Let AD be the angle bisector of acute triangle ABC, and let M be the midpoint of AD. Let P be the point on BM such that APC = 90°, and let Q be the point on CM such that AQB = 90°. Prove that quadrilateral DPMQ is cyclic.

Diagram:

What I have done so far:

If R is the image of A onto BC, we can say that ABRQ and ACRP are cyclic, and M is the circumcenter of ARD. Could someone please provide a solution?

themathboss Aug 24, 2020