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Three midpoints are collinear

Source: Austrian-Polish 2005, Problem 5

July 5, 2015

geometryradical axis

Problem Statement

Given is a convex quadrilateral

ABCD

with

AB=CD

. Draw the triangles

ABE

and

CDF

outside

ABCD

so that

\angle{ABE} = \angle{DCF}

and

\overline{EF}

. Prove that the midpoints of

\overline{AD}

,

\overline{BC}

and

\overline{EF}

are collinear.

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