<Cir-2024-756>, hint

Let O',O", M be the centers of circles K', K", another circle respectively 

Let <O'MB=x, <O"MB=y, then <PMQ=2(x+y). Hence <MPQ=90-(x+y), <MPB=90-x

Hence <QPB=<MPB-<MPQ=y=<RAB.

Suppose AR meets BM at T, BT=AB tany=2BM tanx tany

Suppose CS meets BM at T'. Then AT=AT' 2BM tanx tany