X3492

INTERSECTION OF LINES X4X_83 AND X32X_695

X3492 = X384-Ceva conjugate of X32
< 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) { 4, 83 }: Central Line L(4, 83) { 184, 194 }: Central Line L(184, 194) { 32, 695 }: Central Line L(32, 695) { 39, 1915 }: Central Line L(39, 1915) { 1, 3497 }: Central Line L(1, 3497) { 3500, 3502 }: Central Line L(3500, 3502) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_4 = ORTHOCENTER (0.6122, 0.3958) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_1915 = CROSSSUM OF PU(11) (0.6078, 0.3108) X_1 = INCENTER (0.5714, 0.2333) X_3497 = ISOGONAL CONJUGATE OF X(3496) (0.6174, 0.3711) X_3500 = INTERSECTION OF LINES X(1)X(295) AND X(3)X(238) (0.5973, 0.2216) X_3502 = ISOGONAL CONJUGATE OF X(3494) (0.6508, 0.3268) X_3492 = INTERSECTION OF LINES X(4)X(83) AND X(32)X(695) (0.5108, 0.0518) A B C X384 X32 X4 X83 X184 X194 X695 X39 X1915 X1 X3497 X3500 X3502 X3492 (a, b, c) = (5, 6, 7) | AB = 1

X3492 (INTERSECTION OF LINES X4X_83 AND X32X_695) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{2}(a^{8} - a^{4}b^{2}c^{2} - a^{2}b^{6} - a^{2}c^{6} - 2b^{4}c^{4}) : : (E. Danneels)\)
Search Value (6, 9, 13): \(-3.629915214412\)

X3492 lies on the cubic Z(X384).

▸ Incident Central Lines6 lines

{1, 3497}, {4, 83}, {32, 695}, {39, 1915}, {184, 194}, {3500, 3502}

▸ Functional Relations1 relation