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B_2C_2 diameter of incircle wanted

Source: All-Russian MO 2009 Regional 10. 6

August 27, 2024
geometryincircle

Problem Statement

Circle ω\omega inscribed in triangle ABCABC touches sides BCBC, CACA, ABAB at points A1A_1, B1B_1 and C1C_1 respectively. On the extension of segment AA1AA_1, point AA is taken as point D such that AD=AC1AD= AC_1. Lines DB1DB_1 and DC1DC_1 intersect a second time circle ω\omega at points B2B_2 and C2C_2. Prove that B2C2B_2C_2 is the diameter of circle of ω\omega.
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