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Definition: 3.09: Angle Standing Upon An Arc

And when the straight lines containing an angle cut off some circumference, the angle is said to stand upon that (circumference).

Modern Formulation

We say that the inscribed angle $\alpha$ stands upon the arc $AB$, if it is contained by the straight lines joining the ends of the arc $AB$ with any point on the circumference of a segment of the circle.

Mentioned in:

Proofs: 1 2 3 4 5
Propositions: 6 7 8

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References

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"