2005 IMO Problems/Problem 5
Let be a fixed convex quadrilateral with
and
. Let two variable
points
and
lie of the sides
and
, respectively, and satisfy
. The lines
and
meet at
, the lines
and
meet at
, the lines
and
meet at
. Prove
that the circumcircles of the triangles
, as
and
vary, have a common point other than
.