X3788

X3053com[T(a², a² - b²)]

X3788 = complement of X3767
< 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, 3767 }: Central Line L(2, 3767) { 2, 39 }: Central Line L(2, 39) { 3, 114 }: Central Line L(3, 114) { 140, 141 }: Central Line L(140, 141) { 32, 325 }: Central Line L(32, 325) 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_3767 = com[T(a2, a2 - c2)] (0.6585, 0.2916) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_3788 = comT(a2, a2 - b2))] (0.4769, 0.1541) A B C Ma Mb Mc X2 X3767 X39 X3 X114 X140 X141 X32 X325 X3788 (a, b, c) = (5, 6, 7) | AB = 1

X3788 (X3053com[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 \(f(a,b,c) = (a^{4} + b^{4} + c^{4} - a^{2}b^{2} - a^{2}c^{2})\)
Search Value (6, 9, 13): \(3.385874204042\)
▸ Incident Central Lines13 lines

{2, 39}, {3, 114}, {4, 625}, {5, 3734}, {32, 325}, {69, 1692}, {115, 1975}, {140, 141}, {187, 315}, {316, 3552}, {754, 3053}, {1007, 2548}, {1078, 3314}

▸ Functional Relations2 relations