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In a $\triangle A B C$, let $\angle C=\frac{\pi}{2}$. If $r$ and $R$ are respectively inradius and circumradius of $A B C$, then $R+r=$
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Verified Answer
The correct answer is:
$\frac{a+b}{2}$
$$
x+y=2 R
$$
Now,
$$
\begin{array}{ll}
& a+b=x+r+y+r=2 R+2 r \\
\therefore & R+r=\frac{a+b}{2}
\end{array}
$$
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