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solid geometry - ABCD a square and AE and CF perpendiculars

Source: Romanian IMO Team Selection Test TST 1987, problem 8

September 25, 2005
geometryperpendicular bisectorgeometry proposed

Problem Statement

Let ABCDABCD be a square and aa be the length of his edges. The segments AEAE and CFCF are perpendicular on the square's plane in the same half-space and they have the length AE=aAE=a, CF=bCF=b where a<b<a3a<b<a\sqrt 3. If KK denoted the set of the interior points of the square ABCDABCD determine min⁡M∈K(max⁡(EM,FM))\min_{M\in K} \left( \max ( EM, FM ) \right) and max⁡M∈K(min⁡(EM,FM))\max_{M\in K} \left( \min (EM,FM) \right). Octavian Stanasila
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