Answer
See below
Work Step by Step
The rope forms a chord of the circle and is a maximum distance of 50 feet from the edge of the pond.
From this detail, we can sketch it and get $$\frac{l}{2}=\sqrt 165^2-(165-50)^2\\\frac{l}{2}=20\sqrt 35$$
The length of the rope is $l=40\sqrt 35\approx236.643$
