X160

X37-OF-TANGENTIAL-TRIANGLE

X160 = X95-Ceva conjugate of X6
< 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) { 3, 66 }: Central Line L(3, 66) { 6, 237 }: Central Line L(6, 237) { 206, 57 }: Central Line L(206, 57) { 22, 325 }: Central Line L(22, 325) { 95, 327 }: Central Line L(95, 327) { 154, 418 }: Central Line L(154, 418) 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_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_22 = EXETER POINT (0.4143, -0.1221) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_327 = ISOTOMIC CONJUGATE OF X(182) (0.5260, 0.2156) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_418 = -CEVA-CONJUGATE OF X(216) (0.4854, 0.0640) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) A B C X3 X66 X6 X237 X206 X57 X22 X325 X95 X327 X154 X418 X160 (a, b, c) = (5, 6, 7) | AB = 1

X160 (X37-OF-TANGENTIAL-TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a[(b^{2} + c^{2})\sin 2A + (c^{2} - a^{2})\sin 2B + (b^{2} - a^{2})\sin 2C]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-5.178584683463\)
▸ Incident Central Lines6 lines

{3, 66}, {6, 237}, {22, 325}, {95, 327}, {154, 418}, {206, 57}

▸ Functional Relations5 relations