Question

Let the sides of a triangle be a, b, c and the lengths of the corresponding medians be `m_a , m_b, m_c`. Show that

`sum_{cyc} m_a / a >= {3( m_a + m_b + m_c)} /{a + b + c}`

Difficulty level (1 very easy - 10 very hard): 7

Topics:
Geometry -> Plane Geometry -> Triangles Algebra -> Inequalities Geometry -> Plane Geometry -> Triangle Inequality
Sources:
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