Knowing that Triangle $LAB$ is similar to Triangle $LRQ$, prove that the length of $QR$ is constant while point $L$ varies. There are two circles intersect at points $A$ and $B$. $L$ is a point on first circle that is free to move, whereas $LA$ & $LB$ meet at the second circle again at $Q$ & $R$. $LA$ is not tangent to the second circle.
Should I use proportions from secant segment theorem here to show that $QR$ is not affected by the movement of point $L$? Would that be enough to prove this $QR$ to be constant?