Question Number 47515 by ajfour last updated on 11/Nov/18
Commented by ajfour last updated on 11/Nov/18
$${Find}\:\alpha\:{in}\:{terms}\:{of}\:{R}\:{if}\:{both} \\ $$$${coloured}\:{areas}\:{are}\:{equal}. \\ $$
Answered by mr W last updated on 11/Nov/18
$${A}_{{blue}} ={R}^{\mathrm{2}} \:\mathrm{cot}\:\frac{\alpha}{\mathrm{2}}−\frac{\left(\pi−\alpha\right){R}^{\mathrm{2}} }{\mathrm{2}}={A}_{{yellow}} =\pi{R}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{cot}\:\frac{\alpha}{\mathrm{2}}+\frac{\alpha}{\mathrm{2}}=\frac{\mathrm{3}\pi}{\mathrm{2}} \\ $$$$\Rightarrow\alpha=\mathrm{25}.\mathrm{0932}° \\ $$
Commented by ajfour last updated on 11/Nov/18
$${Thanks}\:{Sir},\:{very}\:{quick}! \\ $$