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Necessary and sufficient condition for an angle to be right

Source: Czech and Slovak Olympiad 1971, National Round, Problem 2

July 9, 2024
geometryright angle

Problem Statement

Let ABCABC be a triangle. Four distinct points D,A,B,ED,A,B,E lie on the line ABAB in this order such that DA=AB=BE.DA=AB=BE. Find necessary and sufficient condition for lengths a=BC,b=ACa=BC,b=AC such that the angle ∠DCE\angle DCE is right.
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