16-2 In the same plane, line $l_{2}$ intersects with line $l_{1}$, and line $l_{3}$ is parallel to line $l_{1}$. The number of points equidistant from these three lines is
(A) 0.
(B) 1.
(C) 2.
(D) 4.
(E) 8.
(16th American High School Mathematics Examination, 1965)
[Solution] Let $l_{4}$ be the line parallel to and equidistant from $l_{1}$ and $l_{3}$, and let the distance be $d$.
Let $l_{5}$ and $l_{6}$ be the two lines parallel to and at a distance $d$ from $l_{2}$.
Then the intersection points $P, Q$ of $l_{4}, l_{5}, l_{6}$ are the solutions.
Therefore, the answer is $(C)$.