Consider all segments dividing the area of a triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
in two equal parts. Find the length of the shortest segment among them, if the side lengths
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
of triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
are given. How many of these shortest segments exist ?
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Consider all segments dividing the area of a triangle $ABC$ in two equal parts. Find the length of the shortest segment among them, if the side lengths $a,$ $b,$ $c$ of triangle $ABC$ are given. How many of these shortest segments exist ?