Question

write the theorem of congurent chords of a circle are equidistance from the centre of the circle​

Answer 1

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

∴

2

1

AB=

2

1

CD

⇒BM=DN

In △OMB and △OND

∠OMB=∠OND=90

0

[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]