  The tangent method has recently been devised by Colomo and Sportiello
(arXiv:1605.01388 [math-ph]) as an efficient way to determine the shape of
arctic curves. Largely conjectural, it has been tested successfully in a
variety of models. However no proof and no general geometric insight have been
given so far, either to show its validity or to allow for an understanding of
why the method actually works. In this paper, we propose a universal framework
which accounts for the tangency part of the tangent method, whenever a
formulation in terms of directed lattice paths is available. Our analysis shows
that the key factor responsible for the tangency property is the concavity of
the entropy (also called the Lagrangean function) of long random lattice paths.
We extend the proof of the tangency to $q$-deformed paths.
