Hi.

Here is a problem I've been trying to solve for some time now. Maybe you could help me.

We have two sets

$\displaystyle \mathcal {Q}$ is a set of those circles in the plane such that for any $\displaystyle x \in \mathbb{R}$ there exists a circle $\displaystyle O \in \mathcal {Q}$ which intersects $\displaystyle x$ axis in $\displaystyle (x,0)$.

$\displaystyle \mathcal {T}$ is a set of those circles in the plane such that for any $\displaystyle x \in \mathbb{R}$ there exists a circle $\displaystyle O \in \mathcal {T}$ which is tangent to $\displaystyle x$ axis in $\displaystyle (x,0)$.