IMO Shortlist 2004 problem G4
In a convex quadrilateral
, the diagonal
bisects neither the angle
nor the angle
. The point
lies inside
and satisfies
Prove that
is a cyclic quadrilateral if and only if
.
%V0
In a convex quadrilateral $ABCD$, the diagonal $BD$ bisects neither the angle $ABC$ nor the angle $CDA$. The point $P$ lies inside $ABCD$ and satisfies $$\angle PBC=\angle DBA \quad \text{and} \quad \angle PDC = \angle BDA.$$
Prove that $ABCD$ is a cyclic quadrilateral if and only if $AP=CP$.
Source: Međunarodna matematička olimpijada, shortlist 2004
Školjka 
