ABC is a right angle triangle, right angled at A. A circle is inscribed in it. The length of two sides containing angle A is 12cm and 5cm find the radius.

Let ABC be the right angled triangle such that ∠A = 90° , AB = 5cm, AC = 12 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,

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

⇒ BC^{2} = 12^{2} + 5^{2}

⇒ BC^{2} = 169

⇒ BC = 13 cm

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

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