Given a triangle let denote the median points of the sides respectively. Prove that

where denotes the the circumradius and the inradius respectively.

*(Adil Abdullayev / RMM)*

**Solution **[Soumava Chakraborty]

We have successively

In all the above denotes the semiperimeter of the triangle. More on Gerretsen’s inequality can be found at this link .