IMO 2017 Shortlist G8
There are 2017 mutually external ir les drawn on a bla kboard, su h that no two are tangent and no three share a ommon t...
Category: Geometry
Problem
There are 2017 mutually external ir les drawn on a bla kboard, su h that no two are tangent and no three share a ommon tangent. A tangent segment is a line segment that is a ommon tangent to two ir les, starting at one tangent point and ending at the other one. Lu iano is drawing tangent segments on the bla kboard, one at a time, so that no tangent segment interse ts any other ir les or previously drawn tangent segments. Lu iano keeps drawing tangent segments until no more an be drawn. Find all possible numbers of tangent segments when he stops drawing. (Australia) Shortlisted problems 9 This page is intentionally left blank 10 IMO 2017, Rio de Janeiro