X3786

X1654com[INVERSE(nT(bc, c²))]

< 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) { 9, 21 }: Central Line L(9, 21) { 8, 314 }: Central Line L(8, 314) { 210, 333 }: Central Line L(210, 333) { 86, 518 }: Central Line L(86, 518) { 81, 612 }: Central Line L(81, 612) { 72, 894 }: Central Line L(72, 894) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_8 = NAGEL POINT (0.4694, 0.1333) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_3786 = com[INVERSE(nT(bc, c2))] (0.4938, 0.1464) A B C X9 X21 X8 X314 X210 X333 X86 X518 X81 X612 X72 X894 X3786 (a, b, c) = (5, 6, 7) | AB = 1

X3786 (X1654com[INVERSE(nT(bc, c²))]) 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 \(f(a,b,c) = a(a + b)(a + c)(a - b - c)(b^{2} + c^{2} + bc)\)
Search Value (6, 9, 13): \(3.900851800480\)
▸ Incident Central Lines14 lines

{1, 3728}, {8, 314}, {9, 21}, {29, 1827}, {58, 1757}, {72, 894}, {81, 612}, {86, 518}, {210, 333}, {228, 3219}, {511, 1654}, {869, 984}, {960, 1043}, {1045, 2292}