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,

CA^{2} = AB^{2} + BC^{2}

⇒ CA^{2} = 8^{2} + 6^{2}

⇒ CA^{2} = 100

⇒ CA = 10 cm

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

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