# GoGeometry Action 18!

- Author:
- Tim Brzezinski

**Suppose, in the applet below,**Slide the slider slowly and carefully observe the dynamics that take place. Be sure to move point

*AB = a*and*BC = b*.*B*around afterwards. If you choose, drag

*A*and/or the large white point as well. Reset the slider and re-slide slowly.

**Write an expression, in terms of**

*a*and*b*, for the length of the black segment (labelled with 3 hash marks.) How can you formally prove your response true?Creation of this applet was inspired by a tweet from Antonio Gutierrez.