X764

TRILINEAR CUBE OF X513

X764 = crosspoint of X244 and X513
< 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) { 1, 513 }: Central Line L(1, 513) { 10, 514 }: Central Line L(10, 514) { 56, 667 }: Central Line L(56, 667) { 76, 693 }: Central Line L(76, 693) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_1 = INCENTER (0.5714, 0.2333) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_693 = ISOTOMIC CONJUGATE OF X(100) (-25.8163, 8.9981) X_764 = TRILINEAR CUBE OF X(513) (1.2143, -0.1166) A B C X244 X513 X1 X10 X514 X56 X667 X76 X693 X764 (a, b, c) = (5, 6, 7) | AB = 1

X764 (TRILINEAR CUBE OF X513) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b - c)^{3} : (c - a)^{3} : (a - b)^{3}\)
Barycentrics: \(a(b - c)^{3} : b(c - a)^{3} : c(a - b)^{3}\)
Search Value (6, 9, 13): \(-1.287854102443\)

X764 lies on the cubic K244.

▸ Incident Central Lines4 lines

{1, 513}, {10, 514}, {56, 667}, {76, 693}

▸ Functional Relations4 relations