PQ and PR are two equal chords of a circle and O is the centre of the circle. Then, prove that OP is the
perpendicular bisector of QR.
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PQ and PR are two equal chords of a circle and O is the centre of the circle. Then, prove that OP is the
perpendicular bisector of QR.
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Answer:
Given, chords RP=RQ
In △PSQ and △PSR
PQ=PR (given)
∠RPS=∠QPS (given)
PS=PS (common)
△PSQ≅△PSR (by SAS)
⇒RS=QS
∠PSR=∠PSQ
But,
∠PSR+∠PSQ=180
o
2∠PSR=180
o
∠PSQ=∠PSR=90
o
then, RS=QS and ∠PSR=90
o
PS is the perpendicular bisector of chord RQ
PS passes through center of circle.