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Question-206615




Question Number 206615 by cortano21 last updated on 20/Apr/24
Answered by mr W last updated on 20/Apr/24
((R−r)/(R+r))=sin 22.5°=((√(2−(√2)))/2)  (2−(√(2−(√2)))R)R=(2+(√(2−(√2))))r  (r/R)=((2−(√(2−(√2))))/(2+(√(2−(√2)))))≈0.4465
$$\frac{{R}−{r}}{{R}+{r}}=\mathrm{sin}\:\mathrm{22}.\mathrm{5}°=\frac{\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}}}{\mathrm{2}} \\ $$$$\left(\mathrm{2}−\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}}{R}\right){R}=\left(\mathrm{2}+\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}}\right){r} \\ $$$$\frac{{r}}{{R}}=\frac{\mathrm{2}−\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}}}{\mathrm{2}+\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}}}\approx\mathrm{0}.\mathrm{4465} \\ $$

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