Question

ABCD is a parallelogram in which AB=20cm and AD=12cm, angle bisector of A meet DC at E and side BC is produced and AE produced meet at F ,then the value of CF is
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Answer 1

Answer:

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

Answer 2

Answer:

AB=20cm

AD=12cm

From the above figure it's evident that ABF is an isosceles triangle with ∠BAF = ∠BFA =x

AB=BF=20cm

BF=20cm

BC+CF=20cm

CF=20-12= 8cm