Given : A circle have two equal chords AB & CD. .e. AB = CD and OM ⊥ AB, ON ⊥ CD
To Prove : OM = ON
Construction : Join OB & OD
Proof : AB = CD (Given)
[∵The perpendicular drawn from the centre of a circle to bisect the chord.]
∴ 1/2 AB = 1/2 CD
⇒ BM = DN
In ∆OMB & ∆OND
∠OMB = ∠OND = 900 [Given]
OB = OD [Radii of same circle]
Side BM = Side DN [Proved above]
∴ ∆OMB ≅ ∆OND [By R.H.S.]
∴ OM = ON [By cpctc]