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Question Number 172723 by mnjuly1970 last updated on 30/Jun/22

Answered by mr W last updated on 30/Jun/22

$$\tan \alpha =\frac{3}{4}=\frac{2\tan \frac{\alpha }{2}}{1-{\tan }^2\frac{\alpha }{2}}$$$$(3\tan \frac{\alpha }{2}-1)(\tan \frac{\alpha }{2}+3)=0$$$$\Rightarrow \tan \frac{\alpha }{2}=\frac{1}{3}$$$$5r+\frac{r}{\tan \frac{\alpha }{2}}=4$$$$8r=4$$$$\Rightarrow r=\frac{1}{2}✓$$

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

$$\mathrm{Great}\mathrm{sir}.$$

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