IMO 2008 Shortlist G6
There is given a convex quadrilateral ABCD. Prove that there exists a point P inside the quadrilateral such that ∠PAB + ...
Category: Geometry
Problem
There is given a convex quadrilateral ABCD. Prove that there exists a point P inside the quadrilateral such that ∠PAB + ∠PDC = ∠PBC + ∠PAD = ∠PCD + ∠PBA = ∠PDA + ∠PCB = 90◦ (1) if and only if the diagonals AC and BD are perpendicular.