Hey! Pretty cool pic!
This drawing is actually very helpful.
Now, extend the 4-ft line until it intersects the circle at the other side. Let x be the length of the extension. This forms two cords of a circle; one is 8 ft (4+4) and the other is (4+x) ft. We will find the length (4+x), which is the diameter of the circle [you may want to verify that a line segment that is perpendicular to a cord and bisects it, goes through the center of the circle and forms the diameter of the circle).
This is where it gets super interesting –
The Intersecting Cords Theorem: If two chords intersect inside a circle then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.
That means that –
4x = 8*8
x = 16
diameter = (x+4) = 20 ft