Notes
angles in the same segment

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Angles in the Same Segment are Equal

Angles in the same segment are equal.

Start with a chord drawn in a circle and join the ends to a point on the circumference of that circle. The angle formed depends only on which segment the point lies in.

This is a simple consequence of the fact that the angle at the circumference is half that at the centre. Since the angle at the centre doesn’t depend on where the point on the circumference is chosen, the angle at the circumference also doesn’t depend on this choice.

category: circle theorems

Revised on June 22, 2021 21:39:24 by Andrew Stacey
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