X1096

TRILINEAR SQUARE OF X19

X1096 = X158-Ceva conjugate of X19
< 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) { 19, 31 }: Central Line L(19, 31) { 33, 42 }: Central Line L(33, 42) { 34, 207 }: Central Line L(34, 207) { 63, 240 }: Central Line L(63, 240) { 213, 607 }: Central Line L(213, 607) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1 = INCENTER (0.5714, 0.2333) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_1096 = TRILINEAR SQUARE OF X(19) (0.6263, 0.5385) A B C X158 X19 X1 X29 X31 X33 X42 X34 X207 X63 X240 X213 X607 X1096 (a, b, c) = (5, 6, 7) | AB = 1

X1096 (TRILINEAR SQUARE OF X19) 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 \(f(A,B,C) = \tan^{2} A\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(0.187085431565\)
▸ Incident Central Lines12 lines

{1, 29}, {4, 1039}, {19, 31}, {25, 1402}, {33, 42}, {34, 207}, {63, 240}, {107, 741}, {213, 607}, {243, 1040}, {278, 614}, {281, 612}

▸ Functional Relations6 relations