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,
BC2 = AC2 + AB2
⇒ BC2 = 122 + 52
⇒ BC2 = 169
⇒ BC = 13 cm
Area of ∆ABC = Area ∆OAB + Area ∆OBC + Area ∆OCA
Given: ABCD is a trapezium where AB||CD and AD = BC