Problem of the Week 913

A Locus of Points

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 A

What is the locus of midpoints of the line segment YX for 0 r 2?

Source: Stan Wagon.

© Copyright 2000 Stan Wagon. Reproduced with permission.