Question

Prove that equal chords of a circle are equidistant from the centre.​

Answer 1

Answer:

Step-by-step explanation:

Chords which are equidistant from the centre are equal in length. GIVEN: Two chords AB and CD of a circle which are equidistant from centre O i.e., OL = OM, where OL perpendicular to AB and OM perpendicular to CD. TO PROVE: AB = CD. CONSTRUCTION: Join OA and OC. or, AB = CD. Hence Proved. Was this answer helpful?

Answer 2

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

• The perpendicular drawn from the centre of a circle to bisect the chord                                        

       1/2AB=1/2CD

     =>BM=DN

     In ΔOMB and ΔOND

      ∠OMB=∠OND=90 degree

      OB=OD{ Radii of same circle }

      Side BM = side DN{Proved above}

• ΔOMB≅ΔOND
• OM=ON