X2656

TRILINEAR POLE OF PU(82)

X2656 = X243-cross conjugate of X1
< 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) { 3, 1047 }: Central Line L(3, 1047) { 296, 851 }: Central Line L(296, 851) { 29, 2638 }: Central Line L(29, 2638) { 1795, 1955 }: Central Line L(1795, 1955) { 1, 2660 }: Central Line L(1, 2660) { 653, 2658 }: Central Line L(653, 2658) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1047 = -CEVA CONJUGATE OF X(1) (0.5281, -0.0076) X_296 = ISOGONAL CONJUGATE OF X(243) (0.7214, -0.0918) X_851 = -HIRST INVERSE OF X(73) (1.4149, 2.4958) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_2638 = DIFFERENCE OF PU(77) (0.6093, 0.0064) X_1795 = INVERSE MIMOSA TRANSFORM OF X(36) (0.7464, -0.0703) X_1955 = CROSSDIFFERENCE OF PU(21) (-1.1271, -5.8688) X_2660 = TRILINEAR POLE OF PU(83) (0.6083, -0.1529) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_2658 = SUM OF PU(83) (0.5613, 0.1772) X_2656 = TRILINEAR POLE OF PU(82) (0.6337, -0.4192) A B C X243 X1 X3 X1047 X296 X851 X29 X2638 X1795 X1955 X2660 X653 X2658 X2656 (a, b, c) = (5, 6, 7) | AB = 1

X2656 (TRILINEAR POLE OF PU(82)) 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 \(f(A,B,C) = 1/[(\sec A + \sec B)(\sec A + \sec C) - (\sec B + \sec C)^{2}]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.014836031274\)
▸ Incident Central Lines6 lines

{1, 2660}, {3, 1047}, {29, 2638}, {296, 851}, {653, 2658}, {1795, 1955}

▸ Functional Relations2 relations