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Some Length Equality

Source: RMO 2024/5

November 3, 2024
geometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral such that AB∥CDAB \parallel CD. Let OO be the circumcenter of ABCDABCD and LL be the point on ADAD such that OLOL is perpendicular to ADAD. Prove that OB⋅(AB+CD)=OL⋅(AC+BD). OB\cdot(AB+CD) = OL\cdot(AC + BD).
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