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Question Number 111135 by ajfour last updated on 02/Sep/20

Answered by mr W last updated on 02/Sep/20

$$2r+R-\sqrt{R^2-r^2}=2R$$$$2r-R=\sqrt{R^2-r^2}$$$$4r^2-4Rr+R^2=R^2-r^2$$$$5r=4R$$$$\Rightarrow \frac{R}{r}=\frac{5}{4}$$

Answered by ajfour last updated on 02/Sep/20

$$R^2=r^2+{(2r-R)}^2$$$$\Rightarrow 4rR=5r^2$$$$\Rightarrow \frac{R}{r}=\frac{5}{4}.$$

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