MathDB

Inequality with convex pentagons

Source: Brazil MO #3

October 20, 2011

inequalitiesgeometryparallelogramtrigonometrygeometry unsolved

Problem Statement

Prove that, for all convex pentagons

P_1 P_2 P_3 P_4 P_5

with area 1, there are indices

i

and

j

(assume

P_7 = P_2

and

P_6 = P_1

) such that:

\text{Area of} \ \triangle P_i P_{i+1} P_{i+2} \le \frac{5 - \sqrt 5}{10} \le \text{Area of} \ \triangle P_j P_{j+1} P_{j+2}