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Question Number 152486 by Tawa11 last updated on 28/Aug/21

	Answered by mr W last updated on 29/Aug/21

	Commented by mr W last updated on 29/Aug/21

	$R = r a d i u s o f b i g s e m i c i r c l e$ $r = r a d i u s o f s m a l l s e m i c i r c l e$ $r = E F = F D = \frac{x}{2}$ $G = c e n t e r o f b i g c i r c l e$ $F = c e n t e r o f s m a l l c i r c l e$ $R = G A = G E = \frac{A C}{2} = \frac{a + b}{2}$ $G B = a - R = \frac{a - b}{2}$ ${G F}^{2} = {G E}^{2} - {E F}^{2} = {(\frac{a + b}{2})}^{2} - {(\frac{x}{2})}^{2}$ ${G F}^{2} = {G B}^{2} + {B F}^{2} = {(\frac{a - b}{2})}^{2} + {(\frac{x}{2})}^{2}$ ${(\frac{a + b}{2})}^{2} - {(\frac{x}{2})}^{2} = {(\frac{a - b}{2})}^{2} + {(\frac{x}{2})}^{2}$ $2 x^{2} = {(a + b)}^{2} - {(a - b)}^{2} = 4 a b$ $\Rightarrow x^{2} = 2 a b$
	Commented by Tawa11 last updated on 29/Aug/21

	$Thanks sir . I appreciate . God bless you sir .$
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