X3681

X1699com(EXTOUCH TRIANGLE)

X3681 = anticomplement of X354
< 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) { 4, 8 }: Fuhrmann Line { 38, 43 }: Central Line L(38, 43) { 63, 100 }: Central Line L(63, 100) { 2, 210 }: Central Line L(2, 210) { 81, 612 }: Central Line L(81, 612) { 1, 748 }: Central Line L(1, 748) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_2 = CENTROID (0.5374, 0.2000) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_1 = INCENTER (0.5714, 0.2333) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) X_3681 = com(EXTOUCH TRIANGLE) (0.4476, 0.0933) A B C X4 X8 X38 X43 X63 X100 X2 X210 X81 X612 X1 X748 X3681 (a, b, c) = (5, 6, 7) | AB = 1

X3681 (X1699com(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 \(f(a,b,c) = a(b^{2} + c^{2} - ab - ac + bc)\)
Search Value (6, 9, 13): \(5.281210822520\)
▸ Linear Combinations1 combination
▸ Incident Central Lines32 lines

{1, 748}, {2, 210}, {4, 8}, {9, 1174}, {31, 1757}, {38, 43}, {42, 984}, {55, 1776}, {63, 100}, {65, 3617}, {69, 3263}, {78, 947}, {81, 612}, {144, 3059}, {145, 960}, {150, 2890}, {374, 391}, {390, 1864}, {392, 3241}, {511, 3578}, {561, 668}, {674, 3060}, {846, 2177}, {896, 3550}, {899, 982}, {986, 3214}, {1005, 2900}, {1376, 3218}, {1474, 2287}, {2836, 2895}, {3057, 3621}, {3555, 3616}

▸ Functional Relations7 relations