2005 Canadian MO Problems/Problem 4

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Problem

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

Let the sides of triangle $ABC$ be $a$ , $b$ , and $c$ . Thus $\dfrac{abc}{4K}=R$ , and $a+b+c=P$ . We plug these in:

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