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locus of center parallelogram

Source: 31-th Vietnamese Mathematical Olympiad 1993

February 17, 2007
geometryparallelogramgeometry unsolved

Problem Statement

ABCDABCD is a quadrilateral such that ABAB is not parallel to CDCD, and BCBC is not parallel to ADAD. Variable points P,Q,R,SP, Q, R, S are taken on AB,BC,CD,DAAB, BC, CD, DA respectively so that PQRSPQRS is a parallelogram. Find the locus of its center.
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