## Παρασκευή, 13 Οκτωβρίου 2017

### 2003 JBMO Shortlist 13

Let $ABC$ be an isosceles triangle with $AB = AC$. A semi-circle of diameter $[EF]$ with $E, F \in [BC]$, is tangent to the sides $AB,AC$ in $M, N$ respectively  and $AE$ intersects the semicircle at $P$. Prove that $PF$ passes through the midpoint of $[MN]$.

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