3 Oct 2013

APMO 1992 Q1: A Semiperimeter Problem: Upper Secondary Mathematics Competition Question

A triangle with sides a, b and c is given. Denote by s the semiperimeter, that is, s = (a+b+c)/2. Construct a triangle with sides s-a, s-b, and s-c. This process is repeated until a triangle can no longer be constructed with the side lengths given.

For which original triangles can this process be repeated indefinitely?

[APMO 1992 Q1]

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