1957 AHSME Problems/Problem 50

Problem

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 $O'$ :

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

Solution

$\fbox{\textbf{(B)}remains stationary}$ .

1957 AHSC (Problems • Answer Key • Resources)
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1957 AHSME Problems/Problem 50

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