Year 11 circle theorems test to download as PDF

This Year 11 circle theorems test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 15-16, and the full answers are on a separate page.

⏱️ Duration : 45 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Angles at the centre and in a semicircle
\(A\), \(B\) and \(C\) are on a circle with centre \(O\). Angle \(AOB=118^\circ\).
1. Find angle \(ACB\) and give a reason. (2 marks)
2. If \(AB\) were a diameter and angle \(CAB=37^\circ\), find angle \(ABC\). (2 marks)
Question 2 – Cyclic quadrilateral
\(ABCD\) is a cyclic quadrilateral. Angle \(A=(4x+5)^\circ\) and angle \(C=(2x+25)^\circ\).
1. Form an equation and solve it to find \(x\). (3 marks)
2. Write down the size of angle \(A\). (1 mark)
Question 3 – Tangents
\(TA\) is a tangent to a circle of radius 8 cm, centre \(O\). \(OT=17\) cm.
1. Work out the length \(TA\). (3 marks)
2. Work out angle \(ATO\) to 1 decimal place. (1 mark)
Question 4 – Alternate segment
\(TA\) is a tangent to a circle at \(A\), centre \(O\). \(B\) is on the circle and angle \(TAB=64^\circ\).
1. Find angle \(AOB\) and give two reasons. (3 marks)
2. Find angle \(OAB\). (1 mark)
Question 5 – Problem: the arch
A circular arch has a chord 30 m wide at its base and the top of the arch is 5 m above the base.
1. Show that the radius \(r\) satisfies \(r^2=15^2+(r-5)^2\). (1 mark)
2. Solve to find \(r\). (3 marks)

How to use this Year 11 circle theorems test

First, revise with the circle theorems lesson and the worksheet. Then sit the test in one go, with a timer set to 45 minutes. After that, mark your work with the circle theorems test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 11 circle theorems test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.