16.20 In the plane of $\triangle A B C$, arbitrarily draw a line $l$ such that the ratios of the distances from $A, B, C$ to line $l$ are $1: 2: 2$ or $2: 1: 2$ or $2: 2: 1$. The number of such lines $l$ is
(A) 3.
(B) 6.
(C) 9.
(D) 12.
(Shenyang City, Liaoning Province, China "Yucai Cup" Junior High School Mathematics Competition, 1988)
[Solution] $\because$ The distances from points $B, C$ to $l$ are equal,
$\therefore$ When $B, C$ are on the same side of $l$, $l \parallel B C$. There are 2 lines parallel and with a distance ratio of $1: 2: 2$.

When $B, C$ are on opposite sides of $l$, using the properties of similar triangles and congruent triangles, it can be proven that the lines $DE$ and $FD$ passing through the trisection points $E, F$ of $AC, AB$ and the midpoint $D$ of the base $BC$ also meet the conditions. That is, for the ratio $1: 2: 2$, there are 4 lines that meet the conditions (as shown in the figure). Similarly, there are 4 lines that meet the conditions for each of the other two ratios, making a total of 12 lines. Therefore, the answer is $(D)$.