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Find n if triangles are equal

Source: APMO 2001

March 19, 2006
geometry unsolvedgeometry

Problem Statement

Find the greatest integer nn, such that there are n+4n+4 points AA, BB, CC, DD, X1,…, XnX_1,\dots,~X_n in the plane with AB≠CDAB\ne CD that satisfy the following condition: for each i=1,2,…,ni=1,2,\dots,n triangles ABXiABX_i and CDXiCDX_i are equal.
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