Question

A right triangle ABC, right angled at A, is circumscribing a circle. If AB = 6 cm and BC = 10 cm, find the radius of the circle.

Answer 1

In right angle triangle ABC,

BC² = AB² + AC²   ...(By Pythagoras theorem)

or AC² = BC² – AB²

= 10² – 6²

= 100 – 36

= 64

∴ AC = 8 cm

Now, join OA, OB and OC.

ar(ΔABC) = ar(ΔAOB) + ar(ΔAOC) + ar(ΔBOC)

⇒ `1/2 xx 6 xx 8 = (1/2 xx 6 xx r) + (1/2 xx 8 xx r) + (1/2 xx 10 xx r)`   ...[∵ Area of triangle = `1/2` × base × height and r = radius of circle]

⇒ 24 = 3r + 4r + 5r

⇒ 12r = 24

⇒ r = 2 cm