Question

In fig., a circle is inscribed in a triangle ABC having side BC = 8 cm, AC = 10 cm and AB = 12 cm. Find AD, BE and CF. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Given that BC = 8 cm, AC = 10 cm and AB = 12 cm

As the lengths of tangents drawn from an external point to a circle are equal.

Let AD = AF = x, CF = CE = y, BD = BE = z

x + y = 10 ...(i)

$y+z=8\Rightarrow y=8-z$

Substituting in (i)

x + 8 - z = 10

x - z = 2 ...(ii)

x + z = 12 ...(iii)

Adding (ii) and (iii), we get,

2x = 14

x = 7

From (i) y = 3

From (ii)

x-z = 2

$\Rightarrow$ 7- z = 2

$\Rightarrow$ z = 5

Therefore AD = 7, BE = 5 and CF = 3