X207

X1-CEVA CONJUGATE OF X34

X207 = X1-beth conjugate of X64
< 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) { 19, 56 }: Central Line L(19, 56) { 33, 64 }: Central Line L(33, 64) { 40, 108 }: Central Line L(40, 108) { 1, 196 }: Central Line L(1, 196) { 204, 221 }: Central Line L(204, 221) { 78, 653 }: Central Line L(78, 653) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_19 = CLAWSON POINT (0.6246, 0.4244) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_40 = BEVAN POINT (0.4286, -0.0292) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_196 = -CEVA CONJUGATE OF X(4) (0.5649, -0.1989) X_204 = -CEVA CONJUGATE OF X(19) (0.6683, 3.3982) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) A B C X1 X34 X19 X56 X33 X64 X40 X108 X196 X204 X221 X78 X653 X207 (a, b, c) = (5, 6, 7) | AB = 1

X207 (X1-CEVA CONJUGATE OF X34) 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 \(f(A,B,C) = (1 - \sec A)(\sec B + \sec C - \sec A - 1)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.088051271957\)
▸ Incident Central Lines7 lines

{1, 196}, {19, 56}, {33, 64}, {34, 1042}, {40, 108}, {78, 653}, {204, 221}

▸ Functional Relations3 relations