X1971

CROSSDIFFERENCE OF PU(38)

X1971 = crosspoint of X98 and X275
< 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) { 6, 25 }: Central Line L(6, 25) { 98, 230 }: Central Line L(98, 230) { 237, 248 }: Central Line L(237, 248) { 50, 647 }: Central Line L(50, 647) { 53, 1629 }: Central Line L(53, 1629) { 217, 1614 }: Central Line L(217, 1614) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1972 = TRILINEAR POLE OF PU(38) (0.5839, -0.3149) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_98 = TARRY POINT (0.8891, -0.2281) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_248 = -LINE CONJUGATE OF X(132) (0.8229, -0.0790) X_50 = -CEVA CONJUGATE OF X(184) (2.1559, 2.8368) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_1629 = TCC-PERSPECTOR OF X(275) (0.6231, 0.4755) X_217 = -CEVA CONJUGATE OF X(51) (0.5928, 0.1915) X_1614 = TCC-PERSPECTOR OF X(54) (0.5582, -0.0024) X_1971 = CROSSDIFFERENCE OF PU(38) (1.3141, 4.2335) A B C X1972 X6 X25 X98 X230 X237 X248 X50 X647 X53 X1629 X217 X1614 X1971 (a, b, c) = (5, 6, 7) | AB = 1

X1971 (CROSSDIFFERENCE OF PU(38)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(\sin^{2} 2A - \sin 2B \sin 2C): :\)
Search Value (6, 9, 13): \(2.212777346604\)
▸ Incident Central Lines8 lines

{6, 25}, {50, 647}, {53, 1629}, {98, 230}, {217, 1614}, {237, 248}, {571, 1613}, {1609, 1619}

▸ Functional Relations6 relations