geometry

The ENTIRE perimeter of the complete circle would be 2πr (30π) so three-quarters of it will be 30π * 3 / 4 = 90π/4 = 45π/2

Your answer is incorrect guest. You need to account for the side lengths OQ and PO, each of which have a side length of 15. 

The circumference of a complete circle would be $30\pi$, so the circumference of $3 \over 4$ of the circle would be $22.5\pi$

We also have to add 30 to the circumference, so the circumference is $\color{brown}\boxed{22.5\pi+30}$