Find the radius of circle $P$ 
$ABCD$ is a rectangle with $AB = CD = 2$. A circle centered at $O$ is tangent to $BC, CD,$ and $AD$ (and hence has radius $1$). Another circle, centered at $P$, is tangent to circle $O$ at point $T$ and is also tangent to $AB$ and $BC$. If line $AT$ is tangent to both circles at $T$, find the radius of circle $P$.

Can someone create a picture for this? I am having a hard time seeing how the circle centered at $P$ can be tangent to the circle centered at $O$.

I don't know if you want a picture as an answer, or a solution as an answer, but here's a picture (roughly to scale, but no promises):

