Hint 1: Use a GSP construction and move point A to various positions. Note that A will not always be located on the same side of segment PQ.
Hint 2: You will probably need some auxiliary constructions. Try rotating the figure about R.
We need a figure which guarantees a right angle. For example, can we show P, Q, and R are points on a circle with PQ as a diameter?
Another example, can we develop a figure where the two segmes PR and RQ must be perpendicular?
GSP file (or construct your own).