Question Number 144139 by bobhans last updated on 22/Jun/21
Answered by liberty last updated on 22/Jun/21
Commented by EDWIN88 last updated on 22/Jun/21
$$\frac{\mathrm{4}}{\mathrm{R}}\:=\:\frac{\mathrm{8}}{\mathrm{12}+\mathrm{R}}\:\Rightarrow\frac{\mathrm{1}}{\mathrm{R}}=\frac{\mathrm{2}}{\mathrm{12}+\mathrm{R}}\:;\:\mathrm{R}=\mathrm{12} \\ $$
Commented by mr W last updated on 22/Jun/21
$$\frac{{R}−\mathrm{4}}{{R}+\mathrm{4}}=\mathrm{sin}\:\mathrm{30}°=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow{R}=\mathrm{12} \\ $$
Answered by mr W last updated on 22/Jun/21
$${R}=\mathrm{3}\sqrt{\mathrm{4}×\mathrm{4}}=\mathrm{12} \\ $$$${general}\:{case}\:{see}\:{Q}\mathrm{77425} \\ $$