Four circle theorem

The Four Circle Theorem states that if four circles are arranged so that each one touches the next in a chain, then the four points where they touch form a special pattern. Specifically, if you draw lines connecting these points, the lines will form a set of intersecting chords inside the main circles. The key insight is that the angles created at the points of contact satisfy certain relationships, ensuring a predictable geometric harmony. This theorem reveals deep connections between circles and angles, highlighting the elegance and symmetry inherent in circle arrangements.