X851

X65-HIRST INVERSE OF X73

X851 is the X65-hirst inverse of X73.
< 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) { 855, 859 }: Euler Line { 2, 3 }: Euler Line { 43, 46 }: Central Line L(43, 46) { 42, 65 }: Central Line L(42, 65) { 226, 228 }: Central Line L(226, 228) { 44, 513 }: Central Line L(44, 513) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_855 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(57) (0.8408, 0.9939) X_859 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(81) (1.1279, 1.7448) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_851 = -HIRST INVERSE OF X(73) (1.4149, 2.4958) A B C X855 X859 X2 X3 X43 X46 X42 X65 X226 X228 X44 X513 X851 (a, b, c) = (5, 6, 7) | AB = 1

X851 (X65-HIRST INVERSE OF X73) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin 2B \sin(C - A) + \sin 2C \sin(B - A) : :\)
Search Value (6, 9, 13): \(-3.990242182884\)
▸ Alternate Coordinates2 forms

  • Trilinears: \((\cos A + \cos B + \cos C) \csc A - (\csc A + \csc B + \csc C) \cos A : :\)

  • Trilinears: \((\sec A + \sec B + \sec C) \csc A - (\csc A + \csc B + \csc C) \sec A : :\)

▸ Incident Central Lines5 lines

{2, 3}, {42, 65}, {43, 46}, {44, 513}, {226, 228}

▸ Functional Relations9 relations

Notes

As a point on the Euler line, X851 has Shinagawa coefficients \((\$bcS_{B}S_{C}\$,-\$bc\$S^{2})\).