X2800

ISOGONAL CONJUGATE OF X2716

X2800 is the isogonal conjugate of X2716.
< 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) { 11, 65 }: Central Line L(11, 65) { 4, 80 }: Central Line L(4, 80) { 1, 104 }: Central Line L(1, 104) { 40, 78 }: Central Line L(40, 78) { 10, 119 }: Central Line L(10, 119) { 8, 153 }: Central Line L(8, 153) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2716 = SR(X(100), X(102)) (0.0130, -0.0504) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_4 = ORTHOCENTER (0.6122, 0.3958) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1 = INCENTER (0.5714, 0.2333) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_40 = BEVAN POINT (0.4286, -0.0292) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_8 = NAGEL POINT (0.4694, 0.1333) X_153 = REFLECTION OF X(20) IN X(100) (-0.1020, 1.1248) X_2800 = ISOGONAL CONJUGATE OF X(2716) (0.2444, 0.7084) A B C X2716 X11 X65 X4 X80 X1 X104 X40 X78 X10 X119 X8 X153 X2800 (a, b, c) = (5, 6, 7) | AB = 1

X2800 (ISOGONAL CONJUGATE OF X2716) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as at X2716
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{5}(b + c) - a^{4}(b + c)^{2} - a^{3}(b - 2c)(2b - c)(b + c) + a^{2}(b - c)^{2}(2b + c)(b + 2c) + a(b - c)^{2}(b + c)(b^{2} - 3bc + c^{2}) - (b^{2} - c^{2})^{2}(b^{2} - bc + c^{2}) : :\)

▸ Incident Central Lines18 lines

{1, 104}, {3, 214}, {4, 80}, {8, 153}, {10, 119}, {11, 65}, {30, 511}, {40, 78}, {72, 1145}, {84, 1320}, {149, 151}, {942, 1387}, {1012, 2099}, {1317, 1364}, {1457, 1735}, {1519, 1737}, {1765, 1953}, {1862, 1902}

▸ Functional Relations2 relations

Notes

Let Ia be the reflection of X1 in the perpendicular bisector of BC, and define Ib and Ic cyclically; then X2800 = X515-of-IaIbIc; IaIbIc is the inner Garcia triangle. (Randy Hutson, February 10, 2016)