Question 97
Let $\gamma$ be a circle, and let $P$ be a point in its plane, not situated on $\gamma$. Two variable lines $\ell$ and $\ell'$ through $P$ meet $\gamma$ at $X$ and $Y$, and $X'$ and $Y'$, respectively. Show that the line through the centres of the circles $PXY'$ and $PX'Y$ passes through a fixed point.
