Draft:Bpow1997-8

Let S be a semicircle of radius R contained in the first quadrant and with center at (R,0). We define a function f from the positive reals to itself by the following procedure. (See picture below.) For a positive real number r, first draw a circle, C(r), of radius r centered at the origin. Next draw a straight line, L(r), through the two points (0,r) and the point of intersection of S and C(r). Then f(r) is defined as the x-coordinate of the point of intersection of L(r) and the x-axis.

What is the limit of f(r) as r goes to zero?

(Before diving in to the problem, what does your geometric intuition say the answer should be?)

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.