$35 \cdot 48$ On a plane, there is a set of points $M$ and seven different circles $C_{1}, C_{2}, \cdots, C_{7}$, where circle $C_{7}$ passes through exactly 7 points in $M$, circle $C_{6}$ passes through exactly 6 points in $M$, $\cdots$, circle $C_{1}$ passes through exactly 1 point in $M$. The minimum number of points in $M$ is
(A) 11.
(B) 12.
(C) 21.
(D) 28.
(China High School Mathematics League, 1986)
[Solution] For circle $C_{7}$, set $M$ needs to have 7 points $A_{1}, A_{2}, \cdots, A_{7}$ (see figure);

For circle $C_{6}$, $M$ needs to add 4 points $A_{8}, A_{9}$, $A_{10}, A_{11}$ (the other two points are $A_{3}, A_{6}$ );

For circle $C_{5}$, $M$ only needs to add one point $A_{12}$; when considering circles $C_{4}, C_{3}, C_{2}, C_{1}$, $M$ does not need to add any more points. Therefore, the minimum number of points in $M$ is 12.
Hence, the answer is $(B)$.