Question 35
In the diagram, $P$ is a point on the semicircle with diameter $AB$. The point $L$ is the foot of the perpendicular from $P$ onto $AB$, and $K$ is the midpoint of $PB$. The tangents to the semicircle at $A,P$ meet at $Q$. The lines $PL,KL$ intersect $QB$ at $M,N$, respectively. Suppose $AQ/AB=5/12$, $QM=25\text{ cm}$ and $MN=x\text{ cm}$. Find $x$.
