PQRS is a cyclic quadrilateral
∠QRS +∠QPS = 180° …………(i)
(pair of opposite angles in a cyclic quadrilateral are supplementary)
Also, QPS +∠SPT = 180° ……(ii)
(Straight line QPT)
From (i) and (ii)
∠QRS = ∠SPT ………. (iii)
Also, ∠RQS = ∠RPS ……(iv)
(Angle subtended by the same chord on the circle are equal)
And ∠RPS = ∠SPT (PS bisects ∠RPT ) …… (v)
From (iii), (iv) and (v)
∠QRS = ∠RQS
⇒ SQ = SR