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Question Number 107572 by ajfour last updated on 11/Aug/20

Commented by ajfour last updated on 11/Aug/20

$T h e c o n e s h a v e b a s e r a d i u s r a n d$ $s e m i - v e r t i c a l a n g l e α / 2 . F i n d$ $r a d i u s o f t h e p i n k s p h e r e t h a t$ $t o u c h e s t h e c o n e s e x t e r n a l l y a n d$ $t o u c h e s t h e p l a n e p a s s i n g t h r o u g h$ $t h e c o n e v e r t i c e s .$
	Answered by mr W last updated on 11/Aug/20

	Commented by mr W last updated on 11/Aug/20

	$b = O B = O A = O C = \frac{2 \sqrt{3} r}{3}$ $β = \frac{π}{2} - \frac{α}{2}$ $R = b \times \tan \frac{β}{2} = \frac{2 \sqrt{3} r}{3} \times \tan (\frac{π}{4} - \frac{α}{4})$ $= \frac{2 \sqrt{3} r}{3} \times \frac{1 - \tan \frac{α}{4}}{1 + \tan \frac{α}{4}}$
	Commented by ajfour last updated on 11/Aug/20

	$P e r f e c t! T h a n k y o u S i r .$
	Commented by otchereabdullai@gmail.com last updated on 12/Aug/20

	$fantastic prof$
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