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Medians: (2a/3, 2b/3, 4c/5) then triangle is impossible

Source: ISI (BS) 2007 #4

April 11, 2012
geometry proposedgeometry

Problem Statement

Show that it is not possible to have a triangle with sides a,b,a,b, and cc whose medians have length 23a,23b\frac{2}{3}a, \frac{2}{3}b and 45c\frac{4}{5}c.
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