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A point variable on a semi-circle

Source: Italy MO 2023 P4

May 7, 2023
geometry

Problem Statement

Fix circle with center OO, diameter ABAB and a point CC on it, different from A,BA, B. Let a point DD, different from A,BA, B, vary on the arc ABAB not containing CC. Let EE lie on CDCD such that BE⊥CDBE \perp CD. Prove that CE⋅EDCE \cdot ED is maximal exactly when BOEDBOED is cyclic.
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