X2597

TRILINEAR POLE OF PU(68)

X2597 = cevapoint of X2601 and X2602
< 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) { 655, 2595 }: Central Line L(655, 2595) { 1, 2603 }: Central Line L(1, 2603) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2601 = CROSSSUM OF PU(69) (0.5810, 0.2254) X_2602 = CROSSDIFFERENCE OF PU(69) (-1237.5118, 1171.2797) X_655 = TRILINEAR POLE OF LINE X(1)X(5) (1.0449, 0.2400) X_2595 = CROSSSUM OF PU(68) (0.5650, 0.2411) X_1 = INCENTER (0.5714, 0.2333) X_2603 = TRILINEAR POLE OF PU(69) (0.0091, 0.2419) X_2597 = TRILINEAR POLE OF PU(68) (-0.0331, 0.2426) A B C X2601 X2602 X655 X2595 X1 X2603 X2597 (a, b, c) = (5, 6, 7) | AB = 1

X2597 (TRILINEAR POLE OF PU(68)) 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 \(f(A,B,C) = 1/[\cos(A - B) \cos(A - C) - \cos^{2}(B - C)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(90.303130081607\)
▸ Incident Central Lines2 lines

{1, 2603}, {655, 2595}

▸ Functional Relations2 relations