X2659

CROSSDIFFERENCE OF PU(83)

X2659 = perspector of conic {{A, B, C,PU(82)}}
< 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, 29 }: Central Line L(1, 29) { 73, 410 }: Central Line L(73, 410) { 185, 412 }: Central Line L(185, 412) { 822, 1021 }: Central Line L(822, 1021) { 415, 1937 }: Central Line L(415, 1937) { 648, 1936 }: Central Line L(648, 1936) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2660 = TRILINEAR POLE OF PU(83) (0.6083, -0.1529) X_1 = INCENTER (0.5714, 0.2333) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_410 = EULER X(29)-1st-SUBSTITUTION POINT (0.5800, 0.3115) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_412 = EULER X(29)-2nd-SUBSTITUTION POINT (0.6482, 0.4899) X_822 = CROSSDIFFERENCE OF X(1) AND X(29) (6.5481, -0.2984) X_1021 = ISOGONAL CONJUGATE OF X(1020) (24.7475, -5.0780) X_415 = -HIRST INVERSE OF X(29) (0.7758, 0.8236) X_1937 = TRILINEAR POLE OF PU(15) (0.8541, -0.3793) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_1936 = CROSSDIFFERENCE OF PU(15) (-1.1948, -3.0115) X_2659 = CROSSDIFFERENCE OF PU(83) (0.7496, 1.2245) A B C X2660 X1 X29 X73 X410 X185 X412 X822 X1021 X415 X1937 X648 X1936 X2659 (a, b, c) = (5, 6, 7) | AB = 1

X2659 (CROSSDIFFERENCE OF PU(83)) 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 \(f(A,B,C) = 1/[(\sec A + \sec B)(\sec A + \sec C)] - 1/(\sec B + \sec C)^{2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(7.762075074006\)
▸ Incident Central Lines7 lines

{1, 29}, {73, 410}, {185, 412}, {415, 1937}, {648, 1936}, {822, 1021}, {823, 2635}

▸ Functional Relations2 relations