* *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. Construct a circle
and then construct another circle inside that original circle.**
**

2. Draw the diameter of the larger circle..

3. Draw a circle using the radius of the smaller circle and the center where the diameter of the larger circle touches the outside of the circle.

4. Construct the midpoint of the segment from the center of the large circle to the center of the newly created circle. Construct another segment from the center of the original smaller circle to the point where the diameter crosses the new circle.

5.The new tangent circle is created by using the midpoint of the segment we just created and the the radius goes from the midpoint to the center of the third triangle.