Geometry problem prove lines are parallel, cyclic quadrilaterals,other parallel lines

Go here for a diagram for this problem: http://i630.photobucket.com/albums/u...tryproblem.jpg

Let ABC be a triangle with orthocentre H and let P be a point on its circumcircle. The line through A parallel to BP meets CH at Q and the line through A parallel to CP meets BH at R.

Prove that QR is parallel to AP

THis question has been bugging me for a very long time. Please put me out of my misery with an easy to follow proof.