Problem

Source: Romanian JBMO TST 1998, Day 2, P2

Tags: geometry, Pure geometry, Concyclic, inscriptible



We´re given an inscriptible quadrilateral $ DEFG $ having some vertices on the sides of a triangle $ ABC, $ and some vertices (at least one of them) coinciding with the vertices of the same triangle. Knowing that the lines $ DF $ and $ EG $ aren´t parallel, find the locus of their intersection. Dan Brânzei