# Math Help - Inscribed circle center problem

1. ## Inscribed circle center problem

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

2. I can prove that if $\angle TCA = \angle TCB$ then we are done. But how to show that these two angles are actually equal?