USAMO 1986 Problem 4

A T-square allows you to construct a straight line through two points and a line perpendicular to a given line through a given point. Circles $\mathrm{C}$ and $\mathrm{C}^{\prime}$ intersect at $\mathrm{X}$ and $\mathrm{Y}$. $\mathrm{XY}$ is a diameter of $\mathrm{C}$. $\mathrm{P}$ is a point on $\mathrm{C}^{\prime}$ inside

C. Using only a $T$-square, find points $\mathrm{Q}, \mathrm{R}$ on $\mathrm{C}$ such that $\mathrm{QR}$ is perpendicular to $\mathrm{XY}$ and $\mathrm{PQ}$ is perpendicular to PR.