Three circles $\Gamma_1,\Gamma_2,\Gamma_3$ are inscribed into an angle(the radius of $\Gamma_1$ is the minimal, and the radius of $\Gamma_3$ is the maximal) in such a way that $\Gamma_2$ touches $\Gamma_1$ and $\Gamma_3$ at points $A$ and $B$ respectively. Let $\ell$ be a tangent to $A$ to $\Gamma_1$. Consider circles $\omega$ touching $\Gamma_1$ and $\ell$. Find the locus of meeting points of common internal tangents to $\omega$ and $\Gamma_3$.
1. **Understanding the Problem:**
   - We have three circles $\Gamma_1, \Gamma_2, \Gamma_3$ inscribed in an angle such that $\Gamma_2$ touches $\Gamma_1$ at point $A$ and $\Gamma_3$ at point $B$.
   - A tangent $\ell$ is drawn from point $A$ to $\Gamma_1$.
   - We consider another circle $\omega$ that touches $\Gamma_1$ and the tangent $\ell$.
   - We need to find the locus of the meeting points of common internal tangents to $\omega$ and $\Gamma_3$.

2. **Analyzing the Geometry:**
   - Since $\omega$ touches $\Gamma_1$ at $A$, the center of $\omega$ lies on the line perpendicular to $\ell$ at $A$.
   - The common internal tangents to $\omega$ and $\Gamma_3$ will intersect at the center of homothety between $\omega$ and $\Gamma_3$.

3. **Homothety Centers:**
   - The center of homothety between two circles that touch each other internally lies on the line joining their centers.
   - For $\omega$ and $\Gamma_3$, this center of homothety must lie on the line segment $AB$ because $\Gamma_2$ touches both $\Gamma_1$ and $\Gamma_3$ at $A$ and $B$ respectively.

4. **Locus of Points:**
   - The locus of the meeting points of the common internal tangents to $\omega$ and $\Gamma_3$ is the line segment $AB$ excluding the points $A$ and $B$ themselves.
   - This is because the homothety center cannot be at the points where the circles touch each other.

5. **Conclusion:**
   - The locus of the meeting points of the common internal tangents to $\omega$ and $\Gamma_3$ is the segment $AB$ excluding the endpoints $A$ and $B$.

\[
\boxed{\Gamma_2 \cap AB \setminus \{A, B\}}
\]