A new proof of Neuberg's theorem and one application (Q2848759)
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scientific article; zbMATH DE number 6212205
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new proof of Neuberg's theorem and one application |
scientific article; zbMATH DE number 6212205 |
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26 September 2013
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convex quadrilateral
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area
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Neuberg's theorem
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A new proof of Neuberg's theorem and one application (English)
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Let \(ABC\) be a triangle and let \(M\) be a point lying in the same plane but not on the sides (or their prolongations) of \(ABC\). If \(H_a\), \(H_b\) and \(H_c\) are the orthocentres of \(MBC\), \(MCA\) and \(MAB\), respectively, then Neuberg's theorem states that the areas of the triangles \(ABC\) and \(H_aH_bH_c\) are equal.NEWLINENEWLINEIn this paper, the authors give a proof of this result using elementary analytic geometry and present some kind of extension for convex quadrilaterals.
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