Question Number 196007 by sonukgindia last updated on 15/Aug/23
Answered by mr W last updated on 15/Aug/23
$${AC}=\frac{{R}}{\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}} \\ $$$$\overset{\frown} {{BC}}=\left(\pi−\alpha\right){R} \\ $$$$\left(\pi−\alpha\right){R}=\frac{{R}}{\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}} \\ $$$$\left(\pi−\alpha\right)\:\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}=\mathrm{1} \\ $$$$\Rightarrow\alpha\approx\mathrm{0}.\mathrm{81047}\:{rad}\:\approx\mathrm{46}.\mathrm{4365}° \\ $$