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Part of 1972 IMO Shortlist

Problems(1)

Prove that there exists a straightline g -IMO ShortList 1973

Source:

9/22/2010
Let n1,n2n_1, n_2 be positive integers. Consider in a plane EE two disjoint sets of points M1M_1 and M2M_2 consisting of 2n12n_1 and 2n22n_2 points, respectively, and such that no three points of the union M1∪M2M_1 \cup M_2 are collinear. Prove that there exists a straightline gg with the following property: Each of the two half-planes determined by gg on EE (gg not being included in either) contains exactly half of the points of M1M_1 and exactly half of the points of M2.M_2.
combinatoricspartitionpoint setgeometrycombinatorial geometryIMO Shortlist