Question

Prove that if the angle subtended by two chord at the centre of a circle are equal then the chord are equal

Answer 1

Given : In C(O,r), ∠AOB = ∠COD.

To prove : AB = CD

Proof : In ∆AOB and ∆COD we have,

✍️ Since radius in circle are same,

⇒OA = OC

✍️ We are given ins statement that,

⇒∠AOB = ∠COD

✍️ Since radius in circle are same,

⇒OB = OD

✍️ Hence ∆AOB ≅ ∆COD by SAS congruency.

⇒AB = CD [ c.p.c.t ]

⇒Q.E.D