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Minimum value of all the longest side

Source: CMO-1996-6

January 3, 2006
geometryCanada

Problem Statement

In the triangle ABCABC, ∠C=90∘,∠A=30∘\angle{C}=90^{\circ},\angle {A}=30^{\circ} and BC=1BC=1. Find the minimum value of the longest side of all inscribed triangles (i.e. triangles with vertices on each of three sides) of the triangle ABCABC.
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