Collinearity of a Triangle's Circumcenter, Incenter, and the Contact Triangle's Orthocenter
Initializing live version

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Let I and O be the incenter and circumcenter of a triangle. Let H be the orthocenter of the triangle's contact triangle (the triangle formed by the points of contact of the incircle with the sides). Then I, O, and H are collinear.
Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA