Problem #11
This month we have three related problems:

You are given an equilateral triangle whose sides have length 1 and a
circle of radius r centered at the centroid of the triangle. What
value of r will minimize to total area of the region consisting of
those points which either lie inside the circle but outside the triangle
or inside the triangle but outside the circle? See the figure below.
 What if the equilateral triangle is replaced by a square?
 By a regular ngon?