write up #7

Tangent Circles

by Kaori Tabeta

GSP files of Tangent Circles

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.

1. In the case of the given point is on the bigger of two circle, and the smaller circle is external to the tangent circle.

Here is GSP file.

2. In the caseof the given point is on the bigger of the circle, and the smaller circle is in ternal to teh tangent circle.

Here is GSP file.

3. In the case of the given point is on the smaller circle of the two circles, and the smallar circle is external to the tangent circle.

Here is GSP file.

4. In the case of the given point is on the smaller circle of the two circles, and the smallar circle is internal to the tangent circle.

Here is GSP file.

In addition, the construction of 1. and 3. are essentially same. Similarly 2. and 4. These only change the length of radium of the circle.

The locus of the center of tangent circle

Dissuss the loci of the tangent circles for all case using above GSP files. Click Here.