Osječki matematički list, Vol. 9 No. 1, 2009.
Professional paper
Feuerbach's theorem
Zdenka Kolar- Begović
orcid.org/0000-0001-8710-8628
; Odjel za matematiku, Sveučilište J. J. Strossmayera, Osijek, Hrvatska
Ana Tonković
; OŠ Vladimir Nazor, Virovitica, Hrvatska
Abstract
The mid-points of the sides of a triangle, the
feet of the altitudes, and the mid-points of the segments from
the orthocenter to the vertices lie on one circle the so called
Euler circle. In 1822 Feuerbach discovered and proved that Euler
circle of a triangle is a tangent to the inscribed circle and to
each of the escribed circles. In the literature this statement is
known as Feuerbach's theorem. There are numerous proofs of this
famous statement. An analytic proof of this theorem is considered in this paper. Some facts concerning inscribed and
escribed circles of a triangle necessary for derivation of the
proof are also explored. Some properties of Euler circle are also considered as well as some historical elements of this concept.
Keywords
triangle; Euler circle; Feuerbach's theorem
Hrčak ID:
42991
URI
Publication date:
12.11.2009.
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