X1352

REFLECTION OF X6 IN X5

X1352 is the reflection of X6 in X5.
< 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) { 6, 5 }: Nine-Point–Symmedian Line { 3, 66 }: Central Line L(3, 66) { 4, 69 }: Central Line L(4, 69) { 2, 98 }: Central Line L(2, 98) { 25, 343 }: Central Line L(25, 343) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_2 = CENTROID (0.5374, 0.2000) X_98 = TARRY POINT (0.8891, -0.2281) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_343 = ISOTOMIC CONJUGATE OF X(275) (0.4345, 0.0893) X_1352 = REFLECTION OF X(6) IN X(5) (0.5122, 0.2306) A B C X6 X5 X3 X66 X4 X69 X2 X98 X25 X343 X1352 (a, b, c) = (5, 6, 7) | AB = 1

X1352 (REFLECTION OF X6 IN X5) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a - 2R \cos(B-C) \cot \omega : :\)
Barycentrics: \(S^{2} S_{A} + S_{B} S_{C} S_{\omega} : :\)
Search Value (6, 9, 13): \(0.112834988204\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(\sin A - \cos(B - C) \cot \omega : :\)

  • Barycentrics: \((\cot A + \cot B + \cot C) \tan A + (\tan A + \tan B + \tan C) \cot A : :\)

  • Barycentrics: \(a^{6} - a^{4} (b^{2} + c^{2}) + a^{2} (b^{2} + c^{2})^{2} - (b^{2} + c^{2}) (b^{2} - c^{2})^{2} : :\)

▸ Incident Central Lines17 lines

{2, 98}, {3, 66}, {4, 69}, {5, 6}, {11, 613}, {12, 611}, {25, 343}, {30, 599}, {70, 1176}, {193, 576}, {206, 1209}, {298, 383}, {299, 1080}, {355, 518}, {381, 524}, {394, 426}, {2794, 3734}

▸ Functional Relations13 relations