Question

Prove that tje right bisectors of a chord of a circle bisect the corresponding arc of a circle

Answer 1

CORRECT QUESTION : -

Prove that the perpendicular bisector of a chord of a circle passes through the center.

SOLUTION : -

Let us suppose PQ doesn't pass through O .

Since PQ ⊥ bisector of AB

∠QOP = 90° --- eq(1)

P is the mid-point of AB

OP is passes from center from this we can say ,

OP ⊥ AB

∠OPA = 90° ---eq(2)

comparing eq.(1) and eq.(2) , we can say ,

==> ∠QOP = ∠OPA

this can be possible only when O , P and Q are on the same line .

It is contraction PQ passes through Q .