Question 35
Two circles of the same radius, $K$ and $L$, intersect in two points, one of which is $P$. Denote by $A$ and $B$, respectively, the points diametrically opposite to $P$ on each of $K$ and $L$. Yet another circle of the same radius is brought to pass through $P$, intersecting $K$ and $L$ in the points $X$ and $Y$, respectively.
Show that the line $XY$ is parallel to the line $AB$.
Show that the line $XY$ is parallel to the line $AB$.