The nine point circle

Author:
Zoltán Kovács
The nine-point circle can be constructed for any given triangle. It passes through nine significant concyclic points defined from the triangle. Those are: the midpoint of each side of the triangle, the foot of each altitude and the midpoint of the line segment from each vertex of the triangle to the orthocenter.
GeoGebra Applet
  1. Select the Relation Tool (from the 10th toolbox) and check if the concyclic points indeed lie on the circle. Click "More" to start a symbolic check.
  2. You may also check that points D and K are not generally coincide.
Technical note: You cannot check whether points J and L lie on the circle here at the moment (you need to use the desktop version instead). If you get the answer "possibly generally true" than the web version of GeoGebra was unable to compute the proof and certainly crashed. In this case you must reload the page to recover GeoGebra to work properly again.

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