X211

X4-CEVA CONJUGATE OF X39

X211 = X4-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) { 5, 141 }: Central Line L(5, 141) { 52, 114 }: Central Line L(52, 114) { 32, 184 }: Central Line L(32, 184) { 51, 1506 }: Central Line L(51, 1506) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_52 = ORTHOCENTER OF ORTHIC TRIANGLE (0.7155, 0.4580) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_1506 = INSIMILICENTER OF MOSES AND NINE-POINT CIRCLES (0.5676, 0.2392) X_211 = -CEVA CONJUGATE OF X(39) (0.6801, 0.4536) A B C X4 X39 X5 X141 X52 X114 X32 X184 X51 X1506 X211 (a, b, c) = (5, 6, 7) | AB = 1

X211 (X4-CEVA CONJUGATE OF X39) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin(A + \omega )[\cos B \sin(B + \omega ) + \cos C \sin(C + \omega ) - \cos A \sin(A + \omega )] : :\)
Barycentrics: \(a^{4} (b^{2} + c^{2}) \cdot (a^{2} b^{2} - b^{4} + a^{2} c^{2} + b^{2} c^{2} - c^{4}) : :\)
Search Value (6, 9, 13): \(-0.885265197581\)

X211 lies on the cubic K1088.

▸ Incident Central Lines24 lines

{5, 141}, {6, 11360}, {32, 184}, {51, 1506}, {52, 114}, {232, 15897}, {263, 2548}, {571, 2909}, {632, 15510}, {688, 2518}, {754, 3491}, {1078, 11673}, {2794, 13419}, {2979, 3096}, {3060, 7752}, {3202, 20960}, {3456, 17970}, {3917, 6292}, {4173, 5007}, {5017, 20987}, {5167, 7747}, {7807, 14962}, {11674, 12110}, {14575, 18796}

▸ Functional Relations5 relations