Inversion helps to solve problems

Inversion is a transformation of the plane that can turn complicated geometric figures into simpler ones. When solving geometry problems, especially those involving circles and tangency, inversion can change the relationships between points, lines, and circles in a way that makes the problem easier to analyze or solve.

Important properties

• Inversion maps circles and lines to other circles or lines.

• Angles are preserved in magnitude (inversion is conformal).

• Points inside the circle of inversion are mapped outside, and vice versa.

• Inversion can turn tangency and intersection problems into simpler configurations.