Edexcel IGCSE Maths
Topic questions Geometry and measures Parts of a circle
17 questions · 71 marks · about 1.5 hours
Here is a prism.
How many faces has the prism?
How many vertices has the prism?
A and B are points on a circle, centre O
Write down the mathematical name of the line AB
Write down the mathematical name of the line CD
Also involves Straight line graphs
[In this question 1 cm = 1 unit on the x-axis and 1 cm = 1 unit on the y-axis]
P is a point on a circle with centre (0, 0) The coordinates of P are (8, 
10)
The line L is the tangent to the circle at the point P L crosses the x-axis at the point Q and crosses the y-axis at the point R
Work out the length of RQ Give your answer correct to 3 significant figures.
The diagram shows equilateral triangle ABC with sides of length 10 cm. A circle is drawn inside the triangle.
D, E and F are points on the circle.
ADB, BEC and CFA are tangents to the circle.
Calculate the total area of the regions shown shaded in the diagram. Give your answer correct to 3 significant figures.
Also involves Tangent to a circle · Angle facts · Properties of triangles and quadrilaterals
A and C are points on a circle, centre O DA is the tangent to the circle at A and DC is the tangent to the circle at C
Angle ADC = 48°
Work out the size of reflex angle AOC
Also involves Tangent to a circle
A and C are points on a circle, centre O DA is the tangent to the circle at A and DC is the tangent to the circle at C
Angle ADC = 48°
Work out the size of reflex angle AOC
Write down the mathematical name for an 8-sided polygon.
What type of angle is the angle marked x?
On the diagram above, draw a chord of the circle.
Change 3.6 metres into centimetres.
Also involves Tangent to a circle
A, B, C and D are points on a circle, centre O
EBF is the tangent to the circle at B
Work out the size of angle DCB
Give a reason for your answer to (a)(i)
Work out the size of angle ADO
25Two circles, C1and C2, are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis.
The centre of circle C1 is at the point with coordinates (–1, 3) and the radius of C1 is 13 cm.
The centre of circle C2 is at the point with coordinates (7, 18) and the radius of C2 is 6 cm.
Work out the distance between the centre of C1and the centre of C2
Explain why circle C1intersects circle C2
10Two circles, C1 and C2, are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis.
The centre of circle C1 is at the point with coordinates (–1, 3) and the radius of C1 is 13 cm.
The centre of circle C2 is at the point with coordinates (7, 18) and the radius of C2 is 6 cm.
Work out the distance between the centre of C1and the centre of C2
Explain why circle C1intersects circle C2
The centre O of a circle has coordinates (4, 7)
The point A, on the circle, has coordinates (6, 11) and AOP is a diameter of the circle.
Find an equation of the tangent to the circle at the point P
Also involves Circle theorems
A, B and C are points on a circle with centre O.
AOC is a diameter of the circle.
AB = 8 cm BC = 15 cm
Angle ABC = 90
Work out the total area of the regions shown shaded in the diagram. Give your answer correct to 3 significant figures.
The diagram shows a line AB.
At the point A draw an acute angle. Label your acute angle a.
The diagram shows a circle with centre O.
Draw a diameter of the circle.
Also involves Tangent to a circle
A, B, C and D are points on a circle. TDV is the tangent to the circle at D.
AB = AD Angle ADT = 71°
Work out the size of angle BCD. Give a reason for each stage of your working.
Also involves Arc length and sector area
The diagram shows a sector OAPB of a circle, centre O.
AB is a chord of the circle. Angle AOB = 80°
The area of sector OAPB is 
cm2
Work out the perimeter of the shaded segment. Give your answer correct to 3 significant figures.
Also involves Tangent to a circle
L, M and N are points on a circle, centre O. QMT is the tangent to the circle at M.
Find the size of angle NOM.
Give a reason for your answer.
Find the size of angle NMQ.
Give a reason for your answer.
Also involves Tangent to a circle · Circle theorems
R and S are points on a circle with centre O.
On the diagram above, shade a segment of the circle.
Write down the mathematical name of the straight line RS.
In the diagram below, P and Q are points on a circle with centre O.
QT is a tangent to the circle. Angle OPQ = 18
Work out the size of angle PQT. Give a reason for each stage of your working.
Also involves Tangent to a circle · Angle facts
In the diagram below, P and Q are points on a circle with centre O.
QT is a tangent to the circle. Angle OPQ = 18
Work out the size of angle PQT. Give a reason for each stage of your working.
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