X294

ISOGONAL CONJUGATE OF X241

X294 is the isogonal conjugate of X241.
< 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) { 6, 7 }: Central Line L(6, 7) { 1, 41 }: Central Line L(1, 41) { 4, 218 }: Central Line L(4, 218) { 8, 220 }: Central Line L(8, 220) { 84, 580 }: Central Line L(84, 580) { 239, 666 }: Central Line L(239, 666) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1 = INCENTER (0.5714, 0.2333) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_4 = ORTHOCENTER (0.6122, 0.3958) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_8 = NAGEL POINT (0.4694, 0.1333) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_666 = TRILINEAR POLE OF LINE X(2)X(11) (1.0982, 0.1428) X_294 = ISOGONAL CONJUGATE OF X(241) (0.9276, -0.0575) A B C X241 X6 X7 X1 X41 X4 X218 X8 X220 X84 X580 X239 X666 X294 (a, b, c) = (5, 6, 7) | AB = 1

X294 (ISOGONAL CONJUGATE OF X241) 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 \(f(a,b,c) = (b + c - a)/(b^{2} + c^{2} - ab - ac)\)
Search Value (6, 9, 13): \(2.052081234010\)
▸ Incident Central Lines11 lines

{1, 41}, {2, 949}, {4, 218}, {6, 7}, {8, 220}, {19, 1041}, {84, 580}, {104, 919}, {239, 666}, {241, 910}, {314, 645}

▸ Functional Relations9 relations

Notes

X294 is the perspector of the anticevian triangle of X105 and the unary cofactor triangle of the intangents triangle. (Randy Hutson, January 15, 2019)