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triangle of medians of ABC similar to ABC criterion

Source: 2011 Saudi Arabia Pre-TST February 2.4 https://artofproblemsolving.com/community/c2745403_2011_

January 1, 2022
similar trianglesgeometryMediansmedian

Problem Statement

Let ABCABC be a triangle with medians mam_a , mbm_b, mcm_c. Prove that: (a) There is a triangle with side lengths mam_a ,mbm_b, mcm_c. (b) This triangle is similar to ABCABC if and only if the squares of the side lengths of triangle ABCABC form an arithmetical sequence.
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