Sum of Circle Areas
- Judah L Schwartz
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 sum of the areas of the BLUE circles is equal to the sum of the areas of the RED circles no matter where you place the BLACK dot. Can you prove this?