A circle is inscribed in a triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
with sides
![a,b,c](/media/m/3/6/4/36454fdb50fc50f021324b33a6b513e3.png)
. Tangents to the circle parallel to the sides of the triangle are contructe. Each of these tangents cuts off a triagnle from
![\triangle ABC](/media/m/1/f/3/1f3c3c0f3e134a169655f9511ba6ea82.png)
. 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](/media/m/3/6/4/36454fdb50fc50f021324b33a6b513e3.png)
).
%V0
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 $a,b,c$).