Question

‘r' is the radius of the circumcircle of a circle of a right-angled triangle ABC at B. If AB=6cm,
BC=8cm, find the radius.​

Answer 1

Answer:

Step-by-step explanation:

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