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Knowing a sum of vectors, prove a sum of vectors

Source: Romanian District Olympiad 2011, Grade IX, Problem 1

October 8, 2018
geometryparallelogramvector

Problem Statement

On the sides AB,BC,CD,DA AB,BC,CD,DA of the parallelogram ABCD, ABCD, consider the points M,N,P, M,N,P, respectively, Q, Q, such that MN→+QP→=AC→. \overrightarrow{MN} +\overrightarrow{QP} =\overrightarrow{AC} . Show that PN→+QM→=DB→. \overrightarrow{PN} +\overrightarrow{QM} = \overrightarrow{DB} .
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