Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

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Solution

Q.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Ans.
(8)

Let O be the centre of the concentric circle of radii 5 cm and 3 cm respectively. Let AB be a chord of the larger circle touching the smaller circle at P

Then AP = PB and OP $⊥$ AB

Applying Pythagoras theorem in $∆$ OPA, we have

$O A^{2} = O P^{2} + A P^{2} \Rightarrow 25 = 9 + A P^{2}$

$\Rightarrow A P^{2} = 16 \Rightarrow A P = 4 c m$

$∴$ $A B = 2 A P = 8 c m$

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