X3821

X3056com(4th EULER TRIANGLE)

X3821 = X10 of 1st Brocard triangle
< 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, 3923 }: Central Line L(2, 3923) { 10, 75 }: Central Line L(10, 75) { 3, 142 }: Central Line L(3, 142) { 2, 846 }: Central Line L(2, 846) { 141, 740 }: Central Line L(141, 740) 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_3923 = com[1st BROCARD TRIANGLE))] (0.5293, 0.2039) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_740 = EVEN (- 1, 1) INFINITY POINT (0.9745, 0.5915) X_3821 = com(4th EULER TRIANGLE) (0.5415, 0.1980) A B C Ma Mb Mc X2 X3923 X10 X75 X3 X142 X846 X141 X740 X3821 (a, b, c) = (5, 6, 7) | AB = 1

X3821 (X3056com(4th EULER TRIANGLE)) 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 \(f(a,b,c) = b^{3} + c^{3} + a^{2}b + a^{2}c + ab^{2} + ac^{2}\)
Search Value (6, 9, 13): \(2.569938753598\)
▸ Incident Central Lines18 lines

{1, 2896}, {2, 846}, {3, 142}, {10, 75}, {45, 3634}, {86, 1326}, {141, 740}, {182, 2792}, {226, 1403}, {519, 599}, {579, 1761}, {752, 1386}, {1352, 2784}, {1698, 3729}, {2085, 3670}, {2092, 3454}, {2887, 3666}, {3094, 3735}

▸ Functional Relations5 relations