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Prove that the right bisector of a cho...

Prove that the right bisector of a chord of a circle, bisects the corresponding arc or the circle.

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Let `AB` be a chord of a circle having its centre at O.
Let `PQ` be the right bisector of the chord `AB`, intersecting `AB \at\ L`
and the circle at `P \and\ Q`
Since the right bisector of a chord always passes through the centre
so `PQ` must pass through the centre `O`.
Join `OA \and\ OB.`
`OA=OB`(Each equal to the radius)
`/_ALO=/_BLO`(Each equal to 90^0)
`OL=OL`(Common)
`/_\OAL~=/_\OBL`(By RHS congruency criterion)
`=>/_AOL=/_BOL`(C.P.C.T)
`/_AOQ=/_BOQ`
`AQ=BQ`(Arcs subtending equal angles at the centre are equal)
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