## X(549) (MIDPOINT OF X(2) AND X(3))

 Interactive Applet

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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = cos(B - C) + 4 cos A,
= 5 cos A + 2 cos B cos C : 5 cos B + 2 cos C cos A : 5 cos C + 2 cos A cos B

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(549) lies on the Euler line. (Antreas Hatzipolakis, 1/20/00, Hyacinthos #201)

X(549) lies on these lines: 2,3    15,395    16,396    35,496    36,495    141,542    182,524    230,574    302,617    303,616    511,597    517,551

X(549) = midpoint of X(I) and X(J) for these (I,J): (2,140), (5,2), (381,547)
X(549) = reflection of X(I) in X(J) for these (I,J): (14,619), (148,13), (616,99), (622,299)
X(549) = complement of X(381)
X(549) = anticomplement of X(547)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.