  Straightedge and compass construction problems are one of the oldest and most
challenging problems in elementary mathematics. The central challenge, for a
human or for a computer program, in solving construction problems is a huge
search space. In this paper we analyze one family of triangle construction
problems, aiming at detecting a small core of the underlying geometry
knowledge. The analysis leads to a small set of needed definitions, lemmas and
primitive construction steps, and consequently, to a simple algorithm for
automated solving of problems from this family. The same approach can be
applied to other families of construction problems.
