We introduce and investigate the concept of a discrete circle in the triangular grid, taking into account the presence of two distinct types of triangles, depending on their orientation. We propose an analytical definition of a discrete circle in this grid, incorporating a non-constant thickness that depends on both the type of the considered triangle and the position of the circle’s center. This varying thickness ensures the edge connectivity of the resulting circle. Building on this analytical definition, we also propose an incremental generation algorithm that is linear in the number of triangles on the circle.