olymmath

APMO 1992 Problem 1

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A triangle with sides a,ba, b, and cc is given. Denote by ss the semiperimeter, that is s=(a+b+c)/2s=(a+b+c) / 2. Construct a triangle with sides s−a,s−bs-a, s-b, and s−cs-c. This process is repeated until a triangle can no longer be constructed with the sidelengths given. For which original triangles can this process be repeated indefinitely?

Dataset text NuminaMath olympiads. Quoted with source.

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a=b=c

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