X1132

ARCTAN(-2) KIEPERT POINT

X1132 is constructed in the manner for X1131, using squares erected inward, so that the three equal angles have common measure arctan(-2), and X1132 lies on the Kiepert hyperbola. (Darij Grinberg 9/22/02)
< 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) { 176, 226 }: Central Line L(176, 226) { 2, 489 }: Central Line L(2, 489) { 20, 486 }: Central Line L(20, 486) { 6, 1131 }: Central Line L(6, 1131) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1152 = ISOGONAL CONJUGATE OF X(1132) (-0.9520, -2.2961) X_176 = EQUAL DETOUR POINT (0.5803, 0.2537) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_2 = CENTROID (0.5374, 0.2000) X_489 = CEVAPOINT OF X(20) AND X(487) (0.4404, 0.3605) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1131 = ARCTAN(2) KIEPERT POINT (0.5904, 0.2888) X_1132 = ARCTAN(-2) KIEPERT POINT (0.8864, -0.3774) A B C X1152 X176 X226 X2 X489 X20 X486 X6 X1131 X1132 (a, b, c) = (5, 6, 7) | AB = 1

X1132 (ARCTAN(-2) KIEPERT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(\sin A - 2 \cos A) : :\)
Barycentrics: \(1/(2 S_{A} - S) : :\)
Search Value (6, 9, 13): \(5.273284003472\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\csc(A - t) : :\), where t = arctan(2)

▸ Incident Central Lines5 lines

{2, 489}, {4, 3312}, {6, 1131}, {20, 486}, {176, 226}

▸ Functional Relations5 relations