Points and lie on the circle, centre .
Find the value of and the value of .
.................................................. [2]
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Syllabus Edition
First teaching 2021
Last exams 2024
Points and lie on the circle, centre .
Find the value of and the value of .
.................................................. [2]
..................................................
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A, B and C are points on the circle, centre O.
Find the obtuse angle AOC.
Angle AOC = ............................................
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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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The points and lie on the circumference of the circle.
Angle and angle .
Find the values of and .
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................................................
................................................
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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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and lie on the circle, centre .
Angle .
Find angle .
Angle .................................................
Find angle .
Angle .................................................
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, and are points on the circle.
is a tangent to the circle at .
bisects angle therefore
Angle and .
Use this information to show that triangle is an isosceles triangle.
Give a geometrical reason for each step of your work.
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, , and lie on the circle.
is a tangent to the circle at .
Angle = 64°.
Work out angle , giving reasons for your answer.
Angle = .......................... because ..........................
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and are points on the circumference of the circle.
The line is a tangent to the circle at .
Find the value of , giving a reason for your answer.
= ............................. because .................................
Find the value of , giving a reason for your answer.
= ............................. because .................................
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In the diagram, A, B, C and D lie on the circumference of a circle, centre O.
Angle ACD = and angle OAB = .
Find an expression, in terms of , in its simplest form for angle AOB .
Angle AOB = ...................................................
Find an expression, in terms of , in its simplest form for angle ACB.
Angle ACB = ...................................................
Find an expression, in terms of , in its simplest form for angle DAB.
Angle DAB = ...................................................
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A, B and C are points on the circle, centre O.
AB and OC intersect at P.
Find the value of .
....................................................
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and lie on the circle, centre .
is a tangent to the circle at .
Angle and angle .
Find angle .
Angle .................................................
Find angle .
Angle .................................................
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The diagram shows a cyclic quadrilateral.
Find the value of .
................................................
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, , and are points on the circumference of a circle with diameter .
and intersect at .
Angle and angle .
Work out the value of .
= ....................................................
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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 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.
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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