X3688

X75com(EXTOUCH TRIANGLE)

X3688 = crosssum of X7 and X56
< 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) { 55, 219 }: Central Line L(55, 219) { 8, 314 }: Central Line L(8, 314) { 37, 674 }: Central Line L(37, 674) { 181, 612 }: Central Line L(181, 612) { 51, 756 }: Central Line L(51, 756) { 38, 1401 }: Central Line L(38, 1401) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3703 = com(EXTOUCH TRIANGLE) (0.4338, 0.1070) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_8 = NAGEL POINT (0.4694, 0.1333) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2078, -0.2856) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_1401 = -BETH CONJUGATE OF X(38) (0.6188, 0.3077) X_3688 = com(EXTOUCH TRIANGLE) (0.5186, 0.1596) A B C X3703 X55 X219 X8 X314 X37 X674 X181 X612 X51 X756 X38 X1401 X3688 (a, b, c) = (5, 6, 7) | AB = 1

X3688 (X75com(EXTOUCH 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 \(f(a,b,c) = a^{2}(b + c - a)(b^{2} + c^{2})\)
Search Value (6, 9, 13): \(3.249142777249\)
▸ Incident Central Lines23 lines

{8, 314}, {9, 3056}, {31, 2273}, {37, 674}, {38, 1401}, {39, 1964}, {42, 2300}, {51, 756}, {55, 219}, {71, 2223}, {77, 1362}, {78, 1682}, {181, 612}, {200, 3169}, {511, 984}, {869, 2092}, {1253, 3270}, {1334, 2293}, {1742, 2808}, {2269, 2340}, {2323, 2330}, {2388, 2667}, {3057, 3059}

▸ Functional Relations5 relations