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Question Number 128947 by ajfour last updated on 11/Jan/21

Commented by ajfour last updated on 11/Jan/21

$F i n d r a d i u s o f t h e b l u e a r c .$
	Answered by mr W last updated on 11/Jan/21

	Commented by mr W last updated on 11/Jan/21

	$a = G F + F E = 1 + \frac{1}{\sqrt{3}}$ $D E = \frac{2}{\sqrt{3}}$ $A E = 2 (1 + \frac{1}{\sqrt{3}})$ $A B = (1 + \frac{1}{\sqrt{3}}) \sin 30 ° = \frac{1}{2} (1 + \frac{1}{\sqrt{3}})$ $B C = 2 (1 + \frac{1}{\sqrt{3}}) - \frac{2}{\sqrt{3}} - 1 - \frac{1}{2} (1 + \frac{1}{\sqrt{3}})$ $= \frac{1}{2} (1 - \frac{1}{\sqrt{3}})$ $H B = (1 + \frac{1}{\sqrt{3}}) \cos 30 ° = \frac{1}{2} (1 + \sqrt{3})$ ${H B}^{2} = (2 R - B C) B C$ $\frac{{(1 + \sqrt{3})}^{2}}{4} = (2 R - \frac{1}{2} (1 - \frac{1}{\sqrt{3}})) \frac{1}{2} (1 - \frac{1}{\sqrt{3}})$ $\Rightarrow R = \frac{3 \sqrt{3} + 4}{2} \approx 4.598076$
	Commented by ajfour last updated on 12/Jan/21

	$T h a n k s S i r! (p o w e r o f p o i n t$ $w r t a c i r c l e i s r e a l l y h e l p f u l) .$
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