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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.