2005 Canadian MO Problems/Problem 3
Revision as of 20:32, 28 July 2006 by Chess64 (talk | contribs) (2005 Canadian MO/Problem 3 moved to 2005 Canadian MO Problems/Problem 3)
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.