AMC 12 2000 Problem 21

Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is $m$ times the area of the square. The ratio of the area of the other small right triangle to the area of the square is

$\textbf {(A)}\ \frac{1}{2m+1} \textbf {(B)}\ m \textbf {(C)}\ 1-m \textbf {(D)}\ \frac{1}{4m} \textbf {(E)}\ \frac{1}{8m^2}$