Circle Theorems: A tangent and radius are perpendicular at the point of contact
In this lesson, we will learn that a tangent and radius are perpendicular at the point of contact. We will prove this result with a general case.
Unit Overview: Circle Theorems 2
Lessons:
4 lessons
Circle Theorems: The alternate segment theorem
In this lesson, we will learn that an angle made with a chord and tangent is equal to the angle subtended by the chord in the alternate segment. We will prove this result with a general case.
Circle Theorems: The perpendicular from the centre to a chord bisects the chord
In this lesson, we will learn that a perpendicular from the centre to a chord bisects the chord. We will prove this result with a general case.
Mixed circle theorem problems
In this lesson, we will practise answering different circle theorem problems that will require us to recall knowledge from each of the circle theorems.
Units in Maths
- Simplifying Surds
- Adding surds
- Multiplying Surds
- Dividing and Rationalising surds
- Solving equations 2 (Simple algebraic fractions)
- Algebraic Fractions
- Factorise and solve a quadratic (a=1)
- Factorise and solve quadratics (a > 1)
- Substitution and Rearranging formulae
- Further Algebra (Change the subject/Binomial expansion)
- Similarity
- Trigonometry 1
- Trigonometry 2
- Trigonometry 3
- Types of Numbers and Rules of Indices
- Negative and Fractional Indices
- Recurring decimals
- Upper and Lower Bounds
- Straight Line Graphs (y=mx+C)
- Straight Line Graphs 2 (Parallel Lines)
- Higher Straight lines (Perpendicular Lines)
- Simultaneous Equations (Linear)
- Scatter Diagrams & Frequency Trees & Averages
- Higher Data 1 (CF and Box Plots)
- Probability 2 (Sample space, Venn diagrams and experimental)
- Higher Probability (Conditional and Further Set Notation)
- Further Quadratic equations
- Quadratic Graphs 1 (a=1)
- Quadratic Graphs 2 (a>1)
- Quadratic sequences
- One linear and one quadratic simultaneous equations
- Parts of a Circle 1 & 2
- Volume and Surface Area 1 (Prisms)
- Volume 2
- Surface Area 2
- Volume and Surface Area 2
- Advanced Trigonometry 1
- Advanced Trigonometry 2
- Advanced Trigonometry 3
- Directed Numbers
- Rules of indices (numbers)
- Standard Form (Writing and converting)
- Standard Form 4 Operations
- Collecting, Indices, Expand and Simplify, Solving Equations 1
- Adding and Subtracting Fractions
- Rotation and Enlargement
- Pythagoras Theorem 1
- Pythagoras Theorem 2
- Factors Multiple and Primes
- Venn Diagrams
- HCF and LCM
- Rounding and Estimating
- Simple Graphs
- Scatter diagrams and Frequency trees
- Averages (From a list and tables, Stem and Leaf)
- Ratio 1 & 2
- Percentage increase and decrease
- Repeated Percentage Change
- Fractions 1, 2, and Fractional Change
- Parts of circles 1 (Semi and quarter circles)
- Parts of circles 2 (Arcs and Sectors)
- Cylinders
- Area and Perimeter
- 4 Rules of Number
- Types of numbers
- Collecting like terms, simplifying
- Expand and simplify brackets
- Rules of Indices
- Solving equations 1 (One step, Two Step and Brackets)
- Reflection
- Factorising (single bracket)
- Solve Inequalities and Represent on Number Line
- Linear Sequences
- Fraction equivalents
- Fractions 1 (adding and subtracting)
- Fractions 2 (multiplying and dividing)
- Fraction Change
- Percentages
- FDP Equivalents
- Decimals
- Ratio 1
- Circles
- Revise - Angles, Polygons, Bearings
- Circle Theorems 1
- Circle Theorems 2
- Functions
- Revise - Simultaneous Equations
- Charts and Tables (Pie Chart and Two way tables)
- Revise - Data (Mean Table, CF Charts)
- Probability 3 (Tree diagrams)
- Histograms
- Cubic and Reciprocal Graphs
- Travel Graphs
- Graphs of Inequalities
- Compound measures
- Volume and Surface Area 1 & 2
- Translate and Vectors 1
- Vectors 2
- Constructions
- Loci
- Angle Facts
- Parallel Lines and Polygons 1
- Polygons 2 (Interior and Exterior)
- Ratio 2 (Ratio and Fractions/Direct Proportion/Best Buy)
- Revise - Solving Equations
- Frequency charts (Data Collection, Bar and Pictograms)
- Probability 1 (Scale and equally likely events)
- Bearings
- Views and Maps
- Constructions & Loci
- Solve equations numerically (Iteration)
- Direct and Inverse Proportion
- Further Algebraic Fractions
- Algebraic Proof
- Circle Graphs
- Data Collection Higher
- Revise - Linear and Quadratic Graphs
- Other Graphs (Trig, Exponetial and Transformations)
- Further graphs (Gradients/Area of curves)
- Volume and Surface Area Higher 3
- Higher Vectors 1
- Higher Vectors 2 and Congruent Triangles
- Enlargement and Similarity
- Area and Perimeter
- Angle Facts
- Similarity
- Constructions & Loci
- Parts of circles 1 (Semi and quarter circles)
- Higher Vectors 1
- Parts of a Circle 1 & 2
- Trigonometry 1
- Circle Theorems 2
- Pythagoras Theorem 2
- Volume and Surface Area 1 (Prisms)
- Rotation and Enlargement
- Pythagoras Theorem 1
- Revise - Angles, Polygons, Bearings
- Views and Maps
- Reflection
- Advanced Trigonometry 1
- Volume and Surface Area 1 & 2
- Trigonometry 3
- Volume and Surface Area Higher 3
- Vectors 2
- Parallel Lines and Polygons 1
- Trigonometry 2
- Polygons 2 (Interior and Exterior)
- Loci
- Circle Theorems 1
- Advanced Trigonometry 2
- Enlargement and Similarity
- Advanced Trigonometry 3
- Circles
- Cylinders
- Bearings
- Higher Vectors 2 and Congruent Triangles
- Constructions
- Parts of circles 2 (Arcs and Sectors)
- Volume and Surface Area 2
- Translate and Vectors 1