1979 AHSME 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}\qquad \textbf{(B) }\frac{\pi r}{h+r}\qquad \textbf{(C) }\frac{\pi}{2h+r}\qquad \textbf{(D) }\frac{\pi r^2}{r^2+h^2}\qquad \textbf{(E) }\text{none of these}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.