Nine-point circle
Circunferencia de los nueve puntos
- Date
- 1822 · confidence high
- Place
- France
- Credited to
- Charles Brianchon, Jean-Victor Poncelet, Karl Wilhelm Feuerbach and Olry Terquem
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Brianchon and Poncelet first proved that the midpoints of the sides and the feet of the altitudes of a triangle lie on the same circle; Feuerbach identified the same six points independently, and in 1822 Olry Terquem added the three midpoints between the vertices and the orthocenter, completing the nine points and coining the name. That same year Feuerbach proved that this circle is tangent to the triangle's incircle and excircles.
Wikidata attributes this milestone to Leonhard Euler, but according to Wikipedia the true discoverers were Brianchon, Poncelet, Feuerbach and Terquem in the early 19th century; no specific city has been confirmed.
What it led to
- Feuerbach's theorem on tangency with the incircle and excircles
- Development of the theory of triangle centers
Built on
- Classical triangle geometry: altitudes, medians and notable points