Grade 9 : Mathematics - 11. Circles (Set 1)

Question 1

A circle has a fixed radius of 7 cm.

What is the length of the longest chord of this circle?

Accepted Answer

B) 14 cm

Answer

A) 7 cm

Answer

C) 21 cm

Answer

D) 28 cm

Question 2

A chord AB in a circle with center $O$ has a perpendicular distance $OM = 3cm$ from the center. The radius $OA = 5cm$.

Calculate the total length of the chord AB.

Accepted Answer

C) 8 cm

Answer

A) 4 cm

Answer

B) 6 cm

Answer

D) 10 cm

Question 3

In a circle with center $O$, two chords AB and CD are equal in length. The perpendicular distance from $O$ to AB is 5 cm.

What is the perpendicular distance from $O$ to CD?

Accepted Answer

B) 5 cm

Answer

A) 2.5 cm

Answer

C) 10 cm

Answer

D) 7.5 cm

Question 4

An arc subtends an angle of $80^\circ$ at the center $O$ of a circle.

What is the angle subtended by this arc at any point on the remaining part of the circle?

Accepted Answer

A) $40^\circ$

Answer

B) $80^\circ$

Answer

C) $160^\circ$

Answer

D) $120^\circ$

Question 5

Line segment AB is the diameter of a circle with center $O$, and $C$ is any point on the circumference.

What is the measure of angle $\angle ACB$?

Accepted Answer

C) $90^\circ$

Answer

A) $45^\circ$

Answer

B) $60^\circ$

Answer

D) $180^\circ$

Question 6

ABCD is a cyclic quadrilateral. Angle $\angle A$ is measured to be $70^\circ$.

Find the measure of its opposite angle $\angle C$.

Accepted Answer

C) $110^\circ$

Answer

A) $70^\circ$

Answer

B) $90^\circ$

Answer

D) $120^\circ$

Question 7

Points A, B, C, and $D$ lie on a circle. Angle $\angle ACB = 55^\circ$, where $C$ and $D$ lie in the same segment of the circle.

What is the measure of angle $\angle ADB$?

Accepted Answer

B) $55^\circ$

Answer

A) $35^\circ$

Answer

C) $110^\circ$

Answer

D) $125^\circ$

Question 8

A chord of length 12 cm is at a distance of 8 cm from the center of a circle.

What is the radius of the circle?

Accepted Answer

A) 10 cm

Answer

B) 12 cm

Answer

C) 14 cm

Answer

D) 16 cm

Question 9

One side of a cyclic quadrilateral is produced to form an exterior angle of $105^\circ$.

What is the measure of the interior opposite angle?

Accepted Answer

C) $105^\circ$

Answer

A) $75^\circ$

Answer

B) $90^\circ$

Answer

D) $115^\circ$

Question 10

How many unique circles can pass through three given non-collinear points?

Accepted Answer

B) Exactly one

Answer

A) Zero

Answer

C) Two

Answer

D) Infinitely many

Question 11

In a circle with center $O$, a chord AB has length equal to the radius $r$ of the circle.

What is the angle subtended by chord AB at the center $O$?

Accepted Answer

C) $60^\circ$

Answer

A) $30^\circ$

Answer

B) $45^\circ$

Answer

D) $90^\circ$

Question 12

Two concentric circles have radii of 10 cm and 6 cm respectively.

Find the length of the chord of the larger circle which touches the smaller circle.

Accepted Answer

C) 16 cm

Answer

A) 8 cm

Answer

B) 12 cm

Answer

D) 20 cm

Question 13

What is the sum of any pair of opposite angles of a cyclic quadrilateral?

Accepted Answer

B) $180^\circ$

Answer

A) $90^\circ$

Answer

C) $270^\circ$

Answer

D) $360^\circ$

Question 14

If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the segment, then the four points are:

Accepted Answer

B) Concyclic

Answer

A) Collinear

Answer

C) Parallel

Answer

D) Perpendicular

Question 15

Arc AB subtends an angle $\angle AOB = 120^\circ$ at the center $O$ of a circle.

Find the angle $\angle APB$ subtended by the arc at point $P$ on the major arc.

Accepted Answer

A) $60^\circ$

Answer

B) $120^\circ$

Answer

C) $240^\circ$

Answer

D) $30^\circ$

Question 16

A parallelogram inscribed in a circle (a cyclic parallelogram) must be a:

Accepted Answer

B) Rectangle

Answer

A) Rhombus

Answer

C) Trapezium

Answer

D) Kite

Question 17

A circle has a radius of 13 cm. A chord is at a perpendicular distance of 5 cm from the center.

What is the total length of the chord?

Accepted Answer

C) 24 cm

Answer

A) 12 cm

Answer

B) 18 cm

Answer

D) 26 cm

Question 18

In a circle, angle $\angle ACB$ formed at the major arc is $45^\circ$.

Find the central angle $\angle AOB$ subtended by the same arc AB.

Accepted Answer

B) $90^\circ$

Answer

A) $45^\circ$

Answer

C) $135^\circ$

Answer

D) $180^\circ$

Question 19

In a cyclic quadrilateral ABCD, the ratio of opposite angles $\angle A$ and $\angle C$ is $2 : 3$.

Find the measure of angle $\angle A$.

Accepted Answer

C) $72^\circ$

Answer

A) $36^\circ$

Answer

B) $54^\circ$

Answer

D) $108^\circ$

Question 20

A chord $AB = 16cm$ is at a distance of 6 cm from the center $O$ of a circle.

What is the diameter of the circle?

Accepted Answer

D) 20 cm

Answer

A) 10 cm

Answer

B) 12 cm

Answer

C) 16 cm

Grade 9 : Mathematics - 11. Circles (Set 1)