X3915

X3710com(TANGENTIAL TRIANGLE)

X3915 = crosspoint of X109 and X765
< 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) circumcircle: Circumcircle of △ABC { 1, 21 }: Central Line L(1, 21) { 8, 238 }: Central Line L(8, 238) { 46, 244 }: Central Line L(46, 244) { 40, 614 }: Central Line L(40, 614) { 10, 748 }: Central Line L(10, 748) { 3, 902 }: Central Line L(3, 902) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_8 = NAGEL POINT (0.4694, 0.1333) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_40 = BEVAN POINT (0.4286, -0.0292) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_3915 = com[TANGENTIAL TRIANGLE))] (0.7045, 0.4082) A B C X3 X109 X765 X1 X21 X8 X238 X46 X244 X40 X614 X10 X748 X902 X3915 (a, b, c) = (5, 6, 7) | AB = 1

X3915 (X3710com(TANGENTIAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(as - bc) : b(bs - ca ) : c(cs - ab)\)
Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{2}(a^{2} + ab + ac - 2bc)\)
Search Value (6, 9, 13): \(-0.385133584433\)
▸ Incident Central Lines44 lines

{1, 21}, {3, 902}, {6, 1334}, {8, 238}, {10, 748}, {32, 3230}, {35, 995}, {40, 614}, {41, 1914}, {42, 3295}, {46, 244}, {48, 3285}, {55, 1191}, {56, 1149}, {65, 1279}, {78, 3749}, {100, 978}, {109, 1106}, {171, 3616}, {212, 1104}, {213, 2241}, {221, 1458}, {386, 2177}, {392, 1472}, {404, 3550}, {517, 582}, {519, 1724}, {601, 1385}, {603, 1319}, {750, 1125}, {944, 3073}, {946, 3011}, {960, 976}, {1001, 1918}, {1042, 1617}, {1055, 3053}, {1253, 1697}, {1388, 1399}, {1451, 2099}, {1829, 2212}, {1834, 3058}, {1935, 3476}, {2098, 2361}, {2268, 2300}

▸ Functional Relations4 relations