X639

COMPLEMENT OF X371

X639 is the complement of X371.
< 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) { 640, 626 }: Central Line L(640, 626) { 5, 141 }: Central Line L(5, 141) { 2, 371 }: Central Line L(2, 371) { 69, 485 }: Central Line L(69, 485) { 32, 615 }: Central Line L(32, 615) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_640 = COMPLEMENT OF X(372) (0.4487, 0.0715) X_626 = COMPLEMENT OF X(32) (0.4861, 0.1333) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_2 = CENTROID (0.5374, 0.2000) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_485 = VECTEN POINT (0.5773, 0.2578) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_639 = COMPLEMENT OF X(371) (0.5235, 0.1951) A B C X640 X626 X5 X141 X2 X371 X69 X485 X32 X615 X639 (a, b, c) = (5, 6, 7) | AB = 1

X639 (COMPLEMENT OF X371) 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 \(f(a,b,c) = [2S_{B}S_{C} + S_{A}a^{2} + 2(b^{2} + c^{2}) \operatorname{area}]/a\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = 2 + \sin 2B + \sin 2C - \cos 2B - \cos 2C\),\(h(a,b,c) : h(b,c,a) : h(c,a,b)\), where \(h(a,b,c) = (a^{2} + 4 \operatorname{area}(ABC))(b^{2} + c^{2}) - (b^{2} - c^{2})^{2}\)
Search Value (6, 9, 13): \(2.727772972011\)
▸ Incident Central Lines6 lines

{2, 371}, {3, 641}, {5, 141}, {32, 615}, {69, 485}, {315, 372}

▸ Functional Relations5 relations