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