X3653

CENTROID OF {X1, X2, X3}

X3653 is the centroid 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) { 2, 355 }: Central Line L(2, 355) { 1, 549 }: Central Line L(1, 549) { 3, 551 }: Central Line L(3, 551) { 381, 1125 }: Central Line L(381, 1125) { 30, 1699 }: Central Line L(30, 1699) { 631, 3241 }: Central Line L(631, 3241) 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_355 = FUHRMANN CENTER (0.5408, 0.2645) X_1 = INCENTER (0.5714, 0.2333) X_549 = MIDPOINT OF X(2) AND X(3) (0.5187, 0.1510) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_1699 = EXSIMILICENTER(BEVAN CIRCLE, NINE-POINT CIRCLE) (0.5986, 0.3416) X_631 = 3/5*OG (0.5224, 0.1608) X_3241 = REFLECTION OF X(2) IN X(1) (0.6054, 0.2666) X_3653 = CENTROID OF {X(1), X(2), X(3)} (0.5363, 0.1784) A B C X2 X355 X1 X549 X3 X551 X381 X1125 X30 X1699 X631 X3241 X3653 (a, b, c) = (5, 6, 7) | AB = 1

X3653 (CENTROID 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 \(f(a,b,c) = bc(7a^{4} + b^{4} + c^{4} - 8a^{2}b^{2} - 8a^{2}c^{2} - 2b^{2}c^{2} + 3k)\), 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): \(3.700680065381\)
▸ Linear Combinations1 combination
▸ Incident Central Lines9 lines

{1, 549}, {2, 355}, {3, 551}, {30, 1699}, {381, 1125}, {517, 3524}, {631, 3241}, {946, 3534}, {3058, 3612}

▸ Functional Relations2 relations