X2802

ISOGONAL CONJUGATE OF X2718

X2802 is the isogonal conjugate of X2718.
< 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, 11 }: Central Line L(10, 11) { 8, 80 }: Central Line L(8, 80) { 1, 88 }: Central Line L(1, 88) { 40, 104 }: Central Line L(40, 104) { 30, 511 }: Central Line L(30, 511) { 119, 946 }: Central Line L(119, 946) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2718 = SR(X(100), X(106)) (0.1429, 0.4666) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_8 = NAGEL POINT (0.4694, 0.1333) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1 = INCENTER (0.5714, 0.2333) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_40 = BEVAN POINT (0.4286, -0.0292) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_946 = MIDPOINT OF X(1) AND X(4) (0.5918, 0.3145) X_2802 = ISOGONAL CONJUGATE OF X(2718) (1.0529, -0.0806) A B C X2718 X10 X11 X8 X80 X1 X88 X40 X104 X30 X511 X119 X946 X2802 (a, b, c) = (5, 6, 7) | AB = 1

X2802 (ISOGONAL CONJUGATE OF X2718) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b^{3} + c^{3} - a^{2}b - a^{2}c - 2b^{2}c - 2bc^{2} + 4abc) : :\) (M. Iliev, 5/13/07)
▸ Incident Central Lines18 lines

{1, 88}, {8, 80}, {10, 11}, {30, 511}, {40, 104}, {56, 2932}, {65, 1317}, {119, 946}, {153, 962}, {643, 759}, {765, 1168}, {1000, 2550}, {1018, 2170}, {1023, 2246}, {1125, 1387}, {1149, 1739}, {1829, 1862}, {1845, 1897}

▸ Functional Relations4 relations

Notes

Let Ia be the reflection of X1 in the perpendicular bisector of BC, and define Ib and Ic cyclically. X2802 = X519-of-IaIbIc; IaIbIc is the inner Garcia triangle. (Randy Hutson, February 10, 2016)