Circle theorems

AQA GCSE Maths

8 ready-made resources for teaching Circle theorems, written for AQA GCSE Maths. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where students usually go wrong, free to read whether or not you sign up.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Tiered worksheetWord, editable
Worksheet mark schemeWord, editable

Foundation tier

Identify and name the parts of a circle: radius, diameter, chord, tangent, arc, sector, segment, and circumference.

Higher tier, in addition

Know and use the fact that the angle in a semicircle is 90°.
Know and use the fact that a tangent to a circle is perpendicular to the radius at the point of contact.
Know and use the fact that the angle at the centre is twice the angle at the circumference when subtended by the same arc.
Know and use the fact that angles in the same segment are equal.
Know and use the fact that opposite angles in a cyclic quadrilateral sum to 180°.
Know and use the fact that the perpendicular from the centre of a circle to a chord bisects the chord.
Know and use the fact that two tangents drawn from the same external point are equal in length.
Know and use the alternate segment theorem.

Where students go wrong

Misidentifying which arc or angle is "subtended" by a given chord or angle.
Forgetting that the opposite-angles rule for a cyclic quadrilateral only applies when all four vertices lie on the circle.
Forgetting to use the tangent-radius right angle when it is needed to solve a problem.
Mixing up which angle is doubled when applying the centre/circumference angle rule.
Not recognising that two tangents drawn from the same external point must be equal in length.

How it gets asked in the exam

"Find the size of angle ..., giving reasons for your answer", "Prove that ...", "ABCD is a cyclic quadrilateral. Find angle ...".

Key vocabulary

Radius, diameter, chord, tangent, arc, sector, segment, circumference, cyclic quadrilateral, subtend, alternate segment.

Assumed prior knowledge

Angle properties, including angles on a straight line, around a point, and in triangles and quadrilaterals.
Correct use of the vocabulary of a circle's parts.

How Speca scaffolds this topic

Provide a circle-theorem "gallery" reference sheet: each theorem shown as a small labelled diagram with its one-line rule directly underneath, in a consistent visual style, so a new diagram can be pattern-matched against the gallery before reasoning from scratch.
Colour-code the angle at the centre and the angle at the circumference consistently in every diagram, regardless of which theorem is being tested.
Extend the general angle "reason bank" from the angle properties and similarity topic with circle-theorem-specific sentence starters, for example: "___ is the angle at the centre and ___ is the angle at the circumference on the same arc, so ___ = 2 × ___."

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