X640

COMPLEMENT OF X372

X640 is the complement of X372.
< 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) { 639, 626 }: Central Line L(639, 626) { 5, 141 }: Central Line L(5, 141) { 2, 372 }: Central Line L(2, 372) { 69, 486 }: Central Line L(69, 486) { 315, 371 }: Central Line L(315, 371) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_639 = COMPLEMENT OF X(371) (0.5235, 0.1951) 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_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_640 = COMPLEMENT OF X(372) (0.4487, 0.0715) A B C X639 X626 X5 X141 X2 X372 X69 X486 X315 X371 X640 (a, b, c) = (5, 6, 7) | AB = 1

X640 (COMPLEMENT OF X372) 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 \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(4.879620959270\)
▸ Incident Central Lines5 lines

{2, 372}, {3, 642}, {5, 141}, {69, 486}, {315, 371}

▸ Functional Relations4 relations