X3101

INTERSECTION OF LINES X2X_19 AND X8X_20

< 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) { 2, 19 }: Central Line L(2, 19) { 8, 20 }: Central Line L(8, 20) { 22, 55 }: Central Line L(22, 55) { 65, 81 }: Central Line L(65, 81) { 57, 347 }: Central Line L(57, 347) { 46, 387 }: Central Line L(46, 387) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_19 = CLAWSON POINT (0.6246, 0.4244) X_8 = NAGEL POINT (0.4694, 0.1333) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_22 = EXETER POINT (0.4143, -0.1221) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_387 = INTERSECTION OF LINES X(1,2) AND X(4,6) (0.5994, 0.2607) X_3101 = INTERSECTION OF LINES X(2)X(19) AND X(8)X(20) (0.3923, -0.1734) A B C X2 X19 X8 X20 X22 X55 X65 X81 X57 X347 X46 X387 X3101 (a, b, c) = (5, 6, 7) | AB = 1

X3101 (INTERSECTION OF LINES X2X_19 AND X8X_20) 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 \(f(a,b,c) = a^{5} + a^{3}bc + (b + c)(a^{4} - a^{2}bc - a(b^{3} + c^{3}) - (b - c)(b^{3} - c^{3}))\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(31.699209034095\)
▸ Incident Central Lines19 lines

{2, 19}, {8, 20}, {22, 55}, {27, 1441}, {46, 387}, {57, 347}, {65, 81}, {71, 1654}, {100, 1297}, {306, 2897}, {329, 1763}, {345, 1760}, {573, 1726}, {1172, 1214}, {1305, 1952}, {1370, 2550}, {1442, 1790}, {1770, 2960}, {1869, 2475}