EduSahara™ Worksheet

Question 1

1.

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)

tangent
(ii)

semi-circle
(iii)

quadrant
(iv)

chord
(v)

circumference

Question 2

2.

Which of the following statements are true?

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

(i)

{b,c,a}
(ii)

{b,d,a}
(iii)

{c,d}
(iv)

{b,a}
(v)

{a,d}

Question 3

3.

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

(i)

90°
(ii)

95°
(iii)

120°
(iv)

100°
(v)

105°

Question 4

4.

In the given figure, GHIJ is a cyclic quadrilateral such that IG bisects ∠JGH and KL is the tangent at I. If ∠IGH = 57°, find ∠KIH

(i)

67°
(ii)

57°
(iii)

62°
(iv)

72°
(v)

87°

Question 5

5.

If JKLM is a cyclic parallelogram, then ∠M

(i)

100°
(ii)

90°
(iii)

120°
(iv)

95°
(v)

105°

Question 6

6.

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

(i)

incentre
(ii)

excentre
(iii)

centroid
(iv)

orthocentre
(v)

circumcentre

Question 7

7.

Which of the following statements are true?

a)	An isosceles trapezium is cyclic.
b)	All parallelograms are cyclic.
c)	The exterior angle of a quadrilateral and its interior opposite angle are supplementary.
d)	A quadrilateral in which the diagonals are equal and bisect each other is cyclic.
e)	Either pair of opposite angles of a cyclic quadrilateral are supplementary.

(i)

{a,d,e}
(ii)

{b,c,e}
(iii)

{c,d}
(iv)

{b,a}
(v)

{b,a,d}

Question 8

8.

Two circles with equal radii are

(i)

not similar
(ii)

concentric
(iii)

congruent
(iv)

only similar but not congruent

Question 9

9.

In the given figure, O is the centre of the circle and HI is the tangent at G. If ∠FDG = 62° and ∠DFE = 43°, find ∠IGD

(i)

28°
(ii)

43°
(iii)

33°
(iv)

58°
(v)

38°

Question 10

10.

In the given figure, O is the centre of the circle and LM is the tangent at I. If ∠JIK = 31° and ∠LIJ = 46°, find ∠KIM

(i)

103°
(ii)

113°
(iii)

133°
(iv)

108°
(v)

118°

Question 11

11.

Which of the following statements are true?

a)	If a rhombus is cyclic, it is a square.
b)	A cyclic quadrilateral is a regular polygon.
c)	If a trapezium is cyclic, it is a rectangle.
d)	If a parallelogram is cyclic, it is a rectangle.
e)	If a kite is cyclic, it is a square.

(i)

{a,d}
(ii)

{e,b,a}
(iii)

{b,a}
(iv)

{c,d,a}
(v)

{c,d}

Question 12

12.

In the given figure, JM is the common tangent to the two circles. JK & JL are also tangents. Given JK = 13 cm, find JL

(i)

15 cm
(ii)

14 cm
(iii)

11 cm
(iv)

13 cm
(v)

12 cm

Question 13

13.

In the given figure, FT & GT are tangents to the circle with centre O. Given OF = 15 cm and FG = 27 cm, find FT

(i)

31.97 cm
(ii)

28.97 cm
(iii)

32.97 cm
(iv)

30.97 cm
(v)

29.97 cm

Question 14

14.

In the given figure, O is the centre of the circle and MN is the tangent at L. If ∠KIL = 36° and ∠IKJ = 59°, find ∠MLK

(i)

66°
(ii)

36°
(iii)

51°
(iv)

41°
(v)

46°

Question 15

15.

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)	Equal length chords subtend equal angles at the centre of the circle.
d)	The farther the chord is from the centre, the larger the angle it subtends at the centre.
e)	No two chords bisects each other.

(i)

{d,a}
(ii)

{d,a,b}
(iii)

{d,e,c}
(iv)

{a,b,c}
(v)

{e,b}

Question 16

16.

If two circles are concentric, then

(i)

their centres are same
(ii)

their radii are same
(iii)

their perimeters are same
(iv)

their diameters are same

Question 17

17.

If two circles of radii 10 cm and 3 cm touch externally, the distance between their centres is

(i)

12 cm
(ii)

15 cm
(iii)

11 cm
(iv)

13 cm
(v)

14 cm

Question 18

18.

The perimeter of a circle is called

(i)

segment
(ii)

radius
(iii)

chord
(iv)

diameter
(v)

circumference

Question 19

19.

Two circles are of radii 6 cm and 2 cm. If the distance between their centres is 11 cm, what is the length of their direct common tangent?

(i)

8.25 cm
(ii)

9.25 cm
(iii)

10.25 cm
(iv)

12.25 cm
(v)

11.25 cm

Question 20

20.

In the given figure, O is the centre of the circle and KL is the tangent at G. If ∠GJI = 50°, find ∠GHI

(i)

130°
(ii)

160°
(iii)

140°
(iv)

145°
(v)

135°

Question 21

21.

In the given figure, two circles intersect at points G & H. A tangent is drawn at point I. From the same point, two lines are drawn passing through points G & H. They meet the other end of the second circle at F & E. Given ∠I = 65°, find ∠EHG

(i)

145°
(ii)

120°
(iii)

115°
(iv)

130°
(v)

125°

Question 22

22.

If IJKL is a cyclic quadrilateral and ∠I − ∠K = 50°, then ∠K

(i)

75°
(ii)

95°
(iii)

80°
(iv)

65°
(v)

70°

Question 23

23.

The mid-point of the diameter of a circle is called

(i)

major segment
(ii)

chord
(iii)

segment
(iv)

centre
(v)

semi-circle

Question 24

24.

In the given figure, GR & HR are tangents to the circle with centre O. Given ∠GRH = 41°, find ∠GOH

(i)

154°
(ii)

169°
(iii)

149°
(iv)

139°
(v)

144°

Question 25

25.

O is the centre of the circle. EF and GF are tangents to the circle. If ∠GHE = 54.5°, find ∠EFG

(i)

101°
(ii)

86°
(iii)

81°
(iv)

71°
(v)

76°

Assignment Key