  We propose a general framework for geometric approximation of circular arcs
by parametric polynomial curves. The approach is based on constrained uniform
approximation of an error function by scalar polynomials. The system of
nonlinear equations for the unknown control points of the approximating
polynomial given in the B\'ezier form is derived and a detailed analysis
provided for some low degree cases which might be important in practice. At
least for these cases the solutions can be, in principal, written in a closed
form, and provide the best known approximants according to the radial distance.
A general conjecture on the optimality of the solution is stated and several
numerical examples conforming theoretical results are given.
