Online Geometry

Feuerbach Theorem: Table of Content

Feuerbach Points and Nine-Point Circle with interactive animation, manipulation, and step-by-step construction.

Feuerbach Point Facts  

iPad Apps IGS Apollonius: Feuerbach Point. Triangle, Incircle, Nine point circle, Tangent circles, Orthocenter, Midpoint 

iPad Apps: Apollonius Software. Feuerbach Point. Triangle, Incircle, Nine point circle, Tangent circles, Orthocenter, Midpoint.
Interactive Geometry Software.

Dynamic Geometry: Internal Feuerbach Point. HTML5 Animation for Tablets iPad, Nexus

GeoGebra, Dynamic Geometry: Internal Feuerbach Point
HTML5 Animation for Tablets (iPad, Nexus..)

Feuerbach Theorem, Acute Triangle illustration  

Feuerbach Theorem, Obtuse Triangle illustration  

Feuerbach Theorem, Right Triangle illustration
 

Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.

Spieker Center

Symmedian (Lemoine) Point

Steiner Point  

Mittenpunkt Point  


Karl Feuerbach (1800-1834) was a geometer who discovered the nine-point circle of a triangle.

One of the most striking theorems in triangle geometry is Feuerbach's theorem. He wrote in his 1822 paper:

The circle which passes through the feet of the altitudes of a triangle touches all four of the circles which are tangent to the three sides of the triangle; it is internally tangent to the inscribed circle and externally tangent to each of the circles which touch the sides of the triangle externally.
 

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