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. $\frac{(a+b+c)}{2}$
• B. a+b+c
• C. $\frac{(a+b-c)}{2}$
• D. Can't be determined.

Answer 1

The correct option is C

$\frac{(a+b-c)}{2}$

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

$r=\frac{(a+b-c)}{2}$