  The equitangent locus of a convex plane curve consists of the points from
which the two tangent segments to the curve have equal length. The equitangent
problem concerns the relation between the curve and its equitangent locus. An
equitangent n-gon of a convex curve is a circumscribed n-gon whose vertices
belong to the equitangent locus. We are interested in curves that admit
1-parameter families of equitangent n-gons. We use methods of sub-Riemannian
geometry: we define a distribution on the space of polygons and study its
bracket generating properties. 1-parameter families of equitangent polygons
correspond to the curves, tangent to this distribution. This distribution is
closely related with the Birkhoff distribution on the space of plane polygons
with a fixed perimeter length whose study, in the framework of the billiard
ball problem, was pioneered by Yu. Baryshnikov, V. Zharnitsky and J. Landsberg
