Who is Carl Feuerbach? Nine point circle? Help?

Answer 1

Karl Feuerbach was a great German mathemitician. Geometers universally regard the so-called Feuerbach theorem as undoubtedly one of the most beautiful theorems in the modern geometry of the triangle. This theorem concerns itself with five important circles related to a triangle. These five circles are the incircle (or circle inscribed in the triangle), the three encircles (or circles touching one side of the triangle and the other two produced), and the nine-point circle (or circle passing through the three midpoints of the sides of the triangle).* Now the Feuerbach theorem says that for any triangle, the nine-point circle is tangent to the incircle and to each of the three encircles of the triangle. This is a beautiful theorum that describes the triangle.

Answer 2

http://en.wikipedia.org/wiki/Nine_point_circle