Compass-and-straightedge Construction
An idealized straightedge is used in compass-and-straightedge constructions in plane geometry. It may be used:
- Given two points, to draw the line connecting them.
- Given a point and a circle, to draw either tangent.
- Given two circles, to draw any of their common tangents.
It may not be marked or used together with the compass so as to transfer the length of one segment to another.
It is possible to do all compass and straightedge constructions without the straightedge. That is, it is possible, using only a compass, to find the intersection of two lines given two points on each, and to find the tangent points to circles. It is not, however, possible to do all constructions using only a straightedge. It is possible to do them with straightedge alone given one circle and its center.
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