X2807

ISOGONAL CONJUGATE OF X2723

X2807 is the isogonal conjugate of X2723.
< 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) { 55, 103 }: Central Line L(55, 103) { 1, 185 }: Central Line L(1, 185) { 101, 102 }: Central Line L(101, 102) { 116, 117 }: Central Line L(116, 117) { 118, 124 }: Central Line L(118, 124) { 150, 151 }: Central Line L(150, 151) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2723 = SR(X(101), X(102)) (0.0484, -0.1355) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_1 = INCENTER (0.5714, 0.2333) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_117 = MIDPOINT OF X(4) AND X(109) (0.4879, 0.4948) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_151 = REFLECTION OF X(20) IN X(109) (0.3395, 1.3793) X_2807 = ISOGONAL CONJUGATE OF X(2723) (0.2915, 0.7328) A B C X2723 X55 X103 X1 X185 X101 X102 X116 X117 X118 X124 X150 X151 X2807 (a, b, c) = (5, 6, 7) | AB = 1

X2807 (ISOGONAL CONJUGATE OF X2723) 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 X2723
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines15 lines

{1, 185}, {3, 692}, {30, 511}, {51, 1699}, {55, 103}, {101, 102}, {116, 117}, {118, 124}, {150, 151}, {389, 946}, {990, 1469}, {1037, 1795}, {1282, 1763}, {1361, 2099}, {1827, 1845}

▸ Functional Relations1 relation