In a $ riangle A B C$, let $\angle C=\frac{\pi}{2}$. If $r$ and $R$ are respectively inradius and circumradius of $A B C$, then $R+r=$

Question

In a $	riangle A B C$, let $\angle C=\frac{\pi}{2}$. If $r$ and $R$ are respectively inradius and circumradius of $A B C$, then $R+r=$

Aicharya · Accepted Answer

$ x+y=2 R $ Now, $ \begin{array}{ll} & a+b=x+r+y+r=2 R+2 r \ 	herefore & R+r=\frac{a+b}{2} \end{array} $

In a $\triangle A B C$, let $\angle C=\frac{\pi}{2}$. If $r$ and $R$ are respectively inradius and…