1957 AHSME Problem 50

In circle O, G is a moving point on diameter \overline{AB}. \overline{AA'} is drawn perpendicular to \overline{AB} and equal to \overline{AG}. \overline{BB'} is drawn perpendicular to \overline{AB}, on the same side of diameter \overline{AB} as \overline{AA'}, and equal to BG. Let O' be the midpoint of \overline{A'B'}. Then, as G moves from A to B, point O':

\begin{array}{l} \textbf{(A)}\ \text{moves on a straight line parallel to }{AB}\qquad \\ \textbf{(B)}\ \text{remains stationary}\qquad\\ \textbf{(C)}\ \text{moves on a straight line perpendicular to }{AB}\qquad\\ \textbf{(D)}\ \text{moves in a small circle intersecting the given circle}\qquad\\ \textbf{(E)}\ \text{follows a path which is neither a circle nor a straight line} \end{array}

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