Question 111
Two circles $k_1$ and $k_2$ with centers $O_1$ and $O_2$, respectively, are externally tangent at point $P$. A circle $k_3$ is externally tangent to $k_1$ at $Q$ and to $k_2$ at $R$. The lines $PQ$ and $PR$ meet $k_3$ at points $A$ and $B$, respectively. If $AO_2$ meets $BO_1$ at a point $S$ prove that $SP \perp O_1O_2$.