Putnam 1957 A7
Source: Putnam 1957
July 1, 2022
Putnamcircletangency
Problem Statement
Each member of a set of circles in the -plane is tangent to the -axis and no two of the circles intersect. Show that
(a) the points of tangency can include all rational points on the axis.
(b) the points of tangency cannot include all the irrational points.