On this day in 1809, Joseph Liouville was born. Also on this day in 1721, Johann Sebastian Bach published his famous Brandenburg Concertos which he dedicated to Christian Ludwig, Margrave of Brandenburg-Schwedt.
Today, I am posting two simple geometry questions. Since it's a weekend, feel free to take your time and enjoy them. Or, if you're feeling slightly more competitive, try to time yourself to see how quickly you can get the answers.
Question 1:
In the diagram above, given that F is the midpoint of CD and that 
Question 2: In the diagram below, arc IFJ is one-quarter of a circle with center H. Given that HJ = IH = 6, and that EFGH is a rectangle with EH + HG = 8, what is the perimeter of the shaded region?
