ILL 1967 Problem 53

In making Euclidean constructions in geometry it is permitted to use a ruler and a pair of compasses. In the constructions considered in this question no compasses are permitted, but the ruler is assumed to have two parallel edges, which can be used for constructing two parallel lines through two given points whose distance is at least equal to the breadth of the rule. Then the distance between the parallel lines is equal to the breadth of the ruler. Carry through the following constructions with such a ruler. Construct:

a) The bisector of a given angle. b) The midpoint of a given rectilinear line segment. c) The center of a circle through three given non-collinear points. d) A line through a given point parallel to a given line.