X2595

CROSSSUM OF PU(68)

X2595 = X2603-Ceva conjugate of X2596
< 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) { 54, 1087 }: Central Line L(54, 1087) { 1048, 2594 }: Central Line L(1048, 2594) { 12, 2607 }: Central Line L(12, 2607) { 655, 2597 }: Central Line L(655, 2597) { 2477, 2606 }: Central Line L(2477, 2606) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2603 = TRILINEAR POLE OF PU(69) (0.0091, 0.2419) X_2596 = CROSSDIFFERENCE OF PU(68) (-2.5195, 3.3880) X_54 = KOSNITA POINT (0.5880, 0.2176) X_1087 = TRILINEAR SQUARE OF X(5) (0.5422, 0.2643) X_1048 = POINT ALGIEBA (0.5862, 0.2176) X_2594 = SUM OF PU(68) (0.5791, 0.2254) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_2607 = CROSSDIFFERENCE OF PU(70) (0.5584, 0.2383) X_655 = TRILINEAR POLE OF LINE X(1)X(5) (1.0449, 0.2400) X_2597 = TRILINEAR POLE OF PU(68) (-0.0331, 0.2426) X_2477 = EXSIMILICENTER{INCIRCLE, SINE-TRIPLE-ANGLE CIRCLE} (0.5953, 0.2101) X_2606 = CROSSSUM OF PU(70) (1.2843, -0.4943) X_2595 = CROSSSUM OF PU(68) (0.5650, 0.2411) A B C X2603 X2596 X54 X1087 X1048 X2594 X12 X2607 X655 X2597 X2477 X2606 X2595 (a, b, c) = (5, 6, 7) | AB = 1

X2595 (CROSSSUM 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 \(f(A,B,C) = \cos(A - B) \cos(A - C) + \cos^{2}(B - C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.220564387029\)
▸ Incident Central Lines5 lines

{12, 2607}, {54, 1087}, {655, 2597}, {1048, 2594}, {2477, 2606}

▸ Functional Relations4 relations