X1218

ISOGONAL CONJUGATE OF X1185

X1218 is the isogonal conjugate of X1185.
< 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) { 37, 76 }: Central Line L(37, 76) { 42, 75 }: Central Line L(42, 75) { 6, 274 }: Central Line L(6, 274) { 25, 286 }: Central Line L(25, 286) { 767, 785 }: Central Line L(767, 785) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1185 = 2nd SARAGOSSA POINT OF X(31) (0.6116, 0.2797) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_286 = -CROSS CONJUGATE OF X(27) (0.6033, 0.3810) X_767 = EVEN (3, 4) CIRCUMCIRCLE POINT (0.8487, -0.2706) X_785 = o-(- 3, - 2) CIRCUMCIRCLE POINT (0.2590, 0.5519) X_1218 = ISOGONAL CONJUGATE OF X(1185) (0.5201, 0.1877) A B C X1185 X37 X76 X42 X75 X6 X274 X25 X286 X767 X785 X1218 (a, b, c) = (5, 6, 7) | AB = 1

X1218 (ISOGONAL CONJUGATE OF X1185) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as in X1185
Search Value (6, 9, 13): \(3.133875477644\)
▸ Incident Central Lines5 lines

{6, 274}, {25, 286}, {37, 76}, {42, 75}, {767, 785}

▸ Functional Relations3 relations