Determine a 1-1 analytic mapping from a "lens" shaped region onto the open unit disc. The region is the non-empty intersection of two open discs. Let w1 and w2 be the two intersection points of the circles, and let L be the line through w1 and w2. Assume that the tangent to the first circle makes angle a with L at w1 and the second one has angle b at w1 (in radian). Can anyone give some clues?