Circle Theorems Worksheet

Circle Theorems at a glance

Circle theorems are a set of angle properties that apply within circles. We can use the circle theorems to work out missing angles. 

To access circle theorems we need to be confident with the names of the key parts of a circle including the centre of the circle, the diameter of the circle, the radius of the circle, a tangent to the circle, a segment of the circle, a sector of the circle and a chord within the circle.

We also need to be confident at labelling angles using three letter notation. For example, angle BCD is the angle created at C when travelling from B to C to D. The centre of a circle is often labelled O, in which case the angle BOD would be the angle at the centre O when travelling from B to O to D.  

The circle theorems are:

• The angle at the centre is twice the angle at the circumference of a circle
• Angles in the same segment are equal
• Opposite angles in a cyclic quadrilateral are equal
• The angle at the circumference of the circle in a semicircle is a right angle
• The angle between a tangent and a radius is a right angle
• Two tangents which meet at a point are equal in length
• The alternate segment theorem
• A triangle made from two radii is an isosceles triangle

Looking forward, students can then progress to additional circle theorems, and other geometry worksheets, for example an angles in polygons worksheet or area and circumference of a circle worksheet.

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