
102 Ruler-and-Compass Constructions
EXERCISES
7.1 Express in the language of this chapter methods of constructing, by ruler and
compasses:
(a) The perpendicular bisector of a line.
(b) The points trisecting a line.
(c) Division of a line into n equal parts.
(d) The tangent to a circle at a given point.
(e) Common tangents to two circles.
7.2 Estimate the degrees of the field extensions corresponding to the constructions
in Exercise 7.1, by giving reasonably good upper bounds.
7.3 Prove using Euclidean geometry that the ‘marked ruler’ construction of Fig-
ure 11 does indeed trisect the given angle AOB.
7.4 Can the angle 2π/5 be trisected using ruler and compasses? ...