Question-166465

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

Commented by ajfour last updated on 20/Feb/22

F i n d \frac{a}{b} i n t e r m s o f α a n d β .

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

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

R = r a d i u s o f c i r c l e

C D = 2 R

A C = 2 R \cos α

A C = \frac{a}{\tan \frac{α}{2}} + \frac{a}{\tan (\frac{π}{4} - \frac{β}{2})}

2 R \cos α = a (\frac{1}{\tan \frac{α}{2}} + \frac{1}{\tan (\frac{π}{4} - \frac{β}{2})})

s i m i l a r l y

2 R \cos β = b (\frac{1}{\tan \frac{β}{2}} + \frac{1}{\tan (\frac{π}{4} - \frac{α}{2})})

\Rightarrow \frac{a}{b} = \frac{\cos α (\frac{1}{\tan \frac{β}{2}} + \frac{1 + \tan \frac{α}{2}}{1 - \tan \frac{α}{2}})}{\cos β (\frac{1}{\tan \frac{α}{2}} + \frac{1 + \tan \frac{β}{2}}{1 - \tan \frac{β}{2}})}

Commented by ajfour last updated on 20/Feb/22

p e r f e c t! t h a n k y o u s i r .

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