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A geometric Inequality on a square

Source: Turkish NMO 1996, 2. Problem

July 31, 2011
inequalitiesgeometry proposedgeometry

Problem Statement

Let ABCDABCD be a square of side length 2, and let MM and NN be points on the sides ABAB and CDCD respectively. The lines CMCM and BNBN meet at PP, while the lines ANAN and DMDM meet at QQ. Prove that ∣PQ∣≥1\left| PQ \right|\ge 1.
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