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Find all possible values of segment PQ

Source: Baltic Way 1996 Q3

March 19, 2011
geometry proposedgeometry

Problem Statement

Let ABCDABCD be a unit square and let PP and QQ be points in the plane such that QQ is the circumcentre of triangle BPCBPC and DD be the circumcentre of triangle PQAPQA. Find all possible values of the length of segment PQPQ.
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