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Theorem - 1 : A line drawn from the centre of a circle to bisect a chord is perpendicular to the chord.

Given : AB is a chord of a circle with centre O. AN = BN and ON is joined

To prove : ON is perpendicular to AB.

Proof :

Statements	Reason
1. in triangles AON and BON OA = OB AN = BN ON = ON	1. Being radius Given Common S.S.S
2.	2. From statement 1
3. are supplementary	3. All are adjacent angle.
4.	4.
5. ON is perpendicular to AB	5. Proved

Theorem - 2 : The perpendicular from the centre to chord bisect the chord.

Given : AB is a chord of a circle with centre O. ON is perpendicular to AB.

To Prove: AN = BN

Proof :

Statement	Reason
1. In AON and BON OA = OB ON is perpendicular to AB ON = ON	1. Radius Given common
2.	2. statement (1) RHS
3. AN = BN	3. statement (2)

Thus perpendicular from O to AB bisects AB.