<Cir-2024-760>, hint

Let M be the midpoint of PQ and O' S O" cuts  O" at N .

Quadrilaterals SMPO' and SO"QM are similar.

Let <SO"M= be X=<SMO' .Since O"S=3 O'S.

3 (tanX )x(tanX)=1(=SO'). Hence tanX=30. SO" tan SO"M=SM. SM tanSMO'=SO'

<SO"M=<STO"=<TSO"=30. Since <SQN=90 and <TQR=0.5 (90-30)=30

Hence <RQT=<RTQ .Triangle RQT is isosceles.