X2647

CROSSSUM OF PU(80)

X2647 = crosspoint of PU(81)
< 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) { 1, 4 }: Incenter–Orthocenter Line { 65, 1046 }: Central Line L(65, 1046) { 21, 1254 }: Central Line L(21, 1254) { 894, 2263 }: Central Line L(894, 2263) { 651, 2648 }: Central Line L(651, 2648) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1254 = ISOGONAL CONJUGATE OF X(1098) (0.6258, 0.3523) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_2263 = -ISOCONJUGATE OF X(949) (0.6079, 0.3177) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_2648 = TRILINEAR POLE OF PU(80) (0.9134, -0.0753) X_2647 = CROSSSUM OF PU(80) (0.5810, 0.2715) A B C X1 X4 X65 X1046 X21 X1254 X894 X2263 X651 X2648 X2647 (a, b, c) = (5, 6, 7) | AB = 1

X2647 (CROSSSUM OF PU(80)) 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 \(f(A,B,C) = (\cos A + \cos B)(\cos A + \cos C) +(\cos B + \cos C)^{2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.773694264615\)
▸ Incident Central Lines5 lines

{1, 4}, {21, 1254}, {65, 1046}, {651, 2648}, {894, 2263}

▸ Functional Relations1 relation

  • X2647 = crosspoint of PU(81)