## Τρίτη, 10 Οκτωβρίου 2017

### 2008 JBMO Shortlist G7

Let $ABC$ be an isosceles triangle with $AC = BC$.  The point $D$ lies on the side $AB$ such that the semicircle with diameter $BD$ and center $O$ is tangent to the side $AC$ in the point $P$ and intersects the side $BC$ at the point $Q$. The radius $OP$ intersects the chord $DQ$ at the point $E$ such that $5 \cdot PE = 3 \cdot DE$. Find the ratio $\frac{AB}{BC}$ .

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