X3329

INTERSECTION OF LINES X2X_6 AND X39X_83

X3229 = crossdifference of PU(148)
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3978 }: Central Line L(2, 3978) { 2, 6 }: Centroid–Symmedian Line { 39, 83 }: Central Line L(39, 83) { 5, 147 }: Central Line L(5, 147) { 182, 262 }: Central Line L(182, 262) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_3978 = com[INVERSE(n(1st BROCARD TRIANGLE))] (-1.5999, -1.4184) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_3329 = INTERSECTION OF LINES X(2)X(6) AND X(39)X(83) (0.5693, 0.2342) A B C Ma Mb Mc X2 X3978 X6 X39 X83 X5 X147 X182 X262 X3329 (a, b, c) = (5, 6, 7) | AB = 1

X3329 (INTERSECTION OF LINES X2X_6 AND X39X_83) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

  • Derived Triangle: Medial Triangle △MaMbMc — vertices Ma, Mb, Mc (Formed by the midpoints of sides BC, CA, AB)

  • Central Lines: {2, 3978}

  • Related Centers: X2 (CENTROID), X3978 (com[INVERSE)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(a^{4} + 2a^{2}b^{2} + 2a^{2}c^{2} + b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.736180303749\)
▸ Incident Central Lines7 lines

{2, 6}, {5, 147}, {39, 83}, {98, 575}, {182, 262}, {427, 1031}, {7761, 7812}

▸ Functional Relations4 relations