X3796

X2com[INVERSE(nT(a², a² + c²))]

X3796 = crossdifference of every pair of points on line X826X2501
< 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, 22 }: Central Line L(6, 22) { 3, 49 }: Central Line L(3, 49) { 2, 154 }: Central Line L(2, 154) { 25, 182 }: Central Line L(25, 182) { 206, 1619 }: Central Line L(206, 1619) { 458, 1629 }: Central Line L(458, 1629) 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_22 = EXETER POINT (0.4143, -0.1221) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_2 = CENTROID (0.5374, 0.2000) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_1619 = TCC-PERSPECTOR OF X(63) (0.4315, -1.6641) X_458 = EULER LINE INTERCEPT OF LINE X(76)X(275) (0.5800, 0.3115) X_1629 = TCC-PERSPECTOR OF X(275) (0.6231, 0.4755) X_3796 = com[INVERSE(nT(a2, a2 + c2))] (0.5298, 0.1200) A B C X6 X22 X3 X49 X2 X154 X25 X182 X206 X1619 X458 X1629 X3796 (a, b, c) = (5, 6, 7) | AB = 1

X3796 (X2com[INVERSE(nT(a², a² + c²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{2}(b^{2} + c^{2} - a^{2})(b^{2} + c^{2} + 3a^{2})\)
Search Value (6, 9, 13): \(12.263391984167\)
▸ Incident Central Lines9 lines

{2, 154}, {3, 49}, {6, 22}, {25, 182}, {206, 1619}, {458, 1629}, {1184, 1691}, {1350, 1993}, {3051, 3053}

▸ Functional Relations3 relations