Question

equal chords of a circle are equidistant from the center!

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Answer 1

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Answer 2

9th

Maths

Circles

Equal Chords

Prove that Equal chords of ...

MATHS

Asked on December 27, 2019 byRïdhïma Gaware

Prove that Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).



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ANSWER

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=900 [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] 

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