2011 | 7 (14) | 65-70
Article title

On some extremal problem in discrete geometry

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Let p, q, r be any three lines in the plane passing through a common point and suppose that O, P, Q, R are any four collinear points such that P  p, Q  q, R  r, P and R are harmonic conjugates with respect to O and Q (that is, |OP|/|PQ|=|OR|/|QR|). For every k  2, we construct a set Xn of n = 4k points, which is distributed on the lines p, q, r, but each element of Xn  {O} is incident to at most n/2 lines spanned by Xn  {O}.
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