Let
be a convex quadrilateral and let
and
be points in
such that
and
are cyclic quadrilaterals. Suppose that there exists a point
on the line segment
such that
and
. Show that the quadrilateral
is cyclic.
Proposed by John Cuya, Peru
%V0
Let $ABCD$ be a convex quadrilateral and let $P$ and $Q$ be points in $ABCD$ such that $PQDA$ and $QPBC$ are cyclic quadrilaterals. Suppose that there exists a point $E$ on the line segment $PQ$ such that $\angle PAE = \angle QDE$ and $\angle PBE = \angle QCE$. Show that the quadrilateral $ABCD$ is cyclic.
Proposed by John Cuya, Peru
Školjka