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 obviously the center. Plugging in points and gives us that . Seeing our answer choices, none of the points work, thus our answer is E.