Orthocenter is Circumcenter of new Triangle
Channel: Saltire Software
Date: 05/11/2020

Let F be the orthocenter of triangle ABC.  Then the circumcenters of the four triangles ABF, ACF, FBC form a triangle.  F is the circumcenter of this new triangle.
To prove this, we show that all three circles have the same radius.  We further show that this is the same radius as the circumcircle of the original triangle.