X3819

X549com(2nd EULER TRIANGLE)

X3819 = complement of X51
< 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, 51 }: Central Line L(2, 51) { 3, 64 }: Central Line L(3, 64) { 122, 129 }: Central Line L(122, 129) { 140, 389 }: Central Line L(140, 389) { 182, 394 }: Central Line L(182, 394) 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_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_122 = -OF-MEDIAL-TRIANGLE (0.5195, -0.0036) X_129 = -OF-ORTHIC-TRIANGLE (0.4587, 0.4847) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_389 = CENTER OF THE TAYLOR CIRCLE (0.6078, 0.2800) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_3819 = com(2nd EULER TRIANGLE) (0.5015, 0.1406) A B C Ma Mb Mc X2 X51 X3 X64 X122 X129 X140 X389 X182 X394 X3819 (a, b, c) = (5, 6, 7) | AB = 1

X3819 (X549com(2nd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{2}(b^{4} + c^{4} - a^{2}b^{2} - a^{2}c^{2} + 4b^{2}c^{2}) : :\)
Search Value (6, 9, 13): \(3.883740397379\)
▸ Incident Central Lines23 lines

{2, 51}, {3, 64}, {25, 3098}, {39, 1613}, {52, 3526}, {122, 129}, {140, 389}, {141, 1368}, {182, 394}, {185, 3523}, {187, 1915}, {210, 2810}, {474, 970}, {575, 1993}, {674, 3742}, {960, 2390}, {982, 3688}, {984, 1401}, {1194, 3231}, {1196, 3094}, {1843, 3619}, {3218, 3690}, {3533, 3567}

▸ Functional Relations2 relations

  • X3819 = complement of X51

  • X3819 = X2 of polar triangle of complement of polar circle

Notes

Let MaMbMc be the medial triangle. Let Ab and Ac be the circumcircle intercepts of line MbMc. Define Bc and Ca cyclically, and define Ba and Cb cyclically. X3819 is the centroid of AbAcBcBaCaCb. (Randy Hutson, July 31 2018)