Answer :

Given,

A right-angled triangle ABC,

AB = 8 cm

BC = 6 cm

Let’s suppose Triangle ABC is right angled such that;

∠B = 90°

O be the center and

r be the radius of the incircle.

AB is a tangent to the circle at point P

BC is a tangent to the circle at point N and

CA is a tangent to the circle at point M

∴ OP = ON = OM = r (radius of the circle)

Area of ∆ABC = 1/2 ×BC×AB = 24 cm^{2}

By Pythagoras theorem;

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

CA^{2} = (8)^{2} + (6)^{2}

CA^{2} = 100 cm

CA = 10 cm

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

r = 2 cm

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