Sum of circle areas
The BLACK dot is connected to all four vertices of a rectangle.
The length of the segment from each vertex to the BLACK dot is the radius of a circle
- BLUE segments are the radii of BLUE circles; RED segments are the radii of RED circles.
The BLACK dot and the vertices of the rectangle are moveable.
Use the spreadsheet to explore relations involving the areas of the circles.
What conjectures did you make? Can you prove them?
Note: You can use the spreadsheet to do calculations, e.g. enter =B1 + B3 in a spreadsheet cell to get the sum Area B_1 + Area B_3. If you want a label, put it in quotes. For example, type "Area B_1" into a cell.
This worksheet is a small modification of a worksheet of the same name created by Judah Schwartz: https://tube.geogebra.org/user/profile/id/25758