1951 AHSME Problem 30

If two poles 20'' and 80'' high are 100'' apart, then the height of the intersection of the lines joining the top of each pole to the foot of the opposite pole is:

\textbf{(A)}\ 50''\qquad\textbf{(B)}\ 40''\qquad\textbf{(C)}\ 16''\qquad\textbf{(D)}\ 60''\qquad\textbf{(E)}\ \text{none of these}

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