If the radii of two concentric circles are 4 | vedclass

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(D) Let $O$ be the centre of two concentric circles $C_{1}$ and $C_{2}$,whose radii are $r_{1} = 4 \, cm$ and $r_{2} = 5 \, cm$.Let $AC$ be a chord of

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$6$

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(D) Let $O$ be the centre of two concentric circles $C_{1}$ and $C_{2}$,whose radii are $r_{1} = 4 \, cm$ and $r_{2} = 5 \, cm$.Let $AC$ be a chord of the larger circle $C_{2}$,which touches the smaller circle $C_{1}$ at point $B$.Join $OB$. Since $AC$ is a tangent to the circle $C_{1}$ at $B$,$OB \perp AC$ (The tangent at any point of a circle is perpendicular to the radius through the point of contact).Now,in the right-angled $	riangle OBC$,by using the Pythagoras theorem:$OC^{2} = BC^{2} + OB^{2}$Substituting the values,we get:$5^{2} = BC^{2} + 4^{2}$$25 = BC^{2} + 16$$BC^{2} = 25 - 16 = 9$$BC = \sqrt{9} = 3 \, cm$Since the perpendicular from the centre to a chord bisects the chord,the length of the chord $AC = 2 	imes BC = 2 	imes 3 = 6 \, cm$.

If the radii of two concentric circles are $4 \, cm$ and $5 \, cm$,then the length of each chord of the larger circle which is tangent to the smaller circle is (in $cm$):

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