The figure below shows a
triangle ABC where A_{1}, B_{1}, and C_{1} are on BC, AC, and AB,
respectively, so that the
incircles
of triangles AB_{1}C_{1}, BA_{1}C_{1}, and
CA_{1}B_{1} are equal. Prove that the
areas
of triangles A_{1}B_{1}C_{1} and A_{2}B_{2}C_{2}
are equal (equivalent triangles).
