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Theorem - 3 : Equal chord of a circle are equidistant from the centre.

Given : AB and CD are two equal chord of a circle with centre O.

To Prove : OM = ON

Construction : OA and OC are joined.

Proof :

Statement	Reason
1. AB = CD	1. Given
2.	2. statement (1)
3. AM = CN	3. OM bisect AB and ON bisects CD.
4. OA = OC	4. Being radius
5.	5. By construction
6.	6. R.H.S
7. OM = ON	7. statement (6)

Theorem – 4 Chords which are equidistant from the centre are equal.

Given : - AB and CD are two chords of a circle with centre O.

OM = ON.

To Prove: AB = CD

Construction : OA and OC are joined.

Proof :

Statement	Reason
1. In AOM and CON OM = ON OA = OC	1. (i) given (ii) given (iii) Being radius.
2.	2. statement (1)
3. AM = CN	3. statement (2)
4. 2 AM = 2 CN	4. statement (3)
5. AB = CD	5. statement (4)