1983 AHSME Problem 13

If xy = a, xz =b, and yz = c, and none of these quantities is 0, then x^2+y^2+z^2 equals

\textbf{(A)}\ \frac{ab+ac+bc}{abc}\qquad \textbf{(B)}\ \frac{a^2+b^2+c^2}{abc}\qquad \textbf{(C)}\ \frac{(a+b+c)^2}{abc}\qquad \textbf{(D)}\ \frac{(ab+ac+bc)^2}{abc}\qquad \textbf{(E)}\ \frac{(ab)^2+(ac)^2+(bc)^2}{abc}

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