2005 Canadian MO Problems/Problem 3
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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.
Solution
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See also
| 2005 Canadian MO (Problems) | ||
| Preceded by Problem 2 | 1 • 2 • 3 • 4 • 5 | Followed by Problem 4 |
