Tangent Circles

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, tangent circles (also known as kissing circles) are circles that intersect in a single point. There are two types of tangency: internal and external. Many problems and constructions in geometry are related to tangent circles; such problems often have real-life applications such as trilateration and maximizing the use of materials. Trilateration is a method for determining the intersections of three sphere surfaces given the centers and radii of the three spheres. The solution is found by formulating the equations for the three sphere surfaces and then solving the three equations for the three unknowns, x, y, and z. To simplify the calculations, the equations are formulated so that the centers of the spheres are on the z=0 plane. Also the formulation is such that one center is at the origin, and one other is on the x-axis. It is possible to formulate the equations in this manner since any three non-colinear points lie on a plane. After finding the solution it can be transformed back to the original coordinate system.