X257

ISOGONAL CONJUGATE OF X172

X257 is the isogonal conjugate of X172.
< 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) { 8, 192 }: Central Line L(8, 192) { 29, 242 }: Central Line L(29, 242) { 1, 385 }: Central Line L(1, 385) { 92, 297 }: Central Line L(92, 297) { 239, 333 }: Central Line L(239, 333) { 75, 698 }: Central Line L(75, 698) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_8 = NAGEL POINT (0.4694, 0.1333) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_242 = -LINE CONJUGATE OF X(71) (0.7507, 0.7161) X_1 = INCENTER (0.5714, 0.2333) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_297 = -HIRST INVERSE OF X(4) (0.8440, 1.0022) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_698 = EVEN (- 4, - 2) INFINITY POINT (1.0503, 0.4852) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) A B C X172 X8 X192 X29 X242 X1 X385 X92 X297 X239 X333 X75 X698 X257 (a, b, c) = (5, 6, 7) | AB = 1

X257 (ISOGONAL CONJUGATE OF X172) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(a^{3} + abc) : 1/(b^{3} + abc) : 1/(c^{3} + abc)\)
Barycentrics: \(1/(a^{2} + bc) : 1/(b^{2} + ca) : 1/(c^{2} + ab)\)
Search Value (6, 9, 13): \(2.978484050838\)
▸ Incident Central Lines10 lines

{1, 385}, {8, 192}, {29, 242}, {65, 894}, {75, 698}, {92, 297}, {194, 986}, {239, 333}, {330, 982}, {335, 694}

▸ Functional Relations8 relations