Definition: 3.08: Angle in the Segment (Inscribed Angle)
And the angle in a segment is the angle contained by the joined straight lines, when any point is taken on the circumference of a segment, and straight lines are joined from it to the ends of the straight line which is the base of the segment.
An inscribed angle is the angle $\alpha$ contained by the straight lines joining the ends of the arc $AB$ with any point on the circumference of a segment of the circle.
Proofs: 2 3 4 5 6 7 8
Propositions: 9 10 11 12 13 14 15
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"