Difference between revisions of "2008 UNCO Math Contest II Problems/Problem 6"
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== Solution == | == Solution == | ||
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== See Also == | == See Also == | ||
Revision as of 14:32, 26 November 2016
Problem
Points 
and 
are on the same side of
line 
in the plane. is 
units away
from 
is 
units away from .
The distance between and is 
. For
all points 
on what is the smallest
value of the sum 
of the distances
from to and from to ?
![[asy] draw((-1,0)--(16,0),arrow=Arrow()); draw((16,0)--(-1,0),arrow=Arrow()); draw((2,0)--(2,5)--(2+sqrt(128),9)--(2+sqrt(128),0),black); draw((2,5)--(8,0)--(2+sqrt(128),9),dashed); dot((2,5));dot((8,0));dot((2+sqrt(128),9)); MP("A",(2,5),W);MP("P",(8,0),S);MP("B",(2+sqrt(128),9),E);MP("L",(14,0),S); MP("5",(2,2.5),W);MP("12",(2+sqrt(128)/2,7),N);MP("9",(2+sqrt(128),4.5),E); [/asy]](http://latex.artofproblemsolving.com/8/a/8/8a89f13972854e2b6a4fc3db792360dd50812d19.png)
Solution
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See Also
| 2008 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
