KöMaL 2013 B4511

The circle $k$ touches the circle $\ell$ internally at point $P$. A line $p$ passing through $P$ intersects the circles again at the points $K$ and $L$, respectively. $u$ is the tangent drawn at a point $U$ of circle $k$. One intersection of $u$ with the circle $\ell$ is $V$, and the intersection of lines $KU$ and $LV$ is $T$. Determine the locus of the point $T$ as $U$ traverses the circle $k$. (Consider both intersections of $u$ and $\ell$; if $U$=$K$, the line $KU$ is the tangent to $k$at $K$. Analogously, if $V$=$L$ then $LV$ is the tangent drawn to $\ell$ at $L$.)