Descartes' theorem

Descartes' theorem, also known as the circles theorem, describes a geometric relationship between four mutually tangent circles. It states that if you have three tangent circles, you can find a fourth circle that is tangent to all three. The theorem provides a formula to calculate the curvature (which is the inverse of the radius) of the fourth circle based on the curvatures of the three given circles. This theorem illustrates a fascinating interplay of geometry and mathematics, showcasing how shapes can interact through tangency.