#### Given a circle and a line, construct the circle
tangent to the circle (at an arbitrary point P) and the line.

#### Case 1: line and circle are disjoint

#### Case 2: line and circle intersect twice

#### These cases are very similar.

Notice that there are two circles that are
tangent to both the circle and the line.

Let's look at the locus of the centers of the
two tangent circles.

As we can tell from the picture for case 1,
the locus is two parabolas.

Click **here**
to see the animation in GSP.

It is also interesting to see the trace of
the perpendicular lines.

Click **here**
to see the animation of the perpendicular lines in GSP.

For case 2, the parabolas intersect.

Click **here**
to open a sketch with an animation in GSP.

It would be interesting to know where the foci
of the parabolas is. Is it the center of the circle? Is the line
the directrix?

Click **here**
for case 3.

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