# Circle Optimization Challenge!

- Author:
- Tim Brzezinski

- Topic:
- Circle

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**, express the*r***length of the green segment**solely as a function of*r*(regardless of**green point**'s location on the chord itself).