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Construction of points with given property

Source: Czech and Slovak Olympiad 2019, National Round, Problem 2

June 6, 2019
constructive geometryrectanglegeometrynational olympiad

Problem Statement

Let be ABCDABCD a rectangle with ∣AB∣=a≥b=∣BC∣|AB|=a\ge b=|BC|. Find points P,QP,Q on the line BDBD such that ∣AP∣=∣PQ∣=∣QC∣|AP|=|PQ|=|QC|. Discuss the solvability with respect to the lengths a,ba,b.
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