Hi!

I must make some observation after i read all the comments to the problem :

1. The first statement of my problem was : 'Prove that in an acute triangle .........'.

2.Charlie see that the relation work for any kind of triangle. I verify with computer what Charlie observe and I modify the statement, but i haven't a solution for 'any triangle'.

3. My solution is like Dennis solution (all credits for him!) only for 'acute triangle'.

4. After this, Praneeth, give a very easy and clever solution for all kind of triangle. Well done Praneeth!

I'm glad for this colaboration!

Idea - observation - solution!