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Source: Bulgaria National Olympiad 2023 Problem 4

April 9, 2023
geometryareaconvex quadrilateral

Problem Statement

Prove that there exists a unique point MM on the side ADAD of a convex quadrilateral ABCDABCD such that SABM+SCDM=SABCD\sqrt{S_{ABM}}+\sqrt{S_{CDM}} = \sqrt{S_{ABCD}} if and only if AB∥CDAB\parallel CD.
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