Collinearity of an Orthocenter, the Incenter, and the Circumcenter

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Let ABC be a triangle with incenter I and circumcenter O. Let the incircle intersect AB, BC, and CA at M, N, and P, respectively. Let the orthocenter (the intersection of the altitudes) of MNP be H. Then H, I, and O are collinear.

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA


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See Example 6 on page 4 of Mathematical Excalibur, Volume 9, No. 2.



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