Join R to the centre, O, of the circle. Triangles OPR and OQR are congruent as they have a 90 degree angle and one side in common plus equal radii, OP and OQ.
So OR is a line of symmetry . If OR crosses PQ at S then SP = 3,so RS = 4 by Pythagoras. If you let OS = x and radius = r you can form two equations in r and x by Pythagoras on OPR and on OPS.
It's easier to eliminate r and find x. Then find r.
Alter
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