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Question Number 166465 by ajfour last updated on 20/Feb/22

Commented by ajfour last updated on 20/Feb/22

$$Find\frac{a}{b}intermsof\alpha and\beta .$$

Answered by mr W last updated on 20/Feb/22

Commented by mr W last updated on 20/Feb/22

$$R=radiusofcircle$$$$CD=2R$$$$AC=2R\cos \alpha$$$$AC=\frac{a}{\tan \frac{\alpha }{2}}+\frac{a}{\tan (\frac{\pi }{4}-\frac{\beta }{2})}$$$$2R\cos \alpha =a(\frac{1}{\tan \frac{\alpha }{2}}+\frac{1}{\tan (\frac{\pi }{4}-\frac{\beta }{2})})$$$$similarly$$$$2R\cos \beta =b(\frac{1}{\tan \frac{\beta }{2}}+\frac{1}{\tan (\frac{\pi }{4}-\frac{\alpha }{2})})$$$$\Rightarrow \frac{a}{b}=\frac{\cos \alpha (\frac{1}{\tan \frac{\beta }{2}}+\frac{1+\tan \frac{\alpha }{2}}{1-\tan \frac{\alpha }{2}})}{\cos \beta (\frac{1}{\tan \frac{\alpha }{2}}+\frac{1+\tan \frac{\beta }{2}}{1-\tan \frac{\beta }{2}})}$$

Commented by ajfour last updated on 20/Feb/22

$$perfect!thankyousir.$$

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