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Circle Theorem: Angles in the Same Segment Are Equal (Mathematics Lesson)

Circle Theorem: Angles in the Same Segment Are Equal

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

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

Question: 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°

A Real Example of How to Use the Circle Theorem that the Angles in the Same Segment Are Equal

The slider below shows a real example of the circle theorem that the angles in the same segment are equal:
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Geometry Lessons
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Note

USEFUL DEFINITIONS

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.