Question 22
Points $M$ and $N$ are the midpoints of sides $AD$ and $BC$, respectively, of rectangle $ABCD$. Point $P$ is a point on the extension of $CD$ such that $MP=65$ cm. Let $Q$ be the point of intersection of $AC$ and the extension of $PM$, as shown in the diagram below. It is given that $QM=26$ cm and $QN=52$ cm. What is the length, in cm, of $NP$?
