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3 points split a segment into 4 equal parts wanted

Source: Czech-Polish-Slovak Match Junior 2019, individual p2 CPSJ

January 20, 2020
geometryCentroidequal segments

Problem Statement

Let ABCABC be a triangle with centroid TT. Denote by MM the midpoint of BCBC. Let DD be a point on the ray opposite to the ray BABA such that AB=BDAB = BD. Similarly, let EE be a point on the ray opposite to the ray CACA such that AC=CEAC = CE. The segments TDT D and TET E intersect the side BCBC in PP and QQ, respectively. Show that the points P,QP, Q and MM split the segment BCBC into four parts of equal length.
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