The goal of Geometric Constraint Solving is to find 2D or 3D placements of some geometric primitives fulfilling some geometric constraints. The common guideline is to solve them by a numerical iterative method (e.g. Newton-Raphson method). A sole solution is obtained whereas many exist. But the number of solutions can be exponential and methods should provide solutions close to a sketch drawn by the user. Assuming that a decomposition-recombination planner is used, we consider irreducible problems. Geometric reasoning can help to simplify the underlying system of equations by changing a few equations and triangularizing it. This triangularization is a geometric construction of solutions, called construction plan. We aim at finding several solutions close to the sketch on a one-dimensional path defined by a global parameter-homotopy using the construction plan. Some numerical instabilities may be encountered due to specific geometric configurations. We address this problem by changing on-the-fly the construction plan. Numerical results show that this hybrid method is efficient and robust.