Inversion (other)
Overview
Important
Inversion is a transformation in the plane that maps points with respect to a fixed circle (the circle of inversion). Besides the basic properties, inversion has many interesting and useful consequences in geometry. For example, it can turn complicated figures into simpler ones, such as mapping circles to lines, or making tangency and collinearity easier to analyze.
Important properties
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A circle passing through the center of inversion maps to a straight line not passing through the center, and vice versa.
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Angles between curves are preserved (inversion is conformal).
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Inversion can simplify problems involving circles and tangents.
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Inversion can be used to prove collinearity or concurrence by transforming the configuration.