MathDB

We say that a polygon

P

is inscribed in another polygon

Q

when all vertices of

P

belong to perimeter of

Q

. We also say in this case that

Q

is circumscribed to

P

. Given a triangle

T

, let

l

be the maximum value of the side of a square inscribed in

T

and

L

be the minimum value of the side of a square circumscribed to

T

. Prove that for every triangle

T

the inequality

L/l \ge 2

holds and find all the triangles

T

for which the equality occurs.

Problem Statement