Circle Tangents

By: Laura Lowe

Problem:  Investigating tangent circles.  Create a GeometerÕs Sketchpad Tool that finds the tangent circle to two given circles.  Use the tool to investigate the tangent circles when the relationship between the given circles is changed.

Here are three situations to consider.

1.  Now letÕs look at the loci of the center of the tangent circle in different situations.  First weÕll look at the case when one circle is inside the other.  Use your GSP tool and animate the point of tangency (A in my construction) when one circle is inside the other.  Trace the center of the tangent circle.  What shape does the locus make?  (Click here to see my animation.)  Why do we get this shape?

2.  Next weÕll look at the case when the two circles intersect.  Use your GSP tool and animate the point of tangency (A in my construction) when the circles intersect.  Trace the center of the tangent circle.  What shape does the locus make?  (Click here to see my animation.)  Why do we get this shape?

3.  Finally, weÕll look at the case when the two circles are disjoint.  Again, use your GSP tool and animate the point of tangency (A in my construction) when the circles intersect.  Trace the center of the tangent circle.  What shape does the locus make?  (Click here to see my animation.)  Why do we get this shape?