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Question Number 83032 by Power last updated on 27/Feb/20

Answered by mr W last updated on 27/Feb/20

Commented by mr W last updated on 27/Feb/20

$$\alpha =\frac{360°}{7}=\frac{2\pi }{7}$$$$\beta =180-2\alpha$$$$AD=a+2a\cos \alpha$$$$AE=AD-a=2a\cos \alpha$$$$b^2=a^2+{\left(2a\cos \alpha \right)}^2-2a\left(2a\cos \alpha \right)\cos \beta$$$$=a^2+4a^2{\cos }^2\alpha +4a^2\cos \alpha \cos 2\alpha$$$$=a^2[3+2\cos 2\alpha (1+2\cos \alpha )]$$$$b=a\sqrt{3+2\cos 2\alpha (1+2\cos \alpha )}$$$$\Rightarrow \frac{b}{a}=\sqrt{3-2\cos \frac{3\pi }{7}(1+2\cos \frac{2\pi }{7})}=\sqrt{2}$$

Commented by Power last updated on 27/Feb/20

$$\mathrm{great}\mathrm{sir}\mathrm{thank}\mathrm{you}$$

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