Begin with one BLACK circle, and inscribe 4 identical, interior, cyclically tangent, CYAN circles, such that they are also tangent to the black circle.

In each of the four cyan circles, inscribe 4 RED interior circles in exactly the same way.

Finally, inscribe a small GREEN circle in the center of the original black circle, tangent to the cyan circles.

Which is larger, this small green circle, or one of the small red circles?

Let's say the radius of a red circle = 1. The radius of a cyan circle would be sqr(2) + 1. The distance between the center of the green circle to the center of a cyan circle would be sqr(2) + 2. That would mean that the distance between the green circle to the center of a red circle (one of the closer ones) is 2. So the green circle is the same size as the red ones

Edited on June 16, 2004, 3:22 pm

Posted by Danny on 2004-06-16 15:20:19