Circle theorems: tangent and radius

Sample Circle theorems: tangent and radius questions

A few of the 17 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 11 markGrade 3-4
   A radius is drawn to the point where a tangent touches a circle. What angle is always formed between the tangent and this radius?
   Show the worked solution

   A tangent to a circle is always perpendicular to the radius at the point of contact, so the angle formed is 90°.
2. Question 21 markGrade 4-5
   A tangent touches a circle at point $T$

What are the common mistakes in Circle theorems: tangent and radius?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Doesn't use the fact that a tangent is perpendicular to the radius at the point of contact

  Forgot that the tangent is perpendicular to the radius at the point of contact, and used only the given angle without accounting for the 90° angle

• Doesn't use the right angle formed between a tangent and the radius

  Repeated the given tangent-chord angle instead of using the 90° tangent-radius fact to find the remaining angle

• Assumes a tangent-radius triangle is isosceles instead of using the fact that the tangent meets the radius at a right angle

  Wrongly assumes triangle OPT is isosceles with base angles both 35°, computing angle TOP = 180 - 35 - 35 = 110° instead of using the tangent-radius right angle (angle OTP = 90°) to get 180 - 90 - 35 = 55°.

Quick answers about Circle theorems: tangent and radius

How many Circle theorems: tangent and radius practice questions are there?

There are 17 self-marking GCSE and IGCSE Maths questions on Circle theorems: tangent and radius, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1) across Foundation and Higher tier. Each one is marked instantly and has a full worked solution.

Do I need an account to practise Circle theorems: tangent and radius?

No. You can start practising Circle theorems: tangent and radius straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.