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Question
In Figure 3, a right triangle ABC, circumscribes a circle of radius r. If AB and BC are of lengths of 8 cm and 6 cm respectively, find the value of r.
Solution
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 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,
CA2 = AB2 + BC2
⇒ CA2 = 82 + 62
⇒ CA2 = 100
⇒ CA = 10 cm
Area of ∆ABC = Area ∆OAB + Area ∆OBC + Area ∆OCA
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