Question

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

Answer 1

Answer:

$\huge\underline\mathbb{\red S\pink {O}\purple {L} \blue {UT} \orange {I}\green {ON :}}$

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

∴

1/12 AB= 1/2 CD

⇒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]

$\huge\underline\mathbb{\red F\pink {O}\purple {L} \blue {LO} \orange {W}\green {ME}}$

$\huge{\underline{\pink{Thanks:)❤}}}$