EduSahara™ Worksheet

Question 1

1.

Which of the following figures represent a tangent ?

(i)

fig V
(ii)

fig I
(iii)

fig III
(iv)

fig II
(v)

fig IV

Question 2

2.

Which of the following statements are true?

a)	One and only one tangent can be drawn to a circle from a point outside it.
b)	Two semi-circles of a circle together make the whole circle.
c)	Every circle has a unique diameter.
d)	An infinite number of chords may be drawn for a circle.
e)	An infinite number of diameters may be drawn for a circle.

(i)

{b,d,e}
(ii)

{a,c,e}
(iii)

{a,b,d}
(iv)

{a,b}
(v)

{c,d}

Question 3

3.

A line which touches a circle at only one point is called a

(i)

semi-circle
(ii)

tangent
(iii)

diameter
(iv)

secant
(v)

segment

Question 4

4.

If two circles
touch internally
,
the number of their common tangents is

(i)

(-1)
(ii)

2
(iii)

4
(iv)

1
(v)

0

Question 5

5.

If two circles
intersect
,
the number of their common tangents is

(i)

2
(ii)

1
(iii)

4
(iv)

(-1)
(v)

3

Question 6

6.

In triangle IJK, if a circle is drawn with JK as diameter and if it passes through I it is a

(i)

acute angled triangle
(ii)

right angle triangle
(iii)

obtuse angled triangle
(iv)

equilateral triangle

Question 7

7.

If the two radii OP and OQ of a circle are at right angles to each other, then the sector OPQ is called a

(i)

quadrant
(ii)

diameter
(iii)

segment
(iv)

tangent
(v)

chord

Question 8

8.

If ABCD is a cyclic quadrilateral and ∠A − ∠C = 38°, then ∠C

(i)

71°
(ii)

101°
(iii)

76°
(iv)

81°
(v)

86°

Question 9

9.

In the given figure, O is the centre of the circle and DF is the tangent at E. If ∠EFG = 40°,∠FEG = 36°, find ∠IED

(i)

91°
(ii)

106°
(iii)

76°
(iv)

86°
(v)

81°

Question 10

10.

In the given figure, FD and FE are tangent segments to the circle with centre O. Given ∠EFG = 24°, find ∠DEO

(i)

39°
(ii)

54°
(iii)

34°
(iv)

24°
(v)

29°

Question 11

11.

A chord of a circle divides the whole circular region into two parts, each called a

(i)

major segment
(ii)

radius
(iii)

semi-circle
(iv)

segment
(v)

diameter

Question 12

12.

Which of the following figures represent a chord ?

(i)

fig V
(ii)

fig I
(iii)

fig IV
(iv)

fig III
(v)

fig II

Question 13

13.

Which of the following statements are true?

a)	If two circles touch each other externally, there is only one common tangent.
b)	There exists four common tangents for any two non-intersecting circles.
c)	If two circles touch each other internally, there is only one common tangent.
d)	If two circles intersect, then two common tangents can be drawn.

(i)

{a,b}
(ii)

{b,c,d}
(iii)

{a,c}
(iv)

{a,d}
(v)

{a,b,c}

Question 14

14.

In the given figure, two circles intersect at points F & G. A tangent is drawn at point H. From the same point, two lines are drawn passing through points F & G. They meet the other end of the second circle at E & D. Given ∠H = 85°, find ∠EFG

(i)

100°
(ii)

105°
(iii)

125°
(iv)

110°
(v)

95°

Question 15

15.

In the given figure, JH and JI are tangent segments to the circle with centre O. Given ∠IJK = 37°, find ∠HIK

(i)

41.5°
(ii)

26.5°
(iii)

56.5°
(iv)

31.5°
(v)

36.5°

Question 16

16.

Which of the following statements are true?

a)	Angles in the opposite segments are complementary.
b)	Angles in the same segment are equal.
c)	Angles subtended by equal length arcs in two circles are equal.
d)	Angles in the opposite segments are supplementary.

(i)

{c,d}
(ii)

{a,d,b}
(iii)

{a,b}
(iv)

{b,d}
(v)

{a,c,b}

Question 17

17.

A chord that passes through the centre of the circle is called

(i)

centre
(ii)

semi-circle
(iii)

diameter
(iv)

segment
(v)

chord

Question 18

18.

In the given figure, AS & BS are tangents to the circle with centre O. Given OA = 12 cm and AB = 21 cm, find AS

(i)

22.69 cm
(ii)

21.69 cm
(iii)

23.69 cm
(iv)

19.69 cm
(v)

20.69 cm

Question 19

19.

If the radius of the circumcircle is half the length of a side of the triangle, then the triangle is

(i)

right angle triangle
(ii)

acute angled triangle
(iii)

equilateral triangle
(iv)

obtuse angled triangle

Question 20

20.

Two concentric circles are of radii 24 cm and 11 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

44.66 cm
(ii)

42.66 cm
(iii)

41.66 cm
(iv)

43.66 cm
(v)

40.66 cm

Question 21

21.

A line which intersects the circle at two distinct points is called a

(i)

secant
(ii)

diameter
(iii)

major segment
(iv)

tangent
(v)

circumference

Question 22

22.

In the given figure, FG and HI are parallel tangents to the circle with centre O. FI is another tangent meeting FG and HI at F and I. Find ∠FOI

(i)

95°
(ii)

105°
(iii)

120°
(iv)

90°
(v)

100°

Question 23

23.

In the given figure, O is the centre of the circle and IK is the tangent at J . If ∠HGJ = 26°, find ∠HIJ

(i)

53°
(ii)

48°
(iii)

68°
(iv)

38°
(v)

43°

Question 24

24.

Which of the following statements are true?

a)	One and only one tangent can be drawn to a circle from a point outside it.
b)	A secant of a circle is a segment having its end points on the circle.
c)	Every circle has a unique diameter.
d)	Diameter of a circle is a part of the semi-circle of the circle.
e)	One and only one tangent can be drawn to pass through a point on a circle.

(i)

{b,e,d}
(ii)

{a,d}
(iii)

{b,e}
(iv)

{c,a,d}
(v)

{d,e}

Question 25

25.

In the given figure, KLMN is cyclic quadrilateral. If ∠LMN = 91°, find ∠JKN

(i)

121°
(ii)

91°
(iii)

101°
(iv)

106°
(v)

96°

Assignment Key