Question 170
Let three circles $\odot O$, $\odot O_1$, $\odot O_2$, each externally tangent to the other two, lie on the same side of a line $\ell$. Let them be tangent to $\ell$ at points $A$, $A_1$, $A_2$ respectively, where point $A$ lies on segment $A_1A_2$. Denote the points of tangency of $\odot O$ with $\odot O_1$ and $\odot O_2$ as $B_1$ and $B_2$ respectively, and the point of tangency of $\odot O_1$ with $\odot O_2$ as $C$. Let line $A_1C$ intersect line $A_2B_2$ at point $D_1$, and line $A_2C$ intersect line $A_1B_1$ at point $D_2$. Prove that line $D_1D_2$ is parallel to line $\ell$.