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max line segment that bisects perimeter of triangle

Source: Czech and Slovak Olympiad 1979, National Round, Problem 5

September 13, 2024
geometryperimeterExtremisation

Problem Statement

Given a triangle ABCABC with side sizes a≥b≥ca \ge b \ge c. Among all pairs of points X,YX, Y on the boundary of triangle ABCABC, which this boundary divides into two parts of equal length, find all such for which the distance is XYX Y maximum.
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