Macedonian Junior Mathematical Olympiad

A circle $k$ with center at $O$ and radius $r$ and a line $p$ which doesn't have a common point with $k$ are given. Let $E$ be the foot of the perpendicular from $O$ to $p$. An arbitrary point $M$ different from $E$ is chosen on $p$ and the two tangents are drawn from $M$ to $k$ which touch the circle $k$ at points $A$ and $B$. If $H$ is the intersection of $AB$ and $OE$, prove that $\overline{OH}=\frac{r^2}{OE}$.