MathNet 2015-part-02 — 191 problems (EN–VI) Question 117

On a circle of radius $r$, the distinct points $A, B, C, D$, and $E$ lie in this order, satisfying $AB = CD = DE \gt r$. Show that the triangle with vertices lying in the centroids of the triangles $ABD$, $BCD$, and $ADE$ is obtuse.