Proof: By Euclid

(related to Proposition: 3.34: Construction of Segment on Given Circle Admitting Given Angle)

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Adapted from (subject to copyright, with kind permission)

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


  1. Presumably, by finding the center of $ABC$ [Prop. 3.1], drawing a straight line between the center and point $B$, and then drawing $EF$ through point $B$, at right angles to the aforementioned straight line [Prop. 1.11] (translator's note). 

  2. It has been shown that it is possible to construct segment of a circle, such that its inscribed angle is equal to a given rectilinear angle and its vertex is located on this segment.