3. (YUG) The incircle is inscribed in a triangle $A B C$ with sides $a, b, c$. Three tangents to the incircle are drawn, each of which is parallel to one side of the triangle $A B C$. These tangents form three smaller triangles (internal to $\triangle A B C$ ) with the sides of $\triangle A B C$. In each of these triangles an incircle is inscribed. Determine the sum of areas of all four incircles.
3. Let $r$ be the radius of the incircle of $\triangle A B C, r_{a}, r_{b}, r_{c}$ the radii of the smaller circles corresponding to $A, B, C$, and $h_{\mathrm{n}}, h_{\mathrm{b}}, h_{c}$ the altitudes from $A, B, C$ respectively. The coefficient of similarity between the smaller triangle at $A$ and the triangle $A B C$ is $1-2 r / h_{n}$, from which we easily obtain $r_{a}=\left(h_{a}-2 r\right) r / h_{a}=(s-a) r / s$. Similarly, $r_{b}=(s-b) r / s$ and $r_{c}=(s-c) r / s$. Now a straightforward computation gives that the sum of areas of the four circles is given by
$$
\Sigma=\frac{(b+c-a)(c+a-b)(a+b-c)\left(a^{2}+b^{2}+c^{2}\right) \pi}{(a+b+c)^{3}} .
$$