Assignment 7

Jonathan Lawson

In this exloration we will look at the case where if given two circles and a point, P, on one of the circles (in these particular cases the larger circle), the construction of a circle that is tangent to both given circles through the given point P.

Ex.

To download the GSP script for this construction click here.

We can also have the smaller given circle is in the interior of the tangent circle.

To download the GSP script for this construction, click here.

 If we look at the locus of the of the center of the tangent circle in both of these cases it appears to be an ellipse.

This is the case when the smaller circle is located inside the tangent circle.  The locus of the tangent circle center is in green.

This is the case when the smaller circle is located external to the tangent circle.  The locus of the tangent circle center is in green.

To understand why the locus is an ellipse refer to Assignment 6, where I give a brief outline on this topic.

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