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PQRE area wanted

Source: 2018 Taiwan APMO preliminary

November 10, 2020
geometry

Problem Statement

Let ABCDABCD be an unit aquare.E,FE,F be the midpoints of CD,BCCD,BC respectively. AEAE intersects the diagonal BDBD at PP. AFAF intersects BD,BEBD,BE at Q,RQ,R respectively. Find the area of quadrilateral PQREPQRE.
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