X1813

INVERSE MIMOSA TRANSFORM OF X650

X1813 = X219-cross conjugate of X59
< 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) { 48, 77 }: Central Line L(48, 77) { 109, 110 }: Central Line L(109, 110) { 283, 296 }: Central Line L(283, 296) { 287, 307 }: Central Line L(287, 307) { 59, 677 }: Central Line L(59, 677) { 101, 651 }: Central Line L(101, 651) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_296 = ISOGONAL CONJUGATE OF X(243) (0.7214, -0.0918) X_287 = -HIRST INVERSE OF X(98) (0.7437, -0.0511) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_59 = ISOGONAL CONJUGATE OF X(11) (0.5333, 0.4355) X_677 = TRILINEAR POLE OF LINE X(3)X(101) (1.3200, 0.4790) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_1813 = INVERSE MIMOSA TRANSFORM OF X(650) (-0.1088, 0.3999) A B C X48 X77 X109 X110 X283 X296 X287 X307 X59 X677 X101 X651 X1813 (a, b, c) = (5, 6, 7) | AB = 1

X1813 (INVERSE MIMOSA TRANSFORM OF X650) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\cos A)/(\cos B - \cos C) : (\cos B)/(\cos C - \cos A) : (\cos C)/(\cos A - \cos B)\)
Barycentrics: \((\sin 2A)/(\cos B - \cos C) : (\sin 2B)/(\cos C - \cos A) : (\sin 2C)/(\cos A - \cos B)\)
Search Value (6, 9, 13): \(-0.638221025097\)

X1813 lies on the MacBeath circumconic.

▸ Incident Central Lines16 lines

{48, 77}, {59, 677}, {65, 1800}, {73, 895}, {101, 651}, {109, 110}, {219, 1804}, {222, 1797}, {224, 1420}, {283, 296}, {284, 1442}, {287, 307}, {347, 1630}, {604, 1445}, {648, 653}, {1214, 1790}

▸ Functional Relations7 relations