CAPS 2015 Problem 1

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

Proposed by Tomáš Jurík, Slovakia