**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.

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.

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.

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.

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.

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