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Vectorial geometry; paralellogram; concurrence

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October 28, 2019
geometryparallelogramvectorial geometry

Problem Statement

On the sides (excluding its endpoints) AB,BC,CD,DA AB,BC,CD,DA of a parallelogram consider the points M,N,P,Q, M,N,P,Q, respectively, such that AP→+AN→+CQ→+CM→=0. \overrightarrow{AP} +\overrightarrow{AN} +\overrightarrow{CQ} +\overrightarrow{CM} = 0. Show that QN,PM,AC QN, PM,AC are concurrent.
Adrian Ivan
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