Feuerbach's Theorem states that the nine-point circle of a triangle is internally tangent to the triangle's incircle and externally tangent to each of its three excircles. Named for Karl Wilhelm Feuerbach, it is a classical result of triangle geometry, and the point of tangency between the nine-point circle and the incircle is now called the Feuerbach point.
Facts
StatementThe nine-point circle of a triangle is internally tangent to the triangle's incircle and externally tangent to each of its three excircles. 1 Connections
Sources
1. Feuerbach's Theorem (Wikipedia)
Wikimedia Foundationopening paragraph, second sentenceQuote, opening paragraph, second sentence
Feuerbach's theorem, published by Feuerbach in 1822, states more generally that the nine-point circle is tangent to the three excircles of the triangle as well as its incircle.
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