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Source: IMO LongList 1959-1966 Problem 47

September 2, 2004
geometrytrigonometryarea of a trianglecountingcombinatoricsIMO LonglistIMO Shortlist

Problem Statement

Consider all segments dividing the area of a triangle ABCABC in two equal parts. Find the length of the shortest segment among them, if the side lengths a,a, b,b, cc of triangle ABCABC are given. How many of these shortest segments exist ?
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