X(69262) = EULER LINE INTERCEPT OF X(51)X(53415)
Barycentrics 2 a^6-a^4 b^2-2 a^2 b^4+b^6-a^4 c^2+12 a^2 b^2 c^2-b^4 c^2-2 a^2 c^4-b^2 c^4+c^6 : :See Gabi Cuc Cucoanes and Francisco Javier García Capitán, euclid 8572.
X(69262) lies on these lines: {2, 3}, {51, 53415}, {110, 45298}, {125, 64605}, {141, 61645}, {154, 54012}, {184, 59699}, {251, 5913}, {373, 23292}, {974, 6053}, {1196, 5355}, {1993, 61657}, {3167, 63084}, {3589, 6467}, {3819, 32269}, {3917, 47582}, {4319, 5432}, {4320, 5433}, {5422, 59553}, {5651, 13567}, {5892, 51425}, {5943, 11064}, {5972, 6688}, {6090, 11433}, {6329, 61659}, {6696, 30443}, {6716, 67281}, {7917, 45201}, {9306, 11245}, {9777, 37669}, {9924, 23327}, {10192, 43650}, {10278, 47173}, {10601, 59543}, {11402, 18928}, {11451, 18583}, {11793, 15739}, {13857, 51130}, {14826, 26869}, {15018, 61655}, {15043, 61607}, {15066, 41588}, {15448, 22352}, {15873, 43652}, {16187, 61646}, {17811, 61506}, {18358, 23293}, {18914, 43598}, {21243, 35283}, {29181, 44106}, {34750, 58434}, {35264, 48906}, {37480, 44935}, {39562, 51732}, {40112, 53863}, {41670, 58480}, {43620, 47297}, {44082, 44882}, {47260, 66122}, {51185, 63650}, {51360, 66531}, {58447, 63632}, {59208, 59558}, {59659, 64854}, {61676, 62375}
X(69262) = midpoint of X(125) and X(64605)
X(69262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5972, 6688, 37649}, {10601, 59543, 61690}
X(69263) = X(1)X(3)∩X(12)X(3742)
Barycentrics a*(a + b - c)*(a - b + c)*(a^3*(b + c) - a*(b + c)^3 + (b^2 - c^2)^2 - a^2*(b^2 - 4*b*c + c^2)) : :X(69263) = 3*X[354]+X[37605]
See Gabi Cuc Cucoanes, David Nguyen and Ercole Suppa, euclid 8575 and euclid 8577.
X(69263) lies on these lines: {1, 3}, {2, 58585}, {11, 12675}, {12, 3742}, {201, 17449}, {388, 64149}, {442, 41556}, {497, 7702}, {499, 37713}, {518, 5433}, {950, 18240}, {960, 31157}, {1071, 11376}, {1125, 5083}, {1279, 1399}, {1317, 5836}, {1357, 58597}, {1358, 58596}, {1359, 58599}, {1361, 58600}, {1362, 58592}, {1364, 58593}, {1393, 4322}, {1404, 61650}, {1457, 46190}, {1463, 58627}, {1469, 58562}, {1788, 3889}, {1858, 12005}, {1898, 50443}, {1935, 29820}, {3022, 58594}, {3023, 58589}, {3024, 58582}, {3027, 58590}, {3028, 58601}, {3296, 64747}, {3306, 11501}, {3320, 58603}, {3324, 58598}, {3325, 58602}, {3555, 24914}, {3616, 58578}, {3649, 58568}, {3697, 26364}, {3740, 7294}, {3753, 37738}, {3812, 10944}, {3873, 7288}, {3881, 3911}, {3892, 4848}, {3918, 41558}, {4067, 41389}, {5249, 10957}, {5252, 5439}, {5434, 58560}, {5552, 24477}, {5603, 64704}, {5777, 17660}, {5883, 63987}, {5901, 67970}, {6284, 58567}, {6285, 58579}, {6797, 32900}, {7354, 13374}, {7743, 26201}, {8581, 58564}, {9850, 11237}, {9956, 20118}, {10039, 12832}, {10106, 58565}, {10167, 12701}, {10391, 37722}, {10527, 41537}, {10528, 64151}, {10896, 12680}, {10956, 24982}, {11375, 17625}, {12573, 58607}, {12608, 41561}, {12672, 18260}, {12688, 58588}, {12736, 13607}, {12739, 17614}, {12953, 63432}, {13369, 30384}, {14151, 17531}, {15172, 24465}, {15950, 66250}, {17626, 18961}, {18247, 44847}, {18970, 58580}, {18976, 58587}, {18977, 58586}, {18982, 58584}, {18990, 58561}, {20418, 67919}, {22759, 54392}, {23708, 40263}, {24816, 58618}, {26481, 51706}, {26741, 50587}, {31937, 37735}, {33812, 64745}, {34790, 38411}, {34791, 40663}, {37740, 67937}, {38053, 60943}, {39897, 58581}, {45288, 58679}, {54377, 54385}, {58563, 60883}, {61663, 64124}, {64160, 67051}
X(69263) = pole of line {650,21103} with respect to Hofstadter inellipse
X(69263) = pole of line {56,5082} with respect to dual conic of Moses-Feuerbach circumconic
X(69263) = X(21)-beth conjugate of X(33596)
X(69263) = X(10018)-of-intouch triangle
X(69263) = X(37605)-of-2nd anti-circumperp-tangential triangle
X(69263) = intersection,other than A,B,C,of the circumconics: {{A,B,C,X(4),X(37622)}}, {{A,B,C,X(46),X(2191)}}, {{A,B,C,X(104),X(33596)}}, {{A,B,C,X(5553),X(10679)}} ,{{A,B,C,X(5708),X(13476)}}, {{A,B,C,X(10965),X(30513)}}, {{A,B,C,X(37579),X(56155)}
X(69263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 36, 33596}, {1, 46, 37622}, {1, 3359, 10965}, {1, 37534, 55}, {1, 59333, 26358}, {354, 2646, 50196}, {942, 1319, 64721}, {1319, 13751, 942}, {1385, 5570, 64043}, {1420, 18398, 65}, {3660, 5045, 65}, {3873, 7288, 41538}, {12005, 44675, 1858}, {16193, 58576, 354}, {17609, 37566, 2099}, {34489, 51816, 26437}, {50196, 66599, 2646}
X(69264) = EULER LINE INTERCEPT OF X(141)X(1568)
Barycentrics 3*a^8*(b^2 + c^2) - 8*a^4*b^2*c^2*(b^2 + c^2) - 3*(b^2 - c^2)^4*(b^2 + c^2) + a^6*(-6*b^4 + 4*b^2*c^2 - 6*c^4) + 2*a^2*(b^2 - c^2)^2*(3*b^4 + 2*b^2*c^2 + 3*c^4) : :X(69264) = X[343]+2*X[18388], 2*X[5480]+X[16789], X[5907]+2*X[58480], 2*X[7687]+X[16165], 5*X[8227]-2*X[51718], 4*X[9729]-X[67921], X[19127]+2*X[67865], 2*X[19925]+X[51692], 5*X[64854]-2*X[66713]
As a point on the Euler line, X(69264) has Shinagawa coefficients: {1/3 (-2 e + 3 (e + f)), f}
See Gabi Cuc Cucoanes and David Nguyen, euclid 8576.
X(69264) lies on these lines: {2, 3}, {141, 1568}, {343, 18388}, {1092, 66712}, {1209, 22660}, {2781, 36518}, {3574, 21969}, {3614, 66719}, {5480, 16789}, {5907, 58480}, {6000, 45303}, {6247, 64179}, {7173, 66724}, {7592, 61544}, {7687, 16165}, {7699, 48876}, {8227, 51718}, {9722, 14836}, {9729, 67921}, {10592, 66610}, {10593, 66593}, {11245, 14852}, {12233, 14831}, {13394, 18400}, {13565, 67869}, {13567, 16226}, {13599, 66732}, {14157, 39884}, {14389, 50435}, {14568, 66449}, {14644, 38110}, {15030, 41580}, {18390, 37649}, {19127, 67865}, {19925, 51692}, {20299, 66758}, {20300, 51737}, {21357, 66739}, {21849, 45089}, {23300, 43273}, {23332, 64100}, {25739, 48906}, {31166, 47353}, {31804, 58922}, {33547, 68316}, {34774, 47354}, {35264, 61606}, {37514, 66716}, {38042, 66741}, {38136, 66750}, {38443, 64037}, {43572, 59553}, {44665, 61690}, {45298, 61701}, {60121, 60241}, {64854, 66713}
X(69264) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 54994}, {2, 381, 34664}, {2, 3545, 16072}, {2, 15078, 140}, {4, 6676, 44239}, {4, 7569, 63679}, {5, 1368, 7577}, {5, 1596, 5133}, {5, 6823, 1594}, {5, 10024, 235}, {5, 13160, 7399}, {5, 15760, 427}, {5, 15761, 7403}, {22, 3091, 66728}, {378, 3090, 64852}, {381, 7540, 3845}, {381, 9909, 4}, {1312, 1313, 47339}, {2043, 2044, 7507}, {6676, 9909, 44210}, {7403, 15761, 1906}, {7547, 7558, 12362}, {7552, 7576, 10154}, {14788, 16868, 5}, {15765, 18585, 12605}
X(69265) = EULER LINE INTERCEPT OF X(14)X(10634)
Barycentrics -((a^2 - b^2 - c^2)*(a^8 - 6*a^4*b^2*c^2 - (b^2 - c^2)^4 - 2*a^6*(b^2 + c^2) + 2*a^2*(b^2 - c^2)^2*(b^2 + c^2))) : :X(69265) = 2*X[5]+X[22], 4*X[140]-X[378], X[52]-4*X[58480], X[265]+2*X[16165], 2*X[343]+X[18445], X[355]+2*X[51692], 2*X[1216]+X[54384], X[1351]+2*X[16789], X[1352]+2*X[19127], X[1993]-4*X[61619], X[11442]+2*X[61752], X[11456]+2*X[67926], X[11605]-4*X[61586], X[13352]-4*X[58447], X[14983]+2*X[38624], 2*X[18388]+X[37478], X[19149]+2*X[34177], 5*X[31267]+X[54146], 5*X[40686]+X[66723]
As a point on the Euler line, X(69265) has Shinagawa coefficients: {1/3 (-((5 e)/4) + 2 (e + f)), -(e/4)}
See Gabi Cuc Cucoanes and David Nguyen, euclid 8576 .
X(69265) lies on these lines:{2, 3}, {13, 10635}, {14, 10634}, {49, 63649}, {52, 58480}, {69, 50461}, {127, 7865}, {141, 51425}, {182, 63735}, {184, 539}, {265, 16165}, {343, 18445}, {355, 51692}, {498, 66719}, {499, 66724}, {542, 19131}, {1060, 3582}, {1062, 3584}, {1092, 44516}, {1147, 64064}, {1209, 6759}, {1216, 54384}, {1351, 16789}, {1352, 10540}, {1879, 10979}, {1993, 61619}, {2781, 14643}, {2980, 18437}, {3098, 51392}, {3519, 9936}, {3796, 14852}, {4550, 51403}, {5050, 45967}, {5449, 10984}, {5476, 9967}, {5654, 23039}, {5655, 7723}, {5891, 41580}, {5892, 61645}, {6193, 9704}, {6243, 12606}, {6288, 9833}, {6515, 15087}, {6689, 11424}, {7592, 63734}, {7603, 22052}, {7689, 64179}, {7736, 22121}, {7737, 18472}, {7749, 19220}, {7753, 10316}, {9019, 14561}, {9300, 22120}, {9730, 61646}, {10056, 18455}, {10072, 18447}, {10263, 12363}, {10653, 18470}, {10654, 18468}, {10897, 35823}, {10898, 35822}, {11178, 19126}, {11179, 19129}, {11433, 15037}, {11442, 61752}, {11456, 67926}, {11457, 34826}, {11515, 37835}, {11516, 37832}, {11605, 61586}, {12161, 41628}, {13340, 61711}, {13352, 58447}, {13353, 39571}, {13394, 44665}, {13557, 37893}, {13754, 61644}, {14389, 39522}, {14627, 64048}, {14845, 38317}, {14855, 23329}, {14983, 38624}, {14993, 43089}, {15038, 63085}, {15068, 37636}, {15080, 25739}, {15151, 20126}, {15362, 38064}, {16226, 32225}, {17508, 23515}, {18388, 37478}, {18390, 37513}, {18435, 67890}, {18438, 20423}, {18911, 63839}, {18951, 43845}, {18952, 61134}, {19149, 34177}, {24301, 28204}, {25043, 46025}, {25406, 38724}, {25738, 64049}, {25740, 50955}, {26881, 41171}, {26937, 67921}, {30522, 34513}, {31267, 54146}, {32140, 52525}, {32348, 61749}, {32885, 40680}, {35268, 44407}, {36753, 41587}, {37470, 44673}, {37495, 66712}, {37511, 50977}, {37515, 43817}, {38224, 57314}, {38796, 57357}, {40686, 66723}, {43608, 66715}, {43652, 43839}, {52520, 64689}, {57305, 57346}, {57307, 57380}, {57311, 57366}, {57344, 57365}, {57355, 57379}, {59648, 61680}, {61715, 62187}, {64036, 67878}, {66716, 67902}
X(69265) = complement of polar conjugate of X(62925)
X(69265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 60763}, {2, 376, 18281}, {2, 381, 14787}, {2, 7552, 10201}, {2, 10304, 65085}, {3, 381, 67337}, {3, 1656, 37452}, {3, 3549, 6639}, {3, 6639, 6640}, {3, 10024, 18404}, {3, 10254, 18531}, {3, 10255, 6643}, {5, 22, 31723}, {5, 428, 381}, {5, 7525, 37444}, {5, 17714, 4}, {381, 3534, 34725}, {381, 7517, 428}, {381, 9909, 7540}, {403, 7495, 7514}, {427, 16618, 12083}, {465, 466, 37068}, {547, 10691, 11585}, {547, 16197, 10691}, {1598, 1656, 50137}, {1656, 12083, 427}, {2043, 2044, 18569}, {2937, 7517, 17714}, {3089, 14786, 3851}, {3090, 7391, 39504}, {3547, 3549, 3}, {3547, 7558, 34002}, {3548, 7400, 3}, {5654, 43653, 23039}, {6636, 7577, 14791}, {6676, 7502, 47525}, {6676, 15760, 3}, {6823, 7542, 3}, {7399, 13383, 7506}, {7493, 18420, 2070}, {7494, 18531, 3}, {7502, 17714, 22}, {7568, 15761, 7503}, {10024, 18404, 63671}, {10127, 13383, 62978}, {11585, 16197, 3}, {14784, 14785, 52295}, {15765, 18585, 7503}, {18586, 18587, 5576}
X(69266) = EULER LINE INTERCEPT OF X(1350)X(31166)
Barycentrics -8*a^10 + 15*a^8*(b^2 + c^2) + (b^2 - c^2)^4*(b^2 + c^2) + 2*a^6*(b^2 + c^2)^2 + 2*a^2*(b^2 - c^2)^2*(3*b^4 + 2*b^2*c^2 + 3*c^4) - 8*a^4*(2*b^6 + b^4*c^2 + b^2*c^4 + 2*c^6) : :X(69266) = X[20]+5*X[22], 2*X[6053]-5*X[16165]
As a point on the Euler line, X(69266) has Shinagawa coefficients: {1/3 (-4 e + 7 (e + f)), e - 3 (e + f)}
See Gabi Cuc Cucoanes and David Nguyen, euclid 8576 .
X(69266) lies on these lines: {2, 3}, {1350, 31166}, {6053, 16165}, {12220, 50979}, {13345, 14836}, {16226, 32191}, {31804, 41628}, {36987, 41580}, {37486, 63649}, {41464, 48906}, {43574, 48874}, {45186, 65094}, {46728, 64062}, {48881, 51394}, {50824, 64039}
X(69266) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {24, 376, 10691}, {376, 9909, 34664}, {550, 2937, 235}
