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 .