As in the figure,

$\displaystyle \odot O,\; AB,\; CT$ are tangency to both $\displaystyle \odot O_1$ and $\displaystyle \odot O_2$ with $\displaystyle T$ the point of tangency to them and $\displaystyle A,B,C$ are on $\displaystyle odot O$. Show that $\displaystyle T$ is the incentre of $\displaystyle \triangle {ABC}$