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EF tangent to circumcircle of ABC, circumcircle of BIC related, incenter I

Source: 2007 Oral Moscow Geometry Olympiad grades 8-9 p4

October 18, 2020
geometrycircumcircleincentertangent

Problem Statement

Let II be the center of a circle inscribed in triangle ABCABC. The circle circumscribed about the triangle BICBIC intersects lines ABAB and ACAC at points EE and FF, respectively. Prove that the line EFEF touches the circle inscribed in the triangle ABCABC.
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