A 2011 IMO Tangency Problem

Let be an acute triangle with circumcircle . Let be a tangent line to at the point and let , , and be the lines obtained by reflecting in the lines , , and , respectively. Let be the triangle formed by the intersections of , , and . Then the circumcircle of is tangent to the circle .

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This is problem 6 in the 2011 International Mathematical Olympiad; see International Mathematical Olympiad Problems.
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