Inversion Tool

The sole purpose of the applet below is to allow experimentation with the inversion in circle. Several properties could be easily observed: a circle inverts into a circle, unless it passes through the center of inversion, in which case it inverts into a straight line. Circles perpendicular to the circle of inversion are invariant under the inversion, etc. (Circles are draggable as are their centers and the marked points on the circumference.)

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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Inversion - Introduction

Angle Preservation Property
Apollonian Circles Theorem
Archimedes' Twin Circles and a Brother
Bisectal Circle
Chain of Inscribed Circles
Circle Inscribed in a Circular Segment
Circle Inversion: Reflection in a Circle
Inversion Tool
Feuerbach's Theorem: a Proof
Four Touching Circles
Hart's Inversor
Inversion in the Incircle
Inversion with a Negative Power
Miquel's Theorem for Circles
Peaucellier Linkage
Polar Circle
Poles and Polars
Ptolemy by Inversion
Radical Axis of Circles Inscribed in a Circular Segment
Steiner's porism
Stereographic Projection and Inversion
Tangent Circles and an Isosceles Triangle
Tangent Circles and an Isosceles Triangle II
Three Tangents, Three Secants
Viviani by Inversion
Simultaneous Diameters in Concurrent Circles
An Euclidean Construction with Inversion
Construction and Properties of Mixtilinear Incircles
Two Quadruplets of Concyclic Points
Seven and the Eighth Circle Theorem
Invert Two Circles Into Equal Ones

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