Contact Triangles of a Triangle

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 .