> The problem looked innocent enough at first glance: given a circle and two points on the plane outside the circle, construct another circle passing trough those two points and touching the first circle at one point.But the solution is in fact quite complicated. Few of my future colleagues at Harvard and Berkeley would have been able to solve it right away. One must use “inversion,” a concept that was not studied in high school and hence could not possibly be allowed in this exam.

I became quite curious about solving this problem, I tried to look up what he means by "inversion" but could not find it. Anyone knows what it could be?

Update: Wikipedia suggests http://en.wikipedia.org/wiki/Inversion_in_a_point but obviously this is covered by high school program and is not very complicated.