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CE=CB_1 wanted, diameter and touchpoint of incircle related

Source: Germany Federal - Bundeswettbewerb Mathematik 2012, round 2, p3

April 14, 2020
geometryincircleequal segmentsdiameter

Problem Statement

The incircle of the triangle ABCABC touches the sides BC,CABC, CA and ABAB in points A1,B1A_1, B_1 and C1C_1 respectively. C1DC_1D is a diameter of the incircle. Finally, let EE be the intersection of the lines B1C1B_1C_1 and A1DA_1D. Prove that the segments CECE and CB1CB_1 have equal length.
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