1.
(a)
In the diagram, O is the centre of the circle.
a
O
Not drawn accurately
Write down the value of a.
Answer ........................................................... degrees
(1)
(b)
53°
b
Not drawn accurately
Write down the value of b.
Answer ........................................................... degrees
(1)
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(c)
In the diagram, O is the centre of the circle.
c
Not drawn accurately
O
Write down the value of c.
Answer ........................................................... degrees
(1)
(d)
d
Not drawn accurately
100°
Write down the value of d.
Answer ........................................................... degrees
(1)
(Total 4 marks)
2.
(a)
In the diagram, O is the centre of the circle.
Not drawn accurately
62°
a
O
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2
Calculate the value of a.
......................................................................................................................................
......................................................................................................................................
Answer ............................................................. degrees
(2)
(b)
40°
x
Not drawn accurately
y
(i)
Write down the value of x.
Answer ............................................................. degrees
(1)
(ii)
Calculate the value of y.
...........................................................................................................................
...........................................................................................................................
Answer ............................................................. degrees
(1)
(Total 4 marks)
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3.
Which one of the following kites is a cyclic quadrilateral? Give a reason for your answer.
Kite 1
70º
Kite 2
Kite 3
110º
70º
70º
140º
Not drawn accurately
70º
Answer ......................................................
Reason ....................................................................................................................................
.................................................................................................................................................
.................................................................................................................................................
(Total 2 marks)
4.
In the diagram, O is the centre of the circle.
A, B, C and D are points on the circumference.
Angle AOC = 130°
B
x
Not drawn accurately
O
130°
C
A
(a)
y
D
Calculate the value of x.
Give a reason for your answer.
Answer x = ..........................degrees
Reason ........................................................................................................................
.....................................................................................................................................
(2)
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(b)
Calculate the value of y.
Give a reason for your answer.
Answer y = ..........................degrees
Reason ........................................................................................................................
(2)
(Total 4 marks)
5.
O is the centre of the circle.
p
not drawn accurately
O
q
110°
(a)
Calculate the value of angle p.
.....................................................................................................................................
Answer p = .............................................. degrees
Reason ........................................................................................................................
(2)
(b)
Calculate the value of angle q.
Give a reason for your answer.
Answer q = .............................................. degrees
Reason ........................................................................................................................
(2)
(Total 4 marks)
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6.
(a)
In the diagram, O is the centre of the circle and P, Q and R are points on the
circumference.
Angle P = 25°
Q
Not drawn accurately
P
25°
R
O
Work out the size of angle R.
......................................................................................................................................
......................................................................................................................................
Answer .......................................................... degrees
(2)
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(b)
A, B, C and D are four points on the circumference of another circle.
AC meets BD at X.
Angle ABD = 56° and angle CXD = 80°
B
C
56°
Not drawn accurately
80°
X
d
A
D
Work out the value of angle d.
You must show all your working.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
Answer .......................................................... degrees
(3)
(Total 5 marks)
7.
A, B, C and D are points on the circumference of a circle.
AC is a diameter of the circle.
Angle BAC = 65°
B
y
C
65º
A
x
D
Not drawn accurately
(a)
Write down the value of x.
Answer .......................................................... degrees
(1)
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(b)
Calculate the value of y.
.....................................................................................................................................
.....................................................................................................................................
Answer .......................................................... degrees
(1)
(Total 2 marks)
8.
(a)
The diagram shows a circle with centre O.
50°
Not drawn accurately
O
x
Work out the size of the angle marked x.
.....................................................................................................................................
.....................................................................................................................................
Answer ........................................................... degrees
(1)
(b)
The diagram shows a different circle with centre O.
50°
O
Not drawn accurately
y
Work out the size of the angle marked y.
.....................................................................................................................................
.....................................................................................................................................
Answer ........................................................... degrees
(1)
The Robert Smyth School
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(c)
A, B and C are points on the circumference of a circle with centre O.
BOC is a diameter of the circle.
Angle ABC = 30°
A
Not drawn accurately
B
30°
O
C
Explain why triangle OAC is equilateral.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 5 marks)
9.
(a)
45
B1
(b)
53
B1
(c)
90
B1
(d)
80
B1
[4]
10.
(a)
(b)
180 – 190 – 62 or 90 – 62
oe
M1
28
A1
(i)
40
(ii)
140
or 180 – their x
Do not ft if answer = 140 in (b)(i)
B1
B1 ft
[4]
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11.
Kite 2 and reason
e.g. 110 + 70 = 180
sum of (opposite) angles = 180
B1 Kite 2
B2
[2]
12.
(a)
(b)
65
1
angle at centre
2
115
B1
B1
B1 ft
ft 180 – their 65 provided reason
given is not contradictory
Opposite angles (of cyclic quad)
or other valid explanation
eg x + y = 180
B1
[4]
13.
(i)
(ii)
70
B1
(opposite angles of) cyclic quadrilateral
B1
140
B1
f.t .their (i)
angle at centre is twice angle at circumference
B1
[4]
14.
(a)
(b)
180 – (90 + 25)
oe
M1
65
A1
Implies or states that C = 56 or BXA = 80
M1
180 – (80 + 56) or implies or states A = 44
44
M1 dep
A1
SC1 44 with no working shown
[5]
15.
(a)
65
B1
(b)
25
B1
[2]
16.
(a)
100
B1
(b)
130
B1
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(c)
OAB = 30 or AOB = 120 or BAC = 90 or AOC = 60
Recognition of isosceles triangles or Angle in a
semi-circle
M1
AOC = 60 or OAC = 60
M1 dep
OAC = 60 or OCA = 60
A1
[5]
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11