X2056

ORION TRANSFORM OF X6

X2056 = perspector of ABC and orthic triangle of symmedial triangle
< 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) { 110, 251 }: Central Line L(110, 251) { 6, 1196 }: Central Line L(6, 1196) { 184, 1613 }: Central Line L(184, 1613) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1196 = 3rd SARAGOSSA POINT OF X(25) (0.6432, 0.2801) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_1613 = TCC-PERSPECTOR OF X(31) (0.7015, 0.3763) X_2056 = ORION TRANSFORM OF X(6) (0.6506, 0.2823) A B C X110 X251 X6 X1196 X184 X1613 X2056 (a, b, c) = (5, 6, 7) | AB = 1

X2056 (ORION TRANSFORM OF X6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(a^{4} - 2a^{2}b^{2} - 2a^{2}c^{2} + b^{2}c^{2}) : :\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(0.272843958861\)
▸ Incident Central Lines3 lines

{6, 1196}, {110, 251}, {184, 1613}

▸ Functional Relations1 relation

  • X2056 = perspector of ABC and orthic triangle of symmedial triangle