Problem:
Points and are units apart. How many lines in a given plane containing and are units from and units from
Answer Choices:
A.
B.
C.
D.
E. more than
Solution:
The set of lines that are units from the point is the set of tangents to the circle with center and radius . Similarly, the set of lines that are units from point is the set of tangents to the circle with center and radius . Thus the desired set of lines is the set of common tangents to the two circles. Since , these two circles are tangent externally, so they have three common tangents.
