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Question Number 185166 by Rupesh123 last updated on 17/Jan/23

	Answered by mnjuly1970 last updated on 18/Jan/23

	$s i n (\frac{A}{2}) = \frac{r}{I A} \Rightarrow r = I A . s i n (\frac{A}{2})$ $s i n (\frac{B}{2}) = \frac{r}{I B} \Rightarrow r = I B . s i n (\frac{B}{2})$ $s i n (\frac{C}{2}) = \frac{r}{I C} \Rightarrow r = I C . s i n (\frac{C}{2})$ $- - - - - - - - -$ $r^{3} = (I A . I B . I C) (s i n (\frac{A}{2}) s i n (\frac{B}{2}) s i n (\frac{C}{2}))$ $4 {R r}^{3} = I A . I B . I C . r$ $4 {R r}^{2} = I A . I B . I C$ $\underset{e u l e r i n e q u a l i t y}{\overset{r ⩽ \frac{R}{2}}{\Rightarrow}} R^{} \overset{3}{} ⩾ I A . I B . I C$
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