Out of two concentric circles,the radius of t | vedclass

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(D) Let $C_1$ and $C_2$ be the circles having the same centre $O$. $AC$ is a chord of the outer circle $C_2$ which touches the inner circle $C_1$ at p

Vedclass · Accepted Answer

$3$

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(D) Let $C_1$ and $C_2$ be the circles having the same centre $O$. $AC$ is a chord of the outer circle $C_2$ which touches the inner circle $C_1$ at point $D$.Join $OD$.Since $AC$ is a tangent to the inner circle at $D$,$OD \perp AC$.$A$ perpendicular drawn from the centre to a chord bisects the chord.Therefore,$AD = DC = \frac{8}{2} = 4 \, cm$.In the right-angled $	riangle AOD$,by Pythagoras theorem:$OA^2 = AD^2 + OD^2$$5^2 = 4^2 + OD^2$$25 = 16 + OD^2$$OD^2 = 25 - 16 = 9$$OD = \sqrt{9} = 3 \, cm$.Thus,the radius of the inner circle is $3 \, cm$.

Out of two concentric circles,the radius of the outer circle is $5 \, cm$ and the chord $AC$ of length $8 \, cm$ is a tangent to the inner circle. Find the radius of the inner circle (in $cm$).

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