In the given diagram OC = 1.5 × OA, then OB is equal to :

1. 3 × OD

2. 1.5 × OD

3. $\dfrac{2}{3}$ × OD

4. OD

From figure,

In △ OAB and △ OCD,

⇒ ∠AOB = ∠COD (Vertically opposite angles are equal)

⇒ ∠OAB = ∠OCD (Alternate angles are equal)

⇒ ∠OBA = ∠ODC (Alternate angles are equal)

∴ △ OAB ~ △ OCD (By A.A.A. postulate)

Given,

⇒ OC = 1.5 × OA

⇒ $\dfrac{OA}{OC} = \dfrac{1}{1.5} = \dfrac{2}{3}$.

We know that,

Corresponding sides of similar triangle are in proportion.

$\therefore \dfrac{OB}{OD} = \dfrac{OA}{OC} \\[1em] \Rightarrow \dfrac{OB}{OD} = \dfrac{2}{3} \\[1em] \Rightarrow OB = \dfrac{2}{3} \times OD.$

Hence, Option 3 is the correct option.