#### Question

In the given figure, SP is bisector of ∠RPT and PQRS is a cyclic quadrilateral. Prove that SQ = SR .

#### Solution

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

Is there an error in this question or solution?

Solution In the Given Figure, Sp is Bisector of ∠Rpt and Pqrs is a Cyclic Quadrilateral. Prove that Sq = Sr . Concept: Cyclic Properties.