analytic geometry, see heath's "archimedes" for synthetic geometry solution.
Prerequisites
algebra, geometry
Problem Text
In an arbelos the two circles inscribed in regions and have equal radii. See Figure 3. Prove this. Find this radius in terms of the radii of the three semicircles that form the arbelos. (This is Proposition 5 in Archimedes' The Book of Lemmas).
and 
have equal radii. See Figure 3. Prove this. Find this radius in terms of the radii of the three semicircles that form the arbelos. (This is Proposition 5 in Archimedes' The Book of Lemmas).