To draw a segment of a circle, accepting an angle equal to a given rectilinear angle, on a given straight line.
It is possible to construct segment of a circle, such that its inscribed angle (in the three illustrated cases above the respective angles $\angle{ABE}$, $\angle{AEB}$, and $\angle{AHB}$) is equal to a given rectilinear angle (in the three illustrated cases above the respective acute $\angle{C}$ , right $\angle{C}$, and obtuse $\angle{C}$) and its legs are adjacent to a given chord ($\overline{AB}$) of this circle.
Proofs: 1
Sections: 1