IMO Shortlist 1992 problem 3
Kvaliteta:
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Avg: 0,0 The diagonals of a quadrilateral are perpendicular: Four squares, are erected externally on its sides. The intersection points of the pairs of straight lines are denoted by respectively (left figure), and the intersection points of the pairs of straight lines are denoted by respectively (right figure). Prove that where and are the two quadrilaterals.
Alternative formulation: Outside a convex quadrilateral with perpendicular diagonals, four squares are constructed (vertices are given in counterclockwise order). Prove that the quadrilaterals and formed by the lines and respectively, are congruent.
Alternative formulation: Outside a convex quadrilateral with perpendicular diagonals, four squares are constructed (vertices are given in counterclockwise order). Prove that the quadrilaterals and formed by the lines and respectively, are congruent.
Izvor: Međunarodna matematička olimpijada, shortlist 1992