Contact Triangles of a Triangle

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Extend two sides of a triangle and construct the circle tangent to those sides and the third 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 and be the radii of the incircle and an excircle of ABC. Let and be the areas of the contact triangles for the incircle and excircle. Then .


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



The statement of the theorem is in Problem 84. Contact Triangles Areas, Incircle, Excircle.

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