The distance from the incenter to the Euler line

Journal article


Franzsen, William N.. (2011). The distance from the incenter to the Euler line. Forum Geometricorum. 11, pp. 231 - 236.
AuthorsFranzsen, William N.
Abstract

It is well known that the incenter of a triangle lies on the Euler line if and only if the triangle is isosceles. A natural question to ask is how far the incenter can be from the Euler line. We find least upper bounds, across all triangles, for that distance relative to several scales. Those bounds are found relative to the semi-perimeter of the triangle, the length of the Euler line and the circumradius, as well as the length of the longest side and the length of the longest median.

Year2011
JournalForum Geometricorum
Journal citation11, pp. 231 - 236
PublisherDepartment of Mathematics, Florida Atlantic University
ISSN1534-1178
Web address (URL)http://forumgeom.fau.edu/FG2011volume11/FG201126.pdf
Open accessOpen access
Page range231 - 236
Research GroupSchool of Arts
Publisher's version
Place of publicationUnited States of America
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https://acuresearchbank.acu.edu.au/item/88135/the-distance-from-the-incenter-to-the-euler-line

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