Question 32
In the plane there are $2012$ congruent triangles of area $1$ which all have the same orientation. Each of these triangles contains the centroids of all the other triangles.
a. Show that the intersection of the $2012$ triangles is a triangle similar to them with area at least $\frac{1}{9}$.
b. Show that the area of the union of these triangles is less than $\frac{22}{9}$.
a. Show that the intersection of the $2012$ triangles is a triangle similar to them with area at least $\frac{1}{9}$.
b. Show that the area of the union of these triangles is less than $\frac{22}{9}$.