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Question Number 96785 by  M±th+et+s last updated on 04/Jun/20

Answered by mr W last updated on 04/Jun/20

Commented by mr W last updated on 04/Jun/20

$$r+r\cos \alpha =a$$$$\Rightarrow \cos \alpha =\frac{a}{r}-1=\frac{144}{80}-1=\frac{4}{5}$$$$\tan \beta =\frac{r}{a-r\sin \alpha }=\frac{1}{\frac{a}{r}-\sin \alpha }=\frac{1}{\frac{144}{80}-\frac{3}{5}}=\frac{5}{6}$$$$\gamma =\frac{\pi }{2}-2\beta$$$$m=\frac{a}{\cos \gamma }=\frac{a}{\sin 2\beta }=\frac{a}{2\sin \beta \cos \beta }$$$$=\frac{144}{2\times \frac{5\times 6}{5^2+6^2}}=\frac{732}{5}=146.4$$

Commented by  M±th+et+s last updated on 04/Jun/20

$$greatworkmrW.thanx$$

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