X1987

1st LEMOINE ANTIPARALLELS POINT

X1987 is discussed in Lemoine’s paper cited at X19. Contributed by Darij Grinberg.
< 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) { 54, 112 }: Central Line L(54, 112) { 237, 248 }: Central Line L(237, 248) { 290, 297 }: Central Line L(290, 297) { 3, 1625 }: Central Line L(3, 1625) { 72, 1956 }: Central Line L(72, 1956) { 69, 1972 }: Central Line L(69, 1972) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_217 = -CEVA CONJUGATE OF X(51) (0.5928, 0.1915) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_54 = KOSNITA POINT (0.5880, 0.2176) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_248 = -LINE CONJUGATE OF X(132) (0.8229, -0.0790) X_290 = ISOGONAL CONJUGATE OF X(237) (0.7829, -0.1380) X_297 = -HIRST INVERSE OF X(4) (0.8440, 1.0022) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1625 = TCC-PERSPECTOR OF X(163) (0.3499, 0.5717) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1956 = TRILINEAR POLE OF PU(21) (0.6554, -0.4540) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_1972 = TRILINEAR POLE OF PU(38) (0.5839, -0.3149) X_1987 = 1st LEMOINE ANTIPARALLELS POINT (0.7533, -0.6902) A B C X217 X237 X54 X112 X248 X290 X297 X3 X1625 X72 X1956 X69 X1972 X1987 (a, b, c) = (5, 6, 7) | AB = 1

X1987 (1st LEMOINE ANTIPARALLELS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\sin A)/(\sin^{2} 2A - \sin 2B \sin 2C) : :\)
Search Value (6, 9, 13): \(-0.001708880327\)
▸ Incident Central Lines6 lines

{3, 1625}, {54, 112}, {69, 1972}, {72, 1956}, {237, 248}, {290, 297}

▸ Functional Relations7 relations