X3993

X984com[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, 37 }: Central Line L(10, 37) { 1, 87 }: Central Line L(1, 87) { 536, 551 }: Central Line L(536, 551) { 75, 1125 }: Central Line L(75, 1125) { 519, 751 }: Central Line L(519, 751) { 226, 1365 }: Central Line L(226, 1365) 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_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1 = INCENTER (0.5714, 0.2333) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_751 = ISOGONAL CONJUGATE OF X(750) (0.5754, 0.2311) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_1365 = BRISSE TRANSFORM OF X(110) (0.7771, 0.1231) X_3993 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.5931, 0.2484) A B C X10 X37 X1 X87 X536 X551 X75 X1125 X519 X751 X226 X1365 X3993 (a, b, c) = (5, 6, 7) | AB = 1

X3993 (X984com[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 \(f(a,b,c) = (b + c)(2a^{2} + ab + ac - bc)\)
Search Value (6, 9, 13): \(1.082747820315\)
▸ Incident Central Lines14 lines

{1, 87}, {10, 37}, {75, 1125}, {226, 1365}, {321, 1962}, {335, 2796}, {518, 3244}, {519, 751}, {536, 551}, {846, 1999}, {1215, 3175}, {1278, 3616}, {2667, 3159}, {3636, 3644}