Question

In Fig. 10.53, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.

Answer 1

In Fig. 10.53, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. The radius of its incircle is 2 cm.

Consider the figure, while going through the following steps.

Since, ABC is a right angled triangle, we have,

AC^2 = AB^2 + BC^2

= 8^2 + 6^2

= 64 + 36

= 100

∴ AC = 10 cm

Area of Δ ABC = Area of Δ OAB + Area of Δ OBC + Area of Δ OCA

1/2 × BC × AB = 1/2 × r × AB + 1/2 × r × AC  + 1/2 × BC × r

1/2 × 6 × 8 = 1/2 × r × 8 + 1/2 × r × 10  + 1/2 × 6 × r

24 = 4r + 5r + 3r

24 = 12r

r =2 cm