Some new inequalities for an interior point of a triangle (Q2902012)
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scientific article; zbMATH DE number 6062777
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some new inequalities for an interior point of a triangle |
scientific article; zbMATH DE number 6062777 |
Statements
Some new inequalities for an interior point of a triangle (English)
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1 August 2012
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triangle
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interior point
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Erdős-Mordell inequality
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Euler inequality
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conjectures
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0.93861836
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0.93605185
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0.9241508
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0.90213674
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The author proves three inequalities connected to a point \(P\) in the plane of an arbitrary triangle \( ABC \). The first inequality concerns the product of the area of \(\triangle ABC\) and the third power of the circumradius of \(\triangle ABC\). The other two inequalities are related to the inradius of the pedal triangle of \(P\) with respect to \(\triangle ABC\). More general conjectures and problems are also given.
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