Arc

Q.

In a circle, the major arc is 3 times the minor arc. The corresponding centre angles and the degree measures of two arcs are

1. ${90}^{o}and{90}^o$

2. ${270}^{o}and{90}^o$

3. ${60}^{o}and{210}^o$

4. ${90}^{o}and{270}^o$

Q.

AB and CD are two parallel chords of a circle of length 24 cm and 10 cm respectively and lie on the same side of its centre O. If the distance between the chords is 7 cm, find the radius of the circle (in cm).

__

Q.

If ABC is an arc of a circle and $\angle ABC={135}^o$, then the ratio of arc $\stackrel{⌢}{ABC}$ to the circumference is

1. 1 : 4

2. 1 : 2

3. 3 : 8

4. 3 : 4

Q.

$PQ$ and $RS$ are two parallel chords of a circle whose centre is $O$ and radius is $10cm$. If $PQ=16cm$ and $RS=12cm$. Find the distance between $PQ$ and $RS$ if they lie on the opposite side of the centre.

1. $10cm$

2. $14cm$

3. $12cm$

4. $11cm$

Q.

The part of the circle between any two points on the circle is called _________.

1. segment

2. arc

3. circumference

4. radius

Q. In Fig. 5, O is the centre of the circle. The angle by the arc BCD at the centre is 140°, BC is produced to P. Find ∠DCP.

Q.

Think and Learn Pvt. Ltd. management has decided to build a basketball court for their employees. The court plan is as shown in the figure.

Can you identify how many circles and arcs are there in the plan?

1. 1 and 4

2. 2 and 3

3. 4 and 1

4. 3 and 2

Q.

Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B. Prove that QA = QB.

Q.

The length of the common chord of two intersecting circles is 30 cm. If the radii of the two circles are 25 cm and 17 cm, find the distance between their centres.

1. 30 cm

2. 25 cm

3. 28 cm

4. 35 cm

Q. The sum of the measures of a minor arc and its corresponding major arc is ________ degrees.

1. 90
2. 180
3. 270
4. 360

Q.

In the given figure, equal chords AB and CD of a circle with centre O cut each other at right angles at E. If M and N are the mid-points of AB and CD respectively, then OMEN is a

1. Rectangle

2. Square

3. Rhombus

4. none of these

Q.

In the diagram, select the major arc and the minor arc of the circle, with respect to the chord AB.

1. XAY, XBY

2. AYB, AXB

3. AXB, AYB

4. XBY, XAY

Q.

In the diagram, select the major arc and the minor arc respectively, of the circle, with respect to the chord $AB.$

1. AYB, AXB

2. XAY, XBY

3. AXB, AYB

4. XBY, XAY

Q. An equilateral triangle ABC is inscribed in a circle with centre O. The measures of ∠BOC is

(a) 30°

(b) 60°

(c) 90°

(d) 120°

Q. Question 1 (iv)
Fill in the blanks:

(iv) An arc is a __________ when its ends are the ends of a diameter.

Q.

When two chords of a circle bisect each other, then which of the following statements is true?

1. Both chords are perpendicular to each other.

2. Both chords are parallel to each other.

3. Both chords are unequal.

4. Both are diameters of the circle.

Q.

In the given figure PQ is the diameter of a circle with centre O, and is perpendicular to the chord AB. If AB = 8cm and QM = 2cm, find the radius of the circle.

1. 5 cm

2. 6 cm

3. 2 cm

4. 4 cm

Q.

Two parallel chords AB and CD are 42cm apart and lie on the opposite sides of the centre of a circle. If AB = 36cm and CD = 48cm, find the radius of the circle.

1. 30 cm

2. 35 cm

3. 10 cm

4. 20 cm

Q.

The shaded part of the circle in the given figure represents a

1. Semi-circle

2. Segment

3. Sector

4. Chord

Q.

Find the measure of the angle subtended by $\widehat{ACB}$ in the given figure:

1. ${280}^{\circ }$

2. ${180}^{\circ }$

3. ${100}^{\circ }$

4. ${380}^{\circ }$

Q. One chord of a circle is known to be 10 cm. The radius of this circle must be

(a) 5 cm

(b) greater than 5 cm

(c) greater than or equal to 5 cm

(d) less than 5 cm

Q. Question 1 (i)
Fill in the blanks:

(i) The centre of a circle lies in the __________ of the circle. (exterior/ interior)

Q. 37. Let M be a point of contact of two internally touching circles . Let line AMB be their common tangent . The chord CD of the bigger circle touches the smaller circle at point N and chord CM and chord DM of bigger circle intersect the smaller circle at points P&R respectively . Prove that ANGLE CMN = ANGLE DMN

Q.

In the given figure AB is the side of a regular hexagon and BC is the side of a regular pentagon. Find $\angle$ AOC.

1. ${130}^o$

2. ${140}^o$

3. ${135}^o$

4. ${132}^o$

Q.

Q.

Question 2
If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

Q.

In the given circle, chords AB and CD intersect each other at P. CP = (x − 4) cm, DP = (y + 10) cm, AP = (x − 1) cm, and BP = (y + 1) cm.

If x + 2y = 23, then what is the sum of the lengths of chords AB and CD?

1. 34 cm

2. 30 cm

3. 32 cm

4. 36 cm

Q.

The circumference of a circle with centre O is divided into three arcs APB, BQC and CRA such that

$\frac{arcAPB}{2}=\frac{arcBQC}{3}=\frac{arcCRA}{4}$. Find $\angle BOA.$

1. ${30}^{\circ }$

2. ${45}^{\circ }$

3. ${60}^{\circ }$

4. ${80}^{\circ }$

Q.

A, B, C and D are four points on a circle. AC and BD intersect at E such that angle BEC =140^o and angle ECD = 25^o, then angle BAC is

1. 130^o

2. 100^o

3. 115^o

4. 90^o

Q. Question 2 (iii)
Write True or False. Give reasons for your answers.

(iii) If a circle is divided into three equal arcs, each is a major arc.