Difference between revisions of "1969 IMO Problems/Problem 5"
(Created page with "Given n > 4 points in the plane such that no three are collinear. Prove that there are at least ³ n-3 ---- 2 ´ convex quadrilaterals whose vertices are four of the given points.") |
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Given n > 4 points in the plane such that no three are collinear. Prove that | Given n > 4 points in the plane such that no three are collinear. Prove that | ||
there are at least | there are at least | ||
| − | + | (n-3)/2 | |
| − | n-3 | ||
| − | |||
| − | |||
| − | |||
convex quadrilaterals whose vertices are four of the | convex quadrilaterals whose vertices are four of the | ||
given points. | given points. | ||
Revision as of 12:06, 20 October 2013
Given n > 4 points in the plane such that no three are collinear. Prove that there are at least (n-3)/2 convex quadrilaterals whose vertices are four of the given points.
