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The Path of Point O'

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June 8, 2009

Problem Statement

In circle O O, G G is a moving point on diameter AB‾ \overline{AB}. AA′‾ \overline{AA'} is drawn perpendicular to AB‾ \overline{AB} and equal to AG‾ \overline{AG}. BB′‾ \overline{BB'} is drawn perpendicular to AB‾ \overline{AB}, on the same side of diameter AB‾ \overline{AB} as AA′‾ \overline{AA'}, and equal to BG BG. Let O′ O' be the midpoint of A′B′‾ \overline{A'B'}. Then, as G G moves from A A to B B, point O′ O': <spanclass=′latex−bold′>(A)</span> moves on a straight line parallel to AB<spanclass=′latex−bold′>(B)</span> remains stationary<spanclass=′latex−bold′>(C)</span> moves on a straight line perpendicular to AB<spanclass=′latex−bold′>(D)</span> moves in a small circle intersecting the given circle<spanclass=′latex−bold′>(E)</span> follows a path which is neither a circle nor a straight line <span class='latex-bold'>(A)</span>\ \text{moves on a straight line parallel to }{AB}\qquad \\ <span class='latex-bold'>(B)</span>\ \text{remains stationary}\qquad \\ <span class='latex-bold'>(C)</span>\ \text{moves on a straight line perpendicular to }{AB}\qquad \\ <span class='latex-bold'>(D)</span>\ \text{moves in a small circle intersecting the given circle}\qquad \\ <span class='latex-bold'>(E)</span>\ \text{follows a path which is neither a circle nor a straight line}
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