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Question Number 80587 by ajfour last updated on 04/Feb/20

Commented by ajfour last updated on 04/Feb/20

$G i v e n : △ A B C i s e q u i l a t e r a l,$ $r a d i u s o f s m a l l c i r c l e i s 1 .$ $F i n d r a d i u s o f o u t e r c i r c l e, a .$
Commented by ajfour last updated on 04/Feb/20

$m r W S i r, M j S S i r, p l e a s e a t t e m p t . .$
Commented by mr W last updated on 04/Feb/20

$i t h i n k i f o n l y t h e r a d i u s o f t h e s m a l l$ $c i r c l e i s g i v e n, t h e a n s w e r i s n o t$ $u n i q u e . s e e e x a m p l e s : b o t h r e d a n d$ $g r e e n c i r c l e s s a t i s f y t h e c o n d i t i o n .$
Commented by mr W last updated on 04/Feb/20

Commented by ajfour last updated on 04/Feb/20

$∠ B P M b e i n g a r i g h t a n g l e,$ $m i g h t m a k e t h e o u t e r c i r c l e$ ${u n i q u e}^{'} S i r . .$
Commented by mr W last updated on 04/Feb/20

$t h e n t h e s o l u t i o n i s u n i q u e, i t h i n k .$
	Answered by ajfour last updated on 04/Feb/20

	Commented by ajfour last updated on 04/Feb/20

	$\tan α = \frac{a - 1}{a}, a \sec α = 2$ $\Rightarrow 1 + {(\frac{a - 1}{a})}^{2} = \frac{4}{a^{2}}$ $\Rightarrow 2 a^{2} - 2 a - 3 = 0$ $\Rightarrow a = \frac{1 + \sqrt{7}}{2} .$
	Commented by mr W last updated on 04/Feb/20

	$n i c e d i a g r a m a n d s o l u t i o n s i r!$ $w e c a n a l s o g e t$ ${(a - 1)}^{2} + a^{2} = 2^{2}$ $2 a^{2} - 2 a - 3 = 0$ $\Rightarrow a = \frac{1 + \sqrt{7}}{2}$
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