I really want to know the following geometry problem is valid or not. (Please don't change the wording of the problem. Please answer it is valid or not. Please answer frankly.)
"ABCD is a parallelogram. Any circle through A and B cuts DA and CB produced at P and Q respectively. Prove that DCQP is cyclic."
If the problem is valid, I also want to know the solution. If the problem is not valid, I also want to know why.
Here the notation like XY means line segment XY. If the points X, Y separate the line XY into three parts, the middle part (between X and Y) is the line segment XY. The part beyond Y (on the opposite side from X) is called XY produced. DCQP is a convex quadrilateral.