Τρίτη, 17 Οκτωβρίου 2017

2006 IMO Shortlist G3

Let $ABCDE$ be a convex pentagon such that $\angle BAC = \angle CAD = \angle DAE$     and     $\angle ABC = \angle ACD = \angle ADE$. The diagonals $BD$ and $CE$ meet at $P$ . Prove that the line $AP$ bisects the side $CD$.

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