International Mathematical Olympiad 1964 Problem 3

A circle is inscribed in triangle $ABC$ with sides $a, b, c$. Tangents to the circle parallel to the sides of the triangle are constructed. Each of these tangents cuts off a triangle from $\triangle ABC$. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of $a, b, c$).