Question

prove that the equal chords of circle subtend equal angles at the centre. for class 9 maths​

Answer 1

Answer:

To Prove: AB = CD. Solution: AC and BD are diameters of a circle which intersect at the center O. We know that the angles subtended by the chords of a circle at the center are equal, then chords are equal. Thus, AB = CD.

Answer 2

Given :

• A circle with center O.
• AB and CD are equal chords of a circle.

i.e. AB = CD

To Prove :

• ∠AOB = ∠DOC

Proof :

★ In △AOB & △DOC

• AO = OD (Radius)
• AB = CD (Given)
• OB = OC (Radius)

∴ △AOB ≅ △DOC (SSS rule)

∴ ∠AOB = ∠DOC (CPCT)

⎔ Hence Proved !

━━━━━━━━━━━━━━━━━━━━━━━━━━