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Construction of a rectangle

Source: Czech and Slovak Olympiad 1977, National Round, Problem 2

October 10, 2024
geometryrectangleconstructiongeometric construction

Problem Statement

The numbers p,q>0p,q>0 are given. Construct a rectangle ABCDABCD with AE=p,AF=qAE=p,AF=q where E,FE,F are midpoints of BC,CD,BC,CD, respectively. Discuss conditions of solvability.
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