X2660

TRILINEAR POLE OF PU(83)

X2660 = isogonal conjugate of X2659
< 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) { 410, 823 }: Central Line L(410, 823) { 4, 1248 }: Central Line L(4, 1248) { 416, 1936 }: Central Line L(416, 1936) { 1, 2656 }: Central Line L(1, 2656) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2659 = CROSSDIFFERENCE OF PU(83) (0.7496, 1.2245) X_410 = EULER X(29)-1st-SUBSTITUTION POINT (0.5800, 0.3115) X_823 = ISOGONAL CONJUGATE OF X(822) (0.5623, 0.6035) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1248 = ISOGONAL CONJUGATE OF X(1047) (0.6139, 0.6190) X_416 = -HIRST INVERSE OF X(21) (0.0862, -0.9805) X_1936 = CROSSDIFFERENCE OF PU(15) (-1.1948, -3.0115) X_1 = INCENTER (0.5714, 0.2333) X_2656 = TRILINEAR POLE OF PU(82) (0.6337, -0.4192) X_2660 = TRILINEAR POLE OF PU(83) (0.6083, -0.1529) A B C X2659 X410 X823 X4 X1248 X416 X1936 X1 X2656 X2660 (a, b, c) = (5, 6, 7) | AB = 1

X2660 (TRILINEAR POLE OF PU(83)) 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 \(f(A,B,C) = (\sec B + \sec C)/(\sec^{2} B + \sec^{2} C - \sec^{2} A + \sec B \sec C - \sec A \sec B - \sec A \sec C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-7.364796987236\)
▸ Incident Central Lines4 lines

{1, 2656}, {4, 1248}, {410, 823}, {416, 1936}

▸ Functional Relations1 relation