Given that

S = the semicircle of radius 1 and center (1,0) having nonnegative y coordinates.

C = the circle of radius r and center (0,0)

Y = the highest point on C

A = the intersection of C and S

X = the x-intercept of the line through Y and AWhat is the locus of midpoints of the line segment YX for

0 r 2?

Source: Stan Wagon.© Copyright 2000 Stan Wagon. Reproduced with permission.