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Part of 2018 Brazil National Olympiad

Problems(2)

Inequality with triangles and squares

Source: Brazilian Mathematical Olympiad 2018 - Q1

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

l

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

T

L

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

T

. Prove that for every triangle

T

L/l \ge 2

holds and find all the triangles

T

for which the equality occurs.

Inequalitygeometrytriangle inequalityinequalitiesBrazilian Math OlympiadBrazilian Math Olympiad 2018

Source:

Every day from day 2, neighboring cubes (cubes with common faces) to red cubes also turn red and are numbered with the day number.