José wrote: Let $P$ be a point outside the circle $C$. Find two points $Q$ and $R$ on the circle, such that $P,Q$ and $R$ are collinear and $Q$ is the midpopint of the segmenet $PR$. (Discuss the number of solutions). $2*PQ^2=PQ*PR=PO^2-R^2=const$ So $PQ=\frac{\sqrt(PO^2-R^2)}{2}$ And $\le 2$ solutions V:)