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Question Number 206615 by cortano21 last updated on 20/Apr/24

Answered by mr W last updated on 20/Apr/24

$$\frac{R-r}{R+r}=\sin 22.5°=\frac{\sqrt{2-\sqrt{2}}}{2}$$$$(2-\sqrt{2-\sqrt{2}}R)R=(2+\sqrt{2-\sqrt{2}})r$$$$\frac{r}{R}=\frac{2-\sqrt{2-\sqrt{2}}}{2+\sqrt{2-\sqrt{2}}}\approx 0.4465$$

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