Difference between revisions of "1965 AHSME Problems/Problem 4"
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Revision as of 09:54, 18 July 2024
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
All AHSME Problems and Solutions |