Q) In the given figure, ∠ ADC = ∠ BCA, prove that Δ ACB ~ Δ ADC. Hence find if AC = 8 cm and AD = 3 cm.

Ans: 

Ans:  In Δ ACB and Δ ADC,

∠ ADC = ∠ BCA   (given)

∠ A  = ∠ A  (common angle)

   Δ ACB ~ Δ ADC   (by AA similarity identity)

Hence proved.

Next, from above similar triangles, we get

Hence,

AB =

BD = AB – AD = – 3 =

Therefore, BD = 55/3 cm.