Problem: In circle is a moving point on diameter . is drawn perpendicular to and equal to is drawn perpendicular to , on the same side of diameter as , and equal to . Let be the midpoint of . Then, as moves from to , point :
Answer Choices:
A. moves on a straight line parallel to
B. remains stationary
C. moves on a straight line perpendicular to AB
D. moves in a small circle intersecting the given circle
E. follows a path which is neither a circle nor a straight line
Solution:
is a trapezoid. Its median is perpendicular to .
is a fixed distance from on the perpendicular to , and therefore the point is stationary.