1967 AHSME Problem 37

Segments AD=10, BE=6, CF=24 are drawn from the vertices of triangle ABC, each perpendicular to a straight line RS, not intersecting the triangle. Points D, E, F are the intersection points of RS with the perpendiculars. If x is the length of the perpendicular segment GH drawn to RS from the intersection point G of the medians of the triangle, then x is:

\textbf{(A)}\ \frac{40}{3}\qquad \textbf{(B)}\ 16\qquad \textbf{(C)}\ \frac{56}{3}\qquad \textbf{(D)}\ \frac{80}{3}\qquad \textbf{(E)}\ \text{undetermined}

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