X3491

INTERSECTION OF LINES X1X_295 AND X4X_69

X3491 = X384-Ceva conjugate of X39
< 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, 69 }: Central Line L(4, 69) { 1, 295 }: Central Line L(1, 295) { 147, 185 }: Central Line L(147, 185) { 39, 695 }: Central Line L(39, 695) { 211, 754 }: Central Line L(211, 754) { 32, 1613 }: Central Line L(32, 1613) 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_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_1 = INCENTER (0.5714, 0.2333) X_295 = ISOGONAL CONJUGATE OF X(242) (1.0582, 0.0142) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_211 = -CEVA CONJUGATE OF X(39) (0.6801, 0.4536) X_754 = EVEN (0, 4) INFINITY POINT (0.1795, -0.2651) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_1613 = TCC-PERSPECTOR OF X(31) (0.7015, 0.3763) X_3491 = INTERSECTION OF LINES X(1)X(295) AND X(4)X(69) (0.5262, 0.2536) A B C X384 X39 X4 X69 X1 X295 X147 X185 X695 X211 X754 X32 X1613 X3491 (a, b, c) = (5, 6, 7) | AB = 1

X3491 (INTERSECTION OF LINES X1X_295 AND X4X_69) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{2}[a^{4}b^{4} + a^{4}c^{4} - a^{2}(b^{6} + c^{6}) + b^{2}c^{2}(b^{4} + c^{4})] : : (E. Danneels)\)
Search Value (6, 9, 13): \(2.637719321874\)

X3491 lies on the cubic Z(X384).

▸ Incident Central Lines8 lines

{1, 295}, {4, 69}, {32, 1613}, {39, 695}, {147, 185}, {211, 754}, {626, 2387}, {3494, 3497}

▸ Functional Relations1 relation