In a parallelogram ABCD, AB = 20 cm and AD = 12 cm. The bisector of angle A meets DC at E and BC produced at F. Find the length of CF.

Given,

Bisector of angle A meets DC at E.

∴ AE bisects angle A.

∴ ∠DAE = ∠BAF = x (let)

From figure,

⇒ ∠AFB = ∠DAE = x (Alternate angles are equal)

In △ ABF,

⇒ ∠AFB = ∠BAF (Both equal to x)

∴ BF = AB = 20 cm (Sides opposite to equal angles are equal)

⇒ BF = BC + CF

⇒ BF = AD + CF (BC = AD, opposite sides of a parallelogram are equal)

⇒ 20 = 12 + CF

⇒ CF = 20 - 12 = 8 cm.

Hence, CF = 8 cm.