The GOLD dot is connected to all four vertices of a rectangle. [br]You can set the size & shape of the rectangles by dragging the GRAY dot.[br]You can place the GOLD dot anywhere in the rectangle.[br][br]The length of the segment from each vertex of the rectangle to the GOLD dot is the side of a regular polygon.[br][br]The sum of the areas of the BLUE polygons is equal to the sum of the areas of the GREEN polygons no matter where you place the GOLD dot. [br][br]Can you prove this? What happens when you drag the GOLD dot outside the rectangle? Why?