2005 Canadian MO Problems/Problem 4

Problem

Let $ABC$ be a triangle with circumradius $R$ , perimeter $P$ and area $K$ . Determine the maximum value of $KP/R^3$ .

It would be convenient if this were an equilateral triangle, so we try an equilateral triangle first:

$\dfrac{KP}{R^3}=\dfrac{27}{4}$

Now we just need to prove that that is the maximum.

2005 Canadian MO (Problems)
Preceded by Problem 3	1 • 2 • 3 • 4 • 5	Followed by Problem 5