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2001 Spain Mathematical Olympiad, Problem 5

Source: Spain Mathematical Olympiad 2001

June 6, 2017
geometry

Problem Statement

A quadrilateral ABCDABCD is inscribed in a circle of radius 1 whose diameter is ABAB. If the quadrilateral ABCDABCD has an incircle, prove that CD≤25−2CD \leq 2 \sqrt{5} - 2.
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