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Bijective function f: points -> lines

Source: Romanian TST 1997

April 18, 2011
functiongeometry unsolvedgeometry

Problem Statement

Let PP be the set of points in the plane and DD the set of lines in the plane. Determine whether there exists a bijective function f:Pā†’Df: P \rightarrow D such that for any three collinear points AA, BB, CC, the lines f(A)f(A), f(B)f(B), f(C)f(C) are either parallel or concurrent.
Gefry Barad
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