X3034

INTERSECTION X10X_116∩X105X_386

X3034 = inverse-in-excircles-radical-circle of X116
< 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, 116 }: Central Line L(10, 116) { 105, 386 }: Central Line L(105, 386) { 528, 3032 }: Central Line L(528, 3032) { 2795, 3029 }: Central Line L(2795, 3029) { 2832, 3030 }: Central Line L(2832, 3030) { 2836, 3031 }: Central Line L(2836, 3031) 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_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_528 = DIRECTION OF VECTOR AX + BX + CX, where X = X(11) (1.0237, -0.1286) X_3032 = INTERSECTION X(10)X(11)∩X(100)X(386) (-1.0163, 1.0198) X_2795 = ISOGONAL CONJUGATE OF X(2711) (1.0383, -0.1059) X_3029 = INTERSECTION X(10)X(115)∩X(98)X(573) (-1.1309, 0.8967) X_2832 = ISOGONAL CONJUGATE OF X(2748) (0.3656, -0.3612) X_3030 = INTERSECTION X(10)X(11)∩X(43)X(57) (2.0571, -0.6532) X_2836 = ISOGONAL CONJUGATE OF X(2752) (0.9756, -0.1904) X_3031 = INTERSECTION X(10)X(125)∩X(74)X(573) (-0.6264, 1.3112) X_3034 = INTERSECTION X(10)X(116)∩X(105)X(386) (1.9547, -0.9878) A B C X10 X116 X105 X386 X528 X3032 X2795 X3029 X2832 X3030 X2836 X3031 X3034 (a, b, c) = (5, 6, 7) | AB = 1

X3034 (INTERSECTION X10X_116∩X105X_386) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b^{3} - b^{2}c + ba^{2} - abc + a^{2}c - ac^{2})(c^{3} - c^{2}b + ca^{2} - abc + a^{2}b - ab^{2}) : :\)
Search Value (6, 9, 13): \(7.079069825931\)

X3034 lies on the Apollonius circle.

▸ Incident Central Lines6 lines

{10, 116}, {105, 386}, {528, 3032}, {2795, 3029}, {2832, 3030}, {2836, 3031}

▸ Functional Relations1 relation

  • X3034 = inverse-in-excircles-radical-circle of X116

Notes

Let A' be the inverse-in-excircles-radical-circle of the midpoint of BC, and define B and C' cyclically. Triangle A'B'C' is inscribed in the Apollonius circle and homothetic to the excentral triangle. X3030 = X112 of A'B'C'. (Randy Hutson, August 29, 2018)