OSN 2008 Problem 7

Given triangle $ABC$ with sidelengths $a,b,c$ . Tangents to incircle of $ABC$ that parallel with triangle's sides form three small triangle (each small triangle has 1 vertex of $ABC$ ). Prove that the sum of area of incircles of these three small triangles and the area of incircle of triangle $ABC$ is equal to $\frac{\pi (a^{2}+b^{2}+c^{2})(b+c-a)(c+a-b)(a+b-c)}{(a+b+c)^{3}}$

(hmm,, looks familiar, isn't it? :wink: )