X3771

X1707com[T(a², a² - b²)]

< 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) { 1, 2 }: Nagel Line { 345, 726 }: Central Line L(345, 726) { 55, 2887 }: Central Line L(55, 2887) { 752, 3052 }: Central Line L(752, 3052) { 1575, 3694 }: Central Line L(1575, 3694) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_2887 = COMPLEMENTARY CONJUGATE OF X(37) (0.4947, 0.1495) X_752 = EVEN (0, 3) INFINITY POINT (0.9166, 0.6478) X_3052 = INTERSECTION X(31)X(42)∩X(32)X(220) (0.6825, 0.3888) X_1575 = EXSIMILICENTER OF SPIEKER AND (1/2)-MOSES CIRCLES (2.5675, 1.8684) X_3694 = com(EXTOUCH TRIANGLE) (0.3640, 0.0432) X_3771 = com[T(a2, a2 - b2)] (0.4508, 0.1151) A B C X1 X2 X345 X726 X55 X2887 X752 X3052 X1575 X3694 X3771 (a, b, c) = (5, 6, 7) | AB = 1

X3771 (X1707com[T(a², a² - b²)]) 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 \(f(a,b,c) = a^{3} + b^{3} + c^{3} - a^{2}b - a^{2}c\)
Search Value (6, 9, 13): \(4.065142541019\)
▸ Incident Central Lines5 lines

{1, 2}, {55, 2887}, {345, 726}, {752, 3052}, {1575, 3694}