Question

Let W be a convex region in R2 and let L be a line segment of length I that connects points on the boundary
of W. As we move one end of L around the boundary, the other end will also move about this boundary, and the
midpoint of L will trace out a curve within W that bounds a (smaller) region G. Find an expression that relates
the area of G to the area of W in terms of the length I of the line segment.