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4

Part of 2001 Czech-Polish-Slovak Match

Problems(1)

The locus of intersection points of two lines

Source: Czech-Polish-Slovak 2001 Q4

4/30/2013
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.
ratiogeometrygeometric transformationhomothetygeometry unsolved