X1054

6th SHARYGIN POINT

X1054 = reflection of X1 in X106
< 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, 106 }: Central Line L(1, 106) { 1, 88 }: Central Line L(1, 88) { 43, 57 }: Central Line L(43, 57) { 105, 165 }: Central Line L(105, 165) { 2, 846 }: Central Line L(2, 846) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_2 = CENTROID (0.5374, 0.2000) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_1054 = 6th SHARYGIN POINT (1.4286, -0.2333) A B C X1 X106 X88 X43 X57 X105 X165 X2 X846 X1054 (a, b, c) = (5, 6, 7) | AB = 1

X1054 (6th SHARYGIN POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(b^{2} + c^{2} - a^{2} - 3bc + ab + ac : :\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(-0.870011732809\)

X1054 lies on the Bevan circle.

▸ Incident Central Lines9 lines

{1, 88}, {2, 846}, {43, 57}, {46, 978}, {81, 1051}, {105, 165}, {474, 986}, {513, 1052}, {905, 1053}

▸ Functional Relations11 relations

Notes

See the description at X1281.