Mathematics
In the figure (ii) given below, SP is the bisector of ∠RPT and PQRS is a cyclic quadrilateral. Prove that SQ = RS.
Circles
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Answer
Since, SP is the bisector of the angle ∠RPT.
So, ∠RPS = ∠SPT
From figure,
∠RPS = ∠RQS (As angle in same segment are equal)
Given, PQRS is a cyclic quadrilateral.
∵ exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.
∠QRS = ∠SPT
∴ ∠QRS = ∠RPS
or,
∠QRS = ∠RQS
In △QRS,
∠QRS = ∠RQS
∴ SQ = RS (As sides opposite to equal angles are equal.)
Hence, proved that SQ = RS.
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