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punctured at the nine-point center. The incenter could be any such point, depending on the specific triangle having that particular orthocentroidal disk.
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must lie in the interior of the orthocentroidal circle, but not coinciding with the nine-point center; that is, it must fall in the open
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are in the open orthocentroidal disk punctured at its own center (and could be at any point therein), while the
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Leversha, Gerry; Smith, G. C. (November 2007), "Euler and triangle geometry",
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The square of the diameter of the orthocentroidal circle is
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302:{\displaystyle D^{2}-{\tfrac {4}{9}}(a^{2}+b^{2}+c^{2}),}
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are in the exterior of the orthocentroidal circle. The
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442:"The distance from the incenter to the Euler line"
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511:Bradley, Christopher J.; Smith, Geoff C. (2006),
382:Bradley, Christopher J.; Smith, Geoff C. (2006),
162:. This diameter also contains the triangle's
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54: Orthocentroidal circle bounded by the
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413:"Euler's triangle determination problem"
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150:is the circle that has the triangle's
513:"The locations of the Brocard points"
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317:are the triangle's side lengths and
174:outside the orthocentroidal circle.
384:"The locations of triangle centers"
180:showed in 1984 that the triangle's
27:Circle constructed from a triangle
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80:(N) both lie along with H and S
576:Circles defined for a triangle
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440:Franzsen, William N. (2011),
345:American Mathematical Monthly
215:of one or the other of the
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536:Altshiller-Court, Nathan,
213:set of potential locations
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482:10.1017/S0025557200182087
158:at opposite ends of its
34:A triangle (black), its
321:is the diameter of its
166:and is a subset of the
560:Orthocentroidal circle
411:Stern, Joseph (2007),
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144:orthocentroidal circle
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146:of a non-equilateral
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562:at Wikimedia Commons
469:Mathematical Gazette
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186:orthocentroidal disk
18:Orthocentroidal disk
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205:second Fermat point
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191:Furthermore, the
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16:(Redirected from
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538:College Geometry
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38:(blue), its
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36:orthocenter
329:References
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70:Euler line
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454:: 231–236
240:−
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570:Category
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182:incenter
160:diameter
156:centroid
148:triangle
140:geometry
114:Incenter
76:(O) and
60:centroid
58:(H) and
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525:: 71–77
396:: 57–70
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428:: 1–9
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311:a, b,
90:and F
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138:In
62:(S)
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