Circle Optimization Challenge!

Creation of this activity was inspired by a problem posted by Alexander Bogomolny. Shown below is a circle with a chord. The chord has pink endpoints. The green point is any point on this chord. The green segment displayed illustrates the shortest distance from the green point to the circle itself. Feel free to move these LARGE POINTS anywhere you'd like AT ANY TIME. Challenge: Given the circle has radius r, express the length of the green segment solely as a function of r (regardless of green point's location on the chord itself).