# IMO 2011 (Problem 6)

Let $ABC$ be an acute triangle with circumcircle $\Gamma$. Let $l$ be a tangent line to $\Gamma$, and let $l_a,l_b$ and $l_c$ be the lines obtained by reflecting $l$ in the lines $BC$ , $CA$ and $AB$ , respectively. Show that the circumcircle of the triangle determined by the lines $l_a,l_b$ and $l_c$ is tangent to the circle $\Gamma$ .