X3506

INTERSECTION OF LINES X2X_98 AND X32X_694

X3506 = X385-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) { 2, 98 }: Central Line L(2, 98) { 32, 694 }: Central Line L(32, 694) { 648, 1974 }: Central Line L(648, 1974) { 1196, 1915 }: Central Line L(1196, 1915) { 1, 3512 }: Central Line L(1, 3512) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_2 = CENTROID (0.5374, 0.2000) X_98 = TARRY POINT (0.8891, -0.2281) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_1974 = BARYCENTRIC PRODUCT OF PU(39) (0.6402, 0.4907) X_1196 = 3rd SARAGOSSA POINT OF X(25) (0.6432, 0.2801) X_1915 = CROSSSUM OF PU(11) (0.6078, 0.3108) X_1 = INCENTER (0.5714, 0.2333) X_3512 = ISOGONAL CONJUGATE OF X(3509) (0.9280, -0.1499) X_3506 = INTERSECTION OF LINES X(2)X(98) AND X(32)X(694) (0.0474, 0.7964) A B C X385 X32 X2 X98 X694 X648 X1974 X1196 X1915 X1 X3512 X3506 (a, b, c) = (5, 6, 7) | AB = 1

X3506 (INTERSECTION OF LINES X2X_98 AND X32X_694) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(a^{8} - a^{4}b^{2}c^{2} - a^{2}b^{6} - a^{2}c^{6} + 2b^{4}c^{4})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.520935526976\)

X3506 lies on the cubic Z(X385).

▸ Incident Central Lines5 lines

{1, 3512}, {2, 98}, {32, 694}, {648, 1974}, {1196, 1915}

▸ Functional Relations1 relation