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Triangle function - find the set of values

Source: Romanian IMO Team Selection Test TST 1988, problem 14

October 1, 2005
functioninequalities proposedinequalities

Problem Statement

Let Δ\Delta denote the set of all triangles in a plane. Consider the function f:Δ→(0,∞)f: \Delta\to(0,\infty) defined by f(ABC)=min⁡(ba,cb)f(ABC) = \min \left( \dfrac ba, \dfrac cb \right), for any triangle ABCABC with BC=a≤CA=b≤AB=cBC=a\leq CA=b\leq AB = c. Find the set of values of ff.
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