This page uses JavaSketchpad. You may drag any of the red points, and the construction will adjust accordingly.
Explanation of the construction: Given a circle of center B radius R and a point A, the inversion of A wrt the circle is the point C on the same ray from B as A such that the circle radius is the geometric mean of the distances of A and C from B, that is, BA*BC = R^2. The construction on this page uses similar right triangles ABD and DBE to get the equal ratios of short to long legs, BA/R = R/BE, which gives BE as the desired distance BC.
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