X3769

X3705com[T(-bc, b²)]

< 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) { 75, 171 }: Central Line L(75, 171) { 31, 312 }: Central Line L(31, 312) { 333, 612 }: Central Line L(333, 612) { 2, 1386 }: Central Line L(2, 1386) { 239, 1376 }: Central Line L(239, 1376) { 190, 1707 }: Central Line L(190, 1707) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_2 = CENTROID (0.5374, 0.2000) X_1386 = MIDPOINT OF INCENTER AND SYMMEDIAN POINT (0.5857, 0.2503) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5265, 0.2074) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_1707 = MIMOSA TRANSFORM OF X(6) (0.7574, 0.4777) X_3769 = com[T(-bc, b2)] (0.8099, 0.4837) A B C X75 X171 X31 X312 X333 X612 X2 X1386 X239 X1376 X190 X1707 X3769 (a, b, c) = (5, 6, 7) | AB = 1

X3769 (X3705com[T(-bc, b²)]) 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 \(f(a,b,c) = 2a^{3} + abc - b^{2}c - bc^{2}\)
Search Value (6, 9, 13): \(-3.223289779668\)
▸ Incident Central Lines16 lines

{2, 1386}, {31, 312}, {43, 1964}, {55, 1999}, {75, 171}, {100, 2352}, {145, 2646}, {190, 1707}, {239, 1376}, {333, 612}, {740, 3550}, {940, 3757}, {1155, 3210}, {1748, 1897}, {2162, 2235}, {3052, 3685}