Question 38
Let $A$ be the sum of all 10 pairwise products of the sides of a convex pentagon, $S$ be the area of the pentagon.
a) Prove that $S \le \frac{1}{5}A$.
b) Does there exist a constant $c \lt 1/5$ such that $S \le cA$?
(I. Voronovich)
a) Prove that $S \le \frac{1}{5}A$.
b) Does there exist a constant $c \lt 1/5$ such that $S \le cA$?
(I. Voronovich)