EduSahara™ Worksheet

Question 1

1.

Which of the following statements are true?

a)	The farther the chord is from the centre, the larger the angle it subtends at the centre.
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)	No two chords bisects each other.
e)	The longest chord of the circle passes through the centre of the circle.

(i)

{a,d,e}
(ii)

{a,b,c}
(iii)

{a,b}
(iv)

{b,c,e}
(v)

{d,c}

Question 2

2.

Which of the following statements are true?

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

(i)

{a,c,b}
(ii)

{a,b}
(iii)

{e,f,b}
(iv)

{b,c}
(v)

{d,c}

Question 3

3.

In the given figure, HK is the common tangent to the two circles. HI & HJ are also tangents. Given HI = 17 cm, find HJ

(i)

18 cm
(ii)

15 cm
(iii)

17 cm
(iv)

16 cm
(v)

19 cm

Question 4

4.

O is the centre of the circumcircle of △FGH. Tangents at F and H intersect at I. If ∠FIH = 39.86°, find ∠HGF

(i)

80.07°
(ii)

85.07°
(iii)

70.07°
(iv)

75.07°
(v)

100.07°

Question 5

5.

In the given figure, the circle circumscribes a rectangle with sides 20.00 cm and 19.00 cm. Find the area of the remaining portion other than the rectangle

(i)

231.93 sq.cm
(ii)

217.93 sq.cm
(iii)

225.93 sq.cm
(iv)

190.93 sq.cm
(v)

203.93 sq.cm

Question 6

6.

In the given figure, ABCD is a square of side 11.00 cm and A, B, C, D are centres of circles which touch externally in pairs. Find the area of the shaded region

(i)

406.21 sq.cm
(ii)

379.21 sq.cm
(iii)

424.21 sq.cm
(iv)

399.21 sq.cm

Question 7

7.

In the given figure, ABCD is a square of side 20.00 cm . At the centre there is a circle with radius 5.00 cm and the same circle quadrants are at the four corners. Find the perimeter of the shaded region.

(i)

116.86 cm
(ii)

109.86 cm
(iii)

102.86 cm
(iv)

97.86 cm
(v)

74.86 cm

Question 8

8.

Which of the following statements are true?

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

(i)

{a,b,d}
(ii)

{a,c,e}
(iii)

{c,d}
(iv)

{a,b}
(v)

{b,d,e}

Question 9

9.

In the given figure, a circle is inscribed touching the sides of an equilateral triangle of side 24 cm. Find the area of the shaded region

(i)

101.56 sq.cm
(ii)

98.56 sq.cm
(iii)

95.56 sq.cm
(iv)

103.56 sq.cm
(v)

93.56 sq.cm

Question 10

10.

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

(i)

3
(ii)

0
(iii)

1
(iv)

2
(v)

4

Question 11

11.

Which of the following statements are true?

a)	The area enclosed by a chord and its minor arc is called minor segment.
b)	The area enclosed by a chord and its major arc is called major segment.
c)	A sector is the area enclosed by two radii and a chord.
d)	A circle divides the plane on which it lies into three parts.
e)	The diameter divides the circle into two unequal parts.

(i)

{e,b}
(ii)

{a,b,d}
(iii)

{c,e,d}
(iv)

{c,a,b}
(v)

{c,a}

Question 12

12.

In the given figure , ABCD is a trapezium. A quarter circle AEFD is removed from the trapezium. If AD = CD = 20 and EB = 5.2 , find the area of the remaining portion

(i)

131.71 sq.cm
(ii)

137.71 sq.cm
(iii)

110.71 sq.cm
(iv)

144.71 sq.cm
(v)

162.71 sq.cm

Question 13

13.

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)

equilateral triangle
(iii)

acute angled triangle
(iv)

obtuse angled triangle

Question 14

14.

The centre of the circle is

(i)

Q
(ii)

N
(iii)

L
(iv)

K
(v)

M

Question 15

15.

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 intersect, then two common tangents can be drawn.
d)	If two circles touch each other internally, there is only one common tangent.

(i)

{a,d}
(ii)

{a,c}
(iii)

{a,b}
(iv)

{b,c,d}
(v)

{a,b,c}

Question 16

16.

In the given figure, EP & FP are tangents to the circle with centre O. Given ∠EOF = 126°, find ∠EPF

(i)

69°
(ii)

59°
(iii)

84°
(iv)

64°
(v)

54°

Question 17

17.

Which of the following figures represent a diameter ?

(i)

fig III
(ii)

fig I
(iii)

fig II
(iv)

fig V
(v)

fig IV

Question 18

18.

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

(i)

3
(ii)

2
(iii)

4
(iv)

5
(v)

1

Question 19

19.

Which of the following statements are true?

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

(i)

{d,a}
(ii)

{d,a,b}
(iii)

{e,b}
(iv)

{a,b,c}
(v)

{d,e,c}

Question 20

20.

In the given figure, O is the centre of the circle and GI is the tangent at H. If ∠FEH = 26°, find ∠FGH + ∠FHG

(i)

79°
(ii)

74°
(iii)

64°
(iv)

94°
(v)

69°

Question 21

21.

If two circles of radii 11 cm and 2 cm touch internally, the distance between their centres is

(i)

9 cm
(ii)

11 cm
(iii)

10 cm
(iv)

7 cm
(v)

8 cm

Question 22

22.

The distance around the circle is called

(i)

arc
(ii)

circumference
(iii)

radius
(iv)

chord
(v)

diameter

Question 23

23.

The major arc of the circle is

(i)

EHF
(ii)

EGF
(iii)

EHFIE
(iv)

JEHFJ
(v)

JEGFJ

Question 24

24.

The angle subtended by the semicircle at the centre is

(i)

210°
(ii)

190°
(iii)

195°
(iv)

180°
(v)

185°

Question 25

25.

Which of the following statements are true?

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

(i)

{e,b,a}
(ii)

{d,c,a}
(iii)

{a,c}
(iv)

{b,a}
(v)

{d,c}

Assignment Key