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in Mathematics by (106k points)
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 Prove that Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).

2 Answers

+1 vote
by (323k points)
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Best answer

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] 

+1 vote
by (84.0k points)

Data:

AB and CD are equal chords of a circle with centre O. OK AB and OL CD.

To Prove:

OK = OL

Construction:

Join AO and CO.

Proof:

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