Collinearity of an Orthocenter, the Incenter, and the Circumcenter

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.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

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

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.







Related Curriculum Standards

US Common Core State Standards, Mathematics