STRAIGHT-LINE AND COMPASS CONSTRUCTIONS.

Problem 1

1. Given a line segment, find the mid-point of that segment.

Solution

1. Let the endpoints of the line be a and b.
2. Draw a circle of radius > 0.5ab (radius ab will suffice) centred on a; draw a circle with identical radius centered on b.
3. Let the points of intersection of these circles be c and d.
4. Construct the line cd.
5. The intersection of ab and cd will be a point, e, half-way between a and b.