ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle.
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