Question

In the given figure, OA·OB = OC·OD, Prove that ΔAOD ∼ ΔCOB.

Answer 1

Given:

OA × OB = OC × OD

To Prove: ΔAOD ∼ ΔCOB

Proof: OA × OB = OC × OD

⇒ `("OA")/("OC") = ("OD")/("OB")`   ...(i)

Now, In ΔAOD and ΔBOC

`("OA")/("OC") = ("OD")/("OB")`   ...(From (i))

∠AOD = ∠BOC   ...(vertically opposite ∠s)

∴ ΔAOD ∼ ΔBOC   ...(SAS similarity)