MathDB

1

Part of 1992 APMO

Problems(1)

Construct a triangle

Source: APMO 1992

3/11/2006
A triangle with sides aa, bb, and cc is given. Denote by ss the semiperimeter, that is s=a+b+c2s = \frac{a + b + c}{2}. Construct a triangle with sides s−as - a, s−bs - b, and s−cs - 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?
geometryinequalitiesgeometric inequalityAPMO