Question

If a $\Delta ABC$ is right angles 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. none of these

Answer 1

The correct option is C $c+a-b$

We know, $cosB=\frac{a^2+c^2-b^2}{2ac}=0$
$\Rightarrow (a+c{)}^2-b^2=2ac$
$\Rightarrow (a+c-b)\left(2s\right)=4\left(\frac{1}{2}ac\right)=4\Delta$
$\Rightarrow a+c-b=2\left(\frac{\Delta }{s}\right)=2r$
Hence C is correct