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Smallest halving cevian

Source: China Southeast Math Olympiad 2015 Day 2 P6

June 6, 2017
geometry

Problem Statement

In △ABC\triangle ABC, we have three edges with lengths BC=a, CA=b AB=cBC=a, \, CA=b \, AB=c, and c<b<a<2cc<b<a<2c. PP and QQ are two points of the edges of △ABC\triangle ABC, and the straight line PQPQ divides △ABC\triangle ABC into two parts with the same area. Find the minimum value of the length of the line segment PQPQ.
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