A Triangle and an External Contact 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. The triangle formed by the three points of tangency is called an external contact triangle.

Let ABC be a triangle. Let and be the radii of the circumcircle and an excircle of ABC. Let be the area of ABC and be the area of the external contact triangle. Then .