IGCSEMathsCambridge (CIE)CoreExam QuestionsGeometryCircle Theorems

Circle Theorems (Cambridge (CIE) IGCSE Maths: Core): Exam Questions

Exam code: 0580 & 0980

1 hour16 questions
Easy
Medium
Hard
12 marks
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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22 marks
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]

How did you do?

32 marks
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 ...........................

.

How did you do?

4a1 mark
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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4b1 mark

On the circle, draw a radius.

[1]

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4c4 marks

Complete the following statements.

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

[2]

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

[2]

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5a2 marks
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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5b1 mark

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

[1]

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1
Sme Calculator2 marks
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.............................

How did you do?

2
Sme Calculator2 marks
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

How did you do?

3
Sme Calculator2 marks

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.............................. 

How did you do?

4
Sme Calculator3 marks
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]

How did you do?

5a
Sme Calculator1 mark
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
Sme Calculator2 marks

Find angle A B C.

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

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1
Sme Calculator5 marks
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]

How did you do?

2
Sme Calculator6 marks
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]

How did you do?

3
Sme Calculator4 marks
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]

How did you do?

4
Sme Calculator6 marks
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]

How did you do?

5
Sme Calculator5 marks
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]

How did you do?

6a
Sme Calculator2 marks
Circle inscribed in rectangle ABCD, with points F, E, and G marked. Diagonal lines from A to C and B to G intersect at the circle.

The points B, C, and D lie on the circumference of the circle, centre O.

The line A B is a tangent to the circle at B.

Find the value of x and the value of y.

How did you do?

6b
Sme Calculator3 marks

B C is 4cm.

Hence, find the radius of the circle.

Round your answer to 3 significant figures.

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6c
Sme Calculator2 marks

Calculate the area of the circle.

Round your answer to 3 significant figures.

How did you do?