Circle Theorems - The Essential Seven
Ever wondered why certain angles in circles behave predictably? Circle theorems give you the power to work out missing angles using reliable geometric rules.
First, let's sort out the key parts of a circle. The radius goes from centre to edge, whilst the diameter crosses the whole circle through the centre. A tangent touches the circle at exactly one point, and a chord connects two points on the circumference.
Here are the seven theorems you absolutely must know. The angle at the centre is twice the angle at the circumference when they subtend the same arc. Angles in the same segment are equal - this means angles that "look at" the same arc from the circumference will always match.
The alternate segment theorem states that the angle between a tangent and chord equals the angle in the opposite segment. Opposite angles in a cyclic quadrilateral add up to 180°, whilst any angle in a semicircle equals 90°. Finally, tangents from the same external point are equal in length, and the angle between a tangent and radius at the point of contact is 90°.
Remember: These theorems work every single time - no exceptions! Learning to spot which theorem applies is half the battle.
