In the figure, A B and C D are two chords of a circle with center O , such that C , O , D are collinear and A B = 1 3 C D . If A B = 3 c m , then what is the radius of the circle?

A B = 3 c m ...(1) A B = 1 3 C D ...(2) Using equation (1) and (2 ) 3 c m = 1 3 C D ⟹ C D = 9 c m Since chord C D passes through the centre of the circle. Hence, it is the diameter of the circle. Now, radius r = 1 2 d i a m e t e r ⟹ r = 1 2 × C D ⟹ r = 1 2 × 9 c m = 4.5 c m So, the radius of circle is 4.5 c m .

E M B I B E

Full Marks Mathematics 9>Chapter 10 - Circles>TEST YOUR SKILLS>Q 10

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9th CBSE

IMPORTANT

Earn 100

A chord $A B$ of a circle with centre $O$ is $10 c m .$ If the chord is $12 c m$ away from center, then what is the radius of the circle ?

Important Questions on Circles

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 10 - Circles>TEST YOUR SKILLS>Q 11

If the diameter

A D

of a circle is

34 c m

and the length of a chord

A B

is

30 c m .

What is the distance of

A B

from the centre ?

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 10 - Circles>TEST YOUR SKILLS>Q 12

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

4 c m

from the centre of a circle of radius

5 c m ?

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 10 - Circles>TEST YOUR SKILLS>Q 13

If the radius of a circle is

13 c m

and the length of its chord is

10 c m

then what is the distance of chord from the center ?

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 10 - Circles>TEST YOUR SKILLS>Q 14

If the distance of

10 c m

long chord from the center of the circle is

12 c m

then what is the diameter of the circle ?

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 10 - Circles>TEST YOUR SKILLS>Q 15

The chords

A B

and

C D

of a circle are each at a distance of

3 c m

from the center of the circle, then which of the following is true ?
(i)

A B = C D

(ii)

A B > C D

(iii)

A B < C D

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 10 - Circles>TEST YOUR SKILLS>Q 16

In the figure $O$ is the circle and radius of the circle is $5 c m .$ What is the length of $P Q ?$

Question Image

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 10 - Circles>TEST YOUR SKILLS>Q 17

In the figure, $A B$ and $C D$ are two chords of a circle with center $O,$ such that $C, O, D$ are collinear and $A B = \frac{1}{3} C D .$ If $A B = 3 c m,$ then what is the radius of the circle?