OME 2006 Problem 3

$ABC$ is an isosceles triangle with $AB = AC$ . Let $P$ be any point of a circle tangent to the sides $AB$ in $B$ and to AC in C. Denote $a$ , $b$ and $c$ to the distances from $P$ to the sides $BC, AC$ and $AB$ respectively. Prove that: $a^2=bc$