Tangent space at a boundary point of closed disc.

Question

I am a beginner at Manifolds. I am reading Tangent space at a point of a manifold $M$.

What I know:

If I take my manifold $M$ to be a closed unit disk then for any point $a$ inside the disk I know that $T_{a}M \cong \mathbb{R^2}$.

My actual question:

Now if I choose my point $a$ to be on the boundary of the closed disc then how to calculate $T_{a}M$? Will, it still be isomorphic to $\mathbb{R^2}$, or does it changes?

Thanks for any insights!!