# Circle Theorems

Scheme of work: GCSE Higher: Year 10: Term 6: Circle Theorems

#### Prerequisite Knowledge

• Understand and use alternate and corresponding angles on parallel lines;
• Derive and use the sum of angles in a triangle (e.g. to deduce use the angle sum in any polygon, and to derive properties of regular polygons)
• Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

#### Success Criteria

• Identify and apply circle definitions and properties, including centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.
• Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results

#### Key Concepts

• Students need a solid understanding of the properties of angles in parallel lines, vertically opposite, angles in a polygon and on a straight line.
• Understanding the various parts of a circle is critical to fully defining the various circle theorems.
• Students need to spend time breaking down the problem by considering the various angle properties that may be relevant.
• Taking time to prove the various theorems illustrates how interconnected all the properties are.
• Encourage students to annotate and draw on the diagrams.

#### Common Misconceptions

• Students often struggle with precisely defining the various angle appropriate angle properties.
• Incomplete angle properties are a common source for losing marks in examinations.
• Angle and line notation often confuses students to an extent they may calculate an angle that was not asked for.
• Students need to relate their written work with the relevant angle rather than writing detached paragraphs.

## Circle Theorems Resources

### Mr Mathematics Blog

#### Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods

#### T- Formulae

Scheme of work: A-Level Further Mathematics: Further Pure 1: The t – formulae

#### Regression, Correlation and Hypothesis Testing

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing