IGCSEMaths: CoreCIETopic QuestionsGeometryCircle Theorems

Syllabus Edition

First teaching 2023

First exams 2025

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Circle Theorems (CIE IGCSE Maths: Core)

Topic Questions

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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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2
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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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3
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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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4a
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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.

[1]

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4b
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On the circle, draw a radius.

[1]

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4c
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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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5a
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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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5b
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Give a geometrical reason why angle A B C space equals space 90 degree.

[1]

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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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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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3
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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 = 12 cm

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

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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................................................ [2]

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5
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Circle theorem question

 

The diagram shows a circle, centre O, with points B and D on the circumference.
The line A C touches the circle at B.
O B is parallel to D C and angle O A B equals 49 degree.

i)

Write down the mathematical name of the line O B.

................................................. [1]
ii)

Write down the reason why angle A B O is 90 degree.

......................................................................................................................................................     

...................................................................................................................................................... [1]

iii)

Find angleA O B.

Angle space A O B space equals space ................................................ [1]
iv)

Write down the reason why angle A D C = angle A O B.

...................................................................................................................................................... [1]

v)

Complete the statement using a mathematical word.

Triangle A O B is ................................................................. to triangle A D C. [1]

A B equals 5.4 space cm.

Calculate

via)

O B,

O B space equals ......................................... cm [2]

vib)

O A,

O A space equals ......................................... cm [2]

via)

the area of triangle O A B.

.........................................cm2 [2]

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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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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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3
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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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4
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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................................ [3]

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5a
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screenshot-2024-02-27-at-11-02-26-am

A, B  and C  are points on the circumference of a circle with diameter A B.

A tangent is drawn at A.

Find angle B A C.

Angle space B A C equals ................................ [1] 

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5b
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Find angle A B C.

Angle space A B C space equals space................................ [2] 

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