X(72413) = X(1296)X(66615)∩X(8705)X(10098)
Barycentrics a^2*(2*a^10+2*b^10-b^8*c^2-11*b^6*c^4+5*b^4*c^6+9*b^2*c^8-4*c^10-a^8*(8*b^2+c^2)+a^6*(6*b^4+8*b^2*c^2-11*c^4)+a^4*(6*b^6-14*b^4*c^2+7*b^2*c^4+5*c^6)+a^2*(-8*b^8+8*b^6*c^2+7*b^4*c^4-16*b^2*c^6+9*c^8))*(2*a^10-4*b^10+9*b^8*c^2+5*b^6*c^4-11*b^4*c^6-b^2*c^8+2*c^10-a^8*(b^2+8*c^2)+a^6*(-11*b^4+8*b^2*c^2+6*c^4)+a^4*(5*b^6+7*b^4*c^2-14*b^2*c^4+6*c^6)+a^2*(9*b^8-16*b^6*c^2+7*b^4*c^4+8*b^2*c^6-8*c^8)) : :Antreas Hatzipolakis and Ivan Pavlov, euclid 9521.
X(72413) lies on the circumcircle and these lines: {1296, 66615}, {8705, 10098}, {11568, 55135}, {23699, 67731}
X(72413) = intersection, other than A, B, C, of circumconics {{A, B, C, X(64), X(30488)}}, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(8705), X(43720)}}, {{A, B, C, X(54998), X(70363)}}
X(72414) = X(4)X(575)∩X(381)X(13378)
Barycentrics 4*a^10-3*a^8*(b^2+c^2)+a^6*(-25*b^4+14*b^2*c^2-25*c^4)+a^2*(b^2-c^2)^2*(9*b^4-2*b^2*c^2+9*c^4)-2*(b^2-c^2)^2*(3*b^6-5*b^4*c^2-5*b^2*c^4+3*c^6)+a^4*(21*b^6-29*b^4*c^2-29*b^2*c^4+21*c^6) : :X(72414) = 7*X[3832]+2*X[47590], -5*X[3843]+2*X[46673], -11*X[3855]+2*X[47592]
Antreas Hatzipolakis and Ivan Pavlov, euclid 9521.
X(72414) lies on these lines: {4, 575}, {381, 13378}, {524, 14866}, {1531, 13860}, {3832, 47590}, {3843, 46673}, {3845, 14856}, {3855, 47592}, {13168, 48895}, {40261, 58883}
X(72414) = midpoint of X(i) and X(j) for these {i,j}: {13378, 50730}
X(72414) = reflection of X(i) in X(j) for these {i,j}: {13378, 381}
X(72414) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 47589, 31748}
X(72415) = X(4)X(263)∩X(115)X(512)
Barycentrics a^2*(b-c)^2*(b+c)^2*(a^4+4*b^2*c^2-a^2*(b^2+c^2)) : :X(72415) = X[5167]+2*X[53419], 2*X[6321]+X[65748], -X[6785]+3*X[14639], -3*X[9166]+X[67630], X[9879]+3*X[14041], X[31848]+2*X[38734], -3*X[41135]+X[46303], -4*X[43291]+X[67540], -X[47287]+4*X[59571]
Antreas Hatzipolakis and Ivan Pavlov, euclid 9521.
X(72415) lies on these lines: {4, 263}, {30, 47638}, {51, 3845}, {115, 512}, {125, 2780}, {230, 32442}, {373, 3363}, {511, 8352}, {526, 16278}, {543, 6786}, {671, 6787}, {1084, 52625}, {1514, IsogConj(X54976)}, {2387, 39563}, {2869, 8754}, {3111, 5461}, {3124, 58754}, {3819, 66349}, {3917, 66392}, {4173, 44518}, {5077, 12525}, {5167, 53419}, {5650, 20326}, {6310, 33229}, {6321, 65748}, {6785, 14639}, {7615, 61689}, {7833, 67151}, {7841, 52658}, {8370, 34236}, {8597, 11673}, {9044, 64258}, {9166, 67630}, {9879, 14041}, {14135, 33249}, {22112, 45722}, {31848, 38734}, {32967, 58211}, {32984, 35687}, {33017, 34095}, {34417, 45723}, {34980, 41221}, {39691, 42068}, {40951, 69141}, {41135, 46303}, {43291, 67540}, {47287, 59571}, {56957, 69100}
X(72415) = midpoint of X(i) and X(j) for these {i,j}: {671, 6787}, {8597, 11673}, {9879, 33873}
X(72415) = reflection of X(i) in X(j) for these {i,j}: {3111, 5461}, {6784, 115}, {6786, 67215}, {32442, 230}, {65751, 6784}
X(72415) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(6784)}}, {{A, B, C, X(263), X(65751)}}, {{A, B, C, X(52038), X(58754)}}
X(72415) = perspector of circumconic {{A, B, C, X(2395), X(31174)}}
X(72415) = pole of line {877, IsogConj(X6037)} with respect to the polar circle
X(72415) = pole of line {1499, 68786} with respect to the Jerabek hyperbola
X(72415) = pole of line {804, 68778} with respect to the Kiepert hyperbola
X(72415) = lies on inconics with perspector: X(5651)
X(72415) = barycentric product X(i)*X(j) for these (i, j): {115, 5651}, {3124, 69380}, {4079, 69390}, {31174, 512}
X(72415) = barycentric quotient X(i)/X(j) for these (i, j): {5651, 4590}, {31174, 670}, {69380, 34537}, {69390, 52612}
X(72415) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {115, 512, 6784}, {512, 6784, 65751}, {543, 67215, 6786}, {671, 6787, 34383}, {9879, 14041, 33873}, {9879, 33873, 55005}
X(72416) = X(5)X(113)∩X(114)X(325)
Barycentrics a^2*(-b^4-c^4+a^2*(b^2+c^2))*(4*b^2*c^2*(b^2-c^2)^2+a^6*(b^2+c^2)-2*a^4*(b^4-3*b^2*c^2+c^4)+a^2*(b^6-3*b^4*c^2-3*b^2*c^4+c^6)) : :X(72416) = -X[9862]+4*X[64490], -4*X[20399]+X[67352], -3*X[23234]+X[67639], X[31850]+2*X[38745]
Antreas Hatzipolakis and Ivan Pavlov, euclid 9521.
X(72416) lies on these lines: {4, 6331}, {5, 113}, {114, 325}, {147, 46303}, {446, 9155}, {542, 6784}, {568, 27374}, {1352, 61689}, {2682, 14915}, {2794, 3111}, {5025, 15072}, {5640, 13862}, {5650, 37451}, {6000, 33228}, {6033, 41330}, {6054, 6785}, {6656, 16836}, {7418, 36213}, {9862, 64490}, {11459, 37446}, {13240, 47353}, {23234, 67639}, {31850, 38745}, {33184, 64100}
X(72416) = midpoint of X(i) and X(j) for these {i,j}: {147, 46303}, {6033, 41330}, {6054, 6785}
X(72416) = reflection of X(i) in X(j) for these {i,j}: {6784, 67220}, {6786, 114}, {65748, 6786}, {65751, 41330}
X(72416) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(6786)}}, {{A, B, C, X(325), X(43917)}}, {{A, B, C, X(6393), X(34087)}}
X(72416) = pole of line {888, 53149} with respect to the polar circle
X(72416) = pole of line {2023, 3003} with respect to the Kiepert hyperbola
X(72416) = pole of line {1976, 43574} with respect to the Stammler hyperbola
X(72416) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {114, 511, 6786}, {511, 6786, 65748}, {6054, 6785, 34383}
X(72417) = X(4)X(6335)∩X(119)X(517)
Barycentrics a*(-2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c))*(-2*a^4*b*c+a^5*(b+c)+4*b*c*(b^2-c^2)^2-2*a^2*b*c*(b^2+c^2)+a*(b-c)^2*(b^3-3*b^2*c-3*b*c^2+c^3)-2*a^3*(b^3-2*b^2*c-2*b*c^2+c^3)) : :X(72417) = X[3937]+2*X[10742], -X[12248]+4*X[64489], -4*X[20400]+X[67420], X[31849]+2*X[38757], -X[38389]+4*X[67864]
Antreas Hatzipolakis and Ivan Pavlov, euclid 9521.
X(72417) lies on these lines: {4, 6335}, {119, 517}, {125, 30444}, {2801, 25436}, {2807, 5587}, {2810, 10711}, {2818, 61729}, {2821, 14431}, {2829, 34583}, {3937, 10742}, {12248, 64489}, {18542, 23154}, {20400, 67420}, {29353, 68548}, {31849, 38757}, {38389, 67864}, {42448, 45631}, {53548, 56416}, {61674, 67216}
X(72417) = midpoint of X(i) and X(j) for these {i,j}: {10711, 61731}
X(72417) = reflection of X(i) in X(j) for these {i,j}: {61672, 119}, {61674, 67216}, {65743, 61672}
X(72417) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(61672)}}, {{A, B, C, X(36798), X(51379)}}, {{A, B, C, X(51367), X(60288)}}
X(72417) = pole of line {891, 43933} with respect to the polar circle
X(72417) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {119, 517, 61672}, {517, 61672, 65743}, {10711, 61731, 2810}
X(72418) = X(4)X(145)∩X(118)X(516)
Barycentrics (2*a^3-a^2*(b+c)-(b-c)^2*(b+c))*(2*a^5-a^4*(b+c)-4*a*(b^2-c^2)^2+2*a^3*(b^2+c^2)+a^2*(-4*b^3+2*b^2*c+2*b*c^2-4*c^3)+(b-c)^2*(5*b^3+9*b^2*c+9*b*c^2+5*c^3)) : :X(72418) = X[152]+2*X[68552], X[1565]+2*X[10741], X[10727]+2*X[17044], X[31851]+2*X[38769]
Antreas Hatzipolakis and Ivan Pavlov, euclid 9521.
X(72418) lies on these lines: {4, 145}, {118, 516}, {152, 68552}, {1565, 10741}, {5845, 10710}, {10727, 17044}, {28182, 36028}, {31851, 38769}
X(72418) = reflection of X(i) in X(j) for these {i,j}: {51406, 118}, {65745, 51406}
X(72418) = perspector of circumconic {{A, B, C, X(2398), X(65336)}}
X(72418) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(51406)}}, {{A, B, C, X(516), X(6336)}}, {{A, B, C, X(910), X(36125)}}, {{A, B, C, X(1320), X(51376)}}, {{A, B, C, X(4080), X(51366)}}, {{A, B, C, X(63851), X(65745)}}
X(72418) = pole of line {900, 53150} with respect to the polar circle
X(72418) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {118, 516, 51406}, {516, 51406, 65745}, {1530, 1541, 1536}
X(72419) = X(2)X(11166)∩X(599)X(5094)
Barycentrics (a^2-2*(b^2+c^2))*(4*a^4-5*b^4+14*b^2*c^2-5*c^4+5*a^2*(b^2+c^2)) : :X(72419) = -4*X[31606]+X[31748], X[34795]+2*X[47589]
Antreas Hatzipolakis and Ivan Pavlov, euclid 9521.
X(72419) lies on these lines: {2, 11166}, {125, 11168}, {141, 12036}, {524, 10162}, {599, 5094}, {1992, 11056}, {3849, 13378}, {3906, 8371}, {5650, 17430}, {6791, 16509}, {8288, 15810}, {9829, 11645}, {9830, 10163}, {20582, 30749}, {31606, 31748}, {34795, 47589}, {44569, 59197}, {51389, 59780}
X(72419) = reflection of X(i) in X(j) for these {i,j}: {13378, 34512}, {30516, 2}, {50729, 30516}
X(72419) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3363), X(5094)}}, {{A, B, C, X(8541), X(11166)}}
X(72419) = pole of line {47352, 47587} with respect to the orthocentroidal circle
X(72419) = pole of line {43697, IsogConj(X3363)} with respect to the Stammler hyperbola
X(72419) = pole of line {8704, 31173} with respect to the Steiner inellipse
X(72419) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3849, 34512, 13378}
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