X3620

H(X6; M, -2)

X3620 = midpoint of X69 and X3618
< 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, 3618 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 20, 1352 }: Central Line L(20, 1352) { 8, 1738 }: Central Line L(8, 1738) { 320, 2345 }: Central Line L(320, 2345) 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_3618 = H(X(6); M,1/2) (0.5624, 0.2269) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_1352 = REFLECTION OF X(6) IN X(5) (0.5122, 0.2306) X_8 = NAGEL POINT (0.4694, 0.1333) X_1738 = MIMOSA TRANSFORM OF X(105) (1.2925, 0.7221) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_2345 = -ISOCONJUGATE OF X(1472) (0.5222, 0.1875) X_3620 = H(X(6); M, -2) (0.4873, 0.1462) A B C X69 X3618 X2 X6 X20 X1352 X8 X1738 X320 X2345 X3620 (a, b, c) = (5, 6, 7) | AB = 1

X3620 (H(X6; M, -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 \(f(a,b,c) = bc(a^{2} - 3b^{2} - 3c^{2})\)
Barycentrics: \(a^{2} - 3b^{2} - 3c^{2} : b^{2} - 3c^{2} - 3a^{2} : c^{2} - 3a^{2} - 3b^{2}\)
Search Value (6, 9, 13): \(3.938537030427\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(\cot A - \cot B - \cot C + 2 \cot \omega : :\)

▸ Incident Central Lines16 lines

{2, 6}, {8, 1738}, {20, 1352}, {66, 3410}, {76, 2996}, {145, 3416}, {253, 3164}, {320, 2345}, {340, 3087}, {511, 3091}, {631, 3564}, {1350, 3146}, {1351, 3090}, {1353, 3526}, {1503, 3522}, {1843, 2979}

▸ Functional Relations3 relations