![http://commons.wikimedia.org/wiki/File:Archimedes%27_Circles.svg](http://www.futilitycloset.com/wp-content/uploads/2014/03/2014-03-20-archimedes-twin-circles.png)
Pick any three points on a line and use each pair of them to define a semicircle, as shown.
Now draw a perpendicular between the two smaller semicircles.
Circles c1 and c2 will always have the same area.
Pick any three points on a line and use each pair of them to define a semicircle, as shown.
Now draw a perpendicular between the two smaller semicircles.
Circles c1 and c2 will always have the same area.