X283

X3-CROSS CONJUGATE OF X21

X283 = isogonal conjugate of X225
< 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) { 1, 21 }: Central Line L(1, 21) { 3, 49 }: Central Line L(3, 49) { 102, 110 }: Central Line L(102, 110) { 78, 212 }: Central Line L(78, 212) { 29, 270 }: Central Line L(29, 270) { 271, 282 }: Central Line L(271, 282) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1 = INCENTER (0.5714, 0.2333) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_271 = ISOGONAL CONJUGATE OF X(208) (1.1546, 2.8606) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) A B C X3 X21 X1 X49 X102 X110 X78 X212 X29 X270 X271 X282 X283 (a, b, c) = (5, 6, 7) | AB = 1

X283 (X3-CROSS CONJUGATE OF X21) 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): \(4.548122601227\)
▸ Incident Central Lines14 lines

{1, 21}, {2, 580}, {3, 49}, {29, 270}, {60, 284}, {77, 603}, {78, 212}, {86, 307}, {102, 110}, {271, 282}, {474, 582}, {643, 1043}, {859, 945}, {1010, 1065}

▸ Functional Relations7 relations