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Question Number 185893 by mr W last updated on 29/Jan/23

Commented by mr W last updated on 29/Jan/23

$l e n g t h o f c o m m o n t a n g e n t l i n e x = ?$
Commented by som(math1967) last updated on 29/Jan/23

$x = \sqrt{7} ?$
Commented by mr W last updated on 29/Jan/23

$y e s, t h a n k s!$
	Answered by a.lgnaoui last updated on 29/Jan/23

	Answered by som(math1967) last updated on 29/Jan/23

	Commented by som(math1967) last updated on 29/Jan/23

	$A B = d i a g o n a l o f s q u a r e$ $= d i s t b e t w e e n t w o c e n t r e = 4 \sqrt{2}$ $B C = 2 + 3 = 5$ $∴ A C = D E = x = \sqrt{{(4 \sqrt{2})}^{2} - 5^{2}} = \sqrt{7}$
	Answered by a.lgnaoui last updated on 29/Jan/23

	$T r i a n g l e A E F r e c t a n g l e e n E$ ${E F}^{2} = {A F}^{2} - 4$ $T r u a n g k e D F E r e c t a n g l e e n F$ ${E F}^{2} = {D E}^{2} - 9$ ${A D}^{2} = {A E}^{2} + {D E}^{2} - A E \times D E \cos (\frac{π}{2} + α) (i)$ ${(4 \sqrt{2})}^{2} = 4 + {D E}^{2} + 4 D E \sin α$ $△ E F D$ $E F = \frac{3}{\tan α}$ $\sin α = \frac{3}{D E} {D E}^{2} = 9 + {E F}^{2}$ $(i) \Rightarrow 32 = 4 + 9 + {E F}^{2} + 4 \frac{3}{\sin α} \sin α$ $32 = 25 + {E F}^{2}$ $E F = \sqrt{7}$
	Answered by ajfour last updated on 29/Jan/23

	Commented by mr W last updated on 29/Jan/23
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