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Question Number 143322 by enter last updated on 13/Jun/21

	Answered by mr W last updated on 13/Jun/21

	Commented by mr W last updated on 13/Jun/21

	$R = r a d i u s o f b i g c i r c l e$ $r = r a d i u s o f s m a l l c i r c l e s$ $O C = R - r$ ${(R - r)}^{2} - r^{2} = {(\frac{R}{2})}^{2}$ $\Rightarrow \frac{r}{R} = \frac{3}{8}$ $\sin α = \frac{r}{R - r} = \frac{3}{5}$ ${B C}^{2} = R^{2} + {(R - r)}^{2} - 2 R (R - r) \sin α$ $= R^{2} + \frac{25 R^{2}}{64} - 2 R \times \frac{5 R}{8} \times \frac{3}{5}$ $= \frac{41 R^{2}}{64}$ $b^{2} = {B D}^{2} = {B C}^{2} - r^{2} = \frac{41 R^{2}}{64} - \frac{9 R^{2}}{64} = \frac{R^{2}}{2}$ $\Rightarrow b = \frac{\sqrt{2} R}{2}$ ${A C}^{2} = R^{2} + {(R - r)}^{2} + 2 R (R - r) \sin α$ $= R^{2} + \frac{25 R^{2}}{64} + 2 R \times \frac{5 R}{8} \times \frac{3}{5}$ $= \frac{137 R^{2}}{64}$ $a^{2} = {A E}^{2} = {A C}^{2} - r^{2} = \frac{137 R^{2}}{64} - \frac{9 R^{2}}{64} = 2 R^{2}$ $\Rightarrow a = \sqrt{2} R$ $\Rightarrow \frac{a}{b} = 2$
	Commented by peter frank last updated on 13/Jun/21

	$s o r r y s i r w h i c h a p p l i c a t i o n a r e$ $u s i n g d r a w i n g ?$
	Commented by mr W last updated on 13/Jun/21

	$i f y o u m e a n t h e i m a g e, i u s e d t h e$ $a p p p h o t o e d i t o r .$
	Commented by Engr_Jidda last updated on 13/Jun/21

	$l i n k t o d o w n l o a d i t p l e a s e$
	Commented by mr W last updated on 13/Jun/21
	https://play.google.com/store/apps/details?id=com.iudesk.android.photo.editor&pcampaignid=MKT-Other-global-all-co-prtnr-py-PartBadge-Mar2515-1
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