X3618

H(X6; M,1/2)

X3618 = reflection of X69 in X3620
< 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) { 69, 3620 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 4, 83 }: Central Line L(4, 83) { 1, 344 }: Central Line L(1, 344) { 393, 458 }: Central Line L(393, 458) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_3620 = H(X(6); M, -2) (0.4873, 0.1462) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_1 = INCENTER (0.5714, 0.2333) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.6218, 0.2693) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_458 = EULER LINE INTERCEPT OF LINE X(76)X(275) (0.5800, 0.3115) X_3618 = H(X(6); M,1/2) (0.5624, 0.2269) A B C X69 X3620 X2 X6 X4 X83 X1 X344 X393 X458 X3618 (a, b, c) = (5, 6, 7) | AB = 1

X3618 (H(X6; M,1/2)) 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 \(f(a,b,c) = bc(3a^{2} + b^{2} + c^{2})\)
Barycentrics: \(\cot B + \cot C + \cot \omega : :\)
Search Value (6, 9, 13): \(1.974784673519\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(3a^{2} + b^{2} + c^{2} : 3b^{2} + c^{2} + a^{2} : 3c^{2} + a^{2} + b^{2}\)

▸ Incident Central Lines30 lines

{1, 344}, {2, 6}, {4, 83}, {8, 1386}, {20, 5085}, {140, 1351}, {159, 1995}, {239, 2345}, {264, 1249}, {297, 3087}, {316, 2030}, {348, 1445}, {388, 1428}, {393, 458}, {459, 1843}, {487, 3311}, {488, 3312}, {497, 2330}, {511, 631}, {575, 1352}, {576, 3525}, {611, 3086}, {613, 3085}, {625, 1692}, {1350, 3523}, {1503, 3091}, {1656, 3564}, {2297, 2999}, {3060, 3313}, {3098, 3524}

▸ Functional Relations8 relations