Question Number 172723 by mnjuly1970 last updated on 30/Jun/22
Answered by mr W last updated on 30/Jun/22
$$\mathrm{tan}\:\alpha=\frac{\mathrm{3}}{\mathrm{4}}=\frac{\mathrm{2}\:\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}}{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \:\frac{\alpha}{\mathrm{2}}} \\ $$$$\left(\mathrm{3}\:\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}−\mathrm{1}\right)\left(\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}+\mathrm{3}\right)=\mathrm{0} \\ $$$$\Rightarrow\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{5}{r}+\frac{{r}}{\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}}=\mathrm{4} \\ $$$$\mathrm{8}{r}=\mathrm{4} \\ $$$$\Rightarrow{r}=\frac{\mathrm{1}}{\mathrm{2}}\:\checkmark \\ $$
Commented by mnjuly1970 last updated on 01/Jul/22
$$\mathrm{very}\:\mathrm{nice}\:\mathrm{solution}\:\:\mathrm{Sir}\:\:\mathrm{W} \\ $$
Commented by Tawa11 last updated on 01/Jul/22
$$\mathrm{Great}\:\mathrm{sir}. \\ $$