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BC^2 = CD \cdot CE wanted, trapezoid with perpendicular diagonals given,

Source: ITAMO 1998 p4

January 25, 2020
geometrytrapezoidperpendicular

Problem Statement

Let ABCDABCD be a trapezoid with the longer base ABAB such that its diagonals ACAC and BDBD are perpendicular. Let OO be the circumcenter of the triangle ABCABC and EE be the intersection of the lines OBOB and CDCD. Prove that BC2=CDā‹…CEBC^2 = CD \cdot CE.
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