Consider two segments of length a,b (a>b) and a segment of length c=√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 ?
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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=√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 ?