X3600

INTERSECTION OF LINES X1X_7 AND X8X_57

X3600 was found by Peter Moses in connection with the 1st Liu point.
< 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) { 8, 1706 }: Central Line L(8, 1706) { 1, 7 }: Soddy Line { 2, 12 }: Central Line L(2, 12) { 8, 57 }: Central Line L(8, 57) { 65, 145 }: Central Line L(65, 145) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_1706 = EXSIMILICENTER(BEVAN CIRCLE, SPIEKER CIRCLE) (0.5323, 0.2107) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_2 = CENTROID (0.5374, 0.2000) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_3600 = INTERSECTION OF LINES X(1)X(7) AND X(8)X(57) (0.5951, 0.2881) A B C X8 X1706 X1 X7 X2 X12 X57 X65 X145 X3600 (a, b, c) = (5, 6, 7) | AB = 1

X3600 (INTERSECTION OF LINES X1X_7 AND X8X_57) 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 \(f(a,b,c) = bc(a - b + c)(a + b - c)(3a^{2} + b^{2} + c^{2} + 2bc)\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = 2a - [(a+b+c)^{2}]/(b + c - a)\)
Search Value (6, 9, 13): \(0.629822908861\)
▸ Linear Combinations1 combination
▸ Incident Central Lines41 lines

{1, 7}, {2, 12}, {3, 1056}, {4, 496}, {8, 57}, {10, 3361}, {21, 1617}, {30, 1058}, {36, 3085}, {55, 3522}, {65, 145}, {100, 1466}, {144, 960}, {171, 1106}, {193, 330}, {226, 452}, {346, 2285}, {354, 3486}, {376, 3295}, {391, 1400}, {443, 956}, {474, 3421}, {495, 631}, {497, 3146}, {515, 938}, {519, 3339}, {553, 3241}, {942, 944}, {948, 1104}, {982, 1254}, {1010, 1014}, {1043, 1434}, {1159, 1483}, {1319, 3485}, {1385, 3487}, {1435, 1891}, {1446, 3424}, {1478, 3086}, {1479, 3543}, {2646, 3475}, {3057, 3474}

▸ Functional Relations3 relations