I plan to post problems which are just our national level. neither IMO nor divisional. I believe the practice for contest works best of it is in the contest range. So, please post no problem which are too hard or too easy.

Personally, I am going to post which I can't solve yet. But, I hope people will share what they can do with hidden solutions.

Just, do one favour. Post problems with category types. I mean, tag a category name with the problem. Just as you think it can be. Because, before solving one may not know how easy or hard it is.

If, this topic goes on, I think the participants who are first or second to attend BdMO and shy to post their problems here (believe me, there is a lot of people like this I know) will also be helpful by just going through the post.

Moreover, if it turns out that, only I am the problem poster, I'll make arrangements to edit the topic name as "Help me preparing for BdMO national 2013"

**$1.$ Pentagon equlibrium.**

Secondary, Higher Secondary (and Junior may be)

from Plane Euclidean Geometry (p-98)$AB=BC=CD=DE=EA$

Secondary, Higher Secondary (and Junior may be)

from Plane Euclidean Geometry (p-98)

$F$ is an arbitary point in $AE$ arc of the circumcircle.

prove,

\[FA+FC+FE=FB+FD\]