Constructing the Set of Points a Fixed Distance From a Given Line
To construct the set of points a fixed distance x from a line AB, with a set of compasses draw circles of radius x with centres at A and B, then draw tangents from one circle to another, parallel to the line.
For example, construct the set of points 2 cm from the line AB below.
Use a compass to draw circles of radius 2 cm with centres at A and B.
Draw tangent lines from the circle at A to the circle at B.
The outside contour is the set of points required.