X3762

X1491com[T(bc, c²)]

X3762 = X663-of-inner-Garcia 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) { 190, 646 }: Central Line L(190, 646) { 514, 661 }: Central Line L(514, 661) { 918, 1086 }: Central Line L(918, 1086) { 900, 1145 }: Central Line L(900, 1145) { 10, 2254 }: Central Line L(10, 2254) { 4, 2814 }: Central Line L(4, 2814) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_646 = BARYCENTRIC MULTIPLIER FOR YFF PARABOLA (-0.0898, 0.2051) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_900 = CROSSDIFFERENCE OF X(6) AND X(101) (0.9566, 0.6107) X_1145 = 3rd EHRMANN POINT (0.3061, 0.2999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_2254 = -ISOCONJUGATE OF X(919) (2.5714, 1.8663) X_4 = ORTHOCENTER (0.6122, 0.3958) X_2814 = ISOGONAL CONJUGATE OF X(2730) (0.0978, -0.1889) X_3762 = com[T(bc, c2)] (-1.5306, -1.4997) A B C X190 X646 X514 X661 X918 X1086 X900 X1145 X10 X2254 X4 X2814 X3762 (a, b, c) = (5, 6, 7) | AB = 1

X3762 (X1491com[T(bc, c²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(bc(b - c)(b + c - 2a) : ca(c - a)(c + a - 2b) : ab(a - b)(a + b - 2c)\)
Search Value (6, 9, 13): \(15.695721873530\)
▸ Incident Central Lines11 lines

{1, 3716}, {4, 2814}, {10, 2254}, {80, 3738}, {153, 2827}, {190, 646}, {514, 661}, {659, 2787}, {900, 1145}, {918, 1086}, {1121, 2481}

▸ Functional Relations6 relations

Notes

The trilinear polar of X3762 passes through X1647. (Randy Hutson, June 7, 2019)