EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Angle Properties of a Circle
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure, AB , BC , CD and DE are chords and AD , BE are diameters passing through the centre O. If ∠AOB = 77°. Find ∠BCD
(i)
133.5°
(ii)
128.5°
(iii)
138.5°
(iv)
158.5°
(v)
143.5°
Question
2
2.
In the given figure, HJ is a chord which is equal to the radius of the circle. Find ∠K and ∠I
(i)
50° & 130°
(ii)
30° & 150°
(iii)
60° & 120°
(iv)
40° & 140°
(v)
45° & 135°
Question
3
3.
In the given figure, O is the centre of the circle. If ∠FGD = 89°, find ∠DEF
(i)
106°
(ii)
96°
(iii)
121°
(iv)
91°
(v)
101°
Question
4
4.
In the given figure, O is the centre of the circle , chord JM is equal to chord ML. If ∠JOK = 65° and ∠JML = 103°, find ∠KLM
(i)
86°
(ii)
101°
(iii)
81°
(iv)
71°
(v)
76°
Question
5
5.
An arc subtends 70° in its alternate segment. The angle made by its corresponding major arc at the centre is
(i)
250°
(ii)
225°
(iii)
220°
(iv)
235°
(v)
230°
Question
6
6.
Which of the following are cyclic quadrilaterals?
a)
rhombus
b)
trapezium
c)
triangle
d)
parallelogram
e)
square
f)
rectangle
(i)
{a,e}
(ii)
{e,f}
(iii)
{b,f}
(iv)
{a,f,e}
(v)
{c,d,e}
Question
7
7.
Which of the following statements are true?
a)
Equal length chords are equidistant from the centre of the circle.
b)
The farther the chord is from the centre, the larger the angle it subtends at the centre.
c)
No two chords bisects each other.
d)
Equal length chords subtend equal angles at the centre of the circle.
e)
The longest chord of the circle passes through the centre of the circle.
(i)
{b,a}
(ii)
{b,c,e}
(iii)
{c,d}
(iv)
{b,a,d}
(v)
{a,d,e}
Question
8
8.
In the given figure, IJ is a side of regular 8-sided polygon and IK is a side of regular 9-sided polygon inscribed in a circle with centre O. Find ∠IJK
(i)
35°
(ii)
30°
(iii)
50°
(iv)
25°
(v)
20°
Question
9
9.
The diameter LM of a circle with centre 'O' is perpendicular to the chord JK. If JK = 14.00 cm and LN = 1.55 cm, find the radius of the circle.
(i)
18.55 cm
(ii)
15.55 cm
(iii)
17.55 cm
(iv)
16.55 cm
(v)
14.55 cm
Question
10
10.
In the given figure, O is the centre of the circle. If ∠DCE = 58° and ∠CEF = 19°, find ∠EGF
(i)
133°
(ii)
113°
(iii)
103°
(iv)
108°
(v)
118°
Question
11
11.
Which of the following statements are true?
a)
Angle subtended by the major arc at the centre is acute.
b)
Angle subtended by the major arc in its alternate segment is obtuse.
c)
The angle subtended in a semicircle is a right angle.
d)
If two chords are equal, then they are equidistant from the centre of the circle.
e)
Angle subtended in the major segment is obtuse.
(i)
{b,c,d}
(ii)
{a,e,d}
(iii)
{a,b}
(iv)
{e,c}
(v)
{a,b,c}
Question
12
12.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 112° and ∠EAB = 100°. Find ∠EAD
(i)
47°
(ii)
32°
(iii)
62°
(iv)
37°
(v)
42°
Question
13
13.
In the given figure, find the angles of the quadrilateral.
(i)
I
=
99°
,
J
=
90°
,
K
=
81°
,
L
=
90°
(ii)
I
=
97°
,
J
=
90°
,
K
=
83°
,
L
=
90°
(iii)
I
=
98°
,
J
=
90°
,
K
=
82°
,
L
=
90°
(iv)
I
=
100°
,
J
=
90°
,
K
=
80°
,
L
=
90°
(v)
I
=
101°
,
J
=
90°
,
K
=
79°
,
L
=
90°
Question
14
14.
In the given figure, O is the centre of the circle and FI is a diameter. If ∠HIE = 91° and ∠EFI = 60°, find ∠FGH
(i)
149°
(ii)
124°
(iii)
134°
(iv)
129°
(v)
119°
Question
15
15.
Two circles touch internally. M is the centre of the bigger circle and lies on the smaller circle. If ∠JKL = 68°, find ∠J
(i)
37°
(ii)
22°
(iii)
27°
(iv)
52°
(v)
32°
Question
16
16.
Which of the following statements are true?
a)
If a trapezium is cyclic, it is a rectangle.
b)
A cyclic quadrilateral is a regular polygon.
c)
If a rhombus is cyclic, it is a square.
d)
If a kite is cyclic, it is a square.
e)
If a parallelogram is cyclic, it is a rectangle.
(i)
{b,e}
(ii)
{d,a,c}
(iii)
{c,e}
(iv)
{b,e,c}
(v)
{a,c}
Question
17
17.
O is the centre of the circle and OE = DE. Find ∠EOC
(i)
130°
(ii)
135°
(iii)
150°
(iv)
120°
(v)
125°
Question
18
18.
If two circles of radii 9 cm and 4 cm touch internally, the distance between their centres is
(i)
5 cm
(ii)
4 cm
(iii)
3 cm
(iv)
6 cm
(v)
7 cm
Question
19
19.
KL is the perpendicular bisector of side IJ of △HIJ. Given ∠HIJ = 85° and ∠KHJ = 31° , find ∠HJI
(i)
48°
(ii)
33°
(iii)
43°
(iv)
38°
(v)
63°
Question
20
20.
Which of the following statements are true?
a)
The longest of all chords of a circle is called diameter.
b)
The midpoint of any diameter of a circle is its centre.
c)
The diameter divides the circle into two unequal parts.
d)
A sector is the area enclosed by two radii and a chord.
e)
Two chords bisect each other.
(i)
{c,a}
(ii)
{d,b}
(iii)
{d,b,a}
(iv)
{a,b}
(v)
{e,c,a}
Question
21
21.
In the given figure, O is the centre of the circle . If ∠DGE = 65° and ∠DCF = 70°, find ∠CHD
(i)
25°
(ii)
35°
(iii)
30°
(iv)
55°
(v)
40°
Question
22
22.
In the given figure, GHIJK is a regular pentagon . Find ∠GKI
(i)
87°
(ii)
72°
(iii)
102°
(iv)
77°
(v)
82°
Question
23
23.
In the given figure, DEFGHI is a regular hexagon. Find ∠DGF
(i)
65°
(ii)
75°
(iii)
60°
(iv)
70°
(v)
90°
Question
24
24.
The point of intersection of the angular bisectors of a triangle is
(i)
centroid
(ii)
excentre
(iii)
orthocentre
(iv)
circumcentre
(v)
incentre
Question
25
25.
In the given figure JL & KL are equal length chords of the circle. Find ∠LJK
(i)
75°
(ii)
50°
(iii)
45°
(iv)
55°
(v)
60°
Assignment Key
1) (ii)
2) (ii)
3) (iv)
4) (iv)
5) (iii)
6) (ii)
7) (v)
8) (v)
9) (iv)
10) (iii)
11) (i)
12) (ii)
13) (i)
14) (v)
15) (ii)
16) (iii)
17) (iv)
18) (i)
19) (ii)
20) (iv)
21) (i)
22) (ii)
23) (iii)
24) (v)
25) (iii)
