Core Circle Theorems
Angle at the centre is always twice the angle at the circumference when both angles are formed by the same two points on the circle. This is one of the most useful theorems you'll encounter – if you spot an angle at the centre, you immediately know the circumference angle is half that size.
Cyclic quadrilaterals are four-sided shapes where all vertices touch the circle's edge. The key rule here is simple: opposite angles always add up to 180°. So if one angle is 70°, the opposite one must be 110°.
Angles in a semicircle are always 90°. Whenever you see an angle formed by drawing lines from both ends of a diameter to any point on the circumference, you've got yourself a right angle – no measuring needed!
Angles subtended by the same arc are equal. If two angles are created using the same two points on the circumference, they'll always be identical in size.
Quick tip: Look for the centre of the circle first – it often holds the key to solving the problem!
