AHSME 1967 Problem 5

A triangle is circumscribed about a circle of radius $r$ inches. If the perimeter of the triangle is $P$ inches and the area is $K$ square inches, then $\frac{P}{K}$ is: $\text{(A)}\text{ independent of the value of} r \text{(B)}\ \frac{\sqrt{2}}{r} \text{(C)}\ \frac{2}{\sqrt{r}} \text{(D)}\ \frac{2}{r} \text{(E)}\ \frac{r}{2}$