1965 AMC 12 Problem 4

Question

Line

l_2

intersects line

l_1

and line

l_3

is parallel to

l_1.

The three lines are distinct and lie in a plane. The number of points equidistant from all three lines is:

0

1

2

4

8

Points equidistant from the two parallel lines lie on their midway parallel

Intersect that midway line with the two angle bisectors of

l_1

and

l_2

Points equidistant from parallel lines

l_1

and

l_3

lie on the unique line midway between them. Points equidistant from intersecting lines

l_1

and

l_2

lie on either of their two angle bisectors. Each angle bisector meets the midway parallel once, giving two points.

Therefore, the correct answer is C.

Problem 4 in other years