X3847

X1420com(3rd EULER TRIANGLE)

< 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) { 8, 11 }: Central Line L(8, 11) { 5, 515 }: Central Line L(5, 515) { 1698, 1706 }: Central Line L(1698, 1706) { 529, 3086 }: Central Line L(529, 3086) { 12, 3622 }: Central Line L(12, 3622) { 496, 3244 }: Central Line L(496, 3244) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_1698 = INSIMILICENTER(BEVAN CIRCLE, NINE-POINTCIRCLE) (0.5306, 0.1933) X_1706 = EXSIMILICENTER(BEVAN CIRCLE, SPIEKER CIRCLE) (0.5323, 0.2107) X_529 = DIRECTION OF VECTOR AX + BX + CX, where X = X(12) (0.8589, 0.6909) X_3086 = INTERSECTION OF LINES X(1)X(2) AND X(4)X(11) (0.6456, 0.3060) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_3622 = H(X(8); M,-1/2) (0.5569, 0.2190) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_3244 = REFLECTION OF X(10) IN X(1) (0.6224, 0.2833) X_3847 = com(3rd EULER TRIANGLE) (0.5237, 0.1197) A B C X8 X11 X5 X515 X1698 X1706 X529 X3086 X12 X3622 X496 X3244 X3847 (a, b, c) = (5, 6, 7) | AB = 1

X3847 (X1420com(3rd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \((b + c - a)(3b^{3} + 3c^{3} + 3ab^{2} + 3ac^{2} - 3b^{2}c - 3bc^{2} - 4abc) : :\)
Search Value (6, 9, 13): \(3.351347607495\)
▸ Incident Central Lines38 lines

{2, 5217}, {3, 6667}, {4, 6691}, {5, 515}, {8, 11}, {10, 3829}, {12, 3622}, {55, 6931}, {56, 5187}, {496, 3244}, {528, 9669}, {529, 3086}, {550, 6681}, {958, 6919}, {1001, 3090}, {1210, 5087}, {1479, 3035}, {1656, 6690}, {1698, 1706}, {2478, 4999}, {3614, 3616}, {3628, 5248}, {3812, 3817}, {3820, 4691}, {3838, 9843}, {3878, 6797}, {3913, 5274}, {4189, 7294}, {4423, 6933}, {5046, 5303}, {5057, 7098}, {5690, 6702}, {5842, 6959}, {5880, 6831}, {6253, 6979}, {6856, 8167}, {6882, 7681}, {6971, 7680}