Difference between revisions of "2005 Canadian MO Problems/Problem 3"
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*[[2005 Canadian MO]] | *[[2005 Canadian MO]] | ||
Revision as of 13:20, 16 September 2006
Problem
Let 
be a set of 
points in the interior of a circle.
- Show that there are three distinct points
and three distinct points 
on the circle such that 
is (strictly) closer to 
than any other point in 
, 
is closer to 
than any other point in and 
is closer to 
than any other point in . - Show that for no value of
can four such points in (and corresponding points on the circle) be guaranteed.
and three distinct points 
on the circle such that 
is (strictly) closer to 
than any other point in 
is closer to 
than any other point in 
is closer to 
than any other point in 
can four such points in Solution
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