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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)

The Circle Oracle — Math Magic Trick of the Day | HelloBanaras