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Prove that I1D, I2E, I3F are concurrent

Source: Mumbai Region RMO 2014 Problem 6

December 7, 2014
geometryincentertrapezoidangle bisectorgeometry unsolved

Problem Statement

Let D,E,FD,E,F be the points of contact of the incircle of an acute-angled triangle ABCABC with BC,CA,ABBC,CA,AB respectively. Let I1,I2,I3I_1,I_2,I_3 be the incentres of the triangles AFE,BDF,CEDAFE, BDF, CED, respectively. Prove that the lines I1D,I2E,I3FI_1D, I_2E, I_3F are concurrent.
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