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Acute triangle contained in right triangle

Source: Czech and Slovak Olympiad 1975, National Round, Problem 1

July 20, 2024
geometryacuteTriangleright triangleareatriangle area

Problem Statement

Let T\mathbf T be a triangle with [T]=1.[\mathbf T]=1. Show that there is a right triangle R\mathbf R such that [R]≤3[\mathbf R]\le\sqrt3 and T⊆R.\mathbf T\subseteq\mathbf R. ([−][-] denotes area of a triangle.)
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