X228

X3-CEVA CONJUGATE OF X71

X228 = X212-beth conjugate of X228
< 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) { 19, 25 }: Central Line L(19, 25) { 31, 32 }: Central Line L(31, 32) { 3, 63 }: Central Line L(3, 63) { 98, 100 }: Central Line L(98, 100) { 42, 181 }: Central Line L(42, 181) { 48, 184 }: Central Line L(48, 184) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_19 = CLAWSON POINT (0.6246, 0.4244) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_98 = TARRY POINT (0.8891, -0.2281) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) A B C X3 X71 X19 X25 X31 X32 X63 X98 X100 X42 X181 X48 X184 X228 (a, b, c) = (5, 6, 7) | AB = 1

X228 (X3-CEVA CONJUGATE OF X71) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\sin 2A)(\sin B + \sin C) : (\sin 2B)(\sin C + \sin A) : (\sin 2C)(\sin A + \sin B)\)
Barycentrics: \((\sin A \sin 2A)(\sin B + \sin C) : (\sin B \sin 2B)(\sin C + \sin A) : (\sin C \sin 2C)(\sin A + \sin B)\)
Search Value (6, 9, 13): \(7.858247558978\)
▸ Incident Central Lines12 lines

{3, 63}, {9, 1011}, {12, 407}, {19, 25}, {28, 943}, {31, 32}, {35, 846}, {42, 181}, {48, 184}, {73, 408}, {98, 100}, {226, 851}

▸ Functional Relations13 relations