Synthetic proofs of two theorems related to the Feuerbach point (Q2880796)
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scientific article; zbMATH DE number 6024852
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Synthetic proofs of two theorems related to the Feuerbach point |
scientific article; zbMATH DE number 6024852 |
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17 April 2012
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Feuerbach point
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anti-Steiner point
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Euler line
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0.8258047
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Synthetic proofs of two theorems related to the Feuerbach point (English)
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In this paper the authors give synthetic proofs of the following results:NEWLINENEWLINETheorem 1. The Feuerbach point of a triangle \(ABC\) is the anti-Steiner point of the Euler line of the intouch triangle of \(ABC\) with respect to the same triangle.NEWLINENEWLINE Theorem 2. The cycle through the feet of the internal bisectors of a triangle \(ABC\) passes through the Feuerbach point of the triangle.NEWLINENEWLINEThese results are already known, but the proofs are new.
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