Problem #9

Given a straightedge with two parallel sides a given distance d apart, one can draw a line parallel to a given line at a distance d from it and one can draw parallel lines between any two points if the distance between the points is greater than d. Using only such a straightedge, give a general procedure for the following constructions.

• Bisect a given angle.
• Bisect a given segment.
• Construct a line parallel to a given line through a point not on the given line.
• Construct a line through a point that is perpendicular to a given line.

Which of the constructions above can be done if you are only allowed to use the straightedge to draw a line parallel to a given line at a distance d from it?

Source: Inspired by a problem proposed, but not used, for the IMO

The solution will be posted shortly.

Back to the Archives