X1402

X42-BETH CONJUGATE OF X42

X1402 = isogonal conjugate of X314
< 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) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 98, 108 }: Central Line L(98, 108) { 31, 184 }: Central Line L(31, 184) { 42, 181 }: Central Line L(42, 181) { 109, 741 }: Central Line L(109, 741) { 21, 961 }: Central Line L(21, 961) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_98 = TARRY POINT (0.8891, -0.2281) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_961 = ISOGONAL CONJUGATE OF X(960) (0.6167, 0.3210) X_1402 = -BETH CONJUGATE OF X(42) (0.6396, 0.3585) A B C X42 X1 X3 X98 X108 X31 X184 X181 X109 X741 X21 X961 X1402 (a, b, c) = (5, 6, 7) | AB = 1

X1402 (X42-BETH CONJUGATE OF X42) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((1 - \cos A)u(a,b,c) : :\), where \(u : v : w\) = X42
Search Value (6, 9, 13): \(0.129009867734\)
▸ Alternate Coordinates2 forms

  • Trilinears: \((\sin^{2} A) (\cos B + \cos C) : :\)

  • Trilinears: \(a^{2} (b + c)/(a - b - c) : :\)

▸ Incident Central Lines17 lines

{1, 3}, {21, 961}, {25, 1096}, {31, 184}, {32, 1395}, {42, 181}, {73, 1245}, {98, 108}, {109, 741}, {172, 893}, {226, 1284}, {923, 1415}, {968, 1011}, {1042, 1410}, {1399, 1408}, {1401, 1458}, {1441, 1447}

▸ Functional Relations6 relations