IT-CESENATICO 2000 Problem 2

Let $ABCD$ be a convex quadrilateral, and write $\alpha=\angle DAB$ , $\beta=\angle ADB$ , $\gamma=\angle ACB$ , $\delta= \angle DBC$ and $\epsilon=\angle DBA$ . Assuming that $\alpha<\pi/2$ , $\beta+\gamma=\pi /2$ , and $\delta+2\epsilon=\pi$ , prove that $(DB+BC)^2=AD^2+AC^2$ .