Feuerbach’s theorem, also known as the nine-point circle theorem, says that for any triangle, there is a circle passing through the following nine points: The midpoints of each side. The foot of the altitude to each side. The midpoint between each vertex and the orthocenter. The orthocenter is the place where the three altitudes intersect. […] The post Feuerbach’s nine-point circle theorem first appeared on John D. Cook....