Circle Theorem: Angles in the Same Segment Are Equal
(KS3, Year 8)

All triangles drawn from a chord in a circle make the same angle at the circumference. circle theorem angles in same segment are equal

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

Question

What is the angle θ in the circle below?
angles in same segment equal example

Step-by-Step:

1

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

Answer:

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.

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

circle segment
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This page was written by Stephen Clarke.