MathNet 2017-part-01 — 176 problems (EN–VI) Question 161

We call a point $P$ inside a triangle $ABC$ marvelous if exactly $27$ rays can be drawn from it, intersecting the sides of $ABC$ such that the triangle is divided into $27$ smaller triangles of equal areas. Determine the total number of marvelous points inside a given triangle $ABC$.
(Naboj)