Problem of Apollonius

So, let's say you have three friends and you want to give them each a present. You have one present that is a circle, and you want to cut it into three pieces so that each of your friends gets a piece that is the same size and shape.

This is a problem that people have been trying to solve for a long time, and it's called the problem of Apollonius. Basically, it's a math problem that asks you to find all the possible circles that can be drawn around three given points.

To solve the problem, you have to think about how circles work. A circle is defined by its center and its radius. So, if you have three points, there might be a circle that goes through all three of them, or there might be two circles that go through two of the points and touch the third one, or there might not be any circle that goes through all three points.

The problem of Apollonius asks you to find all the possible circles that can be drawn around three given points. It's a tricky problem, but it's also really interesting because it helps us understand how circles work and how we can use them to solve all kinds of problems.