X2081

PK-TRANSFORM OF X5

X2081 = X50-Ceva conjugate of X2088
< 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) { 115, 125 }: Central Line L(115, 125) { 50, 647 }: Central Line L(50, 647) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_50 = -CEVA CONJUGATE OF X(184) (2.1559, 2.8368) X_2088 = PK-TRANSFORM OF X(110) (0.2299, -0.3440) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_2081 = PK-TRANSFORM OF X(5) (2.8003, 1.7676) A B C X50 X2088 X115 X125 X647 X2081 (a, b, c) = (5, 6, 7) | AB = 1

X2081 (PK-TRANSFORM OF X5) 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 \(f(A,B,C) = [\cos^{2}(A - B) - \cos^{2}(A - C)]\cos(B - C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(4.853034162757\)
▸ Incident Central Lines2 lines

{50, 647}, {115, 125}

▸ Functional Relations3 relations