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IMO 1968 — Shortlist problems Question 10

IMO Shortlist · IMO 1968 — Shortlist problems

Question 10

(ROM 4) 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?