Apollonius problem

Imagine you have three toys that you really love: a teddy bear, a toy train, and a toy truck. You want to put them all on your bed, but you want to arrange them in a special way. You want them to be far away from each other, but each of them should be the same distance from the other two toys.

This is kind of like a math problem called the Apollonius problem. Instead of toys, we have circles (which are round shapes like balls). We want to draw three circles that are far away from each other, but each of them should be the same distance from the other two circles. We call this distance the radius of the circles.

It might not be easy to draw such circles with our hands, but mathematicians have come up with a special way to solve this problem using math. They use something called algebra (which is like a secret code to solve math problems) and some special tricks to draw the circles on paper.

This problem was named after a really smart mathematician from ancient Greece named Apollonius. People still use the method he discovered to solve this problem today, and it's really helpful in lots of areas of science and engineering where we need to find things that are equally spaced.