Number PatternsCirclesMedium
The Circle Oracle
One angle at the centre quietly fixes the angle out at the rim.
Worked demonstration
ABCD is a cyclic quadrilateral — all four corners lie on one circle. Angle A measures 73°. What is the opposite angle C, in degrees?
Try it yourself
Why it works
The angle at the centre is twice the angle at the circumference on the same arc — a fixed relationship that forces the answer.
Background & Explore Further
Circle theorems govern camera lenses, satellite dishes and the carpenter's use of Thales' theorem to find right angles. Explore the family of angle relationships inside a circle.
Maths Made Magic — Queen Mary University of London (cs4fn)