Abc Is Right Triangle Right Angled At B Such That Bc 6 Cm And Ab Cm Find Radius Of Its In Circle

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.

Answers:

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 in circle.

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