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Inverse points An idea related to the radical axis is that of the inverse point. In this diagram P and Q are inverse points in the blue circle. For any point Q outside the circle, there is a pair of tangents that touch the circle. The midpoint of the line join the points where the tangents touch the circle is P. Conversely, for any point P within the circle, there is a chord perpendicular to the radius through P whose endpoints have tangents that meet at Q. So, any points within the circle have their own unique inverse point outside the circle - and vice versa

Please enable Java for an interactive construction (with Cinderella).

This diagram shows four pairs of inverse points. The four points inside the circle are joined to form a quadrilateral, as are the four outside. How do their shapes relate to each other?

Please enable Java for an interactive construction (with Cinderella). >>> Intro | Quadratic equations | Coordinate geometry | Complex numbers | Conclusion