X2651

CROSSDIFFERENCE OF PU(81)

X2651 = perspector of conic {{A, B, C,PU(80)}}
< 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, 21 }: Central Line L(1, 21) { 65, 409 }: Central Line L(65, 409) { 185, 411 }: Central Line L(185, 411) { 296, 416 }: Central Line L(296, 416) { 243, 648 }: Central Line L(243, 648) { 425, 653 }: Central Line L(425, 653) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2652 = TRILINEAR POLE OF PU(81) (0.9537, -0.1117) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_409 = EULER X(21)-1st-SUBSTITUTION POINT (0.5419, 0.2117) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_411 = EULER X(21)-2nd-SUBSTITUTION POINT (0.4414, -0.0514) X_296 = ISOGONAL CONJUGATE OF X(243) (0.7214, -0.0918) X_416 = -HIRST INVERSE OF X(21) (0.0862, -0.9805) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_425 = -HIRST INVERSE OF X(21) (0.8561, 1.0339) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_2651 = CROSSDIFFERENCE OF PU(81) (6.8757, 8.5193) A B C X2652 X1 X21 X65 X409 X185 X411 X296 X416 X243 X648 X425 X653 X2651 (a, b, c) = (5, 6, 7) | AB = 1

X2651 (CROSSDIFFERENCE OF PU(81)) 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 \(f(A,B,C) = 1/[(\cos A + \cos B)(\cos A + \cos C)] - 1/(\cos B + \cos C)^{2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-58.347323272715\)
▸ Incident Central Lines9 lines

{1, 21}, {65, 409}, {185, 411}, {243, 648}, {296, 416}, {425, 653}, {518, 643}, {661, 1021}, {662, 1155}

▸ Functional Relations2 relations