X(41907)
X(40695) = complement of X(300)
X(40695) = crosspoint of X(2) and X(15)
X(40695) = crosssum of X(6) and X(13)
X(40695) = X(2)-Ceva conjugate of X(623)
X(40695) = perspector of circumconic centered at X(623)
X(40695) = {X(2),X(566)}-harmonic conjugate of X(40696)
X(40696) lies on these lines: {2, 94}, {6, 6151}, {15, 11088}, {16, 1511}, {39, 396}, {50, 11145}, {216, 23303}, {395, 3003}, {471, 11062}, {570, 23302}, {1576, 3132}, {2059, 37850}, {3105, 36978}, {3107, 11624}, {5663, 30261}, {6593, 38432}, {8562, 23283}, {11141, 37775}, {11488, 13351}, {13337, 37640}, {16242, 40578}, {16645, 18573}
X(40696) = isogonal conjugate of X(41908)
X(40696) = complement of X(301)
X(40696) = crosspoint of X(2) and X(16)
X(40696) = crosssum of X(6) and X(14)
X(40696) = X(2)-Ceva conjugate of X(624)
X(40696) = perspector of circumconic centered at X(624)
X(40696) = {X(2),X(566)}-harmonic conjugate of X(40695)
X(40697) lies on the cubic K045 and these lines: {2, 311}, {3, 69}, {4, 8905}, {20, 1273}, {68, 15827}, {75, 7318}, {76, 7383}, {99, 317}, {193, 571}, {253, 35520}, {254, 264}, {325, 1370}, {343, 36751}, {393, 14570}, {394, 34828}, {427, 1007}, {441, 28708}, {524, 10607}, {1225, 7558}, {1232, 32830}, {1272, 32837}, {1369, 37668}, {1609, 6503}, {1975, 6815}, {3260, 6527}, {3265, 34291}, {3547, 28706}, {3620, 14806}, {5596, 37183}, {6340, 8797}, {6389, 28419}, {7499, 34229}, {7799, 14615}, {8220, 19463}, {8221, 19464}, {13512, 31723}, {14360, 31099}, {14790, 32816}, {15574, 40123}, {15589, 40002}, {17135, 17221}, {18354, 18420}, {18750, 32851}, {20806, 37188}, {28406, 28710}, {30698, 32841}, {36181, 39193}
X(40697) = isogonal conjugate of X(39109)
X(40697) = isotomic conjugate of X(254)
X(40697) = anticomplement of X(2165)
X(40697) = anticomplement of the isogonal conjugate of X(1993)
X(40697) = anticomplement of the isotomic conjugate of X(7763)
X(40697) = isotomic conjugate of the anticomplement of X(34853)
X(40697) = isotomic conjugate of the isogonal conjugate of X(155)
X(40697) = isotomic conjugate of the polar conjugate of X(6515)
X(40697) = polar conjugate of the isogonal conjugate of X(6503)
X(40697) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3, 18664}, {24, 5905}, {47, 2}, {63, 37444}, {92, 68}, {162, 14618}, {317, 21270}, {563, 3164}, {571, 192}, {662, 924}, {924, 21221}, {1101, 4558}, {1147, 6360}, {1444, 18658}, {1748, 4}, {1993, 8}, {2167, 11412}, {2180, 17035}, {2190, 5392}, {2349, 25739}, {6563, 21294}, {7763, 6327}, {9723, 4329}, {11547, 5906}, {18605, 1}, {34948, 4440}, {34952, 21220}, {36034, 6334}
X(40697) = X(i)-Ceva conjugate of X(j) for these (i,j): {264, 69}, {7763, 2}
X(40697) = X(i)-cross conjugate of X(j) for these (i,j): {155, 6515}, {34853, 2}
X(40697) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39109}, {25, 921}, {31, 254}, {1096, 15316}, {1973, 6504}
X(40697) = cevapoint of X(155) and X(6503)
X(40697) = crosssum of X(2971) and X(3049)
X(40697) = crossdifference of every pair of points on line {2489, 34952}
X(40697) = barycentric product X(i)*X(j) for these {i,j}: {63, 33808}, {69, 6515}, {76, 155}, {264, 6503}, {304, 920}, {305, 1609}, {3542, 3926}, {7763, 34853}, {8883, 28706}, {9723, 39116}
X(40697) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 254}, {6, 39109}, {63, 921}, {69, 6504}, {155, 6}, {343, 8800}, {394, 15316}, {454, 1609}, {920, 19}, {925, 39416}, {1609, 25}, {1993, 34756}, {3542, 393}, {3580, 16172}, {4558, 13398}, {6503, 3}, {6515, 4}, {8883, 8882}, {15478, 14910}, {27087, 16310}, {33808, 92}, {34853, 2165}, {35603, 8745}, {39113, 39114}, {39116, 847}
X(40697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 6337, 9723}, {487, 488, 6193}, {3926, 40680, 69}, {6389, 36212, 28419}, {13430, 13441, 2}
X(40698) lies on the cubic K045 and these lines: {2, 254}, {3, 96}, {4, 8906}, {24, 925}, {68, 69}, {1093, 30450}, {2165, 3547}, {3548, 37802}, {5962, 37444}, {5963, 7488}, {6193, 39111}, {7401, 14593}
X(40698) = anticomplement of X(40678)
X(40698) = isogonal conjugate of X(39110)
X(40698) = isotomic conjugate of the isogonal conjugate of X(39111)
X(40698) = X(2190)-anticomplementary conjugate of X(254)
X(40698) = X(264)-Ceva conjugate of X(5392)
X(40698) = X(8905)-cross conjugate of X(6193)
X(40698) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39110}, {47, 34428}
X(40698) = cevapoint of X(8906) and X(34853)
X(40698) = crosssum of X(6754) and X(30451)
X(40698) = barycentric product X(i)*X(j) for these {i,j}: {76, 39111}, {5392, 6193}
X(40698) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39110}, {2165, 34428}, {6193, 1993}, {39111, 6}, {39116, 39115}, {39117, 39114}
X(40698) = {X(32132),X(34853)}-harmonic conjugate of X(2)
X(40699) lies on the cubic K200 and these lines: {8, 175}, {20, 30303}, {144, 13387}, {176, 280}, {346, 15891}, {347, 4847}, {1043, 30336}, {5815, 31551}
X(40699) = isotomic conjugate of X(175)
X(40699) = isotomic conjugate of the anticomplement of X(14121)
X(40699) = isotomic conjugate of the isogonal conjugate of X(30336)
X(40699) = X(30336)-anticomplementary conjugate of X(13386)
X(40699) = X(14121)-cross conjugate of X(2)
X(40699) = X(i)-isoconjugate of X(j) for these (i,j): {31, 175}, {41, 16662}, {604, 30413}, {30335, 34033}
X(40699) = cevapoint of X(15891) and X(34911)
X(40699) = barycentric product X(i)*X(j) for these {i,j}: {75, 15891}, {76, 30336}, {85, 34911}
X(40699) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 175}, {7, 16662}, {8, 30413}, {15891, 1}, {30336, 6}, {30412, 9778}, {34911, 9}
X(40699) = {X(4847),X(32087)}-harmonic conjugate of X(40700)
X(40700) lies on the cubic K200 and these lines: {8, 176}, {20, 30302}, {144, 13386}, {175, 280}, {346, 15892}, {347, 4847}, {1043, 30335}, {5815, 31552}
X(40700) = isotomic conjugate of X(176)
X(40700) = isotomic conjugate of the anticomplement of X(7090)
X(40700) = isotomic conjugate of the isogonal conjugate of X(30335)
X(40700) = X(30335)-anticomplementary conjugate of X(13387)
X(40700) = X(7090)-cross conjugate of X(2)
X(40700) = X(i)-isoconjugate of X(j) for these (i,j): {31, 176}, {41, 16663}, {604, 30412}, {30336, 34033}
X(40700) = cevapoint of X(15892) and X(34912)
X(40700) = barycentric product X(i)*X(j) for these {i,j}: {75, 15892}, {76, 30335}, {85, 34912}, {556, 5451}
X(40700) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 176}, {7, 16663}, {8, 30412}, {5451, 174}, {15892, 1}, {30335, 6}, {30413, 9778}, {34912, 9}
X(40700) = {X(4847),X(32087)}-harmonic conjugate of X(40699)
X(40701) lies on the cubic K1069 and these lines: {8, 18026}, {85, 92}, {264, 1441}, {322, 342}, {348, 13149}, {349, 7017}, {1969, 6063}
X(40701) = isotomic conjugate of X(268)
X(40701) = polar conjugate of X(2192)
X(40701) = isotomic conjugate of the isogonal conjugate of X(196)
X(40701) = polar conjugate of the isogonal conjugate of X(347)
X(40701) = X(i)-Ceva conjugate of X(j) for these (i,j): {1969, 331}, {6063, 264}
X(40701) = X(16596)-cross conjugate of X(17896)
X(40701) = X(i)-isoconjugate of X(j) for these (i,j): {3, 7118}, {6, 2188}, {31, 268}, {32, 271}, {41, 1433}, {48, 2192}, {184, 282}, {212, 1436}, {219, 2208}, {255, 7154}, {280, 9247}, {285, 2200}, {577, 7008}, {603, 7367}, {652, 32652}, {1413, 1802}, {1946, 36049}, {2193, 2357}, {2289, 7151}, {6056, 7129}, {7020, 14585}, {14575, 34404}
X(40701) = cevapoint of X(i) and X(j) for these (i,j): {196, 347}, {16596, 17896}
X(40701) = barycentric product X(i)*X(j) for these {i,j}: {75, 342}, {76, 196}, {208, 561}, {221, 18022}, {223, 1969}, {264, 347}, {273, 322}, {329, 331}, {1502, 3209}, {2331, 20567}, {6063, 7952}, {7011, 18027}, {7017, 14256}, {17896, 18026}
X(40701) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2188}, {2, 268}, {4, 2192}, {7, 1433}, {19, 7118}, {34, 2208}, {40, 212}, {75, 271}, {92, 282}, {108, 32652}, {158, 7008}, {196, 6}, {208, 31}, {221, 184}, {223, 48}, {225, 2357}, {227, 228}, {264, 280}, {273, 84}, {278, 1436}, {281, 7367}, {286, 285}, {322, 78}, {329, 219}, {331, 189}, {342, 1}, {347, 3}, {393, 7154}, {653, 36049}, {1118, 7151}, {1119, 1413}, {1817, 2193}, {1847, 1422}, {1969, 34404}, {2052, 7003}, {2199, 9247}, {2324, 1802}, {2331, 41}, {3194, 2194}, {3195, 2175}, {3209, 32}, {6129, 1946}, {7011, 577}, {7013, 255}, {7078, 6056}, {7080, 1260}, {7952, 55}, {8822, 283}, {13149, 37141}, {14256, 222}, {14837, 652}, {16596, 35072}, {17896, 521}, {18026, 13138}, {21075, 2318}, {27398, 2327}, {36118, 8059}, {38357, 3270}, {38362, 3271}, {38374, 3937}, {40149, 1903}
X(40702) lies on the cubic K184 and these lines: {2, 85}, {7, 2478}, {29, 38298}, {57, 17048}, {63, 1847}, {69, 1034}, {75, 225}, {76, 7182}, {78, 664}, {208, 342}, {223, 27398}, {227, 322}, {304, 4554}, {312, 1231}, {329, 10402}, {404, 3188}, {411, 6516}, {658, 7183}, {936, 9312}, {938, 6604}, {1210, 3673}, {1323, 6700}, {1441, 9780}, {1445, 1760}, {1447, 16048}, {1565, 6922}, {1895, 18026}, {3149, 5088}, {3160, 27383}, {3668, 8582}, {3732, 29464}, {3869, 4566}, {4346, 17863}, {4572, 28659}, {4872, 6836}, {5226, 30845}, {5704, 38468}, {6831, 17181}, {6865, 17170}, {7179, 15844}, {9843, 10481}, {12649, 17158}, {18135, 20946}, {18140, 21609}, {18635, 40593}, {18721, 28742}, {18739, 18751}, {18743, 30843}, {18747, 21617}, {20895, 36640}, {21579, 26611}, {26229, 38859}, {27832, 40014}, {28736, 28739}, {31526, 36854}, {31638, 34018}, {34497, 35102}
X(40702) = isogonal conjugate of X(7118)
X(40702) = isotomic conjugate of X(282)
X(40702) = polar conjugate of X(7008)
X(40702) = isotomic conjugate of the anticomplement of X(20206)
X(40702) = isotomic conjugate of the complement of X(5932)
X(40702) = isotomic conjugate of the isogonal conjugate of X(223)
X(40702) = isotomic conjugate of the polar conjugate of X(342)
X(40702) = polar conjugate of the isogonal conjugate of X(7013)
X(40702) = X(i)-Ceva conjugate of X(j) for these (i,j): {76, 85}, {7182, 75}
X(40702) = X(i)-cross conjugate of X(j) for these (i,j): {223, 342}, {329, 322}, {14256, 85}, {20206, 2}
X(40702) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7118}, {3, 7154}, {6, 2192}, {9, 2208}, {19, 2188}, {25, 268}, {31, 282}, {32, 280}, {41, 84}, {48, 7008}, {55, 1436}, {56, 7367}, {184, 7003}, {189, 2175}, {212, 7129}, {213, 285}, {219, 7151}, {220, 1413}, {271, 1973}, {284, 2357}, {309, 9447}, {480, 6612}, {560, 34404}, {607, 1433}, {650, 32652}, {657, 8059}, {663, 36049}, {1253, 1422}, {1440, 14827}, {1903, 2194}, {1946, 40117}, {3063, 13138}, {7020, 9247}, {8641, 37141}
X(40702) = cevapoint of X(i) and X(j) for these (i,j): {2, 5932}, {223, 7013}, {329, 347}
X(40702) = trilinear pole of line {8058, 17896}
X(40702) = barycentric product X(i)*X(j) for these {i,j}: {7, 322}, {40, 6063}, {69, 342}, {75, 347}, {76, 223}, {85, 329}, {196, 304}, {198, 20567}, {208, 305}, {221, 561}, {227, 310}, {264, 7013}, {312, 14256}, {349, 1817}, {664, 17896}, {1088, 7080}, {1441, 8822}, {1446, 27398}, {1502, 2199}, {1969, 7011}, {3209, 40364}, {4554, 14837}, {4569, 8058}, {4572, 6129}, {6611, 28659}, {7035, 38374}, {7114, 18022}, {7182, 7952}
X(40702) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2192}, {2, 282}, {3, 2188}, {4, 7008}, {6, 7118}, {7, 84}, {9, 7367}, {19, 7154}, {34, 7151}, {40, 55}, {56, 2208}, {57, 1436}, {63, 268}, {65, 2357}, {69, 271}, {75, 280}, {76, 34404}, {77, 1433}, {85, 189}, {86, 285}, {92, 7003}, {109, 32652}, {196, 19}, {198, 41}, {208, 25}, {221, 31}, {223, 6}, {226, 1903}, {227, 42}, {264, 7020}, {269, 1413}, {278, 7129}, {279, 1422}, {322, 8}, {329, 9}, {342, 4}, {347, 1}, {651, 36049}, {653, 40117}, {658, 37141}, {664, 13138}, {738, 6612}, {934, 8059}, {1088, 1440}, {1103, 7074}, {1440, 1256}, {1441, 39130}, {1446, 8808}, {1817, 284}, {2187, 2175}, {2199, 32}, {2324, 220}, {2331, 607}, {2360, 2194}, {3182, 28784}, {3194, 2299}, {3195, 2212}, {3209, 1973}, {3342, 7037}, {5514, 3119}, {5932, 3341}, {6063, 309}, {6129, 663}, {6260, 1864}, {6611, 604}, {7011, 48}, {7013, 3}, {7074, 1253}, {7078, 212}, {7080, 200}, {7114, 184}, {7368, 6602}, {7952, 33}, {8058, 3900}, {8822, 21}, {14256, 57}, {14298, 657}, {14837, 650}, {15501, 2342}, {16596, 34591}, {17896, 522}, {21075, 210}, {21871, 1334}, {27398, 2287}, {37421, 10382}, {38357, 2310}, {38374, 244}, {40212, 198}
X(40702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1446, 85}, {75, 18749, 33672}, {78, 34059, 664}, {85, 31627, 348}, {273, 307, 75}, {279, 26563, 85}, {307, 6734, 33298}, {26563, 37780, 279}
X(40703) is the perspector of the circumconic through the polar conjugates of PU(23). (Randy Hutson, December 18, 2020)
X(40703) lies on the cubic K995 and these lines: {4, 24282}, {19, 27}, {158, 304}, {240, 23996}, {242, 5991}, {264, 7018}, {326, 1096}, {331, 33930}, {561, 18695}, {811, 1784}, {1581, 17901}, {1582, 1954}, {1725, 17881}, {1733, 36036}, {1895, 18156}, {1930, 1969}, {1959, 17875}, {2181, 20627}, {3112, 40440}, {6335, 20947}, {7017, 33931}, {8747, 21595}, {14208, 18076}, {14571, 35551}, {18026, 35149}, {18056, 33808}, {18694, 23994}, {20944, 23999}
X(40703) = isotomic conjugate of X(293)
X(40703) = polar conjugate of X(1910)
X(40703) = isotomic conjugate of the isogonal conjugate of X(240)
X(40703) = polar conjugate of the isogonal conjugate of X(1959)
X(40703) = X(17875)-cross conjugate of X(75)
X(40703) = X(i)-isoconjugate of X(j) for these (i,j): {2, 14600}, {3, 1976}, {6, 248}, {25, 17974}, {31, 293}, {32, 287}, {48, 1910}, {69, 14601}, {98, 184}, {110, 878}, {290, 14575}, {336, 560}, {520, 32696}, {577, 6531}, {647, 2715}, {669, 17932}, {685, 39201}, {810, 36084}, {822, 36104}, {879, 1576}, {1691, 15391}, {1821, 9247}, {1974, 6394}, {2395, 32661}, {2422, 4558}, {2966, 3049}, {5967, 14908}, {9154, 23200}, {10547, 20021}, {14585, 16081}, {18024, 40373}, {18877, 35906}, {20031, 32320}, {35912, 40352}
X(40703) = cevapoint of X(240) and X(1959)
X(40703) = crossdifference of every pair of points on line {810, 9247}
X(40703) = barycentric product X(i)*X(j) for these {i,j}: {75, 297}, {76, 240}, {92, 325}, {158, 6393}, {232, 561}, {264, 1959}, {304, 6530}, {336, 36426}, {511, 1969}, {799, 16230}, {811, 2799}, {823, 6333}, {877, 1577}, {1235, 3405}, {1755, 18022}, {1928, 2211}, {1934, 39931}, {2396, 24006}, {4230, 20948}, {4602, 17994}, {6330, 17875}, {20022, 20883}, {32458, 36120}, {34854, 40364}
X(40703) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 248}, {2, 293}, {4, 1910}, {19, 1976}, {31, 14600}, {63, 17974}, {75, 287}, {76, 336}, {92, 98}, {107, 36104}, {132, 2312}, {158, 6531}, {162, 2715}, {232, 31}, {237, 9247}, {240, 6}, {264, 1821}, {297, 1}, {304, 6394}, {318, 15628}, {325, 63}, {427, 3404}, {511, 48}, {648, 36084}, {661, 878}, {684, 822}, {799, 17932}, {811, 2966}, {823, 685}, {868, 3708}, {877, 662}, {1577, 879}, {1581, 15391}, {1755, 184}, {1784, 35906}, {1959, 3}, {1969, 290}, {1973, 14601}, {2052, 36120}, {2211, 560}, {2396, 4592}, {2421, 4575}, {2450, 2083}, {2799, 656}, {2967, 1755}, {3405, 1176}, {3569, 810}, {4230, 163}, {5360, 2200}, {5968, 36060}, {6331, 36036}, {6333, 24018}, {6393, 326}, {6530, 19}, {9417, 14575}, {14206, 35912}, {15595, 8766}, {16230, 661}, {17209, 1437}, {17875, 441}, {17994, 798}, {19189, 2148}, {20022, 34055}, {20883, 20021}, {23996, 3289}, {23997, 32661}, {24006, 2395}, {24019, 32696}, {34854, 1973}, {35908, 2159}, {35910, 35200}, {36126, 20031}, {36212, 255}, {36426, 240}, {39569, 1953}, {39931, 1580}
X(40703) = {X(1784),X(14210)}-harmonic conjugate of X(811)
X(40704) lies on the cubic K994 and these lines: {2, 7182}, {7, 8}, {57, 24602}, {76, 1229}, {226, 4766}, {239, 1462}, {241, 16728}, {274, 1170}, {279, 304}, {312, 1088}, {321, 6063}, {335, 18033}, {344, 348}, {345, 17093}, {655, 37214}, {664, 4318}, {894, 25001}, {918, 3261}, {1016, 1275}, {1111, 23690}, {1280, 34018}, {1323, 14210}, {1427, 18138}, {1458, 39775}, {1876, 30941}, {1921, 4572}, {1930, 10481}, {1975, 3188}, {1996, 28808}, {2171, 3674}, {2263, 3886}, {2284, 28961}, {3100, 31637}, {3160, 18156}, {3263, 3717}, {3662, 17435}, {3673, 4310}, {3685, 14189}, {4327, 26234}, {4358, 4554}, {4569, 35158}, {4573, 16741}, {4847, 21436}, {4869, 10004}, {5328, 30796}, {5807, 14548}, {7056, 18141}, {7081, 9446}, {7112, 30807}, {7205, 20891}, {8817, 10327}, {17078, 17264}, {17087, 19815}, {17095, 17263}, {18135, 20946}, {18743, 31627}, {23839, 24282}, {25585, 26083}, {26167, 26168}, {29824, 35312}, {30062, 30097}, {32851, 37757}, {32939, 33765}, {40030, 40149}
X(40704) = isotomic conjugate of X(294)
X(40704) = isotomic conjugate of the anticomplement of X(17060)
X(40704) = isotomic conjugate of the isogonal conjugate of X(241)
X(40704) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1037, 20533}, {7131, 20344}, {8817, 20552}
X(40704) = X(i)-cross conjugate of X(j) for these (i,j): {918, 883}, {3912, 3263}, {6184, 40216}, {17060, 2}, {35094, 693}
X(40704) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2195}, {31, 294}, {32, 14942}, {33, 32658}, {41, 105}, {55, 1438}, {101, 884}, {212, 8751}, {220, 1416}, {560, 36796}, {604, 28071}, {607, 36057}, {650, 32666}, {657, 32735}, {663, 919}, {673, 2175}, {692, 1024}, {885, 32739}, {1253, 1462}, {1397, 6559}, {1814, 2212}, {1919, 36802}, {2194, 18785}, {2481, 9447}, {3063, 36086}, {6654, 18265}, {8641, 36146}, {9448, 18031}, {14599, 33676}
X(40704) = cevapoint of X(3912) and X(9436)
X(40704) = crosspoint of X(2481) and X(32023)
X(40704) = crossdifference of every pair of points on line {2175, 3063}
X(40704) = barycentric product X(i)*X(j) for these {i,j}: {7, 3263}, {75, 9436}, {76, 241}, {85, 3912}, {226, 18157}, {304, 5236}, {305, 1876}, {331, 25083}, {334, 39775}, {349, 18206}, {518, 6063}, {561, 1458}, {672, 20567}, {693, 883}, {918, 4554}, {1025, 3261}, {1088, 3717}, {1231, 15149}, {1441, 30941}, {1861, 7182}, {2254, 4572}, {2283, 40495}, {3596, 34855}, {4088, 4625}, {4437, 34018}, {10029, 18743}, {10030, 40217}, {18033, 22116}, {18895, 34253}
X(40704) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2195}, {2, 294}, {7, 105}, {8, 28071}, {57, 1438}, {75, 14942}, {76, 36796}, {77, 36057}, {85, 673}, {109, 32666}, {222, 32658}, {226, 18785}, {241, 6}, {269, 1416}, {273, 36124}, {278, 8751}, {279, 1462}, {312, 6559}, {334, 33676}, {348, 1814}, {513, 884}, {514, 1024}, {518, 55}, {651, 919}, {658, 36146}, {664, 36086}, {665, 3063}, {668, 36802}, {672, 41}, {693, 885}, {883, 100}, {918, 650}, {926, 8641}, {934, 32735}, {1025, 101}, {1026, 3939}, {1362, 2223}, {1441, 13576}, {1458, 31}, {1818, 212}, {1861, 33}, {1876, 25}, {2223, 2175}, {2254, 663}, {2283, 692}, {2340, 1253}, {2356, 2212}, {3126, 926}, {3263, 8}, {3286, 2194}, {3323, 3675}, {3675, 3271}, {3676, 1027}, {3693, 220}, {3717, 200}, {3912, 9}, {3930, 1334}, {3932, 210}, {4025, 23696}, {4088, 4041}, {4391, 28132}, {4437, 3693}, {4447, 2330}, {4554, 666}, {4569, 927}, {4684, 4512}, {4712, 2340}, {4899, 3158}, {4925, 4162}, {4966, 3683}, {4998, 5377}, {5089, 607}, {5236, 19}, {6063, 2481}, {6168, 9310}, {7182, 31637}, {9311, 6169}, {9436, 1}, {9454, 9447}, {9455, 9448}, {10029, 8056}, {10030, 6654}, {15149, 1172}, {16593, 2348}, {17094, 10099}, {17435, 14936}, {17755, 3684}, {18157, 333}, {18206, 284}, {20567, 18031}, {21609, 31638}, {22116, 7077}, {23829, 3737}, {24290, 3709}, {25083, 219}, {27509, 23601}, {30941, 21}, {34018, 6185}, {34253, 1914}, {34855, 56}, {35094, 17435}, {36819, 2342}, {36905, 9441}, {39063, 910}, {39775, 238}, {40217, 4876}
X(40704) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {85, 1231, 20911}, {4358, 37780, 4554}, {7182, 21609, 2}
X(40705) lies on the cubic K276 and these lines: {340, 37779}, {1138, 1272}, {40423, 40427}
X(40705) = isotomic conjugate of X(399)
X(40706) lies on the Kiepert circumhyperbola, the cubic K867a, and these lines: {2, 6151}, {4, 617}, {13, 99}, {14, 299}, {17, 630}, {18, 298}, {83, 396}, {98, 5979}, {115, 11121}, {141, 6034}, {531, 12817}, {598, 9763}, {634, 6774}, {671, 14905}, {1078, 3643}, {1327, 33443}, {1328, 33442}, {3180, 7838}, {3642, 31703}, {5460, 33606}, {5464, 12816}, {5978, 14492}, {5981, 14458}, {6114, 22665}, {6674, 10187}, {6771, 14145}, {6775, 11122}, {7811, 22861}, {10612, 22114}, {13582, 14922}, {16644, 33220}, {22487, 40672}, {22846, 25187}, {33603, 33624}, {33605, 33627}
X(40706) = reflection of X(i) in X(j) for these {i,j}: {99, 30471}, {11121, 115}, {22114, 10612}, {36368, 5460}
X(40706) = isotomic conjugate of X(395)
X(40706) = anticomplement of X(22848)
X(40706) = polar conjugate of X(462)
X(40706) = antigonal image of X(11121)
X(40706) = antitomic image of X(11121)
X(40706) = symgonal image of X(30471)
X(40706) = isotomic conjugate of the complement of X(299)
X(40706) = isotomic conjugate of the isogonal conjugate of X(6151)
X(40706) = isotomic conjugate of the polar conjugate of X(38427)
X(40706) = X(i)-cross conjugate of X(j) for these (i,j): {2, 11120}, {6151, 38427}, {11092, 1494}, {23871, 99}
X(40706) = X(i)-isoconjugate of X(j) for these (i,j): {31, 395}, {48, 462}, {661, 35330}, {798, 35315}, {923, 9117}, {2152, 8015}
X(40706) = cevapoint of X(i) and X(j) for these (i,j): {2, 299}, {6, 34009}
X(40706) = trilinear pole of line {298, 523}
X(40706) = barycentric product X(i)*X(j) for these {i,j}: {69, 38427}, {76, 6151}, {298, 11118}, {299, 11120}, {301, 38404}, {850, 10410}
X(40706) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 395}, {4, 462}, {14, 8015}, {18, 36305}, {99, 35315}, {110, 35330}, {298, 533}, {299, 619}, {303, 6672}, {323, 19295}, {470, 23715}, {524, 9117}, {533, 30459}, {617, 15769}, {628, 15778}, {1338, 3129}, {2381, 3457}, {2992, 3480}, {2993, 38932}, {4427, 35344}, {6151, 6}, {7799, 14921}, {10410, 110}, {11089, 11060}, {11118, 13}, {11120, 14}, {16460, 3458}, {19713, 39135}, {19777, 34295}, {19778, 40668}, {23870, 14447}, {23871, 35444}, {27551, 13305}, {34322, 21462}, {35314, 35345}, {38404, 16}, {38427, 4}, {39261, 3130}
X(40706) = {X(299),X(624)}-harmonic conjugate of X(7809)
X(40707) lies on the Kiepert circumhyperbola, the cubic K867b, and these lines: {2, 2981}, {4, 616}, {13, 298}, {14, 99}, {17, 299}, {18, 629}, {83, 395}, {98, 5978}, {115, 11122}, {141, 6034}, {530, 12816}, {598, 9761}, {633, 6771}, {671, 14904}, {1078, 3642}, {1327, 33441}, {1328, 33440}, {3181, 7838}, {3643, 31704}, {5459, 33607}, {5463, 12817}, {5979, 14492}, {5980, 14458}, {6115, 22666}, {6673, 10188}, {6772, 11121}, {6774, 14144}, {7811, 22907}, {10611, 22113}, {13582, 14921}, {16645, 33220}, {22488, 40671}, {22891, 25183}, {33602, 33622}, {33604, 33626}
X(40707) = reflection of X(i) in X(j) for these {i,j}: {99, 30472}, {11122, 115}, {22113, 10611}, {36366, 5459}, {36782, 629}
X(40707) = isotomic conjugate of X(396)
X(40707) = polar conjugate of X(463)
X(40707) = anticomplement of X(22892)
X(40707) = antigonal image of X(11122)
X(40707) = antitomic image of X(11122)
X(40707) = symgonal image of X(30472)
X(40707) = isotomic conjugate of the complement of X(298)
X(40707) = isotomic conjugate of the isogonal conjugate of X(2981)
X(40707) = isotomic conjugate of the polar conjugate of X(38428)
X(40707) = X(i)-cross conjugate of X(j) for these (i,j): {2, 11119}, {2981, 38428}, {11078, 1494}, {23870, 99}
X(40707) = X(i)-isoconjugate of X(j) for these (i,j): {31, 396}, {48, 463}, {661, 35329}, {798, 35314}, {923, 9115}, {2151, 8014}
X(40707) = cevapoint of X(i) and X(j) for these (i,j): {2, 298}, {6, 34008}
X(40707) = trilinear pole of line {299, 523}
X(40707) = barycentric product X(i)*X(j) for these {i,j}: {69, 38428}, {76, 2981}, {298, 11119}, {299, 11117}, {300, 38403}, {850, 10409}
X(40707) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 396}, {4, 463}, {13, 8014}, {17, 36304}, {99, 35314}, {110, 35329}, {298, 618}, {299, 532}, {302, 6671}, {323, 19294}, {471, 23714}, {524, 9115}, {532, 30462}, {616, 15768}, {627, 15802}, {1337, 3130}, {2380, 3458}, {2981, 6}, {2992, 38931}, {2993, 3479}, {4427, 35343}, {7799, 14922}, {10409, 110}, {11084, 11060}, {11117, 14}, {11119, 13}, {16459, 3457}, {19712, 39134}, {19776, 34296}, {19779, 40667}, {23870, 35443}, {23871, 14446}, {27550, 13304}, {34321, 21461}, {35315, 35345}, {38403, 15}, {38428, 4}, {39262, 3129}
X(40707) = {X(298),X(623)}-harmonic conjugate of X(7809)
X(40708) lies on the cubic K1023 and these lines: {2, 694}, {69, 20819}, {99, 19571}, {125, 305}, {141, 9229}, {264, 5117}, {287, 12215}, {306, 7019}, {307, 337}, {334, 1441}, {805, 2373}, {1494, 18829}, {1799, 3917}, {1976, 39292}, {2076, 16985}, {2396, 20021}, {3506, 5152}, {12294, 40413}, {14603, 18024}, {17938, 37183}, {37134, 37202}
X(40708) = isotomic conjugate of X(419)
X(40708) = isotomic conjugate of the isogonal conjugate of X(36214)
X(40708) = isotomic conjugate of the polar conjugate of X(1916)
X(40708) = isogonal conjugate of the polar conjugate of X(18896)
X(40708) = X(18896)-Ceva conjugate of X(1916)
X(40708) = X(i)-cross conjugate of X(j) for these (i,j): {6393, 69}, {36214, 1916}
X(40708) = X(i)-isoconjugate of X(j) for these (i,j): {4, 1933}, {19, 1691}, {25, 1580}, {31, 419}, {92, 14602}, {162, 5027}, {172, 2201}, {242, 7122}, {385, 1973}, {560, 17984}, {804, 32676}, {1914, 7119}, {1966, 1974}, {1969, 18902}, {2203, 4039}, {2210, 7009}, {4164, 8750}
X(40708) = cevapoint of X(i) and X(j) for these (i,j): {125, 6333}, {3917, 36212}
X(40708) = trilinear pole of line {525, 3933}
X(40708) = barycentric product X(i)*X(j) for these {i,j}: {3, 18896}, {63, 1934}, {69, 1916}, {76, 36214}, {125, 39292}, {257, 337}, {304, 1581}, {305, 694}, {335, 7019}, {525, 18829}, {805, 3267}, {1502, 17970}, {1967, 40364}, {3933, 14970}, {6333, 39291}, {6393, 36897}, {7015, 18895}, {8789, 40360}, {9468, 40050}, {14208, 37134}
X(40708) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 419}, {3, 1691}, {48, 1933}, {63, 1580}, {69, 385}, {76, 17984}, {184, 14602}, {256, 2201}, {257, 242}, {291, 7119}, {295, 172}, {304, 1966}, {305, 3978}, {306, 4039}, {325, 39931}, {335, 7009}, {337, 894}, {525, 804}, {647, 5027}, {694, 25}, {805, 112}, {882, 2489}, {905, 4164}, {1581, 19}, {1916, 4}, {1934, 92}, {1967, 1973}, {2196, 7122}, {3265, 24284}, {3267, 14295}, {3564, 12829}, {3917, 8623}, {3926, 12215}, {3933, 732}, {4025, 4107}, {4563, 17941}, {6390, 5026}, {6393, 5976}, {7015, 1914}, {7019, 239}, {7116, 2210}, {8552, 39495}, {8842, 458}, {8858, 32544}, {9468, 1974}, {12215, 4027}, {14251, 2211}, {14417, 11183}, {14575, 18902}, {14941, 32542}, {14970, 32085}, {15391, 1976}, {15413, 14296}, {17970, 32}, {17980, 2207}, {18829, 648}, {18896, 264}, {20975, 2086}, {32010, 31905}, {34897, 36820}, {36212, 36213}, {36214, 6}, {36800, 14006}, {36897, 6531}, {37134, 162}, {37894, 16985}, {39291, 685}, {39292, 18020}, {40050, 14603}, {40360, 18901}, {40364, 1926}
X(40708) = {X(694),X(8842)}-harmonic conjugate of X(20027)
X(40709) lies on the cubic K3421 and these lines: {2, 13}, {3, 125}, {15, 3580}, {18, 94}, {61, 37644}, {62, 14389}, {69, 36296}, {95, 303}, {141, 11081}, {264, 300}, {287, 38414}, {298, 1494}, {343, 465}, {395, 14836}, {476, 36185}, {621, 19772}, {623, 15441}, {627, 8919}, {858, 14538}, {1989, 16645}, {2373, 5995}, {3129, 32223}, {3130, 3818}, {3132, 21243}, {3170, 22998}, {3448, 14170}, {3589, 11083}, {3763, 11142}, {5473, 36186}, {5617, 32461}, {6330, 36306}, {9205, 20578}, {9761, 18777}, {10217, 11064}, {11092, 36967}, {11127, 37779}, {11581, 40334}, {15066, 36208}, {16771, 16964}, {20428, 37974}, {34417, 37333}, {36299, 36889}, {37172, 37643}, {37340, 37648}
X(40709) = isogonal conjugate of X(8739)
X(40709) = isotomic conjugate of X(470)
X(40709) = isotomic conjugate of the complement of X(19772)
X(40709) = isotomic conjugate of the isogonal conjugate of X(36296)
X(40709) = isotomic conjugate of the polar conjugate of X(13)
X(40709) = isogonal conjugate of the polar conjugate of X(300)
X(40709) = X(300)-Ceva conjugate of X(13)
X(40709) = X(36296)-cross conjugate of X(13)
X(40709) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8739}, {4, 2151}, {15, 19}, {31, 470}, {92, 34394}, {162, 6137}, {186, 2154}, {298, 1973}, {1094, 8737}, {2148, 6117}, {2159, 6110}, {2624, 36309}, {3384, 10641}, {6149, 8738}, {8742, 35198}, {23870, 32676}
X(40709) = cevapoint of X(2) and X(19772)
X(40709) = barycentric product X(i)*X(j) for these {i,j}: {3, 300}, {13, 69}, {16, 328}, {76, 36296}, {265, 299}, {298, 10217}, {304, 2153}, {305, 3457}, {525, 23895}, {850, 38414}, {3260, 39377}, {3265, 36306}, {3267, 5995}, {3926, 8737}, {4563, 20578}, {6390, 36307}, {11064, 36308}, {14592, 17403}
X(40709) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 470}, {3, 15}, {5, 6117}, {6, 8739}, {13, 4}, {16, 186}, {30, 6110}, {48, 2151}, {62, 10633}, {69, 298}, {125, 30465}, {184, 34394}, {265, 14}, {299, 340}, {300, 264}, {328, 301}, {343, 33529}, {395, 23715}, {471, 14165}, {476, 36309}, {525, 23870}, {622, 11094}, {647, 6137}, {1989, 8738}, {2153, 19}, {3457, 25}, {3564, 6782}, {4558, 17402}, {5612, 2914}, {5995, 112}, {6104, 10632}, {7100, 39152}, {8014, 463}, {8737, 393}, {8838, 473}, {8919, 36302}, {10217, 13}, {10218, 36210}, {10661, 2902}, {11078, 471}, {11080, 8737}, {11081, 8740}, {11082, 8742}, {11083, 10642}, {11118, 38427}, {11119, 38428}, {11139, 8741}, {11142, 10641}, {11537, 23712}, {11542, 31687}, {14417, 9204}, {14582, 20579}, {16770, 472}, {17403, 14590}, {18777, 23713}, {20578, 2501}, {23895, 648}, {30452, 8754}, {30454, 5095}, {30468, 35235}, {32585, 8603}, {32662, 5994}, {33530, 14918}, {34395, 34397}, {36296, 6}, {36297, 11086}, {36299, 1990}, {36306, 107}, {36307, 17983}, {36308, 16080}, {36839, 36306}, {38414, 110}, {38943, 36303}, {39153, 1870}, {39377, 74}
X(40709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11078, 13}, {2, 16770, 8838}, {3, 37638, 40710}, {8838, 11078, 16770}, {8838, 16770, 13}
X(40710) lies on the cubic K342b and these lines: {2, 14}, {3, 125}, {16, 3580}, {17, 94}, {61, 14389}, {62, 37644}, {69, 36297}, {95, 302}, {141, 11086}, {264, 301}, {287, 38413}, {299, 1494}, {343, 466}, {396, 14836}, {476, 36186}, {622, 19773}, {624, 15442}, {628, 8918}, {858, 14539}, {1989, 16644}, {2373, 5994}, {3129, 3818}, {3130, 32223}, {3131, 21243}, {3171, 22997}, {3448, 14169}, {3589, 11088}, {3763, 11141}, {5474, 36185}, {5613, 32460}, {6330, 36309}, {9204, 20579}, {9763, 18776}, {10218, 11064}, {11078, 36968}, {11126, 37779}, {11582, 40335}, {15066, 36209}, {16770, 16965}, {20429, 37975}, {34417, 37332}, {36298, 36889}, {37173, 37643}, {37341, 37648}
X(40710) = isogonal conjugate of X(8740)
X(40710) = isotomic conjugate of X(471)
X(40710) = isotomic conjugate of the complement of X(19773)
X(40710) = isotomic conjugate of the isogonal conjugate of X(36297)
X(40710) = isotomic conjugate of the polar conjugate of X(14)
X(40710) = isogonal conjugate of the polar conjugate of X(301)
X(40710) = X(301)-Ceva conjugate of X(14)
X(40710) = X(36297)-cross conjugate of X(14)
X(40710) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8740}, {4, 2152}, {16, 19}, {31, 471}, {92, 34395}, {162, 6138}, {186, 2153}, {299, 1973}, {1095, 8738}, {2148, 6116}, {2159, 6111}, {2624, 36306}, {3375, 10642}, {6149, 8737}, {8741, 35199}, {23871, 32676}
X(40710) = cevapoint of X(2) and X(19773)
X(40710) = barycentric product X(i)*X(j) for these {i,j}: {3, 301}, {14, 69}, {15, 328}, {76, 36297}, {265, 298}, {299, 10218}, {304, 2154}, {305, 3458}, {525, 23896}, {850, 38413}, {3260, 39378}, {3265, 36309}, {3267, 5994}, {3926, 8738}, {4563, 20579}, {6390, 36310}, {11064, 36311}, {14592, 17402}
X(40710) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 471}, {3, 16}, {5, 6116}, {6, 8740}, {14, 4}, {15, 186}, {30, 6111}, {48, 2152}, {61, 10632}, {69, 299}, {125, 30468}, {184, 34395}, {265, 13}, {298, 340}, {301, 264}, {328, 300}, {343, 33530}, {396, 23714}, {470, 14165}, {476, 36306}, {525, 23871}, {621, 11093}, {647, 6138}, {1989, 8737}, {2154, 19}, {3458, 25}, {3564, 6783}, {4558, 17403}, {5616, 2914}, {5994, 112}, {6105, 10633}, {7100, 39153}, {8015, 462}, {8738, 393}, {8836, 472}, {8918, 36303}, {10217, 36211}, {10218, 14}, {10662, 2903}, {11085, 8738}, {11086, 8739}, {11087, 8741}, {11088, 10641}, {11092, 470}, {11117, 38428}, {11120, 38427}, {11138, 8742}, {11141, 10642}, {11543, 31688}, {11549, 23713}, {14417, 9205}, {14582, 20578}, {16771, 473}, {17402, 14590}, {18776, 23712}, {20579, 2501}, {23896, 648}, {30453, 8754}, {30455, 5095}, {30465, 35235}, {32586, 8604}, {32662, 5995}, {33529, 14918}, {34394, 34397}, {36296, 11081}, {36297, 6}, {36298, 1990}, {36309, 107}, {36310, 17983}, {36311, 16080}, {36840, 36309}, {38413, 110}, {38944, 36302}, {39152, 1870}, {39378, 74}
X(40710) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11092, 14}, {2, 16771, 8836}, {3, 37638, 40709}, {8836, 11092, 16771}, {8836, 16771, 14}
X(40711) lies on the cubic K867a and these lines: {2, 18}, {3, 539}, {13, 11140}, {15, 37636}, {69, 11516}, {95, 298}, {264, 299}, {303, 40410}, {343, 465}, {472, 33530}, {524, 8604}, {617, 8175}, {636, 15445}, {930, 5473}, {1494, 32037}, {1993, 10678}, {2373, 16807}, {2963, 16644}, {3131, 34507}, {5064, 5865}, {5464, 37850}, {8797, 36301}, {11082, 33458}, {11131, 15108}, {11442, 14539}, {21969, 37332}
X(40711) = isogonal conjugate of X(10641)
X(40711) = isotomic conjugate of X(472)
X(40711) = isotomic conjugate of the anticomplement of X(466)
X(40711) = isotomic conjugate of the isogonal conjugate of X(32586)
X(40711) = isotomic conjugate of the polar conjugate of X(18)
X(40711) = isogonal conjugate of the polar conjugate of X(34390)
X(40711) = X(34390)-Ceva conjugate of X(18)
X(40711) = X(i)-cross conjugate of X(j) for these (i,j): {466, 2}, {32586, 18}
X(40711) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10641}, {19, 62}, {31, 472}, {303, 1973}, {2153, 10633}, {2964, 8741}, {3383, 8739}, {8737, 35198}, {23873, 32676}
X(40711) = barycentric product X(i)*X(j) for these {i,j}: {3, 34390}, {18, 69}, {76, 32586}, {302, 3519}, {305, 21462}, {525, 32037}, {3267, 16807}, {3926, 8742}, {34386, 36301}
X(40711) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 472}, {3, 62}, {6, 10641}, {15, 10633}, {18, 4}, {61, 3518}, {69, 303}, {302, 32002}, {525, 23873}, {2963, 8741}, {3519, 17}, {8175, 36302}, {8604, 8740}, {8742, 393}, {10218, 11582}, {10678, 10632}, {11082, 8737}, {11138, 8738}, {11143, 473}, {16807, 112}, {19778, 470}, {21462, 25}, {32037, 648}, {32586, 6}, {34390, 264}, {36296, 11142}, {36297, 11088}, {36301, 53}, {36305, 462}, {40668, 23715}
X(40711) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11143, 18}, {2, 19778, 11143}
X(40712) lies on the cubic K867b and these lines: {2, 17}, {3, 539}, {14, 11140}, {16, 37636}, {69, 11515}, {95, 299}, {264, 298}, {302, 40410}, {343, 466}, {473, 33529}, {524, 8603}, {616, 8174}, {635, 15444}, {930, 5474}, {1494, 32036}, {1993, 10677}, {2373, 16806}, {2963, 16645}, {3132, 34507}, {5064, 5864}, {5463, 37848}, {8797, 36300}, {11087, 33459}, {11130, 15108}, {11442, 14538}, {21969, 37333}
X(40712) = isogonal conjugate of X(10642)
X(40712) = isotomic conjugate of X(473)
X(40712) = isotomic conjugate of the anticomplement of X(465)
X(40712) = isotomic conjugate of the isogonal conjugate of X(32585)
X(40712) = isotomic conjugate of the polar conjugate of X(17)
X(40712) = isogonal conjugate of the polar conjugate of X(34389)
X(40712) = X(34389)-Ceva conjugate of X(17)
X(40712) = X(i)-cross conjugate of X(j) for these (i,j): {465, 2}, {32585, 17}
X(40712) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10642}, {19, 61}, {31, 473}, {302, 1973}, {2154, 10632}, {2964, 8742}, {3376, 8740}, {8738, 35199}, {23872, 32676}
X(40712) = barycentric product X(i)*X(j) for these {i,j}: {3, 34389}, {17, 69}, {76, 32585}, {303, 3519}, {305, 21461}, {525, 32036}, {3267, 16806}, {3926, 8741}, {34386, 36300}
X(40712) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 473}, {3, 61}, {6, 10642}, {16, 10632}, {17, 4}, {62, 3518}, {69, 302}, {303, 32002}, {525, 23872}, {2963, 8742}, {3519, 18}, {8174, 36303}, {8603, 8739}, {8741, 393}, {10217, 11581}, {10677, 10633}, {11087, 8738}, {11139, 8737}, {11144, 472}, {16806, 112}, {19779, 471}, {21461, 25}, {32036, 648}, {32585, 6}, {34389, 264}, {36296, 11083}, {36297, 11141}, {36300, 53}, {36304, 463}, {40667, 23714}
X(40712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11144, 17}, {2, 19779, 11144}
X(40713) lies on the cubic K867a and these lines: {1, 2}, {9, 7089}, {13, 321}, {57, 36928}, {63, 617}, {75, 299}, {100, 12781}, {226, 36929}, {298, 319}, {303, 5564}, {312, 7043}, {318, 473}, {333, 7026}, {395, 17362}, {396, 594}, {466, 2968}, {472, 5081}, {533, 3578}, {894, 3180}, {956, 21475}, {2345, 37640}, {3181, 17363}, {3452, 5246}, {4060, 5243}, {4363, 5859}, {4385, 11303}, {4644, 5863}, {4665, 33458}, {4886, 5240}, {5015, 11304}, {5245, 5745}, {5295, 37144}, {5687, 21476}, {5814, 37145}, {5839, 37641}, {14829, 36668}, {17117, 34541}
X(40713) = reflection of X(40714) in X(3687)
X(40713) = isotomic conjugate of X(1081)
X(40713) = isotomic conjugate of the isogonal conjugate of X(1250)
X(40713) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2306}, {31, 1081}, {56, 1251}, {513, 36072}, {559, 6186}, {2153, 19373}, {3457, 37772}, {7051, 11072}
X(40713) = barycentric product X(i)*X(j) for these {i,j}: {76, 1250}, {298, 7026}, {312, 1082}, {2307, 3596}, {33653, 33939}
X(40713) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2306}, {2, 1081}, {9, 1251}, {15, 19373}, {101, 36072}, {1082, 57}, {1250, 6}, {2307, 56}, {3219, 559}, {5239, 39153}, {5240, 3179}, {5353, 7051}, {7006, 2307}, {7026, 13}, {7126, 11072}, {19551, 2153}, {33653, 2160}
X(40713) = {X(2),X(8)}-harmonic conjugate of X(40714)
X(40713) = {X(200),X(17294)}-harmonic conjugate of X(40714)
X(40714) lies on the cubic K867band these lines: {1, 2}, {9, 7088}, {14, 321}, {57, 36929}, {63, 616}, {75, 298}, {100, 12780}, {226, 36928}, {299, 319}, {302, 5564}, {312, 7026}, {318, 472}, {333, 7043}, {395, 594}, {396, 17362}, {465, 2968}, {473, 5081}, {532, 3578}, {894, 3181}, {956, 21476}, {2345, 37641}, {3180, 17363}, {3219, 7150}, {3452, 5245}, {4060, 5242}, {4363, 5858}, {4385, 11304}, {4644, 5862}, {4665, 33459}, {4886, 5239}, {5015, 11303}, {5246, 5745}, {5295, 37145}, {5687, 21475}, {5814, 37144}, {5839, 37640}, {14829, 36669}, {17117, 34540}
X(40714) = reflection of X(40713) in X(3687)
X(40714) = isotomic conjugate of X(554)
X(40714) = isotomic conjugate of the isogonal conjugate of X(10638)
X(40714) = X(i)-isoconjugate of X(j) for these (i,j): {6, 33654}, {31, 554}, {56, 33653}, {513, 36073}, {1082, 6186}, {2154, 7051}, {2160, 2307}, {3458, 37773}, {11073, 19373}
X(40714) = barycentric product X(i)*X(j) for these {i,j}: {76, 10638}, {299, 7043}, {312, 559}, {1251, 33939}
X(40714) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 33654}, {2, 554}, {9, 33653}, {16, 7051}, {35, 2307}, {101, 36073}, {559
, 57}, {1251, 2160}, {3219, 1082}, {5240, 39152}, {5357, 19373}, {7043, 14}, {7126, 2154}, {7150, 7052}, {10638, 6}, {19551, 11073}
X(40714) = {X(2),X(8)}-harmonic conjugate of X(40713)
X(40714) = {X(200),X(17294)}-harmonic conjugate of X(40713)
X(40715) lies on the cubic K296 and these lines: {2, 1762}, {69, 17216}, {264, 17861}, {287, 9028}, {306, 15526}, {307, 1367}, {519, 1494}, {648, 40414}, {3187, 39352}, {4357, 40412}, {14429, 34767}, {17879, 20336}
X(40715) = midpoint of X(3187) and X(39352)
X(40715) = reflection of X(306) in X(15526)
X(40715) = isotomic conjugate of X(447)
X(40715) = antitomic image of X(306)
X(40715) = X(i)-isoconjugate of X(j) for these (i,j): {31, 447}, {2203, 16086}
X(40715) = trilinear pole of line {440, 525}
X(40715) = barycentric product X(i)*X(j) for these {i,j}: {306, 16099}, {525, 35169}
X(40715) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 447}, {306, 16086}, {4466, 867}, {16099, 27}, {35169, 648}
X(40716) lies on the cubic K276 and these lines: {75, 1272}, {312, 2895}, {314, 1227}, {3260, 17791}, {3596, 20932}, {17361, 20570}, {20565, 34387}
X(40716) = isotomic conjugate of X(484)
X(40716) = isotomic conjugate of the anticomplement of X(11813)
X(40716) = isotomic conjugate of the complement of X(5180)
X(40716) = isotomic conjugate of the isogonal conjugate of X(3065)
X(40716) = X(i)-cross conjugate of X(j) for these (i,j): {320, 75}, {11813, 2}
X(40716) = X(i)-isoconjugate of X(j) for these (i,j): {6, 19297}, {25, 23071}, {31, 484}, {32, 17484}, {560, 17791}, {1333, 21864}, {2174, 11076}, {6126, 6187}
X(40716) = cevapoint of X(i) and X(j) for these (i,j): {2, 5180}, {3904, 24026}, {3936, 4647}
X(40716) = trilinear pole of line {4359, 4391}
X(40716) = barycentric product X(i)*X(j) for these {i,j}: {75, 21739}, {76, 3065}, {561, 19302}, {11075, 40075}
X(40716) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 19297}, {2, 484}, {10, 21864}, {63, 23071}, {75, 17484}, {76, 17791}, {79, 11076}, {320, 40612}, {3065, 6}, {3218, 6126}, {4511, 26744}, {4560, 35055}, {7343, 2174}, {11075, 6187}, {14452, 11069}, {19302, 31}, {21739, 1}, {26743, 1411}, {34921, 1415}
X(40717) lies on these lines: {4, 1969}, {75, 24430}, {92, 264}, {242, 1921}, {273, 6384}, {286, 6385}, {317, 21276}, {318, 33938}, {331, 40028}, {350, 1874}, {561, 1851}, {811, 1870}, {1875, 18026}, {3261, 4025}, {3583, 23994}, {3975, 35544}, {5089, 6335}, {23978, 30737}
X(40717) = isotomic conjugate of X(295)
X(40717) = polar conjugate of X(292)
X(40717) = isotomic conjugate of the isogonal conjugate of X(242)
X(40717) = polar conjugate of the isotomic conjugate of X(1921)
X(40717) = polar conjugate of the isogonal conjugate of X(239)
X(40717) = X(239)-cross conjugate of X(1921)
X(40717) = X(i)-isoconjugate of X(j) for these (i,j): {3, 1911}, {6, 2196}, {31, 295}, {48, 292}, {63, 1922}, {69, 14598}, {71, 18268}, {77, 18265}, {171, 17970}, {184, 291}, {228, 741}, {304, 18897}, {305, 18893}, {334, 14575}, {335, 9247}, {337, 560}, {603, 7077}, {813, 22383}, {875, 1331}, {876, 32656}, {906, 3572}, {1402, 1808}, {1409, 2311}, {1459, 34067}, {1967, 3955}, {2200, 37128}, {3049, 4584}, {3252, 32658}, {5378, 22096}, {7122, 36214}
X(40717) = cevapoint of X(239) and X(242)
X(40717) = crosssum of X(i) and X(j) for these (i,j): {3, 23186}, {228, 20777}, {22096, 23225}
X(40717) = pole wrt polar circle of trilinear polar of X(292) (line X(42)X(649), or PU(8))
X(40717) = perspector of circumconic through the polar conjugates of PU(8)
X(40717) = barycentric product X(i)*X(j) for these {i,j}: {4, 1921}, {19, 18891}, {27, 35544}, {76, 242}, {92, 350}, {238, 1969}, {239, 264}, {257, 17984}, {273, 3975}, {278, 4087}, {281, 18033}, {286, 3948}, {313, 31905}, {318, 10030}, {331, 3685}, {349, 14024}, {561, 2201}, {862, 6385}, {874, 17924}, {1447, 7017}, {1874, 28660}, {1914, 18022}, {3766, 6335}, {4010, 6331}, {6528, 24459}, {7193, 18027}, {7649, 27853}, {17982, 18035}, {34856, 40071}
X(40717) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2196}, {2, 295}, {4, 292}, {19, 1911}, {25, 1922}, {27, 741}, {28, 18268}, {29, 2311}, {76, 337}, {92, 291}, {238, 48}, {239, 3}, {242, 6}, {257, 36214}, {264, 335}, {281, 7077}, {286, 37128}, {318, 4876}, {331, 7233}, {333, 1808}, {350, 63}, {385, 3955}, {419, 172}, {607, 18265}, {659, 22383}, {740, 71}, {811, 4584}, {812, 1459}, {862, 213}, {874, 1332}, {893, 17970}, {1281, 20741}, {1284, 1409}, {1429, 603}, {1447, 222}, {1783, 34067}, {1861, 3252}, {1874, 1400}, {1897, 813}, {1914, 184}, {1921, 69}, {1969, 334}, {1973, 14598}, {1974, 18897}, {2201, 31}, {2210, 9247}, {2238, 228}, {3570, 1331}, {3573, 906}, {3684, 212}, {3685, 219}, {3716, 652}, {3747, 2200}, {3766, 905}, {3797, 3781}, {3948, 72}, {3975, 78}, {3985, 2318}, {4010, 647}, {4037, 3690}, {4039, 22061}, {4087, 345}, {4107, 22093}, {4124, 7117}, {4366, 7193}, {4375, 22384}, {4432, 22356}, {4435, 1946}, {4448, 22086}, {4455, 3049}, {4760, 3292}, {4974, 22054}, {6331, 4589}, {6335, 660}, {6591, 875}, {6651, 17976}, {6654, 36057}, {7017, 4518}, {7193, 577}, {7235, 2197}, {7649, 3572}, {8299, 20752}, {10030, 77}, {14024, 284}, {14599, 14575}, {14618, 35352}, {16609, 73}, {17031, 22099}, {17475, 20777}, {17493, 7015}, {17755, 1818}, {17793, 20785}, {17924, 876}, {17982, 9506}, {17984, 894}, {18022, 18895}, {18033, 348}, {18786, 7116}, {18891, 304}, {18894, 40373}, {19579, 23186}, {20457, 23223}, {20769, 255}, {21832, 810}, {24459, 520}, {27853, 4561}, {27912, 22148}, {27918, 3937}, {27919, 20778}, {27920, 20797}, {27922, 1797}, {27942, 20786}, {27945, 20761}, {27947, 20804}, {30940, 1444}, {31905, 58}, {33295, 1790}, {33891, 3784}, {34252, 15373}, {34856, 1474}, {35544, 306}, {39044, 20769}, {39914, 23086}, {39916, 20796}
Points associated with CCC cubics: X(40718)-X(40725)
This preamble is contributed by Clark Kimberling and Peter Moses, December 16, 2020.
Let P = p : q : r and U = u : v : w be points in the plane of a triangle ABC, and let
A'B'C' = cevian triangle of P, D'E'F' = cevian triangle of U
A"B"C" = anticevian triangle of P, D"E"F" = anticevian triangle of U
A* = A'D" ∩ A"E', and define B* and C* cyclically, so that
A* = - p u : q u + p v : r u + p w
B* = p v + q u : - q v : r v + q w
C* = p w + r u : q w + r v : - r w
The triangle A*B*C* is here named the (P,U)-cevian-cross triangle (not to be confused with the cross-cevian triangle in TCCT, p. 201)..
The locus of a point X = x : y : z such that the (P,U)-cevian-cross triangle is perspective to the cevian triangle of X is the (P,U)-CCC cubic, given by
(r u + p w)(q^2 u^2 + p q u v + p^2 v^2) y z^2 - (q u + p v) (r^2 u^2 + p r u w + p^2 w^2) y^2 z + (cyclic) = 0
The (P,U)-CCC cubic is the cubic pK(P*,U*), where
P* = q^2 u^2 + p q u v + p^2 v^2)(r^2 u^2 + p r u w + p^2w^2) : :
U* = (q^2 u^2 + p q u v + p^2*v^2)(r^2 u^2 + p r u w + p^2 w^2)(r v + q w) : :
Examples:
(X(15), X(16))-CCC cubic = pK(X(6), X(30)) = K001
(X(2), X(6))-CCC cubic = pK(X(3407), X(14617)) = K421
The locus of a point X = x : y : z such that the (P,U)-cevian-cross triangle is perspective to the anticevian triangle of X is the (P,U)-CCA cubic, given by
2 p u (r^2 u v + 2 q r u w + 2 p r v w + p q w^2) y^2 z - 2 p u (2 q r u v + p r v^2 + q^2 u w + 2 p q v w) y z^2 + (cyclic) = 0.
The (P,U)-CCA cubic is the cubic pK(P*,U*), where
P* = p u : : , and U* = q r u^2 + p^2 v w + 2 p u (r v + q w)) : :
Examples:
((X(2), X(4))_CCA cubic = pK(X(4), X(458)) = K677
((X(2), X(6))_CCA cubic = pK(X(6), X(3329)) = K423
((X(2), X(13))_CCA cubic = pK(X(13), X(8838)) = K420b
((X(2), X(14))_CCA cubic = pK(X(13), X(8836)) = K420a
((X(2), X(30))_CCA cubic = pK(X(30), X(2)) = K472
((X(6), X(98))_CCA cubic = pK(X(1976), X(98)) = K380
((X(13), X(14))_CCA cubic = pK(X(1989), X(265)) = K060
((X(15), X(16))_CCA cubic = pK(X(50), X(3)) = K073
X(40718) lies on the Kiepert circumhyperbola, the (X(1),X(2))-CCC cubic, and these lines: {1, 76}, {2, 31}, {4, 1973}, {10, 213}, {37, 4368}, {40, 3597}, {42, 321}, {43, 2258}, {83, 16889}, {86, 741}, {98, 825}, {226, 1284}, {242, 37892}, {256, 291}, {262, 3402}, {513, 875}, {516, 2051}, {518, 25368}, {671, 923}, {672, 4672}, {726, 24330}, {871, 2296}, {984, 24514}, {1042, 1446}, {1064, 28850}, {1096, 2052}, {1125, 16850}, {1386, 17031}, {1492, 14009}, {1716, 10436}, {1751, 25453}, {1874, 40149}, {1918, 27042}, {2276, 3923}, {2475, 13584}, {2996, 38252}, {3112, 40016}, {3223, 40162}, {3399, 7594}, {3666, 24259}, {3696, 21904}, {3720, 30982}, {3741, 5847}, {3783, 5263}, {3789, 36480}, {3840, 4349}, {3993, 21101}, {4052, 4356}, {4080, 4613}, {4085, 13576}, {4272, 22316}, {4424, 11611}, {4441, 32921}, {4651, 6539}, {4865, 31330}, {4892, 30588}, {4974, 24592}, {5018, 7196}, {5057, 5143}, {6625, 18757}, {7248, 36538}, {8300, 20179}, {8781, 36051}, {10159, 29637}, {10290, 33946}, {10791, 16788}, {12609, 36907}, {13478, 29046}, {16475, 17026}, {16476, 17030}, {16826, 30571}, {17018, 32920}, {17135, 17772}, {17379, 21299}, {17469, 26237}, {17768, 25349}, {17770, 24690}, {19998, 27797}, {23660, 24512}, {24260, 29650}, {24325, 26234}, {25526, 32014}, {26102, 40012}, {26128, 30985}, {28498, 31241}, {28639, 34585}, {29207, 37365}, {30116, 36873}, {30950, 39994}, {30965, 32949}, {30966, 33082}, {31027, 32846}, {34087, 37132}
X(40718) = isogonal conjugate of X(3736)
X(40718) = isotomic conjugate of X(30966)
X(40718) = polar conjugate of X(31909)
X(40718) = X(789)-Ceva conjugate of X(4817)
X(40718) = X(i)-cross conjugate of X(j) for these (i,j): {37, 25425}, {4026, 10}, {4806, 3952}
X(40718) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3736}, {21, 1469}, {28, 3781}, {31, 30966}, {48, 31909}, {56, 3786}, {58, 984}, {81, 2276}, {86, 869}, {99, 788}, {101, 4481}, {110, 1491}, {163, 824}, {284, 7146}, {295, 17569}, {310, 18900}, {662, 3250}, {670, 8630}, {741, 3783}, {759, 3792}, {849, 3773}, {985, 4476}, {1014, 4517}, {1333, 3661}, {1408, 3790}, {1509, 3774}, {2150, 16603}, {2194, 7179}, {2206, 33931}, {2328, 7204}, {3116, 40415}, {3117, 38810}, {3733, 3799}, {3797, 18268}, {3864, 5009}, {4475, 4570}, {4615, 14436}, {14574, 30870}, {16514, 37128}, {17938, 30639}, {30654, 37134}
X(40718) = cevapoint of X(i) and X(j) for these (i,j): {1, 24342}, {6, 16372}, {10, 3993}, {894, 16826}
X(40718) = crosspoint of X(870) and X(14621)
X(40718) = crosssum of X(869) and X(2276)
X(40718) = trilinear pole of line {523, 798}
X(40718) = crossdifference of every pair of points on line {3250, 16514}
X(40718) = barycentric product X(i)*X(j) for these {i,j}: {10, 14621}, {37, 870}, {213, 871}, {321, 985}, {512, 37133}, {514, 4613}, {523, 4586}, {661, 789}, {825, 850}, {1441, 2344}, {1492, 1577}, {2887, 3407}, {3113, 3721}, {3114, 3778}, {3122, 5388}, {3952, 4817}, {4010, 37207}, {5384, 16732}, {14617, 16889}, {20948, 34069}, {24349, 25425}
X(40718) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 30966}, {4, 31909}, {6, 3736}, {9, 3786}, {10, 3661}, {12, 16603}, {37, 984}, {42, 2276}, {65, 7146}, {71, 3781}, {213, 869}, {226, 7179}, {321, 33931}, {512, 3250}, {513, 4481}, {523, 824}, {594, 3773}, {661, 1491}, {740, 3797}, {789, 799}, {798, 788}, {825, 110}, {870, 274}, {871, 6385}, {872, 3774}, {984, 4469}, {985, 81}, {1018, 3799}, {1213, 3775}, {1334, 4517}, {1400, 1469}, {1427, 7204}, {1492, 662}, {1924, 8630}, {2201, 17569}, {2205, 18900}, {2238, 3783}, {2245, 3792}, {2276, 4476}, {2321, 3790}, {2344, 21}, {2887, 3314}, {3113, 38810}, {3125, 4475}, {3407, 40415}, {3696, 27474}, {3700, 4522}, {3747, 16514}, {3778, 3094}, {3842, 27495}, {3943, 4439}, {3952, 3807}, {3993, 27481}, {3997, 3809}, {4010, 4486}, {4024, 4122}, {4033, 4505}, {4586, 99}, {4613, 190}, {4817, 7192}, {4841, 4818}, {4931, 4951}, {5027, 30654}, {5384, 4567}, {8022, 18899}, {14621, 86}, {16584, 3116}, {18898, 38813}, {20948, 30870}, {21010, 25429}, {21832, 30665}, {21904, 3795}, {30664, 4584}, {30670, 4603}, {34069, 163}, {35352, 23596}, {37133, 670}, {37207, 4589}
X(40718) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 26098, 30953}, {2, 33112, 30969}, {1386, 21264, 17031}, {5263, 37678, 3783}
X(40719) lies on the (X(1),X(2))-CCC cubic and these lines: {1, 85}, {2, 7}, {6, 24600}, {10, 6604}, {12, 30617}, {21, 38859}, {29, 1847}, {37, 24352}, {40, 17753}, {56, 4059}, {65, 24805}, {69, 4847}, {75, 200}, {77, 4666}, {78, 20880}, {86, 269}, {145, 5543}, {150, 5587}, {169, 2140}, {218, 24774}, {220, 6706}, {241, 16831}, {273, 14004}, {279, 3616}, {320, 5231}, {331, 39585}, {348, 1125}, {349, 3760}, {350, 6063}, {461, 1119}, {481, 13453}, {482, 13436}, {551, 1323}, {946, 17170}, {948, 17023}, {988, 24214}, {997, 38468}, {1210, 36660}, {1212, 30625}, {1215, 7274}, {1231, 33945}, {1319, 7223}, {1358, 11730}, {1418, 15668}, {1419, 17379}, {1420, 7176}, {1434, 3361}, {1441, 3870}, {1442, 29817}, {1446, 4350}, {1462, 5276}, {1536, 5805}, {1565, 5886}, {1698, 32007}, {1699, 4872}, {1758, 4389}, {2887, 17272}, {3160, 3622}, {3212, 3340}, {3338, 7183}, {3485, 3674}, {3576, 5088}, {3617, 32003}, {3623, 25718}, {3624, 17095}, {3663, 13405}, {3664, 11019}, {3665, 11375}, {3668, 17093}, {3671, 10521}, {3672, 10578}, {3693, 3729}, {3742, 34855}, {3789, 39792}, {3872, 30806}, {3877, 23839}, {3879, 36845}, {3886, 4441}, {3945, 10580}, {3957, 7269}, {4071, 17296}, {4292, 36706}, {4298, 13725}, {4327, 26234}, {4384, 5228}, {4512, 33765}, {4554, 30963}, {4659, 21101}, {4853, 16284}, {4862, 17596}, {4911, 9612}, {4955, 5221}, {5136, 38461}, {5195, 31162}, {5263, 12560}, {5290, 7247}, {5542, 10520}, {5714, 36682}, {5722, 36722}, {6700, 25583}, {6762, 36854}, {7131, 17758}, {7177, 17169}, {7185, 17084}, {7196, 26102}, {7198, 10404}, {7228, 25355}, {7271, 25496}, {7289, 34830}, {7411, 18655}, {7580, 10444}, {8227, 17181}, {8551, 25878}, {9778, 15506}, {9780, 32098}, {10431, 18650}, {10473, 24471}, {11520, 20247}, {14189, 38316}, {17018, 25721}, {17078, 21314}, {17151, 32920}, {17234, 30813}, {17270, 25006}, {17300, 31038}, {17378, 31146}, {18443, 36027}, {19604, 27829}, {19860, 26563}, {21258, 40483}, {21446, 27475}, {23058, 26531}, {24349, 39959}, {24411, 35157}, {26134, 26959}, {27086, 34865}, {30545, 30982}, {30712, 36620}, {31269, 32024}, {31643, 40025}
X(40719) = isotomic conjugate of the isogonal conjugate of X(1471)
X(40719) = X(21446)-Ceva conjugate of X(9312)
X(40719) = X(1001)-cross conjugate of X(4384)
X(40719) = X(i)-isoconjugate of X(j) for these (i,j): {9, 2279}, {41, 27475}, {55, 1002}, {650, 8693}, {663, 37138}, {3063, 32041}
X(40719) = cevapoint of X(i) and X(j) for these (i,j): {1001, 5228}, {24349, 29627}
X(40719) = barycentric product X(i)*X(j) for these {i,j}: {7, 4384}, {56, 21615}, {57, 4441}, {75, 5228}, {76, 1471}, {85, 1001}, {269, 28809}, {273, 23151}, {279, 3886}, {307, 31926}, {664, 4762}, {1014, 4044}, {1088, 37658}, {1434, 3696}, {1893, 17206}, {2280, 6063}, {4554, 4724}, {4573, 4804}
X(40719) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 27475}, {56, 2279}, {57, 1002}, {109, 8693}, {651, 37138}, {664, 32041}, {1001, 9}, {1471, 6}, {1893, 1826}, {2280, 55}, {3696, 2321}, {3886, 346}, {4044, 3701}, {4384, 8}, {4441, 312}, {4702, 2325}, {4724, 650}, {4762, 522}, {4804, 3700}, {5228, 1}, {21615, 3596}, {23151, 78}, {27474, 3790}, {28044, 7079}, {28809, 341}, {31926, 29}, {32735, 36138}, {37658, 200}
X(40719) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 85, 9312}, {1, 9312, 25716}, {2, 7, 9436}, {2, 10025, 9}, {7, 1447, 57}, {145, 31994, 25719}, {226, 36538, 57}, {1125, 10481, 348}, {1441, 7190, 3875}, {3160, 3622, 25723}, {3485, 7195, 3674}, {3616, 32086, 279}, {3664, 11019, 14548}, {5543, 31994, 145}, {7274, 25590, 39126}, {9318, 30949, 40131}, {11375, 24796, 3665}, {13405, 24283, 17594}, {20335, 24333, 9}, {20335, 25521, 25527}
X(40720) lies on the (X(1),X(2))-CCC cubic and these lines: {1, 87}, {2, 1977}, {42, 33784}, {86, 26143}, {238, 7121}, {932, 1001}, {1740, 20971}, {2295, 37677}, {3226, 24343}, {3618, 34249}, {8843, 9791}, {15485, 17105}, {17232, 26986}, {17349, 20669}, {27455, 28395}, {27633, 27672}
X(40720) = X(i)-cross conjugate of X(j) for these (i,j): {25376, 10009}, {30963, 4393}
X(40720) = X(2209)-isoconjugate of X(27494)
X(40720) = barycentric product X(i)*X(j) for these {i,j}: {87, 30963}, {330, 4393}, {2162, 10009}, {4598, 4785}, {4782, 18830}, {6383, 21793}, {6384, 16468}
X(40720) = barycentric quotient X(i)/X(j) for these {i,j}: {330, 27494}, {3993, 3971}, {4393, 192}, {4782, 4083}, {4785, 3835}, {4806, 21051}, {4991, 4970}, {10009, 6382}, {16468, 43}, {21793, 2176}, {21904, 20691}, {23095, 20760}, {25376, 21250}, {30963, 6376}, {34476, 38832}
X(40720) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 33681, 192}, {87, 39914, 330}
X(40721) lies on the (X(1),X(2))-CCC cubic and these lines: {1, 1655}, {2, 6}, {9, 17032}, {42, 894}, {144, 11688}, {192, 714}, {194, 19767}, {257, 2650}, {274, 20970}, {335, 21840}, {350, 1100}, {672, 17120}, {870, 4393}, {1008, 7754}, {1218, 39961}, {1449, 17027}, {1509, 5277}, {2234, 3240}, {2271, 16915}, {2276, 3758}, {2280, 14621}, {2295, 4595}, {2475, 6625}, {3616, 16476}, {3720, 23532}, {3783, 33682}, {3879, 31027}, {3882, 17754}, {4360, 24330}, {4651, 28604}, {4670, 21904}, {4713, 16884}, {4754, 33296}, {5021, 17684}, {5625, 30571}, {7277, 25349}, {8040, 17248}, {16497, 38314}, {16666, 17029}, {16667, 17026}, {16826, 25427}, {17023, 31004}, {17103, 17693}, {17121, 24592}, {17126, 18900}, {17302, 20347}, {17312, 30821}, {17363, 31330}, {17367, 30949}, {17750, 26752}, {20072, 29822}, {20963, 26801}, {26626, 30946}, {26815, 26971}, {29841, 30961}
X(40721) = anticomplement of X(30966)
X(40721) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {798, 39345}, {825, 7192}, {870, 17138}, {985, 17135}, {1492, 512}, {2344, 20245}, {3407, 561}, {4586, 17217}, {4613, 21301}, {9426, 39347}, {14621, 17137}, {34069, 523}, {37133, 21305}
X(40721) = X(4649)-Ceva conjugate of X(4393)
X(40721) = cevapoint of X(1045) and X(25427)
X(40721) = crosspoint of X(4586) and X(4590)
X(40721) = crosssum of X(3124) and X(3250)
X(40721) = crossdifference of every pair of points on line {512, 21763}
X(40721) = barycentric quotient X(30571)/X(30570)
X(40721) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17499, 1655}, {2, 20090, 30941}, {6, 20140, 17349}, {6, 37632, 2}, {42, 894, 17759}, {86, 2238, 2}, {1654, 20536, 2895}, {2663, 3510, 42}, {2665, 39916, 30667}, {17103, 18755, 17693}, {24512, 37678, 2}
X(40722) lies on the (X(1),X(2))-CCC cubic and these lines: {1, 257}, {2, 2112}, {86, 1333}, {870, 17962}, {894, 8424}, {985, 3616}, {3661, 26244}, {4586, 35162}, {6625, 18757}, {17084, 17689}, {17762, 18755}, {22267, 33867}
X(40722) = X(i)-isoconjugate of X(j) for these (i,j): {869, 6625}, {984, 2248}, {2276, 13610}, {3661, 18757}, {3774, 40164}
X(40722) = barycentric product X(i)*X(j) for these {i,j}: {846, 870}, {985, 17762}, {1654, 14621}, {4586, 21196}
X(40722) = barycentric quotient X(i)/X(j) for these {i,j}: {846, 984}, {985, 13610}, {1654, 3661}, {2905, 31909}, {6626, 30966}, {14621, 6625}, {17084, 7179}, {17762, 33931}, {18755, 2276}, {21085, 3773}, {21196, 824}, {22139, 3781}, {27691, 16603}
X(40723) lies on the cubic VT(X(1),X(2)) and these lines: {1, 18299}, {2, 2114}, {57, 7249}, {85, 25496}, {86, 269}, {223, 9312}, {226, 6625}, {348, 26098}, {664, 1215}, {870, 6063}, {2887, 17095}, {4865, 33298}, {5018, 7196}, {10030, 29821}, {15903, 33144}, {17739, 27963}, {24333, 31526}, {32942, 39775}
X(40723) = X(7196)-Ceva conjugate of X(57)
X(40723) = X(8424)-cross conjugate of X(17739)
X(40723) = X(i)-isoconjugate of X(j) for these (i,j): {9, 18784}, {2175, 18760}, {7077, 16366}
X(40723) = barycentric product X(i)*X(j) for these {i,j}: {7, 17739}, {57, 30660}, {85, 8424}, {7249, 27963}, {18759, 20567}
X(40723) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 18784}, {85, 18760}, {1429, 16366}, {8424, 9}, {17739, 8}, {18759, 41}, {27963, 7081}, {30660, 312}
X(40724) lies on the (X(1),X(2))-CCC cubic and these lines: {1, 85}, {2, 2115}, {3, 34179}, {10, 666}, {79, 5377}, {105, 5253}, {673, 1492}, {894, 33676}, {927, 2700}, {1027, 1220}, {2475, 6625}, {5263, 33674}, {6185, 17023}, {6646, 9501}, {6654, 14267}, {9441, 24980}, {11109, 36124}, {24234, 37607}, {24723, 36086}
X(40724) = cevapoint of X(1281) and X(4645)
X(40724) = trilinear pole of line {3509, 4458}
X(40724) = X(i)-isoconjugate of X(j) for these (i,j): {518, 8852}, {672, 3512}, {1458, 7281}, {2223, 7261}, {8299, 30648}, {9455, 18036}
X(40724) = barycentric product X(i)*X(j) for these {i,j}: {105, 17789}, {666, 4458}, {673, 4645}, {2481, 3509}, {5018, 36796}, {17798, 18031}
X(40724) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 3512}, {294, 7281}, {673, 7261}, {1281, 17755}, {1438, 8852}, {3509, 518}, {4071, 3932}, {4458, 918}, {4645, 3912}, {4987, 4966}, {5018, 241}, {17789, 3263}, {17798, 672}, {18031, 18036}, {18262, 9454}, {19554, 2223}, {19557, 8299}, {20715, 3930}, {20741, 1818}
X(40725) lies on the (X(1),X(2))-CCC cubic and these lines: {2, 846}, {81, 17930}, {239, 27916}, {321, 6634}, {350, 27912}, {870, 17962}, {873, 16727}, {894, 9506}, {2702, 9073}, {4375, 6545}, {4760, 27922}, {6652, 27918}, {9278, 25368}, {18822, 29584}, {19936, 29609}
X(40725) = X(6650)-Ceva conjugate of X(239)
X(40725) = X(i)-cross conjugate of X(j) for these (i,j): {659, 17930}, {4366, 239}
X(40725) = X(i)-isoconjugate of X(j) for these (i,j): {291, 17735}, {292, 1757}, {335, 18266}, {660, 5029}, {741, 20693}, {813, 9508}, {1911, 6542}, {1922, 20947}, {2196, 17927}, {2786, 34067}, {4584, 17990}, {6541, 18268}, {18035, 18267}
X(40725) = cevapoint of X(4375) and X(27918)
X(40725) = trilinear pole of line {812, 4974}
X(40725) = barycentric product X(i)*X(j) for these {i,j}: {238, 18032}, {239, 6650}, {350, 1929}, {812, 35148}, {1921, 17962}, {3766, 37135}, {4010, 17930}, {9278, 30940}, {9505, 39044}, {11599, 33295}, {17972, 40717}
X(40725) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 1757}, {239, 6542}, {242, 17927}, {350, 20947}, {659, 9508}, {740, 6541}, {812, 2786}, {1914, 17735}, {1929, 291}, {2210, 18266}, {2238, 20693}, {2702, 813}, {4010, 18004}, {4366, 6651}, {4375, 27929}, {4448, 28602}, {4455, 17990}, {5009, 1326}, {6650, 335}, {6652, 27926}, {7193, 17976}, {8300, 8298}, {8632, 5029}, {9505, 30663}, {17930, 4589}, {17962, 292}, {17972, 295}, {18014, 35352}, {18032, 334}, {31905, 423}, {33295, 17731}, {35148, 4562}, {37135, 660}
X(40726) lies on these lines: {1, 4004}, {2, 12}, {3, 551}, {8, 36006}, {30, 7956}, {35, 19705}, {36, 1001}, {55, 4345}, {57, 5289}, {104, 3545}, {115, 22565}, {165, 10179}, {214, 15934}, {354, 35262}, {381, 10199}, {404, 3241}, {474, 3679}, {499, 17530}, {519, 999}, {547, 32153}, {549, 11249}, {553, 34647}, {597, 22769}, {758, 35272}, {954, 38024}, {956, 19875}, {960, 3361}, {993, 8167}, {1012, 38021}, {1056, 3035}, {1125, 16418}, {1149, 37540}, {1191, 37608}, {1201, 8688}, {1319, 3306}, {1420, 3812}, {1478, 17533}, {1616, 37603}, {2066, 9689}, {2099, 27003}, {2482, 22514}, {3058, 22768}, {3086, 3829}, {3303, 4188}, {3337, 5730}, {3338, 12635}, {3428, 3524}, {3445, 5255}, {3474, 3616}, {3488, 17051}, {3550, 16486}, {3576, 3742}, {3582, 17532}, {3622, 5217}, {3624, 17542}, {3654, 10680}, {3655, 11500}, {3720, 16395}, {3746, 19537}, {3813, 6904}, {3816, 4293}, {3825, 9655}, {3828, 8666}, {3847, 5229}, {3878, 37545}, {3919, 10247}, {3929, 8583}, {4187, 4317}, {4190, 37722}, {4193, 9657}, {4252, 21214}, {4298, 25681}, {4315, 6692}, {4370, 24826}, {4423, 16858}, {4511, 4860}, {4666, 37600}, {4669, 9709}, {4795, 24328}, {4855, 17609}, {4870, 34880}, {4930, 5708}, {4995, 10966}, {5054, 10197}, {5055, 22758}, {5066, 18761}, {5123, 31190}, {5154, 9656}, {5251, 19536}, {5258, 16862}, {5437, 13462}, {5438, 34791}, {5439, 37618}, {5459, 22773}, {5460, 22774}, {5550, 16861}, {5584, 15692}, {5642, 22586}, {5710, 32577}, {5883, 10246}, {5886, 28444}, {6055, 22504}, {6174, 11239}, {6284, 10586}, {6667, 10590}, {6681, 31479}, {6826, 20418}, {6911, 28204}, {6914, 38022}, {6921, 15888}, {6946, 38074}, {7223, 26229}, {7280, 19704}, {7373, 25440}, {7963, 39980}, {8301, 35110}, {8715, 17573}, {9466, 22779}, {9670, 37256}, {9710, 17580}, {10056, 22767}, {10058, 38026}, {10072, 10948}, {10181, 10606}, {10200, 18990}, {10304, 11495}, {10596, 24466}, {10894, 26492}, {10912, 20323}, {11113, 34620}, {11179, 39883}, {11238, 17579}, {11240, 34612}, {11263, 28453}, {11274, 12331}, {11281, 21161}, {11346, 19769}, {11357, 19762}, {11358, 31137}, {11496, 32612}, {11813, 18541}, {12100, 35239}, {12607, 17567}, {13370, 28609}, {13738, 19722}, {16431, 29597}, {17556, 34739}, {17572, 31145}, {17577, 22760}, {17798, 19325}, {18967, 34743}, {19013, 19054}, {19014, 19053}, {19709, 26321}, {19796, 37091}, {19861, 31165}, {22763, 32787}, {22764, 32788}, {25893, 31164}, {26286, 28466}, {31146, 37270}, {31162, 37561}, {34123, 38056}, {36740, 38023}, {37617, 37674}, {38031, 38054}, {38053, 38454}
X(40726) = midpoint of X(999) and X(16417)
X(40726) = reflection of X(1376) in X(16417)
X(40726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 16371, 4421}, {2, 56, 11194}, {2, 5434, 11236}, {2, 11194, 958}, {2, 34605, 31141}, {3, 551, 4428}, {36, 25055, 16370}, {56, 5253, 25524}, {56, 25524, 958}, {404, 3304, 3913}, {474, 5563, 12513}, {993, 19883, 16857}, {3338, 17614, 12635}, {10072, 11112, 11235}, {11194, 25524, 2}, {11238, 17579, 34706}, {13587, 38314, 55}, {16370, 25055, 1001}, {16857, 19883, 8167}
Let A'B'C' be the antipedal triangle of X(2) wrt the medial triangle. Then X(40727) = X(4)-of-A'B'C'. (Randy Hutson, December 18, 2020)
X(40727) lies on the Kiepert circumhyperbola of the Brocard triangle and these lines: {2, 2418}, {3, 543}, {4, 9740}, {5, 9770}, {30, 7620}, {69, 37350}, {76, 5503}, {99, 8860}, {115, 599}, {148, 35955}, {183, 671}, {381, 524}, {385, 10807}, {525, 8371}, {538, 5055}, {597, 14535}, {598, 12156}, {754, 14269}, {1003, 8859}, {1153, 15701}, {1384, 11159}, {1656, 9771}, {1992, 3363}, {2482, 37637}, {2549, 11168}, {2782, 9743}, {2896, 7841}, {2996, 33215}, {3094, 9466}, {3534, 8182}, {3642, 5459}, {3643, 5460}, {3767, 33237}, {3821, 3828}, {3830, 3849}, {3843, 7751}, {3845, 23334}, {3851, 7775}, {3933, 32984}, {5032, 32983}, {5054, 7618}, {5072, 7758}, {5073, 7780}, {5286, 8367}, {5309, 24273}, {5461, 7778}, {5475, 15534}, {5969, 22677}, {7622, 8716}, {7746, 9167}, {7754, 33013}, {7761, 36523}, {7776, 33006}, {7801, 13881}, {8176, 9766}, {8359, 32828}, {8366, 17128}, {8370, 30435}, {8556, 11648}, {8586, 15533}, {8591, 17004}, {8598, 15655}, {9178, 9462}, {9486, 11162}, {9737, 32414}, {9774, 39646}, {9830, 12188}, {10000, 11286}, {10008, 21356}, {10717, 20481}, {11054, 11163}, {11164, 26613}, {12505, 14262}, {12525, 34383}, {13085, 13108}, {13188, 19911}, {13191, 33962}, {14033, 19661}, {14711, 18362}, {15271, 32457}, {15681, 32479}, {16644, 36775}, {18424, 40341}, {23055, 27088}, {32538, 37689}, {32834, 33190}, {32874, 33285}, {33896, 37690}
X(40727) = midpoint of X(i) and X(j) for these {i,j}: {2, 5485}, {4, 9740}, {7610, 34505}
X(40727) = reflection of X(i) in X(j) for these {i,j}: {2, 16509}, {3, 7610}, {381, 7615}, {3534, 8182}, {7618, 15597}, {8182, 13468}, {8716, 7622}, {9737, 32414}, {9741, 12040}, {9766, 8176}, {9770, 5}, {11165, 2}, {11184, 7617}, {13188, 19911}, {23334, 3845}, {34511, 9771}
X(40727) = isotomic conjugate of the isogonal conjugate of X(22111)
X(40727) = anticomplement of X(12040)
X(40727) = complement of X(9741)
X(40727) = complement of the isogonal conjugate of X(39236)
X(40727) = X(39236)-complementary conjugate of X(10)
X(40727) = X(9770)-of-Johnson-triangle
X(40727) = barycentric product X(76)*X(22111)
X(40727) = barycentric quotient X(22111)/X(6)
X(40727) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9741, 12040}, {183, 671, 5077}, {1992, 3363, 15484}, {5485, 16509, 11165}, {7617, 11184, 5055}, {7618, 15597, 5054}, {8667, 18546, 3830}, {9741, 12040, 11165}, {11054, 11163, 22253}, {11159, 22329, 1384}, {11185, 22329, 11159}, {17131, 31173, 15533}, {23055, 32815, 27088}, {42035, 42036, 599}
X(40728) lies on the cubic K1019 and these lines: {1, 6}, {31, 1911}, {32, 560}, {39, 2274}, {41, 904}, {42, 1185}, {43, 7075}, {51, 21813}, {55, 1197}, {81, 17032}, {86, 17750}, {100, 717}, {101, 731}, {171, 1613}, {172, 5156}, {181, 1196}, {190, 32453}, {748, 20965}, {750, 3231}, {869, 3774}, {1201, 20459}, {1206, 17018}, {1334, 2309}, {1500, 3688}, {1740, 3499}, {1964, 39258}, {2053, 21759}, {2211, 2212}, {2225, 30647}, {2235, 3923}, {2271, 23863}, {2276, 3736}, {3094, 3792}, {3271, 5052}, {3550, 21792}, {3730, 5145}, {3997, 33682}, {4259, 20861}, {4383, 17026}, {5017, 7295}, {5364, 16584}, {9463, 17126}, {14974, 20992}, {14997, 17029}, {16549, 18792}, {17027, 32911}, {17028, 37680}, {17030, 17277}, {17033, 17743}, {17034, 18147}, {17122, 21001}, {17349, 26801}, {17350, 19565}, {17379, 26082}, {17475, 32921}, {18899, 19587}, {23632, 36808}
X(40728) = isogonal conjugate of the isotomic conjugate of X(2276)
X(40728) = X(i)-Ceva conjugate of X(j) for these (i,j): {5388, 100}, {8693, 667}
X(40728) = X(i)-isoconjugate of X(j) for these (i,j): {2, 870}, {6, 871}, {75, 14621}, {76, 985}, {244, 5388}, {513, 37133}, {514, 789}, {668, 4817}, {693, 4586}, {825, 40495}, {982, 3114}, {1492, 3261}, {2344, 6063}, {3113, 3662}, {3407, 33930}, {3766, 37207}, {4583, 23597}, {4613, 7199}, {5384, 23989}
X(40728) = crosspoint of X(100) and X(5388)
X(40728) = crosssum of X(i) and X(j) for these (i,j): {2, 4441}, {75, 20917}, {76, 10009}, {28959, 34387}
X(40728) = crossdifference of every pair of points on line {513, 3261}
X(40728) = barycentric product X(i)*X(j) for these {i,j}: {1, 869}, {6, 2276}, {25, 3781}, {31, 984}, {32, 3661}, {41, 7146}, {42, 3736}, {55, 1469}, {56, 4517}, {75, 18900}, {81, 3774}, {100, 788}, {101, 3250}, {292, 16514}, {560, 33931}, {667, 3799}, {668, 8630}, {692, 1491}, {824, 32739}, {983, 3116}, {1110, 4475}, {1253, 7204}, {1397, 3790}, {1402, 3786}, {1576, 4122}, {1911, 3783}, {1914, 3862}, {1918, 30966}, {1919, 3807}, {1922, 3797}, {1980, 4505}, {2175, 7179}, {2200, 31909}, {2206, 3773}, {2210, 3864}, {2284, 29956}, {3117, 17743}, {3257, 14436}, {3792, 6187}, {5386, 14402}, {30665, 34067}
X(40728) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 871}, {31, 870}, {32, 14621}, {101, 37133}, {560, 985}, {692, 789}, {788, 693}, {869, 75}, {984, 561}, {1252, 5388}, {1469, 6063}, {1491, 40495}, {1919, 4817}, {2276, 76}, {3116, 33930}, {3117, 3662}, {3250, 3261}, {3661, 1502}, {3736, 310}, {3774, 321}, {3781, 305}, {3783, 18891}, {3786, 40072}, {3790, 40363}, {3792, 40075}, {3799, 6386}, {3862, 18895}, {4517, 3596}, {7146, 20567}, {8630, 513}, {9447, 2344}, {14436, 3762}, {16514, 1921}, {17415, 3801}, {18899, 2275}, {18900, 1}, {19587, 20917}, {32739, 4586}, {33931, 1928}
X(40728) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1743, 24727}, {6, 1001, 23660}, {6, 2176, 238}, {6, 21769, 16503}, {6, 21788, 1}, {32, 2175, 14599}, {213, 21760, 6}, {1918, 9454, 32}, {3051, 7109, 31}, {3230, 23660, 1001}
X(40729) lies on the cubics K220 and K1019, and on these lines: {1, 2670}, {6, 694}, {7, 16592}, {9, 43}, {37, 4039}, {41, 904}, {42, 22201}, {115, 19637}, {257, 17033}, {798, 1964}, {874, 17280}, {1334, 3774}, {1400, 16584}, {1431, 2279}, {1432, 39970}, {1469, 18784}, {1967, 19587}, {2229, 27447}, {2245, 3863}, {2295, 6378}, {3124, 30647}, {3229, 28369}, {4116, 9427}, {7032, 21755}, {17349, 40432}, {18785, 21796}, {20964, 21815}, {29055, 35106}
X(40729) = isogonal conjugate of X(8033)
X(40729) = X(37137)-Ceva conjugate of X(512)
X(40729) = X(i)-cross conjugate of X(j) for these (i,j): {3725, 213}, {7063, 512}
X(40729) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8033}, {2, 17103}, {7, 27958}, {21, 7196}, {58, 1920}, {81, 1909}, {86, 894}, {99, 4369}, {100, 16737}, {171, 274}, {172, 310}, {190, 17212}, {261, 4032}, {284, 7205}, {314, 7175}, {333, 7176}, {348, 14006}, {385, 18827}, {552, 4095}, {593, 1237}, {662, 4374}, {668, 18200}, {670, 20981}, {741, 3978}, {757, 3963}, {799, 4367}, {873, 2295}, {880, 3572}, {1014, 17787}, {1215, 1509}, {1434, 7081}, {1580, 40017}, {1926, 18268}, {1966, 37128}, {2162, 27891}, {2533, 4610}, {3287, 4625}, {3907, 4573}, {4107, 4589}, {4128, 34537}, {4164, 4639}, {4444, 17941}, {4459, 4620}, {4477, 4635}, {4529, 4616}, {4560, 6649}, {4576, 18111}, {4579, 7199}, {4584, 14296}, {4600, 7200}, {4615, 4922}, {4697, 32014}, {4754, 40439}, {6331, 22093}, {6385, 7122}, {6628, 21021}, {6645, 32010}, {7009, 17206}, {7184, 38810}, {7187, 40415}, {7192, 18047}, {16592, 24037}, {18787, 30940}, {27954, 40164}, {30669, 33295}
X(40729) = cevapoint of X(798) and X(1084)
X(40729) = crosspoint of X(893) and X(904)
X(40729) = crosssum of X(i) and X(j) for these (i,j): {7, 34061}, {333, 39915}, {894, 1909}, {3023, 3287}, {4367, 21755}, {17103, 27958}
X(40729) = crossdifference of every pair of points on line {804, 1966}
X(40729) = barycentric product X(i)*X(j) for these {i,j}: {10, 904}, {37, 893}, {42, 256}, {210, 1431}, {213, 257}, {321, 7104}, {512, 3903}, {694, 2238}, {740, 1967}, {756, 1178}, {798, 27805}, {805, 4155}, {862, 36214}, {872, 32010}, {874, 881}, {882, 3573}, {1334, 1432}, {1402, 4451}, {1500, 40432}, {1581, 3747}, {1824, 7015}, {1826, 7116}, {1918, 7018}, {1927, 35544}, {3709, 37137}, {3948, 9468}, {4041, 29055}, {4079, 4603}
X(40729) = trilinear product X(i)*X(j) for these {i,j}: {10, 7104}, {37, 904}, {42, 893}, {213, 256}, {257, 1918}, {694, 3747}, {733, 4093}, {798, 3903}, {881, 3570}, {1178, 1500}, {1334, 1431}, {1824, 7116}, {1927, 3948}, {1967, 2238}, {2205, 7018}, {2333, 7015}
X(40729) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 8033}, {31, 17103}, {37, 1920}, {41, 27958}, {42, 1909}, {43, 27891}, {65, 7205}, {213, 894}, {256, 310}, {257, 6385}, {512, 4374}, {649, 16737}, {667, 17212}, {669, 4367}, {694, 40017}, {740, 1926}, {756, 1237}, {798, 4369}, {862, 17984}, {872, 1215}, {881, 876}, {893, 274}, {904, 86}, {1084, 16592}, {1178, 873}, {1334, 17787}, {1400, 7196}, {1402, 7176}, {1500, 3963}, {1918, 171}, {1919, 18200}, {1924, 20981}, {1927, 741}, {1967, 18827}, {2205, 172}, {2212, 14006}, {2238, 3978}, {3121, 7200}, {3573, 880}, {3747, 1966}, {3903, 670}, {3948, 14603}, {4117, 4128}, {4155, 14295}, {4451, 40072}, {4455, 14296}, {4826, 4842}, {7063, 40608}, {7104, 81}, {7109, 2295}, {7116, 17206}, {8789, 18268}, {9427, 21755}, {9468, 37128}, {16584, 7187}, {17938, 36066}, {21753, 4754}, {21814, 16720}, {21815, 18905}, {23216, 22373}, {27805, 4602}, {29055, 4625}
X(40730) lies on the cubics K577 and K1019, and on these lines: {1, 2111}, {2, 660}, {31, 1911}, {38, 25813}, {42, 649}, {43, 57}, {55, 813}, {292, 2279}, {335, 3873}, {518, 27919}, {672, 3252}, {1026, 4447}, {1397, 2149}, {2196, 18265}, {2276, 18783}, {4583, 32937}, {4589, 8033}, {8041, 35505}, {17754, 36906}, {24514, 39918}
X(40730) = isogonal conjugate of the isotomic conjugate of X(22116)
X(40730) = X(i)-Ceva conjugate of X(j) for these (i,j): {660, 665}, {1911, 2223}
X(40730) = X(i)-isoconjugate of X(j) for these (i,j): {2, 6654}, {105, 350}, {238, 2481}, {239, 673}, {242, 31637}, {294, 10030}, {666, 812}, {874, 1027}, {927, 3716}, {1416, 4087}, {1429, 36796}, {1438, 1921}, {1447, 14942}, {1462, 3975}, {1914, 18031}, {2195, 18033}, {3684, 34018}, {3766, 36086}, {4124, 39293}, {4435, 34085}, {6185, 17755}, {8632, 36803}, {13576, 33295}, {18785, 30940}, {36057, 40717}
X(40730) = crosssum of X(i) and X(j) for these (i,j): {239, 8299}, {350, 39044}, {659, 35119}, {673, 33674}
X(40730) = crossdifference of every pair of points on line {239, 3766}
X(40730) = barycentric product X(i)*X(j) for these {i,j}: {1, 3252}, {6, 22116}, {31, 40217}, {241, 7077}, {291, 672}, {292, 518}, {295, 5089}, {334, 9454}, {335, 2223}, {660, 665}, {694, 4447}, {741, 3930}, {813, 2254}, {876, 2284}, {918, 34067}, {1026, 3572}, {1458, 4876}, {1861, 2196}, {1911, 3912}, {1922, 3263}, {3932, 18268}, {9455, 18895}, {18265, 40704}, {18827, 39258}, {20683, 37128}
X(40730) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 6654}, {241, 18033}, {291, 18031}, {292, 2481}, {518, 1921}, {660, 36803}, {665, 3766}, {672, 350}, {1026, 27853}, {1458, 10030}, {1911, 673}, {1922, 105}, {2196, 31637}, {2223, 239}, {2284, 874}, {2340, 3975}, {3252, 75}, {3286, 30940}, {3693, 4087}, {3912, 18891}, {3930, 35544}, {4447, 3978}, {5089, 40717}, {7077, 36796}, {8638, 4435}, {9454, 238}, {9455, 1914}, {14598, 1438}, {18265, 294}, {20683, 3948}, {22116, 76}, {34067, 666}, {39258, 740}, {39686, 8299}, {40217, 561}
X(40731) lies on the cubic K1019 and these lines: {1, 21}, {6, 694}, {41, 18784}, {42, 17209}, {171, 1909}, {172, 3955}, {741, 21010}, {757, 983}, {1469, 3736}, {2209, 38814}, {4279, 21511}, {4579, 18787}, {5021, 16058}, {5145, 33718}, {5255, 11104}, {16887, 33064}, {18266, 40214}
X(40731) = X(523)-isoconjugate of X(30670)
X(40731) = crossdifference of every pair of points on line {661, 804}
X(40731) = barycentric product X(i)*X(j) for these {i,j}: {172, 30966}, {662, 3805}, {869, 8033}, {894, 3736}, {1469, 27958}, {2276, 17103}, {3786, 7175}, {3799, 18200}, {3955, 31909}, {4481, 4579}, {4589, 30654}, {17941, 30671}
X(40731) = barycentric quotient X(i)/X(j) for these {i,j}: {163, 30670}, {3736, 257}, {3805, 1577}, {8033, 871}, {30654, 4010}
X(40732) lies on the cubic K1019 and these lines: {1, 2110}, {6, 2223}, {31, 21753}, {39, 20455}, {42, 20459}, {43, 55}, {100, 14621}, {869, 3774}, {1001, 3696}, {1469, 3736}, {2092, 3764}, {2309, 2347}, {3169, 6600}, {4254, 20992}, {4255, 18758}, {4433, 32941}, {4649, 21010}, {5132, 37586}, {20142, 23407}, {20967, 30706}
X(40732) = isogonal conjugate of the isotomic conjugate of X(3789)
X(40732) = X(i)-Ceva conjugate of X(j) for these (i,j): {105, 16514}, {2346, 984}
X(40732) = X(i)-isoconjugate of X(j) for these (i,j): {870, 1002}, {4817, 32041}, {14621, 27475}
X(40732) = crosspoint of X(6) and X(1001)
X(40732) = crosssum of X(2) and X(1002)
X(40732) = barycentric product X(i)*X(j) for these {i,j}: {6, 3789}, {31, 27474}, {869, 4384}, {984, 2280}, {1001, 2276}, {1469, 37658}, {4517, 5228}, {18900, 21615}
X(40732) = barycentric quotient X(i)/X(j) for these {i,j}: {869, 27475}, {2280, 870}, {3789, 76}, {4384, 871}, {18900, 2279}, {27474, 561}
X(40733) lies on the cubic K1019 and these lines: {1, 1573}, {6, 3009}, {41, 1914}, {42, 16515}, {43, 17475}, {213, 7296}, {292, 2279}, {649, 38367}, {869, 2276}, {872, 16525}, {1017, 5008}, {1100, 4687}, {1107, 3876}, {2277, 23548}, {3230, 21754}, {3747, 10987}, {4393, 21904}, {16369, 23407}, {17275, 26772}, {20284, 21779}, {21352, 37673}
X(40733) = isogonal conjugate of the isotomic conjugate of X(27481)
X(40733) = X(6)-Ceva conjugate of X(2276)
X(40733) = X(985)-isoconjugate of X(27494)
X(40733) = crosspoint of X(6) and X(21793)
X(40733) = crosssum of X(2) and X(27494)
X(40733) = crossdifference of every pair of points on line {4784, 4785}
X(40733) = barycentric product X(i)*X(j) for these {i,j}: {1, 3795}, {6, 27481}, {869, 30963}, {984, 16468}, {2276, 4393}, {3661, 21793}, {3736, 3993}, {3773, 34476}, {3799, 4782}
X(40733) = barycentric quotient X(i)/X(j) for these {i,j}: {2276, 27494}, {3795, 75}, {16468, 870}, {21793, 14621}, {27481, 76}, {30963, 871}
X(40733) = {X(869),X(16514)}-harmonic conjugate of X(2276)
X(40734) lies on the cubic K1019 and these lines: {1, 2106}, {6, 741}, {31, 1326}, {41, 58}, {43, 81}, {662, 985}, {688, 875}, {1185, 5145}, {2276, 3736}, {4658, 17175}, {9455, 17104}
X(40734) = barycentric product X(i)*X(j) for these {i,j}: {58, 27495}, {3736, 16826}, {3781, 31904}
X(40734) = barycentric quotient X(i)/X(j) for these {i,j}: {3736, 27483}, {27495, 313}
X(40735) lies on these lines: {1, 20332}, {6, 3009}, {31, 19587}, {42, 2162}, {43, 81}, {55, 36614}, {604, 18266}, {739, 2177}, {1333, 2209}, {1918, 34819}, {4393, 4649}, {17379, 25311}
X(40735) = isogonal conjugate of X(30963)
X(40735) = X(869)-cross conjugate of X(31)
X(40735) = X(i)-isoconjugate of X(j) for these (i,j): {1, 30963}, {2, 4393}, {6, 10009}, {75, 16468}, {76, 21793}, {86, 3993}, {99, 4806}, {190, 4785}, {264, 23095}, {274, 21904}, {306, 31912}, {313, 34476}, {668, 4782}, {870, 3795}, {903, 4759}, {1268, 4991}, {14621, 27481}
X(40735) = cevapoint of X(788) and X(3248)
X(40735) = barycentric product X(i)*X(j) for these {i,j}: {31, 27494}, {1333, 34475}
X(40735) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 10009}, {6, 30963}, {31, 4393}, {32, 16468}, {213, 3993}, {560, 21793}, {667, 4785}, {798, 4806}, {869, 27481}, {1918, 21904}, {1919, 4782}, {2203, 31912}, {2251, 4759}, {9247, 23095}, {27494, 561}, {34475, 27801}
X(40736) lies on the cubic K1019 and these lines: {6, 43}, {31, 7104}, {41, 1922}, {81, 38810}, {213, 2053}, {717, 932}, {4598, 37678}, {18899, 19587}
X(40736) = X(i)-isoconjugate of X(j) for these (i,j): {192, 870}, {789, 3835}, {871, 2176}, {985, 6382}, {3113, 33890}, {3123, 5388}, {4083, 37133}, {4586, 20906}, {4817, 36863}, {6376, 14621}
X(40736) = barycentric product X(i)*X(j) for these {i,j}: {87, 869}, {788, 932}, {984, 7121}, {1469, 2053}, {2162, 2276}, {3250, 34071}, {3736, 23493}, {6384, 18900}, {8630, 18830}
X(40736) = barycentric quotient X(i)/X(j) for these {i,j}: {87, 871}, {788, 20906}, {869, 6376}, {2276, 6382}, {3117, 33890}, {3661, 40367}, {7121, 870}, {8630, 4083}, {18899, 20284}, {18900, 43}, {34071, 37133}
X(40736) = {X(6),X(2162)}-harmonic conjugate of X(34252)
X(40737) lies on the cubics K131, K1026, , and K1176, and on these lines: {1, 2668}, {2, 2107}, {31, 2106}, {42, 894}, {171, 213}, {846, 16362}, {873, 4117}, {1402, 7175}, {1740, 2258}, {1967, 37128}, {1973, 15148}, {3223, 10436}, {4128, 32010}, {5539, 17596}, {13610, 18786}, {16826, 23493}, {18793, 24342}, {25528, 38275}, {33779, 37132}
X(40737) = isogonal conjugate of X(1045)
X(40737) = isogonal conjugate of the isotomic conjugate of X(18298)
X(40737) = X(i)-cross conjugate of X(j) for these (i,j): {86, 1}, {893, 57}
X(40737) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1045}, {2, 21779}, {4, 23079}, {6, 1655}, {42, 39915}, {75, 18756}, {81, 21883}, {99, 9402}, {213, 34021}, {904, 27890}
X(40737) = cevapoint of X(i) and X(j) for these (i,j): {513, 4128}, {649, 4117}, {659, 38978}
X(40737) = trilinear pole of line {798, 4367}
X(40737) = barycentric product X(i)*X(j) for these {i,j}: {6, 18298}, {37128, 39926}
X(40737) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1655}, {6, 1045}, {31, 21779}, {32, 18756}, {42, 21883}, {48, 23079}, {81, 39915}, {86, 34021}, {798, 9402}, {894, 27890}, {18298, 76}, {39926, 3948}
X(40738) lies on the conic {{A,B,C,X(1),X(2)}}, the cubic K1176, and these lines: {1, 257}, {2, 893}, {57, 7249}, {81, 32010}, {86, 3863}, {105, 30670}, {256, 291}, {274, 33891}, {330, 870}, {733, 789}, {1002, 40721}, {1255, 26243}, {1431, 17379}, {1432, 1447}, {2224, 30111}, {2344, 3407}, {4817, 17212}, {10436, 27447}, {16826, 25425}
X(40738) = X(i)-isoconjugate of X(j) for these (i,j): {37, 40731}, {101, 3805}, {171, 2276}, {172, 984}, {660, 30654}, {788, 18047}, {869, 894}, {1469, 2329}, {1580, 3862}, {1691, 3864}, {1909, 40728}, {1920, 18900}, {2295, 3736}, {2330, 7146}, {3250, 4579}, {3661, 7122}, {3774, 17103}, {3781, 7119}, {3799, 20981}, {3802, 30657}, {4517, 7175}, {16514, 18787}
X(40738) = trilinear pole of line {513, 4107}
X(40738) = barycentric product X(i)*X(j) for these {i,j}: {256, 870}, {257, 14621}, {693, 30670}, {871, 904}, {985, 7018}, {3113, 3865}, {3114, 3863}, {4817, 27805}, {32010, 40718}
X(40738) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 40731}, {256, 984}, {257, 3661}, {513, 3805}, {694, 3862}, {870, 1909}, {893, 2276}, {904, 869}, {985, 171}, {1178, 3736}, {1431, 1469}, {1432, 7146}, {1492, 4579}, {1581, 3864}, {2344, 2329}, {3766, 30639}, {3863, 3094}, {3903, 3799}, {4451, 3790}, {4586, 18047}, {4817, 4369}, {7015, 3781}, {7018, 33931}, {7104, 40728}, {7249, 7179}, {8632, 30654}, {14438, 30656}, {14621, 894}, {17493, 3797}, {18786, 3783}, {23597, 4107}, {27805, 3807}, {30670, 100}, {32010, 30966}, {33891, 9865}, {40718, 1215}, {40722, 27954}, {40729, 3774}
X(40739) lies on the cubic K1176 and these lines: {1, 39923}, {2, 2116}, {1001, 14621}, {1002, 40721}, {3923, 32041}, {4334, 40718}, {5263, 37138}, {8926, 24342}
X(40739) = X(i)-isoconjugate of X(j) for these (i,j): {7, 40732}, {56, 3789}, {604, 27474}, {869, 40719}, {984, 1471}, {1001, 1469}, {2276, 5228}, {2280, 7146}
X(40739) = cevapoint of X(1) and X(9746)
X(40739) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 27474}, {9, 3789}, {41, 40732}, {985, 5228}, {1002, 7146}, {2279, 1469}, {2344, 1001}, {14621, 40719}, {27475, 7179}
X(40740) lies on the cubic K1176 and these lines: {1, 335}, {2, 2113}, {660, 27495}, {894, 24479}, {985, 40217}, {1757, 27926}, {9505, 40718}, {24358, 24510}
X(40740) = X(i)-isoconjugate of X(j) for these (i,j): {869, 40725}, {1929, 16514}, {2702, 30665}, {3783, 17962}, {3802, 9506}
X(40740) = barycentric product X(2786)*X(37207)
X(40740) = barycentric quotient X(i)/X(j) for these {i,j}: {1757, 3783}, {2786, 4486}, {6542, 3797}, {8298, 3802}, {9508, 30665}, {14621, 40725}, {17735, 16514}, {30664, 37135}, {37207, 35148}
X(40741) lies on the cubic K1176 and these lines: {2, 2053}, {86, 26143}, {330, 870}, {932, 6645}, {2295, 4598}, {7121, 14621}, {7153, 40719}, {16826, 23493}, {26801, 34252}
X(40741) = X(40718)-Ceva conjugate of X(40720)
X(40741) = barycentric product X(i)*X(j) for these {i,j}: {330, 30661}, {6384, 18754}
X(40741) = barycentric quotient X(i)/X(j) for these {i,j}: {18754, 43}, {30661, 192}
X(40742) lies on the cubic K1176 and these lines: {1, 18795}, {2, 292}, {894, 24576}, {2111, 14621}
X(40742) = X(2665)-isoconjugate of X(16514)
X(40742) = barycentric quotient X(i)/X(j) for these {i,j}: {2664, 3783}, {15148, 17569}, {17759, 3797}, {21788, 16514}
X(40743) lies on the cubic K1176 and these lines: {1, 7168}, {2, 893}, {86, 870}, {894, 19567}, {1045, 27890}, {9401, 26102}
X(40743) = X(40718)-Ceva conjugate of X(870)
X(40743) = X(18298)-isoconjugate of X(18900)
X(40743) = barycentric product X(i)*X(j) for these {i,j}: {870, 1655}, {871, 21779}, {34021, 40718}
X(40743) = barycentric quotient X(i)/X(j) for these {i,j}: {1045, 2276}, {1655, 984}, {18756, 40728}, {21779, 869}, {34021, 30966}
X(40744) lies on these lines: {1, 2210}, {2, 41}, {21, 72}, {42, 1580}, {48, 17379}, {75, 584}, {81, 172}, {86, 2174}, {101, 16826}, {171, 18266}, {218, 16367}, {239, 4251}, {251, 17011}, {284, 894}, {379, 31019}, {572, 17120}, {604, 37677}, {662, 4670}, {1100, 18042}, {1468, 37617}, {1931, 2185}, {1993, 23150}, {2112, 16503}, {2268, 17350}, {2278, 3758}, {2280, 2344}, {2289, 26059}, {2329, 6542}, {2663, 7122}, {3204, 4687}, {3218, 21511}, {3661, 16788}, {3868, 13723}, {4289, 4363}, {4390, 20055}, {5371, 16519}, {5813, 26626}, {8300, 21352}, {9310, 29570}, {9454, 20132}, {11320, 24514}, {11349, 27003}, {11364, 20985}, {16704, 31039}, {16783, 17397}, {17023, 27950}, {17103, 40214}, {17302, 18162}
X(40744) = crosspoint of X(4567) and X(4586)
X(40744) = crosssum of X(3125) and X(3250)
X(40745) lies on these lines: {7, 604}, {81, 4586}, {171, 7369}, {172, 385}, {192, 15370}, {330, 985}, {789, 35105}, {870, 16998}, {894, 1580}, {961, 40738}, {1446, 3407}, {6625, 18757}, {7187, 17103}, {16915, 20911}, {30664, 40742}
X(40745) = X(i)-isoconjugate of X(j) for these (i,j): {256, 2276}, {257, 869}, {694, 3783}, {788, 27805}, {893, 984}, {904, 3661}, {1432, 4517}, {1581, 16514}, {1967, 3797}, {3250, 3903}, {3774, 32010}, {3862, 18786}, {7018, 40728}, {7104, 33931}, {30966, 40729}
X(40745) = trilinear pole of line {4164, 4369}
X(40745) = barycentric product X(i)*X(j) for these {i,j}: {171, 870}, {789, 4367}, {871, 7122}, {894, 14621}, {985, 1909}, {1492, 4374}, {2344, 7196}, {3113, 7184}, {3407, 7187}, {4107, 37207}, {4369, 4586}, {4613, 17212}, {4817, 18047}, {6645, 40738}, {14296, 30664}, {17103, 40718}, {20981, 37133}
X(40745) = barycentric quotient X(i)/X(j) for these {i,j}: {171, 984}, {172, 2276}, {385, 3797}, {870, 7018}, {894, 3661}, {985, 256}, {1215, 3773}, {1492, 3903}, {1580, 3783}, {1691, 16514}, {1909, 33931}, {2330, 4517}, {2533, 4122}, {3907, 4522}, {3955, 3781}, {4032, 16603}, {4107, 4486}, {4164, 30665}, {4367, 1491}, {4369, 824}, {4434, 4439}, {4579, 3799}, {4586, 27805}, {4697, 3775}, {4774, 4951}, {7081, 3790}, {7122, 869}, {7175, 7146}, {7176, 7179}, {7187, 3314}, {14621, 257}, {17103, 30966}, {18047, 3807}, {18200, 4481}, {18787, 3864}, {20981, 3250}, {40731, 4476}, {40738, 40099}
X(40746) lies on the conic {{A,B,C,X(1),X(6)}} and these lines: {1, 32}, {6, 560}, {9, 39977}, {31, 292}, {56, 21771}, {58, 2275}, {86, 1333}, {87, 1716}, {101, 40733}, {106, 825}, {604, 1431}, {713, 789}, {870, 16998}, {996, 5291}, {1126, 4251}, {1220, 4426}, {1252, 5378}, {1400, 18898}, {1438, 5332}, {1449, 9277}, {1492, 5035}, {2220, 40433}, {2276, 37586}, {2280, 25426}, {3226, 4586}, {3661, 4386}, {4372, 33935}, {5042, 36598}, {5156, 14599}, {5337, 30945}, {9111, 30664}, {16946, 39972}, {21010, 21793}, {30670, 35105}
X(40746) = isogonal conjugate of X(3661)
X(40746) = isogonal conjugate of the anticomplement of X(17023)
X(40746) = isogonal conjugate of the complement of X(4393)
X(40746) = isogonal conjugate of the isotomic conjugate of X(14621)
X(40746) = X(21764)-cross conjugate of X(6)
X(40746) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3661}, {2, 984}, {6, 33931}, {8, 7146}, {9, 7179}, {21, 16603}, {37, 30966}, {57, 3790}, {72, 31909}, {75, 2276}, {76, 869}, {81, 3773}, {85, 4517}, {88, 4439}, {92, 3781}, {100, 824}, {190, 1491}, {226, 3786}, {239, 3864}, {291, 3797}, {310, 3774}, {312, 1469}, {321, 3736}, {334, 16514}, {335, 3783}, {346, 7204}, {350, 3862}, {513, 3807}, {514, 3799}, {561, 40728}, {649, 4505}, {651, 4522}, {660, 4486}, {662, 4122}, {668, 3250}, {788, 1978}, {874, 30671}, {983, 3314}, {1002, 27474}, {1016, 4475}, {1255, 3775}, {1502, 18900}, {3094, 7033}, {3117, 7034}, {3573, 23596}, {3789, 27475}, {3792, 18359}, {3795, 27494}, {3802, 40098}, {3805, 27805}, {3952, 4481}, {4407, 40434}, {4469, 40718}, {4562, 30665}, {4604, 4951}, {4606, 4818}, {5386, 33904}, {27495, 30571}, {30870, 32739}
X(40746) = cevapoint of X(6) and X(21793)
X(40746) = crosssum of X(2276) and X(3781)
X(40746) = trilinear pole of line {649, 1980}
X(40746) = crossdifference of every pair of points on line {824, 1491}
X(40746) = barycentric product X(i)*X(j) for these {i,j}: {1, 985}, {6, 14621}, {31, 870}, {57, 2344}, {58, 40718}, {101, 4817}, {172, 40738}, {244, 5384}, {513, 1492}, {514, 825}, {560, 871}, {649, 4586}, {659, 30664}, {667, 789}, {693, 34069}, {813, 23597}, {893, 40745}, {1471, 40739}, {1919, 37133}, {1977, 5388}, {2248, 40722}, {2275, 3407}, {3113, 7032}, {3662, 18898}, {3733, 4613}, {4367, 30670}, {8632, 37207}
X(40746) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 33931}, {6, 3661}, {31, 984}, {32, 2276}, {42, 3773}, {55, 3790}, {56, 7179}, {58, 30966}, {100, 4505}, {101, 3807}, {184, 3781}, {512, 4122}, {560, 869}, {604, 7146}, {649, 824}, {663, 4522}, {667, 1491}, {692, 3799}, {693, 30870}, {789, 6386}, {825, 190}, {870, 561}, {871, 1928}, {902, 4439}, {985, 75}, {1106, 7204}, {1397, 1469}, {1400, 16603}, {1474, 31909}, {1492, 668}, {1501, 40728}, {1911, 3864}, {1914, 3797}, {1917, 18900}, {1919, 3250}, {1922, 3862}, {1980, 788}, {2175, 4517}, {2194, 3786}, {2205, 3774}, {2206, 3736}, {2210, 3783}, {2275, 3314}, {2280, 27474}, {2308, 3775}, {2344, 312}, {3113, 7034}, {3248, 4475}, {3572, 23596}, {4164, 30639}, {4586, 1978}, {4613, 27808}, {4775, 4951}, {4817, 3261}, {5384, 7035}, {8632, 4486}, {14599, 16514}, {14621, 76}, {18898, 17743}, {21747, 4407}, {21793, 27481}, {30664, 4583}, {34069, 100}, {40718, 313}, {40745, 1920}
X(40747) lies on the cubic K1177 and these lines: {1, 32}, {6, 75}, {9, 17038}, {10, 213}, {19, 1974}, {37, 1918}, {65, 21861}, {81, 4586}, {83, 18833}, {158, 2207}, {171, 292}, {596, 20963}, {649, 876}, {729, 789}, {759, 825}, {869, 4386}, {897, 1492}, {910, 34434}, {940, 16524}, {994, 5011}, {1100, 13476}, {1258, 40738}, {1449, 39742}, {1910, 14601}, {1922, 32115}, {2166, 11060}, {2176, 5275}, {2186, 21010}, {2218, 16974}, {3224, 18832}, {4649, 25426}, {5276, 16514}, {8773, 32654}, {16777, 39737}, {16782, 17023}, {16826, 40722}, {16884, 39739}, {16971, 39697}, {16973, 23051}, {17475, 39714}, {17750, 29633}, {17754, 17795}, {21352, 21764}, {21793, 23407}, {21904, 22327}, {29610, 37673}, {36119, 40354}, {37207, 40742}
X(40747) = isogonal conjugate of X(40773)
X(40747) = X(14621)-Ceva conjugate of X(40718)
X(40747) = X(i)-cross conjugate of X(j) for these (i,j): {3288, 4559}, {21840, 37}
X(40747) = X(i)-isoconjugate of X(j) for these (i,j): {2, 3736}, {3, 31909}, {6, 30966}, {21, 7146}, {27, 3781}, {57, 3786}, {58, 3661}, {60, 16603}, {81, 984}, {86, 2276}, {99, 3250}, {100, 4481}, {110, 824}, {257, 40731}, {274, 869}, {284, 7179}, {310, 40728}, {333, 1469}, {593, 3773}, {662, 1491}, {741, 3797}, {788, 799}, {873, 3774}, {985, 4469}, {1019, 3799}, {1171, 3775}, {1333, 33931}, {1412, 3790}, {1434, 4517}, {2287, 7204}, {3094, 40415}, {3116, 38810}, {3314, 38813}, {3733, 3807}, {3783, 37128}, {3792, 24624}, {3805, 4603}, {3862, 33295}, {4122, 4556}, {4475, 4567}, {4476, 14621}, {4522, 4565}, {4584, 30665}, {4602, 8630}, {4627, 4818}, {4634, 14436}, {6385, 18900}, {16514, 18827}, {18829, 30654}, {27483, 40734}
X(40747) = cevapoint of X(i) and X(j) for these (i,j): {37, 21904}, {171, 4649}
X(40747) = crosspoint of X(985) and X(14621)
X(40747) = crosssum of X(984) and X(2276)
X(40747) = trilinear pole of line {661, 669}
X(40747) = crossdifference of every pair of points on line {788, 1491}
X(40747) = trilinear product X(i)*X(j) for these {i,j}: {6, 40718}, {10, 40746}, {37, 985}, {42, 14621}, {65, 2344}, {213, 870}, {512, 4586}, {523, 825}, {649, 4613}, {661, 1492}, {669, 37133}, {789, 798}, {871, 2205}, {1577, 34069}, {2295, 40763}, {2887, 18898}, {3113, 16584}, {3125, 5384}, {3407, 3778}, {4455, 37207}, {4557, 4817}, {20964, 40738}, {21010, 25425}, {21832, 30664}
X(40747) = barycentric product X(i)*X(j) for these {i,j}: {1, 40718}, {10, 985}, {37, 14621}, {42, 870}, {226, 2344}, {512, 789}, {513, 4613}, {523, 1492}, {661, 4586}, {798, 37133}, {825, 1577}, {850, 34069}, {871, 1918}, {1018, 4817}, {2295, 40738}, {2533, 30670}, {3113, 3778}, {3114, 16584}, {3120, 5384}, {3121, 5388}, {3407, 3721}, {4010, 30664}, {17754, 25425}, {18898, 20234}, {21832, 37207}
X(40747) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 30966}, {10, 33931}, {19, 31909}, {31, 3736}, {37, 3661}, {42, 984}, {55, 3786}, {65, 7179}, {210, 3790}, {213, 2276}, {228, 3781}, {512, 1491}, {649, 4481}, {661, 824}, {669, 788}, {756, 3773}, {789, 670}, {798, 3250}, {804, 30639}, {825, 662}, {850, 30870}, {869, 4476}, {870, 310}, {985, 86}, {1018, 3807}, {1042, 7204}, {1400, 7146}, {1402, 1469}, {1492, 99}, {1918, 869}, {1962, 3775}, {2171, 16603}, {2205, 40728}, {2238, 3797}, {2276, 4469}, {2344, 333}, {3122, 4475}, {3407, 38810}, {3721, 3314}, {3724, 3792}, {3747, 3783}, {3952, 4505}, {4041, 4522}, {4455, 30665}, {4557, 3799}, {4586, 799}, {4613, 668}, {4705, 4122}, {4770, 4951}, {4817, 7199}, {4822, 4818}, {5384, 4600}, {7109, 3774}, {7122, 40731}, {7234, 3805}, {9426, 8630}, {14621, 274}, {16584, 3094}, {21751, 3117}, {21805, 4439}, {21806, 4407}, {21832, 4486}, {21904, 27481}, {30664, 4589}, {30670, 4594}, {34069, 110}, {37133, 4602}, {37207, 4639}, {40718, 75}, {40745, 8033}
X(40748) lies on the cubic K1177 and these lines: {1, 18789}, {985, 1001}, {4384, 14621}, {4649, 25426}
X(40748) = isogonal conjugate of X(40774)
X(40748) = X(3720)-cross conjugate of X(870)
X(40748) = X(i)-isoconjugate of X(j) for these (i,j): {6, 27495}, {10, 40734}, {984, 4649}, {2276, 16826}, {3736, 3842}, {3799, 4784}, {3862, 20142}
X(40748) = trilinear product X(i)*X(j) for these {i,j}: {985, 30571}, {4817, 28841}, {14621, 25426}, {27483, 40746}
X(40748) = barycentric product X(i)*X(j) for these {i,j}: {870, 25426}, {985, 27483}, {14621, 30571}
X(40748) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 27495}, {985, 16826}, {1333, 40734}, {25426, 984}, {27483, 33931}, {28841, 3799}, {30571, 3661}
X(40749) lies on the cubic K1177 and these lines: {1, 21}, {6, 1045}, {43, 2229}, {44, 24450}, {171, 213}, {239, 2308}, {274, 4697}, {869, 17126}, {980, 4650}, {1761, 16972}, {1781, 13610}, {1918, 2663}, {1961, 3294}, {2111, 5091}, {3791, 17143}, {4039, 17499}, {4384, 14621}, {4393, 4427}, {4443, 5165}, {5283, 7262}, {13174, 32115}, {16369, 25427}, {16475, 37555}, {16831, 37604}, {17034, 24259}, {20367, 29821}, {21010, 23194}, {21352, 21747}
X(40749) = isogonal conjugate of X(40775)
X(40749) = X(4649)-isoconjugate of X(30570)
X(40749) = crosspoint of X(1492) and X(24041)
X(40749) = crosssum of X(1491) and X(2643)
X(40749) = trilinear product X(6)*X(40721)
X(40749) = barycentric product X(1)*X(40721)
X(40749) = barycentric quotient X(i)/X(j) for these {i,j}: {25426, 30570}, {40721, 75}
X(40749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {81, 3747, 1}, {171, 213, 2664}
X(40750) lies on the cubic K1177 and these lines: {1, 1929}, {2, 6}, {9, 37604}, {37, 171}, {45, 896}, {55, 199}, {58, 16589}, {187, 4653}, {191, 21816}, {213, 37559}, {220, 18253}, {573, 19516}, {644, 2295}, {750, 2276}, {894, 20947}, {942, 16519}, {980, 21989}, {985, 1001}, {1010, 21024}, {1046, 21879}, {1100, 3684}, {1107, 37607}, {1220, 21025}, {1509, 17499}, {1575, 17122}, {1655, 17103}, {1914, 3720}, {2176, 5711}, {2242, 30116}, {2243, 17021}, {2280, 9345}, {2475, 23903}, {3053, 13723}, {3145, 21808}, {3247, 3550}, {3290, 3745}, {3723, 3750}, {3726, 3920}, {3770, 8033}, {3985, 4697}, {3996, 17388}, {4037, 4418}, {4362, 25124}, {4363, 33931}, {4425, 4987}, {4649, 21904}, {4657, 24586}, {4658, 20970}, {5228, 16518}, {5283, 33863}, {5337, 21981}, {5710, 16969}, {6543, 6625}, {8258, 17750}, {9347, 20998}, {11358, 39967}, {14621, 30963}, {16369, 25427}, {16372, 21010}, {16502, 29646}, {16516, 37543}, {16521, 37520}, {16583, 37594}, {16672, 37540}, {16678, 21773}, {16826, 40722}, {16884, 17017}, {16917, 33296}, {16968, 37554}, {17016, 21951}, {17019, 35216}, {17275, 32853}, {21764, 30950}, {21769, 29644}, {21771, 27802}, {21785, 29650}, {23897, 26051}, {23905, 26117}, {25499, 29473}, {25809, 25817}, {29649, 34261}, {29671, 38408}, {36659, 36746}
X(40750) = isogonal conjugate of X(40776)
X(40750) = X(i)-Ceva conjugate of X(j) for these (i,j): {16826, 1001}, {40722, 8424}
X(40750) = crosspoint of X(789) and X(34537)
X(40750) = crosssum of X(i) and X(j) for these (i,j): {788, 1084}, {824, 8287}
X(40750) = crossdifference of every pair of points on line {512, 9508}
X(40750) = trilinear product X(i)*X(j) for these {i,j}: {6, 24342}, {662, 9279}, {1001, 18791}
X(40750) = barycentric product X(i)*X(j) for these {i,j}: {1, 24342}, {99, 9279}, {4384, 18791}
X(40750) = barycentric quotient X(i)/X(j) for these {i,j}: {9279, 523}, {18791, 27475}, {24342, 75}
X(40750) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5277, 18755}, {37, 171, 17735}, {81, 2238, 6}, {81, 37675, 2238}, {940, 5275, 6}, {1030, 20472, 199}, {1929, 8298, 8301}, {1961, 3509, 37}, {3684, 4038, 1100}, {5276, 24512, 6}, {5276, 37633, 24512}, {5283, 37522, 33863}, {16999, 20132, 37678}
X(40751) lies on the cubic K1177 and these lines: {1, 3506}, {6, 256}, {81, 982}, {171, 19554}, {1449, 9277}, {1654, 40722}, {4649, 40744}, {6650, 14621}, {29840, 32853}
X(40751) = isogonal conjugate of X(40777)
X(40751) = X(i)-isoconjugate of X(j) for these (i,j): {984, 13610}, {2248, 3661}, {2276, 6625}, {15377, 31909}, {18757, 33931}
X(40751) = trilinear product X(i)*X(j) for these {i,j}: {6, 40722}, {825, 21196}, {846, 985}, {1654, 40746}, {14621, 18755}, {38814, 40747}
X(40751) = barycentric product X(i)*X(j) for these {i,j}: {1, 40722}, {846, 14621}, {870, 18755}, {985, 1654}, {1492, 21196}, {2344, 17084}, {38814, 40718}
X(40751) = barycentric quotient X(i)/X(j) for these {i,j}: {846, 3661}, {985, 6625}, {1654, 33931}, {18755, 984}, {21879, 3773}, {38814, 30966}, {40722, 75}
X(40752) lies on the cubic K1177 and these lines: {1, 257}, {6, 19579}, {81, 310}, {171, 19565}, {985, 39925}, {1655, 18756}, {4649, 40718}, {17032, 26243}, {21779, 40743}
X(40752) = isogonal conjugate of X(40778)
X(40752) = X(i)-isoconjugate of X(j) for these (i,j): {2276, 40737}, {18298, 40728}
X(40752) = cevapoint of X(30661) and X(40721)
X(40752) = trilinear product X(i)*X(j) for these {i,j}: {6, 40743}, {870, 21779}, {985, 1655}, {1045, 14621}, {39915, 40747}
X(40752) = barycentric product X(i)*X(j) for these {i,j}: {1, 40743}, {870, 1045}, {871, 18756}, {1655, 14621}, {39915, 40718}
X(40752) = barycentric quotient X(i)/X(j) for these {i,j}: {870, 18298}, {985, 40737}, {1045, 984}, {1655, 3661}, {18756, 869}, {21779, 2276}, {23079, 3781}, {39915, 30966}, {40743, 75}
X(40753) lies on the cubic K1177 and these lines: {1, 727}, {6, 43}, {2280, 34071}, {16468, 40720}
X(40753) = isogonal conjugate of X(40780)
X(40753) = X(4393)-cross conjugate of X(16468)
X(40753) = X(i)-isoconjugate of X(j) for these (i,j): {2176, 27494}, {6376, 40735}, {34475, 38832}
X(40753) = cevapoint of X(4393) and X(40720)
X(40753) = barycentric product X(i)*X(j) for these {i,j}: {1, 40720}, {87, 4393}, {330, 16468}, {932, 4785}, {2162, 30963}, {4598, 4782}, {6384, 21793}, {7121, 10009}
X(40753) = trilinear product X(i)*X(j) for these {i,j}: {6, 40720}, {87, 16468}, {330, 21793}, {932, 4782}, {2162, 4393}, {4785, 34071}, {7121, 30963}
X(40753) = barycentric quotient X(i)/X(j) for these {i,j}: {87, 27494}, {4393, 6376}, {4782, 3835}, {4785, 20906}, {16468, 192}, {16606, 34475}, {21793, 43}, {21904, 3971}, {23095, 22370}, {25376, 21426}, {30963, 6382}, {34476, 27644}, {40720, 75}
X(40753) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7121, 17105}, {2162, 34252, 87}
X(40754) lies on the cubic K1177 and these lines: {1, 9453}, {6, 7}, {37, 36086}, {105, 825}, {666, 894}, {885, 2298}, {984, 9501}, {1438, 7194}, {1781, 13610}, {4336, 28071}, {4645, 40724}, {4649, 9505}, {5018, 19554}, {5276, 9318}, {17300, 31637}
X(40754) = isogonal conjugate of X(40781)
X(40754) = cevapoint of X(3509) and X(19557)
X(40754) = trilinear product X(i)*X(j) for the
X(40754) = X(i)-isoconjugate of X(j) for these (i,j): {241, 7281}, {518, 3512}, {672, 7261}, {3912, 8852}, {8299, 24479}, {9454, 18036}, {17755, 30648}
X(40754) = barycentric product X(i)*X(j) for these {i,j}: {1, 40724}, {105, 4645}, {673, 3509}, {1438, 17789}, {2481, 17798}, {4458, 36086}, {5018, 14942}, {18031, 19554}
X(40754) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 7261}, {1438, 3512}, {2195, 7281}, {2481, 18036}, {3509, 3912}, {4645, 3263}, {5018, 9436}, {17798, 518}, {18262, 2223}, {19554, 672}, {19557, 17755}, {19561, 8299}, {20715, 3932}, {20741, 25083}, {40724, 75}
X(40755) lies on the cubic K1177 and these lines: {1, 727}, {213, 8709}, {14621, 20332}
X(40755) = isogonal conjugate of X(40782)
X(40755) = cevapoint of X(18278) and X(19580)
X(40755) = X(i)-isoconjugate of X(j) for these (i,j): {1575, 7168}, {17475, 24576}
X(40755) = trilinear product X(i)*X(j) for these {i,j}: {727, 19565}, {3226, 18278}, {3510, 20332}, {19567, 34077}
X(40755) = barycentric product X(i)*X(j) for these {i,j}: {727, 19567}, {3226, 3510}, {18275, 34077}, {18278, 32020}, {19565, 20332}
X(40755) = barycentric quotient X(i)/X(j) for these {i,j}: {727, 7168}, {3510, 726}, {18274, 17475}, {18278, 1575}, {19567, 35538}, {19580, 17793}, {30634, 20663}
X(40756) lies on the cubic K1177 and these lines: {4393, 4649}
X(40756) = isogonal conjugate of X(40783)
X(40756) = cevapoint of X(43) and X(40780)
X(40756) = X(i)-isoconjugate of X(j) for these (i,j): {87, 3795}, {330, 40733}, {2162, 27481}, {2276, 40720}, {10009, 40736}
X(40756) = barycentric quotient X(i)/X(j) for these {i,j}: {43, 27481}, {985, 40720}, {2176, 3795}, {2209, 40733}
X(40757) lies on the cubic K1177 and these lines: {985, 1002}, {4386, 37138}, {5276, 8693}, {37658, 40739}
X(40757) = isogonal conjugate of X(40784)
X(40757) = X(i)-isoconjugate of X(j) for these (i,j): {56, 27474}, {57, 3789}, {85, 40732}, {984, 5228}, {1001, 7146}, {1469, 4384}, {1471, 3661}, {2276, 40719}, {2280, 7179}, {7204, 37658}
X(40757) = trilinear product X(i)*X(j) for these {i,j}: {6, 40739}, {1002, 2344}
X(40757) = barycentric product X(i)*X(j) for these {i,j}: {1, 40739}, {2344, 27475}
X(40757) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 27474}, {55, 3789}, {985, 40719}, {1002, 7179}, {2175, 40732}, {2279, 7146}, {2344, 4384}, {40739, 75}
X(40758) lies on the cubic K1177 and these lines: {1, 20361}, {6, 3212}, {171, 8932}
X(40758) = isogonal conjugate of X(40785)
X(40758) = X(7220)-isoconjugate of X(28391)
X(40758) = barycentric product X(i)*X(j) for these {i,j}: {4334, 39924}, {18299, 21010}
X(40758) = barycentric quotient X(i)/X(j) for these {i,j}: {17754, 17760}, {21010, 17792}
X(40759) lies on the cubic K1177 and these lines: {1, 1326}, {6, 2669}, {81, 4610}
X(40759) = isogonal conjugate of X(40786)
X(40760) lies on the cubic K1177 and these lines: {5228, 16518}
X(40760) = isogonal conjugate of X(40787)
X(40760) = barycentric quotient X(i)/X(j) for these {i,j}: {17754, 27478}, {21010, 28600}
X(40761) lies on the cubic K1177 and these lines: {1, 41}, {6, 6654}, {673, 24512}
X(40761) = isogonal conjugate of X(40788)
X(40761) = trilinear product X(105)*X(39252)
X(40761) = barycentric product X(673)*X(39252)
X(40761) = barycentric quotient X(39252)/X(3912)
X(40762) lies on the cubic K1177 and these lines: {6, 190}, {727, 20985}, {8709, 16826}
X(40762) = isogonal conjugate of X(40789)
X(40763) lies on the conic {{A,B,C,X(1),X(6)}}, the cubic K1177, and these lines: {1, 257}, {6, 256}, {56, 985}, {58, 3865}, {86, 1178}, {87, 14621}, {106, 30670}, {171, 292}, {1220, 40718}, {1429, 1431}, {1916, 32115}, {3329, 17795}, {4451, 39977}, {4586, 14970}, {4835, 9277}, {7018, 25496}, {7249, 29821}
X(40763) = isogonal conjugate of X(40790)
X(40763) = cevapoint of X(1) and X(17795)
X(40763) = trilinear pole of line {649, 4164}
X(40763) = X(i)-isoconjugate of X(j) for these (i,j): {10, 40731}, {100, 3805}, {171, 984}, {172, 3661}, {385, 3862}, {869, 1909}, {894, 2276}, {1215, 3736}, {1469, 7081}, {1491, 4579}, {1580, 3864}, {1920, 40728}, {2329, 7146}, {2330, 7179}, {3250, 18047}, {3774, 8033}, {3781, 7009}, {3783, 18787}, {3799, 4367}, {3807, 20981}, {4517, 7176}, {4562, 30654}, {5386, 30656}, {7122, 33931}, {16514, 30669}, {20964, 30966}, {22061, 31909}, {30639, 34067}
X(40763) = trilinear product X(i)*X(j) for these {i,j}: {6, 40738}, {256, 985}, {257, 40746}, {513, 30670}, {870, 904}, {893, 14621}, {1178, 40718}, {1432, 2344}, {3407, 3863}, {40432, 40747}
X(40763) = barycentric product X(i)*X(j) for these {i,j}: {1, 40738}, {256, 14621}, {257, 985}, {514, 30670}, {870, 893}, {871, 7104}, {2344, 7249}, {3113, 3863}, {3407, 3865}, {3903, 4817}, {40432, 40718}
X(40763) = barycentric quotient X(i)/X(j) for these {i,j}: {256, 3661}, {257, 33931}, {649, 3805}, {694, 3864}, {812, 30639}, {825, 4579}, {870, 1920}, {893, 984}, {904, 2276}, {985, 894}, {1333, 40731}, {1431, 7146}, {1432, 7179}, {1492, 18047}, {1967, 3862}, {2344, 7081}, {3865, 3314}, {3903, 3807}, {4817, 4374}, {7104, 869}, {7116, 3781}, {14621, 1909}, {18786, 3797}, {23597, 14296}, {27805, 4505}, {30670, 190}, {40432, 30966}, {40718, 3963}, {40738, 75}
X(40764) lies on the cubic K1177 and these lines: {1, 3506}, {85, 14621}, {171, 30648}, {514, 20513}, {985, 9499}
X(40764) = isogonal conjugate of X(40791)
X(40764) = X(2276)-isoconjugate of X(40724)
X(40764) = barycentric quotient X(985)/X(40724)
X(40765) lies on the cubic K1177 and these lines: {6, 3212}, {56, 985}, {65, 4649}, {81, 279}, {85, 14621}, {171, 28391}, {221, 388}, {651, 2295}, {664, 6645}, {1442, 3721}, {6604, 20090}, {7779, 33298}, {17739, 27963}
X(40765) = isogonal conjugate of X(40792)
X(40765) = trilinear product X(i)*X(j) for these {i,j}: {6, 40723}, {56, 17739}, {57, 8424}, {85, 18759}, {604, 30660}, {1431, 27963}
X(40765) = X(i)-Ceva conjugate of X(j) for these (i,j): {7176, 56}, {40723, 8424}
X(40765) = X(i)-isoconjugate of X(j) for these (i,j): {8, 18784}, {41, 18760}, {4876, 16366}
X(40765) = barycentric product X(i)*X(j) for these {i,j}: {1, 40723}, {7, 8424}, {56, 30660}, {57, 17739}, {1432, 27963}, {5018, 39920}, {6063, 18759}
X(40765) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 18760}, {604, 18784}, {1428, 16366}, {8424, 8}, {17739, 312}, {18759, 55}, {27963, 17787}, {30660, 3596}, {40723, 75}
X(40766) lies on the cubic K1177 and these lines: {1, 18783}, {6, 291}, {171, 30648}, {1757, 27926}, {2712, 30664}, {37207, 40718}
X(40766) = isogonal conjugate of X(40793)
X(40766) = trilinear product X(i)*X(j) for these {i,j}: {6, 40740}, {5029, 37207}, {9508, 30664}
X(40766) = X(i)-isoconjugate of X(j) for these (i,j): {1929, 3783}, {2276, 40725}, {2702, 4486}, {3797, 17962}, {3802, 9505}, {6650, 16514}, {30665, 37135}
X(40766) = barycentric product X(i)*X(j) for these {i,j}: {1, 40740}, {2786, 30664}, {9508, 37207}
X(40766) = barycentric quotient X(i)/X(j) for these {i,j}: {985, 40725}, {1757, 3797}, {5029, 30665}, {9508, 4486}, {17735, 3783}, {18266, 16514}, {30664, 35148}, {40740, 75}
X(40767) lies on the cubic K1177 and these lines: {1, 1929}, {10, 1016}, {83, 11599}, {238, 39786}, {239, 27916}, {764, 1019}, {1509, 17205}, {2054, 39971}, {2111, 5091}, {2702, 12194}, {3500, 17972}, {3673, 18032}, {4649, 9505}, {6650, 14621}, {16477, 37135}, {17023, 19936}, {35148, 35172}
X(40767) = isogonal conjugate of X(40794)
X(40767) = X(1929)-Ceva conjugate of X(238)
X(40767) = X(8300)-cross conjugate of X(238)
X(40767) = crossdifference of every pair of points on line {9508, 20693}
X(40767) = X(i)-isoconjugate of X(j) for these (i,j): {291, 1757}, {292, 6542}, {295, 17927}, {334, 18266}, {335, 17735}, {660, 9508}, {741, 6541}, {813, 2786}, {1911, 20947}, {2276, 40740}, {4562, 5029}, {4589, 17990}, {8298, 30663}, {17943, 35352}, {20693, 37128}
X(40767) = trilinear product X(i)*X(j) for these {i,j}: {6, 40725}, {238, 1929}, {239, 17962}, {242, 17972}, {659, 37135}, {812, 2702}, {1914, 6650}, {2054, 33295}, {2210, 18032}, {4010, 17940}, {4366, 9506}, {4455, 17930}, {5009, 11599}, {7193, 17982}, {8300, 9505}, {8632, 35148}
X(40767) = barycentric product X(i)*X(j) for these {i,j}: {1, 40725}, {238, 6650}, {239, 1929}, {350, 17962}, {659, 35148}, {812, 37135}, {1914, 18032}, {2054, 30940}, {2702, 3766}, {4366, 9505}, {9278, 33295}, {9506, 39044}, {17930, 21832}, {17982, 20769}
X(40767) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 6542}, {239, 20947}, {659, 2786}, {985, 40740}, {1914, 1757}, {1929, 335}, {2201, 17927}, {2210, 17735}, {2238, 6541}, {2702, 660}, {3747, 20693}, {5009, 1931}, {6650, 334}, {8300, 6651}, {8632, 9508}, {9505, 40098}, {9506, 30663}, {14599, 18266}, {17930, 4639}, {17940, 4584}, {17962, 291}, {18032, 18895}, {21832, 18004}, {35148, 4583}, {37135, 4562}, {39044, 18035}, {40725, 75}
X(40768) lies on the cubic K1177 and these lines: {1, 20361}, {87, 14621}, {932, 20964}, {4649, 21759}, {15966, 17105}, {18754, 40741}
X(40768) = isogonal conjugate of X(40795)
X(40768) = X(30661)-cross conjugate of X(18754)
X(40768) = cevapoint of X(30661) and X(40741)
X(40768) = trilinear product X(i)*X(j) for these {i,j}: {6, 40741}, {87, 18754}, {2162, 30661}, {16362, 34252}
X(40768) = barycentric product X(i)*X(j) for these {i,j}: {1, 40741}, {87, 30661}, {330, 18754}, {16362, 39914}
X(40768) = barycentric quotient X(i)/X(j) for these {i,j}: {18754, 192}, {30661, 6376}, {40741, 75}
X(40769) lies on the cubic K1177 and these lines: {6, 1045}, {765, 1918}, {985, 39925}, {2107, 8298}, {2382, 16484}, {3733, 18166}
X(40769) = isogonal conjugate of X(40796)
X(40769) = X(4366)-cross conjugate of X(238)
X(40769) = trilinear product X(i)*X(j) for these {i,j}: {238, 2665}, {1914, 39925}, {2107, 33295}
X(40769) = X(i)-isoconjugate of X(j) for these (i,j): {291, 2664}, {292, 17759}, {335, 21788}, {2276, 40742}, {21897, 37128}
X(40769) = barycentric product X(i)*X(j) for these {i,j}: {238, 39925}, {239, 2665}, {2107, 30940}
X(40769) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 17759}, {985, 40742}, {1914, 2664}, {2210, 21788}, {2665, 335}, {3747, 21897}, {4366, 39028}, {5009, 2106}, {8300, 39916}, {39925, 334}
X(40770) lies on the cubics K10067 and K1177 and these lines: {1, 9431}, {6, 2669}, {171, 213}, {172, 1918}, {729, 33770}, {741, 9468}, {940, 3224}, {1509, 9427}, {2086, 6625}, {4649, 21759}, {21008, 21783}, {21755, 40432}
X(40770) = isogonal conjugate of X(1655)
X(40770) = isogonal conjugate of the anticomplement of X(274)
X(40770) = X(i)-cross conjugate of X(j) for these (i,j): {81, 6}, {904, 56}
X(40770) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1655}, {2, 1045}, {37, 39915}, {42, 34021}, {75, 21779}, {76, 18756}, {86, 21883}, {92, 23079}, {799, 9402}, {893, 27890}, {2276, 40743}
X(40770) = cevapoint of X(i) and X(j) for these (i,j): {649, 21755}, {667, 9427}
X(40770) = crosssum of X(21779) and X(23079)
X(40770) = trilinear pole of line {669, 20981}
X(40770) = barycentric product X(i)*X(j) for these {i,j}: {1, 40737}, {31, 18298}, {741, 39926}
X(40770) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 1655}, {31, 1045}, {32, 21779}, {58, 39915}, {81, 34021}, {171, 27890}, {184, 23079}, {213, 21883}, {560, 18756}, {669, 9402}, {985, 40743}, {18298, 561}, {39926, 35544}, {40737, 75}
X(40771) lies on the cubic K1177 and these lines: {1, 18784}, {6, 7061}, {171, 19554}
X(40771) = isogonal conjugate of X(40797)
X(40771) = X(i)-isoconjugate of X(j) for these (i,j): {1469, 17739}, {2276, 40723}, {7146, 8424}
X(40771) = barycentric quotient X(i)/X(j) for these {i,j}: {985, 40723}, {2344, 17739}, {18784, 7146}
X(40722) lies on the cubic K1177 and these lines: {1, 335}, {2664, 40742}
X(40772) = isogonal conjugate of X(40798)
X(40772) = trilinear product X(6)*X(40742)
X(40772) = X(i)-isoconjugate of X(j) for these (i,j): {2665, 3783}, {16514, 39925}
X(40772) = barycentric product X(1)*X(40742)
X(40772) = barycentric quotient X(i)/X(j) for these {i,j}: {2664, 3797}, {21788, 3783}, {40742, 75}
X(40773) lies on the cubic K1178 and these lines: {1, 21}, {2, 39}, {9, 27644}, {37, 86}, {55, 16876}, {75, 27164}, {99, 743}, {110, 761}, {192, 314}, {193, 941}, {213, 3219}, {239, 257}, {241, 1434}, {284, 3512}, {321, 10471}, {325, 26601}, {330, 37870}, {612, 13588}, {662, 16521}, {756, 2664}, {759, 29145}, {869, 984}, {940, 16367}, {988, 37442}, {1010, 16735}, {1014, 2285}, {1015, 29586}, {1045, 3728}, {1213, 24530}, {1214, 7176}, {1255, 39950}, {1409, 1442}, {1412, 16577}, {1444, 2303}, {1500, 6542}, {1575, 29610}, {1654, 2092}, {1778, 16972}, {1790, 3497}, {1975, 19281}, {2176, 40153}, {2185, 7305}, {2223, 3920}, {2234, 24450}, {2256, 23125}, {2275, 17397}, {2276, 3661}, {2277, 17248}, {2287, 16517}, {2667, 24437}, {2669, 31323}, {3009, 3989}, {3247, 18164}, {3286, 21010}, {3294, 33761}, {3672, 16713}, {3729, 10455}, {3752, 16815}, {3770, 27042}, {3774, 27495}, {3799, 3864}, {3802, 4475}, {3809, 4517}, {3888, 14945}, {3912, 16887}, {3995, 27163}, {4016, 18714}, {4225, 37575}, {4261, 5224}, {4277, 17346}, {4278, 30142}, {4359, 16819}, {4360, 29767}, {4374, 21347}, {4384, 4850}, {4393, 16704}, {4414, 5184}, {4419, 17139}, {4649, 20166}, {4656, 17182}, {4664, 30939}, {4687, 16709}, {4704, 17178}, {4921, 16834}, {5030, 37633}, {5069, 17381}, {5088, 24606}, {5089, 14013}, {5249, 24214}, {5256, 21384}, {5266, 37296}, {5275, 11329}, {5276, 21511}, {5277, 19308}, {5297, 35983}, {5308, 17169}, {5333, 16831}, {6385, 34022}, {6586, 16755}, {6707, 24944}, {7096, 40145}, {7146, 25429}, {7179, 31909}, {7291, 22345}, {8025, 18171}, {9331, 29605}, {11110, 16823}, {14005, 39586}, {14008, 29680}, {14009, 29639}, {14552, 20018}, {16047, 33955}, {16053, 16601}, {16054, 24617}, {16349, 16992}, {16366, 17611}, {16476, 17017}, {16552, 32911}, {16571, 17038}, {16604, 29609}, {16672, 18198}, {16673, 17207}, {16687, 23370}, {16700, 25507}, {16710, 27268}, {16742, 29630}, {16744, 29614}, {16777, 18166}, {17000, 19224}, {17011, 20963}, {17023, 24625}, {17143, 17147}, {17183, 20348}, {17196, 24441}, {17202, 17247}, {17205, 29571}, {17210, 17308}, {17212, 21348}, {17244, 33947}, {17316, 30941}, {17324, 28358}, {17326, 27633}, {17448, 29584}, {17458, 18196}, {17524, 37590}, {17776, 27248}, {18165, 20358}, {18172, 29580}, {18602, 31631}, {19310, 19758}, {19822, 19853}, {20691, 29615}, {21840, 39252}, {21858, 32025}, {22172, 25421}, {24239, 37373}, {24464, 30116}, {24557, 26669}, {24790, 26724}, {25255, 40625}, {25512, 26747}, {25660, 26979}, {25946, 37675}, {27065, 27643}, {27784, 28620}, {27785, 28619}, {28618, 31318}, {29641, 33730}, {29643, 30984}, {29766, 34064}, {32009, 39747}, {37096, 37664}, {39957, 39971}
X(40773) = isogonal conjugate of X(40747)
X(40773) = X(i)-Ceva conjugate of X(j) for these (i,j): {30966, 3786}, {40438, 40734}
X(40773) = X(i)-cross conjugate of X(j) for these (i,j): {984, 30966}, {2276, 3736}, {3250, 3799}, {7146, 31909}
X(40773) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40747}, {6, 40718}, {10, 40746}, {37, 985}, {42, 14621}, {65, 2344}, {213, 870}, {512, 4586}, {523, 825}, {649, 4613}, {661, 1492}, {669, 37133}, {789, 798}, {871, 2205}, {1577, 34069}, {2295, 40763}, {2887, 18898}, {3113, 16584}, {3125, 5384}, {3407, 3778}, {4455, 37207}, {4557, 4817}, {20964, 40738}, {21010, 25425}, {21832, 30664}
X(40773) = cevapoint of X(984) and X(2276)
X(40773) = crosspoint of X(256) and X(30571)
X(40773) = crosssum of X(i) and X(j) for these (i,j): {1, 40749}, {6, 40750}, {37, 21904}, {81, 40759}, {171, 4649}, {985, 40751}, {5228, 40765}, {14621, 40752}, {40753, 40768}, {40754, 40761}, {40755, 40762}, {40766, 40772}
X(40773) = trilinear pole of line {788, 1491}
X(40773) = crossdifference of every pair of points on line {661, 669}
X(40773) = trilinear product X(i)*X(j) for these {i,j}: {2, 3736}, {3, 31909}, {6, 30966}, {21, 7146}, {27, 3781}, {57, 3786}, {58, 3661}, {60, 16603}, {81, 984}, {86, 2276}, {99, 3250}, {100, 4481}, {110, 824}, {257, 40731}, {274, 869}, {284, 7179}, {310, 40728}, {333, 1469}, {593, 3773}, {662, 1491}, {741, 3797}, {788, 799}, {873, 3774}, {985, 4469}, {1019, 3799}, {1171, 3775}, {1333, 33931}, {1412, 3790}, {1434, 4517}, {2287, 7204}, {3094, 40415}, {3116, 38810}, {3314, 38813}, {3733, 3807}, {3783, 37128}, {3792, 24624}, {3805, 4603}, {3862, 33295}, {4122, 4556}, {4475, 4567}, {4476, 14621}, {4522, 4565}, {4584, 30665}, {4602, 8630}, {4627, 4818}, {4634, 14436}, {6385, 18900}, {16514, 18827}, {18829, 30654}, {27483, 40734}
X(40773) = barycentric product X(i)*X(j) for these {i,j}: {1, 30966}, {7, 3786}, {21, 7179}, {58, 33931}, {63, 31909}, {75, 3736}, {81, 3661}, {86, 984}, {99, 1491}, {190, 4481}, {274, 2276}, {286, 3781}, {310, 869}, {314, 1469}, {333, 7146}, {337, 17569}, {662, 824}, {670, 788}, {757, 3773}, {799, 3250}, {805, 30639}, {870, 4476}, {1014, 3790}, {1019, 3807}, {1043, 7204}, {1414, 4522}, {1576, 30870}, {2185, 16603}, {3094, 38810}, {3733, 4505}, {3775, 40438}, {3783, 18827}, {3792, 14616}, {3797, 37128}, {3799, 7192}, {3805, 4594}, {3862, 30940}, {3864, 33295}, {4469, 14621}, {4475, 4600}, {4486, 4584}, {4589, 30665}, {4609, 8630}, {4614, 4818}, {6385, 40728}, {7018, 40731}, {16514, 40017}
X(40773) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40718}, {6, 40747}, {58, 985}, {81, 14621}, {86, 870}, {99, 789}, {100, 4613}, {110, 1492}, {163, 825}, {284, 2344}, {310, 871}, {662, 4586}, {788, 512}, {799, 37133}, {824, 1577}, {869, 42}, {984, 10}, {1019, 4817}, {1178, 40763}, {1333, 40746}, {1469, 65}, {1491, 523}, {1576, 34069}, {2276, 37}, {3094, 3721}, {3116, 3778}, {3117, 16584}, {3250, 661}, {3314, 20234}, {3661, 321}, {3736, 1}, {3773, 1089}, {3774, 1500}, {3775, 4647}, {3781, 72}, {3783, 740}, {3786, 8}, {3789, 3696}, {3790, 3701}, {3792, 758}, {3795, 3993}, {3797, 3948}, {3799, 3952}, {3802, 4368}, {3805, 2533}, {3807, 4033}, {4122, 4036}, {4407, 4714}, {4439, 3992}, {4469, 3661}, {4475, 3120}, {4476, 984}, {4481, 514}, {4505, 27808}, {4517, 210}, {4522, 4086}, {4570, 5384}, {4584, 37207}, {4601, 5388}, {4818, 4815}, {7146, 226}, {7179, 1441}, {7204, 3668}, {8630, 669}, {14436, 14407}, {16514, 2238}, {16603, 6358}, {17569, 242}, {18899, 21751}, {18900, 1918}, {19584, 21101}, {25429, 17754}, {27474, 4044}, {30639, 14295}, {30665, 4010}, {30966, 75}, {31909, 92}, {33931, 313}, {38810, 3114}, {38814, 40722}, {39915, 40743}, {40415, 3113}, {40432, 40738}, {40728, 213}, {40731, 171}, {40733, 21904}, {40734, 4649}, {40736, 21759}
X(40773) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 846, 3747}, {1, 18206, 81}, {2, 1655, 3948}, {2, 18600, 16752}, {37, 16696, 86}, {37, 37596, 16826}, {38, 10458, 5208}, {81, 1931, 58}, {81, 28606, 25058}, {192, 16738, 314}, {333, 3666, 25059}, {333, 33296, 239}, {980, 5283, 2}, {984, 3736, 3786}, {1107, 3666, 239}, {3912, 16887, 30965}, {4687, 16709, 25508}, {16831, 17175, 5333}, {18169, 35623, 3794}
X(40774) lies on the cubic K1178 and these lines: {1, 672}, {2, 726}, {10, 1655}, {37, 291}, {42, 846}, {190, 40718}, {813, 40766}, {984, 2276}, {1698, 18135}, {2308, 8616}, {3773, 30966}, {3778, 25421}, {3799, 3864}, {3932, 25349}, {4368, 17261}, {5283, 12782}, {6541, 31027}, {15481, 21904}, {24690, 32846}, {32935, 37632}
X(40774) = isogonal conjugate of X(40748)
X(40774) = X(i)-Ceva conjugate of X(j) for these (i,j): {291, 3783}, {1268, 3661}, {40433, 869}
X(40774) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40748}, {985, 30571}, {4817, 28841}, {14621, 25426}, {27483, 40746}
X(40774) = trilinear product X(i)*X(j) for these {i,j}: {6, 27495}, {10, 40734}, {984, 4649}, {2276, 16826}, {3736, 3842}, {3799, 4784}, {3862, 20142}
X(40774) = barycentric product X(i)*X(j) for these {i,j}: {1, 27495}, {321, 40734}, {984, 16826}, {3661, 4649}, {3799, 28840}, {3807, 4784}, {3864, 20142}
X(40774) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40748}, {869, 25426}, {984, 27483}, {2276, 30571}, {4649, 14621}, {4784, 4817}, {16826, 870}, {27495, 75}, {40734, 81}
X(40774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 28600, 30571}, {291, 30571, 28600}, {984, 2276, 3783}, {984, 3795, 3789}, {2276, 3789, 3795}, {3789, 3795, 3783}
X(40775) lies on the cubic K1178 and these lines: {1, 2106}, {10, 1655}, {19, 15148}, {37, 1045}, {75, 34021}, {274, 18298}, {846, 18785}, {1573, 35040}, {2276, 30570}, {2665, 40737}, {9278, 24578}, {13476, 24437}, {13610, 18206}, {24342, 40742}, {25347, 25457}, {39252, 40747}
X(40775) = isogonal conjugate of X(40749)
X(40775) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40749}, {6, 40721}
X(40775) = cevapoint of X(1491) and X(2643)
X(40775) = barycentric product X(16826)*X(30570)
X(40775) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40721}, {6, 40749}, {30570, 27483}
X(40776) lies on the conic {{A,B,C,X(2),X(6)}}, the cubic K1178, and these lines: {1, 2054}, {6, 1931}, {37, 319}, {42, 846}, {81, 2248}, {1400, 1442}, {1655, 27809}, {1880, 7282}, {1989, 14616}, {4649, 40744}, {5224, 39982}, {6625, 6650}, {9281, 28606}, {24530, 39798}, {40721, 40740}
X(40776) = isogonal conjugate of X(40750)
X(40776) = X(25426)-cross conjugate of X(1002)
X(40776) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40750}, {6, 24342}, {662, 9279}, {1001, 18791}
X(40776) = cevapoint of X(i) and X(j) for these (i,j): {788, 1084}, {824, 8287}
X(40776) = trilinear pole of line {512, 9508}
X(40776) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 24342}, {6, 40750}, {512, 9279}, {2279, 18791}
X(40777) lies on the cubic K1178 and these lines: {37, 171}, {313, 1920}, {983, 5311}, {1655, 6625}
X(40777) = isogonal conjugate of X(40751)
X(40777) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40751}, {6, 40722}, {825, 21196}, {846, 985}, {1654, 40746}, {14621, 18755}, {38814, 40747}
X(40777) = trilinear product X(i)*X(j) for these {i,j}: {984, 13610}, {2248, 3661}, {2276, 6625}, {15377, 31909}, {18757, 33931}
X(40777) = barycentric product X(i)*X(j) for these {i,j}: {984, 6625}, {2248, 33931}, {3661, 13610}
X(40777) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40722}, {6, 40751}, {869, 18755}, {984, 1654}, {1491, 21196}, {2248, 985}, {2276, 846}, {3661, 17762}, {3736, 38814}, {3773, 27569}, {6625, 870}, {7146, 17084}, {13610, 14621}, {18757, 40746}
X(40778) lies on the cubic K1178 and these lines: {1, 2670}, {37, 1655}, {172, 1918}, {846, 16362}, {40728, 40731}
X(40778) = isogonal conjugate of X(40752)
X(40778) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40752}, {6, 40743}, {870, 21779}, {985, 1655}, {1045, 14621}, {39915, 40747}
X(40778) = crosssum of X(30661) and X(40721)
X(40778) = trilinear product X(i)*X(j) for these {i,j}: {2276, 40737}, {18298, 40728}
X(40778) = barycentric product X(i)*X(j) for these {i,j}: {869, 18298}, {984, 40737}, {3661, 40770}
X(40778) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40743}, {6, 40752}, {869, 1045}, {2276, 1655}, {3736, 39915}, {3774, 21883}, {18298, 871}, {18900, 18756}, {40728, 21779}, {40737, 870}, {40770, 14621}
X(40779) lies on the Feuerbach circumhyperbola, the cubic K1178, and these lines: {1, 672}, {2, 2481}, {4, 5089}, {6, 2346}, {7, 37}, {8, 1212}, {9, 2293}, {21, 220}, {45, 1156}, {55, 294}, {79, 17732}, {104, 8693}, {218, 943}, {256, 21811}, {279, 27253}, {314, 346}, {650, 885}, {941, 3779}, {1172, 7071}, {1252, 5377}, {1320, 34522}, {1621, 7123}, {1642, 14947}, {1655, 18299}, {1742, 3062}, {2276, 5222}, {2295, 17097}, {2298, 20992}, {2320, 6603}, {2344, 40757}, {2345, 2997}, {3000, 16676}, {3008, 17756}, {3161, 7155}, {3208, 3680}, {3247, 10390}, {3475, 40606}, {3691, 4866}, {4050, 31509}, {4814, 23893}, {4876, 24498}, {5134, 5561}, {5226, 21856}, {5281, 16588}, {5283, 39587}, {5435, 9444}, {5526, 15175}, {7160, 16572}, {7320, 40133}, {9330, 36197}, {9442, 9502}, {10481, 30494}, {17316, 24635}, {18166, 34820}, {24036, 36479}, {25066, 39581}, {25242, 34284}, {26242, 37597}, {27109, 27304}, {27396, 30479}, {29571, 30949}
X(40779) = isogonal conjugate of X(5228)
X(40779) = X(27475)-Ceva conjugate of X(1002)
X(40779) = X(i)-cross conjugate of X(j) for these (i,j): {4517, 8}, {6182, 100}
X(40779) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5228}, {2, 1471}, {6, 40719}, {7, 2280}, {34, 23151}, {56, 4384}, {57, 1001}, {73, 31926}, {109, 4762}, {269, 37658}, {604, 4441}, {651, 4724}, {1106, 28809}, {1397, 21615}, {1407, 3886}, {1408, 4044}, {1412, 3696}, {1790, 1893}, {4565, 4804}, {7177, 28044}
X(40779) = crosssum of X(i) and X(j) for these (i,j): {1471, 2280}, {3243, 17754}
X(40779) = trilinear pole of line {650, 926} (the line through X(650) parallel to its trilinear polar)
X(40779) = barycentric product X(i)*X(j) for these {i,j}: {8, 1002}, {9, 27475}, {312, 2279}, {522, 37138}, {650, 32041}, {984, 40739}, {3661, 40757}, {4391, 8693}
X(40779) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40719}, {6, 5228}, {8, 4441}, {9, 4384}, {31, 1471}, {41, 2280}, {55, 1001}, {200, 3886}, {210, 3696}, {219, 23151}, {220, 37658}, {312, 21615}, {346, 28809}, {650, 4762}, {663, 4724}, {1002, 7}, {1172, 31926}, {1824, 1893}, {2279, 57}, {2321, 4044}, {3689, 4702}, {4041, 4804}, {4517, 3789}, {7071, 28044}, {8693, 651}, {27475, 85}, {32041, 4554}, {32724, 32735}, {36138, 36146}, {37138, 664}, {40739, 870}, {40757, 14621}
X(40780) lies on the cubic K1178 and these lines: {1, 20332}, {2, 726}, {37, 87}, {43, 17459}, {75, 31270}, {192, 34832}, {4664, 31170}, {4704, 25284}, {8026, 31008}
X(40780) = isogonal conjugate of X(40753)
X(40780) = X(40756)-Ceva conjugate of X(43)
X(40780) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40753}, {6, 40720}, {87, 16468}, {330, 21793}, {932, 4782}, {2162, 4393}, {4785, 34071}, {7121, 30963}
X(40780) = crosssum of X(4393) and X(40720)
X(40780) = trilinear product X(i)*X(j) for these {i,j}: {2176, 27494}, {6376, 40735}, {34475, 38832}
X(40780) = barycentric product X(i)*X(j) for these {i,j}: {43, 27494}, {3661, 40756}, {6382, 40735}, {27644, 34475}
X(40780) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40720}, {6, 40753}, {43, 4393}, {192, 30963}, {2176, 16468}, {2209, 21793}, {4083, 4785}, {6376, 10009}, {20691, 3993}, {20979, 4782}, {21337, 25376}, {21834, 4806}, {27494, 6384}, {40735, 2162}, {40756, 14621}
X(40781) lies on the cubic K1178 and these lines: {1, 2115}, {2, 20940}, {55, 846}, {518, 40764}, {650, 824}, {1252, 3219}
X(40781) = isogonal conjugate of X(40754)
X(40781) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40754}, {6, 40724}, {105, 3509}, {294, 5018}, {673, 17798}, {919, 4458}, {1438, 4645}, {2481, 19554}, {18031, 18262}, {20741, 36124}
X(40781) = crosspoint of X(3512) and X(24479)
X(40781) = crosssum of X(3509) and X(19557)
X(40781) = trilinear product X(i)*X(j) for these {i,j}: {241, 7281}, {518, 3512}, {672, 7261}, {3912, 8852}, {8299, 24479}, {9454, 18036}, {17755, 30648}
X(40781) = barycentric product X(i)*X(j) for these {i,j}: {518, 7261}, {2223, 18036}, {3263, 8852}, {3512, 3912}, {3661, 40764}, {7281, 9436}, {17755, 24479}
X(40781) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40724}, {6, 40754}, {518, 4645}, {672, 3509}, {1458, 5018}, {2223, 17798}, {2254, 4458}, {3512, 673}, {3912, 17789}, {3930, 4071}, {7261, 2481}, {7281, 14942}, {8299, 1281}, {8852, 105}, {9454, 19554}, {9455, 18262}, {17755, 18037}, {20683, 20715}, {20752, 20741}, {40764, 14621}
X(40782) lies on the cubic K1178 and these lines: {1, 40736}, {37, 33680}, {1107, 4083}, {1655, 2276}
X(40782) = isogonal conjugate of X(40755)
X(40782) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40755}, {727, 19565}, {3226, 18278}, {3510, 20332}, {19567, 34077}
X(40782) = crosssum of X(18278) and X(19580)
X(40782) = trilinear product X(i)*X(j) for these {i,j}: {1575, 7168}, {17475, 24576}
X(40782) = barycentric product X(i)*X(j) for these {i,j}: {726, 7168}, {17793, 24576}, {20663, 30633}
X(40782) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40755}, {726, 19567}, {1575, 19565}, {3009, 3510}, {7168, 3226}, {17475, 19579}, {17793, 19581}, {20663, 19580}, {20777, 23186}, {21760, 18278}
X(40783) lies on the cubic K1178 and these lines: {1, 2053}, {37, 87}, {330, 1655}, {846, 2162}, {1107, 14823}, {2276, 3117}, {2319, 17592}, {4704, 7155}, {16514, 40736}, {16525, 21759}, {21793, 40753}, {27458, 32776}
X(40783) = isogonal conjugate of X(40756)
X(40783) = X(27481)-cross conjugate of X(3795)
X(40783) = crosspoint of X(87) and X(40753)
X(40783) = crosssum of X(43) and X(40780)
X(40783) = trilinear product X(i)*X(j) for these {i,j}: {87, 3795}, {330, 40733}, {2162, 27481}, {2276, 40720}, {10009, 40736}
X(40783) = barycentric product X(i)*X(j) for these {i,j}: {87, 27481}, {330, 3795}, {984, 40720}, {3661, 40753}, {6384, 40733}
X(40783) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40756}, {3795, 192}, {27481, 6376}, {40720, 870}, {40733, 43}, {40736, 40735}, {40753, 14621}
X(40784) lies on the cubic K1178 and these lines: {1, 2114}, {2, 10030}, {7, 37}, {57, 846}, {85, 1655}, {344, 26125}, {497, 3666}, {980, 3663}, {984, 1469}, {1001, 1471}, {1423, 3731}, {1429, 16484}, {1462, 8543}, {2275, 17084}, {2276, 7179}, {3674, 5283}, {4310, 37596}, {4335, 4907}, {4657, 17077}, {5701, 38186}, {5805, 24248}, {16591, 33149}, {17257, 25099}, {20367, 31394}, {20616, 30617}, {21615, 28809}, {25065, 33869}, {28091, 28093}, {37632, 39930}
X(40784) = isogonal conjugate of X(40757)
X(40784) = X(7)-Ceva conjugate of X(1469)
X(40784) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40757}, {6, 40739}, {1002, 2344}
X(40784) = trilinear product X(i)*X(j) for these {i,j}: {56, 27474}, {57, 3789}, {85, 40732}, {984, 5228}, {1001, 7146}, {1469, 4384}, {1471, 3661}, {2276, 40719}, {2280, 7179}, {7204, 37658}
X(40784) = barycentric product X(i)*X(j) for these {i,j}: {7, 3789}, {57, 27474}, {984, 40719}, {1001, 7179}, {1469, 4441}, {1471, 33931}, {3661, 5228}, {3886, 7204}, {4384, 7146}, {6063, 40732}
X(40784) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40739}, {6, 40757}, {1469, 1002}, {1471, 985}, {2280, 2344}, {3789, 8}, {5228, 14621}, {7146, 27475}, {27474, 312}, {40719, 870}, {40732, 55}
X(40785) lies on the cubic K1178 and these lines: {1, 2053}, {2, 10030}, {984, 7220}
X(40785) = isogonal conjugate of X(40758)
X(40785) = trilinear product X(7220)*X(28391)
X(40785) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40758}, {7220, 39924}, {17760, 20917}, {17792, 24349}, {18758, 21010}
X(40786) lies on the cubic K1178 and these lines: {846, 8845}, {1655, 4037}, {21085, 21883}
X(40786) = isogonal conjugate of X(40759)
X(40786) = barycentric quotient X(6)/X(40759)
X(40787) lies on the cubic K1178 and these lines: {2276, 5222}, {4817, 25425}
X(40787) = isogonal conjugate of X(40760)
X(40787) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40760}, {27478, 20917}, {28600, 24349}
X(40788) lies on the cubic K1178 and these lines: {1, 2110}, {85, 1655}, {514, 27854}, {846, 9499}, {2276, 27475}
X(40788) = isogonal conjugate of X(40761)
X(40788) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40761}, {105, 39252}
X(40788) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40761}, {672, 39252}
X(40789) lies on the cubic K1178 and these lines: {1, 2109}, {649, 38348}, {846, 2162}
X(40789) = isogonal conjugate of X(40762)
X(40789) = barycentric quotient X(6)/X(40762)
X(40790) lies on the cubic K1178 and these lines: {1, 2}, {12, 21531}, {35, 237}, {36, 14096}, {37, 256}, {38, 18208}, {55, 11328}, {86, 38810}, {87, 5749}, {171, 172}, {291, 37596}, {319, 872}, {420, 6198}, {756, 1959}, {846, 1334}, {894, 7184}, {980, 12782}, {984, 1469}, {1045, 2321}, {1215, 1237}, {1376, 21008}, {1429, 17122}, {1442, 39977}, {1478, 37190}, {1500, 3229}, {1655, 3971}, {1740, 2345}, {1964, 17289}, {2276, 3117}, {2309, 17280}, {2330, 36213}, {2344, 4386}, {2663, 3879}, {2667, 17315}, {3051, 5280}, {3061, 21332}, {3208, 17594}, {3219, 17799}, {3231, 16785}, {3250, 29955}, {3585, 14957}, {3589, 18170}, {3618, 18194}, {3736, 3773}, {3746, 37338}, {3750, 19589}, {3761, 20023}, {3765, 32931}, {3799, 3864}, {3997, 40749}, {5010, 37184}, {5299, 20965}, {5337, 11364}, {6358, 17901}, {7032, 17368}, {7229, 25570}, {7951, 37988}, {12197, 37527}, {16696, 21865}, {16706, 17445}, {17137, 33085}, {17263, 24757}, {17281, 24696}, {17592, 20284}, {18169, 33164}, {20556, 33106}, {21278, 27261}, {22277, 24437}, {25144, 28358}, {26244, 40763}, {26978, 33147}
X(40790) = isogonal conjugate of X(40763)
X(40790) = X(3862)-Ceva conjugate of X(3783)
X(40790) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40763}, {6, 40738}, {256, 985}, {257, 40746}, {513, 30670}, {870, 904}, {893, 14621}, {1178, 40718}, {1432, 2344}, {3407, 3863}, {40432, 40747}
X(40790) = crosssum of X(1) and X(17795)
X(40790) = crossdifference of every pair of points on line {649, 4164}
X(40790) = trilinear product X(i)*X(j) for these {i,j}: {10, 40731}, {100, 3805}, {171, 984}, {172, 3661}, {385, 3862}, {869, 1909}, {894, 2276}, {1215, 3736}, {1469, 7081}, {1491, 4579}, {1580, 3864}, {1920, 40728}, {2329, 7146}, {2330, 7179}, {3250, 18047}, {3774, 8033}, {3781, 7009}, {3783, 18787}, {3799, 4367}, {3807, 20981}, {4517, 7176}, {4562, 30654}, {5386, 30656}, {7122, 33931}, {16514, 30669}, {20964, 30966}, {22061, 31909}, {30639, 34067}
X(40790) = barycentric product X(i)*X(j) for these {i,j}: {171, 3661}, {172, 33931}, {190, 3805}, {321, 40731}, {385, 3864}, {813, 30639}, {824, 4579}, {869, 1920}, {894, 984}, {1469, 17787}, {1491, 18047}, {1909, 2276}, {1966, 3862}, {2295, 30966}, {2329, 7179}, {3736, 3963}, {3783, 30669}, {3786, 4032}, {3790, 7175}, {3797, 18787}, {3799, 4369}, {3807, 4367}, {4505, 20981}, {4517, 7196}, {4583, 30654}, {7081, 7146}
X(40790) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40738}, {6, 40763}, {101, 30670}, {171, 14621}, {172, 985}, {869, 893}, {894, 870}, {984, 257}, {1469, 1432}, {1920, 871}, {2276, 256}, {2295, 40718}, {2330, 2344}, {3094, 3865}, {3116, 3863}, {3661, 7018}, {3736, 40432}, {3783, 17493}, {3799, 27805}, {3805, 514}, {3862, 1581}, {3864, 1916}, {4164, 23597}, {4367, 4817}, {4579, 4586}, {7122, 40746}, {7146, 7249}, {16514, 18786}, {18047, 789}, {18900, 7104}, {20964, 40747}, {30654, 659}, {30656, 4809}, {40728, 904}, {40731, 81}
X(40790) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3507, 42}, {8, 43, 4489}, {37, 17792, 256}, {171, 2329, 1580}, {869, 3661, 3783}, {894, 7184, 7240}, {2295, 4447, 171}, {3661, 3809, 869}, {7081, 17752, 4039}
X(40791) lies on the cubic K1178 and these lines: {1, 41}, {1281, 40724}, {1655, 18760}, {2276, 7179}, {3509, 40754}
X(40791) = isogonal conjugate of X(40764)
X(40791) = trilinear product X(2276)*X(40724)
X(40791) = barycentric product X(i)*X(j) for these {i,j}: {984, 40724}, {3661, 40754}
X(40791) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40764}, {40724, 870}, {40754, 14621}
X(40792) lies on the cubic K1178 and these lines: {37, 17084}, {846, 1334}, {1655, 18760}, {2329, 40771}
X(40792) = isogonal conjugate of X(40765)
X(40792) = X(17611)-cross conjugate of X(9)
X(40792) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40765}, {6, 40723}, {56, 17739}, {57, 8424}, {85, 18759}, {604, 30660}, {1431, 27963}
X(40792) = trilinear product X(i)*X(j) for these {i,j}: {8, 18784}, {41, 18760}, {4876, 16366}
X(40792) = barycentric product X(i)*X(j) for these {i,j}: {55, 18760}, {312, 18784}, {3661, 40771}, {4518, 16366}
X(40792) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40723}, {6, 40765}, {8, 30660}, {9, 17739}, {55, 8424}, {2175, 18759}, {2329, 27963}, {7281, 39920}, {16366, 1447}, {18760, 6063}, {18784, 57}, {40771, 14621}
X(40793) lies on the cubic K1178 and these lines: {1, 2113}, {2, 846}, {37, 9505}, {238, 39786}, {1001, 17962}
X(40793) = isogonal conjugate of X(40766)
X(40793) = X(3802)-cross conjugate of X(3783)
X(40793) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40766}, {6, 40740}, {5029, 37207}, {9508, 30664}
X(40793) = trilinear product X(i)*X(j) for these {i,j}: {1929, 3783}, {2276, 40725}, {2702, 4486}, {3797, 17962}, {3802, 9505}, {6650, 16514}, {30665, 37135}
X(40793) = barycentric product X(i)*X(j) for these {i,j}: {984, 40725}, {1929, 3797}, {3661, 40767}, {3783, 6650}, {4486, 37135}, {16514, 18032}, {30665, 35148}
X(40793) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40740}, {6, 40766}, {2702, 30664}, {3783, 6542}, {3797, 20947}, {3802, 6651}, {16514, 1757}, {17569, 423}, {30665, 2786}, {37135, 37207}, {40725, 870}, {40767, 14621}
X(40794) lies on the cubic K1178 and these lines: {1, 39}, {8, 6630}, {10, 4562}, {35, 34067}, {37, 9505}, {58, 4567}, {334, 18140}, {335, 29569}, {756, 9510}, {813, 1334}, {846, 8933}, {876, 6372}, {984, 2113}, {1655, 6625}, {1909, 4583}, {3634, 40095}, {3842, 24505}, {4447, 17799}, {4517, 40730}, {4589, 6626}, {6651, 40740}, {16826, 40098}, {17316, 40217}, {17735, 40766}, {18895, 33943}, {24518, 32931}
X(40794) = isogonal conjugate of X(40767)
X(40794) = X(30663)-Ceva conjugate of X(291)
X(40794) = X(1757)-cross conjugate of X(291)
X(40794) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40767}, {6, 40725}, {238, 1929}, {239, 17962}, {242, 17972}, {659, 37135}, {812, 2702}, {1914, 6650}, {2054, 33295}, {2210, 18032}, {4010, 17940}, {4366, 9506}, {4455, 17930}, {5009, 11599}, {7193, 17982}, {8300, 9505}, {8632, 35148}
X(40794) = trilinear pole of line {9508, 20693}
X(40794) = trilinear product X(i)*X(j) for these {i,j}: {291, 1757}, {292, 6542}, {295, 17927}, {334, 18266}, {335, 17735}, {660, 9508}, {741, 6541}, {813, 2786}, {1911, 20947}, {2276, 40740}, {4562, 5029}, {4589, 17990}, {8298, 30663}, {17943, 35352}, {20693, 37128}
X(40794) = barycentric product X(i)*X(j) for these {i,j}: {291, 6542}, {292, 20947}, {334, 17735}, {335, 1757}, {660, 2786}, {984, 40740}, {3661, 40766}, {4562, 9508}, {4583, 5029}, {4584, 18004}, {4639, 17990}, {6541, 37128}, {6651, 30663}, {8298, 40098}, {18266, 18895}, {18827, 20693}
X(40794) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40725}, {6, 40767}, {291, 6650}, {292, 1929}, {335, 18032}, {660, 35148}, {813, 37135}, {1757, 239}, {1911, 17962}, {1931, 33295}, {2196, 17972}, {2786, 3766}, {4584, 17930}, {5029, 659}, {6541, 3948}, {6542, 350}, {6651, 39044}, {8298, 4366}, {9508, 812}, {17731, 30940}, {17735, 238}, {17976, 20769}, {17990, 21832}, {18266, 1914}, {18267, 18263}, {20693, 740}, {20947, 1921}, {27929, 27855}, {34067, 2702}, {38348, 4375}, {40740, 870}, {40766, 14621}
X(40794) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 22116, 291}, {292, 3864, 291}
X(40795) lies on the cubic K1178 and these lines: {846, 16360}, {1655, 3971}
X(40795) = isogonal conjugate of X(40768)
X(40795) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40768}, {6, 40741}, {87, 18754}, {2162, 30661}, {16362, 34252}
X(40795) = crosssum of X(30661) and X(40741)
X(40795) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40741}, {6, 40768}, {43, 30661}, {2176, 18754}
X(40796) lies on the cubic K1178 and these lines: {1, 2111}, {2, 38}, {42, 660}, {43, 9361}, {171, 813}, {846, 16362}, {1500, 35040}, {1621, 1911}, {2276, 18795}, {3572, 4979}, {3971, 4583}, {4589, 39915}, {21788, 40772}, {24169, 40094}, {39916, 40742}
X(40796) = isogonal conjugate of X(40769)
X(40796) = X(17759)-cross conjugate of X(291)
X(40796) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40769}, {238, 2665}, {1914, 39925}, {2107, 33295}
X(40796) = trilinear product X(i)*X(j) for these {i,j}: {291, 2664}, {292, 17759}, {335, 21788}, {2276, 40742}, {21897, 37128}
X(40796) = barycentric product X(i)*X(j) for these {i,j}: {291, 17759}, {334, 21788}, {335, 2664}, {984, 40742}, {3661, 40772}, {18827, 21897}, {30663, 39916}
X(40796) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40769}, {291, 39925}, {292, 2665}, {2106, 33295}, {2664, 239}, {2669, 30940}, {15148, 31905}, {17759, 350}, {20796, 20769}, {21788, 238}, {21897, 740}, {27854, 27855}, {39916, 39044}, {40742, 870}, {40772, 14621}
X(40796) = {X(2),X(40155)}-harmonic conjugate of X(291)
X(40797) lies on the cubic K1178 and these lines: {1, 256}, {2, 20940}, {37, 17084}, {8424, 40765}
X(40797) = isogonal conjugate of X(40771)
X(40797) = trilinear product X(i)*X(j) for these {i,j}: {1469, 17739}, {2276, 40723}, {7146, 8424}
X(40797) = barycentric product X(i)*X(j) for these {i,j}: {984, 40723}, {1469, 30660}, {3661, 40765}, {7146, 17739}, {7179, 8424}
X(40797) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40771}, {7179, 18760}, {40723, 870}, {40765, 14621}
X(40798) lies on the cubic K1178 and these lines: {1, 1655}, {2, 18795}, {846, 8934}, {1914, 40769}, {18786, 27919}
X(40798) = isogonal conjugate of X(40772)
X(40798) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40772}, {6, 40742}
X(40798) = trilinear product X(i)*X(j) for these {i,j}: {2665, 3783}, {16514, 39925}
X(40798) = barycentric product X(i)*X(j) for these {i,j}: {2665, 3797}, {3661, 40769}, {3783, 39925}
X(40798) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40742}, {6, 40772}, {3783, 17759}, {3802, 39916}, {16514, 2664}, {40769, 14621}
X(40799) lies on the cubic K1179 and these lines: {2, 6394}, {3, 232}, {6, 3964}, {32, 1092}, {39, 16391}, {83, 7736}, {95, 17907}, {184, 11672}, {237, 577}, {248, 9306}, {574, 11060}, {647, 2422}, {729, 35575}, {3224, 34870}, {5063, 32740}, {10311, 11328}, {10313, 37465}, {10314, 37338}, {10316, 19210}, {15355, 37183}, {33871, 39238}
X(40799) = isogonal conjugate of X(40814)
X(40799) = isotomic conjugate of X(40822)
X(40799) = X(33569)-cross conjugate of X(14966)
X(40799) = cevapoint of X(i) and X(j) for these (i,j): {3, 11328}, {182, 9306}
X(40799) = crosssum of X(6776) and X(7735)
X(40799) = trilinear pole of line {669, 32320}
X(40799) = crossdifference of every pair of points on line {1513, 30735}
X(40799) = X(i)-isoconjugate of X(j) for these (i,j): {2, 4008}, {75, 7735}, {92, 6776}, {158, 37188}, {304, 6620}, {662, 30735}, {1513, 1821}, {1577, 35278}
X(40799) = trilinear product X(798)*X(35575)
X(40799) = barycentric product X(512)*X(35575)
X(40799) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 4008}, {32, 7735}, {184, 6776}, {237, 1513}, {512, 30735}, {577, 37188}, {1576, 35278}, {1974, 6620}, {34396, 9755}, {35575, 670}
X(40800) lies on the cubic K1179 and these lines: {3, 3164}, {5, 13855}, {182, 14379}, {577, 1971}, {5020, 28783}, {6374, 6394}, {22341, 37694}, {36608, 38283}
X(40800) = isogonal conjugate of X(3168)
X(40800) = isotomic conjugate of the polar conjugate of X(1988)
X(40800) = X(2)-cross conjugate of X(3)
X(40800) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3168}, {19, 3164}, {92, 32445}, {158, 6638}
X(40800) = cevapoint of X(i) and X(j) for these (i,j): {3, 38283}, {6, 31382}
X(40800) = trilinear pole of line {22089, 32320}
X(40800) = barycentric product X(69)*X(1988)
X(40800) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 3164}, {6, 3168}, {184, 32445}, {577, 6638}, {1988, 4}, {14533, 26887}
X(40801) lies on the hyperbolas {{A,B,C,X(2),X(3)}} and {{A,B,C,X(4),X(25)}}, the cubic K1179, and these lines: {2, 6524}, {3, 232}, {4, 325}, {5, 14376}, {6, 2967}, {22, 97}, {24, 28724}, {25, 394}, {98, 9307}, {114, 37074}, {132, 37071}, {250, 37930}, {262, 458}, {264, 13860}, {378, 5968}, {381, 34897}, {427, 14593}, {523, 9756}, {648, 9755}, {842, 36176}, {1073, 5020}, {1214, 19544}, {1297, 15355}, {1351, 10311}, {1485, 19165}, {1593, 9737}, {1824, 3998}, {1843, 14486}, {1885, 15591}, {1995, 14919}, {2333, 3682}, {3092, 9732}, {3093, 9733}, {3172, 13335}, {3199, 30270}, {3515, 5171}, {3563, 35575}, {5094, 14356}, {5191, 11181}, {5481, 22240}, {5999, 33971}, {6644, 18876}, {6677, 15312}, {7390, 8813}, {7485, 31626}, {7866, 39604}, {8430, 14687}, {9734, 11410}, {10519, 37187}, {10607, 39803}, {11174, 37124}, {11472, 30209}, {14576, 37485}, {17907, 37450}, {23350, 35911}, {34129, 34841}, {34854, 37344}, {37581, 40152}
X(40801) = isogonal conjugate of X(6776)
X(40801) = isogonal conjugate of the anticomplement of X(1352)
X(40801) = isogonal conjugate of the complement of X(5921)
X(40801) = X(i)-cross conjugate of X(j) for these (i,j): {3148, 6}, {3288, 648}, {12294, 4}
X(40801) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6776}, {3, 4008}, {19, 37188}, {63, 7735}, {293, 1513}, {326, 6620}, {656, 35278}, {4575, 30735}
X(40801) = cevapoint of X(i) and X(j) for these (i,j): {3, 1351}, {458, 9308}, {1843, 14096}
X(40801) = trilinear pole of line {520, 2451}
X(40801) = polar conjugate of X(40814)
X(40801) = pole wrt polar circle of trilinear polar of X(40814) (line X(1513)X(30735))
X(40801) = barycentric product X(2501)*X(35575)
X(40801) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 37188}, {6, 6776}, {19, 4008}, {25, 7735}, {112, 35278}, {232, 1513}, {2207, 6620}, {2501, 30735}, {10311, 9755}, {35575, 4563}
X(40802) lies on the conic {{A,B,C,X(2),X(6)}}, the cubic 1179, and these lines: {2, 4176}, {3, 1976}, {6, 3964}, {25, 394}, {42, 611}, {69, 297}, {76, 16081}, {111, 15066}, {141, 2165}, {251, 1993}, {263, 1351}, {287, 1975}, {323, 1383}, {343, 13854}, {458, 18906}, {524, 34288}, {525, 2395}, {599, 1989}, {941, 15988}, {1583, 8576}, {1584, 8577}, {1691, 35302}, {1915, 37672}, {1994, 39955}, {2963, 3763}, {3108, 5422}, {3981, 8770}, {5017, 18898}, {5024, 11166}, {6660, 33878}, {8675, 9178}, {8749, 35910}, {8791, 37638}, {8794, 34384}, {8882, 20806}, {9605, 11175}, {10601, 39951}, {10602, 16098}, {15595, 39645}
X(40802) = isogonal conjugate of X(7735)
X(40802) = isotomic conjugate of X(40814)
X(40802) = isogonal conjugate of the anticomplement of X(7778)
X(40802) = isogonal conjugate of the complement of X(37668)
X(40802) = X(5028)-cross conjugate of X(6)
X(40802) = cevapoint of X(i) and X(j) for these (i,j): {6, 1350}, {69, 18906}, {183, 1975}
X(40802) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7735}, {6, 4008}, {19, 6776}, {63, 6620}, {163, 30735}, {661, 35278}, {1096, 37188}, {1513, 1910}, {2186, 9755}
X(40802) = trilinear pole of line {512, 684}
X(40802) = barycentric product X(523)*X(35575)
X(40802) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4008}, {3, 6776}, {6, 7735}, {25, 6620}, {110, 35278}, {182, 9755}, {394, 37188}, {511, 1513}, {523, 30735}, {1350, 7710}, {1351, 9752}, {5921, 9747}, {35575, 99}
X(40803) lies on the cubic K1179 and these lines: {262, 1007}, {263, 1351}, {327, 40330}, {1352, 23878}, {13354, 14252}, {14927, 39682}, {26714, 35387}
X(40803) = isogonal conjugate of X(9755)
X(40803) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9755}, {182, 4008}
X(40803) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 9755}, {263, 7735}, {2186, 4008}, {26714, 35278}
X(40804) lies on the cubics K12, K630, K1179, and these lines:" {3, 1625}, {5, 525}, {76, 39604}, {114, 9289}, {182, 15407}, {249, 1092}, {827, 1298}, {1972, 15595}, {6663, 36952}, {9306, 34157}, {23098, 36212}
X(40804) = isogonal conjugate of X(32545)
X(40804) = X(14941)-Ceva conjugate of X(511)
X(40804) = X(2967)-cross conjugate of X(511)
X(40804) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32545}, {98, 1955}, {401, 1910}, {1821, 1971}, {6130, 36084}
X(40804) = crossdifference of every pair of points on line {1971, 6130}
X(40804) = trilinear product X(i)*X(j) for these {i,j}: {240, 14941}, {511, 1956}, {1755, 1972}, {1959, 1987}
X(40804) = barycentric product X(i)*X(j) for these {i,j}: {297, 14941}, {325, 1987}, {511, 1972}, {1956, 1959}
X(40804) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 32545}, {237, 1971}, {297, 16089}, {511, 401}, {1755, 1955}, {1956, 1821}, {1972, 290}, {1987, 98}, {3569, 6130}, {14941, 287}
X(40804) = {X(1987),X(14941)}-harmonic conjugate of X(39683)
X(40805) lies on the cubic K1179 and these lines: {2, 6}, {3, 1625}, {20, 38297}, {39, 11793}, {154, 160}, {216, 3819}, {217, 631}, {232, 3917}, {327, 458}, {376, 3331}, {571, 1915}, {577, 1971}, {1092, 1970}, {2211, 10519}, {2979, 15355}, {3199, 15644}, {3224, 32654}, {3269, 11459}, {5063, 9225}, {5651, 10311}, {5891, 14961}, {5907, 22401}, {6090, 6786}, {7998, 22240}, {7999, 39575}, {9308, 16089}, {9418, 20885}, {9419, 22712}, {11444, 22416}, {15068, 39849}, {15905, 38283}, {28407, 34850}, {33786, 34870}
X(40805) = isogonal conjugate of X(40815)
X(40805) = crosspoint of X(34537) and X(35575)
X(40805) = crossdifference of every pair of points on line {512, 6130}
X(40805) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3289, 6}, {6, 21001, 230}, {577, 9306, 1971}, {3051, 7736, 6}
X(40806) lies on the cubic K1179 and these lines: {2, 36897}, {3, 3224}
X(40806) = isogonal conjugate of X(40816)
X(40807) lies on the cubic K1179 and these lines: {2, 6331}, {3, 3164}, {6, 194}, {877, 3552}, {5999, 33971}, {6776, 39355}, {11003, 11794}
X(40807) = isogonal conjugate of X(40817)
X(40807) = anticomplement of X(40822)
X(40807) = X(35575)-anticomplementary conjugate of X(21305)
X(40808) lies on the cubic K1179 and these lines: {2, 34208}, {182, 3224}
X(40808) = isogonal conjugate of X(40818)
X(40809) lies on the cubics X297 and K1179, and on these lines: {2, 34208}, {3, 2971}, {5, 2996}, {6, 1196}, {183, 35136}, {381, 5203}, {6340, 8797}, {11479, 14489}
X(40809) = isogonal conjugate of X(40819)
X(40809) = trilinear product X(i)*X(j) for these {i,j}: {1007, 38252}, {1351, 8769}
X(40809) = X(1707)-isoconjugate of X(7612)
X(40809) = barycentric product X(i)*X(j) for these {i,j}: {1007, 8770}, {1351, 2996}, {6391, 37174}, {10008, 14248}
X(40809) = barycentric quotient X(i)/X(j) for these {i,j}: {1351, 193}, {8770, 7612}
Let AB, AC, BC, BA, CA, CB be as in the construction of the conic described in ADGEOM #4589 (Tran Quang Hung, Randy Hutson, 5/26/2018) for P,Q = PU(1). Let A' be the intersection of the tangents to the conic at AB and AC. Define B' and C' cyclically. The lines AA', BB', CC' concur in X(40810). (Randy Hutson, January 22, 2021)
X(40810) lies on the cubics X1012 and K1179, and on these lines: {2, 36897}, {3, 3493}, {6, 694}, {69, 18829}, {114, 262}, {141, 523}, {160, 17938}, {182, 2065}, {250, 1974}, {264, 5117}, {446, 511}, {805, 842}, {1581, 7146}, {3425, 17970}, {3613, 6665}, {3818, 38947}, {5968, 6786}, {9307, 15595}, {9513, 39291}, {14970, 17500}
X(40810) = isogonal conjugate of X(40820)
X(40810) = isotomic conjugate of X(14382)
X(40810) = isotomic conjugate of the isogonal conjugate of X(14251)
X(40810) = X(699)-complementary conjugate of X(16609)
X(40810) = X(694)-Ceva conjugate of X(511)
X(40810) = X(i)-cross conjugate of X(j) for these (i,j): {684, 18829}, {2679, 3569}, {36790, 511}
X(40810) = X(i)-isoconjugate of X(j) for these (i,j): {31, 14382}, {98, 1580}, {290, 1933}, {293, 419}, {385, 1910}, {804, 36084}, {1691, 1821}, {1926, 14601}, {1966, 1976}, {5027, 36036}, {24284, 36104}
X(40810) = cevapoint of X(2679) and X(3569)
X(40810) = crosssum of X(i) and X(j) for these (i,j): {6, 32540}, {385, 4027}
X(40810) = crossdifference of every pair of points on line {804, 1691}
X(40810) = trilinear product X(i)*X(j) for these {i,j}: {75, 14251}, {237, 1934}, {240, 36214}, {325, 1967}, {511, 1581}, {694, 1959}, {1755, 1916}, {3569, 37134}, {9417, 18896}, {17970, 40703}, {23996, 36897}
X(40810) = barycentric product X(i)*X(j) for these {i,j}: {76, 14251}, {232, 40708}, {237, 18896}, {297, 36214}, {325, 694}, {511, 1916}, {805, 2799}, {882, 2396}, {1581, 1959}, {1755, 1934}, {3569, 18829}, {6393, 17980}, {32458, 34238}, {36790, 36897}
X(40810) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 14382}, {232, 419}, {237, 1691}, {297, 17984}, {325, 3978}, {511, 385}, {684, 24284}, {694, 98}, {805, 2966}, {881, 2422}, {882, 2395}, {1581, 1821}, {1755, 1580}, {1916, 290}, {1959, 1966}, {1967, 1910}, {2396, 880}, {2421, 17941}, {2491, 5027}, {2679, 35078}, {2799, 14295}, {2967, 39931}, {3569, 804}, {8789, 14601}, {9155, 5026}, {9417, 1933}, {9418, 14602}, {9468, 1976}, {11672, 36213}, {14251, 6}, {17938, 2715}, {17970, 248}, {17980, 6531}, {18872, 5967}, {18896, 18024}, {36212, 12215}, {36213, 4027}, {36214, 287}, {36790, 5976}, {36897, 34536}, {37134, 36036}, {39092, 39941}
X(40811) lies on the cubic K1179 and these lines: {2, 4176}, {3, 9292}, {695, 5013}, {699, 35575}, {3224, 34870}
X(40811) = isogonal conjugate of X(40821)
X(40811) = X(i)-isoconjugate of X(j) for these (i,j): {3223, 7735}, {3224, 4008}
X(40811) = barycentric product X(23301)*X(35575)
X(40811) = barycentric quotient X(i)/X(j) for these {i,j}: {1613, 7735}, {1740, 4008}, {11325, 6620}, {20794, 6776}, {23301, 30735}, {35575, 3222}
X(40812) lies on the cubic K1179 and these lines: {6, 2987}, {3148, 3563}, {9306, 34157}, {14253, 36212}
X(40813) lies on the cubic K1179 and these lines: {2, 34403}, {3, 64}, {6, 15394}, {141, 253}, {459, 18840}, {1352, 5922}, {3343, 17825}, {31942, 33537}
X(40813) = X(610)-isoconjugate of X(3424)
X(40813) = barycentric product X(i)*X(j) for these {i,j}: {64, 37668}, {253, 1350}, {10002, 15394}, {19611, 23052}
X(40813) = barycentric quotient X(i)/X(j) for these {i,j}: {64, 3424}, {1350, 20}, {10002, 14249}, {23052, 1895}, {37668, 14615}
Let A'B'C' be the Artzt triangle. Let A" be the perspector of conic {{A,B,C,B',C'}}, and define B" and C" cyclically. The lines AA", BB", CC" concur in X(40814). (Randy Hutson, January 22, 2021)
X(40814) lies on the cubic K790 and these lines: {2, 39}, {4, 51}, {6, 264}, {22, 12203}, {25, 39646}, {32, 401}, {83, 5392}, {94, 598}, {98, 3148}, {125, 5117}, {184, 419}, {193, 14615}, {237, 11257}, {262, 37988}, {297, 3981}, {311, 3618}, {315, 6515}, {316, 37644}, {327, 3815}, {343, 6656}, {394, 7754}, {441, 5305}, {460, 11245}, {511, 37190}, {578, 37124}, {671, 34289}, {800, 3164}, {1232, 3619}, {1235, 11427}, {1236, 37645}, {1249, 21447}, {1316, 14265}, {1975, 37344}, {1992, 3260}, {1993, 7760}, {1994, 7894}, {1995, 38664}, {2782, 11328}, {2996, 37874}, {3053, 35941}, {3060, 14957}, {3095, 21531}, {3096, 37636}, {3186, 6467}, {3580, 7790}, {3596, 26665}, {3673, 26001}, {3710, 4385}, {3917, 12251}, {4027, 33336}, {4054, 25935}, {5013, 37067}, {5222, 34387}, {5304, 30737}, {5749, 34388}, {5943, 6248}, {6376, 25007}, {6620, 6776}, {6660, 14880}, {7388, 11090}, {7389, 11091}, {7735, 37188}, {7770, 10601}, {7782, 35296}, {7850, 37779}, {7878, 34545}, {8573, 20477}, {9747, 9755}, {9786, 37200}, {10063, 40790}, {10349, 33301}, {11188, 25051}, {11331, 26958}, {11333, 35275}, {11438, 35474}, {13335, 35926}, {14096, 22712}, {15988, 34283}, {17862, 26531}, {18033, 26016}, {19768, 25875}, {26913, 33314}, {37778, 40138}
X(40814) = isogonal conjugate of X(40799)
X(40814) = isotomic conjugate of X(40802)
X(40814) = polar conjugate of X(40801)
X(40814) = pole wrt polar circle of trilinear polar of X(40801) (line X(520)X(2451))
X(40814) = isotomic conjugate of the isogonal conjugate of X(7735)
X(40814) = polar conjugate of the isogonal conjugate of X(6776)
X(40814) = X(264)-Ceva conjugate of X(9747)
X(40814) = X(798)-isoconjugate of X(35575)
X(40814) = cevapoint of X(6776) and X(7735)
X(40814) = crosspoint of X(i) and X(j) for these (i,j): {4, 19222}, {262, 9307}
X(40814) = crosssum of X(i) and X(j) for these (i,j): {3, 11328}, {182, 9306}
X(40814) = trilinear pole of line {1513, 30735}
X(40814) = crossdifference of every pair of points on line {669, 32320}
X(40814) = trilinear product X(i)*X(j) for these {i,j}: {2, 4008}, {75, 7735}, {92, 6776}, {158, 37188}, {304, 6620}, {662, 30735}, {1513, 1821}, {1577, 35278}
X(40814) = barycentric product X(i)*X(j) for these {i,j}: {75, 4008}, {76, 7735}, {99, 30735}, {264, 6776}, {290, 1513}, {305, 6620}, {327, 9755}, {850, 35278}, {2052, 37188}
X(40814) = barycentric quotient X(i)/X(j) for these {i,j}: {99, 35575}, {1513, 511}, {4008, 1}, {6620, 25}, {6776, 3}, {7710, 1350}, {7735, 6}, {9747, 5921}, {9752, 1351}, {9755, 182}, {30735, 523}, {35278, 110}, {37188, 394}
X(40814) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 194, 36212}, {4, 3168, 34854}, {76, 3978, 305}, {237, 39906, 11257}, {5254, 13567, 297}, {6392, 26164, 76}
X(40815) lies on the conic {{A,B,C,X(2)X(6)}}, the cubic K790, and these lines: {6, 401}, {25, 3168}, {194, 2987}, {263, 6776}, {1976, 32545}
X(40815) = isogonal conjugate of X(40805)
X(40815) = trilinear pole of line {512, 6130}
X(40816) lies on the cubic K790 and this line: {194, 36213}
X(40816) = isogonal conjugate of X(40806)
X(40817) lies on the cubic K790 and these lines: {194, 3289}, {1613, 6638}, {2211, 3168}, {9418, 11325}
X(40817) = isogonal conjugate of X(40807)
X(40818) lies on the cubic K790 and this line: {194, 3167}
X(40818) = isogonal conjugate of X(40808)
X(40819) lies on the cubics K295 and K790, and on these lines: {2, 3167}, {6, 34208}
X(40819) = isogonal conjugate of X(40809)
X(40819) = X(i)-isoconjugate of X(j) for these (i,j): {1007, 38252}, {1351, 8769}
X(40819) = trilinear product X(1707)*X(7612)
X(40819) = barycentric product X(193)*X(7612)
X(40819) = barycentric quotient X(i)/X(j) for these {i,j}: {193, 1007}, {3053, 1351}, {6337, 10008}, {6353, 37174}, {7612, 2996}
X(40820) lies on the cubics K693, K79, and K1013, and on these lines: {2, 98}, {6, 36897}, {25, 685}, {32, 8870}, {51, 13137}, {248, 19222}, {251, 2395}, {262, 2065}, {290, 3114}, {305, 31614}, {419, 14602}, {1215, 39043}, {1316, 14265}, {1403, 36065}, {1501, 2715}, {1580, 16609}, {1910, 2344}, {2966, 14614}, {3117, 15391}, {3167, 17932}, {3407, 34238}, {3978, 14382}, {5286, 8861}, {5306, 34369}, {5943, 15630}, {7735, 36899}, {8623, 20026}, {11328, 32540}, {35906, 36874}
X(40820) = isogonal conjugate of X(40810)
X(40820) = isogonal conjugate of the isotomic conjugate of X(14382)
X(40820) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 32545}, {685, 5027}
X(40820) = X(i)-cross conjugate of X(j) for these (i,j): {6, 32544}, {385, 98}, {12829, 385}
X(40820) = X(i)-isoconjugate of X(j) for these (i,j): {75, 14251}, {237, 1934}, {240, 36214}, {325, 1967}, {511, 1581}, {694, 1959}, {1755, 1916}, {3569, 37134}, {9417, 18896}, {17970, 40703}, {23996, 36897}
X(40820) = cevapoint of X(i) and X(j) for these (i,j): {6, 32540}, {385, 4027}
X(40820) = crosspoint of X(6) and X(32542)
X(40820) = crosssum of X(2679) and X(3569)
X(40820) = trilinear pole of line {804, 1691}
X(40820) = trilinear product X(i)*X(j) for these {i,j}: {31, 14382}, {98, 1580}, {290, 1933}, {293, 419}, {385, 1910}, {804, 36084}, {1691, 1821}, {1926, 14601}, {1966, 1976}, {5027, 36036}, {24284, 36104}
X(40820) = barycentric product X(i)*X(j) for these {i,j}: {6, 14382}, {98, 385}, {248, 17984}, {287, 419}, {290, 1691}, {685, 24284}, {804, 2966}, {880, 2422}, {1580, 1821}, {1910, 1966}, {1976, 3978}, {2395, 17941}, {2715, 14295}, {4027, 36897}, {5026, 9154}, {6531, 12215}, {12829, 40428}, {14601, 14603}, {14602, 18024}, {34536, 36213}
X(40820) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 14251}, {98, 1916}, {248, 36214}, {287, 40708}, {290, 18896}, {385, 325}, {419, 297}, {804, 2799}, {1580, 1959}, {1691, 511}, {1821, 1934}, {1910, 1581}, {1933, 1755}, {1976, 694}, {2422, 882}, {2715, 805}, {2966, 18829}, {4027, 5976}, {5027, 3569}, {5976, 32458}, {12215, 6393}, {12829, 114}, {14382, 76}, {14600, 17970}, {14601, 9468}, {14602, 237}, {17941, 2396}, {18902, 9418}, {24284, 6333}, {36084, 37134}, {36213, 36790}
X(40820) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5967, 34761, 14355}, {34396, 34536, 32545}
X(40820) =
X(40821) lies on the cubic K790 and these lines: {6, 194}, {3504, 5020}
X(40821) = isogonal conjugate of X(40811)
X(40821) = trilinear product X(i)*X(j) for these {i,j}: {3223, 7735}, {3224, 4008}
X(40821) = barycentric product X(i)*X(j) for these {i,j}: {2998, 7735}, {3223, 4008}
X(40821) = barycentric quotient X(i)/X(j) for these {i,j}: {4008, 17149}, {6620, 3186}, {7735, 194}
X(40822) lies on these lines: {2, 6331}, {3, 17984}, {5, 264}, {76, 141}, {182, 14382}, {276, 14376}, {290, 1352}, {308, 2165}, {327, 24206}, {7876, 26166}, {13862, 30737}, {16089, 33971}
X(40822) = isogonal conjugate of X(40823)
X(40822) = isotomic conjugate of X(40799)
X(40822) = complement of X(40807)
X(40822) = X(1924)-isoconjugate of X(35575)
X(40822) = barycentric product X(i)*X(j) for these {i,j}: {561, 4008}, {670, 30735}, {1502, 7735}, {1513, 18024}, {6620, 40050}, {6776, 18022}, {18027, 37188}
X(40822) = barycentric quotient X(i)/X(j) for these {i,j}: {670, 35575}, {1513, 237}, {4008, 31}, {6620, 1974}, {6776, 184}, {7735, 32}, {9755, 34396}, {30735, 512}, {35278, 1576}, {37188, 577}
X(40822) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 6374, 6393}, {1502, 14603, 40050}
X(40823) lies on these lines: {6, 2967}, {32, 1092}, {54, 8743}, {184, 2211}, {251, 1993}, {699, 35575}, {1501, 23606}, {3407, 7774}, {9418, 14585}, {9419, 14575}
X(40823) = isogonal conjugate of X(40822)
X(40823) = trilinear product X(1924)*X(35575)
X(40823) = X(i)-isoconjugate of X(j) for these (i,j): {76, 4008}, {561, 7735}, {799, 30735}, {1969, 6776}, {6620, 40364}, {20948, 35278}
X(40823) = barycentric product X(669)*X(35575)
X(40823) = barycentric quotient X(i)/X(j) for these {i,j}: {560, 4008}, {669, 30735}, {1501, 7735}, {9418, 1513}, {14574, 35278}, {14575, 6776}, {14585, 37188}, {35575, 4609}
X(40824) lies on the Kiepert circumhyperbola and these lines: {2, 4176}, {4, 325}, {69, 98}, {76, 14064}, {83, 7736}, {94, 9464}, {99, 7710}, {183, 7612}, {262, 1007}, {275, 34254}, {305, 2052}, {384, 5395}, {598, 7799}, {599, 11172}, {631, 3406}, {671, 16041}, {2996, 5025}, {3090, 3399}, {3266, 34289}, {3407, 7774}, {3424, 5921}, {5207, 14458}, {5392, 8024}, {5466, 30474}, {5485, 32836}, {5989, 39874}, {6337, 9744}, {7607, 34229}, {7608, 34803}, {7868, 18840}, {7892, 32835}, {7897, 11606}, {7901, 32834}, {8781, 37690}, {8889, 37892}, {10153, 23055}, {10155, 37647}, {10159, 32832}, {11163, 14039}, {11167, 21356}, {11174, 14069}, {13862, 14484}, {14035, 18845}, {14046, 32869}, {14047, 32870}, {14063, 32840}, {14067, 32871}, {16277, 40123}, {18844, 32876}, {32532, 32896}, {32838, 32953}, {32839, 32952}, {32879, 32996}, {32880, 33287}, {32970, 39095}
X(40824) = isogonal conjugate of X(40825)
X(40824) = isotomic conjugate of X(7735)
X(40824) = polar conjugate of X(6620)
X(40824) = isotomic conjugate of the anticomplement of X(7778)
X(40824) = isotomic conjugate of the complement of X(37668)
X(40824) = X(7778)-cross conjugate of X(2)
X(40824) = cevapoint of X(i) and X(j) for these (i,j): {2, 37668}, {3926, 10008}
X(40824) = trilinear pole of line {523, 4143}
X(40824) = X(i)-isoconjugate of X(j) for these (i,j): {31, 7735}, {32, 4008}, {48, 6620}, {798, 35278}, {1973, 6776}, {3402, 9755}
X(40824) = trilinear product X(1577)*X(35575)
X(40824) = barycentric product X(850)*X(35575)
X(40824) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 7735}, {4, 6620}, {69, 6776}, {75, 4008}, {99, 35278}, {183, 9755}, {325, 1513}, {850, 30735}, {1007, 9752}, {3926, 37188}, {35575, 110}, {37668, 7710}
X(40825) lies on these lines: {3, 6}, {25, 1501}, {69, 7807}, {81, 21485}, {115, 36990}, {141, 32954}, {154, 1196}, {172, 611}, {184, 1184}, {193, 6393}, {217, 19125}, {230, 1352}, {251, 5422}, {385, 39141}, {524, 11288}, {597, 11287}, {613, 1914}, {1003, 18906}, {1194, 3796}, {1285, 22521}, {1353, 37459}, {1386, 1572}, {1428, 16502}, {1503, 3767}, {1513, 6776}, {1569, 36784}, {1611, 9306}, {1613, 3167}, {1627, 1993}, {1899, 22135}, {1915, 5020}, {1971, 34809}, {1974, 2207}, {1992, 35297}, {2211, 3172}, {2548, 3589}, {2715, 5941}, {2916, 9700}, {3051, 11402}, {3231, 6090}, {3291, 35259}, {3506, 8780}, {3564, 37466}, {3618, 6656}, {3763, 7749}, {3787, 37672}, {3818, 13881}, {3830, 6034}, {3981, 9909}, {5012, 5359}, {5026, 22253}, {5182, 5976}, {5207, 7887}, {5286, 25406}, {5304, 37182}, {5306, 11179}, {5354, 11003}, {5480, 7737}, {5622, 38641}, {5921, 37689}, {6531, 33971}, {6800, 9465}, {6811, 39875}, {6813, 39876}, {7083, 14599}, {7485, 34945}, {7736, 37450}, {7745, 14561}, {7746, 10516}, {7754, 12215}, {8363, 31404}, {8667, 14994}, {8743, 19128}, {9300, 38064}, {10312, 39588}, {11286, 24256}, {11360, 16285}, {11898, 15993}, {12177, 12829}, {13860, 39095}, {13910, 31411}, {14537, 38072}, {14567, 26864}, {14585, 19459}, {14605, 15303}, {14901, 16010}, {17349, 21993}, {18583, 18907}, {19153, 21177}, {24206, 37637}, {32738, 32740}, {35302, 36790}, {36696, 38651}, {38642, 39656}
X(40825) = midpoint of X(6) and X(3053)
X(40825) = isogonal conjugate of X(40824)
X(40825) = isogonal conjugate of the isotomic conjugate of X(7735)
X(40825) = isogonal conjugate of the polar conjugate of X(6620)
X(40825) = X(1577)-isoconjugate of X(35575)
X(40825) = crosspoint of X(6620) and X(7735)
X(40825) = crosssum of X(i) and X(j) for these (i,j): {2, 37668}, {3926, 10008}
X(40825) = crossdifference of every pair of points on line {523, 4143}
X(40825) = trilinear product X(i)*X(j) for these {i,j}: {31, 7735}, {32, 4008}, {48, 6620}, {798, 35278}, {1973, 6776}, {3402, 9755}
X(40825) = barycentric product X(i)*X(j) for these {i,j}: {3, 6620}, {6, 7735}, {25, 6776}, {31, 4008}, {263, 9755}, {512, 35278}, {1513, 1976}, {1576, 30735}, {2207, 37188}
X(40825) = barycentric quotient X(i)/X(j) for these {i,j}: {1576, 35575}, {4008, 561}, {6620, 264}, {6776, 305}, {7735, 76}, {9755, 20023}, {35278, 670}
X(40825) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1350, 5028}, {6, 1384, 11173}, {6, 1691, 3}, {6, 5017, 1351}, {6, 5085, 39}, {6, 11477, 1570}, {6, 13330, 5093}, {6, 31884, 10542}, {32, 1692, 6}, {32, 39764, 5052}, {39, 5033, 5085}, {187, 5028, 1350}, {193, 16925, 6393}, {575, 5039, 6}, {1342, 1343, 13356}, {1351, 1384, 5017}, {1351, 5017, 11173}, {1687, 1688, 13355}, {1692, 5052, 39764}, {2021, 5052, 3094}, {2024, 35432, 3095}, {3172, 19118, 2211}, {5007, 5034, 6}, {5050, 30435, 6}, {5052, 39764, 6}, {5058, 5062, 7772}, {6423, 6424, 3}, {12050, 12051, 32}, {19145, 19146, 3}
X(40826) lies on these lines: {2, 18023}, {76, 524}, {264, 468}, {290, 5967}, {308, 1383}, {313, 4062}, {327, 3260}, {599, 8785}, {892, 8542}, {1502, 3266}, {2367, 11636}, {3734, 4590}, {5486, 11185}, {7771, 11594}, {7835, 36953}, {14295, 34763}, {18027, 37778}, {20573, 40822}
X(40826) = isotomic conjugate of X(574)
X(40826) = polar conjugate of X(8541)
X(40826) = isotomic conjugate of the complement of X(11185)
X(40826) = isotomic conjugate of the isogonal conjugate of X(598)
X(40826) = anticomplement of crosspoint of X(2) and X(574)
X(40826) = anticomplement of crosssum of X(6) and X(598)
X(40826) = X(i)-cross conjugate of X(j) for these (i,j): {23297, 598}, {26235, 76}
X(40826) = X(i)-isoconjugate of X(j) for these (i,j): {31, 574}, {32, 36263}, {48, 8541}, {163, 17414}, {560, 599}, {798, 9145}, {1917, 9464}, {1919, 3908}, {1923, 10130}, {1924, 9146}, {5094, 9247}, {8288, 23995}
X(40826) = cevapoint of X(i) and X(j) for these (i,j): {2, 11185}, {76, 11059}
X(40826) = trilinear pole of line {690, 850}
X(40826) = barycentric product X(i)*X(j) for these {i,j}: {76, 598}, {308, 23297}, {316, 10512}, {670, 8599}, {850, 35138}, {1383, 1502}, {3266, 18818}, {10511, 40074}, {30489, 40016}
X(40826) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 574}, {4, 8541}, {75, 36263}, {76, 599}, {99, 9145}, {264, 5094}, {308, 10130}, {316, 10510}, {338, 8288}, {523, 17414}, {598, 6}, {668, 3908}, {670, 9146}, {850, 3906}, {892, 32583}, {1236, 19510}, {1383, 32}, {1502, 9464}, {3260, 13857}, {3264, 4141}, {3266, 39785}, {8599, 512}, {8785, 8586}, {10511, 3455}, {10512, 67}, {11054, 9872}, {11059, 11165}, {11185, 8542}, {11636, 1576}, {18818, 111}, {20380, 39689}, {23287, 351}, {23297, 39}, {26235, 15810}, {30489, 3051}, {30491, 3049}, {35138, 110}
X(40827) lies on these lines: {65, 314}, {76, 940}, {86, 313}, {264, 4185}, {274, 1920}, {290, 1798}, {308, 1169}, {310, 349}, {670, 20911}, {1502, 34284}, {2368, 8707}, {5209, 37607}, {18896, 40017}, {19701, 30022}, {30940, 40409}
X(40827) = isotomic conjugate of X(2092)
X(40827) = isotomic conjugate of the complement of X(314)
X(40827) = isotomic conjugate of the isogonal conjugate of X(14534)
X(40827) = X(i)-cross conjugate of X(j) for these (i,j): {2, 31643}, {693, 670}, {17496, 99}, {37759, 14616}
X(40827) = X(i)-isoconjugate of X(j) for these (i,j): {6, 3725}, {31, 2092}, {32, 2292}, {42, 2300}, {213, 1193}, {228, 2354}, {429, 9247}, {560, 1211}, {669, 3882}, {872, 40153}, {1228, 1917}, {1397, 21033}, {1400, 20967}, {1402, 2269}, {1501, 18697}, {1829, 2200}, {1918, 3666}, {1923, 27067}, {1973, 22076}, {2205, 4357}, {2206, 21810}, {2333, 22345}
X(40827) = cevapoint of X(i) and X(j) for these (i,j): {2, 314}, {75, 27792}, {76, 274}, {86, 14829}, {1240, 30710}
X(40827) = trilinear pole of line {850, 4374}
X(40827) = barycentric product X(i)*X(j) for these {i,j}: {76, 14534}, {86, 1240}, {274, 30710}, {310, 1220}, {314, 31643}, {561, 2363}, {670, 4581}, {961, 40072}, {1169, 1502}, {1798, 18022}, {2298, 6385}, {6331, 15420}
X(40827) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3725}, {2, 2092}, {21, 20967}, {27, 2354}, {69, 22076}, {75, 2292}, {76, 1211}, {81, 2300}, {86, 1193}, {261, 4267}, {264, 429}, {274, 3666}, {286, 1829}, {308, 27067}, {310, 4357}, {312, 21033}, {313, 20653}, {314, 960}, {321, 21810}, {333, 2269}, {561, 18697}, {799, 3882}, {961, 1402}, {1169, 32}, {1220, 42}, {1240, 10}, {1444, 22345}, {1502, 1228}, {1509, 40153}, {1791, 228}, {1798, 184}, {1812, 22074}, {1920, 27697}, {2298, 213}, {2359, 2200}, {2363, 31}, {3261, 21124}, {3596, 3704}, {4581, 512}, {6385, 20911}, {6648, 4559}, {7192, 6371}, {8033, 28369}, {8707, 4557}, {14534, 6}, {14624, 1500}, {15420, 647}, {17206, 22097}, {18155, 17420}, {18697, 6042}, {28660, 3687}, {30710, 37}, {31643, 65}, {40452, 3185}
X(40828) lies on these lines: {12, 3596}, {76, 1211}, {264, 429}, {290, 34259}, {308, 941}, {313, 20653}, {349, 561}, {931, 2367}, {1228, 1502}, {4417, 28660}, {5224, 34265}, {5331, 37678}, {5718, 30022}, {6376, 31359}, {18140, 37870}, {18152, 40011}, {27801, 40363}
X(40828) = isotomic conjugate of X(5019)
X(40828) = isotomic conjugate of the isogonal conjugate of X(34258)
X(40828) = X(i)-isoconjugate of X(j) for these (i,j): {31, 5019}, {32, 1468}, {163, 8639}, {560, 940}, {1397, 2268}, {1501, 10436}, {1917, 34284}, {4185, 9247}, {5307, 14575}
X(40828) = cevapoint of X(4417) and X(5224)
X(40828) = barycentric product X(i)*X(j) for these {i,j}: {76, 34258}, {561, 31359}, {941, 1502}, {959, 40363}, {1928, 2258}, {18022, 34259}, {27801, 37870}
X(40828) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 5019}, {75, 1468}, {76, 940}, {264, 4185}, {312, 2268}, {523, 8639}, {561, 10436}, {850, 8672}, {931, 1576}, {941, 32}, {959, 1397}, {1502, 34284}, {1969, 5307}, {2258, 560}, {3596, 958}, {5224, 34281}, {5331, 2206}, {27801, 31993}, {28659, 11679}, {31359, 31}, {32038, 1415}, {34258, 6}, {34259, 184}, {35519, 17418}, {37870, 1333}
X(40829) lies on these lines: on lines {5094, 7788}, {11057, 11058}, {19601, 35138}
X(40829) = isotomic conjugate of X(14537)
X(40829) = isotomic conjugate of the anticomplement of X(40344)
X(40829) = isotomic conjugate of the complement of X(11057)
X(40829) = X(40344)-cross conjugate of X(2)
X(40829) = X(31)-isoconjugate of X(14537)
X(40829) = cevapoint of X(2) and X(11057)
X(40829) = trilinear pole of line {3906, 7799}
X(40829) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 14537}, {11057, 19601}
X(40830) lies on these lines: {64, 14615}, {76, 801}, {264, 1105}, {308, 26166}, {1502, 32830}, {3926, 18027}
X(40830) = isotomic conjugate of X(800)
X(40830) = isotomic conjugate of the complement of X(14615)
X(40830) = isotomic conjugate of the isogonal conjugate of X(801)
X(40830) = X(3265)-cross conjugate of X(670)
X(40830) = X(i)-isoconjugate of X(j) for these (i,j): {31, 800}, {32, 774}, {185, 1973}, {235, 9247}, {560, 13567}, {798, 1624}, {820, 2207}, {1501, 17858}, {1918, 18603}, {1974, 6508}, {2179, 16035}
X(40830) = cevapoint of X(i) and X(j) for these (i,j): {2, 14615}, {76, 39