Equal sections AC and BD are set aside from the ends of section AB in different directions. The distance between the midpoints of section AC and BD is a and the length of section CD is b. What is the length of segment AB?

Answer:
Equal sections AC and BD are set aside from the ends of section AB in different directions. The distance between the midpoints of section AC and BD is a and the length of section CD is b. What is the length of segment AB?