EduSahara™ Worksheet

Question 1

1.

Which of the following statements are true?

a)	The longest chord of the circle passes through the centre of the circle.
b)	Equal length chords are equidistant from the centre of the circle.
c)	The farther the chord is from the centre, the larger the angle it subtends at the centre.
d)	Equal length chords subtend equal angles at the centre of the circle.
e)	No two chords bisects each other.

(i)

{c,e,d}
(ii)

{e,b}
(iii)

{a,b,d}
(iv)

{c,a}
(v)

{c,a,b}

Question 2

2.

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

(i)

segment
(ii)

tangent
(iii)

chord
(iv)

circumference
(v)

quadrant

Question 3

3.

Two circles with equal radii are

(i)

only similar but not congruent
(ii)

concentric
(iii)

not similar
(iv)

congruent

Question 4

4.

The angle between a tangent to a circle and the radius drawn at the point of contact is

(i)

105°
(ii)

90°
(iii)

95°
(iv)

100°
(v)

120°

Question 5

5.

In the given figure, DEFG is cyclic quadrilateral. If ∠EFG = 83°, find ∠CDG

(i)

98°
(ii)

93°
(iii)

113°
(iv)

83°
(v)

88°

Question 6

6.

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

(i)

{b,d}
(ii)

{b,d,c}
(iii)

{c,d}
(iv)

{e,a,c}
(v)

{a,c}

Question 7

7.

Which of the following statements are true?

a)	If a circle can be inscribed in a quadrilateral, it must be a kite.
b)	It is always possible to inscribe a circle in a regular polygon.
c)	If a circle can be inscribed in a quadrilateral, the sum of the lengths of a pair of opposite sides is equal to the other pair.
d)	If a circle can be inscribed in a quadrilateral, then it must be a square.
e)	It is always possible to inscribe a circle in a quadrilateral.

(i)

{a,b}
(ii)

{e,a,b}
(iii)

{b,c}
(iv)

{d,c,b}
(v)

{d,c}

Question 8

8.

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

(i)

(-1)
(ii)

2
(iii)

0
(iv)

1
(v)

3

Question 9

9.

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

(i)

tangent
(ii)

secant
(iii)

quadrant
(iv)

centre
(v)

circumference

Question 10

10.

Which of the following statements are true?

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

(i)

{b,c}
(ii)

{d,c}
(iii)

{a,b}
(iv)

{a,c,b}
(v)

{a,d,b}

Question 11

11.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠IGJ = 34° and ∠GIH = 45°, find ∠KJI

(i)

39°
(ii)

44°
(iii)

34°
(iv)

49°
(v)

64°

Question 12

12.

Which of the following figures represent a secant ?

(i)

fig III
(ii)

fig V
(iii)

fig I
(iv)

fig IV
(v)

fig II

Question 13

13.

In the given figure, FD and FE are tangent segments to the circle with centre O. Given ∠EFG = 21°, find ∠DEG

(i)

44.5°
(ii)

64.5°
(iii)

49.5°
(iv)

39.5°
(v)

34.5°

Question 14

14.

Which of the following statements are true?

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

(i)

{b,d}
(ii)

{c,d,e}
(iii)

{a,b,e}
(iv)

{a,c,d}
(v)

{a,c}

Question 15

15.

(i)

9.82 cm
(ii)

11.82 cm
(iii)

7.82 cm
(iv)

10.82 cm
(v)

8.82 cm

Question 16

16.

In the given figure, two circles intersect at points C & D. A tangent is drawn at point E. From the same point, two lines are drawn passing through points C & D. They meet the other end of the second circle at B & A. Given ∠E = 61°, find ∠ABC

(i)

66°
(ii)

76°
(iii)

71°
(iv)

91°
(v)

61°

Question 17

17.

Half of a circle is called

(i)

major segment
(ii)

centre
(iii)

segment
(iv)

semi-circle
(v)

chord

Question 18

18.

The opposite angles in a cyclic quadrilateral are

(i)

equal
(ii)

linear pair
(iii)

complementary
(iv)

supplementary

Question 19

19.

In the given figure, O is the centre of the circle and GH is the tangent at F. If ∠ECF = 60° and ∠CED = 48°, find ∠HFC

(i)

30°
(ii)

45°
(iii)

40°
(iv)

35°
(v)

60°

Question 20

20.

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

(i)

equilateral triangle
(ii)

obtuse angled triangle
(iii)

right angle triangle
(iv)

acute angled triangle

Question 21

21.

The point of intersection of the angular bisectors of a triangle is

(i)

incentre
(ii)

orthocentre
(iii)

excentre
(iv)

circumcentre
(v)

centroid

Question 22

22.

Two circles are of radii 4 cm and 2 cm. If the distance between their centres is 8 cm, what is the length of their transverse common tangent?

(i)

6.29 cm
(ii)

4.29 cm
(iii)

7.29 cm
(iv)

3.29 cm
(v)

5.29 cm

Question 23

23.

If JKLM is a cyclic quadrilateral and ∠J − ∠L = 6°, then ∠L

(i)

92°
(ii)

117°
(iii)

102°
(iv)

97°
(v)

87°

Question 24

24.

Two circles with radii R and r touch internally. If the distance between their centres is d, then

(i)

d < R + r
(ii)

d = R + r
(iii)

d > R - r
(iv)

d = R - r
(v)

d < R - r

Question 25

25.

Which of the following statements are true?

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

(i)

{a,d,b}
(ii)

{a,b}
(iii)

{a,c,b}
(iv)

{c,d}
(v)

{b,d}

Assignment Key