Question

In the given figure, ∠ADC = ∠BCA; prove that ΔACB ∼ ΔADC. Hence find BD if AC = 8 cm and AD = 3 cm.

Answer 1

Given, AC = 8 cm, AD = 3 cm

and ∠ADC = ∠BCA

From the figure in ΔADC and ΔBCA

∠A = ∠A  ...(Common)

∠ADC = ∠BCA  ...(Given)

So, by AA similarity criteria

ΔADC ∼ ΔBCA

∵ Corresponding sides are in the same ratio

`(AC)/(AD) = (AB)/(AC)`

`8/3 = (AB)/8`

AB = `(8 xx 8)/3`

= `64/3` cm

Now from the figure,

BD = AB – AD

= `64/3 - 3`

= `(64 - 9)/3`

= `55/3`

BD = `18 1/3` cm.