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Question

A circle is inscribed inside a right-angled triangle. If BC = a, CA= b and AB = c, then the radius of the circle is ____.


A

(a+b+c)2

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B

a+b+c

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C

(a+bc)2

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D

Can't be determined.

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Solution

The correct option is C

(a+bc)2


The triangle ABC is drawn as described in the question. D.E and F are the points of contacts of the tangents.

OECD is a square.

OE=OD= CD = CE = r, where r is the radius of the circle.

BE = a - r

BE = BF = a - r ..... (tangents froman external point are equal)

AD = b - r

AD = AF = b - r ..... (tangents froman external point are equal)

We know that BA = BF + FA

c = b - r + a - r

2r = a + b - c

r = (a+bc)2


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