IGCSEMaths: CoreCIEExam QuestionsGeometryCircle Theorems

Syllabus Edition

First teaching 2021

Last exams 2024

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Circle Theorems (CIE IGCSE Maths: Core)

Exam Questions

45 mins15 questions
Easy
Medium
Hard
1
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qp2e-0580-32-paper-3-nov-2020-cie-igcse-maths

i)
Complete this statement.

X comma space Y spaceand Z are points on the .................................................. of the circle, centre O.

[1]

ii)
Give a reason why angle X Y Z is 90°.
[1]

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2a
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q9-058033-octnov2018-cie-igcse-maths-core

A comma space B and C are points on the circumference of the circle, centre O.
The straight line D E touches the circle at B.

Write down the mathematical name for the line D E.

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2b
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On the circle, draw a radius.

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2c
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Complete the following statements.

i)
Angle A B D = ............... because

[2]

ii)
Angle A C B = ............... because

[2]

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3a
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q9-058031-mayjune2018-cie-igcse-maths-core

A comma space B and C are points on the circumference of a circle, centre O.

Write down the mathematical name for

i)
the straight line A C,
[1]
ii)
the straight line A B.

[1]

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3b
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Give a geometrical reason why angle A B C space equals space 90 degree.

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4
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qp2a-0580-31-paper-3-oct-nov-2019-cie-igcse-maths

In the diagram,space A comma space B space and C are points on the circle, centre O.

i)
On the diagram, draw a chord.
[1]
ii)
Explain why angle A B C is 90°.
[1]

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5
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q6b-058033-mayjune2019-cie-igcse-maths-core

In the diagram, B and D are points on the circumference of a circle, centre O.
A C is a straight line touching the circle at B only and B D is a straight line through O.
Complete the statement.

Angle A B D = ................ because ...........................

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1
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qp7c-0580-31-paper-3-nov-2020-cie-igcse-maths

A comma space B and C are points on a circle.
A C is a diameter of the circle.

Find the value of a.

a equals.............................

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2
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The diagram shows the vertices of a triangle lying on the circumference of a circle with centre O.

q7e-058032-mayjune2019-cie-igcse-maths-core

Find the value of b.
Give a reason for your answer.

b = .................... because.............................. 

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3
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q2d-058033-mayjune2018-cie-igcse-maths-core

The points A comma space B and C lie on the circumference of a circle, centre O.
P B R is a tangent to the circle and angle B A C space equals space 37 degree.

Find the value of j and the value of k.

j space equals ................................. 
space k space equals space................................ 

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4
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q4c-058031-mayjune2019-cie-igcse-maths-core

The points E comma space F and G lie on the circumference of a circle, centrespace O.
J G H is a tangent to the circle.

Find the value of x and the value of y.

x space equals space.............................................. space y space equals space.............................................. space

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5a
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cie-core-2017-jun-12-q20

A, B and C are points on the circumference of a circle with diameter AB.
A tangent is drawn at A.

 
Find angle BAC,

Angle BAC = ................................................ 

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5b
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Find angle ABC.

Angle ABC = ................................................

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1
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qp8a-0580-33-paper-3-nov-2020-cie-igcse-maths

P and Q are points on the circle, centre O.
A P B is a tangent to the circle at P.

i)
Write down the mathematical name for the line P Q.
[1]
ii)
Explain why angle O P B is 90°.
[1]
iii)
Find the value of x.
x = ................................................. [3]

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2
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qp5c-0580-32-paper-3-oct-nov-2019-cie-igcse-maths

The diagram shows a circle, centre O comma with diameter E F.
Angle D F E = 63°.

i)
Find angle D E F.
Angle D E F = ................................................... [2]
ii)
E F = 12cm

Calculate D F.
D F = ............................................. cm [2]

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3
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qp3c-0580-32-paper-3-march-2020-cie-igcse-maths

The diagram shows a circle, centre O, with diameter C E.
A comma space B comma space C comma space D and E lie on the circumference of the circle.

i)
Find the value of x.
Give a reason for your answer.
x = ..................... because ...........................
[3]
ii)
Find the value of y.
Give a reason for your answer.
y = ..................... because ....................................
[2]
iii)
Draw a tangent to the circle at A.
[1]

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4
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cie-igcse-2020-may-jun-p4-tz3-q8bi

K, L and M are points on the circle.
KS is a tangent to the circle at K.
KM is a diameter and triangle KLM is isosceles.
 
Find the value of z.
 

z equals................................................ 

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5
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cie-core-2017-jun-31-q4a

 

The diagram shows a circle, centre O, with points B and D on the circumference.
The line AC touches the circle at B.
OB is parallel to DC and angle OAB = 49°.

i)
Write down the mathematical name of the line OB.
 

 [1]

ii)
Write down the reason why angle ABO is 90°.
 
 [1]
iii)
Find angle AOB.

Angle AOB = ................................................ [1]

 

iv)
Write down the reason why angle ADC = angle AOB.
  

 [1]

 

v)
Complete the statement using a mathematical word.
 
 

Triangle AOB is ................................................................. to triangle ADC. [1]

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