CAPS 2001 Problem 4

Distinct points $A$ and $B$ are given on the plane. Consider all triangles $ABC$ in this plane on whose sides $BC,CA$ points $D,E$ respectively can be taken so that (i) $\frac{BD}{BC}=\frac{CE}{CA}=\frac{1}{3}$ ; (ii) points $A,B,D,E$ lie on a circle in this order.

Find the locus of the intersection points of lines $AD$ and $BE$ .