Constructions (other)

Beyond the basic constructions, many geometric problems require constructing more complex figures or points, such as dividing a segment into $n$ equal parts, constructing tangents from a point to a circle, or finding centers of special circles (like the incircle or circumcircle) of a triangle. These constructions are achieved by combining basic steps and sometimes require clever use of geometric properties.

Important properties

• All constructions must use only a straightedge and compass.

• Complex constructions are built from sequences of basic constructions.

• Many constructions rely on properties of triangles, circles, and parallel/perpendicular lines.

• Some constructions, like trisecting an angle, are impossible with just straightedge and compass.