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.

Begin by constructing the GSP
Tool. Click here to see how.

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?

Click here to see my solutions.