Apollonian theorem

The Apollonian theorem relates to geometry and the properties of circles. It states that if you have three circles that intersect at a single point, you can construct another circle that is tangent to all three. This means that the new circle just touches each of the three circles at one point, without crossing them. The theorem highlights the beauty of geometric relationships and has applications in various fields, such as mathematics and engineering, demonstrating how different shapes can interact in space.