X3505

INTERSECTION OF LINES X32X_695 AND X98X_783

< 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) { 32, 695 }: Central Line L(32, 695) { 98, 783 }: Central Line L(98, 783) { 2, 3186 }: Central Line L(2, 3186) { 3510, 3512 }: Central Line L(3510, 3512) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_98 = TARRY POINT (0.8891, -0.2281) X_783 = o-(- 4, 4) CIRCUMCIRCLE POINT (0.9757, -0.0828) X_2 = CENTROID (0.5374, 0.2000) X_3186 = -CEVA CONJUGATE OF X(4) (0.6627, 0.4791) X_3510 = INTERSECTION OF LINES X(1)X(76) AND X(6)X(43) (1.7132, 1.1732) X_3512 = ISOGONAL CONJUGATE OF X(3509) (0.9280, -0.1499) X_3505 = INTERSECTION OF LINES X(32)X(695) AND X(98)X(783) (-1.3189, -3.9357) A B C X32 X695 X98 X783 X2 X3186 X3510 X3512 X3505 (a, b, c) = (5, 6, 7) | AB = 1

X3505 (INTERSECTION OF LINES X32X_695 AND X98X_783) 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 \(f(a,b,c) = a(b^{6} + c^{6} - a^{6} - a^{2}b^{2}c^{2})/(a^{4} + b^{2}c^{2}) (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.473889365145\)

X3505 lies on the cubic Z(X385).

▸ Incident Central Lines4 lines

{2, 3186}, {32, 695}, {98, 783}, {3510, 3512}