Fancier animation: Stewart Calculus problem with limits

Consider a fixed circle with equation and a shrinking circle with radius r and center at the origin.  P is the point , Q is the upper point of intersection of the two circles, and R is the point of intersection of the line PQ and the x-axis.  What happens to R as shrinks, that is as ?  (Stewart, James - Calculus Concepts and Contexts, Section 2.3, problem 44, pg. 119)

(See How I made the diagram below to see how this figure was generated.  It was a bit of a pain, but does make for a nice illustration.)