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Question Number 193635 by mr W last updated on 17/Jun/23

Commented by mr W last updated on 17/Jun/23

$f i n d t h e l a r g e s t c i r c l e a n d t h e l a r g e s t$ $s q u a r e w h i c h y o u c a n c o m p l e t e l y$ $c o v e r w i t h t h r e e c i r c u l a r p l a t e s w i t h$ $r a d i u s 1 r e s p e c t i v e l y .$
	Answered by mr W last updated on 18/Jun/23

	Commented by mr W last updated on 18/Jun/23

	$Δ A B C = e q u i l a t e r a l w i t h s i d e l e n g t h$ $s = 2 \times r = 2$ $R = \frac{2}{3} \times \frac{\sqrt{3} s}{2} = \frac{s}{\sqrt{3}} = \frac{2}{\sqrt{3}} \approx 1.155$
	Answered by mr W last updated on 18/Jun/23

	Commented by mr W last updated on 18/Jun/23

	$Δ A B C = e q u i l a t e r a l w i t h s i d e l e n g t h$ $s = 2 \times r = 2$ $\sqrt{s^{2} - a^{2}} = a - \frac{s}{\sqrt{2}}$ $2 a^{2} - \sqrt{2} s a - \frac{s^{2}}{2} = 0$ $a^{2} - \sqrt{2} a - 1 = 0$ $\Rightarrow a = \frac{\sqrt{2} + \sqrt{6}}{2} \approx 1.932$
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