A puzzle I thought up

No.11025641 ViewReplyOriginalReport
If you can't solve this you don't belong on /sci/
It goes like this:
Prove that given n-1 points inside of a polygon with n sides, there will be a pair of points that can be connected by a line segment which lies entirely inside the polygon.

Bonus problem (you don't have to be able to solve this): can you improve this result to less than n-1 points?