In Fig, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.

Given: ∠B=90^o

BC=6cm

AB= 8cm.

To find: The value of r.

Theorem Used:

Pythagoras theorem:

In a right-angled triangle, the squares of the hypotenuse is equal to the sum of the squares of the other two sides.

Explanation:

AB, BC and CA are tangent 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
CA = 10cm
Area of △ABC = Area of △OAB + Area of △OBC + Area of △OCA