Circle Theorem: Angles in the Same Segment Are Equal
(KS3, Year 8)
The LessonAll 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
QuestionWhat is the angle θ in the circle below?
The angles subtended by the chord at the circumference of the circle are equal.
θ = 40°
Answer:The angle θ is 40°.
Lesson SlidesThe slider below shows a real example of the circle theorem where the angles in the same segment are equal. Open the slider in a new tab
Useful DefinitionsA 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.
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