Definition

Compass-and-straightedge or ruler-and-compass construction is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

Tools

The compass can be opened arbitrarily wide, but it has no markings on it. Circles can only be drawn starting from two given points: the centre and a point on the circle. The compass collapses when it's not drawing a circle, so it cannot be used to copy a length to another place.

The straightedge is infinitely long, but it has no markings on it and has only one edge, unlike ordinary rulers. It can only be used to draw a line segment between two points or to extend an existing line.

Rules

Each construction must be exact. "Eyeballing it" and getting close does not count as a solution. Each construction must terminate. That is, it must have a finite number of steps, and not be the limit of ever closer approximations.

Constructions

All compass and straightedge constructions consist of repeated application of five basic constructions using the points, lines and circles that have already been constructed.

These are: Creating the line through two existing points
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Creating the circle through one point with centre another point
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Creating the point which is the intersection of two existing, non-parallel lines

Creating the one or two points in the intersection of a line and a circle (if they intersect)
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Creating the one or two points in the intersection of two circles (if they intersect)