Length of the Arc

Q. In a circle of radius 63 cm, if the length of the circular arc is 22 cm, then find the angle subtended by it at the centre.

1. ${20}^{\circ }$
2. ${30}^{\circ }$
3. ${40}^{\circ }$
4. ${60}^{\circ }$

Q. If O is the centre of the circle of radius 5 cm and P is a point such that OP = 6 cm, then P lies:

1. inside the circle
2. on the circle
3. information is not sufficient
4. outside the circle

Q. Perimeter of Figure - I Figure - II.

1. =
2. <
3. >

Q. Find the length of the arc if it subtends ${135}^o$ angle at center of circle whose radius is 14 cm.

1. 22 cm
2. 33 cm
3. 66 cm
4. 11 cm

Q. The measure of the minor arc of a circle is 160°. Find the measures of the corresponding central angle and the corresponding major arc.

Q. Sort the following according to length in descending order ( top to bottom).

1. Circumference
2. 270° arc
3. Radius
4. Diameter

Q. Find the length of the arc which subtends ${120}^o$ angle at centre of circle whose radius is 21 cm.

1. 11 cm
2. 44 cm
3. 22 cm
4. 88 cm

Q. In the given figure, seg SD and seg TN are diameters. Name those minor arcs, major arcs and semi-circular arcs whose end-points are also the end-points of these diameters.

Q. In the figure, arc AXB is a semicircle; m∠PAB = 40°. Hence, find the values of


(1) m∠APB
(2) m(arc PYB)
(3) m(arc AZP)

Q. In the figure, seg PN and seg TC are the diameters of a circle. Write the measures of the arcs formed by the end-points of these diameters and explain your answers.

Q. The area of a circle is $81\pi sq.cms$. Find the length of the arc subtending an angle of ${300}^o$ at the centre and the area of corresponding sector.

Q. In a circle with centre P, a chord of length 16 cm is at a distance of 8 cm from the centre. Find the radius of this circle.

Q. The radius of a circle is 17 cm. Find the length of a chord which is at a distance of 8 cm from the centre of the circle.

Q. A chord of length $16$ cm is drawn in a circle at a distance of $15$ cm from its center. Find the radius of the circle.

1. $12$ cm
2. $15$ cm
3. $17$ cm
4. $34$ cm

Q. Fill in the blanks.
In the circle with centre O


(1) Seg OD is a ........ .
(2) Seg AB is a ......... .
(3) Seg PQ is a ......... .
(4) The length of Seg AB is ........ that of seg OD.

Q. A subtends an angle of 180° at the centre of the circle.

1. semicircle
2. quarter circle
3. circle

Q. Identify the open curve.

1. $4$ only
2. $1$ only
3. $1,4$ only
4. $1,2,3$ only

Q. The radius of a circle is 13 cm and the length of a chord of the circle is 10 cm. Find the distance of the chord from the centre of the circle.

Q. A chord of a circle is 30 cm long. Its distance from the centre is 8 cm. Find the radius of the circle.

Q.

What is the area of a sector with a central angle of$185$and a diameter of $6.4$?

Q. Find the length of the arc which is part of a sector whose area is 77 $c{m}^2$ and the radius of the circle is 7 cm.

1. 11 cm
2. 22 cm
3. 44 cm
4. 66 cm

Q. If skating track of length 55 m, as shown in figure, subtends ${150}^o$ angle at center of circle, find radius of circle.

1. 11 m
2. 14 m
3. 21 m
4. 42 m

Q.

ABC is a right-angled triangle and $O$ is the mid point of the side opposite to the right angle. Explain why $O$ is equidistant from $A,B$ and $C$.

Q. A chord AB of length 10 cm is drawn inside a circle of radius 5 cm. Write the measures of the arcs formed.

Q. Find the distance travelled by the minute hand(length of arc), in 15 minutes if its length is 7 cm.

1. 10 cm
2. 11 cm
3. 14 cm
4. 21 cm

Q. Find the distance covered by the minute hand in 10 minutes if its length is 21 cm.

1. 11 cm
2. 22 cm
3. 14 cm
4. 21 cm