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Find the length of a chord which is at a distance of 3 cm from

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Find the length of a chord which is at a distance of $3 c m$ from the centre of a circle of radius $5 c m$

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Find the length of a chord which is at a distance of

3 c m

from the centre of a circle of radius

5 c m

10 mins ago

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Text solutionVerified

Consider

A B

as the chord of the circle with

O

as the center and radius

5 c m

Construct

OE ⊥ A B

It is given that

O A = 5 c m

and

OE = 3 c m

The perpendicular from the centre of a circle to a chord bisects the chord

Consider

△ OE A

Using the Pythagoras theorem it can be written as

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

By substituting the values we get

5^{2} = A E^{2} + 3^{2}

On further calculation

A E^{2} = 5^{2} - 3^{2}

So, we get

A E^{2} = 25 - 9

By subtraction

A E^{2} = 16

By taking the square root

A E = 16

So we get

A E = 4 c m

We know that

A B = 2 A E

By substituting the values

A B = 2 \times 4

So we get

A B = 8 c m

Therefore, the length of the chord is

8 c m

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Question Text	Find the length of a chord which is at a distance of $3 c m$ from the centre of a circle of radius $5 c m$
Answer Type	Text solution:1
Upvotes	150

Find the length of a chord which is at a distance of 3 cm from the centre of a circle of radius 5 cm

Text solutionVerified

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Find the length of a chord which is at a distance of $3 c m$ from the centre of a circle of radius $5 c m$