GoGeometry Action 18!
Suppose, in the applet below, AB = a and BC = b.
Slide the slider slowly and carefully observe the dynamics that take place.
Be sure to move point 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.