University of South Carolina High School Math Contest/1993 Exam/Problem 25
Problem
What is the center of the circle passing through the point 
and tangent to the circle 
at 
? (Two circles are tangent at a point 
if they intersect at and at no other point.)
Solution
Let the circle we are looking for be 
where 
is the center. Plugging in points and gives us that 
. Seeing our answer choices, none of the points work, thus our answer is E.
