Creation of this applet was inspired by a [url=http://www.gogeometry.com/school-college/3/p1241-quadrilateral-exterior-angle-bisector-circle-cyclic.htm]problem[/url] posted by [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] (GoGeometry). [br][br]Even though you can move the colored vertices of the quadrilateral anywhere you'd like, this applet will work best if the quadrilateral remains [b]CONVEX. [/b](If you don't remember what it means for a polygon to be convex, [url=https://www.geogebra.org/m/knnPDMR3]click here[/url] for a quick refresher). [br][br][b]Note:[/b][br]The [b][color=#1e84cc]blue[/color][/b] and [b][color=#cc0000]red[/color][/b] sliders control the measures of the angles with [b][color=#1e84cc]blue[/color][/b] and [b][color=#cc0000]red[/color][/b] vertices, respectively. [br][br]How would you, in your own words, describe the phenomena you observe here? [br][br][color=#bf9000][b]How can we formally prove that the 4 yellow points (soon to appear) ALWAYS LIE ON A CIRCLE? [/b][/color]