1965 AHSME Problems/Problem 4
Problem
Line intersects line and line is parallel to . The three lines are distinct and lie in a plane. The number of points equidistant from all three lines is:
Solution
The lines are coplanar, , and intersects . Therefore, also intersects . The locus of all points equidistant from parallel lines and is a third parallel line in between them. Let this line be , and let the distance from to either or be . The points equidistant from lines , , and must all lie on and be a distance from line . There are only 2 points, on either side of , which satisfy these conditions. Thus, our answer is .
See Also
1965 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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