X3113

GtX(31)

X3113 = trilinear pole of line X1577X1924
< 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) { 31, 561 }: Central Line L(31, 561) { 75, 560 }: Central Line L(75, 560) { 313, 983 }: Central Line L(313, 983) { 1, 1927 }: Central Line L(1, 1927) { 870, 1441 }: Central Line L(870, 1441) { 321, 2205 }: Central Line L(321, 2205) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3116 = ISOGONAL CONJUGATE OF GtX(31) (0.5881, 0.2260) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_560 = 4th POWER POINT (0.6520, 0.3639) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_983 = ISOGONAL CONJUGATE OF X(982) (0.5890, 0.2731) X_1 = INCENTER (0.5714, 0.2333) X_1927 = TRILINEAR POLE OF PU(13) (0.9865, 0.0569) X_870 = ISOGONAL CONJUGATE OF X(869) (0.5328, 0.2015) X_1441 = -BETH CONJUGATE OF X(313) (0.5459, 0.2242) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_2205 = -ISOCONJUGATE OF X(310) (0.6477, 0.3479) X_3113 = GtX(31) (0.5552, 0.2402) A B C X3116 X31 X561 X75 X560 X313 X983 X1 X1927 X870 X1441 X321 X2205 X3113 (a, b, c) = (5, 6, 7) | AB = 1

X3113 (GtX(31)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b^{2} - c^{2})/(a^{2}(b^{6} - c^{6})) : :\)
Barycentrics: \(1/(b^{2}c^{2} + b^{4} + c^{4}) : :\)
Search Value (6, 9, 13): \(1.973724325801\)
▸ Incident Central Lines6 lines

{1, 1927}, {31, 561}, {75, 560}, {313, 983}, {321, 2205}, {870, 1441}

▸ Functional Relations2 relations