X3087

INTERSECTION OF LINES X2X_95 AND X4X_6

Let A'B'C' be the anti-Euler triangle. X3087 is the radical center of the circumcircles of triangles A'BC, B'CA, C'AB. (Randy Hutson, June 7, 2019)
< 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) { 4, 6 }: Van Aubel Line { 2, 95 }: Central Line L(2, 95) { 20, 216 }: Central Line L(20, 216) { 29, 1778 }: Central Line L(29, 1778) { 19, 1877 }: Central Line L(19, 1877) { 32, 3088 }: Central Line L(32, 3088) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_1778 = MIMOSA TRANSFORM OF X(1171) (0.7708, 0.4831) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1877 = ZOSMA TRANSFORM OF X(517) (0.6803, 0.6665) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_3088 = INTERSECTION OF LINES X(2)X(3) AND X(33)X(3086) (0.5981, 0.3588) X_3087 = INTERSECTION OF LINES X(2)X(95) AND X(4)X(6) (0.6081, 0.3527) A B C X4 X6 X2 X95 X20 X216 X29 X1778 X19 X1877 X32 X3088 X3087 (a, b, c) = (5, 6, 7) | AB = 1

X3087 (INTERSECTION OF LINES X2X_95 AND X4X_6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(nbsp; = \sec A + \csc B \csc C : :\)
Barycentrics: \(\tan A + \cot B + \cot C : :\)
Search Value (6, 9, 13): \(1.748108010698\)
▸ Incident Central Lines6 lines

{2, 95}, {4, 6}, {19, 1877}, {20, 216}, {29, 1778}, {32, 3088}

▸ Functional Relations1 relation

  • X3087 = polar conjugate of X8797