« Vrati se
There is given a convex quadrilateral ABCD. Prove that there exists a point P inside the quadrilateral such that
\angle PAB + \angle PDC = \angle PBC + \angle PAD = \angle PCD + \angle PBA = \angle PDA + \angle PCB = 90^{\circ}
if and only if the diagonals AC and BD are perpendicular.

Proposed by Dukan Dukic, Serbia

Slični zadaci

2222IMO Shortlist 2006 problem G68
2245IMO Shortlist 2007 problem C52
2279IMO Shortlist 2008 problem G37
2281IMO Shortlist 2008 problem G51
2302IMO Shortlist 2009 problem C60
2309IMO Shortlist 2009 problem G51