X571

ORTHOHARMONIC OF X52

X571 = inverse-in-Brocard-circle of X570
< 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) { 3, 6 }: Brocard Axis { 4, 96 }: Central Line L(4, 96) { 66, 248 }: Central Line L(66, 248) { 160, 184 }: Central Line L(160, 184) { 206, 237 }: Central Line L(206, 237) { 112, 393 }: Central Line L(112, 393) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_96 = ISOGONAL CONJUGATE OF X(52) (-0.0943, -0.0197) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_248 = -LINE CONJUGATE OF X(132) (0.8229, -0.0790) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_571 = ORTHOHARMONIC OF X(52) (0.7141, 0.4556) A B C X3 X6 X4 X96 X66 X248 X160 X184 X206 X237 X112 X393 X571 (a, b, c) = (5, 6, 7) | AB = 1

X571 (ORTHOHARMONIC OF X52) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin A \cos 2A\) (M. Iliev, 4/12/07)
Search Value (6, 9, 13): \(-4.238654963023\)
▸ Incident Central Lines8 lines

{3, 6}, {4, 96}, {66, 248}, {112, 393}, {160, 184}, {206, 237}, {230, 427}, {608, 913}

▸ Functional Relations13 relations

Notes

Let OAOBOC be the Kosnita triangle. Let A″ be the barycentric product OB*OC, and define B″ and C″ cyclically. The lines AA″, BB″, CC″ concur in X571. (Randy Hutson, December 2, 2017)