$35 \cdot 35$ plane has 6 lines intersecting each other, but only three pass through the same point, then the number of non-overlapping line segments intercepted is
(A) 24.
(B) 33.
(C) 36.
(D) 21.
(1st "Five Sheep Cup" Junior High School Mathematics Competition, 1989)
[Solution] If there are no three lines intersecting at the same point on a plane, then each line intersects with other lines at 5 points, cutting off 4 non-overlapping segments.

However, in the given set of lines, three lines intersect at one point, which results in 3 fewer segments being cut, so the number of non-overlapping segments cut by these lines is
$$
6 \cdot 4-3=21 \text { (segments). }
$$

Therefore, the answer is $(D)$.