Let $ABC$ be a triangle with centroid $T$. Denote by $M$ the midpoint of $BC$. Let $D$ be a point on the ray opposite to the ray $BA$ such that $AB = BD$. Similarly, let $E$ be a point on the ray opposite to the ray $CA$ such that $AC = CE$. The segments $T D$ and $T E$ intersect the side $BC$ in $P$ and $Q$, respectively. Show that the points $P, Q$ and $M$ split the segment $BC$ into four parts of equal length.
Problem
Source: Czech-Polish-Slovak Match Junior 2019, individual p2 CPSJ
Tags: geometry, Centroid, equal segments