There are six closed disc in plane such that none contains the centre of any other disc (even on the boundary). Show that they do not have a common point.
I tried using pigeon hole as this question was given in pigeon hole sheet but could not got any break through but now I got it thanks a lot
Let us reason by contradiction :
Assume there exists a point belonging to all these discs. Then consider the lines going from this point to the centers of the discs. What can you say about the angles between these lines?
You can then easily get to an absurdity from that. Therefore, you know the initial hypothesis is false.