#
Tangent Circle

##
By Na Young

Given two circles A and B. Construct a circle
tangent to the two circles

with
one point of tangency being the designated point.

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**

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Picture

### First, we make a line connecting a point A and a
given point on the circle and then call the intersection point C. We construct
a circle C which is the same radius with a circle B. We call the intersection
point of a circle C and a line AC
a point E. Next, make a midpoint of a segment BE and a perpendicular line from
that point. We can construct a point D in this way. The point D is a center of
circle tangent to the two circles.

###

GSP
picture

The locus of a center of a tangent circle is an ellipse.

It can confirm using GSPÕs animation button.

GSP
picture

Next,
we will make a different tangent circle.

LetÕs construct the
tangent circle to two given circles when the smaller circle is internal to the
tangent circle.

GSP
picture

First, we
construct a line through a center and one point of the big

circle. Call the
intersection point B and make a circle of a same radius of a small circle A.
Then we obtain a point C and construct a parallel line of a segment AC from a
point B. The intersection point of a parallel line and a small circle is D.
This is a tangent point that we want to find. Connecting D and A, we can find a
center of a tangent circle O.

The locus of a center of a
tangent circle is an ellipse ,with GSP, we can animate around the big circle
and trace the locus of the center as follows:

GSP
picture

In this investigation I found an
interesting method using GSP.

At
first, I donÕt know how to think and to use GSP. But seeing a screen of GSP and
using a pencil I draw the imaginary picture. In the picture I draw lines and
segments and through the experience, I found answers of problems.

Through
this problem solving, I knew how to use GSP and how to think using GSP. Before
solving this problem, I think GSP is just a showing mathod, however, I became
to know an important of the investigation.

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