EduSahara™ Worksheet

Question 1

1.

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 2

2.

Which of the following statements are true?

a)	If two circles touch externally, the square of the distance between their centres is the sum of the squares of their radii.
b)	If two circles touch internally, the distance between their centres is the difference of their radii.
c)	If two circles touch internally, their centres and the point of contact form a scalene triangle.
d)	If two circles touch externally, their centres and the point of contact form an isosceles triangle.
e)	If two circles touch externally, the distance between their centres is the sum of their radii.
f)	If two circles touch internally, the square of the distance between their centres is the difference of the squares of their radii.

(i)

{b,e}
(ii)

{c,e}
(iii)

{d,f,b}
(iv)

{a,b}
(v)

{a,e,b}

Question 3

3.

In the given figure, O is the centre of the circle , chord BE is equal to chord ED. If ∠BOC = 83° and ∠BED = 110°, find ∠CDE

(i)

106.5°
(ii)

91.5°
(iii)

76.5°
(iv)

81.5°
(v)

86.5°

Question 4

4.

In the given figure, O is the centre of the circle. If ∠EHF = 68° and ∠EDG = 71°, find ∠DGF

(i)

71°
(ii)

41°
(iii)

56°
(iv)

51°
(v)

46°

Question 5

5.

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

(i)

incentre
(ii)

centroid
(iii)

orthocentre
(iv)

excentre
(v)

circumcentre

Question 6

6.

In the given figure, O is the centre of the circle. If ∠FDE = 55.8° and ∠DEF = 76.62°, find the angle ∠DGE

(i)

57.58°
(ii)

52.58°
(iii)

77.58°
(iv)

62.58°
(v)

47.58°

Question 7

7.

△CDE is inscribed in a circle with centre O. If ∠COD = 146° and ∠DOE = 159°, find ∠ECD

(i)

84.5°
(ii)

109.5°
(iii)

89.5°
(iv)

79.5°
(v)

94.5°

Question 8

8.

IJKLMN is a hexagon inscribed in a circle. Given ∠IJK = 129° & ∠KLM = 118°, find ∠MNI

(i)

128°
(ii)

123°
(iii)

118°
(iv)

143°
(v)

113°

Question 9

9.

In the given figure, BE & CD are two chords of equal length. Given ∠CDO = 40.5°, find ∠BOE

(i)

104°
(ii)

129°
(iii)

99°
(iv)

114°
(v)

109°

Question 10

10.

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)	A sector is the area enclosed by two radii and a chord.
d)	The midpoint of any diameter of a circle is its centre.
e)	The diameter divides the circle into two unequal parts.

(i)

{c,d}
(ii)

{b,d}
(iii)

{a,b}
(iv)

{e,a,b}
(v)

{c,d,b}

Question 11

11.

In the given figure, O is the centre of the circle, and OG ⟂ CD. If ∠CDE = 38.5°, find ∠COE

(i)

92°
(ii)

107°
(iii)

87°
(iv)

82°
(v)

77°

Question 12

12.

Two circles touch internally. E is the centre of the bigger circle and lies on the smaller circle. If ∠BCD = 68°, find ∠B

(i)

37°
(ii)

32°
(iii)

22°
(iv)

52°
(v)

27°

Question 13

13.

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 complementary.
d)	Angles in the opposite segments are supplementary.