I am having trouble with a problem from my online math class. I tried using the basic angle properties of circles, but didn't get anywhere:

Let ABCD be a cyclic quadrilateral. Let P be the intersection of AD and BC, and let Q be the intersection of AB and CD. Prove that the angle bisectors of DPC and AQD are perpendicular.

h t t p : / / l a t e x . a r t o f p r o b l e m s o l v i n g . c o m / 9 / b / b / 9 b b c 2 7 f b a 7 9 0 f 3 7 5 3 7 6 5 5 6 0 5 9 2 9 b a f b 8 9 9 1 5 0 e 5 d . p n g

delete all the spaces to get the link.