## X(550) (MIDPOINT OF X(3) AND X(20))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon , select the center name from the list and, then, click on the vertices A, B and C successively.

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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,
= 3 cos A - 2 cos B cos C : 3 cos B - 2 cos C cos A : 3 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(550) lies on the Euler line. (Antreas Hatzipolakis, 1/20/00, Hyacinthos #201)

X(550) lies on these lines: 2,3    15,397    16,398    35,495    36,496    40,952    74,930    156,1092    165,355

X(550) = midpoint of X(3) and X(20)
X(550) = reflection of X(I) in X(J) for these (I,J): (3,548), (4,140), (5,3), (382,546)
X(550) = complement of X(382)
X(550) = anticomplement of X(546)

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