2015 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 2

Problem

Show that if $S$ is a set of finitely many non-collinear points in the plane (i.e., not all of the points are on the same line), then there is a line which contains exactly two of the points of $S$. Is the claim true if $S$ has infinitely many points? Hint: Use an extremal configuration.

Solution

See also

2015 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions

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