Question Number 212802 by Spillover last updated on 24/Oct/24
Answered by mr W last updated on 24/Oct/24
Commented by mr W last updated on 24/Oct/24
$$\left(\mathrm{2}{R}\right)^{\mathrm{2}} −\left(\mathrm{2}{r}\right)^{\mathrm{2}} =\left({R}+{r}\right)^{\mathrm{2}} −\left({R}−{r}\right)^{\mathrm{2}} \\ $$$$\left(\frac{{R}}{{r}}\right)^{\mathrm{2}} −\left(\frac{{R}}{{r}}\right)−\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\frac{{R}}{{r}}=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}=\varphi \\ $$