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Two concentric circles are of radii 5 cm and 3 cm. Find the le

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

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Two concentric circles are of radii

5 c m

and

3 c m

. Find the length of the chord of the larger circle which touches the smaller circle.

6 mins ago

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Text solutionVerified

Let

O

be the centre of the concentric circle of radii

5

cm and

3

cm respectively. Let

A B

be a chord of the larger circle touching the smaller circle at

P

Then

A P = PB

and

OP ⊥ A B

Applying Pythagoras theorem in

△ OP A

, we have

O A^{2} = OP^{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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Question Text	Two concentric circles are of radii $5 c m$ and $3 c m$ . Find the length of the chord of the larger circle which touches the smaller circle.
Answer Type	Text solution:1
Upvotes	150