Number PatternsCirclesMedium
The Circle Oracle
One angle at the centre quietly fixes the angle out at the rim.
Worked demonstration
PQ is a diameter of a circle and R is another point on the circle, so angle PRQ is a right angle. If angle RPQ is 47°, what is angle RQP, 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)