Answer:
What kind of proof do you need?
M, Q, and N are collinear, with Q between M and N.
Triangle QPM is isosceles (PM=PQ).
That makes PN greater than PQ.
If you need a formal proof, it looks as if you can use trigonometry and the law of sines.
If you need a formal two-column proof using Euclidean geometry, I'm not sure how you would do it....
Explanation: