GoGeometry Action 136!

Creation of this applet was inspired by a problem posted by Antonio Gutierrez (GoGeometry). Even though you can move the colored vertices of the quadrilateral anywhere you'd like, this applet will work best if the quadrilateral remains CONVEX. (If you don't remember what it means for a polygon to be convex, click here for a quick refresher). Note: The blue and red sliders control the measures of the angles with blue and red vertices, respectively. How would you, in your own words, describe the phenomena you observe here? How can we formally prove that the 4 yellow points (soon to appear) ALWAYS LIE ON A CIRCLE?

Quick (Silent) Demo