Q: Positioning Circles in a Ring I am working on a program and need to be able to draw circles around the ring.  The circle currently in the ring is manually placed.  Is there an equation for drawing non overlapping circles inside a ring?


A: Your ring is made from two circles. So the first circle on the ring is one which touches the two circles defining the ring. That part should be easy: make the diameter of the small circle equal to the width of the ring, i.e. to the difference between the radii of the circles which form the ring. The distance between the center of the small circle and the center of the ring should be the average of the radii of the circles forming the ring, i.e. half their sum.
To place a second circle next to the first, you have to construct a triangle from three known edge lengths. The centers of the circles (including the one for the ring) correspond to the triangle corners, and the edge lengths correspond to the sums of the radii. Obviously the seoncd circle should have the same size as the first one if your ring is really formed by concentric circles.
If you repeat this procedure, things may or may not work out nicely. If they do, then the redii of the circles involved fulfill certain relations, and the result is called a steiner chain. Thanks to dtldarek for providing that reference.
