X3619

H(X6; M, -1/2)

X3619 = {X2,X69}-harmonic conjugate of 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) { 2, 69 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 631, 1352 }: Central Line L(631, 1352) { 4, 3096 }: Central Line L(4, 3096) { 511, 3090 }: Central Line L(511, 3090) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3618 = H(X(6); M,1/2) (0.5624, 0.2269) X_2 = CENTROID (0.5374, 0.2000) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_631 = 3/5*OG (0.5224, 0.1608) X_1352 = REFLECTION OF X(6) IN X(5) (0.5122, 0.2306) X_4 = ORTHOCENTER (0.6122, 0.3958) X_3096 = INTERSECTION OF LINES X(2)X(32) AND X(76)X(141) (0.5156, 0.1716) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_3090 = INTERSECTION OF LINES X(2)X(3) AND X(11)X(1058) (0.5481, 0.2279) X_3619 = H(X(6); M, -1/2) (0.5195, 0.1807) A B C X3618 X2 X69 X6 X631 X1352 X4 X3096 X511 X3090 X3619 (a, b, c) = (5, 6, 7) | AB = 1

X3619 (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 \(f(a,b,c) = bc(a^{2} + 3b^{2} + 3c^{2})\)
Barycentrics: \(a^{2} + 3b^{2} + 3c^{2} : b^{2} + 3c^{2} + 3a^{2} : c^{2} + 3a^{2} + 3b^{2}\)
Search Value (6, 9, 13): \(3.096928877467\)
▸ Incident Central Lines8 lines

{2, 6}, {4, 3096}, {182, 3525}, {511, 3090}, {631, 1352}, {1350, 3091}, {1503, 3523}, {3526, 3564}

▸ Functional Relations2 relations