MathDB

A7

Part of 1957 Putnam

Problems(1)

Putnam 1957 A7

Source: Putnam 1957

7/1/2022
Each member of a set of circles in the xyxy-plane is tangent to the xx-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.
Putnamcircletangency