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

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.

Details

See Euler line of intouch triangle.

External Links

Circumcircle (Wolfram MathWorld)

Contact Triangle (Wolfram MathWorld)

Incircle (Wolfram MathWorld)

Orthocenter (Wolfram MathWorld)

Permanent Citation

Jay Warendorff

"Collinearity of a Triangle's Circumcenter, Incenter, and the Contact Triangle's Orthocenter"
http://demonstrations.wolfram.com/CollinearityOfATrianglesCircumcenterIncenterAndTheContactTri/
Wolfram Demonstrations Project
Published: March 7, 2011