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A chord of length 16 cm is drawn in a circle of radius 10 cm.

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A chord of length $16 c m$ is drawn in a circle of radius $10 c m$ . Find the distance of the chord from the centre of the circle.

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A chord of length

16 c m

is drawn in a circle of radius

10 c m

. Find the distance of the chord from the centre of the circle.

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Consider

A B

as the chord with

O

as the centre and radius

10 c m

So we get

O A = 10 c m

and

A B = 16 c m

Construct

O L ⊥ A B

Perpendicular from the centre of a circle to a chord bisect the chord

So we get

A L = \frac{1}{2} \times A B

By substituting the values

A L = \frac{1}{2} \times 16

So we get

A l = 8 c m

Consider

△ O L A

Using the Pythagoras theorem it can be written as

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

By substituting the values we get

1 0^{2} = O L^{2} + 8^{2}

On further calculation

O L^{2} = 1 0^{2} - 8^{2}

So we get

O L^{2} = 100 - 64

By subtraction

O L^{2} = 36

By taking the square root

O L = 36

So we get

O L = 6 c m

Therefore, the distance of the chord from the centre of the circle is

6 c m

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Question Text	A chord of length $16 c m$ is drawn in a circle of radius $10 c m$ . Find the distance of the chord from the centre of the circle.
Answer Type	Text solution:1
Upvotes	150

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the centre of the circle.

Text solutionVerified

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A chord of length $16 c m$ is drawn in a circle of radius $10 c m$ . Find the distance of the chord from the centre of the circle.