1. Circle theorems workout
Get out your PPT notes from Friday.
Circle theorems workout

2. Click the rectangles to reveal each answer.
Label the circle
Click the rectangles to reveal each answer. ?
radius ?
sector ?
diameter ?
tangent ?
chord ?
circumference ?
segment

3. Explain what we mean by ‘subtended’.
You can use the diagram to help.
The blue angle is subtended by the red line. It is formed by lines starting from either end of the line.

4. Complete the circle theorem.
Click on the correct answer.
Angles in the same segment ... 
... are equal. 
... sum to 180°. 
... sum to 360°.

5. Angles in the same segment are equal.
Find the lettered angles. Click on to reveal the answer. ?
12°
26° a° b°
82°
38°
77° d° e° c° ? ? ?
a = 26°
b = 12°
c = 39°
d = 39°
e = 49°

6. Complete the circle theorem.
Click on the correct answer.
The angle subtended at the centre is ...   
half
equal to
twice
... the angle subtended at the circumference.

7. Find the lettered angles. Click on to reveal the answer.
The angle subtended at the centre is twice the angle subtended at the circumference.
Find the lettered angles. Click on to reveal the answer. ?
90° a°
12° b°
53° c° ? ? ?
a = 45°
b = 78°
c = 37°

8. Complete the circle theorem.
Click on the correct answer. 
... are equal.
Opposite corners of a cyclic quadrilateral ... 
... sum to 180°. a 
... sum to 360°.
a + b = 180°
c + b = 180
a = c
AND …
Opposite corner and the exterior angle are equal b c

9. Opposite corners of a cyclic quadrilateral sum to 180°.
Find the lettered angles. Click on to reveal the answer. ? d°
101°
114° c°
127°
60° a° b° e°
42° ? ? ?
a = 120°
b = 53°
c = 101°
d = 114°
e = 126°

10. Complete the circle theorem.
Click on the correct answer.
An angle subtended at the circumference by a diameter ... 
... is acute. 
... is obtuse. 
... is 90°.

11. An angle subtended at the circumference by a diameter is 90°.
Find the lettered angles. Click on to reveal the answer. ? a°
28°
35°
28° b° c°
10°
35° e° d° ? ? ?
c = 55°
d = 55°
e = 25°
a = 62°
b = 62°

12. Complete the circle theorem.
Click on the correct answer.
The angle between a chord and ...  
a tangent
a diameter
... is ...  
twice
equal to
... the angle subtended by the chord in the opposite segment.

13. Find the lettered angles. Click on to reveal the answer.
The angle between a chord and a tangent is equal to the angle subtended by the chord in the opposite segment.
Find the lettered angles. Click on to reveal the answer. ? a°
67°
41° b° c° d°
39° e°
64° ? ? ?
a = 41°
b = 67°
c = 90°
d = 51°
e = 58°

14. Exam style question
110°
30° C x° A
AC is the diameter of a circle and B is a point on the circumference of the circle.
Find angle x. B y ?
y = 180 – 110 – 30
y = 40° (angles in a triangle)
x = 90 – y
x = 50° (angles subtended by the diameter)

15. Exam style question ? The diagram shows a circle, centre O.B C A P Q O
98°
57°
The diagram shows a circle, centre O.
PQ is a tangent to the circle at C.
Angle PCA = 57°
Angle AOB = 98°
Calculate the size of angle OBC. ?
ABC = 57° (alternate segment theorem)
ABO = ½(180 – 98)
ABO = 41° (angles in isosceles triangle)
OBC = 57 – 41
OBC = 16°