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AD = DE = EC = n, AB = 33, AC = 21,BC = m where m,n integers

Source: 1982 Swedish Mathematical Competition p4

March 28, 2021
geometryequal segments

Problem Statement

ABCABC is a triangle with AB=33AB = 33, AC=21AC = 21 and BC=mBC = m, an integer. There are points DD, EE on the sides ABAB, ACAC respectively such that AD=DE=EC=nAD = DE = EC = n, an integer. Find mm.