MathDB

15

Part of 2014 Harvard-MIT Mathematics Tournament

Problems(1)

2014 Guts #15: Pivot Lines in a Pentagon

Source:

4/20/2014
Given a regular pentagon of area 11, a pivot line is a line not passing through any of the pentagon's vertices such that there are 33 vertices of the pentagon on one side of the line and 22 on the other. A pivot point is a point inside the pentagon with only finitely many non-pivot lines passing through it. Find the area of the region of pivot points.
geometry