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In the given figure, the diameter CD of a circle with centre O

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In the given figure, the diameter $C D$ of a circle with centre $O$ is perpendicular to chord $A B$ . If $A B = 12 c m$ and $CE = 3 c m$ calculate the radius of the circle.

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Benjamin Discussed

In the given figure, the diameter

C D

of a circle with centre

O

is perpendicular to chord

A B

. If

A B = 12 c m

and

CE = 3 c m

calculate the radius of the circle.

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Text solutionVerified

From the figure, we know that

C D

is the diameter of the circle with centre

O

which is perpendicular to chord

A B

Draw the line

O A

It is given that

A B = 12 c m

and

CE = 3 c m

Consider

O A = OC = r c m

It can be written as

OE = (r - 3) c m

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

We know that

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

By substituting the values

A E = \frac{1}{2} \times 12

So we get

A E = 6 c m

Consider

△ OE A

By using the Pythagoras theorem

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

By substituting the values

r^{2} = (r - 3)^{2} + 6^{2}

So we get

r^{2} = r^{2} - 6 r + 9 + 36

On further calculation

r^{2} - r^{2} + 6 r = 45

So we get

6 r = 45

By division

r = \frac{45}{6}

r = 7.5 c m

Therefore, the radius of the circle is

7.5 c m

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Question Text	In the given figure, the diameter $C D$ of a circle with centre $O$ is perpendicular to chord $A B$ . If $A B = 12 c m$ and $CE = 3 c m$ calculate the radius of the circle.
Answer Type	Text solution:1
Upvotes	150

In the given figure, the diameter CD of a circle with centre O is perpendicular to chord AB. If AB=12 cm and CE=3 cm calculate the radius of the circle.

Text solutionVerified

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In the given figure, the diameter $C D$ of a circle with centre $O$ is perpendicular to chord $A B$ . If $A B = 12 c m$ and $CE = 3 c m$ calculate the radius of the circle.