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
In Branch
Principal Result Of
Source Karl Wilhelm Feuerbach (Wikipedia)
Proved By
Source ProofWiki: Feuerbach's Theorem - ProofWiki
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.
Karl Wilhelm Feuerbach (Wikipedia)
Principal Result Of: Karl Wilhelm Feuerbach, Lead, 1822 bookQuote, Principal Result Of: Karl Wilhelm Feuerbach, Lead, 1822 book
a theorem on the nine-point circle, which is now known as Feuerbach's theorem
ProofWiki: Feuerbach's Theorem - ProofWiki
ProofWikiProved By: Karl Wilhelm Feuerbach, Historical NoteQuote, Proved By: Karl Wilhelm Feuerbach, Historical Note
Feuerbach's Theorem was proved in $1822$ by Karl Wilhelm Feuerbach.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.