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Circle in triangle

Source: 239 2014 S7

January 14, 2020
geometry

Problem Statement

A circle ω\omega is strictly inside triangle ABCABC. The tangents from AA to ω\omega intersect BCBC in A1,A2A_1,A_2 define B1,B2,C1,C2B_1,B_2,C_1,C_2 similarly. Prove that if five of six points A1,A2,B1,B2,C1,C2A_1,A_2,B_1,B_2,C_1,C_2 lie on a circle the sixth one lie on the circle too.
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