Question

In the given figure, AB = 10 cm, CD = 8 cm = OB, then OD is equal to ______.

विकल्प

• 10 cm

• 3.2 cm

• 6.4 cm

• 8 cm

Answer 1

In the given figure, AB = 10 cm, CD = 8 cm = OB, then OD is equal to 6.4 cm.

Explanation:

From figure,

In △ AOB and △ COD,

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

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

∴ △ AOB ~ △ COD (By A.A. postulate)

We know that,

Corresponding sides of similar triangle are in proportion.

∴ `(OB)/(OD) = (AB)/(CD)`

⇒ `8/(OD) = 10/8`

⇒ OD = `(8 × 8)/10`

⇒ OD = `64/10` = 6.4 cm