EduSahara™ Worksheet

Question 1

1.

In the given figure, CR & DR are tangents to the circle with centre O. Given ∠CRD = 57°, find ∠COD

(i)

153°
(ii)

133°
(iii)

128°
(iv)

123°
(v)

138°

Question 2

2.

Find the missing angle in the following figure?

(i)

26°
(ii)

31°
(iii)

46°
(iv)

21°
(v)

16°

Question 3

3.

Two circles touch internally. G is the centre of the bigger circle and lies on the smaller circle. If ∠DEF = 54°, find ∠D

(i)

51°
(ii)

66°
(iii)

41°
(iv)

36°
(v)

46°

Question 4

4.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠IGJ = 31° and ∠GIH = 44°, find ∠LJG

(i)

59°
(ii)

89°
(iii)

74°
(iv)

64°
(v)

69°

Question 5

5.

In the given figure, JM is the common tangent to the two circles. JK & JL are also tangents. Given JK = 10 cm, find JL

(i)

8 cm
(ii)

11 cm
(iii)

9 cm
(iv)

10 cm
(v)

12 cm

Question 6

6.

Circles having common centre are called

(i)

similar circles
(ii)

concentric circles
(iii)

intersecting circles
(iv)

congruent circles

Question 7

7.

Which of the following statements are true?

a)	A chord divides a circle into two segments.
b)	The diameter is the longest chord.
c)	Atmost one chord can be drawn on a circle with a certain length.
d)	A chord divides a circle into two sectors.
e)	The radius is the shortest chord.

(i)

{d,b,a}
(ii)

{a,b}
(iii)

{d,b}
(iv)

{e,c,a}
(v)

{c,a}

Question 8

8.

Which of the following figures represent a diameter ?

(i)

fig V
(ii)

fig III
(iii)

fig II
(iv)

fig IV
(v)

fig I

Question 9

9.

If the radius of a circle is 49 cm, what is its circumference?

(i)

309 cm
(ii)

306 cm
(iii)

307 cm
(iv)

310 cm
(v)

308 cm

Question 10

10.

Which of the following statements are true?

a)

A circle divides the plane into three mutually disjoint sets of points.

b)

All diameters of a circle are chords.

c)

22
7
is a rational number.

d)

All chords of a circle are diameters.

e)

π
is a rational number.

(i)

{d,a}
(ii)

{a,b,c}
(iii)

{d,e,c}
(iv)

{e,b}
(v)

{d,a,b}

Question 11

11.

In the below figure, BCPA is a quadrant of a circle. BC = 12.00 cm and CQA is a semicircle with CA as the diameter. Find the area of the shaded region

(i)

77.00 sq.cm
(ii)

67.00 sq.cm
(iii)

75.00 sq.cm
(iv)

72.00 sq.cm
(v)

69.00 sq.cm

Question 12

12.

In the given figure, the radius of the circle is 5 cm. Find the area of the major sector

(i)

53.93 sq.cm
(ii)

58.93 sq.cm
(iii)

63.93 sq.cm
(iv)

61.93 sq.cm
(v)

55.93 sq.cm

Question 13

13.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠JHI = 57°, find ∠KJI

(i)

72°
(ii)

57°
(iii)

62°
(iv)

87°
(v)

67°

Question 14

14.

Which of the following statements are true?

a)	Two chords bisect each other.
b)	The longest of all chords of a circle is called diameter.
c)	The midpoint of any diameter of a circle is its centre.
d)	The diameter divides the circle into two unequal parts.
e)	A sector is the area enclosed by two radii and a chord.

(i)

{d,c}
(ii)

{d,c,b}
(iii)

{a,b}
(iv)

{e,a,b}
(v)

{b,c}

Question 15

15.

In the given figure, O is the centre of the circle. E is a point on chord CD such that CE = ED. Find ∠OEC

(i)

90°
(ii)

100°
(iii)

105°
(iv)

95°
(v)

120°

Question 16

16.

The distance around the circle is called

(i)

circumference
(ii)

radius
(iii)

chord
(iv)

diameter
(v)

arc

Question 17

17.

Which of the following statements are true?

a)	Every circle has a unique centre.
b)	Every circle has a unique diameter.
c)	A circle consists of an infinite number of points.
d)	Each radius of a circle is also a chord of the circle.
e)	A line can meet a circle atmost at two points.

(i)

{d,c}
(ii)

{b,a}
(iii)

{a,c,e}
(iv)

{b,a,c}
(v)

{b,d,e}

Question 18

18.

Which of the following figures represent a secant ?

(i)

fig III
(ii)

fig V
(iii)

fig IV
(iv)

fig I
(v)

fig II

Question 19

19.

Two circles with equal radii are

(i)

not similar
(ii)

only similar but not congruent
(iii)

congruent
(iv)

concentric

Question 20

20.

Which of the following statements are true?

a)	Atmost one tangent can be drawn through a point inside the circle.
b)	The sides of a triangle can be tangents to a circle.
c)	Two tangents to a circle always intersect.
d)	Only one tangent can be drawn through a point on a circle.
e)	Only two tangents can be drawn from a point outside the circle.

(i)

{a,c,e}
(ii)

{b,d,e}
(iii)

{c,d}
(iv)

{a,b}
(v)

{a,b,d}

Question 21

21.

Which of the following statements are true?

a)	Atmost one circle can be drawn passing through three non-collinear points.
b)	Exactly two tangents can be drawn parallel to a secant.
c)	Only one circle can be drawn with a centre.
d)	Infinite circles can be drawn passing through three collinear points.
e)	Only one circle can be drawn passing through two points.

(i)

{e,c,a}
(ii)

{a,b}
(iii)

{c,a}
(iv)

{d,b}
(v)

{d,b,a}

Question 22

22.

In the given figure, DR & ER are tangents to the circle with centre O. Given ∠R = 50°, find ∠D

(i)

30°
(ii)

55°
(iii)

35°
(iv)

40°
(v)

25°

Question 23

23.

Which of the following figures represent a chord ?

(i)

fig I
(ii)

fig III
(iii)

fig V
(iv)

fig IV
(v)

fig II

Question 24

24.

The angle subtended by the semicircle at the centre is

(i)

180°
(ii)

185°
(iii)

190°
(iv)

210°
(v)

195°

Question 25

25.

Which of the following statements are true?

a)	Atmost one common tangent can be drawn for any two concentric circles.
b)	Atmost three common tangents can be drawn touching two circles which touch each other.
c)	A maximum of four common tangents can be drawn touching any two circles.
d)	Atmost two common tangents can be drawn touching any two circles.

(i)

{b,c}
(ii)

{a,d,b}
(iii)

{a,c,b}
(iv)

{a,b}
(v)

{d,c}

Assignment Key