Problem: In circle O,G is a moving point on diameter AB. AA′ is drawn perpendicular to AB and equal to AG.BB′ is drawn perpendicular to AB, on the same side of diameter AB as AA′, and equal to BG. Let O′ be the midpoint of A′B′. Then, as G moves from A to B, point O′:
Answer Choices:
A. moves on a straight line parallel to AB
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:
A′ABB′ is a trapezoid. Its median OO′ is perpendicular to AB.
OO′=21​(AA′+BB′)=21​(AG+BG)=21​AB.
∴O′ is a fixed distance from O on the perpendicular to AB, and therefore the point O′ is stationary.