Length of Chord Projected from Point on Intersecting Circle

Theorem
Let $C_1$ and $C_2$ be two circles which intersect at $A$ and $B$.

Let $T$ be a point on $C$.

Let $P$ and $Q$ be the points $TA$ and $TB$ intersect $C_2$.


 * Chord-Projected-from-Point-on-Intersecting-Circle.png

Then $PQ$ is constant, wherever $T$ is positioned on $C_1$.