MathDB

A convex polygon

G

is placed inside a convex polygon

F

so that their boundaries have no common points. A segment

s

joining two points on the boundary of

F

is called a support chord for

G

if s contains a side or only a vertex of

G

. Prove that (a) there exists a support chord for

G

such that its midpoint lies on the boundary of

G

, (b) there exist at least two such chords.
(P Pushkar)

Problem Statement