Circle Theorems Mastery
The Ultimate Step-by-Step Visual Guide for GCSE & O-Levels
Hello Students! Circle geometry doesn't have to be a mystery. Once you stop seeing lines and start seeing relationships, these questions become the easiest marks on your exam paper. Today, we decode the 7 "Golden Rules" of circles.
Visual Learning is Better!
Watch me solve actual past paper questions using these 7 theorems.
Watch Video LessonThe 7 Essential Theorems
Angle at the Centre
The angle subtended by an arc at the centre is exactly double the angle at the circumference.
Teacher's Hint: Look for the "Arrowhead" shape!
Angles in the Same Segment
Angles subtended by the same arc at the circumference are always equal.
Teacher's Hint: This is the famous "Bow-Tie" theorem.
Angle in a Semicircle
Any angle drawn from a diameter to the circumference is a perfect 90° right angle.
Cyclic Quadrilaterals
In a 4-sided shape where all corners touch the circle, opposite angles always add up to 180°.
The Tangent-Radius Rule
A tangent line meets the radius at exactly 90°. They are perpendicular at the point of contact.
Tangents from a Point
Two tangents drawn from the same external point are identical in length.
Alternate Segment Theorem
The angle between a tangent and a chord equals the angle in the opposite segment.
💡 Expert Exam Strategy
- State the Theorem: You must write the name of the theorem to get the "Reasoning" mark.
- Radii are Radii: Always mark all radii in a diagram. They create isosceles triangles!
- Check for Centers: If O is marked, Theorem 1 and 5 are likely needed.
📝 Practice Makes Perfect
Solve these problems and compare your answers with my video explanation.
