Analytical \& Descriptive Questions \( \mathrm{P} \) Let \( A B C \) be a triangle having \( O \...

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Analytical \& Descriptive Questions
\( \mathrm{P} \)
Let \( A B C \) be a triangle having \( O \) and \( I \) as its
WV circumcentre and incentre, respectively. If \( R \) and \( r \) are the circumradius and the inradius respectively, then prove that \( (I O)^{2}=R^{2}-2 R r \). Further show that the \( \triangle B I O \) is a right angled triangle if and only if \( b \) is the arithmetic mean of \( a \) and \( c \).
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