X₁₀₀

ANTICOMPLEMENT OF FEUERBACH POINT

X₁₀₀ is the anticomplement of Feuerbach point.

5, 6, 7 3, 4, 5 Kepler Kimberling

X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Anticomplementary Triangle △K_aK_bK_c — vertices K_a, K_b, K_c (Formed by lines through A, B, C parallel to opposite sides)

• Central Lines: {2, 11}

• Related Centers: X₂ (CENTROID), X₁₁ (FEUERBACH POINT)

Trilinears: \(1/(b - c) : :\)

Barycentrics: \(a (a - b) \cdot (a - c) : :\)

Tripolars: \(|b - c| : :\)

Search Value (6, 9, 13): \(2.601836134976\)

▸ Alternate Coordinates2 forms

• Trilinears: \((a - b)(a - c) : :\)

• Barycentrics: \(a/(b - c) : :\)

▸ Linear Combinations1 combination

• X₁₀₀ = \(2R\) X₁ - \(3R\) X₂ + \(2r\) X₃, \(3\) X₁ - X₁₂₆₅₃, X₁ - \(3\) X₁₅₀₁₅, \(4\) X₂₁₄ - X₁₃₂₀, \(2\) X₂₁₄ + X₅₅₄₁, \(6\) X₂₁₄ - X₁₂₆₅₃, \(2\) X₂₁₄ - \(3\) X₁₅₀₁₅, \(2\) X₁₀₅₄ - \(3\) X₁₄₁₉₃, X₁₃₂₀ + \(2\) X₅₅₄₁, \(3\) X₁₃₂₀ - \(2\) X₁₂₆₅₃, X₁₃₂₀ - \(6\) X₁₅₀₁₅, \(3\) X₅₅₄₁ + X₁₂₆₅₃, X₅₅₄₁ + \(3\) X₁₅₀₁₅, \(3\) X₁₀₀₈₇ - \(2\) X₂₅₄₃₉, X₁₂₆₅₃ - \(9\) X₁₅₀₁₅, \(3\) X₁₃₂₇₈ - \(4\) X₂₅₄₃₉, X₁₃₂₇₉ - \(4\) X₂₅₄₄₀, \(3\) X₂ - \(4\) X₃₀₃₅, \(3\) X₂ + \(2\) X₆₁₅₄, \(9\) X₂ - \(8\) X₆₆₆₇, \(3\) X₂ + X₂₀₀₉₅, \(9\) X₂ - \(10\) X₃₁₂₃₅, \(6\) X₂ - \(5\) X₃₁₂₇₂, \(3\) X₂ - \(8\) X₃₅₀₂₃, \(5\) X₂ - \(4\) X₄₅₃₁₀, X₁₁ - \(3\) X₆₁₇₄, \(3\) X₁₁ - \(4\) X₆₆₆₇, \(4\) X₁₁ - \(3\) X₁₀₇₀₇, \(2\) X₁₁ + X₂₀₀₉₅, \(3\) X₁₁ - \(5\) X₃₁₂₃₅, \(4\) X₁₁ - \(5\) X₃₁₂₇₂, X₁₁ - \(4\) X₃₅₀₂₃, \(5\) X₁₁ - \(6\) X₄₅₃₁₀, X₁₄₉ - \(4\) X₃₀₃₅, X₁₄₉ + \(2\) X₆₁₅₄, X₁₄₉ - \(6\) X₆₁₇₄, \(3\) X₁₄₉ - \(8\) X₆₆₆₇, \(2\) X₁₄₉ - \(3\) X₁₀₇₀₇, \(3\) X₁₄₉ - \(10\) X₃₁₂₃₅, \(2\) X₁₄₉ - \(5\) X₃₁₂₇₂, X₁₄₉ - \(8\) X₃₅₀₂₃, \(5\) X₁₄₉ - \(12\) X₄₅₃₁₀, \(2\) X₃₀₃₅ + X₆₁₅₄, \(2\) X₃₀₃₅ - \(3\) X₆₁₇₄, \(3\) X₃₀₃₅ - \(2\) X₆₆₆₇, \(8\) X₃₀₃₅ - \(3\) X₁₀₇₀₇, \(4\) X₃₀₃₅ + X₂₀₀₉₅, \(6\) X₃₀₃₅ - \(5\) X₃₁₂₃₅, \(8\) X₃₀₃₅ - \(5\) X₃₁₂₇₂, \(5\) X₃₀₃₅ - \(3\) X₄₅₃₁₀, and many more

X₁₀₀ lies on the circumcircle, the circumcopnic with center X₉, the incircle of anticomplementary triangle, the cubics K299, K603, K661, K662, K817, K889, K1122.

▸ Incident Central Lines1512 lines

{1, 88}, {2, 11}, {3, 8}, {4, 119}, {5, 10738}, {6, 739}, {7, 1004}, {9, 1005}, {10, 21}, {12, 2475}, {19, 7466}, {20, 153}, {22, 197}, {23, 2752}, {25, 1862}, {28, 5174}, {30, 2687}, {31, 43}, {32, 713}, {33, 35973}, {34, 35974}, {36, 519}, {37, 111}, {38, 3961}, {39, 32454}, {40, 78}, {41, 3501}, {42, 81}, {44, 2384}, {45, 9330}, {46, 224}, {56, 145}, {57, 1280}, {58, 3293}, {59, 521}, {63, 103}, {65, 12739}, {69, 5848}, {71, 2249}, {72, 74}, {75, 675}, {76, 767}, {79, 35982}, {85, 2369}, {86, 29822}, {89, 39428}, {92, 917}, {98, 228}, {99, 668}, {101, 644}, {107, 823}, {108, 653}, {109, 651}, {110, 643}, {112, 162}, {113, 10767}, {114, 10768}, {115, 10769}, {116, 10770}, {117, 10771}, {118, 10772}, {121, 10774}, {122, 10775}, {123, 10776}, {124, 10777}, {125, 10778}, {126, 10779}, {127, 10780}, {140, 1484}, {141, 33086}, {142, 2346}, {144, 480}, {146, 12327}, {147, 12178}, {148, 13173}, {169, 25082}, {172, 20691}, {182, 12199}, {183, 4441}, {184, 3045}, {187, 5291}, {189, 35987}, {190, 659}, {191, 3678}, {192, 9082}, {194, 12338}, {198, 346}, {199, 3969}, {209, 40571}, {210, 3219}, {212, 25308}, {213, 729}, {219, 23707}, {226, 3256}, {227, 4296}, {229, 3178}, {230, 17737}, {238, 899}, {239, 2223}, {242, 35993}, {260, 7588}, {274, 2368}, {278, 2376}, {279, 2377}, {281, 1013}, {283, 35995}, {286, 39438}, {292, 3121}, {294, 6184}, {306, 1817}, {312, 1311}, {313, 37219}, {314, 40600}, {318, 7412}, {319, 1444}, {322, 17134}, {325, 2856}, {329, 972}, {333, 4184}, {341, 2370}, {344, 1486}, {350, 9073}, {354, 3957}, {355, 6906}, {371, 19082}, {372, 19081}, {376, 3421}, {377, 3085}, {381, 22938}, {382, 22799}, {384, 26752}, {385, 17759}, {386, 3032}, {387, 36000}, {388, 4190}, {394, 7074}, {402, 13268}, {405, 5175}, {409, 21674}, {442, 943}, {474, 1387}, {476, 4036}, {477, 36001}, {484, 758}, {485, 35772}, {486, 35773}, {487, 12343}, {488, 12344}, {491, 26513}, {492, 26512}, {493, 13275}, {494, 13276}, {495, 11112}, {496, 13747}, {498, 2476}, {499, 5533}, {511, 2699}, {512, 2703}, {513, 765}, {514, 1308}, {515, 2077}, {516, 908}, {517, 953}, {518, 840}, {520, 2719}, {522, 655}, {523, 1290}, {524, 2721}, {525, 2722}, {527, 30295}, {529, 15326}, {535, 4316}, {536, 4396}, {545, 38530}, {548, 38754}, {550, 38753}, {551, 36006}, {560, 697}, {573, 29068}, {574, 16975}, {593, 6043}, {594, 1030}, {595, 3216}, {601, 37699}, {604, 3169}, {610, 3692}, {612, 17594}, {614, 3749}, {616, 12337}, {617, 12336}, {627, 22558}, {628, 22557}, {631, 5082}, {645, 931}, {646, 8707}, {648, 36077}, {649, 660}, {650, 919}, {656, 39026}, {658, 664}, {661, 2702}, {666, 31150}, {667, 898}, {669, 9362}, {672, 3684}, {677, 4131}, {689, 6386}, {691, 4567}, {693, 927}, {699, 2205}, {701, 18900}, {715, 1918}, {717, 40728}, {719, 41267}, {726, 32845}, {728, 2371}, {731, 869}, {733, 893}, {735, 14620}, {740, 3724}, {743, 2276}, {745, 21035}, {748, 8616}, {751, 20973}, {752, 32843}, {753, 984}, {755, 3954}, {756, 846}, {761, 3661}, {788, 35009}, {789, 874}, {805, 4603}, {825, 1492}, {827, 4599}, {831, 4568}, {835, 4033}, {839, 27808}, {842, 37959}, {843, 21839}, {850, 2864}, {851, 3936}, {855, 36926}, {872, 39441}, {883, 6183}, {891, 39443}, {894, 6015}, {896, 1757}, {903, 24405}, {905, 35350}, {910, 3693}, {912, 43078}, {929, 4391}, {932, 4595}, {935, 7476}, {936, 5250}, {938, 26062}, {940, 17018}, {941, 34261}, {942, 45395}, {946, 6915}, {950, 24982}, {954, 33993}, {958, 3036}, {960, 17638}, {962, 1537}, {964, 19763}, {968, 5268}, {971, 17613}, {976, 986}, {978, 3915}, {982, 3938}, {983, 41886}, {985, 3795}, {993, 3679}, {995, 37610}, {997, 3877}, {999, 3241}, {1006, 3419}, {1010, 26115}, {1011, 5278}, {1014, 3879}, {1037, 30619}, {1043, 4225}, {1045, 20964}, {1052, 45233}, {1055, 35291}, {1056, 11239}, {1058, 17567}, {1078, 17143}, {1086, 17724}, {1089, 2372}, {1100, 8700}, {1110, 1734}, {1113, 2580}, {1114, 2581}, {1125, 3746}, {1149, 12029}, {1158, 12528}, {1191, 28280}, {1193, 5255}, {1201, 37588}, {1211, 33083}, {1215, 4418}, {1220, 4267}, {1224, 27787}, {1229, 26268}, {1250, 5362}, {1253, 1958}, {1255, 1929}, {1257, 18673}, {1261, 7293}, {1265, 3556}, {1267, 9098}, {1268, 46896}, {1270, 11498}, {1271, 11497}, {1276, 44689}, {1277, 44688}, {1279, 7292}, {1284, 4442}, {1289, 4244}, {1292, 2414}, {1293, 2827}, {1294, 2828}, {1296, 2830}, {1297, 2831}, {1299, 31384}, {1300, 7414}, {1301, 7435}, {1302, 42716}, {1304, 5379}, {1309, 4397}, {1310, 4561}, {1312, 10782}, {1313, 10781}, {1319, 3880}, {1324, 16086}, {1325, 12030}, {1326, 30576}, {1329, 5046}, {1333, 21858}, {1334, 35106}, {1335, 9679}, {1375, 28757}, {1381, 3307}, {1382, 3308}, {1385, 4861}, {1386, 17012}, {1388, 10912}, {1389, 19920}, {1402, 1999}, {1403, 3210}, {1414, 4614}, {1415, 8687}, {1420, 2136}, {1421, 43048}, {1429, 19589}, {1445, 1998}, {1449, 17223}, {1458, 9364}, {1462, 43063}, {1465, 4318}, {1466, 3600}, {1468, 37603}, {1470, 3476}, {1476, 12640}, {1478, 17579}, {1479, 4193}, {1482, 6924}, {1483, 37535}, {1490, 2057}, {1499, 2746}, {1500, 2375}, {1503, 2747}, {1575, 1914}, {1577, 2690}, {1580, 3507}, {1593, 12138}, {1610, 2933}, {1612, 1714}, {1613, 21780}, {1615, 38876}, {1616, 28370}, {1617, 5435}, {1618, 6099}, {1624, 4243}, {1631, 17233}, {1634, 8050}, {1644, 31171}, {1657, 38756}, {1697, 3890}, {1698, 5047}, {1699, 15017}, {1706, 3601}, {1707, 28527}, {1708, 2900}, {1726, 29306}, {1737, 10073}, {1738, 3011}, {1739, 30117}, {1740, 2209}, {1743, 17222}, {1754, 3190}, {1761, 3949}, {1764, 35614}, {1766, 12530}, {1769, 46119}, {1770, 21077}, {1771, 3562}, {1788, 3189}, {1791, 3704}, {1792, 7270}, {1812, 22276}, {1813, 8059}, {1814, 24499}, {1816, 3682}, {1818, 1936}, {1824, 3563}, {1836, 31053}, {1837, 12743}, {1908, 3774}, {1931, 12031}, {1959, 2700}, {1983, 29044}, {2071, 2694}, {2078, 3911}, {2082, 26690}, {2092, 2298}, {2149, 32689}, {2161, 40988}, {2178, 17314}, {2220, 33760}, {2229, 41333}, {2238, 17735}, {2239, 3783}, {2265, 36278}, {2280, 17754}, {2284, 8693}, {2292, 5293}, {2295, 18755}, {2308, 28517}, {2320, 24297}, {2330, 15988}, {2340, 9441}, {2344, 19584}, {2345, 36744}, {2347, 23617}, {2352, 3187}, {2365, 3719}, {2367, 27801}, {2373, 20336}, {2374, 7438}, {2380, 42680}, {2381, 42677}, {2397, 9058}, {2427, 32722}, {2478, 4294}, {2481, 40619}, {2551, 6872}, {2611, 16598}, {2635, 23693}, {2646, 5836}, {2651, 37783}, {2664, 3747}, {2688, 14206}, {2689, 4086}, {2692, 4404}, {2698, 5360}, {2701, 4041}, {2705, 4729}, {2708, 6211}, {2711, 20683}, {2715, 36084}, {2723, 7360}, {2724, 28058}, {2725, 3912}, {2726, 3685}, {2727, 24018}, {2728, 6332}, {2729, 14210}, {2730, 44448}, {2734, 10538}, {2736, 4468}, {2737, 4462}, {2740, 14207}, {2742, 3309}, {2743, 3667}, {2744, 6000}, {2745, 6001}, {2748, 4401}, {2751, 3220}, {2757, 4723}, {2758, 3992}, {2766, 37964}, {2770, 42713}, {2796, 21093}, {2810, 3937}, {2841, 38512}, {2857, 42703}, {2859, 3267}, {2860, 3261}, {2861, 3262}, {2862, 3263}, {2863, 3264}, {2887, 29846}, {2888, 12341}, {2893, 40999}, {2895, 41811}, {2896, 11494}, {2899, 4186}, {2915, 3695}, {2991, 20455}, {3006, 32850}, {3025, 31877}, {3030, 3271}, {3051, 21792}, {3052, 4383}, {3057, 12740}, {3059, 38451}, {3065, 3647}, {3068, 13922}, {3069, 13991}, {3086, 6921}, {3090, 23513}, {3091, 11496}, {3098, 12499}, {3100, 9371}, {3120, 17719}, {3126, 5377}, {3145, 38903}, {3146, 27525}, {3193, 14868}, {3196, 4370}, {3197, 38875}, {3207, 4513}, {3208, 9310}, {3214, 5247}, {3222, 36860}, {3231, 21788}, {3234, 3239}, {3242, 4392}, {3244, 5563}, {3245, 4867}, {3251, 5376}, {3259, 31512}, {3286, 16704}, {3303, 3622}, {3304, 3623}, {3305, 4512}, {3333, 8000}, {3336, 3874}, {3337, 3881}, {3338, 3889}, {3339, 11520}, {3359, 18446}, {3361, 4917}, {3413, 36735}, {3414, 36736}, {3416, 33077}, {3428, 22775}, {3448, 13204}, {3474, 5905}, {3486, 5554}, {3488, 37249}, {3496, 33299}, {3509, 3930}, {3522, 38759}, {3523, 12777}, {3526, 34126}, {3555, 37582}, {3560, 5818}, {3565, 22280}, {3576, 3872}, {3582, 6681}, {3583, 3814}, {3584, 3822}, {3612, 3897}, {3621, 5204}, {3624, 17535}, {3625, 5288}, {3626, 5258}, {3632, 7280}, {3634, 5259}, {3648, 5951}, {3660, 37789}, {3662, 33122}, {3666, 3920}, {3675, 10699}, {3680, 45036}, {3683, 3740}, {3687, 5314}, {3694, 5279}, {3697, 31445}, {3700, 9090}, {3701, 7283}, {3703, 6636}, {3705, 5014}, {3711, 5220}, {3713, 37499}, {3715, 33519}, {3720, 3750}, {3723, 28338}, {3729, 24309}, {3739, 9110}, {3741, 32918}, {3742, 3748}, {3744, 3752}, {3745, 17011}, {3753, 6797}, {3756, 43055}, {3757, 4359}, {3759, 3941}, {3762, 39444}, {3771, 25957}, {3772, 29665}, {3780, 33863}, {3782, 33102}, {3784, 23155}, {3797, 8628}, {3802, 25800}, {3812, 37080}, {3813, 5433}, {3820, 11113}, {3821, 32775}, {3825, 4857}, {3828, 16861}, {3831, 35206}, {3832, 38758}, {3836, 29632}, {3840, 32943}, {3841, 31254}, {3846, 32947}, {3851, 38141}, {3876, 12514}, {3878, 11010}, {3884, 37563}, {3893, 11256}, {3900, 4564}, {3903, 29055}, {3914, 33133}, {3916, 28173}, {3918, 35016}, {3919, 5425}, {3923, 32931}, {3924, 24440}, {3927, 28145}, {3940, 28159}, {3943, 19297}, {3944, 33094}, {3948, 46501}, {3951, 28149}, {3968, 5426}, {3971, 32936}, {3980, 29670}, {3983, 5302}, {3984, 12511}, {3989, 28499}, {3990, 26717}, {3996, 4210}, {3999, 4864}, {4000, 26228}, {4023, 37656}, {4030, 15246}, {4042, 5361}, {4043, 26266}, {4062, 32846}, {4068, 27811}, {4069, 4606}, {4076, 6079}, {4080, 19636}, {4083, 43362}, {4084, 41696}, {4085, 29631}, {4090, 32938}, {4094, 5147}, {4105, 9358}, {4115, 15322}, {4123, 20243}, {4187, 15171}, {4191, 10453}, {4192, 4388}, {4197, 10198}, {4199, 41809}, {4200, 11398}, {4222, 40101}, {4224, 29641}, {4228, 33116}, {4240, 11848}, {4250, 26705}, {4251, 16549}, {4254, 5749}, {4255, 5710}, {4261, 9079}, {4262, 16788}, {4265, 33170}, {4293, 34605}, {4297, 6736}, {4302, 11114}, {4308, 8278}, {4312, 31164}, {4313, 37248}, {4314, 8582}, {4319, 26669}, {4342, 34639}, {4360, 20990}, {4362, 32860}, {4363, 24344}, {4367, 6631}, {4378, 4555}, {4384, 23407}, {4385, 45136}, {4393, 21010}, {4394, 6078}, {4415, 33100}, {4416, 41430}, {4417, 6327}, {4422, 16686}, {4424, 30115}, {4430, 23958}, {4432, 9458}, {4433, 4447}, {4437, 20468}, {4438, 33117}, {4440, 21320}, {4454, 24328}, {4458, 6742}, {4467, 4477}, {4471, 17354}, {4482, 23891}, {4487, 23205}, {4497, 17377}, {4498, 28520}, {4559, 32693}, {4562, 4586}, {4569, 6606}, {4570, 4636}, {4572, 34083}, {4574, 36080}, {4575, 36050}, {4585, 4588}, {4589, 4600}, {4596, 6578}, {4601, 9150}, {4617, 41353}, {4618, 14421}, {4621, 8684}, {4641, 4849}, {4646, 17016}, {4650, 28488}, {4652, 28193}, {4655, 33065}, {4660, 25760}, {4661, 27778}, {4663, 21870}, {4666, 5437}, {4671, 5695}, {4678, 17548}, {4682, 9507}, {4685, 4921}, {4687, 9094}, {4696, 22345}, {4722, 9340}, {4730, 39155}, {4737, 23206}, {4738, 39445}, {4757, 16126}, {4760, 24358}, {4763, 8645}, {4807, 39577}, {4825, 5385}, {4834, 29341}, {4847, 5659}, {4848, 12437}, {4853, 7987}, {4860, 42871}, {4865, 29849}, {4872, 33864}, {4876, 19557}, {4882, 16192}, {4893, 28875}, {4904, 26140}, {4919, 17439}, {4970, 32928}, {4973, 5131}, {4981, 38000}, {4999, 37291}, {5011, 38884}, {5012, 20986}, {5015, 37431}, {5016, 37399}, {5030, 45751}, {5061, 35104}, {5067, 38319}, {5078, 5096}, {5081, 37305}, {5088, 30806}, {5090, 12137}, {5091, 14839}, {5124, 17362}, {5125, 41227}, {5126, 35271}, {5128, 11523}, {5154, 10896}, {5172, 5427}, {5177, 10585}, {5178, 6684}, {5180, 28174}, {5183, 44663}, {5187, 5225}, {5219, 8543}, {5222, 21477}, {5227, 38883}, {5229, 31295}, {5230, 37030}, {5249, 13405}, {5252, 18976}, {5256, 5269}, {5261, 37435}, {5262, 5266}, {5265, 12632}, {5273, 20835}, {5275, 31477}, {5283, 31451}, {5287, 37553}, {5300, 37231}, {5308, 16412}, {5310, 33157}, {5311, 17592}, {5324, 33118}, {5328, 30332}, {5329, 33088}, {5330, 5697}, {5333, 43223}, {5347, 33093}, {5367, 10638}, {5384, 5386}, {5391, 9099}, {5445, 14795}, {5450, 5881}, {5520, 36175}, {5540, 24036}, {5550, 16408}, {5558, 12631}, {5584, 20007}, {5587, 6246}, {5597, 13228}, {5598, 13230}, {5601, 11492}, {5602, 11493}, {5603, 6911}, {5638, 11651}, {5639, 11652}, {5688, 6262}, {5689, 6263}, {5693, 40256}, {5698, 31018}, {5701, 38347}, {5703, 37229}, {5709, 9946}, {5711, 19767}, {5718, 33112}, {5727, 34701}, {5730, 12702}, {5739, 7085}, {5745, 25006}, {5748, 9812}, {5790, 6914}, {5815, 37426}, {5839, 36743}, {5842, 6840}, {5844, 22765}, {5880, 17718}, {5882, 37561}, {5886, 6946}, {5901, 45976}, {5903, 22836}, {5904, 37572}, {5921, 39877}, {5966, 21807}, {6011, 22003}, {6012, 33951}, {6049, 41426}, {6060, 6617}, {6075, 22102}, {6126, 46819}, {6161, 6551}, {6193, 12328}, {6194, 22556}, {6200, 35856}, {6223, 12330}, {6225, 12335}, {6253, 6895}, {6260, 46435}, {6361, 6985}, {6396, 35857}, {6462, 11503}, {6463, 11504}, {6540, 32042}, {6558, 6574}, {6584, 8702}, {6595, 7161}, {6596, 17097}, {6599, 12639}, {6604, 38859}, {6605, 8012}, {6645, 17693}, {6648, 32038}, {6666, 46916}, {6679, 29850}, {6685, 32772}, {6691, 37722}, {6700, 10624}, {6733, 45874}, {6737, 43174}, {6765, 15803}, {6767, 16417}, {6789, 34587}, {6827, 32554}, {6830, 37820}, {6839, 7680}, {6845, 18517}, {6850, 10522}, {6853, 31659}, {6871, 10588}, {6875, 38128}, {6876, 35239}, {6885, 10532}, {6891, 12116}, {6910, 19843}, {6918, 38038}, {6920, 9956}, {6931, 10591}, {6933, 31418}, {6934, 40245}, {6937, 26487}, {6941, 10525}, {6942, 11249}, {6944, 10531}, {6945, 26333}, {6948, 12115}, {6950, 22758}, {6952, 26470}, {6960, 15908}, {6961, 10785}, {6979, 7681}, {6981, 10598}, {6996, 20556}, {6999, 27526}, {7012, 36067}, {7017, 39429}, {7035, 8640}, {7046, 37441}, {7077, 14200}, {7083, 11345}, {7095, 40214}, {7098, 41538}, {7109, 21779}, {7110, 21065}, {7115, 32688}, {7123, 30706}, {7226, 28567}, {7262, 28502}, {7287, 29345}, {7288, 8668}, {7291, 25083}, {7320, 22754}, {7354, 12607}, {7373, 17573}, {7377, 28789}, {7427, 24808}, {7450, 23181}, {7461, 26704}, {7483, 31419}, {7489, 38042}, {7493, 28420}, {7504, 25639}, {7508, 38112}, {7538, 27410}, {7549, 14679}, {7585, 19000}, {7586, 18999}, {7587, 12748}, {7589, 8126}, {7671, 8257}, {7674, 8730}, {7705, 10826}, {7783, 21226}, {7787, 11490}, {7824, 26801}, {7951, 17577}, {7967, 10269}, {7982, 25485}, {7984, 31525}, {7989, 38161}, {7991, 11682}, {8021, 40435}, {8025, 18185}, {8027, 38018}, {8052, 21295}, {8053, 17277}, {8054, 46126}, {8069, 18391}, {8075, 8103}, {8076, 8104}, {8077, 8097}, {8107, 11685}, {8108, 11686}, {8109, 12733}, {8110, 12734}, {8168, 11194}, {8193, 9912}, {8197, 12460}, {8204, 12461}, {8214, 12741}, {8215, 12742}, {8224, 11687}, {8225, 12744}, {8227, 16174}, {8256, 10950}, {8270, 17080}, {8271, 17092}, {8273, 15717}, {8545, 47375}, {8583, 9951}, {8591, 12326}, {8641, 10006}, {8649, 9283}, {8652, 35327}, {8691, 37210}, {8696, 16885}, {8701, 37212}, {8728, 26060}, {8750, 32691}, {8758, 37782}, {8817, 13577}, {8844, 33889}, {8852, 18235}, {8935, 21085}, {8972, 13887}, {8988, 13893}, {9056, 42718}, {9057, 42719}, {9059, 24004}, {9067, 41314}, {9075, 33931}, {9076, 37221}, {9077, 17289}, {9078, 29679}, {9083, 18743}, {9084, 42724}, {9086, 21580}, {9095, 30829}, {9103, 28605}, {9105, 19804}, {9271, 9272}, {9305, 30694}, {9317, 21232}, {9318, 24685}, {9369, 22344}, {9471, 17755}, {9509, 20998}, {9534, 16452}, {9540, 13913}, {9580, 30827}, {9623, 30282}, {9668, 17556}, {9670, 31246}, {9708, 16370}, {9710, 24953}, {9776, 10578}, {9841, 12125}, {9857, 12498}, {9859, 41229}, {9874, 12333}, {9913, 11414}, {9957, 17614}, {10025, 39421}, {10032, 17781}, {10039, 10057}, {10165, 34486}, {10167, 17658}, {10174, 10536}, {10199, 34719}, {10222, 45977}, {10315, 40129}, {10386, 17527}, {10423, 36095}, {10434, 11679}, {10441, 45394}, {10448, 37574}, {10449, 16451}, {10595, 37622}, {10647, 37794}, {10648, 37795}, {10791, 12198}, {10860, 11678}, {10861, 15298}, {10882, 10890}, {10884, 37560}, {10915, 12749}, {10916, 12750}, {11012, 11362}, {11061, 32256}, {11101, 27690}, {11108, 19877}, {11110, 19874}, {11124, 30613}, {11236, 12943}, {11246, 17483}, {11263, 37731}, {11274, 37587}, {11329, 17316}, {11343, 29611}, {11350, 34255}, {11358, 19684}, {11512, 28011}, {11683, 45744}, {11689, 15323}, {11691, 12518}, {11814, 24709}, {11822, 12462}, {11823, 12463}, {11824, 12753}, {11825, 12754}, {11826, 12761}, {11828, 12765}, {11829, 12766}, {11900, 12729}, {12334, 12383}, {12340, 12384}, {12342, 12849}, {12387, 12389}, {12410, 37257}, {12432, 15932}, {12512, 12527}, {12516, 12533}, {12517, 12534}, {12519, 12535}, {12609, 33593}, {12611, 12699}, {12635, 37567}, {12647, 14793}, {12680, 46677}, {12701, 25681}, {12780, 40714}, {12781, 40713}, {12848, 18801}, {13145, 33858}, {13206, 13219}, {13245, 28162}, {13256, 36082}, {13595, 20988}, {13624, 32634}, {13675, 13678}, {13740, 26030}, {13743, 18357}, {13744, 38950}, {13795, 13798}, {13883, 19078}, {13935, 13977}, {13936, 19077}, {13940, 13941}, {13947, 13976}, {14008, 44411}, {14074, 45695}, {14189, 37780}, {14204, 18359}, {14213, 26708}, {14459, 17772}, {14511, 38707}, {14621, 40732}, {14667, 14686}, {14716, 34409}, {14969, 14996}, {14997, 30653}, {15175, 17057}, {15253, 37771}, {15254, 35595}, {15338, 15680}, {15440, 32656}, {15485, 17125}, {15507, 17777}, {15519, 23089}, {15523, 33079}, {15556, 20612}, {15569, 17021}, {15587, 15837}, {15625, 23361}, {15702, 38069}, {15703, 38084}, {15726, 43080}, {15733, 37787}, {16056, 18139}, {16058, 26038}, {16061, 26965}, {16113, 21075}, {16202, 38032}, {16342, 19853}, {16378, 17794}, {16395, 37507}, {16405, 37502}, {16409, 26103}, {16465, 41539}, {16477, 21747}, {16484, 30950}, {16552, 24047}, {16574, 33847}, {16592, 21341}, {16613, 28282}, {16666, 28310}, {16667, 28314}, {16669, 28298}, {16670, 28302}, {16687, 17150}, {16693, 20475}, {16706, 26230}, {16777, 28326}, {16778, 17156}, {16814, 28334}, {16823, 24589}, {16826, 25946}, {16828, 17557}, {16858, 19875}, {16859, 46932}, {16865, 46933}, {16872, 21278}, {16884, 28330}, {16920, 26687}, {16968, 39255}, {17017, 17716}, {17025, 38315}, {17061, 33150}, {17063, 17715}, {17124, 17782}, {17142, 18048}, {17147, 32926}, {17154, 24841}, {17155, 32920}, {17165, 32939}, {17184, 33068}, {17234, 29830}, {17263, 26261}, {17264, 26262}, {17280, 23868}, {17292, 21516}, {17349, 20992}, {17353, 35263}, {17367, 21540}, {17388, 21773}, {17449, 18201}, {17469, 29821}, {17475, 25804}, {17484, 17768}, {17494, 43986}, {17495, 20045}, {17532, 31479}, {17541, 27091}, {17546, 25542}, {17553, 19870}, {17570, 46931}, {17574, 38213}, {17593, 46901}, {17599, 29815}, {17600, 29816}, {17602, 33155}, {17603, 30284}, {17654, 31788}, {17668, 29007}, {17682, 28742}, {17686, 27020}, {17697, 26029}, {17717, 33104}, {17720, 33134}, {17725, 33143}, {17752, 18758}, {17761, 25532}, {17766, 32844}, {17889, 33127}, {17943, 40501}, {18064, 34020}, {18108, 36081}, {18166, 40433}, {18191, 22313}, {18265, 40848}, {18480, 21669}, {18481, 37403}, {18518, 35251}, {18519, 34627}, {18621, 35260}, {18642, 43735}, {18750, 41905}, {19314, 39581}, {19537, 20050}, {19582, 28077}, {19785, 37099}, {19822, 37090}, {19862, 33709}, {19876, 38104}, {19916, 44805}, {20011, 37639}, {20012, 37683}, {20103, 40998}, {20104, 31262}, {20118, 24914}, {20173, 26267}, {20323, 32427}, {20352, 20878}, {20470, 29824}, {20670, 24504}, {20777, 25298}, {20794, 25311}, {20846, 37601}, {20887, 29010}, {20967, 27064}, {20972, 40400}, {20974, 24484}, {21000, 37679}, {21002, 37681}, {21004, 21711}, {21026, 29862}, {21061, 37508}, {21081, 37294}, {21105, 24126}, {21221, 26075}, {21231, 24435}, {21285, 33298}, {21302, 36030}, {21553, 31546}, {21740, 37562}, {21842, 22837}, {21856, 28055}, {21891, 22311}, {22060, 29308}, {22149, 29228}, {22277, 41610}, {22300, 41723}, {22329, 37857}, {22559, 22647}, {22791, 37251}, {23363, 43350}, {23374, 29437}, {23600, 37419}, {23622, 24578}, {23844, 25253}, {23865, 27013}, {23969, 36096}, {24052, 28841}, {24165, 32923}, {24169, 29656}, {24170, 33953}, {24174, 28082}, {24178, 28027}, {24248, 33151}, {24318, 24712}, {24320, 27549}, {24392, 31231}, {24403, 26273}, {24447, 30997}, {24477, 37578}, {24612, 37416}, {24627, 37575}, {24635, 28043}, {24703, 27131}, {24723, 26580}, {24789, 29681}, {24850, 24852}, {24892, 32865}, {24943, 33174}, {25066, 33950}, {25312, 43360}, {25557, 37703}, {25737, 30236}, {25768, 25872}, {25940, 37555}, {25959, 30811}, {25961, 29642}, {26034, 32782}, {26128, 29848}, {26321, 37705}, {26393, 26394}, {26417, 26418}, {26493, 26494}, {26502, 26503}, {26611, 38357}, {26641, 35185}, {26733, 36074}, {26744, 36910}, {26892, 29326}, {26893, 29009}, {27097, 33828}, {27184, 32950}, {27248, 33830}, {27299, 33819}, {27518, 36855}, {27558, 37405}, {27622, 30029}, {27804, 34064}, {27805, 30670}, {28070, 41795}, {28125, 28869}, {28444, 38074}, {28523, 42043}, {28563, 36263}, {28795, 36698}, {29349, 38389}, {29473, 40006}, {29511, 46502}, {29615, 35276}, {29627, 37272}, {29634, 32774}, {29649, 32915}, {29658, 33128}, {29662, 33141}, {29671, 33072}, {29673, 33119}, {29674, 33156}, {29678, 33111}, {29683, 33135}, {29687, 33158}, {29814, 37674}, {29840, 41346}, {30147, 37571}, {30247, 37217}, {30626, 32735}, {30725, 46116}, {30733, 41507}, {30913, 32666}, {30942, 32941}, {30996, 40546}, {31141, 34626}, {31143, 33082}, {31204, 33138}, {31330, 32916}, {31385, 39437}, {31423, 38133}, {31544, 31547}, {31545, 31548}, {31798, 40262}, {31847, 38569}, {32076, 42014}, {32157, 32198}, {32347, 32354}, {32468, 41526}, {32612, 37727}, {32636, 34791}, {32641, 32685}, {32665, 32686}, {32681, 36083}, {32683, 36088}, {32684, 36039}, {32687, 36092}, {32690, 36097}, {32710, 37979}, {32778, 33074}, {32781, 32783}, {32847, 32848}, {32854, 32855}, {32856, 32857}, {32925, 32934}, {33064, 33067}, {33080, 33084}, {33081, 33085}, {33098, 33101}, {33105, 33109}, {33107, 37662}, {33136, 33140}, {33139, 35466}, {33142, 37646}, {33144, 33146}, {33145, 33152}, {33161, 33165}, {33162, 33167}, {33166, 44416}, {33171, 33172}, {33667, 41697}, {33956, 44784}, {33994, 42884}, {34140, 37758}, {34168, 42699}, {34404, 39451}, {34606, 37299}, {34880, 37738}, {34921, 35057}, {34927, 34932}, {35004, 37733}, {35249, 37430}, {35616, 35638}, {35657, 35659}, {35788, 35852}, {35789, 35853}, {36154, 38570}, {36508, 38286}, {36565, 37549}, {36977, 40293}, {37254, 39570}, {37262, 37581}, {37264, 37547}, {37308, 37730}, {37371, 37799}, {37442, 37573}, {37557, 39582}, {37604, 42042}, {37658, 42316}, {38711, 46636}, {40097, 46588}, {40216, 40419}, {40300, 40302}, {43816, 43847}, {43974, 43991}, {45269, 45272}, {45508, 45520}, {45509, 45521}

▸ Functional Relations100 relations

• X₁₀₀ = midpoint of X_i and X_j for these {i,j}: {1, 5541}, {3, 12331}, {4, 13199}, {8, 6224}, {9, 5528}, {11, 6154}, {20, 153}, {40, 6326}, {104, 38665}, {119, 10993}, {149, 20095}, {191, 13146}, {901, 14513}, {1145, 10609}, {1155, 3689}, {1317, 13996}, {1490, 2950}, {1657, 38756}, {1768, 5531}, {2932, 5687}, {3218, 3935}, {3245, 4867}, {3913, 22560}, {5537, 44425}, {7991, 13253}, {11500, 12332}, {12119, 12751}, {12515, 12738}, {13269, 13270}, {18524, 35000}, {24466, 37725}, {32845, 32927}

• X₁₀₀ = reflection of X_i in X_j for these {i,j}: {1, 214}, {2, 6174}, {3, 33814}, {4, 119}, {7, 10427}, {8, 1145}, {9, 6594}, {11, 3035}, {20, 24466}, {21, 35204}, {80, 10}, {104, 3}, {105, 46409}, {144, 6068}, {145, 1317}, {149, 11}, {153, 37725}, {382, 22799}, {765, 46973}, {908, 6745}, {962, 1537}, {1156, 9}, {1290, 36167}, {1320, 1}, {1482, 19907}, {1484, 140}, {1768, 46684}, {2611, 16598}, {2687, 46635}, {2975, 4996}, {3035, 35023}, {3065, 3647}, {3218, 1155}, {3244, 33812}, {3254, 142}, {3583, 3814}, {3868, 11570}, {3870, 41553}, {3935, 3689}, {4511, 5440}, {5057, 908}, {5080, 17757}, {5176, 6735}, {5375, 38310}, {5905, 12831}, {6075, 22102}, {6163, 765}, {6224, 10609}, {6264, 11715}, {6265, 22935}, {6595, 13089}, {6599, 12639}, {6909, 2077}, {7972, 33337}, {7982, 25485}, {7984, 31525}, {9318, 24685}, {9809, 13257}, {9897, 15863}, {10090, 25440}, {10265, 6684}, {10609, 9945}, {10698, 6265}, {10707, 2}, {10724, 4}, {10728, 10742}, {10738, 5}, {10742, 11698}, {10755, 6}, {10767, 113}, {10768, 114}, {10769, 115}, {10770, 116}, {10771, 117}, {10772, 118}, {10773, 120}, {10774, 121}, {10775, 122}, {10776, 123}, {10777, 124}, {10778, 125}, {10779, 126}, {10780, 127}, {10781, 1313}, {10782, 1312}, {11219, 10164}, {11256, 11260}, {11604, 442}, {11609, 2092}, {12248, 38761}, {12515, 3579}, {12528, 12665}, {12531, 8}, {12532, 72}, {12641, 12640}, {12649, 12832}, {12690, 12019}, {12699, 12611}, {12737, 1385}, {12761, 18242}, {12764, 1329}, {12773, 38602}, {12848, 25606}, {12868, 12631}, {13199, 10993}, {13243, 1768}, {13266, 659}, {13268, 402}, {13277, 9508}, {13278, 10087}, {13279, 10090}, {14217, 946}, {14923, 39776}, {14947, 6184}, {17636, 5836}, {17638, 960}, {17652, 9957}, {17654, 31788}, {17763, 4434}, {19914, 5690}, {19916, 44805}, {20067, 15326}, {20095, 6154}, {20119, 2550}, {21630, 1125}, {24297, 40587}, {24712, 24318}, {24852, 24850}, {25416, 12735}, {25438, 8715}, {26015, 3911}, {26726, 3244}, {31512, 3259}, {32198, 32157}, {32454, 39}, {34151, 15632}, {34195, 39778}, {34772, 41541}, {34789, 21635}, {34894, 6600}, {36002, 44425}, {36175, 5520}, {36237, 190}, {36845, 41556}, {36846, 41554}, {37726, 6713}, {38460, 1319}, {38521, 38643}, {38665, 12331}, {38669, 104}, {38693, 34474}, {38753, 550}, {41575, 41558}, {42322, 4394}, {43735, 18642}, {45393, 11517}, {46435, 6260}, {46685, 14740}, {47320, 3678}

• X₁₀₀ = isogonal conjugate of X₅₁₃

• X₁₀₀ = isotomic conjugate of X₆₉₃

• X₁₀₀ = anticomplement of X₁₁

• X₁₀₀ = complement of X₁₄₉

• X₁₀₀ = Stevanovic circle inverse of X₉₁₉

• X₁₀₀ = Conway circle inverse of X₃₈₄₇₈

• X₁₀₀ = polar circle inverse of X₅₅₂₁

• X₁₀₀ = orthoptic circle of the Steiner inellipe inverse of X₁₂₀

• X₁₀₀ = orthoptic circle of the Steiner circumellipe inverse of X₂₀₃₄₄

• X₁₀₀ = de Longchamps circle inverse of X₃₄₁₈₈

• X₁₀₀ = Schoutte circle inverse of X₃₅₁₀₇

• X₁₀₀ = second Brocard Circle inverse of X₃₈₅₂₁

• X₁₀₀ = polar conjugate of X₁₇₉₂₄

• X₁₀₀ = antitomic image of X₁₄₉₄₇

• X₁₀₀ = anticomplement of the anticomplement of X₃₀₃₅

• X₁₀₀ = anticomplement of the anticomplement of the anticomplement of X₆₆₆₇

• X₁₀₀ = complement of the complement of X₂₀₀₉₅

• X₁₀₀ = anticomplement of the isogonal conjugate of X₅₉

• X₁₀₀ = complement of the isogonal conjugate of X₃₄₄₆

• X₁₀₀ = anticomplement of the isotomic conjugate of X₄₉₉₈

• X₁₀₀ = complement of the isotomic conjugate of X₈₀₄₇

• X₁₀₀ = isogonal conjugate of the anticomplement of X₅₁₃

• X₁₀₀ = isogonal conjugate of the complement of X₅₁₃

• X₁₀₀ = isotomic conjugate of the anticomplement of X₆₅₀

• X₁₀₀ = isotomic conjugate of the complement of X₁₇₄₉₄

• X₁₀₀ = isotomic conjugate of the isogonal conjugate of X₆₉₂

• X₁₀₀ = isogonal conjugate of the isotomic conjugate of X₆₆₈

• X₁₀₀ = isotomic conjugate of the polar conjugate of X₁₇₈₃

• X₁₀₀ = isogonal conjugate of the polar conjugate of X₆₃₃₅

• X₁₀₀ = polar conjugate of the isotomic conjugate of X₁₃₃₂

• X₁₀₀ = polar conjugate of the isogonal conjugate of X₉₀₆

• X₁₀₀ = Thomson isogonal conjugate of X₅₁₇

• X₁₀₀ = Lucas-isogonal conjugate of X₅₁₇

• X₁₀₀ = excentral isogonal conjugate of X₂₉₅₇

• X₁₀₀ = tangential isogonal conjugate of X₃₈₈₆₃

• X₁₀₀ = psi-transform of X₁₀₈₃

• X₁₀₀ = circumcircle-antipode of X₁₀₄

• X₁₀₀ = Ψ(X_i,X_j) for these (i,j): (1, 2), 2,37), (3, 63), (4, 8), (6, 1), (7, 8), (48, 3), (56, 55), (68, 72)

• X₁₀₀ = X₁-line conjugate of X₂₄₄

• X₁₀₀ = X₁₁₃-of-the-hexyl-triangle

• X₁₀₀ = concurrence of reflections in sides of ABC of line X₄X₈

• X₁₀₀ = perspector of Hutson-Moses hyperbola

• X₁₀₀ = trilinear pole of line X₁X₆ (and PU(28)) (van Aubel line of excentral triangle)

• X₁₀₀ = trilinear product of PU(33)

• X₁₀₀ = trilinear product of intercepts of circumcircle and Nagel line

• X₁₀₀ = polar conjugate of X₁₇₉₂₄

• X₁₀₀ = pole wrt polar circle of trilinear polar of X₁₇₉₂₄ (line X₁₁X₂₉₆₉)

• X₁₀₀ = the point of intersection, other than A, B, and C, of the circumcircle and the circumellipse centered at X₁ (viz., {A, B, C,X₁₀₀,X₆₆₄,X₁₁₂₀,X₁₃₂₀}})

• X₁₀₀ = the point of intersection, other than A, B, and C, of the circumcircle and the circumellipse centered at X₉ (viz., {A, B, C,X₁₀₀,X₆₅₈,X₆₆₂,X₇₉₉,X₁₈₂₁,X₂₅₈₀,X₂₅₈₁,PU(34)}})

• X₁₀₀ = the point of intersection, other than A, B, and C, of the circumcircle and hyperbola {A, B, C,PU(8)}}

• X₁₀₀ = the point of intersection, other than A, B, and C, of the circumcircle and hyperbola {A, B, C,PU(32)}}

• X₁₀₀ = center of hyperbola passing through X₁, X₉, and the excenters

• X₁₀₀ = X₁₂₅-of-excentral-triangle

• X₁₀₀ = trilinear pole wrt 1st circumperp triangle of line X₃X₁₄₂

• X₁₀₀ = X₁₁₀-of-1st-circumperp-triangle

• X₁₀₀ = reflection of X₁₂₉₀ in the Euler line

• X₁₀₀ = reflection of X₂₇₀₃ in the Brocard axis

• X₁₀₀ = reflection of X₉₀₁ in line X₁X₃

• X₁₀₀ = cevapoint of X₅₉ and inverse-in-circumcircle-of-X₅₉

• X₁₀₀ = inverse-in-{circumcircle, nine-point circle}-inverter of X₁₂₀

• X₁₀₀ = exsimilicenter of circumcircle and AC-incircle

• X₁₀₀ = X_i-aleph conjugate of X_j for these (i,j) (1,1052), (100,1), (190,63), (643,411), (666,673), (765,100), (1016,190)

• X₁₀₀ = X_i-beth conjugate of X_j for these (i,j): (8, 80), (21, 106), (100, 109), (333, 673), (643, 100), (765, 100)

• X₁₀₀ = the point of intersection, other than A, B, and C, of the circumcircle and ellipse {A, B, C,PU(75)}}

• X₁₀₀ = crossdifference of PU(27)

• X₁₀₀ = homothetic center of 2nd Schiffler triangle and excenters-midpoints triangle

• X₁₀₀ = Feuerbach image of X₂

• X₁₀₀ = Cundy-Parry Phi transform of X₁₄₂₆₆

• X₁₀₀ = perspector of anti-Mandart-incircle and anticomplementary triangles

• X₁₀₀ = intersection of antipedal lines of X₁₃₈₁ and X₁₃₈₂

• X₁₀₀ = eigencenter of Gemini triangle 2

• X₁₀₀ = barycentric product of vertices of Gemini triangle 5

• X₁₀₀ = barycentric product of vertices of Gemini triangle 6

• X₁₀₀ = perspector of ABC and side-triangle of Gemini triangles 29 and 30

• X₁₀₀ = homothetic center of 2nd Schiffler triangle and excenters-midpoints triangle

• X₁₀₀ = barycentric product of vertices of Gemini triangle 29

• X₁₀₀ = barycentric product of vertices of Gemini triangle 30

• X₁₀₀ = intersection, other than A, B, C, of {ABC, Gemini 29}-circumconic and {ABC, Gemini 30}-circumconic

• X₁₀₀ = barycentric product of circumcircle intercepts of line X₂X₃₇

• X₁₀₀ = excentral-to-ABC barycentric image of X₁₇₆₈

• X₁₀₀ = intouch-to-ABC barycentric image of X₁₁

• X₁₀₀ = ABC-to-excentral barycentric image of X₁₁

• X₁₀₀ = trilinear pole, wrt circumtangential triangle, of line X₁X₃

• X₁₀₀ = BSS(a^2→a) of X₁₁₀

• X₁₀₀ = Collings transform of X_i for these i: {1, 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, 40587, 40600, 40653, 41540, 41862, 41886, 43182, 45036}

• X₁₀₀ = X_i-anticomplementary conjugate of X_j for these (i,j): {31, 17036}, {59, 8}, {100, 33650}, {101, 37781}, {109, 149}, {249, 21273}, {651, 150}, {664, 21293}, {692, 39351}, {765, 3436}, {1016, 21286}, {1101, 2975}, {1110, 144}, {1252, 329}, {1262, 7}, {1275, 21285}, {1331, 34188}, {1415, 4440}, {2149, 2}, {4551, 3448}, {4552, 21294}, {4559, 21221}, {4564, 69}, {4567, 20245}, {4570, 3869}, {4619, 693}, {4620, 17137}, {4998, 6327}, {7012, 4}, {7045, 3434}, {7115, 5905}, {7339, 36845}, {9268, 5176}, {23357, 18662}, {23979, 3210}, {23990, 3177}, {24027, 145}, {24041, 35614}, {31615, 20295}, {39293, 20556}, {44717, 4329}, {46102, 21270}

• X₁₀₀ = X_i-complementary conjugate of X_j for these (i,j): {31, 5375}, {3446, 10}, {8047, 2887}, {42552, 124}

• X₁₀₀ = X_i-Ceva conjugate of X_j for these (i,j): {1, 6163}, {2, 5375}, {6, 9266}, {59, 2975}, {99, 190}, {190, 644}, {249, 38871}, {643, 1331}, {662, 101}, {664, 651}, {666, 2284}, {668, 1332}, {765, 1}, {835, 4756}, {898, 23343}, {1016, 6}, {1252, 1621}, {1262, 38869}, {1275, 220}, {3257, 1023}, {4076, 145}, {4555, 4585}, {4564, 9}, {4567, 37}, {4570, 21}, {4596, 662}, {4600, 81}, {4601, 213}, {4603, 46148}, {4618, 3257}, {4998, 2}, {5376, 44}, {5377, 518}, {5378, 238}, {5379, 72}, {5381, 3230}, {5382, 1743}, {5383, 2176}, {5384, 984}, {5385, 45}, {5387, 16784}, {5388, 40728}, {6012, 1633}, {6079, 17780}, {6335, 1783}, {6606, 664}, {6648, 4559}, {7012, 3869}, {7035, 32911}, {7045, 63}, {8269, 934}, {8706, 3699}, {8707, 3952}, {8708, 4557}, {8709, 3570}, {9059, 4767}, {13136, 2427}, {15742, 8}, {23586, 38876}, {23984, 38875}, {24041, 33761}, {31615, 1252}, {31628, 650}, {34071, 932}, {34537, 38853}, {35574, 42720}, {36086, 3573}, {36147, 4579}, {36797, 1897}, {36802, 2398}, {37212, 1018}, {39272, 36086}, {39444, 36237}, {46102, 219}, {46649, 12531}

• X₁₀₀ = X_i-cross conjugate of X_j for these (i,j): {1, 765}, {3, 59}, {6, 1016}, {9, 4564}, {35, 4570}, {36, 9268}, {37, 4567}, {40, 7012}, {43, 7035}, {44, 5376}, {45, 5385}, {55, 1252}, {72, 5379}, {101, 651}, {109, 13138}, {165, 7045}, {170, 24011}, {171, 4600}, {190, 932}, {197, 7115}, {198, 1262}, {213, 4601}, {219, 46102}, {220, 1275}, {238, 5378}, {512, 2298}, {513, 1}, {514, 2346}, {518, 5377}, {521, 8}, {522, 21}, {523, 943}, {610, 7128}, {644, 27834}, {647, 40406}, {649, 81}, {650, 2}, {652, 40399}, {654, 2990}, {656, 1257}, {659, 105}, {661, 1255}, {663, 23617}, {665, 2991}, {667, 6}, {692, 1783}, {798, 1258}, {846, 24041}, {890, 739}, {900, 104}, {906, 1332}, {926, 294}, {928, 8759}, {984, 5384}, {1018, 190}, {1019, 40433}, {1021, 40435}, {1023, 3257}, {1026, 660}, {1030, 249}, {1376, 4998}, {1415, 46640}, {1491, 1390}, {1615, 23586}, {1631, 15378}, {1633, 934}, {1635, 88}, {1734, 75}, {1743, 5382}, {1960, 40400}, {2176, 5383}, {2254, 1280}, {2283, 677}, {2284, 666}, {2427, 13136}, {2509, 30701}, {2516, 8056}, {2804, 45393}, {2820, 43736}, {2821, 9372}, {2915, 250}, {2933, 15386}, {2939, 24000}, {2947, 24032}, {2977, 15344}, {3063, 17743}, {3126, 518}, {3185, 2149}, {3197, 23984}, {3230, 5381}, {3251, 44}, {3257, 9271}, {3309, 7}, {3573, 37135}, {3659, 6733}, {3667, 1476}, {3733, 1126}, {3737, 1220}, {3738, 1320}, {3882, 3903}, {3887, 1156}, {3900, 9}, {3913, 4076}, {3939, 644}, {4040, 86}, {4057, 58}, {4063, 82}, {4083, 983}, {4105, 6605}, {4394, 57}, {4401, 1014}, {4427, 34594}, {4436, 99}, {4455, 292}, {4491, 106}, {4551, 1897}, {4553, 668}, {4557, 101}, {4559, 44765}, {4705, 37}, {4730, 2161}, {4775, 40401}, {4777, 15175}, {4782, 985}, {4790, 25417}, {4825, 45}, {4834, 2214}, {4893, 40434}, {4926, 15446}, {5277, 4590}, {5687, 15742}, {6003, 17097}, {6050, 39956}, {6161, 513}, {6182, 40779}, {6366, 34894}, {6586, 40403}, {6600, 6065}, {7234, 42}, {7239, 1978}, {7252, 40394}, {8043, 1224}, {8632, 20332}, {8640, 31}, {8641, 7123}, {8659, 1462}, {8662, 2221}, {8674, 80}, {8676, 1172}, {8678, 941}, {8683, 1293}, {8702, 7161}, {9001, 1000}, {9441, 39293}, {9508, 291}, {11124, 650}, {12331, 46649}, {13589, 1290}, {14392, 41798}, {14419, 34893}, {14589, 31615}, {15313, 4}, {15624, 1110}, {16553, 35049}, {16784, 5387}, {17494, 1621}, {18004, 15168}, {21003, 1438}, {21005, 251}, {21007, 83}, {21173, 1222}, {21189, 40436}, {21779, 34537}, {21786, 46638}, {21789, 2983}, {21791, 38810}, {21894, 39698}, {21901, 1221}, {23067, 1331}, {23224, 42019}, {23343, 898}, {23703, 36037}, {23832, 901}, {23845, 109}, {23865, 1174}, {23867, 38813}, {24052, 4632}, {24290, 335}, {28217, 15179}, {35057, 32635}, {35326, 43190}, {35338, 664}, {35341, 37206}, {35342, 662}, {38469, 43073}, {39199, 1167}, {39200, 36052}, {40728, 5388}, {43049, 3870}, {46611, 2687}

• X₁₀₀ = X_i-isoconjugate of X_j for these (i,j): {1, 513}, {2, 649}, {3, 7649}, {4, 1459}, {6, 514}, {7, 663}, {8, 43924}, {9, 3669}, {10, 3733}, {11, 109}, {19, 905}, {21, 4017}, {25, 4025}, {27, 647}, {28, 656}, {31, 693}, {32, 3261}, {34, 521}, {37, 1019}, {38, 18108}, {39, 10566}, {41, 24002}, {42, 7192}, {43, 43931}, {44, 1022}, {48, 17924}, {54, 21102}, {55, 3676}, {56, 522}, {57, 650}, {58, 523}, {59, 21132}, {63, 6591}, {64, 21172}, {65, 3737}, {71, 17925}, {74, 11125}, {75, 667}, {76, 1919}, {77, 18344}, {78, 43923}, {79, 2605}, {81, 661}, {82, 2530}, {83, 21123}, {84, 6129}, {85, 3063}, {86, 512}, {87, 4083}, {88, 1635}, {89, 4893}, {91, 34948}, {92, 22383}, {99, 3122}, {100, 244}, {101, 1086}, {103, 676}, {104, 1769}, {105, 2254}, {106, 900}, {108, 7004}, {110, 3120}, {111, 4750}, {112, 4466}, {115, 4556}, {158, 23224}, {162, 18210}, {163, 16732}, {174, 6729}, {184, 46107}, {190, 1015}, {200, 43932}, {210, 7203}, {213, 7199}, {222, 3064}, {225, 23189}, {226, 7252}, {238, 876}, {239, 3572}, {241, 1024}, {249, 21131}, {250, 21134}, {251, 16892}, {256, 4367}, {257, 20981}, {266, 6728}, {267, 31947}, {269, 3900}, {273, 1946}, {274, 798}, {278, 652}, {279, 657}, {284, 7178}, {286, 810}, {291, 659}, {292, 812}, {306, 43925}, {310, 669}, {330, 20979}, {333, 7180}, {335, 8632}, {350, 875}, {386, 43927}, {393, 4091}, {479, 4105}, {516, 2424}, {518, 1027}, {519, 23345}, {520, 8747}, {525, 1474}, {536, 23892}, {560, 40495}, {561, 1980}, {593, 4024}, {595, 40086}, {596, 4057}, {603, 44426}, {604, 4391}, {608, 6332}, {651, 2170}, {653, 7117}, {654, 2006}, {658, 14936}, {660, 27846}, {662, 3125}, {664, 3271}, {665, 673}, {668, 3248}, {679, 3251}, {692, 1111}, {694, 4107}, {726, 23355}, {727, 3837}, {738, 4130}, {739, 4728}, {741, 4010}, {751, 4378}, {753, 4809}, {757, 4705}, {764, 765}, {788, 870}, {799, 3121}, {813, 27918}, {824, 40746}, {832, 977}, {834, 43531}, {849, 4036}, {850, 2206}, {871, 8630}, {884, 9436}, {885, 1458}, {890, 31002}, {891, 37129}, {893, 4369}, {897, 14419}, {898, 19945}, {899, 43928}, {901, 1647}, {902, 6548}, {903, 1960}, {904, 4374}, {908, 2423}, {909, 10015}, {918, 1438}, {932, 3123}, {934, 2310}, {959, 17418}, {961, 17420}, {963, 7661}, {967, 45745}, {983, 3777}, {985, 1491}, {996, 9002}, {998, 9001}, {1002, 4724}, {1014, 4041}, {1016, 21143}, {1018, 16726}, {1021, 1427}, {1026, 43921}, {1042, 7253}, {1043, 7250}, {1054, 6164}, {1088, 8641}, {1096, 4131}, {1106, 4397}, {1120, 6085}, {1126, 4977}, {1146, 1461}, {1149, 23836}, {1155, 35348}, {1156, 14413}, {1169, 21124}, {1170, 21127}, {1171, 4988}, {1173, 21103}, {1174, 21104}, {1175, 23752}, {1176, 21108}, {1177, 21109}, {1178, 2533}, {1193, 4581}, {1220, 6371}, {1222, 6363}, {1252, 6545}, {1255, 4979}, {1262, 42462}, {1279, 35355}, {1293, 3756}, {1318, 39771}, {1319, 23838}, {1323, 23351}, {1326, 18014}, {1331, 2969}, {1333, 1577}, {1334, 17096}, {1357, 3699}, {1358, 3939}, {1364, 36127}, {1365, 4636}, {1395, 35518}, {1396, 8611}, {1397, 35519}, {1400, 4560}, {1402, 18155}, {1407, 3239}, {1408, 4086}, {1411, 3738}, {1412, 3700}, {1413, 8058}, {1414, 4516}, {1415, 4858}, {1417, 4768}, {1421, 42552}, {1422, 14298}, {1431, 3907}, {1432, 3287}, {1434, 3709}, {1436, 14837}, {1437, 24006}, {1457, 43728}, {1472, 2517}, {1476, 6615}, {1486, 26721}, {1492, 4475}, {1509, 4079}, {1565, 8750}, {1576, 21207}, {1581, 4164}, {1638, 2291}, {1643, 37131}, {1646, 4607}, {1751, 43060}, {1783, 3942}, {1790, 2501}, {1795, 39534}, {1813, 8735}, {1826, 7254}, {1875, 37628}, {1876, 23696}, {1897, 3937}, {1911, 3766}, {1914, 4444}, {1924, 6385}, {1929, 9508}, {1967, 14296}, {1973, 15413}, {1977, 1978}, {2087, 3257}, {2109, 25381}, {2149, 40166}, {2156, 16757}, {2160, 14838}, {2161, 3960}, {2162, 3835}, {2163, 4777}, {2164, 21188}, {2183, 2401}, {2191, 3309}, {2194, 4077}, {2195, 43042}, {2203, 14208}, {2207, 30805}, {2208, 17896}, {2214, 14349}, {2215, 23882}, {2217, 21189}, {2218, 23800}, {2221, 6590}, {2226, 6544}, {2248, 21196}, {2258, 43067}, {2276, 4817}, {2279, 4762}, {2287, 7216}, {2296, 2978}, {2297, 8712}, {2299, 17094}, {2308, 4608}, {2311, 7212}, {2316, 30725}, {2319, 43051}, {2333, 15419}, {2334, 4778}, {2340, 43930}, {2348, 37626}, {2349, 14399}, {2350, 17494}, {2353, 21178}, {2354, 15420}, {2364, 43052}, {2382, 36848}, {2384, 14475}, {2395, 17209}, {2426, 15634}, {2432, 34050}, {2433, 18653}, {2486, 43076}, {2488, 21453}, {2489, 17206}, {2504, 9085}, {2509, 40188}, {2516, 36603}, {2526, 39958}, {2611, 13486}, {2616, 18180}, {2623, 17167}, {2718, 24457}, {2720, 35015}, {2786, 17962}, {2787, 17954}, {2832, 34893}, {2973, 32656}, {2983, 29162}, {2985, 23751}, {2998, 23572}, {3011, 35365}, {3022, 4626}, {3049, 44129}, {3119, 4617}, {3124, 4610}, {3224, 21191}, {3226, 6373}, {3227, 3768}, {3249, 31625}, {3250, 14621}, {3270, 36118}, {3285, 4049}, {3310, 34234}, {3423, 47123}, {3433, 21185}, {3435, 21186}, {3437, 21187}, {3444, 21192}, {3445, 3667}, {3446, 21201}, {3447, 21203}, {3449, 21118}, {3450, 21119}, {3451, 21120}, {3453, 21121}, {3455, 21205}, {3500, 21348}, {3668, 21789}, {3675, 36086}, {3762, 9456}, {3778, 7255}, {3798, 8770}, {3801, 38813}, {3803, 23051}, {3805, 40763}, {3862, 23597}, {3880, 37627}, {3912, 43929}, {3954, 39179}, {4040, 13476}, {4062, 43926}, {4063, 39798}, {4081, 6614}, {4128, 4594}, {4132, 39949}, {4142, 34250}, {4160, 34916}, {4162, 19604}, {4163, 7023}, {4303, 14775}, {4306, 23289}, {4373, 8643}, {4379, 30650}, {4382, 30651}, {4394, 8056}, {4401, 7241}, {4440, 9262}, {4449, 9309}, {4453, 6187}, {4455, 18827}, {4458, 8852}, {4459, 29055}, {4462, 38266}, {4467, 6186}, {4481, 40747}, {4491, 39697}, {4498, 39956}, {4521, 40151}, {4534, 38828}, {4551, 18191}, {4557, 17205}, {4559, 17197}, {4561, 42067}, {4565, 21044}, {4584, 39786}, {4598, 6377}, {4600, 8034}, {4603, 16592}, {4618, 42084}, {4637, 36197}, {4638, 35092}, {4707, 34079}, {4775, 39704}, {4784, 30571}, {4786, 21448}, {4790, 25430}, {4791, 28607}, {4813, 25417}, {4823, 34819}, {4834, 30598}, {4885, 9315}, {4932, 39967}, {4943, 16079}, {4957, 34073}, {4960, 28625}, {4978, 28615}, {4983, 40438}, {5009, 35352}, {5029, 6650}, {5209, 18002}, {5317, 24018}, {5331, 8672}, {5620, 42741}, {6005, 10013}, {6006, 41436}, {6149, 43082}, {6161, 46972}, {6336, 22086}, {6372, 40433}, {6381, 23349}, {6384, 8640}, {6549, 23344}, {6550, 9268}, {6551, 24188}, {6586, 14377}, {6588, 42467}, {6589, 13478}, {6610, 23893}, {6629, 9178}, {6730, 7370}, {7035, 8027}, {7077, 43041}, {7087, 20517}, {7121, 20906}, {7169, 21174}, {7234, 32010}, {7260, 21755}, {7316, 14432}, {7339, 23615}, {7658, 11051}, {8050, 8054}, {8059, 38357}, {8578, 44184}, {8648, 18815}, {8656, 36588}, {8659, 36807}, {8677, 36123}, {8690, 21963}, {8713, 10579}, {8714, 34444}, {8917, 17427}, {9217, 21200}, {9259, 42555}, {9265, 21211}, {9267, 9359}, {9269, 9325}, {9292, 17215}, {9299, 18149}, {9311, 20980}, {9361, 38238}, {9505, 38348}, {9506, 27929}, {10428, 23757}, {10490, 10495}, {10492, 18888}, {10509, 10581}, {14370, 21194}, {14554, 21786}, {15378, 21133}, {15382, 20504}, {16099, 42662}, {16606, 18197}, {16695, 42027}, {16702, 23894}, {16737, 40729}, {16887, 18105}, {17216, 32713}, {17217, 23493}, {17222, 45677}, {17435, 36146}, {17731, 18001}, {17758, 21007}, {17780, 43922}, {18018, 21122}, {18101, 46153}, {18359, 21758}, {18771, 21105}, {18772, 21106}, {18830, 38986}, {20295, 40148}, {20516, 34183}, {20518, 41528}, {20908, 34077}, {20974, 43190}, {21003, 39714}, {21110, 38826}, {21113, 42346}, {21138, 34071}, {21173, 34434}, {21175, 34436}, {21176, 34437}, {21179, 34441}, {21180, 34442}, {21183, 34446}, {21190, 34427}, {21202, 34179}, {21206, 36615}, {21208, 40519}, {21385, 39982}, {21763, 42328}, {21828, 24624}, {21832, 37128}, {22084, 26705}, {22108, 34578}, {22350, 43933}, {23100, 23990}, {23707, 30691}, {23723, 34429}, {23729, 38825}, {23807, 34248}, {23845, 40451}, {23989, 32739}, {24027, 42455}, {25426, 28840}, {26932, 32674}, {26933, 32691}, {28209, 41434}, {29198, 39972}, {29226, 36598}, {30723, 34820}, {30724, 33635}, {32039, 40610}, {32641, 42754}, {32714, 34591}, {34018, 46388}, {34051, 46393}, {34858, 36038}, {35014, 36110}, {36037, 42753}, {40076, 47234}, {40397, 40628}, {40409, 40627}, {40738, 45882}, {41799, 45877}, {42290, 45755}

• X₁₀₀ = cevapoint of X_i and X_j for these (i,j): {1, 513}, {2, 17494}, {3, 521}, {6, 667}, {9, 3900}, {10, 522}, {11, 15914}, {37, 4705}, {42, 649}, {43, 8640}, {44, 3251}, {45, 4825}, {55, 650}, {57, 43049}, {101, 3939}, {119, 2804}, {142, 514}, {171, 7234}, {190, 4595}, {214, 3738}, {442, 523}, {512, 2092}, {518, 3126}, {525, 18642}, {656, 18673}, {659, 8299}, {661, 1962}, {663, 2347}, {665, 20455}, {669, 21753}, {678, 1635}, {692, 906}, {899, 38349}, {900, 1145}, {905, 7289}, {918, 17060}, {926, 6184}, {1018, 4557}, {1019, 18166}, {1021, 8021}, {1734, 15624}, {1960, 20972}, {2530, 18183}, {3158, 4394}, {3257, 9272}, {3293, 4057}, {3307, 3308}, {3309, 6600}, {3647, 35057}, {3667, 12640}, {3737, 4267}, {3795, 4782}, {3887, 6594}, {4041, 21811}, {4083, 41886}, {4097, 4401}, {4105, 8012}, {4477, 18235}, {4551, 23067}, {4730, 40988}, {4775, 20973}, {4777, 17057}, {4802, 41862}, {6161, 46973}, {6260, 8058}, {6366, 10427}, {6608, 42438}, {8043, 27787}, {8298, 9508}, {8632, 20663}, {8641, 30706}, {8674, 35204}, {8678, 34261}, {8702, 13089}, {10472, 23880}, {11124, 14589}, {11517, 15313}, {14077, 15346}, {15347, 30198}, {15348, 30199}

• X₁₀₀ = crosspoint of X_i and X_j for these (i,j): {1, 9282}, {2, 8047}, {6, 9265}, {99, 662}, {101, 34071}, {190, 664}, {643, 36797}, {668, 6335}, {3257, 4618}, {4596, 37212}, {4600, 6632}, {4998, 31615}

• X₁₀₀ = crosssum of X_i and X_j for these (i,j): {1, 1054}, {2, 9263}, {6, 16686}, {10, 22045}, {37, 22323}, {244, 764}, {512, 661}, {514, 3835}, {523, 31946}, {649, 663}, {650, 4162}, {659, 38348}, {667, 22383}, {693, 23807}, {812, 27854}, {891, 14434}, {1015, 8027}, {1635, 3251}, {1646, 14441}, {3120, 21132}, {3122, 21143}, {3259, 6550}, {4107, 4375}, {4979, 4983}, {6363, 6615}, {8677, 42769}, {33917, 39011}

• X₁₀₀ = crossdifference of every pair of points on line {244, 665}

• X₁₀₀ = X_i-lineconjugate of X_j for these (i,j): {1, 244}, {101, 1635}, {292, 3121}, {294, 14936}, {4618, 14421}, {8649, 9283}, {10699, 3675}, {39443, 891}

• X₁₀₀ = barycentric product X_i*X_j for these {i,j}: {1, 190}, {3, 6335}, {4, 1332}, {6, 668}, {7, 644}, {8, 651}, {9, 664}, {10, 662}, {11, 31615}, {12, 4612}, {19, 4561}, {21, 4552}, {31, 1978}, {32, 6386}, {35, 15455}, {36, 36804}, {37, 99}, {40, 44327}, {41, 4572}, {42, 799}, {43, 4598}, {44, 4555}, {45, 4597}, {55, 4554}, {56, 646}, {57, 3699}, {58, 4033}, {59, 4391}, {63, 1897}, {65, 645}, {69, 1783}, {71, 811}, {72, 648}, {74, 42716}, {75, 101}, {76, 692}, {78, 653}, {80, 4585}, {81, 3952}, {82, 4568}, {83, 4553}, {85, 3939}, {86, 1018}, {87, 4595}, {88, 17780}, {89, 4767}, {92, 1331}, {98, 42717}, {102, 42718}, {103, 42719}, {104, 2397}, {105, 42720}, {106, 24004}, {107, 3998}, {108, 345}, {109, 312}, {110, 321}, {111, 42721}, {112, 20336}, {145, 27834}, {162, 306}, {163, 313}, {171, 27805}, {181, 4631}, {192, 932}, {200, 658}, {210, 4573}, {212, 46404}, {213, 670}, {219, 18026}, {220, 4569}, {226, 643}, {228, 6331}, {238, 4562}, {239, 660}, {241, 36802}, {244, 6632}, {249, 4036}, {256, 18047}, {257, 4579}, {261, 21859}, {264, 906}, {269, 6558}, {273, 4587}, {274, 4557}, {278, 4571}, {279, 4578}, {281, 6516}, {286, 4574}, {291, 3570}, {292, 874}, {294, 883}, {304, 8750}, {314, 4559}, {318, 1813}, {322, 36049}, {329, 13138}, {333, 4551}, {335, 3573}, {341, 1461}, {344, 1292}, {346, 934}, {350, 813}, {386, 37218}, {476, 42701}, {480, 36838}, {512, 4601}, {513, 1016}, {514, 765}, {517, 13136}, {518, 666}, {519, 3257}, {521, 46102}, {522, 4564}, {523, 4567}, {524, 5380}, {525, 5379}, {536, 898}, {556, 6733}, {561, 32739}, {598, 3908}, {612, 37215}, {649, 7035}, {650, 4998}, {655, 4511}, {661, 4600}, {667, 31625}, {673, 1026}, {675, 42723}, {677, 30807}, {689, 21814}, {691, 42713}, {693, 1252}, {728, 4626}, {739, 41314}, {740, 4584}, {751, 4482}, {752, 5386}, {754, 5389}, {756, 4610}, {757, 4103}, {758, 47318}, {788, 5388}, {789, 2276}, {812, 5378}, {823, 3682}, {824, 5384}, {825, 33931}, {831, 17289}, {833, 32777}, {835, 28606}, {839, 4261}, {840, 42722}, {869, 37133}, {889, 3230}, {891, 5381}, {892, 21839}, {894, 3903}, {899, 4607}, {900, 5376}, {901, 4358}, {903, 1023}, {905, 15742}, {908, 36037}, {914, 36106}, {918, 5377}, {919, 3263}, {925, 42700}, {927, 3693}, {931, 31993}, {933, 42698}, {958, 32038}, {960, 6648}, {982, 4621}, {983, 33946}, {984, 4586}, {985, 3807}, {1001, 32041}, {1014, 30730}, {1020, 1043}, {1025, 14942}, {1042, 7258}, {1089, 4556}, {1098, 4605}, {1100, 6540}, {1110, 3261}, {1125, 37212}, {1212, 6606}, {1213, 4596}, {1214, 36797}, {1215, 4603}, {1220, 3882}, {1222, 21362}, {1253, 46406}, {1255, 4427}, {1257, 14543}, {1260, 13149}, {1262, 4397}, {1265, 32714}, {1267, 6135}, {1268, 35342}, {1275, 3900}, {1278, 29227}, {1290, 32849}, {1293, 18743}, {1296, 42724}, {1301, 42699}, {1302, 42704}, {1305, 27396}, {1308, 17264}, {1310, 2345}, {1319, 4582}, {1333, 27808}, {1334, 4625}, {1376, 30610}, {1400, 7257}, {1414, 2321}, {1415, 3596}, {1427, 7256}, {1429, 36801}, {1434, 4069}, {1441, 5546}, {1473, 42384}, {1476, 25268}, {1492, 3661}, {1500, 4623}, {1509, 40521}, {1575, 8709}, {1576, 27801}, {1577, 4570}, {1633, 30701}, {1698, 37211}, {1757, 35148}, {1824, 4563}, {1826, 4592}, {1911, 27853}, {1914, 4583}, {1918, 4602}, {1921, 34067}, {1930, 4628}, {1962, 4632}, {1969, 32656}, {1983, 20566}, {1997, 30236}, {2087, 6635}, {2149, 35519}, {2162, 36863}, {2176, 18830}, {2205, 4609}, {2214, 33948}, {2222, 32851}, {2223, 36803}, {2238, 4589}, {2283, 36796}, {2284, 2481}, {2287, 4566}, {2295, 4594}, {2323, 35174}, {2339, 14594}, {2340, 34085}, {2361, 46405}, {2398, 36101}, {2427, 18816}, {2702, 20947}, {2703, 17790}, {2715, 42703}, {2742, 37788}, {2743, 37758}, {2748, 37756}, {2753, 37857}, {2832, 5387}, {3006, 36087}, {3035, 31628}, {3112, 46148}, {3175, 8690}, {3198, 44326}, {3219, 6742}, {3222, 21877}, {3227, 23343}, {3239, 7045}, {3240, 37209}, {3262, 32641}, {3264, 32665}, {3290, 35574}, {3293, 37205}, {3436, 46640}, {3616, 4606}, {3666, 8707}, {3667, 5382}, {3668, 7259}, {3669, 4076}, {3672, 6574}, {3679, 4604}, {3681, 43190}, {3687, 36098}, {3692, 36118}, {3701, 4565}, {3717, 36146}, {3718, 32674}, {3719, 36127}, {3739, 8708}, {3747, 4639}, {3752, 8706}, {3762, 9268}, {3783, 37207}, {3797, 30664}, {3799, 14621}, {3869, 44765}, {3870, 37206}, {3888, 17743}, {3909, 40394}, {3912, 36086}, {3935, 37143}, {3943, 4622}, {3954, 4577}, {3969, 13486}, {3990, 6528}, {3992, 4591}, {3995, 34594}, {4024, 24041}, {4037, 36066}, {4039, 37134}, {4041, 4620}, {4043, 43076}, {4062, 36085}, {4079, 24037}, {4082, 4637}, {4083, 5383}, {4115, 40438}, {4357, 36147}, {4359, 8701}, {4370, 4618}, {4384, 37138}, {4417, 36050}, {4420, 38340}, {4421, 42343}, {4436, 32009}, {4441, 8693}, {4463, 44766}, {4505, 40746}, {4512, 4624}, {4515, 4616}, {4558, 41013}, {4576, 18098}, {4588, 4671}, {4590, 4705}, {4593, 21035}, {4599, 15523}, {4613, 40773}, {4614, 5257}, {4615, 21805}, {4617, 5423}, {4619, 24026}, {4629, 4647}, {4633, 37593}, {4636, 6358}, {4638, 4738}, {4663, 35177}, {4664, 29351}, {4687, 6013}, {4699, 29199}, {4752, 39704}, {4756, 25417}, {4777, 5385}, {4781, 40434}, {4812, 29026}, {4850, 9059}, {4980, 28176}, {4997, 23703}, {5222, 37223}, {5223, 32040}, {5291, 35147}, {5293, 8052}, {5297, 37210}, {5360, 43187}, {5375, 8047}, {5391, 6136}, {5435, 31343}, {5526, 35171}, {5545, 42712}, {6011, 33116}, {6012, 17279}, {6014, 30829}, {6065, 24002}, {6079, 16610}, {6163, 6630}, {6164, 6634}, {6332, 7012}, {6376, 34071}, {6381, 34075}, {6542, 37135}, {6554, 8269}, {6559, 41353}, {6577, 18137}, {6603, 35157}, {6605, 35312}, {6614, 30693}, {6631, 9282}, {6735, 37136}, {6745, 37139}, {6790, 46119}, {7017, 36059}, {7080, 37141}, {7081, 37137}, {7115, 35518}, {7239, 40415}, {7260, 20964}, {8050, 32911}, {8056, 43290}, {8652, 28605}, {8684, 33891}, {8694, 19804}, {8699, 20942}, {9058, 17740}, {9067, 17756}, {9070, 32779}, {9265, 9296}, {9266, 9295}, {9271, 17487}, {9278, 17934}, {9361, 9362}, {11124, 31619}, {11495, 42303}, {11611, 17944}, {13396, 17281}, {13397, 17776}, {14947, 40865}, {15322, 28653}, {15624, 31624}, {16514, 41072}, {16593, 39272}, {16777, 32042}, {16785, 35181}, {17459, 35572}, {17787, 29055}, {17796, 35156}, {17863, 29163}, {17930, 20693}, {18140, 40519}, {18147, 29014}, {19604, 30720}, {19799, 32691}, {20332, 23354}, {20440, 20640}, {20453, 20696}, {20568, 23344}, {20901, 31616}, {20911, 32736}, {20940, 40150}, {21272, 23617}, {21453, 35341}, {21802, 35137}, {21833, 31614}, {21874, 35136}, {21899, 37880}, {22003, 40430}, {22456, 42702}, {23067, 31623}, {23493, 36860}, {23704, 35160}, {23832, 36805}, {23845, 32017}, {23891, 37129}, {23981, 36795}, {23990, 40495}, {24589, 28210}, {25001, 43344}, {25660, 29151}, {26700, 42033}, {26706, 28420}, {26711, 33168}, {26714, 42711}, {28148, 42029}, {28162, 42034}, {28474, 41316}, {28583, 41315}, {28847, 30758}, {30555, 31130}, {30625, 42301}, {30963, 43077}, {31633, 42552}, {32008, 35338}, {32018, 35327}, {32094, 46972}, {32676, 40071}, {32718, 35543}, {32931, 35009}, {33113, 33637}, {33157, 43348}, {35280, 39749}, {35517, 36039}, {36077, 42706}, {36080, 44140}, {37204, 41267}, {38828, 44720}, {40728, 46132}, {41839, 43350}, {44426, 44717}

• X₁₀₀ = barycentric quotient X_i/X_j for these {i,j}: {1, 514}, {2, 693}, {3, 905}, {4, 17924}, {6, 513}, {7, 24002}, {8, 4391}, {9, 522}, {10, 1577}, {11, 40166}, {19, 7649}, {21, 4560}, {22, 16757}, {25, 6591}, {28, 17925}, {31, 649}, {32, 667}, {33, 3064}, {35, 14838}, {36, 3960}, {37, 523}, {38, 16892}, {39, 2530}, {40, 14837}, {41, 663}, {42, 661}, {43, 3835}, {44, 900}, {45, 4777}, {46, 21188}, {48, 1459}, {55, 650}, {56, 3669}, {57, 3676}, {58, 1019}, {59, 651}, {63, 4025}, {65, 7178}, {69, 15413}, {71, 656}, {72, 525}, {75, 3261}, {76, 40495}, {78, 6332}, {81, 7192}, {82, 10566}, {86, 7199}, {88, 6548}, {92, 46107}, {99, 274}, {101, 1}, {104, 2401}, {106, 1022}, {108, 278}, {109, 57}, {110, 81}, {112, 28}, {145, 4462}, {162, 27}, {163, 58}, {165, 7658}, {169, 21185}, {171, 4369}, {172, 4367}, {184, 22383}, {187, 14419}, {190, 75}, {191, 21192}, {192, 20906}, {194, 23807}, {197, 6588}, {198, 6129}, {200, 3239}, {210, 3700}, {212, 652}, {213, 512}, {218, 3309}, {219, 521}, {220, 3900}, {226, 4077}, {228, 647}, {238, 812}, {239, 3766}, {241, 43042}, {244, 6545}, {251, 18108}, {255, 4091}, {259, 6728}, {260, 10492}, {281, 44426}, {284, 3737}, {291, 4444}, {292, 876}, {294, 885}, {306, 14208}, {312, 35519}, {313, 20948}, {318, 46110}, {319, 18160}, {321, 850}, {326, 30805}, {329, 17896}, {333, 18155}, {345, 35518}, {346, 4397}, {354, 21104}, {385, 14296}, {386, 14349}, {391, 4811}, {394, 4131}, {405, 23882}, and many more

• X₁₀₀ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {1, 244, 3315}, {1, 404, 5253}, {1, 750, 37633}, {1, 1054, 244}, {1, 8715, 3871}, {1, 15015, 214}, {1, 25438, 13278}, {1, 25440, 404}, {2, 11, 31272}, {2, 55, 1621}, {2, 149, 11}, {2, 1621, 5284}, {2, 2550, 33108}, {2, 3434, 11680}, {2, 5274, 10584}, {2, 17784, 3434}, {2, 20075, 497}, {2, 20095, 149}, {2, 26007, 31226}, {2, 26073, 24988}, {2, 26795, 27134}, {2, 26846, 27190}, {2, 27134, 28743}, {2, 33110, 2886}, {2, 34607, 34611}, {3, 8, 2975}, {3, 104, 38693}, {3, 2932, 17100}, {3, 2975, 5303}, {3, 5687, 8}, {3, 12645, 32153}, {3, 12773, 38602}, {3, 32141, 11491}, {3, 33814, 34474}, {3, 38665, 38669}, {3, 45145, 47045}, {4, 5552, 11681}, {6, 1979, 1977}, {6, 37540, 17126}, {8, 17100, 104}, {8, 17740, 33089}, {9, 35445, 35258}, {10, 21, 5260}, {10, 35, 21}, {10, 21098, 21054}, {10, 32917, 5235}, {11, 149, 10707}, {11, 3035, 2}, {11, 6174, 3035}, {11, 31235, 6667}, {20, 7080, 3436}, {31, 43, 32911}, {35, 80, 10058}, {36, 7972, 10074}, {37, 21899, 21833}, {40, 78, 3869}, {40, 6796, 411}, {42, 171, 81}, {43, 3550, 31}, {46, 3811, 3868}, {55, 1376, 2}, {55, 4413, 1001}, {55, 4423, 4428}, {55, 11502, 497}, {55, 36497, 4972}, {56, 3913, 145}, {57, 3158, 3870}, {57, 3870, 3873}, {57, 37736, 5083}, {57, 41553, 14151}, {63, 200, 3681}, {65, 34772, 34195}, {65, 41541, 12739}, {75, 20940, 20901}, {88, 3315, 244}, {101, 1018, 644}, {101, 4752, 1023}, {104, 34474, 3}, {109, 3939, 1331}, {109, 4551, 651}, {119, 11248, 12775}, {119, 13199, 10724}, {145, 4188, 56}, {149, 3035, 31272}, {165, 200, 63}, {165, 1768, 46684}, {165, 5531, 1768}, {190, 3699, 3952}, {190, 3952, 4756}, {190, 17780, 4767}, {190, 43290, 3699}, {197, 37577, 22}, {198, 346, 38869}, {200, 1768, 46685}, {210, 4640, 3219}, {214, 5541, 1320}, {214, 8715, 10087}, {214, 9324, 14193}, {228, 32932, 11688}, {230, 21956, 17737}, {238, 899, 37680}, and many more

Notes

Let L_A be the reflection of the line X₁X₃ in line BC, and define L_B and L_C cyclically. Let A' = L_B∩L_C, B' = L_C∩L_A, C' = L_A∩L_B. The lines AA', BB', CC' concur in X₁₀₀. (Randy Hutson, 9/23/2011)

Let I_a be the reflection of X₁ in the perpendicular bisector of BC, and define I_b and I_c cyclically; then X₁₀₀ = X₃₆-of-I_aI_bI_c. Also, let P be a point on line X₄X₈ other than X₄. Let A' be the reflection of P in BC, and define B' and C' cyclically. The circumcircles of AB'C', BC'A', and CA'B' concur at X₁₀₀. (Randy Hutson, 9/5/2015)

Let J_aJ_bJ_c be the excentral triangle. The Euler lines of triangles BCJ_a, CAJ_b, ABJ_c concur in X₁₀₀. (Randy Hutson, June 27, 2018)