The Lesson

All triangles drawn from a chord in a circle make the same angle at the circumference.

How to Use the Circle Theorem where the Angles in the Same Segment Are Equal


What is the angle θ in the circle below?



The angles subtended by the chord at the circumference of the circle are equal.
θ = 40°


The angle θ is 40°.

Lesson Slides

The slider below shows a real example of the circle theorem where the angles in the same segment are equal.

Useful Definitions

A semicircle is half a circle. A chord is a line whose endpoints lie on the circle.

A segment is a region, not containing the center, bounded by a chord and an arc lying between the chord's endpoints.