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.
Solution
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