Exploring Analyic Geometry with Mathematica®

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Circle Through Two Points, Center on Circle



Show that the radii of the two circles passing through the points (0,a) and (0,-a) with centers on the circle "tancir4_1.gif" are both given by


This is a special case of TangentCircles2D[{obj1,obj2},line | circle] where the two objects are points.


Two equations can be formed using the fact that points (0,a) and (0,-a) are on the circle. A third equation can be formed since the center is on a given circle. Solve three equations in three unknowns.


To initialize Descarta2D, select the input cell bracket and press SHIFT-Enter.

This initialization assumes that the Descarta2D software has been copied into one of the standard directories for AddOns which are on the Mathematica search path, $Path.



Solve three equations in three unknowns. The solutions with negative radii are invalid and discarded.



Copyright © 1999-2007 Donald L. Vossler, Descarta2D Publishing