Grade 9 : Mathematics - 11. Circles (Set 2)

Question 1

A circular garden has a measured radius of 7.5 cm on a scaled blueprint.

What is the full length of the diameter of this circle?

Accepted Answer

B) 15 cm

Answer

A) 12 cm

Answer

C) 18 cm

Answer

D) 20 cm

Question 2

A circle has center $O$ and radius 10 cm. A perpendicular segment from $O$ to a chord AB measures 6 cm.

Find the total length of the chord AB.

Accepted Answer

C) 16 cm

Answer

A) 12 cm

Answer

B) 14 cm

Answer

D) 18 cm

Question 3

A chord of length 24 cm is at a distance of 5 cm from the center of a circular ring.

What is the radius of the circular ring?

Accepted Answer

A) 13 cm

Answer

B) 15 cm

Answer

C) 17 cm

Answer

D) 19 cm

Question 4

In a circle with center $O$, points $A$, $B$, and $C$ lie on the circumference such that arc AB subtends $\angle AOB = 110^\circ$ at the center.

Find the measure of angle $\angle ACB$ on the remaining part of the circle.

Accepted Answer

B) $55^\circ$

Answer

A) $45^\circ$

Answer

C) $65^\circ$

Answer

D) $75^\circ$

Question 5

Segment AB is a diameter of a circle, and $C$ is any point on the circle. In $ riangle ABC$, $\angle CAB = 35^\circ$.

Find the measure of $\angle ABC$.

Accepted Answer

C) $55^\circ$

Answer

A) $35^\circ$

Answer

B) $45^\circ$

Answer

D) $65^\circ$

Question 6

In a cyclic quadrilateral ABCD, angle $\angle A$ is measured to be $72^\circ$.

What is the measure of the opposite angle $\angle C$?

Accepted Answer

A) $108^\circ$

Answer

B) $98^\circ$

Answer

C) $118^\circ$

Answer

D) $72^\circ$

Question 7

Side BC of cyclic quadrilateral ABCD is extended to point $E$. The exterior angle $\angle DCE$ measures $85^\circ$.

What is the measure of the interior opposite angle $\angle BAD$?

Accepted Answer

B) $85^\circ$

Answer

A) $95^\circ$

Answer

C) $105^\circ$

Answer

D) $75^\circ$

Question 8

Two concentric circles have radii of 13 cm and 5 cm. A chord of the larger circle is tangent to the smaller circle.

Find the length of this chord.

Accepted Answer

C) 24 cm

Answer

A) 20 cm

Answer

B) 22 cm

Answer

D) 26 cm

Question 9

Two parallel chords of length 16 cm each are drawn on opposite sides of the center in a circle of radius 10 cm.

What is the distance between these two parallel chords?

Accepted Answer

B) 12 cm

Answer

A) 10 cm

Answer

C) 14 cm

Answer

D) 16 cm

Question 10

Points A, B, C, D lie in order on a circle. Chord AB subtends angles $\angle ACB$ and $\angle ADB$ in the same segment.

If $\angle ACB = 42^\circ$, what is the measure of $\angle ADB$?

Accepted Answer

B) $42^\circ$

Answer

A) $21^\circ$

Answer

C) $84^\circ$

Answer

D) $138^\circ$

Question 11

A circular running track has a radius of 21 m. A contractor charges $\5 per meter to construct a fence around it.

Find the total cost of fencing the circular track (use $\pi = \frac{22}{7}$).

Accepted Answer

C) $\660

Answer

A) $\520

Answer

B) $\600

Answer

D) $\720

Question 12

In a cyclic quadrilateral PQRS, opposite angles are given as $\angle P = (3x + 15)^\circ$ and $\angle R = (2x + 10)^\circ$.

Determine the value of $x$.

Accepted Answer

B) $31^\circ$

Answer

A) $25^\circ$

Answer

C) $35^\circ$

Answer

D) $40^\circ$

Question 13

A circle has a radius of 17 cm. A straight chord is positioned 15 cm away from the center.

Calculate the length of the chord.

Accepted Answer

C) 16 cm

Answer

A) 12 cm

Answer

B) 14 cm

Answer

D) 18 cm

Question 14

Chords AB and CD of a circle are equal in length. The angle subtended by AB at the center $O$ is $\angle AOB = 75^\circ$.

What is the measure of angle $\angle COD$ subtended by chord CD at center $O$?

Accepted Answer

A) $75^\circ$

Answer

B) $105^\circ$

Answer

C) $150^\circ$

Answer

D) $37.5^\circ$

Question 15

Consider a parallelogram inscribed inside a circle so that all four vertices lie on the circumference.

What specific geometric figure must this cyclic parallelogram be?

Accepted Answer

C) Rectangle

Answer

A) Rhombus

Answer

B) Trapezium

Answer

D) Kite

Question 16

Statement: Given three distinct non-collinear points $P$, $Q$, and $R$ in a plane.

How many distinct circles can be drawn passing through all three points?

Accepted Answer

C) Exactly one

Answer

A) Infinitely many

Answer

B) Two

Answer

D) Zero

Question 17

A major arc subtends a reflex central angle of $240^\circ$ at the center $O$ of a circle.

Find the angle subtended by this arc at any point on the remaining circumference.

Accepted Answer

B) $120^\circ$

Answer

A) $60^\circ$

Answer

C) $180^\circ$

Answer

D) $240^\circ$

Question 18

Two concentric circles have radii 18 cm and 12 cm.

What is the width of the ring (annulus) bounded by these two circles?

Accepted Answer

B) 6 cm

Answer

A) 4 cm

Answer

C) 8 cm

Answer

D) 10 cm

Question 19

A chord measures 30 cm in length and lies at a distance of 8 cm from the center of a circle.

Find the radius of the circle.

Accepted Answer

C) 17 cm

Answer

A) 15 cm

Answer

B) 16 cm

Answer

D) 18 cm

Question 20

In a circular pool, a divider rope of length 10 m is stretched across. A swimmer at center $O$ is 12 m away from the midpoint of the rope.

What is the radius of the circular pool?

Accepted Answer

C) 13 m

Answer

A) 11 m

Answer

B) 12 m

Answer

D) 14 m

Grade 9 : Mathematics - 11. Circles (Set 2)