A circle is inscribed in a triangle with sides . Tangents to the circle parallel to the sides of the triangle are contructe. Each of these tangents cuts off a triagnle from . In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of ).
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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 $a,b,c$).
Izvor: Međunarodna matematička olimpijada, shortlist 1964
Školjka 
with sides 
. Tangents to the circle parallel to the sides of the triangle are contructe. Each of these tangents cuts off a triagnle from 
. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of