Altitudes, Orthocenters, and Circumcircles
Sarah Mason
The picture below demonstrates the unique relationship
between the orthocenter (H) of triangle ABC, the circumcircle
of triangle ABC, and the circumcircles of triangles AHC, CHB,
and BHA.
To investigate a particular aspect, select
one of the below listed conjectures.
The orthocenters
of the three smaller triangles are located on the opposing vertices
of ABC.
The circumcircles
of triangles AHC, CHB, and BHA intersect at the orthocenter of
triangle ABC.
All four circumcircles
have the same radius.
The circumcenters
of all four triangles form parallelograms when connected to certain
vertices.
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