Assignment 7 - Problem #1 for Kanita
Ducloux

Tangent Circles

Prepare a retrospective summary of
the following problem:
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.

Frustrating! Hair pulling! Problematic!
That's how I would describe this problem.
I took notes on the lesson and even asked Dr. Wilson for help.
But I was still lost. So, after much prayer, meditation, studying
my notes, and trying to recall my discussion with Dr. Wilson,
I was finally able to do something similar to the what Dr. Wilson
illustrated.

**1. Draw a circle within a circle
and a point (B) on one of the circles.**

**2. Find the radius of the small
circle and construct a circle of the same radius with point of
trangency (B) being the center of the new circle.**

**3. Construct a line through the
center of the large cirlce and the point of tangency (B).**

**4. Construct a segment connecting
K to the center of the original small circle and find the midpoint
(E).**

**5. Construct the perpendicular bisector
of the segment. The intersection of the perpendicular bisector
and the line connecting B to the center the of the original small
circle is point F.**

**6. Finally, construct the tangent
circle with center F and point of tangency B.**

**After all of that, I thought I was
finished until I discovered that there was another such circle
tangent to the two given circles. How do I find it? I should be
able to use what I've already done. There should be a relationship
between the two circles. Let's see what I found.**

**In step 4, instead of connecting
K to the center of the original small circle, connect to the second
point of intersection (K2).**

**5B. Construct the perpendicular
bisector of the segment. The intersection of the perpendicular
bisector and the line connecting B to the center the of the original
small circle is point F.**

**6. Finally, construct the tangent
circle with center F2
and point of tangency B.**

**Let's look at the picture without
all of the lines. The two green circles are the tangent circles
at Point B.**

**I was glad when I finallly finished
this problem.**

return