X3947

X3601com[INVERSE(n(INCENTRAL 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) { 10, 12 }: Central Line L(10, 12) { 495, 946 }: Central Line L(495, 946) { 142, 1329 }: Central Line L(142, 1329) { 388, 1125 }: Central Line L(388, 1125) { 7, 1698 }: Central Line L(7, 1698) { 551, 1388 }: Central Line L(551, 1388) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_495 = JOHNSON MIDPOINT (0.5666, 0.2382) X_946 = MIDPOINT OF X(1) AND X(4) (0.5918, 0.3145) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4903, 0.1280) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1698 = INSIMILICENTER(BEVAN CIRCLE, NINE-POINTCIRCLE) (0.5306, 0.1933) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_1388 = POINT ANCHA (0.4835, 0.0718) X_3947 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.5700, 0.2485) A B C X10 X12 X495 X946 X142 X1329 X388 X1125 X7 X1698 X551 X1388 X3947 (a, b, c) = (5, 6, 7) | AB = 1

X3947 (X3601com[INVERSE(n(INCENTRAL TRIANGLE))]) 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 \(f(a,b,c) = (b + c)(a + b - c)(a - b + c)(a + 3b + 3c)\)
Search Value (6, 9, 13): \(1.184292586244\)
▸ Incident Central Lines21 lines

{1, 3091}, {2, 3361}, {7, 1698}, {10, 12}, {57, 3634}, {142, 1329}, {227, 3743}, {354, 3614}, {388, 1125}, {495, 946}, {516, 3085}, {519, 3485}, {551, 1388}, {1089, 1441}, {1478, 3612}, {1770, 3584}, {2099, 3625}, {3090, 3333}, {3340, 3626}, {3476, 3636}, {3600, 3624}