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Miklós Schweitzer 1958- Problem 4

Source:

October 21, 2015

geometrycollege contests

Problem Statement

4. Let

P_1 P_2 P_3 P_4 P_5 P_6

be a convex hexagon. Denote by

T

its area and by

t

the area of the triangle

Q_1 Q_2 Q_3

, where

Q_1,Q_2

and

Q_3

are the midpoints of

P_1P_4,P_2P_5,P_3P_6

respectively. Prove that

t<\frac{1}{4}T

. (G. 3)

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