MathNet 2015-part-02 — 191 problems (EN–VI) Question 79

A magical triangulation is a partition of a triangle on smaller triangles by a finite number of segments whose endpoints are vertices of the triangle or points in its interior, such that in every point (including the vertices of the triangle) meets the same number of segments.
What is the maximal number of smaller triangles on which we can divide the triangle in a magical triangulation?