Problem

Source: Argentina TST Iberoamerican 2008 problem 2

Tags: geometry unsolved, geometry



Two circunmferences $ \Gamma_1$ $ \Gamma_2$ intersect at $ A$ and $ B$ $ r_1$ is the tangent from $ A$ to $ \Gamma_1$ and $ r_2$ is the tangent from $ B$ to $ \Gamma_2$ $ r_1 \cap r_2=C$ $ T= r_1 \cap \Gamma_2$ ($ T \neq A$) We consider a point $ X$ in $ \Gamma_1$ which is distinct from $ A$ and $ B$. $ XA \cap \Gamma_2 =Y$ ($ Y \neq A$) $ YB \cap XC=Z$ Prove that $ TZ \parallel XY$