According to the question,
We have,
ABCD is a parallelogram
AB = 10 cm
AD = 6cm.
The bisector of ∠A meets DC at E.
AE and BC produced meet at F.
Since, AF bisects ∠A,
We get,
∠BAE = ∠EAD … (1)
∠EAD = ∠EFB … (2) [Alternate angles]
From equations (1) and (2),
We get,
∠BAE = ∠EFB
Since sides opposite to equal angles are equal,
We get,
BF = AB
Here, AB = 10 cm
So, BF = 10 cm
⇒ BC + CF = 10 cm
6 cm + CF = 10 cm [BC = AD = 6 cm, opposite sides of a parallelogram]
⇒ CF = 10 – 6 cm = 4 cm
⇒ CF = 4 cm