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.[more]
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 .[less]
The statement of the theorem is in Problem 85. Contact Triangles Areas, Incircle, Excircle.