Problem: The locus of the mid-point of a line segment that is drawn from a given external point to a given circle with center and radius , is:
Answer Choices:
A. a straight line perpendicular to
B. a straight line parallel to
C. a circle with center and radius
D. a circle with center at the midpoint of and radius
E. a circle with center at the mid-point and radius
Solution:
Let be any line segment through such that lies on the given circle with center and radius . Let be the midpoint of and let be the midpoint of . To see that the required locus is a circle with center and radius , consider the similar triangles and . For any point on the given circle, . is the correct choice.
