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Polish MO 2022 P4

Source: Polish MO 2022 P4

February 12, 2022
geometry

Problem Statement

Given quadrilateral ABCDABCD inscribed into a circle with diagonal ACAC as diameter. Let EE be a point on segment BCBC s.t. ∢DAC=∢EAB\sphericalangle DAC=\sphericalangle EAB. Point MM is midpoint of CECE. Prove that BM=DMBM=DM.
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