In the given figure, ∠ACB=∠CDA, AC=8cm, AD=3cm . . .

Question : In the given figure, ∠ACB=∠CDA, AC=8cm, AD=3cm, then BD is 

a) 22/3 cm

b) 26/3 cm

c) 55/3 cm

d) 64/3 cm

Doubt by Vanshika

Solution :

∠ACB=∠CDA (Given)

⇒ ∠ACB=∠ADC

AC=8cm

AD=3cm

BD=?

In ΔACB and ΔADC

∠A=∠A (Common)

∠ACB=∠ADC (Given)

ΔACB~ΔADC (By AA Similarity Criteria)

AC/AD = AB/AC (By corresponding parts of similar triangle)

8/3 = AB/8
AB = 16/3 cm 

From the figure 
BD=AB-AD
BD=64/3-3
BD=(64-9)/3
BD=55/3 cm 

Hence, c) is the correct option.