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Four circles of equal radius touching

Source: Germany 2003 - Problem 2

December 22, 2022
geometryincentercircumcirclemidpointCenterTriangle

Problem Statement

There are four circles k1,k2,k3k_1 , k_2 , k_3 and k4k_4 of equal radius inside the triangle ABCABC. The circle k1k_1 touches the sides AB,CAAB, CA and the circle k4k_4 , k2k_2 touches the sides AB,BCAB,BC and k4k_4, and k3k_3 touches the sides AC,BCAC, BC and k4.k_4. Prove that the center of k4k_4 lies on the line connecting the incenter and circumcenter of ABC.ABC.
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