This article is the third in a series of activities that discusses some interesting relationships with triangles. The first article (EJ1259412) introduced the various circles and centres involved with a triangle, as well as the Euler Line (named after the famous mathematician Leonhard Euler) which passes through four of the five centres. The second article (EJ1261802) used both algebra and geometry to a variety of sizes of important properties of the triangle (its area, its circumradius and inradius amongst others), in terms of the lengths of its three sides. In this article, Feuerbach's theorem is presented and gives a relationship between the incircle and its nine-point-circle--that they just touch each other, meeting in just one point, with a common tangent at that point. In fact, his theorem goes further--it also states that the nine-point-circle just touches each of the three excircles of the triangle; an excircle is a circle which has one side as a tangent, as well as the extensions of the other two sides.