Geometry Problem 85. Contact Triangles Areas, Incircle, Excircle, Contact Triangles. High School, College, Math Education

In the figure below, given a triangle
ABC, S_{1} is the area of contact triangle of the
incircle, S_{a}, S_{b}, and S_{c} are
the areas of the contact triangles of the excircles. Prove that:
.
.