¶ 1996 AMC8 Problem 8
Problem:
Points and are units apart. Points and are units apart. Points and are units apart. If and are as close as possible, then the number of units between them is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The shortest distance occurs when the four points are collinear. Then and so that as shown.
.jpg)
Once and are chosen, can be anywhere on the circle of radius centered at . The closest point to would be on the segment between and . Then could be anywhere on the circle of radius centered at . Once again the closest point to is on the line segment between and . Thus the distance from to is units.
.jpg)
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions