X757

ISOGONAL CONJUGATE OF X756

X757 is the isogonal conjugate of X756.
< 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) { 58, 86 }: Central Line L(58, 86) { 171, 319 }: Central Line L(171, 319) { 6, 662 }: Central Line L(6, 662) { 81, 593 }: Central Line L(81, 593) { 60, 1014 }: Central Line L(60, 1014) { 763, 849 }: Central Line L(763, 849) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_593 = 1st HATZIPOLAKIS-YIU POINT (0.6202, 0.3026) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_1014 = ISOGONAL CONJUGATE OF X(210) (0.6222, 0.3285) X_763 = ISOGONAL CONJUGATE OF X(762) (0.6080, 0.2866) X_849 = 4th HATZIPOLAKIS-YIU POINT (0.6376, 0.3351) X_757 = ISOGONAL CONJUGATE OF X(756) (0.5971, 0.2688) A B C X756 X58 X86 X171 X319 X6 X662 X81 X593 X60 X1014 X763 X849 X757 (a, b, c) = (5, 6, 7) | AB = 1

X757 (ISOGONAL CONJUGATE OF X756) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b + c) ^{-2} : (c + a) ^{-2} : (a + b) ^{-2}\)
Barycentrics: \(a(b + c) ^{-2} : b(c + a) ^{-2} : c(a + b) ^{-2}\)
Search Value (6, 9, 13): \(1.028192172661\)
▸ Incident Central Lines6 lines

{6, 662}, {58, 86}, {60, 1014}, {81, 593}, {171, 319}, {763, 849}

▸ Functional Relations5 relations