CIE IGCSE Maths: Extended

Topic Questions

IGCSEMaths: ExtendedCIETopic Questions3. Geometry3.4 Circle Theorems

Syllabus Edition

First teaching 2021

Last exams 2024

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3.4 Circle Theorems

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1
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cie-igcse-2020-may-june-p2-tz1-q15

P, R and Q are points on the circle.
A B is a tangent to the circle at Q.
Q R bisects angle P Q B therefore
Angle B Q R equals x degree  and x less than 60.


Use this information to show that triangle P Q R is an isosceles triangle.
Give a geometrical reason for each step of your work.

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2
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cie-igcse-2020-march-p2-tz2-q15


A, B, C and D lie on the circle.
P C Q is a tangent to the circle at C.
Angle A C Q = 64°.

Work out angle A B C, giving reasons for your answer.


Angle A B C = .......................... because ..........................

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3a
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cie-igcse-q26-circles

A comma space B comma space C and D are points on the circumference of the circle.
The line X Y is a tangent to the circle at A.

Find the value of x, giving a reason for your answer.
    

x= ............................. because .................................

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3b
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Find the value of y, giving a reason for your answer.
  

y = ............................. because .................................

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4a
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cie-igcse-2019-oct-nov-p2-tz2-q19

In the diagram, A, B, C and D lie on the circumference of a circle, centre O.
Angle ACD = x degree and angle OAB = 2 x degree.

Find an expression, in terms of x, in its simplest form for angle AOB .

Angle AOB = ................................................... 

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4b
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Find an expression, in terms of x, in its simplest form for angle ACB.

Angle ACB = ...................................................

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4c
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Find an expression, in terms of x, in its simplest form for angle DAB.

Angle DAB = ...................................................

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5
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cie-igcse-2019-march-p2-q15

A, B and C are points on the circle, centre O.
AB and OC intersect at P.
 
Find the value of w.
 

w equals....................................................

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6a
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cie-igcse-2020-mary-jun-p2-tz2-q20

A comma space B comma space C and D lie on the circle, centre O.
T A is a tangent to the circle at A.
Angle A B C equals 131 degree and angle A D B space equals space 20 degree.

Find angle B A T.
 

Angle B A T equals.................................................

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6b
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Find angle O A B.
 

Angle O A B equals.................................................

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1
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cie-igcse-2020-may-june-p2-tz1-q10

Points A comma space B comma space C comma space D comma space E and F lie on the circle, centre O.

Find the value of x and the value of y.


x equals .................................................. [2]

y equals ..................................................    

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2
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cie-igcse-2019-may-june-1-q8

A, B and C are points on the circle, centre O.

Find the obtuse angle AOC.
 

Angle AOC = ............................................ 

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3
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cie-igcse-2018-oct-nov-p2-tz2-q2
The diagram shows a circle, centre O.
AB and DE are chords of the circle.
M is the mid-point of AB and N is the mid-point of DE.
AB = DE = 9 cm and OM = 5 cm.

Find ON.
 

ON = ......................................... cm

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4
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cie-igcse-2018-may-jun-3-p2-q20

The points A comma space B comma space C comma space D and E lie on the circumference of the circle.
Angle D C E equals 47 degree and angle C E A equals 85 degree.

Find the values of w comma space x and y.

w equals................................................     
x equals................................................     
y equals................................................     

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5
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cie-igcse-2018-march-p2-14

A, B, C and D are points on the circumference of the circle.
AC and BD intersect at X.

Complete the statement.


Triangle ADX is ..................................................... to triangle BCX.

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6a
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cie-igcse-2020-mary-jun-p2-tz2-q20

A comma space B comma space C and D lie on the circle, centre O.
Angle A B C equals 131 degree.

Find angle A D C.
 

Angle A D C equals.................................................

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6b
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Find angle A O C.
 

Angle A O C equals................................................. 

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1
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cie-igcse-2020-oct-nov-p2-tz1-q20

The diagram shows a cyclic quadrilateral.

Find the value of y.

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

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2
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cie-igcse-2019-may-jun-p2-tz3-q19

J, K, L and M are points on the circumference of a circle with diameter J L.
J L and K M intersect at N.
Angle J N K equals 104 degree and angle M L J equals 22 degree.

Work out the value of d.
 

d = ....................................................

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3
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q8-4-4-hard-edexcel-gcse-maths

A comma space B comma space D and E are points on a circle.
A B C and E D C are straight lines.

Prove that triangle B C D is similar to triangle E C A.
You must give reasons for your working.

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4
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q23-paper1hr-june2019-edexcel-igcse-maths

B comma space C comma space D and F are points on a circle.
A B C, A F D, space B F E spaceand space C D E spaceare straight lines.

Work out the size of angle x.
Show your working clearly.

x = ......................

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5
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q19-paper1hr-jan2019-edexcel-igcse-maths

B comma space C comma space D and E are points on a circle.

A B is the tangent at B to the circle.
A B is parallel to E D.
Angle space A B E space equals space 73 degree

Work out the size of angle D C E.
Give a reason for each stage of your working.

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