# Class 9

Explore popular questions from Circles for Class 9. This collection covers Circles previous year Class 9 questions hand picked by experienced teachers.

## Mathematics

Circles

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Q 1. A sector of {tex} 120 ^ { \circ } {/tex} cut out from a circle has an area of {tex} 9 \frac { 3 } { 7 } {/tex} sq {tex} \mathrm { cm } . {/tex} The radius of the circle is

{tex} 3 \mathrm { cm } {/tex}

B

{tex} 2.5 \mathrm { cm } {/tex}

C

{tex} 3.5 \mathrm { cm } {/tex}

D

{tex} 3.6 \mathrm { cm } {/tex}

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Q 2. {tex} \mathrm {AB}{/tex} and {tex} \mathrm { CD } {/tex} are two chords of a circle such that {tex} \mathrm { AB } = 8 \mathrm { cm } , \mathrm { CD } = 10 \mathrm { cm } {/tex} and {tex} \mathrm { AB } \| \mathrm { CD } {/tex}. If the perpendicular distance between {tex} \mathrm { AB } {/tex} and {tex} \mathrm { CD } {/tex} is {tex} 2 \mathrm { cm } , {/tex} then what is the radius of the circle equal to?

{tex} \frac { ( 5 \sqrt { 17 } ) } { 4 } \mathrm { cm } {/tex}

B

{tex} \frac { ( 4 \sqrt { 17 } ) } { 5 } \mathrm { cm } {/tex}

C

{tex} \frac { ( 3 \sqrt { 17 } ) } { 5 } \mathrm { cm } {/tex}

D

{tex} \sqrt { 17 } \mathrm { cm } {/tex}

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Q 3. In given figure, {tex}\mathrm {ABCD} {/tex} and {tex}\mathrm {ABEF} {/tex} are two cyclic quadrilaterals. If {tex} \angle \mathrm { BCD } = 110 ^ { \circ } , {/tex} then {tex} \angle \mathrm { BEF } = {/tex}

A

{tex} 55 ^ { \circ } {/tex}

B

{tex} 70 ^ { \circ } {/tex}

C

{tex} 90 ^ { \circ } {/tex}

{tex} 110 ^ { \circ } {/tex}

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Q 4. The line {tex}\mathrm {BE} {/tex} is a diameter of the given circle. If {tex} \angle \mathrm { BAC } = 33 ^ { \circ } {/tex} and {tex} \angle \mathrm { EBC } = 57 ^ { \circ } . {/tex} Then {tex} \angle \mathrm { CAE } = {/tex}

{tex} 57 ^ { \circ } {/tex}

B

{tex} 33 ^ { \circ } {/tex}

C

{tex} 48 ^ { \circ } {/tex}

D

{tex} 90 ^ { \circ } {/tex}

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Q 5. In the adjoining figure, circles with centres at {tex}\mathrm {L} {/tex}, {tex}\mathrm {M} {/tex} and {tex}\mathrm {N} {/tex} each have a radius of 2 units and are placed as shown here. If {tex}\mathrm {PQRS} {/tex} is the smallest rectangle that will enclose the 3 circles, what is the area of {tex}\mathrm {PQRS} {/tex}?

A

8 sq units

B

12 sq units

C

16 sq units

32 sq units.

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Q 6. Given, a quadrilateral {tex}\mathrm {ABCD} {/tex} is inscribed in a circle as shown in the figure below. If {tex} \angle \mathrm { B } = 125 ^ { \circ } , {/tex} then {tex} \angle \mathrm { E } {/tex} is equal to:

{tex} 55 ^ { \circ } {/tex}

B

{tex} 125 ^ { \circ } {/tex}

C

{tex} 130 ^ { \circ } {/tex}

D

{tex} 62.5 ^ { \circ } {/tex}

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Q 7. In the figure given below, if {tex} \angle \mathrm { AOP } = 75 ^ { \circ } {/tex} and {tex} \angle \mathrm { AOB } = 120 ^ { \circ } {/tex}, then what is {tex} \angle \mathrm { AQP } {/tex} ?

A

{tex} 45 ^ { \circ } {/tex}

{tex} 37.5 ^ { \circ } {/tex}

C

{tex} 30 ^ { \circ } {/tex}

D

{tex} 22.5 ^ { \circ } {/tex}

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Q 8. {tex}\mathrm {ABCD} {/tex} is a cyclic quadrilateral such that {tex} \mathrm {A B} {/tex} is a diameter of the circle circumscribing it and {tex} \angle \mathrm {A D C }= 140 ^ { \circ } , {/tex} then {tex} \angle \mathrm {B A C} {/tex} is equal to

A

{tex} 80 ^ { \circ } {/tex}

{tex} 50 ^ { \circ } {/tex}

C

{tex} 40 ^ { \circ } {/tex}

D

{tex} 30 ^ { \circ } {/tex}