An arbelos is the region enclosed by three mutually tangent semicircles; it is the region inside the larger semicircle and outside the two smaller semicircles (see figure).

a. Given an arbelos in which the diameter of the largest circle is 1, what positions of point B maximize the area of the arbelos?

b. Show that the area of the arbelos is the area of a circle whose diameter is the distance BD in the figure.

Solution Step 1 : (a)The given diagram is