Problem

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Tags: geometry, triangle inequality, IMO Shortlist



Consider two segments of length $a, b \ (a > b)$ and a segment of length $c = \sqrt{ab}$. (a) For what values of $a/b$ can these segments be sides of a triangle ? (b) For what values of $a/b$ is this triangle right-angled, obtuse-angled, or acute-angled ?