IMO 1964 Problem 3

A circle is inscribed in a triangle $ABC$ with sides $a,b,c$ . Tangents to the circle parallel to the sides of the triangle are contructe. Each of these tangents cuts off a triagnle 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 $a,b,c$ ).