## Τρίτη, 17 Οκτωβρίου 2017

### 2006 IMO Shortlist G8

Let $ABCD$ be a convex quadrilateral.  A circle passing through the points $A$ and $D$ and a circle passing through the points $B$ and $C$ are externally tangent at a point P inside the quadrilateral. Suppose that $\angle P AB + \angle PDC \le 90^\circ$  and  $\angle PBA + \angle PCD \le 90^\circ$ . Prove that $AB + CD \ge BC + AD$.

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