Mathematics - Properties of Triangle Question with Solution | TestHub

For a right-angled triangle with the right angle at $A$, side $a$ is the hypotenuse. The circumradius $R=a/2$. The inradius $r=\frac{b+c-a}{2}$. Therefore, $r+R=\frac{b+c-a}{2}+\frac{a}{2}=\frac{b+c-a+a}{2}=\frac{b+c}{2}$.