Circle theorems (8300 - Higher - Geometry and measures)

Topic:

Circle theorems

Specification references (in recommended teaching order)

	Specification content	Specification notes
G10	Apply and prove the standard circle theorems concerning angles, radii, tangents and chords and use them to prove related results	including angle at centre is equal to twice angle at circumference; angle in a semi-circle is 90°; angles in the same segment are equal; opposite angles in a cyclic quadrilateral sum to 180°; tangent at any point on a circle is perpendicular to the radius at that point tangents from an external point are equal in length; the perpendicular from the centre to a chord bisects the chord; alternate segment theorem

The subject content (above) matches that set out in the Department for Education’s Mathematics GCSE subject content and assessment objectives document.

The expectation is that:

All students will develop confidence and competence with the content identified by standard type
All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

Teaching resources

Teaching resources - see below

99+

Downloadable resource in format. 29/08/2014

Diagnostic Questions - circle theorem

AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017

Diagnostic Questions - circle theorems 1

AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017

Diagnostic Questions - circle theorems 2

AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017

Diagnostic Questions - circle theorems 3

AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017

Diagnostic Questions - circle theorum 1

AQA have teamed with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.20/07/2017

Circle Theorem Proofs

A fantastic, student friendly powerpoint which provides clear proofs for six circle theorems. You will need to register for a TES account to access this resource, this is free of charge. 21/08/2015

Eight Circle Theorems

Eight circle theorems are demonstrated through a PDF handout and dynamic Geogebra files along with proofs of each result.21/08/2015

GCSE Circle theorem Revision Cards

The pack contains 18 flash cards which should be printed back to back so that the question is on one side and the answer is on the other.21/08/2015

Circle Theorem Bingo

Students design their own bingo grid from the numbers provided, then answer questions based on three theorems (tangent at right angles to radius; angle in a semicircle; perpendicular from the centre bisects a chord.) You will need to register for a TES account to access this resource, this is free of charge. 21/08/2015

Eight Circle Theorems

Eight circle theorems are demonstrated through a PDF handout and dynamic Geogebra files along with proofs of each result.21/08/2015

Maths is Fun - Circle Theorems

An introduction to circle theorems followed by ten online multiple choice questions.21/08/2015

Blank Circle Theorems

A helpful worksheet on which students can make annotations and draw the diagrams to illustrate five circle theorems including the Alternate Segment Theorem and the sum of angles in a cyclic quadrilateral.21/08/2015

Circle theorems - Tick or Trash

Students are presented with 5 questions and two answers for each. They must identify which is correct (tick) and which is incorrect (trash). A template is included for students to design a similar activity of their own. You will need to register for a TES account to access this resource, this is free of charge. 21/08/2015

The Great Angle Chase

A challenging activity in which students study the given diagram and use the given angles to identify all other angles in the diagram. They also need to identify other geometrical properties such as cyclic quadrilaterals and parallel lines.21/08/2015

Circle Theorems - Alternate Segment Theorem

Question sheet15/05/2010

32 KB