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