EduSahara™ Worksheet

Question 1

1.

In the given figure, the bisectors of ∠A , ∠B & ∠C of △ABC meet the circumcircle at D , E & F. If ∠A = 60°, find ∠D

(i)

75°
(ii)

70°
(iii)

65°
(iv)

90°
(v)

60°

Question 2

2.

Two circles with equal radii are

(i)

congruent
(ii)

not similar
(iii)

only similar but not congruent
(iv)

concentric

Question 3

3.

Angle subtended by the major arc at the centre is

(i)

obtuse angle
(ii)

complete angle
(iii)

reflex angle
(iv)

acute angle
(v)

right angle

Question 4

4.

O is the centre of the circle and OG = FG. Find reflex ∠GOE

(i)

255°
(ii)

240°
(iii)

245°
(iv)

250°
(v)

270°

Question 5

5.

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)	The longest chord of the circle passes through 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)	Equal length chords are equidistant from the centre of the circle.

(i)

{b,c,e}
(ii)

{a,b,c}
(iii)

{d,c}
(iv)

{a,b}
(v)

{a,d,e}

Question 6

6.

An arc subtends 78° in its alternate segment. The arc is

(i)

quadrant
(ii)

minor arc
(iii)

minor segment
(iv)

major arc
(v)

semi-circle

Question 7

7.

In the given figure, O is the centre of the circle . If ∠FIG = 80° and ∠FEH = 65°, find ∠EJF

(i)

35°
(ii)

60°
(iii)

30°
(iv)

45°
(v)

40°

Question 8

8.

In the given figure, O is the centre of the circle. If ∠OFH = 29°, find ∠G

(i)

149°
(ii)

119°
(iii)

129°
(iv)

124°
(v)

134°

Question 9

9.

FG is a line segment and I is its mid-point. Three semi-circles are drawn with FI , IG and FG as diameters. H , J and I respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given FH = 6 cm

(i)

5.00 cm
(ii)

2.00 cm
(iii)

6.00 cm
(iv)

3.00 cm
(v)

4.00 cm

Question 10

10.

KL is the perpendicular bisector of side IJ of △HIJ. Given ∠HIJ = 47° and ∠KHJ = 50° , find ∠HJI

(i)

33°
(ii)

38°
(iii)

43°
(iv)

63°
(v)

48°

Question 11

11.

In the given figure, O is the centre of the circle. If ∠NLM = 55.5°, find reflex ∠MOK

(i)

264°
(ii)

249°
(iii)

279°
(iv)

254°
(v)

259°

Question 12

12.

The angle subtended by the diameter at any point on the circle is

(i)

90°
(ii)

120°
(iii)

100°
(iv)

95°
(v)

105°

Question 13

13.

An arc subtends 85° in its alternate segment. Its corresponding major arc subtends what angle in its (major arc) alternate segment?

(i)

100°
(ii)

125°
(iii)

105°
(iv)

95°
(v)

110°

Question 14

14.

In the given figure, HI , IJ , JK and KL are chords and HK , IL are diameters passing through the centre O. If ∠HOI = 56°. Find ∠IJK

(i)

123°
(ii)

133°
(iii)

148°
(iv)

118°
(v)

128°

Question 15

15.

If two circles of radii 8 cm and 2 cm touch externally, the distance between their centres is

(i)

8 cm
(ii)

12 cm
(iii)

9 cm
(iv)

11 cm
(v)

10 cm

Question 16

16.

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

(i)

centroid
(ii)

circumcentre
(iii)

orthocentre
(iv)

excentre
(v)

incentre

Question 17

17.

In the given figure, AB is a side of regular 5-sided polygon and AC is a side of regular 10-sided polygon inscribed in a circle with centre O. Find ∠ACB

(i)

46°
(ii)

41°
(iii)

51°
(iv)

66°
(v)

36°

Question 18

18.

In the given figure, a pentagon is inscribed in a circle with centre O. Given FG = GH = HI and ∠FGH = 100°. Find ∠FEG

(i)

45°
(ii)

70°
(iii)

50°
(iv)

55°
(v)

40°

Question 19

19.

In the given figure, △FBC is a scalene triangle. DB & EB trisect ∠FBC. Similarly CD & CE trisect ∠BCF. Given ∠CFB = 108°, find ∠CEB

(i)

137°
(ii)

142°
(iii)

132°
(iv)

147°
(v)

162°

Question 20

20.

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)

obtuse angled triangle
(iii)

equilateral triangle
(iv)

acute angled triangle

Question 21

21.

Which of the following are not cyclic quadrilaterals?

a)	kite
b)	square
c)	rhombus
d)	rectangle
e)	isosceles trapezium

(i)

{d,c,a}
(ii)

{d,c}
(iii)

{b,a}
(iv)

{a,c}
(v)

{e,b,a}

Question 22

22.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 105° and ∠EAB = 103°. Find ∠CDE

(i)

124.5°
(ii)

114.5°
(iii)

129.5°
(iv)

119.5°
(v)

144.5°

Question 23

23.

Which of the following statements are true?

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

(i)

{c,a}
(ii)

{a,b}
(iii)

{d,b,a}
(iv)

{e,c,a}
(v)

{d,b}

Question 24

24.

In the given figure, O is the centre of the circle and GI is a diameter. If ∠HFG = 64°, find ∠HGI

(i)

31°
(ii)

36°
(iii)

56°
(iv)

26°
(v)

41°

Question 25

25.

In the given figure, KI and LH are two lines passing through the points of intersection of the two circles at J and G. If ∠LKJ = 88° , find ∠JIH

(i)

102°
(ii)

97°
(iii)

92°
(iv)

122°
(v)

107°

Assignment Key