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IJ'(GA locus problem from a computational geometer. Doris Schattschneider
Given fixed points A, B and a line, construct circles through A and B that are tangent to the line, if possible. What is the locus of the points of tangency as the line moves up or down (with A and B remaining fixed)?
This geometry problem arose when Scott Drysdale, a computer scientist, wanted to implement an algorithm to construct a Delauney triangulation of a set of points in the plane, using the "empty circle" technique. Once the construction has been made with Sketchpad, it is easy to see the answer to the question above. It took Drysdale and a colleague more than a week to find the answer analytically.
Drag the line up and down to trace the locus of the points of tangency of the circles.O+On
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