Question

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

Answer 1

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