All in One Mathematics>Chapter 9 - Circles>Exam Practice>Q 29

MEDIUM

9th CBSE

IMPORTANT

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Prove that the line joining the mid-points of two parallel chords of a circle passes through the centre.

Important Questions on Circles

MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 9 - Circles>Exam Practice>Q 30

In the given figure,

O

is the centre of the circle,

∠ A D B = 30 °

and

∠ A B C = 40 °

. Find the measure of

∠ C A B

.

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MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 9 - Circles>Exam Practice>Q 32

In the given figure,

A B C E

is a cyclic quadrilateral and

O

is the centre of circle. If

∠ A E C = 110 °

, then find

∠ A B C

and

∠ A D C

.

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MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 9 - Circles>Exam Practice>Q 33

In figure,

A B C D

is a cyclic quadrilateral and

O

is the centre of the circle. If

∠ B O D = 160 °

, then find the measure of

∠ B P D

.

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MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 9 - Circles>Exam Practice>Q 34

A B

and

A C

arc two equal chords of a circle. Prove that the bisector of the

∠ B A C

passes through the centre of the circle.

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9th CBSE

IMPORTANT

All in One Mathematics>Chapter 9 - Circles>Exam Practice>Q 35

If a line segment joining mid-points of two chords of a circle passes through the centre of the circle. Prove that the two chords are parallel.

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9th CBSE

IMPORTANT

All in One Mathematics>Chapter 9 - Circles>Exam Practice>Q 36

In the given figure, if

y = 3 x

, then find the magnitude of

x

.

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HARD

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 9 - Circles>Exam Practice>Q 37

In the given figure, sides

A B

and

D C

of a cyclic quadrilateral

A B C D

are produced to meet at

E

. Sides

A D

and

B C

are produced to meet at

F

. If

∠ A D C = 80 °

and

∠ B E C = 50 °

, then find

∠ B A D

and

∠ C F D

.

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MEDIUM

9th CBSE

IMPORTANT

All in One Mathematics>Chapter 9 - Circles>Exam Practice>Q 38

In the given figure $A B C D$ is a cyclic quadrilateral, in which $A C$ and $B D$ are its diagonals. If $∠ D B C = 55 °$ and $∠ B A C = 45 °$ , then find $∠ B C D$ .

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