Tangent Circles

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1. Make script tools for construction of the tangent circles. Click here for script tool.

Let Black circle= Circle A, Green Circle= Circle B, and Black Circle = Tangent Circle.

In the first case we will observe when Circle A is inside of circle B....

Now if we trace alone the point of tangency along Circle A we will see the locus of the centers of both circles. As you can see the trace produces a circle....

Even when we move Circle A close to being tangent to Circle B we still get a circle....

What if Circle A and Circle B intersect?.....

Notice now that the locus produces a figure like an ellipse....

What if Circle B is inside of Circle A?.....

Do you see that Circle B is inside Circle A but also tangent to it...notice that the locus is an ellipse also!! Looking at the second graph, by moving the centers of the two circles closer you can see that the ellipse is becoming a circle...By the third graph where the centers are side by side, the trace now produces a circle....

What if both Cirle A and Circle B are completely disjoint from one another?...

Notice that the locus of the center of both circles produces an hyperbola... and the line containing the centers of both circles goes through the vertices of the hyperbola....