MathDB

Two triangles

ABC

and

A'B'C'

are positioned in the space such that the length of every side of

\triangle ABC

is not less than

a

, and the length of every side of

\triangle A'B'C'

is not less than

a'

. Prove that one can select a vertex of

\triangle ABC

and a vertex of

\triangle A'B'C'

so that the distance between the two selected vertices is not less than \sqrt {\frac {a^2 \plus{} a'^2}{3}}.

Problem Statement