# Tangent Circles

### By: Kimberly Young
and Mindy Swain

###

### Assignment # 7:

### 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.

### We chose to do problem #1
and constuct a script tool for this problem.

### The following link will give
you the GSP file with the tool. Click
here.

### In order to constuct a tangent
circle for the two given circles (green), we first place a point
on the big circle,B, and made a line connecting this point with
the center of the big circle. Next we made a new cicle with center
B and the same radius as the small circle (circle A). Then we
made a segement from A to C and found its midpoint. We constructed
a perpendicular line through that midpoint. This gave us point
D, around which we constructed a circle that is tangent to both
given circles.

### In our scipt tool we also
included an animation button that traces point D as point B rotates
around the big circle. This trace outlines the locus of the center
of the tangent circle which is an elipse with two foci of point
A and the center of the big circle.