A Relation between the Contact Triangles of a Triangle

Extending two sides in a triangle, construct the circle tangent to those sides and the other side of the triangle. The resulting circle is called an excircle.
A contact triangle is a triangle formed from the points of tangency between the sides of a triangle and its incircle or the extended sides of the triangle and one of its excircles.
Let ABC be a triangle. Let be the area of the internal contact triangle and , , and be the areas of the external contact triangles. Then .

THINGS TO TRY

SNAPSHOTS

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

DETAILS

    • 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.