1968 AHSME Problems/Problem 30
Contents
[hide]Problem
Convex polygons and are drawn in the same plane with and sides, respectively, . If and do not have any line segment in common, then the maximum number of intersections of and is:
Solution 1
Notice how can pass through each line segment of at most twice. To have more than two intersections, the line passing through would have a zigzag shape which is impossible for convex polygons. Therefore, the intersections does not depend on and the answer is
Solution 2
Try to get the answer experimentally. Draw two of the simplest shapes: a square and a triangle and maximize the number of intersections. You will discover it is 6, and the only expression provided that will give 6 is
Note : this solution isn’t risk free, as the option of “None of These” is given as well.
See also
1968 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 29 |
Followed by Problem 31 | |
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