Question

In the given figure, OA x OB = OC x OD. Which of the following options is correct?

Options

• ∠A = ∠C

• ∠A = ∠B

• ∠A = ∠D

• AOAD ~ A ОВС

Answer 1

∠A = ∠C

Explanation:

From the given condition OA × OB = OC, × we can write the ratio as `(OA)/(OC) = (OD)/(OB)`. Also, ∠AOD = ∠COB because they are vertically opposite angles. Therefore, by the SAS similarity criterion, ΔAOD ∼ ΔCOB, which implies their corresponding angles are equal, so ∠A = ∠C.