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Question Number 142017 by cherokeesay last updated on 25/May/21

Commented by cherokeesay last updated on 25/May/21

$$$$1) Calculate R 2) Calculate the% of the area of ​​the hatched part compared to the area of ​​the half disk of Radius R.

Commented by mr W last updated on 26/May/21

$$bettersolvethis:$$

Commented by mr W last updated on 26/May/21

Answered by help last updated on 26/May/21

$$2+\sqrt{3}$$

Answered by help last updated on 26/May/21

Commented by cherokeesay last updated on 26/May/21

$$thankyousir!$$$$verynice.$$

Answered by mr W last updated on 26/May/21

$${(\frac{3}{r}-\frac{1}{R})}^2=2(\frac{3}{r^2}+\frac{1}{R^2})$$$$\frac{3R^2}{r^2}-\frac{6R}{r}-1=0$$$$\Rightarrow \frac{R}{r}=\frac{3+2\sqrt{3}}{3}$$$$\Rightarrow R=(1+\frac{2}{\sqrt{3}})\sqrt{3}=2+\sqrt{3}$$

Commented by cherokeesay last updated on 26/May/21

$$thankyoumisterW.$$$$$$

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