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Rectangle and an arithmetic sequence

Source: Greek national M.O. 2000, Final Round, problem 1

November 20, 2011
geometryrectanglegeometry unsolved

Problem Statement

Consider a rectangle ABCDABCD with AB=aAB = a and AD=b.AD = b. Let ll be a line through O,O, the center of the rectangle, that cuts ADAD in EE such that AE/ED=1/2AE/ED = 1/2. Let MM be any point on l,l, interior to the rectangle. Find the necessary and sufficient condition on aa and bb that the four distances from M to lines AD,AB,DC,BCAD, AB, DC, BC in this order form an arithmetic progression.
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