1. The problem statement, all variables and given/known data Here it is: Let Ω be a convex region in R2 and let L be a line segment of length ι that connects points on the boundary of Ω. 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 Ω that bounds a (smaller) region Γ. Find an expression that relates the area of Γ to the area of Ω in terms of the length ι. 2. Relevant equations See above. 3. The attempt at a solution I have no idea. This is well beyond the scope of our course. The instructor put this out to get his students to reach out to the mathematics community and get involved in discussions of (multivariable) calculus. The closest I have come to encountering such a problem is related rates, but I have no idea how to do this.