Inversion in a circle

Inversion in a circle is a geometric transformation where points are mapped to new locations relative to a fixed circle called the "inversion circle." For any point outside the circle, its inverse is found along the line connecting it to the circle's center, at a distance inversely proportional to the original point's distance from the center. Specifically, the product of the distances from the center to the original point and its inverse equals the square of the circle's radius. This transformation preserves angles and transforms lines into circles, helping to analyze complex geometric problems by simplifying shapes and relationships.