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Question Number 211537 by cherokeesay last updated on 12/Sep/24

Answered by mr W last updated on 12/Sep/24

$$\sqrt{{(R-2)}^2-2^2}-2=\sqrt{R^2-6^2}$$$$\sqrt{R^2-4R}=2+\sqrt{R^2-6^2}$$$$8-R=\sqrt{R^2-6^2}$$$$\Rightarrow R=\frac{50}{8}$$$$ratio=\frac{2^2}{0.5R^2}=\frac{128}{625}=20.48\mathrm{\%}$$

Commented by mr W last updated on 12/Sep/24

$$thanks!$$

Answered by A5T last updated on 12/Sep/24

$$6^2=x(2R-x)\Rightarrow 2R-x=\frac{36}{x}...\left(i\right)$$$${(R-2)}^2=2^2+{(2+R-x)}^2\Rightarrow 2R-x=\frac{4}{x-4}...\left(ii\right)$$$$\left(i\right)\mathrm{\&}\left(ii\right)\Rightarrow \frac{4}{x-4}=\frac{36}{x}\Rightarrow x=9x-36\Rightarrow x=\frac{9}{2}\Rightarrow R=\frac{25}{4}$$$$\Rightarrow \frac{\left[green\right]}{\left[white\right]}=\frac{4}{\frac{625}{32}}=\frac{128}{625}=0.2048$$

Commented by A5T last updated on 12/Sep/24

Commented by cherokeesay last updated on 12/Sep/24

$$perfect!$$

Answered by a.lgnaoui last updated on 12/Sep/24

Commented by a.lgnaoui last updated on 12/Sep/24

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