X3967

X3752com[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) { 210, 321 }: Central Line L(210, 321) { 43, 536 }: Central Line L(43, 536) { 37, 714 }: Central Line L(37, 714) { 312, 518 }: Central Line L(312, 518) { 72, 1089 }: Central Line L(72, 1089) { 42, 3175 }: Central Line L(42, 3175) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_714 = EVEN (- 3, - 1) INFINITY POINT (1.0302, 0.5186) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1089 = TRILINEAR SQUARE OF X(10) (0.4606, 0.1381) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_3175 = -CEVA CONJUGATE OF X(10) (0.7147, 0.3456) X_3967 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.4681, 0.1585) A B C X210 X321 X43 X536 X37 X714 X312 X518 X72 X1089 X42 X3175 X3967 (a, b, c) = (5, 6, 7) | AB = 1

X3967 (X3752com[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 \(f(a,b,c) = (b + c)(a^{2} - ab - ac + 2bc)\)
Search Value (6, 9, 13): \(4.338458507606\)
▸ Incident Central Lines16 lines

{12, 3710}, {37, 714}, {42, 3175}, {43, 536}, {65, 3701}, {72, 1089}, {75, 3740}, {210, 321}, {312, 518}, {329, 3416}, {726, 3752}, {908, 3703}, {1376, 3729}, {1901, 3610}, {2886, 3717}, {3681, 3706}