Question

In Figure 3, a right triangle ABC, circumscribes a circle of radius r. If AB and BC are of lengths of 8 cm and 6 cm respectively, find the value of r.

Answer 1

Let ABC be the right angled triangle such that ∠B = 90° , BC = 6 cm, AB = 8 cm. Let O be the centre and r be the radius of the incircle.

AB, BC and CA are tangents to the circle at P, N and M.

∴ OP = ON = OM = r (radius of the circle)

By Pythagoras theorem,

 CA² = AB² + BC²

⇒ CA² = 8² + 6²

⇒ CA² = 100

⇒ CA = 10 cm

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