X1502

ISOGONAL CONJUGATE OF X1501

X1502 is the isogonal conjugate of X1501.
< 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) { 76, 141 }: Central Line L(76, 141) { 99, 160 }: Central Line L(99, 160) { 2, 308 }: Central Line L(2, 308) { 69, 290 }: Central Line L(69, 290) { 66, 315 }: Central Line L(66, 315) { 264, 305 }: Central Line L(264, 305) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1501 = TRILINEAR 5th POWER POINT (0.6596, 0.3922) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_99 = STEINER POINT (0.1109, 0.4322) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) X_2 = CENTROID (0.5374, 0.2000) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4915, 0.1700) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_290 = ISOGONAL CONJUGATE OF X(237) (0.7829, -0.1380) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_1502 = ISOGONAL CONJUGATE OF X(1501) (0.3682, 0.0896) A B C X1501 X76 X141 X99 X160 X2 X308 X69 X290 X66 X315 X264 X305 X1502 (a, b, c) = (5, 6, 7) | AB = 1

X1502 (ISOGONAL CONJUGATE OF X1501) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{-5} : b^{- 5} : c^{- 5}\)
Barycentrics: \(a^{- 4} : b^{- 4} : c^{- 4}\)
Search Value (6, 9, 13): \(6.346495489831\)
▸ Incident Central Lines13 lines

{1, 704}, {2, 308}, {6, 706}, {31, 708}, {32, 710}, {66, 315}, {69, 290}, {75, 700}, {76, 141}, {99, 160}, {264, 305}, {311, 327}, {313, 561}

▸ Functional Relations10 relations

Notes

X1502 is the Brianchon point (perspector) of the inellipse that is the barycentric square of the de Longchamps line. The center of this inellipse is X626. (Randy Hutson, October 15, 2018)