IMO 1987 LL MON43

Let 2n + 3 points be given in the plane in such a way that

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IMO 1987 LL MON43

Origin: MON

Problem

Let 2n + 3 points be given in the plane in such a way that no three lie on a line and no four lie on a circle. Prove that the number of circles that pass through three of these points and contain exactly n interior points is not less than 1 2n+3  .