Equilateral triangle ABC has a circle inscribed in it. Inside the circle is inscribed another equilateral triangle, DEF. What is the ratio of AB to DE? (Answer from back of book: 4 to 1). I would expect the answer to be 2, but we don't know how to get the answer.
I tried make a picture of what I mean (attached), but the letters came out wrong.
Edit: Ignore the point labels in the figure. I need the ratio of one side of the big triangle to one side of the little triangle. Thanks.