Chords of a circle which are equidistant from the centre are equal.

Explanation

Given:
A circle have two equal chords `AB` and `CD`.
`AB=CD` and `OM` perpendicular to `AB`, `ON` perpendicular to `CD`.
To Prove : `OM=ON`
Proof: `AB=CD` (Given)
`∵` The perpendicular drawn from the centre of a circle to bisect the chord,
`∴1/2AB=1/2CD`
`⇒BM=DN`
In `△OMB` and `△OND`
`∠OMB=∠OND=90^@` [Given]
`OB=OD` [Radii of same circle]
Side `BM=`Side `DN` [Proved above]
`∴△OMB≅△OND` [By `R.H.S.`]
`∴OM=ON` [By `C.P.C.T`]
Hence Proved.