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maths circle theorem revision with answers
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Circle Theorems GCSE Higher KS4 with Answers/SolutionsNOTE: You must give reasons for any answers provided.
All diagrams are NOT DRAWN TO SCALE.
1. (a) A, B and C are points on the circumference of a circle, centre, O.
AC is the diameter of the circle.
Write down the size of angle ABC.
* (b) Given that AB = 6cm and BC = 8cm, work out
(i) the diameter of the circle, (ii) the area of the triangle
(iii) the area and circumference of the circle, leaving your answer in terms of
(c) D is a point on the circumference of the circle above such that angle BDC = 60˚.
(i) Write down the size of angle CAB. (ii) Work out the size of angle ACB.
mathsmalakiss.com 1
, 2. P, Q, R and S are points on the circumference of a circle.
Angle PRS = 65˚ and angle QSR = 44˚.
Find the size of angle (i) PQS (ii) QPR
3. P, Q and R are points on the circumference of a circle, centre, O.
PR is the diameter of the circle and ST is a tangent to the circle at the point R.
Angle QRS = 58˚.
(a) Work out the size of angle QRP.
(b) Work out the size of angle QPR.
mathsmalakiss.com 2
, 4. R
37
S T
U
O DD
O
D
R, S and T are points on the circumference of a circle, centre O.
ST is a diameter and Angle RST = 37.
U is the point on ST such that angle RUS is a right angle.
(a) Work out the size of angle URT.
(b) Work out the size of angle ROT.
(c) Work out the size of angle ORU.
(d) Find the size of angle ORT.
mathsmalakiss.com 3
, B
5.
A 48
O
C
D
A, B, C and D are points on the circumference of a circle, centre O.
BD is a diameter of the circle. Angle CAB = 48.
(a) Write down the size of angle BCD.
(b) Find the size of angle BDC.
(c) Find the size of angle BOC.
(d) Find the size of angle CAD.
(e) Find the size of angle COD.
(f) Find the size of angle OCB.
mathsmalakiss.com 4
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