GoGeometry Action 67!

Creation of this applet was inspired by a tweet from Antonio Gutierrez. Below, you will find a circle inscribed in a square. (You can move the vertices of the square around if you'd like.) Slide the slider slowly and carefully observe what happens. How does this applet informally show that the area of the green triangle is 1/40 the area of the square? How can we formally prove this true?

Quick (Silent) Demo