IT-CESENATICO 2003 Problem 3

Let a semicircle is given with diameter $AB$ and centre $O$ and let $C$ be a arbitrary point on the segment $OB$ . Point $D$ on the semicircle is such that $CD$ is perpendicular to $AB$ . A circle with centre $P$ is tangent to the arc $BD$ at $F$ and to the segment $CD$ and $AB$ at $E$ and $G$ respectively. Prove that the triangle $ADG$ is isosceles.