X1258

ISOGONAL CONJUGATE OF X1107

X1258 is the isogonal conjugate of X1107.
< 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) { 81, 172 }: Central Line L(81, 172) { 6, 330 }: Central Line L(6, 330) { 213, 274 }: Central Line L(213, 274) { 171, 904 }: Central Line L(171, 904) { 291, 1193 }: Central Line L(291, 1193) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1107 = CROSSPOINT OF X(1) AND X(274) (0.5495, 0.2072) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_330 = ISOTOMIC CONJUGATE OF X(192) (0.4364, 0.1391) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_904 = -HIRST INVERSE OF X(256) (0.6163, 0.2816) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_1193 = 3rd SARAGOSSA POINT OF X(1) (0.5959, 0.2573) X_1258 = ISOGONAL CONJUGATE OF X(1107) (0.5907, 0.2599) A B C X1107 X81 X172 X6 X330 X213 X274 X171 X904 X291 X1193 X1258 (a, b, c) = (5, 6, 7) | AB = 1

X1258 (ISOGONAL CONJUGATE OF X1107) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as in X1107
Search Value (6, 9, 13): \(1.190913421782\)
▸ Incident Central Lines5 lines

{6, 330}, {81, 172}, {171, 904}, {213, 274}, {291, 1193}

▸ Functional Relations3 relations