X3931

X581com[INVERSE(n(HEXYL TRIANGLE))]

< 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) { 10, 37 }: Central Line L(10, 37) { 42, 72 }: Central Line L(42, 72) { 226, 227 }: Central Line L(226, 227) { 4, 941 }: Central Line L(4, 941) { 386, 960 }: Central Line L(386, 960) 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_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_227 = -CEVA CONJUGATE OF X(65) (0.4792, -0.0460) X_4 = ORTHOCENTER (0.6122, 0.3958) X_941 = ISOGONAL CONJUGATE OF X(940) (0.5671, 0.2256) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_3931 = com[INVERSE(n(HEXYL TRIANGLE))] (0.5669, 0.2249) A B C X1 X3 X10 X37 X42 X72 X226 X227 X4 X941 X386 X960 X3931 (a, b, c) = (5, 6, 7) | AB = 1

X3931 (X581com[INVERSE(n(HEXYL 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 \(f(a,b,c) = a(b + c)(a^{2} + b^{2} + c^{2} + 2ab + 2ac)\)
Search Value (6, 9, 13): \(1.836631911317\)
▸ Incident Central Lines28 lines

{1, 3}, {2, 3702}, {4, 941}, {10, 37}, {38, 3555}, {42, 72}, {210, 3293}, {226, 227}, {386, 960}, {392, 1193}, {405, 968}, {595, 1386}, {756, 3214}, {975, 1376}, {976, 2177}, {984, 1716}, {1089, 3175}, {1100, 2241}, {1125, 3752}, {1181, 1409}, {1427, 3671}, {1441, 3672}, {1465, 3485}, {1706, 3247}, {1724, 3683}, {1785, 1882}, {1962, 3753}, {2887, 3178}