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Question Number 166749 by Tawa11 last updated on 27/Feb/22

Commented by mr W last updated on 27/Feb/22

$$thisquestionisntimesrepeated.$$

Answered by mr W last updated on 27/Feb/22

Commented by Tawa11 last updated on 27/Feb/22

$$\mathrm{Wow},\mathrm{thanks}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}\mathrm{your}\mathrm{time}.$$

Commented by mr W last updated on 27/Feb/22

$$R=10,r=\frac{R}{2}=5$$$$\tan \frac{\alpha }{2}=\frac{5}{10}=\frac{1}{2}$$$$\cos \frac{\alpha }{2}=\frac{2}{\sqrt{5}}\Rightarrow \cos \alpha =2\times \frac{4}{5}-1=\frac{3}{5}\Rightarrow \sin \alpha =\frac{4}{5}$$$$A_{red}=A_1+A_2-2\times A_3$$$$A_{red}=\frac{R^2}{2}(\alpha -\sin \alpha )+\frac{r^2}{2}(\pi -\alpha -\sin \alpha )-2\times \frac{r^2}{2}(\frac{\pi }{2}-1)$$$$A_{red}=\frac{R^2}{2}({\sin }^{-1}\frac{4}{5}-\frac{4}{5})+\frac{r^2}{2}(2-{\sin }^{-1}\frac{4}{5}-\frac{4}{5})$$$$A_{red}=\frac{R^2}{8}(3{\sin }^{-1}\frac{4}{5}-2)\approx 0.097735R^2$$$$A_{red}=\frac{{10}^2}{8}(3{\sin }^{-1}\frac{4}{5}-2)\approx 9.773570$$

Commented by mr W last updated on 27/Feb/22

Commented by mr W last updated on 27/Feb/22

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