midpoints of a cyclic ABCD form another cyclic, area of circles' inequality
Source: 2010 Balkan Shortlist G2 BMO
April 4, 2020
geometrycirclesareasgeometric inequalitycyclic quadrilateralmidpointsCyclic
Problem Statement
Consider a cyclic quadrilateral such that the midpoints of its sides form another cyclic quadrilateral. Prove that the area of the smaller circle is less than or equal to half the area of the bigger circle