Prove that equal chords of a circle subtend equal angles at the centre

Open in App

Solution

In $Δ A O B$ and $Δ C O D$ ,
AB $=$ CD (Given)
AO $=$ CO (radius)
OB $=$ OD (radius)
By S.S.S congruency, $Δ A O B ≅ Δ C O D$
$\Rightarrow ∠ A O B = ∠ C O D$ .

Suggest Corrections

Similar questions

Q. Prove that equal chords subtend equal angles at the centre of the circle.

Q. Prove that if chords of congruent circles subtend equal angles at their centre, then the chords are equal.

Question 2
Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Q. Recall that two circles are congruent, if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres

Join BYJU'S Learning Program

Prove that equal chords of a circle subtend equal angles at the centre

In ΔAOB and ΔCOD,AB=CD (Given)AO=CO (radius)OB=OD (radius)By S.S.S congruency, ΔAOB≅ΔCOD⇒∠AOB=∠COD.

In $Δ A O B$ and $Δ C O D$ ,
AB $=$ CD (Given)
AO $=$ CO (radius)
OB $=$ OD (radius)
By S.S.S congruency, $Δ A O B ≅ Δ C O D$
$\Rightarrow ∠ A O B = ∠ C O D$ .