A Relation between the Contact Triangles of a Triangle

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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 .


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 85. Contact Triangles Areas, Incircle, Excircle.

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