Number PatternsCirclesMedium
The Circle Oracle
One angle at the centre quietly fixes the angle out at the rim.
Worked demonstration
In a circle, the angle at the centre standing on an arc is 106°. A point on the major arc forms the angle at the circumference on the same arc. By the circle theorem, what is that angle, 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)