X2655

CROSSDIFFERENCE OF PU(82)

X2655 = X296-Ceva 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) { 1, 4 }: Incenter–Orthocenter Line { 65, 1047 }: Central Line L(65, 1047) { 296, 851 }: Central Line L(296, 851) { 412, 820 }: Central Line L(412, 820) { 109, 1955 }: Central Line L(109, 1955) { 1248, 1935 }: Central Line L(1248, 1935) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_296 = ISOGONAL CONJUGATE OF X(243) (0.7214, -0.0918) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1047 = -CEVA CONJUGATE OF X(1) (0.5281, -0.0076) X_851 = -HIRST INVERSE OF X(73) (1.4149, 2.4958) X_412 = EULER X(29)-2nd-SUBSTITUTION POINT (0.6482, 0.4899) X_820 = CROSSPOINT OF X(1) AND X(255) (0.5413, 0.0659) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_1955 = CROSSDIFFERENCE OF PU(21) (-1.1271, -5.8688) X_1248 = ISOGONAL CONJUGATE OF X(1047) (0.6139, 0.6190) X_1935 = CROSSSUM OF PU(15) (0.5117, 0.2061) X_2655 = CROSSDIFFERENCE OF PU(82) (-2.9838, -13.9181) A B C X296 X1 X4 X65 X1047 X851 X412 X820 X109 X1955 X1248 X1935 X2655 (a, b, c) = (5, 6, 7) | AB = 1

X2655 (CROSSDIFFERENCE 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 \(f(A,B,C) = (\sec A + \sec B)(\sec A + \sec C) - (\sec B + \sec C)^{2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.340188962021\)
▸ Incident Central Lines7 lines

{1, 4}, {65, 1047}, {109, 1955}, {296, 851}, {412, 820}, {1155, 2636}, {1248, 1935}

▸ Functional Relations3 relations