X3117

ISOGONAL CONJUGATE OF TgX(32)

X3117 is the isogonal conjugate of tgx(32).
< 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) { 2, 39 }: Central Line L(2, 39) { 32, 184 }: Central Line L(32, 184) { 187, 353 }: Central Line L(187, 353) { 3, 695 }: Central Line L(3, 695) { 6, 694 }: Central Line L(6, 694) { 99, 707 }: Central Line L(99, 707) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3114 = TgX(32) (0.5198, 0.2057) X_2 = CENTROID (0.5374, 0.2000) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_353 = INVERSE-IN-BROCARD-CIRCLE OF X(111) (0.5667, 0.1759) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_99 = STEINER POINT (0.1109, 0.4322) X_707 = EVEN (- 4, 2) CIRCUMCIRCLE POINT (1.0099, 0.1232) X_3117 = ISOGONAL CONJUGATE OF TgX(32) (0.6152, 0.2589) A B C X3114 X2 X39 X32 X184 X187 X353 X3 X695 X6 X694 X99 X707 X3117 (a, b, c) = (5, 6, 7) | AB = 1

X3117 (ISOGONAL CONJUGATE OF TgX(32)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{3}(b^{4} + c^{4} + b^{2}c^{2}) : :\)
Search Value (6, 9, 13): \(0.822397279633\)
▸ Incident Central Lines9 lines

{2, 39}, {3, 695}, {6, 694}, {32, 184}, {99, 707}, {110, 737}, {187, 353}, {982, 2275}, {1334, 3009}

▸ Functional Relations2 relations

Notes

Let P1' and U1' be the Steiner-circumellipse-inverses of P(1) and U(1), resp. Then X3117 = P(1)U1'∩U(1)P1'. (Randy Hutson, January 17, 2020)