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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 $5$ cm and $3$ cm. 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

cm and

3

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

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

O A = 3

cm and

OP = 5

To find: length of

PQ

By using Pythagoras Theorem, we have

O A^{2} + A P^{2} = O P^{2}

⟹ A P^{2} = 5^{2} - 3^{2}

⟹ A P^{2} = 25 - 9

A P = 16 = 4

As we know that perpendicular drawn from center to chord of circle bisects the chord

∴ PQ = 2 A P = 2 \times 4 = 8

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Question Text	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.
Answer Type	Text solution:1
Upvotes	150