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find the area,

Source: KGZ national 3-problem

May 10, 2016
geometry

Problem Statement

Given a △ABC\triangle ABC with sides a,b,c.a,b,c. Three tangents are drawn to the incircle of △ABC\triangle ABC parallel to the sides of △ABC\triangle ABC.These tangents cut three new little triangles.Three little incircles are drawn into new little triangles.Find the sum of the area of these 4 incircles.
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