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There exist A, B, C such that lengths AB and AC are close

Source: Chinese TST 2007 2nd quiz P3

January 3, 2009
inequalitiescombinatorial geometryanalytic geometrygeometry

Problem Statement

Assume there are n≥3 n\ge3 points in the plane, Prove that there exist three points A,B,C A,B,C satisfying 1\le\frac{AB}{AC}\le\frac{n\plus{}1}{n\minus{}1}.
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