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Condition on sides of a quadrilateral and some diagonals

Source: RMO (Mumbai Region) 2015 P1

December 6, 2015
inequalitiesinequalities proposedrearrangement inequalityAM-GMgeometrygeometry proposed

Problem Statement

Let ABCDABCD be a convex quadrilateral with AB=aAB=a, BC=bBC=b, CD=cCD=c and DA=dDA=d. Suppose a2+b2+c2+d2=ab+bc+cd+da,a^2+b^2+c^2+d^2=ab+bc+cd+da, and the area of ABCDABCD is 6060 sq. units. If the length of one of the diagonals is 3030 units, determine the length of the other diagonal.
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