Thread: another circle geometry question~~~ really urgent

in a traingle ABC, <BAC=80 and Q is the point on BC such that AQ bisects the angle BAC. There is also a point P on AB such that <QPC=40 and P is distinct from A. Prove that PQ=QC

any help would be awesome!!
thanx in advnace

We have , then the quadrilater can be inscribed in a circle.
Yields , so the triangle is isosceles, then