X1022

INTERSECTION OF LINES X1X_513 AND X2X_514

X1022 = crossdifference of every pair of points on line X44X678
< 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) { 105, 106 }: Central Line L(105, 106) { 1, 513 }: Central Line L(1, 513) { 2, 514 }: Central Line L(2, 514) { 89, 649 }: Central Line L(89, 649) { 81, 1019 }: Central Line L(81, 1019) { 291, 876 }: Central Line L(291, 876) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1023 = INTERSECTION OF LINES X(1)X(6) AND X(100)X(101) (2.1429, 2.0996) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_1 = INCENTER (0.5714, 0.2333) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_2 = CENTROID (0.5374, 0.2000) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_89 = ISOGONAL CONJUGATE OF X(45) (0.5963, 0.2697) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_1019 = -CEVA CONJUGATE OF X(1) (-29.0952, 18.1962) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_876 = ISOTOMIC CONJUGATE OF X(874) (0.9873, -0.0185) X_1022 = INTERSECTION OF LINES X(1)X(513) AND X(2)X(514) (1.0000, -0.0000) A B C X1023 X105 X106 X1 X513 X2 X514 X89 X649 X81 X1019 X291 X876 X1022 (a, b, c) = (5, 6, 7) | AB = 1

X1022 (INTERSECTION OF LINES X1X_513 AND X2X_514) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b - c)/(2a - b - c)\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-0.295133231810\)
▸ Incident Central Lines7 lines

{1, 513}, {2, 514}, {81, 1019}, {89, 649}, {105, 106}, {291, 876}, {812, 903}

▸ Functional Relations5 relations