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Ratio of areas in a familiar situation

Source: RMO 2012

December 2, 2012
ratiogeometrytrigonometryarea of a triangle

Problem Statement

Let ABCABC be a triangle. Let D,ED,E be points on the segment BCBC such that BD=DE=ECBD=DE=EC. Let FF be the mid-point of ACAC. Let BFBF intersect ADAD in PP and AEAE in QQ respectively. Determine the ratio of the area of the triangle APQAPQ to that of the quadrilateral PDEQPDEQ.
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