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The locus of intersection points of two lines

Source: Czech-Polish-Slovak 2001 Q4

April 30, 2013
ratiogeometrygeometric transformationhomothetygeometry unsolved

Problem Statement

Distinct points AA and BB are given on the plane. Consider all triangles ABCABC in this plane on whose sides BC,CABC,CA points D,ED,E respectively can be taken so that (i) BDBC=CECA=13\frac{BD}{BC}=\frac{CE}{CA}=\frac{1}{3}; (ii) points A,B,D,EA,B,D,E lie on a circle in this order.
Find the locus of the intersection points of lines ADAD and BEBE.
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