
IMO 2011 (Problem 6)
Let $\displaystyle ABC$ be an acute triangle with circumcircle $\displaystyle \Gamma$. Let $\displaystyle l$ be a tangent line to $\displaystyle \Gamma$, and let $\displaystyle l_a,l_b$ and $\displaystyle l_c$ be the lines obtained by reflecting $\displaystyle l$ in the lines $\displaystyle BC$ , $\displaystyle CA$ and $\displaystyle AB$ , respectively. Show that the circumcircle of the triangle determined by the lines $\displaystyle l_a,l_b$ and $\displaystyle l_c$ is tangent to the circle $\displaystyle \Gamma$ .