4. Let $A B C$ be a triangle having $O$ and $I$ as its circumcentre and incentre respectively. If $R$ and $r$ are the circumradius and the inradius, respectively, then prove that (IO) $2 = R 2 - 2 R r$. Further show that the triangle BIO is a right-angled triangle if and only if $b$ is the arithmetic mean of a and c.\\