X3782

X2887com[T(-bc, c²)]

X3782 = pole of de Longchamps line wrt incircle
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 30 }: Central Line L(1, 30) { 2, 45 }: Central Line L(2, 45) { 141, 321 }: Central Line L(141, 321) { 306, 536 }: Central Line L(306, 536) { 7, 940 }: Central Line L(7, 940) { 11, 982 }: Central Line L(11, 982) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_2 = CENTROID (0.5374, 0.2000) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727) X_7 = GERGONNE POINT (0.5903, 0.2769) X_940 = POINT ALDEBARAN (0.5757, 0.2411) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) X_3782 = com[T(-bc, c2)] (0.5557, 0.1921) A B C X1 X30 X2 X45 X141 X321 X306 X536 X7 X940 X11 X982 X3782 (a, b, c) = (5, 6, 7) | AB = 1

X3782 (X2887com[T(-bc, c²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b^{3} + c^{3} + ab^{2} + ac^{2} - b^{2}c - c^{2}b)\)
Search Value (6, 9, 13): \(2.324757003671\)
▸ Incident Central Lines21 lines

{1, 30}, {2, 45}, {5, 3670}, {7, 940}, {11, 982}, {12, 986}, {38, 2886}, {75, 1211}, {141, 321}, {210, 1738}, {226, 1465}, {306, 536}, {312, 3662}, {320, 1999}, {516, 3744}, {524, 3187}, {726, 2887}, {908, 3752}, {1266, 3687}, {1699, 3677}, {3242, 3434}

▸ Functional Relations3 relations