I don't think we need to know I will use to denote the measure of a length. My idea is something like this:
1) Since the base is equilateral we know (see Equilateral triangle - Wikipedia, the free encyclopedia). There are many ways to show that (for example see Viviani's Theorem Viviani's theorem - Wikipedia, the free encyclopedia). Hence
2) Since the tangents to the circle DF and DA are drawn from the same point (i.e. D), we know Therefore, and Since we also know that
3) We now use the right triangle and the tangent function to obtain the radius.
Does this answer your question? Let me know if anything is unclear/incorrect.