Out of the two concentric circles,


Out of the 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.


Let Cand C2 be the two circles having same centre O. AC is a chord which touches the C1 at point D.

Join $O D$.

Also, $O D \perp A C$

$\therefore \quad A D=D C=4 \mathrm{~cm} \quad$ [perpendicular line OD bisects the chord]

In right angled $\triangle A O D, \quad O A^{2}=A D^{2}+D O^{2}$

[by Pythagoras theorem, i.e., (hypotenuse) $^{2}=(\text { base })^{2}+$ (perpendicular) $^{2}$ ]

$\Rightarrow \quad D O^{2}=5^{2}-4^{2}$


$\Rightarrow \quad D O=3 \mathrm{~cm}$

$\therefore$ Radius of the inner circle $O D=3 \mathrm{~cm}$

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