MathDB
Quadrilateral is parallelogram

Source: Romanian District Olympiad 2024 9.1

March 10, 2024
geometryvector

Problem Statement

Let ABCDABCD be a convex quadrilateral whose diagonals intersect at O.O. Given that AB→+AD→+AO→=BC→+DC→+OC→,\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{AO}=\overrightarrow{BC}+\overrightarrow{DC}+\overrightarrow{OC},prove that ABCDABCD is a parallelogram.
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