AHSME 1979 Problem 21

The length of the hypotenuse of a right triangle is $h$ , and the radius of the inscribed circle is $r$. The ratio of the area of the circle to the area of the triangle is $\textbf{(A) }\frac{\pi r}{h+2r} \textbf{(B) }\frac{\pi r}{h+r} \textbf{(C) }\frac{\pi}{2h+r} \textbf{(D) }\frac{\pi r^2}{r^2+h^2} \textbf{(E) }\text{none of these}$