$37 \cdot 6$ points $(x, y)$ where both $x, y$ are rational numbers are called rational points. In a circle with radius $r$ and center $(a, b)$, if $a$ is a rational number and $b$ is an irrational number, the number of rational points on this circle is
(A) at most one.
(B) at most two.
(C) at most three.
(D) infinitely many.
(1st "Hope Cup" National Mathematics Invitational Competition, 1990)