Segment $K L$ is the diameter of a certain circle. Through its endpoints $K$ and $L$, two lines are drawn, intersecting the circle at points $P$ and $Q$, respectively, lying on the same side of the line $K L$. Find the radius of the circle if $\angle P K L=60^{\circ}$ and the point of intersection of the lines $K P$ and $Q L$ is 1 unit away from points $P$ and $Q$.