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MathNet 2016-part-01 — 184 problems (EN–VI) Question 118

Math Olympiad Vault · MathNet 2016-part-01 — 184 problems (EN–VI)

Question 118

Let $E$ be the intersection point of the segments $AB$ and $CD$. Points $X$ and $Y$ are marked in the plane such that the quadrilaterals $AECX$ and $BEDY$ are parallelograms.
Prove that the lines $AD$, $BC$, and $XY$ are either pairwise parallel or concurrent.
(M. Karpuk, A. Voidelevich)