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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

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

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A 2011 IMO Tangency Problem