Tangent Circles

By Natalie Streiner

 

We are going to investigate the tangent circle to two circles.

We will be looking at three cases specifically:

i.             When one given circle lies completely inside the other

ii.          When the two given circles over lap

iii.       When the two given circles are disjoint

 

To help us with this investigation we will use the script tool “Circle Tangent to Two Circles” available in Assignment #5.

 

When one given circle lies completely inside another…

Here, the green circle is the circle tangent to the two blue circles. We notice that this tangent circle lies completely inside the larger circle and outside of the smaller circle, as well.

Now, let’s see what happens when we trace the center of our tangent circle.

We see that this trace forms an ellipse.

 

When two given circles overlap…

Once again, the green circle is our tangent circle. Again we also see that the tangent circle lies inside of on of the circles it is tangent to and outside the other.

Now, let’s see what happens when we trace the center of our tangent circle.

Just as the first case, this trace forms an ellipse, this one being narrower than the first.

 

When the two given circles are disjoint…

Here we see one of the disjoint circles lies completely inside the tangent circle. When thinking about it, this makes sense. If the circles are disjoint, and a tangent hits both of these circles at exactly one, then it makes sense that one of the disjoint circles lays inside the tangent circle. Now, let’s see what happens when we trace the center of our tangent circle.

Here, instead of an ellipse we see that the trace forms a hyperbola. This hyperbola is formed since the circles are disjoint, and the center of the tangent circle must trace two separate circles.

 

 

 

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