MathDB
Show that an angle is obtuse

Source: Czech-Polish-Slovak Match 2015, Problem 1

June 19, 2015
geometry

Problem Statement

On a circle of radius rr, the distinct points AA, BB, CC, DD, and EE lie in this order, satisfying AB=CD=DE>rAB=CD=DE>r. Show that the triangle with vertices lying in the centroids of the triangles ABDABD, BCDBCD, and ADEADE is obtuse.
Proposed by Tomáš Jurík, Slovakia