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ASU 464 All Soviet Union MO 1988 quadrilaterals equal areas, area bisector

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August 7, 2019
geometryareasequal areasconvex

Problem Statement

ABCDABCD is a convex quadrilateral. The midpoints of the diagonals and the midpoints of ABAB and CDCD form another convex quadrilateral QQ. The midpoints of the diagonals and the midpoints of BCBC and CACA form a third convex quadrilateral Q′Q'. The areas of QQ and Q′Q' are equal. Show that either ACAC or BDBD divides ABCDABCD into two parts of equal area.
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