X3744

X31com[n(MEDIAL)*n(INCENTRAL)]

X3744 = complement of X5014
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 37, 82 }: Central Line L(37, 82) { 210, 238 }: Central Line L(210, 238) { 145, 345 }: Central Line L(145, 345) { 31, 518 }: Central Line L(31, 518) { 72, 595 }: Central Line L(72, 595) 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_3 = CIRCUMCENTER (0.5000, 0.1021) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_3744 = com[n(MEDIAL)*n(INCENTRAL)] (0.5815, 0.2517) A B C X1 X3 X37 X82 X210 X238 X145 X345 X31 X518 X72 X595 X3744 (a, b, c) = (5, 6, 7) | AB = 1

X3744 (X31com[n(MEDIAL)*n(INCENTRAL)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a(2a^{2} + b^{2} + c^{2} - ab - ac)\)
Search Value (6, 9, 13): \(1.431005930985\)
▸ Linear Combinations1 combination
▸ Incident Central Lines23 lines

{1, 3}, {2, 1279}, {8, 1104}, {31, 518}, {37, 82}, {38, 902}, {42, 1386}, {58, 3555}, {63, 3052}, {72, 595}, {78, 1191}, {81, 643}, {145, 345}, {210, 238}, {612, 1001}, {614, 1376}, {748, 3246}, {749, 1100}, {960, 976}, {1455, 3476}, {2298, 2346}, {2886, 3011}, {2999, 3158}

▸ Functional Relations3 relations