X878

ISOGONAL CONJUGATE OF X877

X878 is the isogonal conjugate of X877.
< 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) { 3, 525 }: Central Line L(3, 525) { 32, 512 }: Central Line L(32, 512) { 25, 669 }: Central Line L(25, 669) { 184, 647 }: Central Line L(184, 647) { 98, 804 }: Central Line L(98, 804) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_877 = INTERSECTION OF LINES X(4)X(69) AND X(99)X(112) (0.8267, 0.7499) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_98 = TARRY POINT (0.8891, -0.2281) X_804 = ODD (- 2, 2) INFINITY POINT (0.9171, 0.6474) X_878 = ISOGONAL CONJUGATE OF X(877) (1.1192, 0.0431) A B C X877 X3 X525 X32 X512 X25 X669 X184 X647 X98 X804 X878 (a, b, c) = (5, 6, 7) | AB = 1

X878 (ISOGONAL CONJUGATE OF X877) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{2}u(bv - cw)/(a^{2}u^{2} - bcvw) : :\), where \(u : v : w\) = X4
Search Value (6, 9, 13): \(-4.913745947733\)
▸ Incident Central Lines5 lines

{3, 525}, {25, 669}, {32, 512}, {98, 804}, {184, 647}

▸ Functional Relations4 relations