M2596

Part of Kvant 2020

Problems(1)

Geometrical inequality with circumscribed quadrilateral

Source: Kvant Magazine No. 3 2020 M2596

\omega{}

is inscribed in the quadrilateral

ABCD

. Prove that the diameter of the circle

\omega{}

does not exceed the length of the segment connecting the midpoints of the sides

BC

AD

.
Proposed by O. Yuzhakov

geometrygeometric inequalityKvant