An important issue in dynamic geometry is the reachability problem that asks whether there is a continuous path that, from a given starting geometric configuration, continuously leads to an ending configuration. In this work we report on a technique to compute a continuous evaluation path, if one exists, that solves the reachability problem for geometric constructions with one variant parameter. The technique is developed in the framework of a constructive geometric constraintbased dynamic geometry system, uses the A∗ algorithm and minimizes the variant parameter arc length.