Given: OA × OB = OC × OD
To Prove: ∠A = ∠C and ∠B = ∠D
Now, OA .OB = OC.OD
∠AOD = ∠COB (vertically opposite angles)
∴ △AOD ~ △COB (by SAS similarity criterion)
We know that if two triangles are similar then their corresponding angles are equal.
⇒ ∠A = ∠C and ∠B = ∠D
Hence Proved