GoGeometry Action 193!

Creation of this resource was inspired by [url=https://www.gogeometry.com/school-college/p967-three-equilateral-triangle-midpoint-animation.htm]this problem[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][b][br]How would you describe the phenomenon you see here? [br]How can formally prove this true? [/b]
LARGE POINTS are moveable here. Move them where you'd like!

Information: GoGeometry Action 193!