Let S be a semicircle rising from the origin and lying on the positive x-axis: S is the upper-half of the unit circle centered at (1, 0). Consider also a circle, C, centered at the origin and let A, B be the points of intersection of C with the positive y-axis and with S, respectively. Extend the line AB rightward, letting X be its intersection with the x-axis. What happens to X as C becomes smaller and smaller, its radius approaching zero?
This problem is from a paper that I highly recommend:
Intuitively Misconceived Solutions to Problems by S Avital & E Barbeau, "For tthe Learning of Mathematics", vol. 11, No. 3, Nov. 1991, pp. 2-8.