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Question Number 44395 by ajfour last updated on 28/Sep/18

Commented by ajfour last updated on 28/Sep/18

$F i n d r a d i u s o f t h e g r e e n c i r c l e,$ $i n t e r m s o f R a n d r .$
Commented by ajfour last updated on 28/Sep/18

Commented by ajfour last updated on 28/Sep/18

${(R + s)}^{2} = x^{2} + {(R - s)}^{2}$ $\Rightarrow x^{2} = 4 R s; y^{2} = 4 r s$ $a n d {(x + y)}^{2} = 4 r R$ $\Rightarrow x y = 4 s \sqrt{R r}$ $\Rightarrow 4 s (R + r) + 8 s \sqrt{R r} = 4 R r$ $\Rightarrow s = \frac{R r}{R + r + 2 \sqrt{R r}}$ $o r s = \frac{R r}{{(\sqrt{R} + \sqrt{r})}^{2}} .$
	Answered by rahul 19 last updated on 28/Sep/18

	$L e t r a d i u s o f g r e e n c i r c l e = x$ $\Rightarrow \frac{1}{\sqrt{x}} = \frac{1}{\sqrt{R}} + \frac{1}{\sqrt{r}} .$
	Commented by ajfour last updated on 28/Sep/18

	$w h e r e f r o m d o y o u i n f e r t h i s ?$
	Commented by rahul 19 last updated on 28/Sep/18

	$S i r, y o u h a v e p o s t e d t h e s a m e Q . s o m e$ $t i m e b a c k a n d t h a t t i m e i g a v e a p r o o f$ $a l s o, i r e m e m b e r e d t h e r e s u l t :)$
	Commented by ajfour last updated on 28/Sep/18

	$s e e m s l i k e l y . .$
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