Question

A $\Delta$ ABC is right angled at B. Then, the diameter of the incircle of the triangle is

• A. 2(c + a - b )
• B. c + a - 2b
• C. c + a - b
• D. c - a+ b

Answer 1

The correct option is C

c + a - b

$r=\frac{\Delta }{s}=\frac{\left(1/2\right).ac}{\left(1/2\right).(a+b+c)}=\frac{ac}{a+b+c}=\frac{ac(c+a-b)}{(c+a{)}^2-b^2}=\frac{ac(c+a-b)}{c^2+2ca+a^2-b^2}=\frac{ac(c+a-b)}{2ca+b^2-b^2}=\frac{c+a-b}{2}(\because a^2+c^2=b^2)$