IMO Shortlist 1964 problem 2


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2. travnja 2012.
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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