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Question Number 87369 by ajfour last updated on 04/Apr/20

Commented by ajfour last updated on 04/Apr/20

$$Ithink,\frac{R}{r}=3+2\sqrt{2}only,Sir.$$

Commented by ajfour last updated on 04/Apr/20

$$FindR/r.$$

Commented by Prithwish Sen 1 last updated on 04/Apr/20

$$3\pm 2\sqrt{2}$$

Commented by Prithwish Sen 1 last updated on 04/Apr/20

$$\mathrm{yes}.\mathrm{thank}\mathrm{you}.$$

Answered by mr W last updated on 04/Apr/20

Commented by mr W last updated on 04/Apr/20

$$\beta +\gamma =\frac{\pi }{2}$$$$\cos \beta =\frac{R-r}{R+r}$$$$\cos \gamma =\frac{R-r}{R+r}=\cos \beta$$$$\Rightarrow \beta =\gamma =\frac{\pi }{4}$$$$\frac{R-r}{R+r}=\frac{\sqrt{2}}{2}$$$$\frac{\frac{R}{r}-1}{\frac{R}{r}+1}=\frac{\sqrt{2}}{2}$$$$\Rightarrow \frac{R}{r}=\frac{2+\sqrt{2}}{2-\sqrt{2}}=3+2\sqrt{2}$$

Commented by Prithwish Sen 1 last updated on 04/Apr/20

$$\mathrm{wow}!\mathrm{excellent}\mathrm{sir}.$$

Commented by ajfour last updated on 04/Apr/20

$$ThankyoubothmrWSir\mathrm{\&}SenSir.$$

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