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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