IMO 2020 Shortlist G4
In the plane, there are n ě 6 pairwise disjoint disks D1,D2,...,Dn with radii R1 ě R2 ě ... ě Rn. For every i “ 1,2,...,...
Category: Geometry
Problem
In the plane, there are n ě 6 pairwise disjoint disks D1,D2,...,Dn with radii
R1 ě R2 ě ... ě Rn. For every i “ 1,2,...,n, a point Pi is chosen in disk Di. Let O be an
arbitrary point in the plane. Prove that
OP1 OP2 ... OPn ě R6 R7 ... Rn.
(A disk is assumed to contain its boundary.)
(Iran)