X3656

X3-EXTRAVERSION OF {X1, X2, X3}

< 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, 30 }: Central Line L(1, 30) { 2, 392 }: Central Line L(2, 392) { 3, 551 }: Central Line L(3, 551) { 40, 549 }: Central Line L(40, 549) { 355, 381 }: Central Line L(355, 381) { 376, 962 }: Central Line L(376, 962) 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_30 = EULER INFINITY POINT (0.7469, 0.7481) X_2 = CENTROID (0.5374, 0.2000) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_40 = BEVAN POINT (0.4286, -0.0292) X_549 = MIDPOINT OF X(2) AND X(3) (0.5187, 0.1510) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_962 = LONGUET-HIGGINS POINT (0.7551, 0.6582) X_3656 = -EXTRAVERSION OF {X(1), X(2), X(3)} (0.6088, 0.3312) A B C X1 X30 X2 X392 X3 X551 X40 X549 X355 X381 X376 X962 X3656 (a, b, c) = (5, 6, 7) | AB = 1

X3656 (X3-EXTRAVERSION OF {X1, X2, X3}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[a^{4} + b^{4} + c^{4} - 2(b^{2}c^{2} + c^{2}a^{2} + a^{2}b^{2} + 3k)]\), where \(k = a(b^{3} + c^{3} - a^{2}b - a^{2}c - b^{2}c - bc^{2} + 2abc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.462685592251\)
▸ Linear Combinations1 combination
▸ Incident Central Lines18 lines

{1, 30}, {2, 392}, {3, 551}, {4, 1392}, {8, 3545}, {40, 549}, {57, 1387}, {119, 3577}, {355, 381}, {376, 962}, {496, 3340}, {516, 3534}, {553, 999}, {940, 1480}, {944, 3543}, {952, 1699}, {1388, 1770}, {3524, 3579}