X3924

X3710com(INCENTRAL TRIANGLE)

< 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) { 1, 2 }: Nagel Line { 31, 65 }: Central Line L(31, 65) { 34, 207 }: Central Line L(34, 207) { 56, 244 }: Central Line L(56, 244) { 81, 409 }: Central Line L(81, 409) { 40, 902 }: Central Line L(40, 902) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_409 = EULER X(21)-1st-SUBSTITUTION POINT (0.5419, 0.2117) X_40 = BEVAN POINT (0.4286, -0.0292) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_3924 = com[INCENTRAL TRIANGLE))] (0.6526, 0.3128) A B C X1 X2 X31 X65 X34 X207 X56 X244 X81 X409 X40 X902 X3924 (a, b, c) = (5, 6, 7) | AB = 1

X3924 (X3710com(INCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(a^{3} + b^{3} + c^{3} - b^{2}c - bc^{2})\)
Search Value (6, 9, 13): \(0.552413828177\)
▸ Incident Central Lines34 lines

{1, 2}, {4, 3120}, {6, 2294}, {7, 2647}, {21, 986}, {28, 2206}, {31, 65}, {32, 3125}, {34, 207}, {38, 958}, {40, 902}, {56, 244}, {81, 409}, {227, 1319}, {405, 2292}, {517, 582}, {604, 1880}, {607, 2170}, {748, 960}, {758, 1724}, {942, 1468}, {977, 1220}, {982, 2975}, {993, 3670}, {1106, 1455}, {1148, 1870}, {1191, 2099}, {1253, 1279}, {1453, 2308}, {1616, 2098}, {1837, 3772}, {1854, 2310}, {2331, 3554}, {2646, 3752}