X293

ISOGONAL CONJUGATE OF X240

X293 is the isogonal conjugate of X240.
< 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) { 31, 92 }: Central Line L(31, 92) { 1, 163 }: Central Line L(1, 163) { 98, 109 }: Central Line L(98, 109) { 72, 248 }: Central Line L(72, 248) { 255, 304 }: Central Line L(255, 304) { 287, 306 }: Central Line L(287, 306) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_1 = INCENTER (0.5714, 0.2333) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_98 = TARRY POINT (0.8891, -0.2281) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_248 = -LINE CONJUGATE OF X(132) (0.8229, -0.0790) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_304 = ISOTOMIC CONJUGATE OF X(19) (0.3683, 0.0513) X_287 = -HIRST INVERSE OF X(98) (0.7437, -0.0511) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_293 = ISOGONAL CONJUGATE OF X(240) (0.7839, -0.0636) A B C X240 X31 X92 X1 X163 X98 X109 X72 X248 X255 X304 X287 X306 X293 (a, b, c) = (5, 6, 7) | AB = 1

X293 (ISOGONAL CONJUGATE OF X240) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos A \sec(A + \omega ) : \cos B \sec(B + \omega ) : \cos C \sec(C + \omega )\)
Barycentrics: \(\sin 2A \sec(A + \omega ) : \sin 2B \sec(B + \omega ) : \sin 2C \sec(C + \omega )\)
Search Value (6, 9, 13): \(2.039640071981\)
▸ Incident Central Lines6 lines

{1, 163}, {31, 92}, {72, 248}, {98, 109}, {255, 304}, {287, 306}

▸ Functional Relations3 relations