Editing Nine-point circle (section)

==Tangent circles==
[[File:Circ9pnt3.svg|right|thumb|250px|The nine-point circle is tangent to the incircle and excircles.]]
In 1822 Karl Feuerbach discovered that any triangle's nine-point circle is externally [[Tangent circles|tangent]] to that triangle's three [[excircle]]s and internally tangent to its [[incircle]]; this result is known as [[Feuerbach's theorem]].  He proved that:<blockquote>... the circle which passes through the feet of the altitudes of a triangle is tangent to all four circles which in turn are tangent to the three sides of the triangle...</blockquote> {{sfn|Feuerbach|Buzengeiger|1822}}

The [[triangle center]] at which the incircle and the nine-point circle touch is called the [[Feuerbach point]].