and are points on the circumference of a circle, centre .
and are tangents to the circle.
AngleÂ
Work out the size of angle .
Give a reason for each stage in your working.
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and are points on the circumference of a circle, centre .
and are tangents to the circle.
AngleÂ
Work out the size of angle .
Give a reason for each stage in your working.
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and are points on the circumference of a circle, centre .
 is a tangent to the circle.
 is a straight line.
AngleÂ
Work out the size of the angle marked .
Give reasons for your answer.
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and are points on the circumference of a circle, centre .
 is a diameter of the circle.
and are tangents to the circle.
Angle .
Work out the size of angle .
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and are points on the circumference of a circle, centre .
Angle .
Find the size of angle in terms of .
Give a reason for each stage of your working.
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and are points on the circumference of a circle, centre .
 is a straight line.
AngleÂ
Find the size of angle .
Give a reason for each stage in your working.
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The points and lie on a circle.
 is a straight line.
AngleÂ
Work out the size of angle .
You must give a reason for each stage of your working.
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is a quadrilateral.
Prove that  is not a cyclic quadrilateral.
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and are points on a circle.
and are tangents.
Work out the size of angle .
.....................................degrees
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and are points on a circle.
.
Is the centre of the circle?
Tick a box.
Yes           No
Show working to support your answer.
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, and are points on a circle.
 is a straight line.
 is a tangent to the circle.
Sam is trying to work out the size of angle .
Here is his working.
   |
angles in the same segment are equal angles at a point on a straight line add up to 180° |
Make a criticism of his working.
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and are points on a circle.
 is a tangent to the circle.
Write down the size of angle .
Give a reason for your answer.
............................degreesÂ
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and are points on a circle.
Circle the line that is a diameter of the circle.
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In the diagram,
Explain why angle HDF is 82°.
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The diagram shows a circle, centre O.
Points A, B, C and D lie on the circumference of the circle.
EDF is a tangent to the circle.
Angle ABC = 82° and angle ODC = 57°.
Work out the value of x.
x = ......................Â
Work out the value of y.
y = ..................
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A, B, C and D are points on the circumference of a circle.
PQ is a tangent to the circle at D.
Angle BDQ = 72° and angle ABD = 63°.
Work out angle x.
Give a reason for your answer.
Angle x = ...................° because ......................
Work out angle y.
Give a reason for your answer.
Angle y = ...................° because .....................
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A, B, C and D are points on the circumference of a circle, centre O.
Angle BAD = 52°.
Work out angle x.
Give a reason for your answer.
x = ................................... ° reason ..................................................................................
Work out angle y.
Give a reason for your answer.
y = ................................... ° reason ..................................................................................
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and are points on a circle, centre
is a diameter of the circle.
Angle
Calculate the size of angle
Give a reason for each stage of your working.
Angle DFG = .......................................................
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and are points on the circumference of a circle, centre .
and are tangents to the circle.
AngleÂ
AngleÂ
Work out the size of angle .
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Â
and are points on the circumference of a circle, centre .
 is a diameter of the circle.
and intersect at E.
AngleÂ
AngleÂ
Work out the size of angle .
You must show all your working.
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and are points on a circle, centre .
is a tangent to the circle.
AngleÂ
Work out the size of angle .
Give reasons for each stage of your working.
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and are points on the circumference of a circle, centre .
 is a straight line.
is the tangent at to the circle.
AngleÂ
Work out the size of angle .
Give a reason for each stage of your working.
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and are points on a circle, centre .
 is a tangent to the circle.
 is a straight line.
Angle .
Find the size of angle , in terms of .
Give your answer in its simplest form.
Give reasons for each stage of your working.
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and are diameters of a circle, centre .
Prove that triangle and triangle are congruent.
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and are four points on the circumference of a circle.
and are straight lines.
Prove that triangle and triangle are similar.
You must give reasons for each stage of your working.
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and are points on a circle.
is the tangent at to the circle.
Angle
Angle
Work out the size of angle .
Give reasons for your working.
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and are points on a circle.
and are straight lines.
Prove that is not a diameter of the circle.
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and are points on a circle.
Angle
Prove that
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A and B are points on the circumference of a circle, centre O.
CA and CB are tangents to the circle.
Prove that triangle OAC is congruent to triangle OBC.
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A, B, C and D are points on the circumference of a circle, centre O.
AC is a diameter of the circle.
Angle ABD = 58°.
Angle CDB = 22°.
Work out the sizes of angle ACD and ACB, giving reasons for your answers.
Angle ACD = ...........................°
Angle ACB = ...........................°
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In the diagram,
Calculate the acute angle AOC.
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and are points on a circle.
and are straight lines.
Prove that triangle is similar to triangle .
You must give reasons for your working.
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and are points on the circumference of a circle, centre .
is a tangent to the circle.
Show that
You must give a reason for each stage of your working.
Dylan was asked to give some possible values for and .
He said, " could be 200 and could be 110, because 200 − 110 = 90"
Is Dylan correct?
You must give a reason for your answer.
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and are points on the circumference of a circle centre .
Prove that angle is twice the size of angle .
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and are points on the circumference of a circle, centre .
is a diameter of the circle.
Prove that angle isÂ
You must not use any circle theorems in your proof.
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 is a regular pentagon.
and are points on a circle, centre .
and are tangents to the circle.
is a straight line.
Prove that .
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and are points on a circle.
 is a tangent to the circle.
AngleÂ
Prove that angleÂ
Give reasons for each stage in your working.
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and are points on a circle.
is the tangent at to the circle.
is parallel to .
Work out the size of angle .
Give a reason for each stage of your working.
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and are points on a circle.
, , and are straight lines.
Work out the size of angle .
Show your working clearly.
= ......................
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and are points on a circle with centre .
Angle
The area of the shaded segment is 200cm2
Calculate the radius of the circle.
Give your answer correct to 3 significant figures.
...................................................... cm
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and are three points on the circumference of a circle, centre .
and are tangents to the circle.
is a kite.
Angle is
Prove that angle isÂ
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and are points on a circle.
The tangent at is shown.
and are straight lines.
Prove that Â
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and are points on a circle.
is a tangent.
Assume that triangle is isosceles with
Prove that is parallel to .
In fact, triangle is equilateral.
Tick the two boxes for the statements that must be correct.Â
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Here is a cyclic quadrilateral.
Work out the size of angle .
.....................degrees
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and are points on a circle.
and are straight lines.
Work out the size of angle.
You must show your working which may be on the diagram.
..........................degrees
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A, B, C and D are points on the circumference of a circle, centre O.
Angle BAD = 112° and angle DCO = 33°.
Show that angle y = 35°.
Give reasons for each stage of your working.
Work out angle z.
Give reasons for your answer.
Angle z = ......................... ° because ........................................................................................
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A, B, C and D are points on the circumference of a circle, centre O.
Angle CAD = 28° and CD = 6.4cm.
BD is a diameter of the circle.
Calculate the area of the circle.
...................... cm2
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