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
).
%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 $a,b,c$).
Školjka