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Problems Geometry Plane geometry Geometrical inequalities Inequalities in a triangle Inequalities in a triangle involving medians

13–13 2.0

Prove that $(a + b - c) / 2 < m_{c} < (a + b) / 2$ , where $a$ , $b$ and $c$ are the lengths of the sides of an arbitrary triangle and $m_{c}$ is the median to side $c$ .