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Proposition: 3.34: Construction of Segment on Given Circle Admitting Given Angle

(Proposition 34 from Book 3 of Euclid's “Elements”)

To cut off a segment, accepting an angle equal to a given rectilinear angle, from a given circle. * Let $ABC$ be the given circle, and $D$ the given rectilinear angle. * So it is required to cut off a segment, accepting an angle equal to the given rectilinear angle $D$, from the given circle $ABC$.

Modern Formulation

It is possible to construct segment of a circle, such that its inscribed angle ($\angle{CAB}$) is equal to a given rectilinear angle ($\angle D$) and its vertex ($A$) is located on this segment.

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References

Adapted from (subject to copyright, with kind permission)

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

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016