X1646

TRIPOLAR CENTROID OF X513

X1646 is the tripolar centroid of 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) { 2, 37 }: Central Line L(2, 37) { 88, 292 }: Central Line L(88, 292) { 244, 665 }: Central Line L(244, 665) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_665 = CROSSDIFFERENCE OF X(2) AND X(11) (1.4579, 1.0988) X_1646 = TRIPOLAR CENTROID OF X(513) (1.2353, 0.7735) A B C X2 X37 X88 X292 X244 X665 X1646 (a, b, c) = (5, 6, 7) | AB = 1

X1646 (TRIPOLAR CENTROID OF X513) 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 \(f(a,b,c) = a(b - c)^{2}(2bc - ab - ac)\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(-3.481646952813\)
▸ Incident Central Lines3 lines

{2, 37}, {88, 292}, {244, 665}

▸ Functional Relations4 relations