Prior Content: Angles (Including Parallel Lines), Angles in Polygons, Constructions, Solving Quadratics, Forming Equations, Algebraic Proof, Circles & Sectors, Pythagoras, Similar Shapes
Possible Next Steps: Drawing & Using Graphs, Linear Graphs & Gradients
Contents
- 1.0 Whole Angle Circle Theorem Resources
- 1.1 Isosceles Triangles from Radii
- 1.2 The Angle in a Semi-Circle is a Right Angle
- 1.3 The Angle in the Centre is Twice the Angle at the Circumference
- 1.4 The Angles in Same Segments are Equal
- 1.5 Opposite Angles in a Cyclic Quadrilateral Sum to 180 Degrees
- 1.6 The Perpendicular Bisector of a Chord Passes Through the Centre
- 1.7 The Angle Between the Tangent and Radius is a Right Angle
- 1.8 The Angles in Alternate Segments are Equal
- 2.1 Intersecting Chords: Intersecting within a Circle (& Whole Intersecting Chords Resources)
- 2.2 Intersecting Chords: Two Chords Intersecting Outside a Circle
- 2.3 Intersecting Chords: One Chord, One Tangent
- 2.4 Intersecting Chords: Two Tangents are Equidistant from a Point to a Circle
- Whole Topic Summary Resources (Including Past Paper Questions)
1.0 Whole Angle Circle Theorem Resources
Teaching Videos, Exercises & Activities
Tutorial Videos
Circle Theorems – GCSE Higher Maths by 1st Class Maths
Circle Theorems – GCSE Maths Higher by HEGARTYMATHS
All of the Circle Theorems in 10 Minutes!! by The GCSE Maths Tutor
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
- Transum Matching Pairs Activity
- Andy Lutwyche
- Notes To Complete
- Codebreaker
- Codebreaker (2)
- Codebreaker (3)
- Crack The Safe
- Defuse The Bomb – (True or False)
- Fill In The Blanks
- (Geometric Proof) Codebreaker
- Recognising Codebreaker
- Defuse The Bomb – (True or False) 2
- Combined Codebreaker
- Show that…
- Card Sort/Worksheet
- Logos – KS4 Worksheets
- Broken Turntable – Worksheet – KS4
- Don Steward
- Circle Theorems Using Parallels
- Measuring Angles on Circular Grids
- Circle theorems presentations (folder)✦ (original by Don Steward; copy hosted on Jo Morgan’s Drive)
- The Chalkface
- Circle Theorems Investigation: PDF · Interactive page
- Blank circle theorems✦
- Ben Sparks (GeoGebra)
- Acute Learning Problem Pairs
- Level 2 FM: Circle Theorems as PowerPoint or PDF
- Transum
- Goal Free Problems
- Mr Draper Maths Interleaving Circle Theorems 1
- Go Teach Maths
- BossMaths
- G10a Circle Theorems✦ (12 interactive GeoGebra applets)
- GeoGebra
- Interwoven Maths
- Introducing Circle Theorems✦ (by Nathan Day)
- Solving equations with circle theorems✦ (by Nathan Day)
- Solving further equations with circle theorems✦ (by Karen Hancock)
- @rodrigotweets1
Worksheets
- Dr Austin Maths
- Corbettmaths
- Circle Theorems Practice Questions & Solutions
- Circle Theorems Worksheet & Solutions
- Circle Theorems Proof Worksheet & Video Solutions
- Circle Theorems AQA Level 2 Practice Questions & Solutions
- Maths 4 Everyone
- Pixi Maths
- Miss Konstantine (MathsHKO)
- Maths Genie
- Circle Theorems: Booklet · Worksheet · Solutions · Lesson · Topic page
- Proof of the Circle Theorems: Booklet · Worksheet · Solutions · Lesson · Topic page
- Naiker Maths
- Physics & Maths Tutor
- Access Maths
- MME
- MathsPad
- 1st Class Maths
- MissMorrisMaths
- Keyboardmonkey
- Maths Malakiss
- Circle theorems problems (with answers)✦ (original by Maths Malakiss; original mathsmalakiss.com site no longer online; copy hosted on Jo Morgan’s Drive)
- Mr Morley Maths
- Circle Theorems: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
- Pret Homework (@MathedUp)
- Circle Theorems (@MathedUp, pptx)
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 442l: Use the theorems: the angle at the centre is double the angle at circumference and the angle between a radius and a tangent is 90, using a quadrilateral inside the circle.
- 442m: Use the theorems: the angle at the centre is double the angle at the circumference and the angle between a radius and a tangent is 90, using a quadrilateral outside the circle.
- 442n: Use the theorems: the angle at the centre is double the angle at the circumference and opposite angles in a cyclic quadrilateral add to 180.
- 442o: Use the theorems: angles in same segment are equal and an angle in a semicircle is 90.
- 442p: Use the theorems: opposite angles in a cyclic quadrilateral add to 180 and an angle in a semicircle is 90.
- 442q: Use the theorems: the angle at the centre is double the angle at the circumference and the alternate segment theorem.
- 442r: Use the theorems: the angle between a radius and a tangent is 90 and the alternate segment theorem.
- 442s: Use the theorems: opposite angles of cyclic quadrilateral add to 180 and the alternate segment theorem.
- 442t: Use the theorems: opposite angles of cyclic quadrilateral add to 180 and the alternate segment theorem, with an isosceles triangle.
- 442u: Use parallel lines combined with the theorems: opposite angles in a cyclic quadrilateral add to 180 and alternate segment theorem.
- 442v: Solve problems involving triangles intersecting to form a cyclic quadrilateral.
- 442w: Form and solve linear equations using circle theorems.
- 442x: Form and solve simultaneous equations using circle theorems.
- 442z: Determine the angle between a tangent and an extended side.
- 442: Exam Practice: Circle theorems
Further Practice
- Practise Questions
Extension Materials
Worksheet
1.1 Isosceles Triangles from Radii
Teaching Videos, Exercises & Activities
Tutorial Videos
Circle Theorems Theorem Angles Angle Semicircle Isosceles Triangle Centre Circumference Right Angle by Mathsterclass
Circle theorems – tangent and radius meet at 90 degrees by GraphicMaths
Circle Theorems – Angle at the Centre is Twice the Angle at the Circumference – Full Lesson by Radford Mathematics
Online Platforms (with Videos & Exercises)
Activities & Resources
Worksheets
- Dr Austin Maths
- Maths 4 Everyone
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 442j: Use the theorems: angle at the centre is double the angle at the circumference and the radii of a circle are equal in length.
- 442k: Use the theorems: the angle between tangent and radius is 90 and radii of a circle are equal in length.
- 442: Exam Practice: Circle theorems
Further Practice
- Practise Questions
Extension Materials
1.2 The Angle in a Semi-Circle is a Right Angle
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Angle in a Semi-Circle Proof
Online Platforms (with Videos & Exercises)
- Khan Academy
- Proofs with inscribed shapes: Videos & practice
Activities & Resources
- Don Steward
- Ben Sparks (GeoGebra)
- Angle in a Semicircle Proof: GeoGebra
- Interactive Maths
- Goal Free Problems
Worksheets
Dr Frost Resources
Dr Frost Video
K643: Know That the Angle in a Semicircle is 90 Degrees.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 442c: Know that the angle in a semicircle is 90 degrees.
- 444a: Prove that the angle in a semicircle is 90^° (not yet active)
- 442: Exam Practice: Circle theorems
- 444: Exam Practice: Proofs of circle theorems
Further Practice
- Practise Questions
Extension Materials
Other Videos & Multimedia
Worksheet
1.3 The Angle in the Centre is Twice the Angle at the Circumference
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Angles at Centre & Circumference
Online Platforms (with Videos & Exercises)
- Khan Academy
- Inscribed angles: Videos & practice
Activities & Resources
- Ben Sparks (GeoGebra)
- Angle at the Centre Proof: GeoGebra
- Interactive Maths
- Go Teach Maths
Worksheets
Dr Frost Resources
Dr Frost Video
K645: Know That the Angle at the Centre is Twice the Angle at the Circumference.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 442a: Know that the angle at the centre is twice the angle at the circumference.
- 442i: Determine an angle in an arrowhead centred at the circle centre.
- 444b: Prove that the angle at the centre of a circle is twice the angle at the circumference. (not yet active)
- 442: Exam Practice: Circle theorems
- 444: Exam Practice: Proofs of circle theorems
Further Practice
- Practise Questions
Extension Materials
Worksheet
1.4 The Angles in Same Segments are Equal
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Angles in the Same Segment Proof
Online Platforms (with Videos & Exercises)
Activities & Resources
- Ben Sparks (GeoGebra)
- Angles in the Same Segment Proof: GeoGebra
- Interactive Maths
Worksheets
Dr Frost Resources
Dr Frost Video
K646: Know That Angles in the Same Segment are Equal.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 442b: Know that angles in the same segment are equal.
- 444c: Prove that angles in the same segment are equal. (not yet active)
- 442: Exam Practice: Circle theorems
- 444: Exam Practice: Proofs of circle theorems
Further Practice
- Practise Questions
Extension Materials
Worksheet
1.5 Opposite Angles in a Cyclic Quadrilateral Sum to 180 Degrees
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Angles in a Cyclic Quadrilateral Proof
Online Platforms (with Videos & Exercises)
- Khan Academy
- Inscribed shapes & cyclic quadrilaterals: Videos & practice
Activities & Resources
- Don Steward
- Ben Sparks (GeoGebra)
- Opposite Angles in a Cyclic Quadrilateral Proof: GeoGebra
- Interactive Maths
- Go Teach Maths
Worksheets
Dr Frost Resources
Dr Frost Video
K647: Know That Opposite Angles in a Cyclic Quadrilateral Add to 180.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 442d: Know that opposite angles in a cyclic quadrilateral add to 180.
- 444d: Prove that opposite angles of a cyclic quadrilateral add to 180^° (not yet active)
- 442: Exam Practice: Circle theorems
- 444: Exam Practice: Proofs of circle theorems
Further Practice
- Practise Questions
Extension Materials
Activities
1.6 The Perpendicular Bisector of a Chord Passes Through the Centre
Teaching Videos, Exercises & Activities
Tutorial Videos
Circle Geometry Grade 11 : Line from Center by Kevinmathscience
Circle Theorems: Line drawn from centre perpendicular to chord by Math Truly
Distance from Center of Circle to Chord by GeometryConceptVideos
Online Platforms (with Videos & Exercises)
Activities & Resources
- Ben Sparks (GeoGebra)
- Chord Bisector Proof: GeoGebra
- Go Teach Maths
Worksheets
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 317b: Understand and use the relationship between a chord and its perpendicular bisector.
- 317c: Determine the length of a perpendicular bisector of a chord in a circle.
- 317d: Use the property that equal chords are equidistant from the centre of a circle.
- 317: Exam Practice: Further terms in relation to circles, including chord and segment
Further Practice
- Practise Questions
Extension Materials
Worksheet
1.7 The Angle Between the Tangent and Radius is a Right Angle
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Radius Tangent Proof
Online Platforms (with Videos & Exercises)
- Khan Academy
- Tangents of circles: Videos & practice
Activities & Resources
- Don Steward
- Ben Sparks (GeoGebra)
- Tangent and Radius Proof: GeoGebra
- Interactive Maths
Worksheets
Dr Frost Resources
Dr Frost Video
K644: Know That Angle Between a Tangent and the Radius at the Point of Contact is 90.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 442e: Know that the angle between a tangent and the radius at the point of contact is 90.
- 442h: Use Pythagoras’ theorem alongside circle theorems.
- 442: Exam Practice: Circle theorems
Further Practice
- Practise Questions
Extension Materials
Worksheet
1.8 The Angles in Alternate Segments are Equal
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Alternate Segment Theorem Proof
Dr Frost Resources
Dr Frost Video
K648: Know That the Angle Between the Tangent and a Chord is Equal to the Angle in the Alternate Segment.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 442f: Know that the angle between the tangent and a chord is equal to the angle in the alternate segment (alternate segment theorem / tangent-chord theorem).
- 444e: Prove the alternate segment theorem / tangent-chord theorem. (not yet active)
- 442: Exam Practice: Circle theorems
- 444: Exam Practice: Proofs of circle theorems
Further Practice
- Practise Questions
Extension Materials
Worksheet
2.1 Intersecting Chords: Intersecting within a Circle (& Whole Intersecting Chords Resources)
Teaching Videos, Exercises & Activities
Tutorial Videos
Circle Theorems: Intersecting Chords – IGCSE Maths by Addvance Maths
Online Platforms (with Videos & Exercises)
Activities & Resources
- Transum
- Interactive Maths
- Intersecting Chords: GeoGebra
- Go Teach Maths
Worksheets
- Corbettmaths
- Intersecting Chords Practice Questions & Solutions
- Mathshelper (Jon Stone)
Dr Frost Resources
Dr Frost Video
Intersecting Chord and Intersecting Secant Theorems
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 443a: Use the intersecting chord theorem to determine an unknown length.
- 443b: Use the intersecting chord theorem to determine the radius of a circle.
- 443c: Use the intersecting chord theorem to form and solve a quadratic equation.
- 443g: Combine the intersecting chord and intersecting secant theorems.
- 444f: Prove the intersecting chord theorem. (not yet active)
- 443: Exam Practice: Intersecting chord and intersecting secant theorems
- 444: Exam Practice: Proofs of circle theorems
Further Practice
- Practise Questions
Extension Materials
Worksheet
2.2 Intersecting Chords: Two Chords Intersecting Outside a Circle
Teaching Videos, Exercises & Activities
Tutorial Videos
Intersecting Secants Theorem by MathSux
GCSE Tutorial Intersecting Chord Theorem Tangent Secant linked pair) by ukmathsteacher
Power Theorems – Chords, Secants & Tangents – Circle Theorems – Geometry by The Organic Chemistry Tutor
Online Platforms (with Videos & Exercises)
Activities & Resources
Worksheets
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 443d: Use the intersecting secant theorem to form and solve a linear equation.
- 443f: Use the intersecting secant theorem to form and solve a quadratic equation.
- 444g: Prove the intersecting secant theorem. (not yet active)
- 443: Exam Practice: Intersecting chord and intersecting secant theorems
- 444: Exam Practice: Proofs of circle theorems
Further Practice
- Practise Questions
Extension Materials
Worksheet
2.3 Intersecting Chords: One Chord, One Tangent
Teaching Videos, Exercises & Activities
Tutorial Videos
Tangent and Secant Theorem by MathSux
Proving the tangent secant theorem by Joel Speranza Math
Online Platforms (with Videos & Exercises)
Activities & Resources
Worksheets
- MadAsMaths (T. Madas)
- Advanced Mensuration Q5 (difficulty 5 of 5)
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 443e: Use the intersecting secant theorem involving a secant and a tangent. (not yet active)
- 443: Exam Practice: Intersecting chord and intersecting secant theorems
Further Practice
- Practise Questions
Extension Materials
Worksheet
2.4 Intersecting Chords: Two Tangents are Equidistant from a Point to a Circle
Teaching Videos, Exercises & Activities
Tutorial Videos
Proof: Segments tangent to circle from outside point are congruent by Khan Academy
TANGENT LINES AND CIRCLES EXPLAINED! by Mashup Math
Inscribed Polygons and Circumscribed Polygons, Circles – Geometry by The Organic Chemistry Tutor
Online Platforms (with Videos & Exercises)
Activities & Resources
- Don Steward
- Ben Sparks (GeoGebra)
- Tangents from a Point Proof: GeoGebra
- Interactive Maths
- Goal Free Problems
Worksheets
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 442g: Know that tangents which meet at the same point are equal in length (possibly involving other circle theorems).
- 442y: Solve problems involving multiple pairs of tangents to a circle.
- 442: Exam Practice: Circle theorems
Further Practice
- Practise Questions
Extension Materials
Worksheet
Whole Topic Summary Resources (Including Past Paper Questions)
Download Circle Theorems PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic Resources
Acute Learning Problem Pairs
- Circle theorems as PowerPoint or PDF
Videos & Other Multimedia
Corbett Maths Circle Theorems
Corbett Maths Circle Theorem Questions
Sound Understanding The Circle of Theorems
Activities & Resources
- Transum Matching Pairs Activity
- NRICH (student problems)
- Don Steward
- m34maths
Worksheets
- Corbettmaths
- Circle Theorems Practice Questions & Solutions
- Circle Theorems Worksheet & Solutions
- Circle Theorems Proof Worksheet & Video Solutions
- Circle Theorems AQA Level 2 Practice Questions & Solutions
- Dr Austin Maths
- Maths 4 Everyone
- MathedUp
- Circle Theorems: Worksheet · Practice · Quiz · Question Gallery
- Circle Theorems & Proof: Worksheet · Practice · Quiz · Question Gallery
- Mathsaurus (Kevin Olding)
- Chelekmaths (@MrLevMaths)
External Whole Topic Past Paper Style Questions
- Transum
- Exam-style questions: Circle
- NCETM
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.