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Geometrical inequality with circumscribed quadrilateral

Source: Kvant Magazine No. 3 2020 M2596

March 10, 2023
geometrygeometric inequalityKvant

Problem Statement

The circle ω\omega{} is inscribed in the quadrilateral ABCDABCD. Prove that the diameter of the circle ω\omega{} does not exceed the length of the segment connecting the midpoints of the sides BCBC and ADAD.
Proposed by O. Yuzhakov
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