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find angle C when (a^3+b^3+c^3)/(a+b+c)= c^2

Source: 1997 Estonia National Olympiad Final Round grade 11 p2

March 11, 2020

Triangleanglesgeometry

Problem Statement

Side lengths

a,b,c

of a triangle satisfy

\frac{a^3+b^3+c^3}{a+b+c}= c^2

. Find the measure of the angle opposite to side

c