X3929

X154com[INVERSE(n(EXTANGENTS TRIANGLE))]

X3929 = 2nd-extouch-to-excentral similarity image of X2
< 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) { 2, 7 }: Centroid–Gergonne Line { 30, 40 }: Central Line L(30, 40) { 165, 210 }: Central Line L(165, 210) { 220, 222 }: Central Line L(220, 222) { 84, 376 }: Central Line L(84, 376) { 612, 896 }: Central Line L(612, 896) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_40 = BEVAN POINT (0.4286, -0.0292) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_896 = INTERSECTION OF LINES X(1)X(21) AND X(9)X(750) (2.0357, 2.1579) X_3929 = com[INVERSE(n(EXTANGENTS TRIANGLE))] (0.4895, 0.1302) A B C X2 X7 X30 X40 X165 X210 X220 X222 X84 X376 X612 X896 X3929 (a, b, c) = (5, 6, 7) | AB = 1

X3929 (X154com[INVERSE(n(EXTANGENTS TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(t(A,B,C) : t(B,C,A) : t(C,A,B)\), where \(t(A,B,C) = 3 \cot A + \csc A\) (Peter Moses, 1/13/2012)
Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(3a^{2} - 3b^{2} - 3c^{2} - 2bc)\)
Search Value (6, 9, 13): \(4.418146538785\)
▸ Incident Central Lines30 lines

{1, 3683}, {2, 7}, {10, 3474}, {30, 40}, {44, 2999}, {72, 3601}, {81, 3247}, {84, 376}, {165, 210}, {201, 1394}, {219, 2003}, {220, 222}, {238, 3677}, {333, 3729}, {519, 1697}, {612, 896}, {728, 3719}, {846, 3751}, {912, 3576}, {940, 3731}, {958, 3340}, {960, 1420}, {984, 1707}, {991, 2318}, {1155, 3715}, {1214, 1419}, {1621, 3243}, {1743, 3666}, {3158, 3681}, {3534, 3587}

▸ Functional Relations1 relation

  • X3929 = 2nd-extouch-to-excentral similarity image of X2