Question

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 1

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.