Question

Two chords PQ and RS of the circle with Centre O intersect each other at M.If OM bisects angle SMQ, prove that SM=QM​

Answer 1

Answer:

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=180o2∠PSR=180o∠PSQ=∠PSR=90o

then, RS=QS and ∠PSR=90o

PS is the perpendicular bisector of chord RQ

PS passes through center of circle.