Assignment 7: Tangent Circles

Presented by: Amanda Oudi

**Investigation**: Given two circles and a point on one of the circles. Construct a
circle tangent to the two circles with one point of tangency being the
designated point.

**Discussion**:

I will begin by discussing
the construction of a circle tangent to two circles using GSP in a step-by-step
manner.

1.
Using the circle
tool, create a circle with center A

2.
Using the circle
tool, create another circle with center B. Draw this circle so that is lies
inside circle A

3. Draw a line that passes through the center of circle A and a point C on the circumference of the circle.

4.
Now we want to
construct a circle with center C that is congruent to circle B. Do so by
constructing a circle with center C with radius of circle B

5.
Label the
intersection of AC with circle C point D (we will label D as the intersection
point that lies outside of circle A)

6.
Construct
segment BD by joining point D and the center of circle B

7.
Find the
midpoint of BD and construct a perpendicular line to BD passing through the
midpoint

8.
Label the
intersection of the perpendicular line with AC point E

9.
Point E is now
the center of the tangent circle

10.
Construct the tangent circle with center
E and radius EC

A snapshot of the resulting
construction:

Here, we see that circle E
is tangent to our two given circles, circle A and circle B, and point C is the
one point of tangency.

This investigation was an interesting one because my knowledge about tangent circles is rather limited. I learned about tangent circles (construction of them) in Math 5200, but never investigated the trace of the center or the loci, so I found that this was a good exploration that utilized GSP.